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Areas of Science Sports Science Pure Mathematics Difficulty Time Required Short (2-5 days) Prerequisites You should have a familiarity with basic algebra. Material Availability Readily available Cost Very Low (under \$20) Safety No issues

Abstract

If you've ever played or watched basketball, you might already know that your chances of successfully banking a shot on the backboard are higher in certain positions on the basketball court, even when keeping the distance from the hoop the same. Ever wondered what would account for this? Do you think you could actually explain this using geometry? This science project will put your knowledge of geometry and algebra to good use. You will calculate and quantify how much more difficult it is to score from different positions. You will also build a scale model to test your calculations. Will these results line up with the on-court experience?

Objective

Use algebra and geometry to calculate the relative probability of making a successful bank shot from different positions on the court, keeping the distance to the hoop constant. Then test if you can reproduce your predictions with a scale model.

Credits

Sabine De Brabandere, PhD, Science Buddies

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.

APA Style

Last edit date: 2020-01-12

Introduction

People say playing sports helps improve academic results. Would academic analysis of the game also improve your performance on the court? Test it out with this science project. Have a close look at the geometry of shooting a basket using the backboard. Would geometric analysis indicate that shooting from the side of the hoop—as shown in Figure 1—is easier, more difficult, or equally difficult than shooting from a more central position? Could geometric analysis help you make better decisions on the court?

Figure 1. Making a shot from a sideways position relative to the hoop.

A basketball shot at the hoop is a great example of projectile motion, or the motion of an object (in this case a ball) that moves through the air. The science of projectile motion lets you predict the projectile's (here a ball's) trajectory, or the exact path the projectile (or ball) will take.

In real basketball, the ball follows a complicated three-dimensional trajectory as it moves through the air, bounces off the backboard, and goes into the net. However, it is an example of a compound motion, combining a vertical and a horizontal motion. Both these motions are independent of each other, and thus, can be studied separately. In this science project, you will study the horizontal movement of the basketball, which reduces the three-dimensional motion to two dimensions. This "bird's-eye view" of the ball's movement will result in easier analysis for your science project.

Are you surprised that the ball's vertical and horizontal motions happen independently?

You can experiment with this type of compound motion by letting identical objects (like two coins) fall to the ground using different paths (e.g. one coin launched off sideways from a table, while the second one is nudged right off the edge and falls straight down from the table). See when both objects land. If vertical movement (falling to the ground) happens independent of the horizontal movement, both coins should touch the ground at the same time, even though the first object took a longer path.

Your goal is to determine the relative difficulty to shoot the basket using the backboard from different positions on the court. Imagine looking at the court from a bird's-eye (top-down) viewpoint. Now imagine a player is shooting a ball. What would you see? Can you visualize the trajectory of the ball being shot, bouncing off the backboard, and landing in the basket? Do you imagine a trajectory as shown in Figure 2?

Figure 2. Top-down view of the trajectory of a banked shot. This figure also shows the angle of incidence being equal to the angle of reflection, as it is assumed the ball has no spin.

Figure 2 also introduces the angle of incidence and the angle of reflection for a projectile. The angle of incidence is the angle between the path of the ball as it approaches a surface (here the backboard) and the line perpendicular to the surface (a line perpendicular to a surface is also called normal to the surface or the surface normal ) . The angle of reflection represents the angle between the path of the ball as it bounces back from a surface and the line perpendicular to the surface. In this science project, you will assume the ball is thrown without spin. In this case, projectile motion predicts the ball will bounce back under the same angle, or in other words, the angle of incidence equals the angle of reflection.

In the first part of your science project, you will use algebra and geometry to study one aspect of the shot and determine its impact on relative difficulty of making a shot from different positions that are the same distance from the hoop. Here is a short review of some properties of triangles that will be used in the calculations.

The Pythagorean theorem is probably the first thing that comes to mind when thinking of triangles. It is valid in right triangles and states that the square of the hypotenuse (the length of the side opposite the right [90°] angle) equals the sum of the squares of the length of the other two sides.

Do you also remember the special properties of the 30-60-90 and the 45-45-90 triangles?

A 30-60-90 triangle is a triangle with 30°, 60° and 90° angles, as shown in Figure 3. One side of this triangle has a length exactly half of the length of the hypotenuse. Can you use the Pythagorean theorem to verify that the length of the other side is $\sqrt{3}/2$ times the length of the hypotenuse?

Figure 3. Representation of the 30-60-90 triangle, for which the length of one side is half the length of the hypotenuse. In this figure, the lengths a, b, and c represent the length of each side of the triangle, while the Greek letters α and β represent the angles.

A 45-45-90 triangle is special because two sides of this right triangle have equal lengths. Can you use the Pythagorean theorem to verify this length is exactly $\sqrt{2}/2$ times the length of the hypotenuse?

You will also need to know the properties of similar triangles. Similar triangles are triangles that have identical angles, but might differ in size. Figure 4 shows two similar triangles. Note the corresponding sides of similar triangles have lengths in the same ratio. In other words, if a triangle with sides a, b, and c is similar to a triangle with sides A, B, and C, then a/A = b/B= c/C.

Figure 4. Representation of two similar triangles. Note that the ratios of the lengths of corresponding sides of similar triangles are identical.

There is one more mathematical concept to introduce before you can start your calculations. In this science project, you will study one aspect of the shot and calculate how this influences chances of scoring when the player is placed at different locations on the court. Scientists use relative probability to express how much more or less likely something is expected to happen compared to a chosen baseline. A relative probability higher than 1 indicates it is more probable, or easier, to successfully shoot a banked shot from that position than from the baseline position. A relative probability lower than 1 indicates it is less probable, or more difficult, to successfully shoot a banked shot from that position than it is from the baseline position.

Now, time to get started! Make sure you keep your science project in mind the next time you are deciding whether or not to use the backboard to take a shot!

Terms and Concepts

• Projectile motion
• Trajectory
• Compound motion
• Independent
• Angle of incidence
• Angle of reflection
• Pythagorean theorem
• Right triangles
• Hypotenuse
• 30-60-90 triangle
• 45-45-90 triangle
• Similar triangles
• Relative probability

Questions

• What property allows analysis of the projectile motion in the horizontal plane and the vertical direction separately?
• How does the trajectory of a basketball shot look in the horizontal plane?
• What is the angle of incidence and the angle of reflection for a ball hitting an object and how are they related, assuming the ball has no spin?
• What does relative probabilities of 200% or 50% indicate?
• How are the lengths of the three sides of a right triangle related?
• Do you expect any position on the court to have a higher chance of resulting in a score using the backboard when analyzing the geometry of the situation?
• Do you expect any players placed on the court at equal distance from the center of the basket to have a better chance of scoring using the backboard in the real game?

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Materials and Equipment

• Test ball, approximately 4.5 cm diameter. A mini sports squeeze ball like the mini sports foam balls from Amazon.com work well.
• Note: You will need to scale the dimensions of the cardboard tube and the number of poster boards up or down to accommodate a smaller or larger ball.
• Books (2), identical thickness
• Flat wall making a 90° angle with a flat floor
• Ruler, metric
• Poster boards (2), 22 x 28 inch; flexible or hard poster board will both work.
• Thick markers, black and red
• Compass
• Protractor
• Sheet of paper
• Tape that does not damage the wall
• Scissors
• Cardboard roll (50 cm long if you work with a 4.5 cm ball); the inner tube of packing paper works well. Note : Choose something that comes on a sturdy cardboard tube, not on a flimsy wrapping paper tube.)
• Cutting board
• Toilet paper roll
• Utility knife or craft knife
• Highlighter
• Lab Notebook

Disclaimer: Science Buddies participates in affiliate programs with Home Science Tools, Amazon.com, Carolina Biological, and Jameco Electronics. Proceeds from the affiliate programs help support Science Buddies, a 501(c)(3) public charity, and keep our resources free for everyone. Our top priority is student learning. If you have any comments (positive or negative) related to purchases you've made for science projects from recommendations on our site, please let us know. Write to us at scibuddy@sciencebuddies.org.

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PDF date: 2020-01-22

Experimental Procedure

Defining the Variables

For this science project, you will position your player at a fixed distance from the middle of the basket. Three meters (m) will be used as the example in this procedure. Feel free to replace this distance by your own preferred distance. It is important to stick to one distance throughout the project, though, as you want to study the influence of the player's angular position. Also note that metric units are used, as this is the convention for science projects.

Once you have specified the distance, the position of the player is defined by the angle that the line from the player through the middle of the basket makes with a line parallel to the backboard, as shown in Figure 5.

Figure 5. Players are positioned at a constant distance from the center of the basket and varying angular positions. The 90° position is chosen as baseline, which means the probabilities will be calculated relative to the 90° position.

The 90° position is chosen as baseline, which means you will calculate how much more or less difficult it is to make the shot from the 30°, 45°, and 60° positions with respect to the 90° position.

Calculating the Chance to Score

Depending on the player's angular position, the player will have to aim the ball at a different location on the backboard for the ball to end up in the basket, as shown in Figure 6.

Figure 6. Players at different locations need to aim the ball at a different spot on the backboard to make the ball bounce into the basket.

The player always aims to get the ball in the middle of the basket. Fortunately, there is some wiggle room. As shown in Figure 7, the ball can bounce off of a slightly different spot on the backboard and still bounce into the basket.

Figure 7. A player placed at a specific position can throw a ball to a slightly different spot on the backboard and still make the shot. The contact area on the backboard that will result in a shot can be used as an indicator of how difficult it is to shoot from that position.

How much wiggle room a player has is one indicator of how difficult it is to make the shot. You can calculate relative probabilities by comparing the length of this "wiggle room" (the length of the area on the backboard that a player can hit and still make the shot) for different player positions. In this approach, you calculate the relative sizes of the areas at which a player can choose to aim as explained later in the procedure. This works if you assume that the player can aim the ball perfectly every time. Another approach is to calculate the angular wiggle room the player has when aiming the ball (for example, plus or minus two degrees), assuming the player knows exactly which spot on the backboard to aim at. The calculations are slightly different in this case, as explained in the Variations section. In the real game, the relative probability is a combination of both of these and other aspects.

Some general notes before you start the calculations:

• Although in sports the distances are often indicated in inches and yards, calculations will be done in the metric system (centimeters and meters). Be sure to make appropriate conversions where needed.
• All figures indicate the angle defining the position of the player as β. The first time you go through these calculations, fill in the angle 30°. At later iterations, you will do the calculations for the 45°, the 60°, and the 90° positions. Fill in the appropriate number for β each time you go through the calculations.
• At any step in your calculations, remember to verify if the obtained distances make sense. As an example, a ball hitting the backboard at 10 m away from the center of the backboard does not seem correct. Frequent checks will help you catch mistakes early on.
1. Copy the table in your lab notebook; it will allow you to systematically keep track of your calculations as you go through them for different angular positions.
1. Note: If you are able to work symbolically until you arrive at an expression for X1 as a function of the other variables (β, Xtot, Ytot, ...)- please do set up the equation and plug in the numbers at the end. If this is difficult for you, plug in numbers at each step.
 Player's positiondefined by angle β 30° 45° 60° 90° Ball lands central Xtot (m) Ytot (m) Y2 (m) Y1 (m) X2 (m) X1 (m) Ball lands left Xtot (m) Ytot (m) Y2 (m) Y1 (m) X2 (m) X1 (m) Ball lands right Xtot (m) Ytot (m) Y2 (m) Y1 (m) X2 (m) X1 (m) Length contact line (m) Relative probability 1

Table 1. Table in which to note down the intermediate and end results of your calculations.
1. Make a drawing similar to the one shown in Figure 8. Concentrate on the yellow triangle.
1. Calculate the length of all sides of the yellow right triangle. Note that you know angle β and the length of the hypotenuse.
2. Add the appropriate distances, if any, to obtain the length of Xtot (the distance in the X direction from the player's position to the middle of the ball as it enters the hoop) and Ytot (the distance in the Y direction from the player's position to the backboard) indicated in black in the figure. Note that you might have to convert inches into meters.
3. Note your results down in your lab notebook in the "Ball lands central" rows in your table like Table 1.

Figure 8. A drawing of the setup helps identify the geometry and translate the problem into a mathematical equation.
1. Make a drawing similar to the one in Figure 9. You want to find X1, as this will indicate the distance from the center line where the ball needs to hit the backboard and bounce back into the basket. Note that the drawing is made to reflect that the ball bounces back into the center of the basket. The center line refers to the line perpendicular to the backboard going trough the center of the basket.
1. Concentrate on green (with sides X2, Y2, Z2) and blue (with sides X1, Y1, Z1) triangles. Since the angle of incidence is equal to the angle of reflection, these two triangles are similar. Use this information to write down an equation between Y1, Y2, X1, X2.
2. As you can see from the Figure 9, Y2 and Ytot are identical. You also know Y1, and you are trying to find X1. You still need to identify X2.
3. Since you know Xtot from step 2, find an equation that relates X 1, X2, and Xtot.
4. Use the equation obtained in step 3.c. to express X2 as a function of X1 and Xtot.
5. Substitute your expression for X2 in terms of X1 and Xtot in the equation you formed in step 3.a.
6. Reorganize your expressions so you get X1 as a function Ytot, Y1, and Xtot.
7. If you did not do it yet, plug the values for Ytot, Y1, and Xtot into your expression from step 3.f., and solve for X1. Record your result in your data table next to the variable X1 (m) - ball lands central.
8. Do a reality check; is the spot indicated by your distance still within the backboard?

Figure 9. The mathematical properties of similar triangles (drawn in green and blue in this figure) are used to solve the problem.
1. Repeat step 3. When necessary, change your procedure to account for the situation where the ball barely makes it through the left edge of the basket, as shown in Figure 10 (light yellow ball).
1. Start by making a new drawing or by adding the new situation to your previous drawing in a different color.
2. Identify which, if any of the variables Ytot, Y1, Y1, X2, and Xtot are unchanged. Record these in your data table.
3. For the variables that do change, do you know by how much they will change? For example, Xtot will be less or more as the ball will enter to the left or to the right of the central position. Can you identify how much less, knowing a basketball has a diameter of 9.4 inches and the radius of the basket is 9 inches?
4. Can you see if the relationships between the variables you established in step 3.a. and 3.b. still hold? If so, you can use the relationship established in step 3.f. with the new values of Ytot, Y1, and Xtot to calculate the distance X1 (m) - ball lands left. This is the farthest point to the left for the angle β that will still result in the ball bouncing into the basket.
5. Do a reality check; is the spot indicated by your distance still within the backboard?

Figure 10. Figure showing the situation where the ball barely makes it through the basket to the right (light blue) or to the left (light yellow) of the central position.
1. Repeat step 4 considering the situation where the ball barely makes it through the basket to the right of the central position, as shown in Figure 10 (light blue ball). This calculation will yield distance X1 (m), ball lands right. This is the farthest point to the right for this angle β that will still result in the ball bouncing into the basket.
2. To calculate the length of the area on the backboard that will result in the ball bouncing into the basket, subtract distance [X1 (m) - ball lands right] from distance [X1 (m) - ball lands left]. Note your results down in your data table. This completes your calculations for angle 30°. Once you have done the calculations for all the angles in the following steps, you can calculate the relative probability.
3. Repeat steps 2–6 again for the following positions: 45° and 60°.
4. Repeat steps 2–6 again for the 90° position. Note that this position looks slightly different, as indicated in Figure 11. Verify that the equations you identified are still valid for this configuration.

Three different trajectories of a basketball bouncing off of the backboard and into the basket when shot from a position perpendicular to the backboard. A basketball can be bounced slightly to the left or right of center and still make it into the basket due to the size of the basket being larger than the ball.

Figure 11. Figure showing the configuration for the 90° position for the ball entering in the center (orange), to the right (light blue), or to the left (light pink) of the central position.
1. Now that you have obtained the lengths that make the shot, you are ready to calculate the relative probability.
1. Divide the obtained length for each position by the length for the 90° position. Note the 90° position should have a "1" as relative probability, as this position was chosen as the baseline.
2. Do your results confirm or contradict what you expected? Does it seem logical in retrospect?

Testing Your Calculations with a Scale Model

Now that you have calculated the relative probability using geometry, you can test if you can reproduce these numbers using a scale model. How to build the scale model and take data is explained in the procedure of the science Project Idea Basketball: Will You Bank the Shot?

Put your players in your scale model at the same positions as you did for your calculations: a 3 m distance from the center of the hoop (scaled down to the distance in your model) and at 30°, 45°, 60°, and 90° angles.

Use the data from your scale model trails to calculate the length of the area on the backboard that bounces the ball back into the basket and the relative probabilities.

This section will provide you with some information about how to analyze your results.

1. Compare the results obtained from your scale model with the results obtained from your calculations:
1. For each angular position, compare the length of the contact line that made the shot.
2. Compare for each angular position the obtained relative probability.
2. If you see any differences between your scale model results and your calculated results, try to answer the following questions:
1. Can you explain what causes these differences?
2. Is the result of your scale model more accurate than, less accurate than, or the same as the results of your calculations?
3. Can you think of ways to improve your calculations or your scale model?
3. Make scatter plots of your data. Where possible, plot both your calculated results and test model results on the same graph, using color coding to differentiate between the calculated and scale model results. Here are some suggestions:
1. Plot your relative probability (on the y-axis) versus the player's position (angle).
2. Plot the length of the area that results in a score (on the y-axis) versus the player's position (angle).
3. Plot both the minimum distance from the central line and the maximum distance from the central line on the y-axis versus the player's angular position (angle) on the x-axis.
4. Do you see a trend in your plots or your data? What could you conclude? Does one position result in more scores using the backboard than the other?
5. Are your findings in alignment with what you expected?
1. If you play basketball, did you have a similar experience on the court?
2. If you can find "shot charts" for real basketball players indicating the success rate of banked shots for different positions on the court, compare them with your findings.
3. Can you explain any differences identified in step 5.a. or 5.b.? What other factors (geometric and non-geometric) might influence your chance to score. As an example, would aiming be more accurate at large or small angles?
4. You constrained yourself to two dimensions for this science project; would adding the vertical motion change your calculations?
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If you like this project, you might enjoy exploring these related careers:

Mathematician

Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more

Athletic Trainer

Sports injuries can be painful and debilitating. Athletic trainers help athletes, and other physically active people, avoid such injuries, while also working to improve their strength and conditioning. Should a sports injury occur, athletic trainers help to evaluate the injury, determine the treatment needed, and design a fitness regime to rehabilitate the athlete so he or she is ready to go out and compete again. Read more

Statistician

Statisticians use the power of math and probability theory to answer questions that affect the lives of millions of people. They tell educators which teaching method works best, tell policy-makers what levels of pesticides are acceptable in fresh fruit, tell doctors which treatment works best, and tell builders which type of paint is the most durable. They are employed in virtually every type of industry imaginable, from engineering, manufacturing, and medicine to animal science, food production, transportation, and education. Everybody needs a statistician! Read more

Physicist

Physicists have a big goal in mind—to understand the nature of the entire universe and everything in it! To reach that goal, they observe and measure natural events seen on Earth and in the universe, and then develop theories, using mathematics, to explain why those phenomena occur. Physicists take on the challenge of explaining events that happen on the grandest scale imaginable to those that happen at the level of the smallest atomic particles. Their theories are then applied to human-scale projects to bring people new technologies, like computers, lasers, and fusion energy. Read more

Variations

• In this science project, you changed the position of the player by changing the angle and keeping the distance to the center of the hoop constant. Try the project again, this time keeping the angle constant and analyzing the influence of changing the distance to the hoop.
• If you have some basic trigonometry knowledge, you can find a symbolic expression for the relative probability as a function of the player's angular position. Then plot this function, with relative probability on the y-axis and the player's angular position on the x-axis. This will give you information about how the relative probability changes with changing angular position, taking all positions (all angles) into account.
• Ask some of your basketball-playing friends to test their success rates from the analyzed positions, using the backboard. Compare the average of these real-life results with the results obtained in your calculations and/or your test situation. Analyze what might account for the differences between your calculations, your scale model, and shooting on an actual court.
• The calculations in this science project assume that the player can throw the ball with perfect aim every time. In reality, there may be some error when the player throws the ball, resulting in the ball going a few degrees to the left or to the right, as shown in Figure 12. Can you calculate the relative probabilities using this angular "wiggle room" instead of the linear wiggle room on the backboard? How do the two methods compare; do they give the same results, or are they different?

Three different trajectories of a basketball bouncing off of the backboard and into the basket when shot from the left side of the basket. A basketball can be bounced slightly to the left or right of center and still make it into the basket due to the size of the basket being larger than the ball.

Figure 12. You can also calculate the relative probability to successfully bank a shot by comparing the angular wiggle room for different positions on the court. The player displayed in this drawing has wiggle room of δ degrees.
• Use geometry and algebra to analyze in which direction you should throw the ball for a running player to catch it.
• Look up "shot charts" for real basketball players (for example, do an online image search for "NBA shot chart") and compare your data to these shot charts. Does data from real basketball games match the trends you saw in your experiment, or not? What other factors do you think could influence a real game that were not present in your experiment?

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# Find the limit $\lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right)$

## Step-by-step Solution

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$\frac{1}{e^{3}}$
Got another answer? Verify it here!

## Step-by-step Solution

Problem to solve:

$\lim_{x\to\:1}\left(1+3\cdot\:lnx\right)^{\left(\frac{1}{sen\:\left(1-x\right)}\right)}$

Specify the solving method

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Evaluate the limit $\lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right)$ by replacing all occurrences of $x$ by $1$

$\left(1+3\ln\left(1\right)\right)^{\frac{1}{\sin\left(1-1\cdot 1\right)}}$

Learn how to solve limits of exponential functions problems step by step online.

$\left(1+3\ln\left(1\right)\right)^{\frac{1}{\sin\left(1-1\cdot 1\right)}}$

Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(1)lim((1+3ln(x))^(1/(sin(1-x))). Evaluate the limit \lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right) by replacing all occurrences of x by 1. Simplifying, we get. Apply the formula for limits that result in the indeterminate form 1^{\infty}, which is as follows: \lim_{x\to a}f(x)^{g(x)}=\lim_{x\to a}e^{\left[g(x)\cdot\left(f(x)-1\right)\right]}. Multiplying the fraction by 3\ln\left(x\right).

$\frac{1}{e^{3}}$

$0.049787$
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# If sin x= 4/5, how do you find cos x?

cosx= $\frac{3}{5}$
Use Trignometrical identity cosx = $\sqrt{1 - {\sin}^{2} x}$
cos x = $\sqrt{1 - \frac{16}{25}}$ =$\sqrt{\frac{9}{25}}$ = $\frac{3}{5}$ to be the value in the first quadranr.


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• Huaiyang Zhou

Articles written in Journal of Earth System Science

• Anaerobic oxidation of methane in coastal sediment from Guishan Island (Pearl River Estuary), South China Sea

The concentrations of CH4, SO$^{2−}_{4}$, 𝛴 CO2 and the carbon isotope compositions of 𝛴 CO2 and CH4 in the pore-water of the GS sedimentary core collected from Guishan Island (Pearl River Estuary), South China Sea,were determined. The methane concentration in the pore-water shows dramatic changes and sulfate concentration gradients are linear at the base of the sulfate reduction zone for the station. The carbon isotope of methane becomes heavier at the sulfate-methane transition (SMT)likely because of the Raleigh distillation effect; 12CH4 was oxidized faster than 13CH4 and this caused the enrichment of residual methane 𝛿13C and 𝛿13C-𝛿 CO2 minimum. The geochemical proﬁles of the pore-water support the existence of anaerobic oxidation of methane (AOM), which is mainly controlled by the quality and quantity of the sedimentary organic matter. As inferred from the index of 𝛿13C-TOC value and TOC/TN ratio, the organic matter is a mix of mainly refractory terrestrial component plus some labile alga marine-derived in the study area. A large amount of labile organic matter (mainly labile alga marine-derived) is consumed via the process of sedimentary organic matter diagenesis, and this reduces the amount of labile organic matter incorporated into the base of the sulfate reduction zone. Due to the scarcity of labile organic matter, the sulfate will in turn be consumed by its reaction with methane and therefore AOM takes place.Based on a diffussion model, the portion of pore-water sulfate reduction via AOM is 58.6%,and the percentage of 𝛴 CO2 in the pore-water derived from AOM is 41.4%. Thus, AOM plays an important role in the carbon and sulfur cycling in the marine sediments of Pearl River Estuary.

• # Journal of Earth System Science

Volume 129, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


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# Does it converge?

Compute $\frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \dots + \frac{F_k}{2^k} + \dots$ where $$F_k$$ represents the the $$k^\text{th}$$ term of the Fibonacci sequence: $$1, 1, 2, 3, 5, 8, 13, ...$$

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Surd Equations Reducible to Quadratic | Math Algebra

Surd Equations Reducible to Quadratic for Math Algebra is done squaring both sides for removing surds and radical expressions. Make sure to check whether the solutions are correct by substituting them into the original surd equations.

Practice Questions for Surd Equations Reducible to Quadratic | Math Algebra

Question 1

Solve $$x = \sqrt{x+2}$$.

Question 2

Solve $$3x = \sqrt{x^2+32}$$.

Question 3

Solve $$x + 2\sqrt{x+1} = 7$$.

Question 4

Solve $$\sqrt{2x+3} – \sqrt{x-2} = 2$$.


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## Vavg Formula

Then the RMS voltage (V RMS) of a sinusoidal waveform is determined by multiplying the peak voltage value by 0. The average value, which is the value measured on a dc voltmeter, for a full-wave rectified sinusoidal voltage is twice that of the half-wave, as shown in the following formula: VAVG is approximately 63. An atom of a monoatomic gas can move in three independent directions so the gas has three degrees of freedom due to its translational motion. Note that ffmpeg integrates a default down-mix (and up-mix) system that should be preferred (see "-ac" option) unless you have very specific needs. It is possible, however, to have negative Voltage Unbalance readings if the device is a Series 600 Power Meter or a Series 2000 Circuit Monitor. 2a (s - si) = v2 - v2i for a 3. Previous articles on MasteringElectronicsDesign. 0319988 kg/mol Remember that kg m 2 s-2 is called a Joule and that the unit on R is usually written J/K mol. Solve: (b) Model: The car is represented by the particle model as a dot. So the peak voltage occurs at 1 and -1 points. On the last tab of the heat transfer resistance tool dialog in HTflux you will find a very versatile tool to calculate the heat transfers coefficients (resistances) of pipe flows for gases and liquids. F = 10 kg (5 m/s - 0 m/s) / 12 sec. View and Download Carrier 19XRV start-up and service instructions online. If two bacteria will exist in 30 minutes, and four in 60 minutes, etc. The circuit consists of the series connection diode D and a resistor R. For a sine wave, the negative half of the waveform would cancel out the positive half and average to zero over one cycle. p(t) = iv = v2/R = i2R. Obviously your triangular wave had its bottom peak at ground potential to make Vavg=Vmax/2. Twenty-one standard models provide tightly regulated outputs at 3W of isolated power while packaged in a miniature …. Homework Statement Basically, I need to understand how to calculate Irms and I*rms given a Vrms and an impedance Z. The dog's average velocity, vavg = 5m/s; the time, t = 12 seconds. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2. is often written as v which is said as “v bar” or just. Average Speed = (a + b)/2. A rating curve (fig. Using this we can simulate different resistance values by varying the PWM duty-cycle. 1k points) nsep. If s avg represents the average speed of an object (in meters per second) during a time interval t (in seconds), and the distance traveled in that time is equal to d (in meters), then: s avg = d / t. The VA Formulary Search tool is an aid for VA and Non-VA user to easily search for formulary items. 2 Remapping examples. Find the volume per organism, assuming a spherical shape. A dye is injected at the inlet of the pipe. That is, the ratio F/m = a = g (2). ffmpeg reads from an arbitrary number o. Hello, I have DC-DC buck converter in my circuit. Advertisement published in Chemical Engineering Education, Volume 26, No 3 (1992) MILLIKEN & COMPANY College Relations Department, M-285 P. 31447 kg m 2 s-2 K-1 mol-1) (304. repeatlast If set to 1, force the filter to extend the last frame of secondary streams until the end of the primary stream. distance d = Vavg * t = 6. Worth Publishers. How do I generate a calculation to linearize data that has an inverse relationship? This video shows how to transform data from a Boyle's Law experiment so that the data falls along a straight line. Root mean square velocity. web; books; video; audio; software; images; Toggle navigation. 414 x Vrms 2. 6 Summary Further reading. 637 *Vp Where Vp is the maximum/ Peak value of voltage in that cycle. 637 times the amplitude (2*Vp/π), Vrms doesn't sounds right to me. | Vavg - V1-2 | + | Vavg - V1-3 | + | Vavg - V2-3 | 2 x Vavg % voltage imbalance = x 100 The maximum allowable voltage imbalance is 2%. 0319988 kg/mol Remember that kg m 2 s-2 is called a Joule and that the unit on R is usually written J/K mol. ffmpeg calls the libavformat library (containing demuxers) to read input files and get packets containing encoded data from them. 01-0 =V0314×0. When a velocity is changing as a result of a constant acceleration, the average velocity can be found by adding the initial and final velocities, and dividing by 2. ) The average is also called an arithmetic mean. v2 = 2gh for h10. In its time on Earth, NCO has been successfully ported and tested on so many 32- and 64-bit platforms that if we did not write them down here we would forget their names: IBM AIX 4. In less formal terms, Boyle's Law can be stated:. 707 * Vpeak, Vavg = 0. Free solve for a variable calculator - solve the equation for different variables step-by-step This website uses cookies to ensure you get the best experience. The velocity of particle travelling in a straight line is given by v=6t-3t^2 m/s where t is in secound. For any list of numbers holds: The root mean square (rms) is always equal or higher than the average (avg). Calculator Use. Then the RMS voltage (V RMS) of a sinusoidal waveform is determined by multiplying the peak voltage value by 0. Average Voltage (Vavg) The level of a waveform defined by the condition that the area enclosed by the curve above this level is exactly equal to the area enclosed by the curve below this level. Voltage This table shows the relationship between Power in [dBm] or [Watts] and Voltage in RMS, peak, peak-to-peak for sinusoidal signals in 50-Ohm systems. Voltage Unbalance is calculated using the following formula: Vunbalance = [(Vavg-Vphase) divided by Vavg]. Which of the following pairs of compounds have the same empirical formula?. When there are multiple input files, ffmpeg tries to keep them synchronized by tracking lowest timestamp on any active input stream. 4-5 Months of age: Breastfeed every 2-4 hours or Formula 24-45 ounces. The average value is also given by the equation; Vavg = 0. Advertisement published in Chemical Engineering Education, Volume 26, No 3 (1992) MILLIKEN & COMPANY College Relations Department, M-285 P. Solve each formula for the quantity given. Let vavg, vp and vrms be respectively the average, the most probable and the root mean square speeds of gas asked May 13, 2019 in Physics by RenuK ( 68. However the official formulary is the VA National Formulary (VANF) spreadsheet that contains additional restrictions and conditions that are not shown on the VA Formulary Search. White- Fluid Mechanics Manual Solution. Presume the jump height is the same, the less time, he takes to jump the same distance, the more velocity the person create, the higher the person will go. Homework Equations x(t) = A*cos(ωt) (SHM mathematical model) v(t) = -Vmax*sin(ωt) Fave = 1/(b-a)∫f(x)dx The Attempt at a Solution As soon as i get started with this problem, I hit a brick wall. On the last tab of the heat transfer resistance tool dialog in HTflux you will find a very versatile tool to calculate the heat transfers coefficients (resistances) of pipe flows for gases and liquids. 7 km/hr = 23700 m/3600 sec = 6. 120v Vrms input so 170 Vpp I get 162 vavg using the. Where vo (also called 'vi') is equal to zero 1. Avoid Circuit or Wire Exposure. And the reason is that you're not going that speed v the whole time. i = Average Veolocity, Vint. A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions: • The gas is composed of. Can anyone tell me what the Excel formulae would be for calculating an Exponential Moving Average (EMA) on a set of data. The Speed of Nitrogen Molecules The kinetic theory of gases states that the kinetic energy of a gas is directly proportional to the temperature of the gas. What is the average force for the dog? Answer: The mass, m = 10 kg. • Vavg is the average voltage (add all three, divide by three). 2a (s – si) = v2 – v2i for s 4. We'll say t₀=0 and t₁ =10. A family drove 1080 miles to their vacation lodge. Sadly, their attempt to push the fat chicken horizontally across a level ground into the oven proved futile since the oven was a couple meters off the ground. V pp = 2√2 * V rms. However, mass m and energy E can be converted to each other according to the well-known formula proposed by Albert Einstein (1879–1955): E ϭ mc2 (5–1) where c is the speed of light in a vacuum, which is c ϭ 2. When the two flasks are connected the pressure in the system drops to 2 atm. As the word states, Average Velocity is the average value of the known velocities. VAVG - Tells Excel to compute the average of the numbers from the preceding numeric cells in the same column. Therefore its internal energy, U, follows the equation U = 3/2 RT. You might be required to find an average volume as a part of a middle school or high school. Some options can be changed during the operation of the filter using a command. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5. 23 x 1043 organisms 2. 732 = 115,401W = 115. Thread starter Sajan Well i seem to recall seeing Vrms written down with a formula to the right that is not the whole calculation for an RMS value. In addition, the velocity of the fluid for a fully developed flow will be at its fastest at the. Download Solutions Manual - Materials Processing in Manufacturing Demargo. The Peak-to-peak Voltage calculator calculates the peak-to-peak Voltage, VP-P, value from either the peak voltage, the RMS voltage, or the average voltage. 2 trend, namely, Kalol -Ahmedabad - Wasna trend. 3 Two sinusoidal phasors out of phase by angle θ. Peak voltage can be obtained by following 3 methods: 1. This average is an equally weighted ensemble mean unless weights have been specified in the GDFILE entry as described above or in input_arg2. Vavg = (Vf + Vi)/2 (note, it's a +, not a -) in any case of constant acceleration. vavg vp π 2 = (15) The table below lists the average and most probable neutron velocities and energies. Example question: Given Vrms = 120 V at an angle of 30° and an impedance of Z = 10 Ω, find Irms and I*rms. 318Vpk: Sine wave with DC offset: Vrms= *sqrt(Vdc 2 +Vpk 2 /2) Vavg= Vdc: Half sine with duration T and frequency f: Vrms= Vpk*sqrt(f*T/2) Vavg= 2f*T*Vpk/PI: Positive square wave with duration T and frequency f: Vrms= Vpk*sqrt(f*T) Vavg= f*T*Vpk. As illustrated in the ﬁgure, the slope can be positive, negative, or zero. A Pulse Width Modulation (PWM) Signal is a method for generating an analog signal using a digital source. Using the given conversion factors, we find (a) the distance d in rods to be d = 4. ) The average is also called an arithmetic mean. Army Corps of Engineers Riprap Design for Flood Channels STEPHEN T. impute vcov. Another question with rigged numbers. Choose from 500 different sets of physics kinematics formulas flashcards on Quizlet. OER University - Anvari. 11 x Vavg; 1. Nevertheless, velocity analysis is still one of the most time consuming parts of seismic processing. 68” is proportional to the “discharge coefficient” Cd for the hole. 637 times the peak voltage”. vavg vrms nishant22, RMS voltage for a given waveform is the voltage that produces the same heating effect in a resistive load as a DC voltage with the same value. Enter two values and the calculator will solve for the third. The following body composition measurements. Note that this formula applies for constant acceleration only. (V/Vavg); //rasio antara. The invention relates to a CFD (computational fluid dynamics) based method for computing equivalent length of a valve. 92 m/s 2 for 3. Average Velocity Formula: vavg = x/ t x is the DISPLACEMENT where x = xf - xi (final position - initial position) and t is the time interval over which the displacement occurs. It's surprising to many people to find that line voltage is not really 115 Volts peak but is really around 160Vpk. V2-3 = Voltage between phases 2 and 3. Full text of "A grammar of the Greek language" See other formats. vf or rather vf stands for final velocity. (30) If calculated DC gain ratio is not within limits specified in table 4, perform Section IV below. • Vavg is the average voltage (add all three, divide by three). The load on the pipe is calculated using the following formula W = CwB2 (2). Bethe Formula; Average velocity Vavg is defined as the average speed. 280 116 MPa 3. Multiply by 3600 and you get watt-seconds, which is also known as Joules. 2) Lindeburg, Michael R. A sinewave is defined by the trigonometric sine function. Classic; Flipcard; Magazine; Vavg (0-10s) = 0. Simple AC Circuit Calculations Chapter 1 - Basic AC Theory PDF Version. Write a formula for the velocity of the air flow as a function of time. 0)*(8) and your answer = 48m in case you desire to alter it. Conversion Felix Obere This presentation includes forward-looking statements. Kinematics deals with describing motion in terms of displacement,velocity, and acceleration. Solids: Liquids: 0 – 4 months: Breastmilk only: Breastmilk only: 4 – 6 months: Breastmilk onlySee also: What if my 4-5 month old seems developmentally ready for solids?: Continue nursing on cue. v = s/t for s2. A simple process, such as controlling temperature, may be performed in multiple ways. The pulse waveform is shown in Figure 1. 3) is a graphic representation of the relation between stage and streamflow for a given river or stream. Kinetic Theory of Gases, Kinetic Equation. , the sequence is. Atomic Mass Formula Atomic mass in an atom or group of an atom is the sum of the masses of protons, neutrons and electrons. 7071, which is the same as one divided by the square root of two ( 1/√ 2 ). 6 Summary Further reading. The first application of integrals that we'll take a look at is the average value of a function. s defines the following functions: fit. It calculates the RMS voltage based on the above formulas for each. Only if all numbers in the list are positive and equal then rms = avg. The Peak-to-peak Voltage calculator calculates the peak-to-peak Voltage, VP-P, value from either the peak voltage, the RMS voltage, or the average voltage. Homework Equations x(t) = A*cos(ωt) (SHM mathematical model) v(t) = -Vmax*sin(ωt) Fave = 1/(b-a)∫f(x)dx The Attempt at a Solution As soon as i get started with this problem, I hit a brick wall. If you have to do it manually, use the formula A = 100 x Vavg/V0. repeatlast If set to 1, force the filter to extend the last frame of secondary streams until the end of the primary stream. You can also enter scientific notation in the format 3. Jacksonville, North Carolina - Hourly Rate - Get a free salary comparison based on job title, skills, experience and education. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2. Like Reply. Note that ffmpeg integrates a default down-mix (and up-mix) system that should be preferred (see "-ac" option) unless you have very specific needs. Suggested Videos. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. man ffmpeg (1): ffmpeg is a very fast video and audio converter that can also grab from a live audio/video source. Volume is a measurement of how much space is occupied by a substance. If you are looking to do the more accurate 3. For any list of numbers holds: The root mean square (rms) is always equal or higher than the average (avg). Several velocity analysis methods have been used in the past but today most velocities are picked interactively using combination displays on processing workstations. The formula is expressed algebraically as: Where: v = Instantaneous velocity (m/s) Δx = Vector change in position (m) Δt = Change in. The sequence of odd integers could be written {2j + 1j }∞ j=0 or {2j − 1j }∞ j=1. Kimi Raikkonen's late surge sent his Alfa Romeo C39 to the top of the charts on the second day of pre-season testing with a fastest lap of 1m17. Microchip PIC Lab-1 PCB for 18 Pin PIC Microcontrollers PCB has lots of peripherals and highly flexible in connecting devices. 45e9, with no spaces between numbers and the exponent indicator, e. why the generating voltage in India is 11kV or why is it be transmitted as multiples of 11. Average Velocity Formula. Important Equations to Remember. All you need to calculate average velocity is the total displacement, or change in position, and the total time. Displacement equals the original velocity multiplied by time plus one half the acceleration multiplied by the square of time. However, when looking at a mole of ideal gas, it is impossible to measure the velocity of each molecule at every instant of time. Note: Ifyou use the Antique Electronic Supply variable capacitor # CV-471,you needonly usetwoofthethree sections with no modifications; their model. Half of the total secondary voltage appears between the. diphenyl ether, C 12 H 10 O, and phenol, C 6 H 5 OH. Enter 50 in the time box and choose seconds from its menu. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5. Using the given conversion factors, we find (a) the distance d in rods to be d = 4. 7 km/hr accelerates at a uniform rate of 0. In physics, you can calculate power based on force and speed. Now look at your graph. Rearranging equation 1 to make v the subject of the formula gives v=u+at – – – – – – – I When a body moves from one place to another, it is impossible to keep it at the exact same velocity at all times. Then the RMS voltage (V RMS) of a sinusoidal waveform is determined by multiplying the peak voltage value by 0. Therefore, given a known value for R1 we can calculate the overall resistance (z) of the circuit. The ratio t1/T is the pulse signal duty-cycle. shortest If set to 1, force the output to terminate when the shortest input terminates. RIGOL DS1000Z User’s Guide III Use Proper Fuse. Kinetic Theory of Gases, Kinetic Equation. We can plug 10(seconds) and 0(seconds) for t₀ and t₁ in order to find our average velocity during the first ten seconds. To compute VP-P from the peak voltage, the peak voltage is multiplied by 2. a = Vfinal / t. For power. For the case of 440 V line-to-line: V (440/ ) 359. 0127 Tube Length (m) 1. Free solve for a variable calculator - solve the equation for different variables step-by-step This website uses cookies to ensure you get the best experience. 707 * Vpeak, Vavg = 0. 414 x Vrms= Vp; Vavg=. Heat transfer of pipe flows. 3535 * V pp. The name of the command is the name of the option and the argument is the. 3) is a graphic representation of the relation between stage and streamflow for a given river or stream. Following is the formula for Vpp to Vrms conversion. 2a (s – si) = v2 – v2i for a 3. vavg vrms nishant22, RMS voltage for a given waveform is the voltage that produces the same heating effect in a resistive load as a DC voltage with the same value. The Peak-to-peak Voltage calculator calculates the peak-to-peak Voltage, VP-P, value from either the peak voltage, the RMS voltage, or the average voltage. If you are looking to do the more accurate 3. In a similar vein, the temperature of these mercury atoms is 4 times that of the hydrogen molecules in part b. 2 Remapping examples. vavg = ½ (vf + vi) for vi 2. Kinetic Theory of Gases, Kinetic Equation. 4 Phase and Hilbert transforms 1. Mister Jung @ Windermere. P= Vavg×Iavg is valid only for pure contineous dc both voltage and current. vavg vp π 2 = (15) The table below lists the average and most probable neutron velocities and energies. A simple process, such as controlling temperature, may be performed in multiple ways. Worth Publishers. So I've put together this explanation which uses as little math as possible, and hopefully explains the concepts in an intuitive way. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5. 5 m/s(b) Distance travelled, s = 12. Using this we can simulate different resistance values by varying the PWM duty-cycle. K-12 Lesson Plans: Students investigate the motion of a car traveling on an inclined plane and along a flat surface. Physics For Scientists and Engineers. Vavg is the average calculated volume. For Current: If i use the CT, its secondary will provide AC current, and due to the negative cycle my ADC would not detect that negative voltage. • Dmax is the maximum deviation from average (the voltage furthest away from the average, whether greater or less than the average). Vavg T2 T Vtdt T T = − F HG I 1 KJ z 1 1 2 *() Eqn 1 If a voltage (current) is either constant or periodic, then measuring its average is independent of the interval over which a measurement is made. This can be done by dividing 100 cm by each of the times in column 5. x, FreeBSD 4. , the general formula is: Number of organisms = N = 2(t/30 min) = 2(t/0. Ninguna Categoria; Subido por Alex Ibacache Fluidos- Frank M. This online chemistry calculator may be used to calculate root mean square velocity, mean velocity (a. 11 x Vavg; 1. That is, the ratio F/m = a = g (2). s defines the following functions: fit. Favourite answer. 5 s later the student hears the associated clap of thunder. 3 Operating systems compatible with NCO. A simple process, such as controlling temperature, may be performed in multiple ways. A stands for Accuracy. The slope of such graphs is equal to the velocity of the object. Army Corps of Engineers riprap design guidance for flood channels is presented, and the limitations and basis of sev eral empirical coefficients are discussed. The VA Formulary Search tool is an aid for VA and Non-VA user to easily search for formulary items. A velocity is a vector unit, and average velocity can be. References - Books: 1) Tipler, Paul A. v avg = average velocity (m/s) v i = the initial velocity (m/s). Vavg= d ∆t Average Speed. If I make the assumption that the power factor is 0. Do not touch exposed junctions and components when the unit is powered. 12 For low-speed (laminar) flow in a tube of radius ro, the velocity u takes the form u=B ∆p 2 2 ro − r µ ( ) where µ is viscosity. Then the Vcc can be estimated as Vcc = Vavg + Vdrop/2 The method can be recursively used to improve the value of Vcc, if there is no prior information on Vcc. Milne’s Predictor Formula Milne’s Corrector Formula Adams–Bashforth Predictor Formula Adams–Moulton Corrector Formula Exercises Previous Years’ Questions Answer Keys Test Engineering Mathematics Answer Keys Part 3 Civil Engineering Unit 1 EngineeringMechanics Chapter 1 Introduction—Forcesand Equilibrium Introduction Newtonian MecHanics. If you know average value of voltage then you can use following formula to get peak voltage: Vpeak = (V. acetylene, C 2 H 2 , and benzene, C 6 H 6 b. Voltage This table shows the relationship between Power in [dBm] or [Watts] and Voltage in RMS, peak, peak-to-peak for sinusoidal signals in 50-Ohm systems. D=Vavg*T Vavg= (Vi+Vf)/2 A= (Vf-Vi)/T New formulas from other definitions: D= Vi*T + ½ *A*T2 and Vf2 = Vi2 + 2*A*D Pg 55 1) A car with an intial speed of 23. Fluorophosphate cathodes with the chemical formula NaxV2(PO4)2O2yF3–2y(0 ≤ x≤ 4, 0 ≤ y≤ 1) are some of the few known sodium-ion cathode materials with the potential to be competitive with conventional lithium-ion cathodes. What does vf minus vi divided by t mean? Top Answer. A Homogeneous Equilibrium Model Improved for Pipe Flows Jung Seob Kim and Heather Jean Dunsheath Table I Sozzi and Sutherland Nozzle 2 Test Data vs. Microchip PIC Lab-1 PCB for 18 Pin PIC Microcontrollers PCB has lots of peripherals and highly flexible in connecting devices. Click CALCULATE and your answer is 2. 5 s later the student hears the associated clap of thunder. 23 x 1043 organisms 2. Question: Please Answer All Parts. This is a special case of constant acceleration with acceleration = 0. In order for this to occur the fluid must travel through a length of a straight pipe. Only one of these phases undergoes a solid solution reaction, in the interval between 1. Difference between Vavg and Vrms If my Vp is let say 10V and I was to rectify it using ideal diodes and caps, wouldn't the output be 2*10V/π=6. Box 261501 San Diego, CA 92196 (858) 566-2372 (858) 240-2299 FAX. Average Speed = Total Distance/Total Time. Gaseous molecules follow a Maxwell-Boltzmann distribution which is depends on the applied temperature and the molecular weight of the gaseous molecules. Where vo (also called 'vi') is equal to zero 1. The method is based on depth-averaged velocity rather than shear stress, which was the. ethane, C 2 H 6, and butane, C 4 H 10 c. You can also enter scientific notation in the format 3. No matter which formula you choose to use, it will always boil down to this one. Another question with rigged numbers. Say im driving, and accelerate after a red light uniformly, and reach 30 mph in 2 seconds. One method for describing the motion of an object is through the use of velocity-time graphs which show the velocity of the object as a function of time. HEM Predictions Test #1 Test #2 Test #3 Tube Diameter (m) 0. Fluorophosphate cathodes with the chemical formula NaxV2(PO4)2O2yF3–2y(0 ≤ x≤ 4, 0 ≤ y≤ 1) are some of the few known sodium-ion cathode materials with the potential to be competitive with conventional lithium-ion cathodes. Peak-to-peak voltage, VPP, is a voltage waveform which is measured from the top of the waveform, called the crest, all the way down to the bottom of the waveform, called the trough. 3 vols DC-DC converter. This gives the average speed of the car for each 100 cm distance. 1/27/2003 © Heat Sinks Page 4 Thermal data MIN TYP MAX θ JC - - 1,17 °C/W θ JA 100 - - 43,7 °C/W PMAX is to be derated linearly at a rate of 0. There are actually a lot of ways to describe an average. Write vAvg like this : =interval(max({1}CreationDate),min({1}CreationDate)) For the first point, I think that you cannot filter a field with the help of a condition on another field. This same equation also holds true for current and all we have to do is swap Voltage in the equation for Current. But how fast is the position changing with time and in what direction? To understand this, we define average velocity and average speed. Click CALCULATE and your answer is 2. The method is based on depth-averaged velocity rather than shear stress, which was the. 7% of Vp for a full-wave rectified voltage. as func8on of vel. 0319988 kg/mol Remember that kg m 2 s-2 is called a Joule and that the unit on R is usually written J/K mol. 8 volts , Vout (25 C) = [ 4 / (4 + 10. The support for this method can also be found in Parseval's Theorem. Voltage This table shows the relationship between Power in [dBm] or [Watts] and Voltage in RMS, peak, peak-to-peak for sinusoidal signals in 50-Ohm systems. The velocity of particle travelling in a straight line is given by v=6t-3t^2 m/s where t is in secound. 7% of Vp for a full-wave rectified voltage. However, if we only want to calculate an average speed vavg, the following formula can be used: vavg = Δs/Δt where Δs is the change in distance over a period of time Δt. In the case of symmetrical waveforms like the square wave, a quarter cycle faithfully represents all four quarter cycles of the waveform. vavg vrms nishant22, RMS voltage for a given waveform is the voltage that produces the same heating effect in a resistive load as a DC voltage with the same value. 3 Na per formula unit. F = 10 kg (5 m/s - 0 m/s) / 12 sec. P is the total energy converted in one cycle, divided by the period T of the cycle, so:. The Peak-to-peak Voltage calculator calculates the peak-to-peak Voltage, VP-P, value from either the peak voltage, the RMS voltage, or the average voltage. $u(t)=U_m \, \sin(\omega t + \varphi_{0u})=U_m \, \sin( 2 \pi f t + \varphi_{0u} )$ $u(t)\,\dot{=}\,100 \cdot \sin( 2 \pi 50 t + \frac{\pi}{4} )\,\mathrm V = 100\cdot \sin( 100 \pi t + \frac{\pi}{4} )\,\mathrm V$. V = πr2h for r, where r is a radius 9. On the last tab of the heat transfer resistance tool dialog in HTflux you will find a very versatile tool to calculate the heat transfers coefficients (resistances) of pipe flows for gases and liquids. Calculator Use. A bridge rectifier with an efficient filter is ideal for any type of general power supply applications like charging a battery, powering a dc device (like a motor, led etc) etc. 3 Two sinusoidal phasors out of phase by angle θ. Assuming sinusoidal waveform, let the. If I make the assumption that the power factor is 0. Dome and air load options are available. The distance traveled during constant acceleration is the same as travelling at the average velocity of the trip. This is not really a DC voltage, it's just a number we would get if we had taken the average of the full wave signal over time. • Dmax is the maximum deviation from average (the voltage furthest away from the average, whether greater or less than the average). The formula for RMS voltage in analytical method is; VRMS = Vavg x π / 2√2. A) Find The Average Power P_avg Created By Force F. 8 m/s Here is the above set-up done with units: v = [(3) (8. This formula is valid for a set of n discrete values. If you're seeing this message, it means we're having trouble loading external resources on our website. MicroPower Direct Introduces ME300RU Series Of DC/DC Converters January 30, 2019 – The ME300RU series, available from MicroPower Direct, is a series of DC/DC converters. V L(dc) =average value of load voltage. works for fully developed laminar pipe flow in round pipes since V Vavg Ac (Vmax / 2)Ac. • Dmax is the maximum deviation from average (the voltage furthest away from the average, whether greater or less than the average). Remember that we will be using the cartesian coordinate system throughout. F = 50 kg m/s / 12 sec. Materiales de aprendizaje gratuitos. The ratio t1/T is the pulse signal duty-cycle. V AVG = V PEAK x 0. Example #1: Calculate the rms speed of an oxygen gas molecule, O 2, at 31. x = xi + vit + ½ at2 for xi 7. However the official formulary is the VA National Formulary (VANF) spreadsheet that contains additional restrictions and conditions that are not shown on the VA Formulary Search. $u(t)=U_m \, \sin(\omega t + \varphi_{0u})=U_m \, \sin( 2 \pi f t + \varphi_{0u} )$ $u(t)\,\dot{=}\,100 \cdot \sin( 2 \pi 50 t + \frac{\pi}{4} )\,\mathrm V = 100\cdot \sin( 100 \pi t + \frac{\pi}{4} )\,\mathrm V$. ethane, C 2 H 6, and butane, C 4 H 10 c. We'll say t₀=0 and t₁ =10. 45e9, with no spaces between numbers and the exponent indicator, e. The mRNA abundance of each indicated gene was calculated using the formula 2 −ΔΔCt, and the results are expressed as fold changes. This set focuses on formulas, important numbers, word problems, and linear motion terminology. The link between the mass of an element and the number of atoms it contains is the relative atomic mass of the element. 4 m/s Pkg p20 Chemical formula writing worksheet. As shown in other articles in this website (How to Derive the RMS Value of a Trapezoidal Waveform and How to Derive the RMS Value of a Triangle Waveform), the RMS definition is an integral over the signal period as. To find the reason behind Vrms=Umax/sqr2 (2) you'll have to integrate a sine function from 0 to 180 degrees. We will study motion of a body in one direction in this chapter. Where vo (also called 'vi') is equal to zero 1. Army Corps of Engineers riprap design guidance for flood channels is presented, and the limitations and basis of sev eral empirical coefficients are discussed. The AMPLITUDE of a sine wave is the maximum vertical distance reached, in either direction from the centre line of the wave. It is sometimes used on extremely high-voltage, low-current power supplies for cathode-ray and similar electron tubes, which require very little load current from the supply. 2a (s – si) = v2 – v2i for s 4. Vavg=2*Vpeak/pi where Vpeak is the peak value of the original siine wave. It can also convert between arbitrary sample rates and resize video on the fly with a high quality polyphase filter. Enter 180 in the velocity box and choose miles per hour from its menu. P is the total energy converted in one cycle, divided by the period T of the cycle, so:. ) Here's hoping this calculator helps you with those math problems. com talked about how to calculate the RMS of simple signals like a sine wave, trapezoidal and triangle signals, pulse and square signals. Unit of acceleration = m/s2 or ms-2 If the velocity of a body decreases, then it will experience a …. V2-3 = Voltage between phases 2 and 3. However, if we only want to calculate an average speed vavg, the following formula can be used: vavg = Δs/Δt where Δs is the change in distance over a period of time Δt. (30) If calculated DC gain ratio is not within limits specified in table 4, perform Section IV below. The average value is also given by the equation; Vavg = 0. 414 x Vrms 2. D=Vavg*T Vavg= (Vi+Vf)/2 A= (Vf-Vi)/T. This formula is used Vout (37 C) - Vout (25 C) = 0. 40) to derive the following relations for turbulent flat-plate flow. How to Calculate Average Velocity. The Capacitor Filter. 1k points) nsep. The formula used to calculate the average speed and average velocity is virtually the same, v = D/t, s = d/t, with only slight difference that in the first case, direction is to be mentioned. This gives the average speed of the car for each 100 cm distance. 6 Summary Further reading. Heat transfer of pipe flows. That was hard enough for me to do at school 20-25 years ago. You might say this is always the case, but it's not true of many applications of pulse transformers or in most forward converters. The values are shown in Figure 4. Fully developed flow occurs when the viscous effects due to the shear stress between the fluid particles and pipe wall create a fully developed velocity profile. Solution Manual - Fluid Mechanics 4th Edition - Frank M. 955*Vs which isn't what i get from the simulation from multisim. 7 V Figure (c): Full Wave Rectifier Turn Ratio Figure (d): Full Wave Rectifier Turn Ratio Peak Inverse Voltage. The pulse waveform is shown in Figure 1. Vavg is the average calculated volume. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5. Formula Sheet for PHY 101 Final Exam Ch 2-7,9-10,19, 26- 29 [In some relations, the “~” symbol is being use to represent a direct proportion] Ch 3: Linear Motion a = Δv/t (average acceleration) vavg = Δd/t (average velocity) vf = vi + at (final velocity: how fast?). 3 V for germanium. warning('If you use summary or anova on the result, lm methods use the\nsum of squared residuals rather than the Rubin formula for computing \nresidual variance and standard errors. He has held positions at Imperial College, MIT, Caltech, CERN and the University of Rome. You can use the formula \text{speed} = \frac{\text{distance}}{\text{time}} to find. Title: Here are some useful equations Author: NJIT Last modified by: Academic Consulting Created Date: 9/13/2008 1:31:00 AM Company: NJIT Other titles. Formula for finding low quarter distribution uniformity LQavg Vavg WHERE DUlq = Low Quarter Distribution Uniformity LQavg = Average Catch in Lower Quarter Vavg = Average Catch Overall DUlq = DRIP IRRIGATION Three Simple Steps to Getting Started Step 1: Determine the water needs of plant. Enzyme-linked Immunosorbent Assay (ELISA) The concentrations of NF-κB-responsive genes (IL-8, TNF-a and IL-1β) were evaluated in cell culture supernatants according to the manufacturer’s protocol (Joyee. impute vcov. Obviously your triangular wave had its bottom peak at ground potential to make Vavg=Vmax/2. Sine Wave Fundamentals: Practice Problem #1 By Patrick Hoppe. To get these actual transfer coefficients quite some fluid dynamical calculations are necessary. I measured the output current by measuring. vavg = 1 2 (v0 + vf ) = s0 + vf t − 1 2 at2 v2 f = v2 0 + 2a(sf − s0) = s0 + vavgt PROJECTILE MOTION A projectile fired with initial velocity v0 at angle θ to the ground will trace a parabolic. 921 v r m s. • Vavg is the average voltage (add all three, divide by three). vxit ; ½axt 2 Pos. The coefficient of restitution, e = [(vB)2 – (vA)2] / [(vA)1 – (vB)1], relates therelative velocities of the. 2a (s - si) = v2 - v2i for s 4. Students observe the pattern of drops left by the moving car. However in case of inductor for contineous currrent the average and rms is always same. 168 m furlong ) 5. The average velocity formula: average velocity = (change in position) / (change in time) If we were given a position function, s(t), which gave the position of an object at time t, then the average velocity between time t sub 1 and t sub 2 is given by the formula: V avg = [s(t 2) - s(t 1)] / (t 2 - t 1) or, Δd/Δt. It is akin to Ohm’s Law, but something I was never taught in tech school –I had to learn it myself much later –now I use it at least weekly. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. axt velocity as func8on Of 8me ; xf= xi. Part (a) What was the student's overall average velocity vavg, x, in m/s, for the trip assuming the student spent equal times at speeds v1 and v2? Part (b) If the student traveled for T1seconds at speed v1, and. This wouldn’t provide much insight into the signal’s effective amplitude, so most meters compute Vavg based on the absolute value of the waveform. However, mass m and energy E can be converted to each other according to the well-known formula proposed by Albert Einstein (1879–1955): E ϭ mc2 (5–1) where c is the speed of light in a vacuum, which is c ϭ 2. 637 *Vp Where Vp is the maximum/ Peak value of voltage in that cycle. That's the formula for average acceleration. By using this website, you agree to our Cookie Policy. Average speed does not have to equal the magnitude of the average velocity. Watch Now 148. Least squares fit. Where Vavg is the average voltage given for Vin and the current duty-cycle (d) in %. Microchip PIC Lab-1 PCB for 18 Pin PIC Microcontrollers PCB has lots of peripherals and highly flexible in connecting devices. Solutions Manual for Fluid Mechanics Seventh Edition in SI Units Viscous Flow in Ducts PROPRIETARY AND CONFIDENTIAL. h interface. 35355 * V pp. Fluid Mechanics McGraw-Hill Series in Mechanical Engineering CONSULTING EDITORS Jack P. Average Speed = (a + b)/2. Worth Publishers. The following fact tells us how to compute this. vavg = ½ (vf + vi) for vi 2. The distance traveled during constant acceleration is the same as travelling at the average velocity of the trip. v ¯ = ( 8 3 π) 1 / 2 v r m s = 0. Ness Engineering, Inc. acetylene, C 2 H 2, and benzene, C 6 H 6 b. 2 trend, namely, Kalol -Ahmedabad - Wasna trend. The instantaneous velocity is just the velocity of an object at a specific point in time. (V/Vavg); //rasio antara. is often written as v which is said as "v bar" or just. Using the formula, average speed = distance/time (vavg = d/t), calculate the average speed for each 100 cm distance. One method for describing the motion of an object is through the use of velocity-time graphs which show the velocity of the object as a function of time. Solve each formula for the quantity given. Two expressions expr1 and expr2 can be combined to form another expression "expr1;expr2". We use lower case p(t) because this is the expression for the instantaneous powerat time t. The Vrms is defined as square root of the mean of the squares of the values for the one time period of the sine wave. You should know that the velocity/time equation is just one important equation using velocity , but others exist. Press this link to have it generating a spreadsheet and sending it to your browser Press this link to display the XLSGEN script generated by this program Press this link to display the source of this program. Again, Vprolate, and the PSEM volume calculation are least sensitive to changes in the SEM magnification. Introduction to Motion. 07V ? I mean, I calculated the area under the curve of a sin function and I found it's. Avoid Circuit or Wire Exposure. For example using the formula above we can state that: Vadj = (Vin / 100) * d. 707 * Vpeak, Vavg = 0. asked by Matt on July 13, 2013; math. It only takes a minute to sign up. x, FreeBSD 4. Solution ¯ is found by calculating the one-way time to pass through each layer, summing the time increments to a given depth and dividing the sum into the depth; is found from equation (4. d = ½ * a * t². x = xi + vit + ½ at2 for xi 7. Sound travels at 343 m/s in the air. , ls or mkdir. Some options can be changed during the operation of the filter using a command. Determine their average speed on. It is a vector quantity where u is the initial velocity of the object, v is its final velocity and t is the time taken. Ft = m (V2 - V1) for V1 5. Any waveform swinging around zero has a Vavg of zero. ffplay [options] [input_url]Description. Yes, watt-hours is a measure of energy, just like kilowatt-hours. Vrms/Vavg/Vmax/Vmin: 10Hz～8MHz square wave,10Hz～20KHz sine wave/triangular wave/ sawtooth wave Storage Inbuilt 8MB U disk storage for waveform data and images: : 99. The load on the pipe is calculated using the following formula W = CwB2 (2). If I make the assumption that the power factor is 0. Here is the datasheet spec. PN M010044. This is the equation you need to use: v = (3RT) / M You may, if you wish, read more about the above equation here. Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. Ness Engineering, Inc. Part (a) What was the student's overall average velocity vavg, x, in m/s, for the trip assuming the student spent equal times at speeds v1 and v2? Part (b) If the student traveled for T1seconds at speed v1, and. For a sine wave: Vrms = 0. We'll be using the NEMA formula for maximum unbalanced voltage Vmu = (100 × Dmax) ÷ Vavg. V(avg) = ∆x/∆t 2. The Center-Tapped Full-Wave Rectifier. The slope of such graphs is equal to the velocity of the object. 167 125 10MB Read more. The Bacnet interface only provides amp draw for the 3 phases (153. Voltage Conversion Factors Date: 01/10/2001 at 07:02:27 From: Bobby Coleman Subject: Trigonometry conversions When I try to convert rms voltage to peak voltage, then peak voltage to average voltage, I get one answer, but when I convert the peak voltage to rms voltage, then rms voltage to average voltage, I get a different answer, but close to the first. Average Voltage (Vavg) The level of a waveform defined by the condition that the area enclosed by the curve above this level is exactly equal to the area enclosed by the curve below this level. 07V ? I mean, I calculated the area under the curve of a sin function and I found it's. This wouldn’t provide much insight into the signal’s effective amplitude, so most meters compute Vavg based on the absolute value of the waveform. Summary Introduction Foreword Top Summary operators summary This manual describes NCO, which stands for netCDF Operators. 318 X 10 V Vavg = 3. 2-2_amd64 NAME ffplay - FFplay media player SYNOPSIS ffplay [options] [input_url] DESCRIPTION FFplay is a very simple and portable media player using the FFmpeg libraries and the SDL library. True RMS Voltage Calculation with C Xiao Xu 11/14/12 Design Team 7 Abstract The ability to acquire fast and accurate True RMS values is extremely beneficial to applications in various industries such as medical, industrial and even businesses. Obviously your triangular wave had its bottom peak at ground potential to make Vavg=Vmax/2. com talked about how to calculate the RMS of simple signals like a sine wave, trapezoidal and triangle signals, pulse and square signals. Army Corps of Engineers Riprap Design for Flood Channels STEPHEN T. Usually, we are interested in the mean power delivered, which is normally written P. Fluid Mechanics Frank White 5th Ed - ID:5c142a11d322e. This is a special case of constant acceleration with acceleration = 0. Online physics calculator to calculate the kinematic velocity from the given acceleration, displacement and initial velocity values using Kinematics Equation Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. View Test Prep - formula_sheet_final2 from PHYSICS 211 at Metropolitan State University Of Denver. Volumes calculated using Vavg ^ con- sistently show the largest errors. 5 m/s(b) Distance travelled, s = 12. The Capacitor Filter. Calculate v = (v + u) / 2. 1k points) nsep. We'll say t₀=0 and t₁ =10. Homework Statement Basically, I need to understand how to calculate Irms and I*rms given a Vrms and an impedance Z. The instantaneous value of a sine wave one quarter of the way through the cycle will be equal to the peak value. Sauriol Rev. As an example, if a 20V DC source is using up 20W of power, then a 20Vrms sinusoidal or non Voltage Source Vx Vessel Equilibrium Temperature Tx Specifically, Vavg T2 T Vtdt T T = − F HG I 1 KJ z 1 1 2 *() Eqn 1 If a voltage (current) is either constant or periodic, then measuring its average is independent of the interval over which a. 45e9, with no spaces between numbers and the exponent indicator, e. (29) Calculate DC gain ratio using formula given in (15) above. Consider using ideal body weight in obese patients. Watch Now 148. True RMS is a consistent and standard way to measure and compare dynamic signals of all shapes and sizes. vavg) Example - Justin Gatlin begins his run at the starting line. If you are looking to do the more accurate 3. You might be required to find an average volume as a part of a middle school or high school. This formula is used Vout (37 C) - Vout (25 C) = 0. Because work equals force times distance, you can write the equation for power the following way, assuming that the force acts along the direction of travel: where s is the distance traveled. Online physics calculator to calculate the kinematic velocity from the given acceleration, displacement and initial velocity values using Kinematics Equation Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. However, with the recent advancements in the automation and measurement infrastructures, it is now possible to improve the efficiency of DS operation. Formula Sheet for PHY 101 Final Exam Ch 2-7,9-10,19, 26- 29 [In some relations, the "~" symbol is being use to represent a direct proportion] Ch 3: Linear Motion a = Δv/t (average acceleration) vavg = Δd/t (average velocity) vf = vi + at (final velocity: how fast?). It is akin to Ohm's Law, but something I was never taught in tech school -I had to learn it myself much later -now I use it at least weekly. don't forget friction. 35355 * V pp. This same equation also holds true for current and all we have to do is swap Voltage in the equation for Current. Bethe Formula; Average velocity Vavg is defined as the average speed. The red rectangle is the contribution from the original velocity of the object. v ¯ = ( 8 3 π) 1 / 2 v r m s = 0. Breastfeed every 1-3 hours or Formula 18-40 ounces. A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions: • The gas is composed of. Example question: Given Vrms = 120 V at an angle of 30° and an impedance of Z = 10 Ω, find Irms and I*rms. What is changing is the temperature on the left hand side of the formula, so that means we will have a one-dimensional matrix as a result from the calculation. find kVa by hypotenuse formula for trafo capacity. Vout (37 C) = [ 4 / (4 + 7. In this problem, we basically use the same rules and formula as the secant line slope formula, except we use different notation. F = ma for a 5. The half wave rectifier utilizes alternate half cycles of the input sinusoid. Therefore, Vavg = V m /2π [1+1] + V m /2π [-1-1] = 2V m /2π – 2V m /2π = 0 The average value of a sinusoidal alternating quantity for a complete cycle will be equal to zero. V(avg) = ∆x/∆t 2. It only takes a minute to sign up. This formula is valid for a set of n discrete values. Voltage and current exhibiting cyclic behavior is referred to as. It only takes a minute to sign up. A student witnesses a flash of lightning and then t = 6. 3 Na per formula unit. Nevertheless, velocity analysis is still one of the most time consuming parts of seismic processing. Vavg T2 T Vtdt T T = − F HG I 1 KJ z 1 1 2 *() Eqn 1 If a voltage (current) is either constant or periodic, then measuring its average is independent of the interval over which a measurement is made. Related Post: Peak Voltage and Peak to Peak Voltage Calculator How to Calculate RMS Voltage Value ? As discussed before about the Root Mean Square (RMS) or V RMS voltage, It is DC equivalent voltage of a sine wave i. 40) to derive the following relations for turbulent flat-plate flow. Part (a) How long does it take her to reach a speed of V in seconds? Part (b) If she then brakes to a stop in T seconds, what is her acceleration in meters per square second? Solution: (a). 637Vpk: Half rectified wave: Vrms= Vpk/2: Vavg= 0. 637 (Figure 2). Joined Mar 31, 2012 25,632. Instantaneous Voltage and Current Values in a Series RLC Circuit Task number: 1543 An AC series circuit consists of a resistor with resistance of 90 Ω, a coil with inductance of 1. An AC function can represent either a power source or a signal source with the shape of an AC waveform generally following that of a mathematical sinusoid being defined as: A(t) = A. 63 m/s/s on the moon, what is the speed of an object if it fell for 5 seconds. 166 kg m/s. Where vo (also called 'vi') is equal to zero 1. Two expressions expr1 and expr2 can be combined to form another expression "expr1;expr2". Accurate, reliable salary and compensation comparisons for. 0319988 v = 486. The instantaneous value of a sine wave one quarter of the way through the cycle will be equal to the peak value. Dengan pendekatan rumus integral sinus kuadrat diperoleh tegangan rata-rata VRMS = Vp/Ö2 atau kira-kira = 0. It is used with the Arithmetic command. The Vrms is defined as square root of the mean of the squares of the values for the one time period of the sine wave. skip to page content. Answer / soumya ranjan panigrahi we know form factor is the cause of generating voltage in India is 11kV or it be transmitted as multiples of 11, because of simple to desine. Solution: (a) For air, take ρ = 1. Write vAvg like this : =interval(max({1}CreationDate),min({1}CreationDate)) For the first point, I think that you cannot filter a field with the help of a condition on another field. For power. 37V instead of 10V/√2=7. All you need to calculate average velocity is the total displacement, or change in position, and the total time. This can be done by dividing 100 cm by each of the times in column 5. The link between the mass of an element and the number of atoms it contains is the relative atomic mass of the element. This set focuses on formulas, important numbers, word problems, and linear motion terminology. $u(t)=U_m \, \sin(\omega t + \varphi_{0u})=U_m \, \sin( 2 \pi f t + \varphi_{0u} )$ $u(t)\,\dot{=}\,100 \cdot \sin( 2 \pi 50 t + \frac{\pi}{4} )\,\mathrm V = 100\cdot \sin( 100 \pi t + \frac{\pi}{4} )\,\mathrm V$. Any waveform swinging around zero has a Vavg of zero. then, according to what you wrote. 4 Phase and Hilbert transforms 1. It is possible to specify separate constants to add to the real and imaginary parts of the data, however the imaginary constant will only be used if the current dimension of the input data has an imaginary part. We will study motion of a body in one direction in this chapter. In this problem, we basically use the same rules and formula as the secant line slope formula, except we use different notation.


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# [SOLVED]Poles of \Gamma(z)

#### dwsmith

##### Well-known member
Compute the residue of $\Gamma(z)$ at each of its poles.

So the poles are at the negative integers and 0. I suspect there must be a formula than since this is an infinite set.

$\Gamma(z) = \dfrac{e^{-\gamma z}}{z}\prod\limits_{n=1}^{\infty}\left(1+\dfrac{z}{n}\right)^{-1}e^{z/n}$

Should I start by logarithmically differentiating?

#### Jose27

##### New member
Just a thought (I don't know if it'll work), but maybe using the $\Gamma$ function's integral representation (remember we have to split the integral several times in order to extend it past a certain integer) and using Fubini's theorem. Something along these lines.

#### dwsmith

##### Well-known member
Just a thought (I don't know if it'll work), but maybe using the $\Gamma$ function's integral representation (remember we have to split the integral several times in order to extend it past a certain integer) and using Fubini's theorem. Something along these lines.
$\displaystyle\Gamma(z) =\int_0^{\infty}e^{-t}t^z\dfrac{dt}{t}$

What should I do with this?

---------- Post added at 21:29 ---------- Previous post was at 20:37 ----------

The $\text{Res} = \lim\limits_{z\to -m}(z+m)\Gamma(z)$ and we can write $\Gamma(z) = \dfrac{\Gamma(z+m)}{(z+m-1)(z+m-2)\cdots (z+1)z}$ for the $\text{Re} z> -m$.

By substitution, we have
$$\text{Res} = \lim_{z\to -m}(z+m)\Gamma(z) = \lim_{z\to -m}(z+m)\frac{\Gamma(z+m)}{(z+m-1)(z+m-2)\cdots (z+1)z}.$$

By definition, we have $(z+m)\Gamma(z+m) = \Gamma(z+m+1)$.

So
$$\text{Res} = \lim_{z\to -m}\frac{\Gamma(z+m+1)}{(z+m-1)(z+m-2)\cdots (z+1)z} = \frac{\Gamma(1) = 1}{(-1)(-2)\cdots (-m)} = \frac{(-1)^m}{m!}.$$

Last edited:

#### Opalg

##### MHB Oldtimer
Staff member
$$\text{Res} = \ldots = \frac{(-1)^m}{m!}.$$
That is correct. The functional equation $\Gamma(z+1) = z\Gamma(z)$ is the key to the calculation.


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# Algorithm 922

Algorithm 922: A mixed finite element method for Helmholtz transmission eigenvalues. Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method has two major advantages: 1) the formulation leads to a generalized eigenvalue problem naturally without the need to invert a related linear system, and 2) the nonphysical zero transmission eigenvalue, which has an infinitely dimensional eigenspace, is eliminated. To solve the resulting non-Hermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method is proposed. To make the computation efficient, the search interval is decided using a Faber-Krahn type inequality for transmission eignevalues and the interval is updated at each iteration. The algorithm is implemented using Matlab. The code can be easily used in the qualitative methods in inverse scattering and modified to compute transmission eigenvalues for other models such as elasticity problem.

This software is also peer reviewed by journal TOMS.

## References in zbMATH (referenced in 32 articles )

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Browse Questions

# For what value of $\lambda$ is the function defined by $f$ defined by $f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if$ x $$\leq 0$}\\ 4x + 1,& \quad \text{if$x$> 0}\\ \end{array} \right.$ Continuous at $x = 0$?

This question is separated into two parts

Toolbox:
• If $f$ is a real function on a subset of the real numbers and $c$ be a point in the domain of $f$, then $f$ is continuous at $c$ if $\lim\limits_{\large x\to c} f(x) = f(c)$.
At $x=0$
LHL=$\lim\limits_{\large x\to 0}\lambda(x^2-2x)$
$\quad\;\;\;=0$
RHL=$\lim\limits_{\large x\to 0}(4x+1)$
$\quad\;\;\;=1$
$f(0)$=LHL $\neq$ RHL
$\Rightarrow f$ is not continuous at $x=0$ whatever value of $\lambda\in R$


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## Chemistry and Chemical Reactivity (9th Edition)

$CO_2$: $1.316\ g\div44.01\ g/mol=0.0299\ mol$ C: $0.0299\ mol\times12.01\ g/mol=0.359\ g$ $H_2O$: $0.269\ g\div18.01\ g/mol=0.0149\ mol$ H: $2\times0.0149\ mol\times1.008\ g/mol=0.0300\ g$ O: $(0.509-0.359-0.0300)\ g\div 16.00\ g/mol=0.00750\ mol$ Dividing by the smallest value: C: $0.0299/0.00750=4.0$ H: $2\times0.0149/0.00750=4.0$ Empirical formula: $C_4H_4O$