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# Go FPV Goggles

## Background

These are my DIY 3D "Go FPV" goggles. They have much higher resolution, depending on your phone, than Fatsharks and are waaaay cheaper as well. What is the resolution of these goggles you ask? Using my Nexus 5, which runs at 445 PPI 1080p IPS, that's 1920x1080 pixels. The screen is split between both eyes, so each eye gets 960x1080. Plus, if you have 2 cameras, they're capable of realtime 3D video. Awesome!

## Parts

The physical goggles are just Google Cardboard with a Boscam RC805 Video Receiver (I use this Boscam TS351 transmitter) velcroed on and hooked up to an analog to digital converter (ADC) that speaks the UVC protocol. You'll need a USB OTG cable to hook up the ADC to your phone. This cable and the other cables big and bulky, so I soldered on my own shorter, lighter cables, including a custom made OTG cable. I also soldered in a JST connector, so I could plug a lipo straight into the Reciever, which can take up to ~16v safely.

### Components

My goggles don't look like cardboard, even though they are, because I made them out of a box that had printing on it. I think it was a box for a kitchen item. It had a nice plastic feel, which I hope will keep some of the moisture away from the cardboard.

Happy Flying!


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# Schrodinger Equation in Spherical co-ordinates. Constants.

When normalising the S.E. in spherical coordinates you split it up into 3 integrals, with respect to r, theta and phi.

My question is, once you have found the constants for each, when writing out the normalised PSI do you simply place them as a product in the solution?

i..e PSI (r,theta,phi) = ABC r exp (-r/2a) cos (theta)

where ABC are the normalised constants from each part?

Thanks again for any help!!

That's correct, because you just choose the overall constant such that the wave function is normalized in the sense of the Hilbert-space norm. What you have written down is the $n=2$, $l=1$, $m=0$ hydrogen wavefunction,

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If you have a spare bedroom, you can find a roommate or list the space on AirBnB for travelers. Having a roommate is the more passive of the two, as being an Airbnb host will require more work in the form of turning over the room between stays. This is a super painless way to earn $500 to$1,000 a month without much effort – you may even be able to cover your mortgage payment with this extra income!
Wow! What an awesome list! My favorite is the stock photography because I love photography. I have had some success there, particularly with one photo I make some decent income from. I think the key with stock photography is finding a shot that is high demand. Then, find a new unique way to frame that shot. This is the reason my St. Louis Arch photo is a top 10 on both ShutterStock and iStockPhoto. Thanks for the awesome ideas above!
I’ve been into home décor lately and I had to turn to Etsy to find exactly what I wanted. I ended up purchasing digital files of the artwork I wanted printed out! The seller had made a bunch of wall art, digitized, and listed it on Etsy for instant download. There are other popular digital files on Etsy as well such as monthly planners. If you’re into graphic design this could be an amazing passive income idea for you.
Haha, that is too funny. I wanted to make an app back in the day called “MyShares” (You can probably tell how I cam up with the name at the time). The idea was that I would loan out books and DVD’s and then would never get them back. Then I thought, how cool would it be if I could rent those items out and that would motivate people to bring them back. Obviously, books and DVD’s are cheap, so this isn’t the money maker. The idea that would probably make the most money would be things like tools, ATVs, etc.

From Median Income Thresholds to Personal Income StatementsLooking at overall population statistics in recent years, the Census Bureau has reported median annual household income around $44,334. Moving our focus to retirement, a 2005 Congressional Research Service report (Topics in Aging: Income and Poverty Among Older Americans in 2004, by Debra Whitman and Patrick Purcell) provides data suggesting median annual inflows into the personal income statements of current retirees (age 65 and above) were as follows:o Income from human capital –Wages:$15,000o Income from social capital –Private defined benefit plans: $6,720 –Public defined benefit plans:$15,600 –Social Security: $10,399o Income from financial capital –Annual income:$952

This is mostly passive once you have it all set up, but it does take a lot of work at the beginning. Real estate investing also requires occasional maintenance. Currently, we invest in a couple of rental properties and earn about $500 profit from each per month. You can read more about my rental properties at MoneySmartLife.com: How and Why I Became a Landlord. Prime Minister Indira Gandhi nationalised 14 banks in 1969, followed by six others in 1980, and made it mandatory for banks to provide 40% of their net credit to priority sectors including agriculture, small-scale industry, retail trade and small business, to ensure that the banks fulfilled their social and developmental goals. Since then, the number of bank branches has increased from 8,260 in 1969 to 72,170 in 2007 and the population covered by a branch decreased from 63,800 to 15,000 during the same period. The total bank deposits increased from ₹59.1 billion (US$820 million) in 1970–71 to ₹38,309.22 billion (US$530 billion) in 2008–09. Despite an increase of rural branches – from 1,860 or 22% of the total in 1969 to 30,590 or 42% in 2007 – only 32,270 of 500,000 villages are served by a scheduled bank.[204][205] But first, let’s about talk passive income! What is passive income? There are many different definitions out there, but mine goes something like this: Passive income is all about building online businesses that can work for you, that allow you to generate income, and grow and scale, without a real-time presence. In other words, you don’t trade time for money. You build something up front that can continue to work for you over time. The one thing I learned though from all those childhood experiences though is that you never can depend on one source of income. Eventually my mom caught on and stopped giving me all those extra bags of chips and I had to figure out a new way to make money. No matter how safe something seems there’s always the chance that you could lose that income and be stuck with nothing.$6,000 test - The gross income from the presence of a nonresident in Connecticut does not exceed \$6,000 in the taxable year.  Important: An employee’s wages for services performed in Connecticut are taxable, regardless of amount, unless the employee’s services meet the Ancillary Activity Test. Also, reportable Connecticut Lottery winnings are taxable regardless of amount.
This equation implies two things. First buying one more unit of good x implies buying {\displaystyle {\frac {P_{x}}{P_{y}}}} less units of good y. So, {\displaystyle {\frac {P_{x}}{P_{y}}}} is the relative price of a unit of x as to the number of units given up in y. Second, if the price of x falls for a fixed {\displaystyle Y} , then its relative price falls. The usual hypothesis is that the quantity demanded of x would increase at the lower price, the law of demand. The generalization to more than two goods consists of modelling y as a composite good.

Because of safety concerns for the prospective applicant, as well as security and communication issues, the CIA Recruitment Center does not accept resumes, nor can we return phone calls, e-mails or other forms of communication, from US citizens living outside of the US. When you return permanently to the US (not on vacation or leave), please visit the CIA Careers page and apply online for the position of interest.

In addition to opening a brokerage account, you can also invest in peer-to-peer lending firms like Lending Club. I’ve been using Lending Club for a few years, and my net annualized return was 6.02% percent last year. Picking the right investments is easy since the platform offers automatic investing, but you can also pick your own notes if you're brave and want to learn the best ways to leverage the Lending Club platform.


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Allied (or co-interior) angles are supplementary. Same Side Interior Angle Theorem Example → Alternate Interior Angles Are Always Sometimes Or Never Congruent. Properties of Interior Angles . Posted on January 17, 2021 by admin. The sum of a pair of co-interior angles made by a transversal with parallel lines is always 180°. In this triangle ∠ x, ∠y and ∠z are all interior angles. ! The sum of a pair of co-interior angles is always equal to 180 degrees if the two lines are parallel to each other. Log in Sign up. Right angles are congruent. These angles are smaller than a straight angle and larger than a right angle. 5. right angle. This obtuse angle is defined if the angles are between 90 degree and 180 degree. Example 7. (vi) Co-interior or Conjoined or Allied Angles : Two pairs of co-interior or allied angles are marked as … Pics of : Alternate Interior Angles Are Always Congruent. Example 9. Please keep a pen and paper ready for rough work but keep your books away. Required fields are marked *. The two angles lie on the inside of a pair of parallel lines. Co interior angles formed by two parallel lines cut by a transversal are. The third line that intersects the two lines is called the transversal. Allied (or co-interior) angles are supplementary. Skip to content. Thank you for watching my blog friend Related Posts ' 11 NOV Volume and Surface Area of a Cylinder Formulas – Right Circular Cylinder. reid208218. Your email address will not be published. Let us now talk about the exterior and interior angles of the triangle. Example 9. revolution. 0.0 0 votes 0 votes Rate! e 5 f g 5 h The lines make an F shape. Co-interior angles are the pair of non-adjacent interior angles … Sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°. The Interior Angles of a Triangle add up to 180° Let's try a triangle: 90° + 60° + 30° = 180° It works for this triangle. The angles which are formed inside the two parallel lines,when intersected by a transversal, are equal to its alternate pairs. On parallel lines, co-interior (or C) angles add up to 180°. right angle. Co-interior angles always lie on the same side of the transversal, never on opposite sides. Note for example that the angles ∠ABD and ∠ACD are always equal no matter what you do. This is an important axiom in geometry. Sum of the measure of an angle and its vertically opposite angle is always. Post Author: sivaalluri. iii) Two angles on a straight line forms a linear pair. ∠s, are angles that share a common vertex and edge but do not share any interior points.In other words, they are angles that are side by side, or adjacent, sharing an "arm". Revolution. Obtuse Angle. Corresponding angles are always equal. asked Jul 16, 2019 in Class VI Maths by aditya23 ( -2,145 points) properties of angles and lines (including parallel lines) Consecutive interior angles are the two pairs of angles that: have distinct vertex points, lie on the same side of the transversal and; are both interior. These add up to 180 degrees (e and c are also interior). The above two angles are equal if two lines which cut by transversal are parallel. Angles 2 and 7 above, as well as angles 3 and 6 are examples of alternate interior angles. What Does George Soros' Open Society Foundations Network Fund? The following figures give the some examples of co … When two lines are crossed by another line (i.e. d and f are interior angles. Because the sum to be 180, they are “Supplementary Angles”. These angles are called alternate interior angles. revolution. A line segment has definite length. Any two angles that add up to 180 degrees are known as supplementary angles. Mrwadeturner T2 Corresponding And Alt Interior Proving Alternate Interior Angles Are Congruent The Same Hence when two lines are cut by a transversal if the alternate interior angles are equal in measure then the lines are always parallel. i,e. An introduction to alternate corresponding and co interior angles in parallel lines parallel lines are lines which are always the same distance apart and never meet. Right Angle. Arrowheads show lines are. Co-Interior Angles exist in a “C” shape and do NOT equal equal each other. They are supplementary (both angles add up to 180 degrees). Alternate, Co-Interior and Corresponding Angles Alternate interior angles Interior angles that lie inside the line and on opposite sides of the transversal. Co-interior angles 3. The rotation from A to D forms a straight line and measures 180 degrees. Facts about Angles 8: reflex angle. Co-interior Angles. x = Find the value of a. would always make the two lines parallel? Interior Angles. The History of the United States' Golden Presidential Dollars, How the COVID-19 Pandemic Has Changed Schools and Education in Lasting Ways. Alternate interior angles are always sometimes or never congruent. If two angles are right angles then they are congruent. Straight angle. 11. 3. Corresponding angles are always equal. Mrwadeturner t2 corresponding and alt alternate interior angles are congruent angles and parallel lines untitled doent. Angles that are not interior as well as alternate are never accurately described as alternate interior angles. Two lines are parallel if and only if the two angles of any pair of consecutive interior angles of any transversal are supplementary (sum to 180°). Question 11 of 20. The Consecutive Interior Angles Theorem states that if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary (= 180°) What is the Alternate Interior Angles Theorem? So if all pairs of consecutive angles in a quadrilatetal are supplementary. The Consecutive Interior Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. In a rectangle, diagonals are always equal. Using some of the above results, we can prove that the sum of the three angles inside any triangle always … The sum of the three interior angles in a triangle is always 180°. A co-interior angle is formed when two lines are intersected by a third line in two distinct points. SETS. Co-interior angles: Co-interior angles are both inside the parallel lines, and on the same side of the transversal. Home ; Sample Page; Menu; Post navigation ← Alternate Interior Angles Diagram. co-interior angles In each diagram the two marked angles are called co-interior angles and lie on the same side of the transversal. And ive labeled the measures of the interior angles. : ) Here Is The Answer: i) The sum of a pair of co-interior angles is always 180 o. ii) Alternate angles are always equal. If the lines AB and CD are parallel then $$\alpha + \beta = {180^ \circ }$$. Three lines are concurrent if and only if they have a common point. Two straight lines are cut by a transversal so that the co-interior angles are equal. These angles are congruent. X-planation Properties of the angles formed by … The relation between the co-interior angles is determined by the co-interior angle theorem. Alternate exterior angles are complementary. Here’s How Online Games Like Prodigy Are Revolutionizing Education. (097º) Notes by Ella Onyems and Revisely See more at revisely.co.uk The word obtuse means blunt. The formula is = (−) ×, where is the sum of the interior angles of the polygon, and equals the number of sides in the polygon.. Straight Angle. Download jpg. As you can see, the 'C' shape may appear back to front, but this doesn't affect the angle measurements. Corresponding angles 2. From the above diagram, we can say that the triangle has three interior angles. They are called co-interior angles or allied angles. If the lines are parallel the co-interior angles are supplementary (add up to 180 degrees). Every Learner Deserves Support Whilst Studying at Home . An Interior Angle is an angle inside a shape. If the two lines l and m are parallel, then the sum of two co-interior angles is always 180°. Vertically opposite angles are always equal. They are “inside together”. Right angle. Learn alternate interior angles with free interactive flashcards. Co-interior “C” angles always add up to 180°. Corresponding “F” angles are always equal. Everything you always wanted to know. In irregular polygons, like this one above, the sum of the interior angles would always be the same, but the value of an individual angles wouldn’t be since they are different sizes! Hope It Helps You!! This Co-Interior Angles Worksheet Worksheet is suitable for 6th - 9th Grade. Alternate “Z” angles are always equal. These names are used both when lines are parallel and when lines are not parallel. Choose from 500 different sets of alternate interior angles flashcards on Quizlet. co-interior angle. b. If the two lines l and m are parallel, then the sum of two co-interior angles is always 180°. In the case of non parallel lines alternate interior angles don t have any specific properties. Vertically opposite angles are always equal. Alternate interior angles are the angles formed on the inner side of two lines but on the opposite sides. On parallel lines co interior or c angles add up to 180. Co-interior angles are those angles that: have different vertices; lie between two lines; and are on the same side of the transversal; When a transversal intersects two parallel lines, the co-interior angles are always supplementary. Straight angle. i.e., a + b = 180° and c + d = 180°. Parallel Lines and Co-Interior Angles. However they always ADD up to equal 180 degrees. Vertically opposite angles are always equal. Try it and convince yourself this is true. Co interior angles formed by two parallel lines cut by a. The Consecutive Interior Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. Points Lines Planes And Angles Always Sometimes Or Never Free Art Ideas For Teens Teaching Teens High School, Always Sometimes Never Quadrilaterals Quadrilaterals Teaching Geometry Geometry Practice, Polynomials Always Sometimes Or Never Polynomials Polynomial Functions Classifying Polynomial, Special Angle Pairs Always Sometimes Or Never Angle Pairs Interior And Exterior Angles Critical Thinking, Special Angle Pairs Always Sometimes Or Never Angle Pairs Teaching Geometry Angle Pairs Activities, Points Lines Planes And Angles Always Sometimes Or Never Free Middle School Math Resources High School Math Classroom Math Instruction, Special Quadrilaterals Card Sort Math Geometry Teaching Math Math Interactive Notebook, Your email address will not be published. And then angle FAC is going to be congruent to angle ABD, because they're corresponding angles. Therefore, a complete rotation is 360 degrees. In this diagram the two angles are not equal, j is obtuse and k is acute. Toggle navigation. Alternate interior angles are supplementary. If the transversal cuts across parallel lines (the usual case) then the interior angles are supplementary (add to 180°). This is an important axiom in geometry. Angle Sum of a Triangle. Same-side interior angles are angles that are created when two parallel lines are cut by another line, called a transversal. If we colour the lines that make co-interior angles, we will see a "U " shape. In the above figure, the pairs of alternate interior angles are: 1 and 3 ; 2 and 4; Co-Interior Angles. y = Find the value of m. Vertcally Opposite. Revolution . Solution: Key Terms. It has the angle between 180 degree and 360 degree. x = Find the value of a. When two parallel lines are cut by a transversal the alternate interior angles are congruent. On MathsGee Skills QnA students, teachers and enthusiasts can ask and answer any interview questions. $$\angle$$a and$$\angle$$c are the pair of interior angles lying to the same side of the transversal. The interior angles on the same side of a transversal taken together form the co interior angles. Chapter 6 Lines and Angles- MCQ Online Test 2 Class 9 Maths 1. Zero Thrice the measure of the original angle Double the measure of the original angle Equal to the measure of the original angle. Alternate interior angles alternate interior angles properties. And we view AC and BD as the parallel lines and AB as a transversal. This pair of angles are called co-interior angles and they will always add up to 180°. Allied (or co-interior) angles are supplementary. And when corresponding angles are equal then by using vertically opposite angle property the alternate angles must be equal. straight angle. Alternate interior angles formed by two parallel lines cut by a transversals are. When the two lines are not parallel, the sum of the two co-interior angles would not be exactly 180 degrees. They are called interior angles. The lines make a Z shape. 2) Alternate interior angles are congruent. Here, in the figure; a and b are co-interior angles; and c and d are co-interior angles. An interior angle is an angle inside the shape. This helps us identify co-interior angles. Co-Exterior angles Therefore the sum of the interior angles is always 180° 2) Exterior Angles An exterior angle of the triangle is the angle between one side of a triangle and the extension of an adjacent side. (iv) Interior angles on the same side of the transversal ∠4 and ∠5 ∠3 and ∠6; Note: Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles. Right angle. Co-interior Angles – are angles on the same side of the transversal and inside the parallel lines. 2. 2. 1. They are called Co-interior angles. a = Find the value of y. straight angle. Co-interior Angles. Some of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180. Example 7. Proof : co- interior angles are on a straight line and add up to 180 degrees In the above triangle, ∠ a ∠b ∠c are interior angles while ∠ d is an exterior angle. Learn vocabulary terms and more with flashcards games and other study tools. My self Sivaramakrishna Alluri. Co-interior angles are between the lines and on the same side of the transversal. Save my name, email, and website in this browser for the next time I comment. So these are alternate interior angles. 1) Vertical angles are congruent. Use theorems about lines and angles to solve problemstheorems include. If a transversal intersects two parallel lines, each pair of co-interior angles are supplementary (their sum is 180$$^\circ$$) Conversely, if a transversal intersects two lines such that a pair of co-interior angles are supplementary, then the two lines are parallel. If two angles are alternate interior angles then they are on opposite sides of the transversal. They make a C or U shape. a = Find the value of y. straight angle. No negative marking for incorrect choice. Whats people lookup in this blog: Alternate Interior Angles Are Always … 3. right angle. transversal), then the pair of angles on one the same side of the transversal but outside the two lines are called co-exterior angles. That's a very complicated way of saying this orange angle and this magenta angle right here. Search. 0 ; if a transversal intersects two parallel lines then angles formed on the same side of it will be =to 180 these are co interior angles. Means of co interior angle 2 See answers Answers nisha414 Expert; When two lines are cut by a third line (transversal) co-interior angles are between the pair of lines on the same side of the transversal. Asked by sweet pea on september 24 2015. Corresponding angles formed by two parallel lines cut by a transversal are. 1. Each of those angles has a congruent alternate interior angle at the next vertex that is adjacent and supplementary to the other angle of the quadrilateral. Rate! 4) Same-side interior angles are complementary. 3) Corresponding angles are supplementary. In general, interior alternate angles are simply called as alternate angles only. Step 4 - Putting it into Practice. Use the information given in the diagram to find: a. x b. y c. z d. u e. p. Solution: Key Terms. Co-Interior Angles. Vertical corresponding alternate interior. Opposite angles are congruent As you drag any vertex in the parallelogram above, note that the opposite angles are congruent (equal in measure). 12. Revolution. Relation Between the Angles when Line m is Parallel to Line n The measure of fourth angle is (a) 140c (b) 150c (c) 105c (d) 120c Ans : (b) 150c Sum of all angles of a quadrilateral =360c Fourth angle =360 210cc- =150c 3. Mrwadeturner t2 corresponding and alt alternate interior angles are congruent angles and parallel lines untitled doent. There will be total 20 MCQ in this test. Fact Check: Is the COVID-19 Vaccine Safe. 1) Interior Angles. alternate interior angles. In the above-given figure, you can see, two parallel lines are intersected by a transversal. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. The measure of this angle is x. Solution: Key Terms. To explore the truth of this rule, try Math Warehouse's interactive triangle, which allows you to drag around the different sides of a triangle and explore the relationship between the angles and sides.No matter how you position the three sides of the triangle, the total degrees of all interior angles (the three angles inside the triangle) is always 180°. alternate angle. It follows that a 180-degree rotation is a half-circle. Click hereto get an answer to your question  Prove that the base angles of an isosceles trapezium are equal Corresponding angles are always equal. Categories: / No Responses / by sivaalluri March 24, 2019. co-interior angle. A family business built on years of expert craft. See Interior angles of a polygon. These are alternate interior angles, and we've already proved if this is x then that is x. (iii) the sum of the interior angles on the same side of the transversal is 180°, then the two straight lines are parallel to each other. The interior angles of a triangle are the angles inside the triangle. A pair of congruent angles is right angles. Adjacent angles, often abbreviated as adj. Well, the interior angles are kind of the angles that are closer to each other in the two parallel lines, but they're on opposite side of the transversal. Lines and on the diagram to find: a. x b. y c. d.! Step 3: 1 and 3 ; 2 and 7 above, as you move points a or b the. T have … they are known as corresponding angles are smaller than a angle... Browser for the next time I comment angles are always equal no matter you. Angles don ’ t co interior angles are always any specific properties all pairs of alternate interior angles. the between... R10 000 to be won by first 5 Gold Status High Learners ; co-interior angles are than! ' Open Society Foundations Network Fund c ” angles always add to 180° called angles! Of consecutive angles in turn the parallel lines plane always intersect at a point and are! = find the value 180 comes from How many degrees are in a triangle corresponding! People lookup in this blog: alternate interior angles of the transversal which are inside the parallel is. 2 and 7 above, as you can see, the sum of a transversal, equal... The measure of the formula, − is a half-circle QnA students, teachers and enthusiasts can ask answer! That Quiz — where a math practice test is always equal to 180 degrees ) are examples of angles! Set up the formula, − is a way to determine How many triangles the polygon can be divided.. Using vertically opposite angle is formed when two lines are parallel the co-interior angle Theorem: co-interior angles is equal! By 10°: 80° + 70° + 30° = 180° and c are also interior.! Colour the lines and Angles- MCQ Online test 2 Class 9 Maths 1 formed. Talk about the exterior and interior angles. » co-interior angles are always equal to the side... And do not equal equal each other your books away = vertically opposite angle defined! Solve problemstheorems include transversal are in the case of non – parallel lines cut by a.... Angles each measuring 70c in measure then the alterate interior angles in a plane always intersect at a point does... Are always … corresponding angles are always parallel the value 180 comes from How many degrees in. Of y. straight angle note for Example that the angles formed by two parallel,... Of an angle inside a shape by 10°: 80° + 70° + 30° = 180° it works. Foundations Network Fund angles ”, never on opposite sides of the transversal then the lines AB and are... Never on opposite sides \angle\ ) c are also interior ) 're corresponding angles. and. And then angle FAC is going to be 180, they are congruent be won by first 5 Gold High..., teachers and enthusiasts can ask and answer any interview questions always wanted to know a little bit they a... But on the same side interior angle is formed when two parallel lines is always equal no matter type. Saying this orange angle and its vertically opposite angle is always co interior angles are always this ∠. Congruent angles and lie on the same side of the triangle has three interior angles are the inside. Are inside the triangle sub topics mentioned above is if they have a common point always... Diagram below, which statement is true 3 and 6 are examples of co-interior is! Like Prodigy are Revolutionizing Education only if they are congruent acute angles each measuring 70c are formed the... 3 ; 2 and 4 ; co-interior angles: co-interior angles are between 90 degree and degree! Is true 90 degree and 360 degree colour the lines are not parallel + +! The rotation from a to d forms a straight angle and its opposite., alternate interior angles lying to the measure of an angle and this magenta angle right here measures degrees... Of angles are both inside the parallel lines be less than 180° Volume and Surface Area of pair! ∠C Everything you always wanted to know made by a transversal then the angles. Because not all congruent angles and lie on the same side interior angle is always co interior angles are always it... A linear pair blog friend Related Posts ' 11 NOV Volume and Surface Area of a of... Angles – are angles that are created when two straight lines are always corresponding. B. v c. w d. x e. y a pair of parallel lines cut by a third line intersects! Hence when two parallel lines are crossed by another line ( i.e click on 'Other angle pair ' visit... As angles 3 and 6 are examples of co-interior angles made by a transversal be divided into complicated! Angles on a straight line and measures 180 degrees formed inside the parallel lines are crossed a! This test ∠ x, ∠y and ∠z are all interior angles shown always add up to degrees... Transversal the alternate angles must be less than 180° any two angles a! Four angles that are not parallel, then the alterate interior angles. given,... And enthusiasts can ask and answer any interview questions lines that make co-interior angles!... View AC and BD as the parallel lines is always equal two straight lines are parallel, then angles. » Mathematics » co-interior angles made by a transversal are side interior is. Angle between 180 degree and 180 degree and 360 degree angles ; and c + d =.. Another line ( i.e same size Solution: Key Terms 9 Maths 1 angles on the inside the! The formula for finding the sum of the transversal are “ supplementary angles ” of angle! Cd are parallel then \ ( \angle\ ) a and\ ( \angle\ ) a (! A = find the angle measurement of interior angles. blog friend Related Posts ' 11 NOV Volume Surface. Vertically opposite angle property the alternate interior angles in a quadrilatetal are supplementary AB as a transversal are,... As … co-interior angles are always … corresponding angles. 3: 1 and 3 ; 2 and above! What you do when the two marked angles are always equal lines make... Of || lines, when intersected by a transversal an angle inside the two lines are by... Formed inside the parallel lines cut by a transversals are below, which statement is?. These are alternate interior angles formed by two parallel lines, co-interior ( or c ) add. However they always add up to 180 lines untitled doent 2 and 4 ; angles. Ac and BD as the parallel lines are called co-interior angles are equal to its alternate.! Alternate angles are right angles then they are known as supplementary angles ” lines they. We 've already proved if this is x then that is x ) a and\ ( )! D forms a linear pair called the transversal and inside the two marked are! Cut by a transversal taken together form the co interior angles are not equal each. Skills QnA students, teachers and enthusiasts can ask and answer any interview questions the co-interior angles is always.! Rough work but keep your books away so in the above-given figure the! Are co-interior angles is always 180° George Soros ' Open Society Foundations Network Fund the line and on same! Common point = ∠c Everything you always wanted to know are marked …... Created with that Quiz — where a math practice test is always k is acute, because 're! ; a and b are co-interior angles is always equal if the two lines cut! Identify corresponding alternate and co interior angles. and then angle FAC is going to be to! Are inside the two angles are always equal to the same size, then the alternate angles... } \ ) make co-interior angles. built on years of expert craft Circular Cylinder are equal if angles. You always wanted to know are parallel ∠c are interior angles formed on sub! D = 180° following figures give the some examples of co-interior angles always lie on the same side the!


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# BLX – Magellan BLX Topo File Format¶

Driver short name

BLX

BLX is the format for storing topographic data in Magellan GPS units. This driver supports both reading and writing. In addition the 4 overview levels inherent in the BLX format can be used with the driver.

The BLX format is tile based, for the moment the tile size is fixed to 128x128 size. Furthermore the dimensions must be a multiple of the tile size.

The data type is fixed to Int16 and the value for undefined values is fixed to -32768. In the BLX format undefined values are only really supported on tile level. For undefined pixels in non-empty tiles see the FILLUNDEF/FILLUNDEFVAL options.

## Driver capabilities¶

Supports CreateCopy()

This driver supports the GDALDriver::CreateCopy() operation

Supports Georeferencing

This driver supports georeferencing

Supports VirtualIO

This driver supports virtual I/O operations (/vsimem/, etc.)

## Georeferencing¶

The BLX projection is fixed to WGS84 and georeferencing from BLX is supported in the form of one tiepoint and pixelsize.

## Creation Issues¶

Creation Options:

• ZSCALE=1: Set the desired quantization increment for write access. A higher value will result in better compression and lower vertical resolution.

• BIGENDIAN=YES: If BIGENDIAN is defined, the output file will be in XLB format (big endian blx).

• FILLUNDEF=YES: If FILLUNDEF is yes the value of FILLUNDEFVAL will be used instead of -32768 for non-empty tiles. This is needed since the BLX format only support undefined values for full tiles, not individual pixels.

• FILLUNDEFVAL=0: See FILLUNDEF


text:
Calculating eigenfrequencies, loss-rates, anharmonicities, and Kerr parameters¶

Qcircuit.f_k_A_chi(pretty_print=False, **kwargs)[source]

Returns the eigenfrequency, loss-rates, anharmonicity, and Kerr parameters of the circuit.

Returns these quantities in the form [[f_0,f_1,..],[k_0,k_1,..],[A_0,A_1,..],[[A_0,chi_01,..],[chi_10,A_1,..]..]]

Each quantity is returned as a numpy arrays, where each index corresponds to a normal mode, ordered with increasing normal mode frequency. All quantities are provided in units of Hertz, not in angular frequency.

This method is equivalent to calling

[_.eigenfrequencies(**kwargs),_.loss_rates(**kwargs), _.anharmonicities(**kwargs),_.kerr(**kwargs)]

For more details, refer to the functions

qucat.Qcircuit.eigenfrequencies()

qucat.Qcircuit.loss_rates()

qucat.Qcircuit.anharmonicities()

qucat.Qcircuit.kerr()

Parameters
• pretty_print (Boolean, optional) – If set to True, this method will print a summary of the system parameters as a table.

• kwargs – Values for un-specified circuit components, ex: L=1e-9.

Returns

[[f_0,f_1,..],[k_0,k_1,..],[A_0,A_1,..],[[A_0,chi_01,..],[chi_10,A_1,..]..]]

Return type

List of numpy arrays


text:
# Codeforces Round #378 Div. 2 review

Link Codeforces Round #378 Div. 2 (Contest 733) A. Grasshopper And the String Link: Problem Category: Implementation Even this is a first problem, I get wrong answer for first time submission. It is necessary to consider a corner case at the “end of the text”. Some other solution is inserting extra ‘A’ at the end of text so that you can handle it in the same way. (ex. latte0119’s solution)

B. Parade Link: Problem Category: math Below implementation is a little bit optimized solution for not to use memory of $$O(N)$$, but use $$O(1)$$. But in the contest, it is better to consider solve it as fast as possible rather […]

# Codeforces Round #377 Div. 2 review

Link Codeforces Round #377 Div. 2 (Contest 732) A. Buy a Shovel Problem It can be paid without change if the change is 0 or $$r$$.

B. Cormen — The Best Friend Of a Man Problem At day $$i$$, dog need to walk $$k-a[i-1]$$ times.

C. Sanatorium Problem Basic idea to the solution is not difficult, just check all the popssibility of what time start eating (enter room) and what time end eating (exit room). But the corner case handling makes this problem difficult and I cannot answer correctly in one time. Rather than below, more elegant/ short code solution can be found at pekempey’s solution.

D. Exams […]

# Codeforces Round #374 Div. 2 review

Link Codeforces Round #374 Div. 2 (Contest 721) Editorial A. One-dimensional Japanese Crossword Problem Just count consecutive ‘B’ in the sequence.

B. Passwords Problem This is also easy, just count the number for each string length. You even don’t need to process any string manipulation.

C. Journey Problem I felt it is difficult than problem D. During the contest, I tried to solve it by DFS but I got TLE.

To get answer, we can use DP (dynamic programming) to reduce computational complexity as $$O(mn)$$.

D. Maxim and Array Problem Basic strategy to get minimum product is as follows, 1. If the product is positive, […]

# Codeforces Round #373 Div. 2 review

Link Codeforces Round #373 Div. 2 (Contest 719) A. Vitya in the Countryside Problem Basically, check last 2 character to determine its direction is “UP” or “DOWN”. Special case comes when the last number is 0 or 15, in that case the direction changes and you can determine the direction without looking second last character.

B. Anatoly and Cockroaches Problem We can consider 2 patterns for final alignment. Pattern 0 is to align “rbrbrb…” and pattern 1 is to align “brbrbr…”. We will compare the original alignment and final alignment. For each position i, we need to change the color to… Case A: r to b Case B: b to r If […]


text:
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Chapter 11.4, Problem 21E
BuyFindarrow_forward

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Capital investment and production Suppose that for a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested, with x =   30 y   +   20 y 2 . At what rate will production increase if $10,000 is invested and if the investment capital is increasing at a rate of$1000 per month?

To determine

To calculate: The rate of change of production if $10,000 is invested and the investment capital is increasing at a rate of$1000 per month if x=30y+20y2.

Explanation

Given Information:

For a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested with,

x=30y+20y2

The amount invested is $10,000 and investment capital is increasing at the rate of$1000 per month.

Formula used:

The derivative formula,

ddxxn=nxn1

Calculation:

As it is provided that for a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested with,

x=30y+20y2

Now, the rate at which the production is changing will be obtained by differentiating the above equation with respect to t as,

dxdt=30dydt+

### Still sussing out bartleby?

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#### Evaluate the expression sin Exercises 116. 230

Finite Mathematics and Applied Calculus (MindTap Course List)

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text:
# simple exercise of euclidean geometry

I've to solve this simple exercise but i can't see how.
Problem: let $AB$ and $CD$ two equivalent ropes of one circle of centre $O$. Let $P$ and $Q$ two points that belong on the extentions of the previous ropes such that $BP$ and $DQ$ are equivalent. So show that the centre $O$ belong on the axis of the segment $PQ$ .

• What is a "rope of a circle"? Can you provide a drawing? Even a snapshot of a hand drawing, with the points labelled, would suffice. – Brian Tung Aug 19 '15 at 18:33
• @Brian Tung in the figure you can see the rope of a circle. I don't know the right english term – dario Aug 19 '15 at 18:41
• Ahh, OK, they're called "chords." – Brian Tung Aug 19 '15 at 18:42
• By "axis," do you mean "perpendicular bisector"? That is, the line that is perpendicular to $\overline{PQ}$ and intersects it at its midpoint? – Brian Tung Aug 19 '15 at 18:46
• yes that's right – dario Aug 19 '15 at 20:57

First, show that $OP = OQ$; that is, both $P$ and $Q$ lie on a circle with center $O$:

• $OB = OD$ (both on the same circle)
• $BP = DQ$ (given)
• $\triangle OAB \cong \triangle OCD$ (side-side-side, see below)

• $OA = OC$ (both on the same circle)
• $OB = OD$ (both on the same circle)
• $AB = CD$ (given)
• $m\angle OBA = m\angle ODC$ (corresponding angles of congruent triangles)

• $m\angle OBP = m\angle ODQ$ (supplementary angles of equal angles)
• $\triangle OBP = \triangle ODQ$ (side-angle-side)
• $OP = OQ$ (corresponding sides of congruent triangles)

Now consider triangle $OPQ$. Let $R$ be the midpoint of $PQ$. Then

• $PR = QR$ (midpoint)
• $OP = OQ$ (proved above)
• $\triangle OPQ$ is isosceles
• $m\angle OPQ = m\angle OQP$ (base angles of isosceles triangle)
• $\triangle OPR \cong \triangle OQR$ (side-angle-side)
• $m\angle ORP = m\angle ORQ$ (corresponding angles of congruent triangles)
• $m\angle ORP = m\angle ORQ = 90$ (congruent supplementary angles)

Therefore $\overline{OR}$ is the perpendicular bisector of $\overline{PQ}$.


text:
How can I get the power of a specific frequency band after FFT?

I need help with my matlab code. I have recorded EEG data and now I want to analyse it in matlab. I want to find the mean power of specific frequency ranges (theta: 4-8 Hz,alpha: 8-12Hz etc.). For that I performed a fft. Next I used the interp1 function to find the amplitudes at specific frequency ranges. But I am not sure if I have done it correctly...It would be great if someone can look at the code.

%p2 is the data in the time domain
% Variables

fftlength = 1024;                                % Set FFT length
stepsize = 32;                                   % Set step size
samples = fftlength:stepsize:length(p2);    % create an index array
c = 1:fftlength;

%Specify hanning window

hanning = [1:fftlength]';
hanning_in = 2* pi() * (hanning - (fftlength+1)/2)/(fftlength+1);

%rescaled x-axis to match sample length?

hanning1 = (sin(hanning_in)./hanning_in).^2;

f=[128/fftlength:128/fftlength:128];   % frequency index for the spectral
array

bp_p2=cell(1,1);

channel=1;

for kk = 1:length(samples)

k = samples(kk);

spectrum = fft(p2(k-fftlength+1:k,:) .* hanning1)/fftlength; % apply window
to filtered data

spectrum2 =(sqrt(spectrum .* conj(spectrum)));  % get magnitude uV

% theta (4-8),alpha (8-12),beta low(12-16), beta high(16-25)

theta=mean(interp1(f,spectrum2(:,channel),[4:f:8]));
alpha=mean(interp1(f,spectrum2(:,channel),[8:f:12]));
betalow=mean(interp1(f,spectrum2(:,channel),[12:f:16]));
betahigh=mean(interp1(f,spectrum2(:,channel),[16:f:25]));

%creating an array
%store all iteration loop outputs in a matrix

m(kk,:)=[theta alpha betalow betahigh];

end

To get the total power across bins, sum the power in each bin. Also you need to compensate for your window loss if you want an accurate result.

For a rectangular window, the power in each DFT bin is given as:

$$P = \frac{Y[k]Y[k]^*}{N^2} = \bigg(\frac{|Y[k]|}{N}\bigg)^2$$

and $$P_{dB} = 20Log_{10}\bigg(\frac{|Y[k]|}{N}\bigg)$$

The total power over a range of such bins would be:

$$P_{k} = \frac{\Sigma_k(|Y[k]|^2)}{N^2}$$

Windowing Loss

When we apply a window, the coherent gain and non-coherent gain are affected differently. If the N samples are coherent (such as a frequency completely contained in a bin), the output grows at rate N (direct summation). If the N samples are non-coherent (spread across bins), the output grows at the rate of $$\sqrt{N}$$ (rms summation).

If we are only concerned with the signal power in each bin, we would use the coherent gain which is given as

$$G_c = \frac{\Sigma w[n]}{N}$$

where $$w[n]$$ are the window coefficients. (For example the Blackman(30) window has a coherent gain of 0.406 or -7.83 dB):

Likewise non-coherent samples grow at $$\sqrt{N}$$. The non-coherent gain refers to the change in DFT output level of the non-coherent samples (such as white noise) due to the window function.

The normalized non-coherent gain is the rms value of the window weights given as:

$$G_{nc} = \sqrt{\frac{\Sigma w[n]^2}{N}}$$

The SNR change or processing gain of the window would be the ratio of the two, in dB this would be:

$$PG = 20log_{10}\bigg( \frac{G_c}{G_{nc}} \bigg)$$

If you are only interested in the signal power level and not signal to noise ratio, so you would simply compensate for the power computed by using $$G_c$$.

It may confusing to some how the power for a single tone can be effected differently by the window than the power in a signal that is spread evenly across multiple tones as described above. An intuitive explanation of this is that windowing the time domain function results in each bin in the FFT having an equivalent noise bandwidth (ENBW) that exceeds one bin. A rectangular window in comparison has an ENBW of exactly one bin, so when we sum the power of all the bins in the frequency domain, Parseval's theorem proves correct in that the total power from that summation is equal to the total power in the time domain signal. However if we window in time with something other than a rectangular window, the effect of the wider ENBW means that each bin in frequency is now reporting the power for that bin PLUS adjacent bins. So in this case when we sum the reported power over all bins, the total summation will over-estimate the actual noise power. In a case of a single tone, or tones that are spaced wider than the ENBW, each bin will accurately report the power for each tone when we have scaled the result by the recripocal of $$\sum W_n$$ where $$W$$ is the windowing funciton. (for the rectangular window this scaling results to $$1/N$$).


text:
# Limit with arctan: $\lim_{x\rightarrow 0} \frac{x\sin 3x}{\arctan x^2}$

$$\lim_{x\rightarrow 0} \frac{x\sin 3x}{\arctan x^2}$$

NB! I haven't learnt about L'Hôpital's rule yet, so I'm still solving limits using common limits.

### What I've done so far

$$\lim_{x\rightarrow0}\left[\frac{x}{\arctan x^2}\cdot 3x\cdot \frac{\sin 3x}{3x}\right] = 0\cdot1\cdot\lim_{x\rightarrow0}\left[\frac{x}{\arctan x^2}\right] = 0??$$ Obviously I'm wrong, but I thought I'd show what I tried.

• Do you have this inequality: $\sin x \leq x \leq \tan x$ for $x \geq 0$? And the limits that follow from it: $\sin x / x \rightarrow 0$, etc.? – Simon S Nov 3 '14 at 23:46

You should put in $$\frac{x^2}{\arctan x^2}$$ that has limit $1$: $$\lim_{x\to0}\frac{x\sin3x}{\arctan x^2}= \lim_{x\to0}3\frac{\sin3x}{3x}\frac{x^2}{\arctan x^2}=\dots$$ If you don't know the limit above, just substitute $t=\arctan x^2$, so $x^2=\tan t$ and the limit is $$\lim_{x\to0}\frac{x^2}{\arctan x^2}=\lim_{t\to0}\frac{\tan t}{t}$$ that you should be able to manage.

Starting as you did, we want to find the limit of $$\frac{3x^2}{\arctan(x^2)}\cdot\frac{\sin(3x)}{3x}.$$ Only the first term gives any trouble. Let $x$ be not too large, and let $x^2=\tan w$, You want to find $$\lim_{w\to 0} \frac{3\tan w}{w},$$ which is not difficult. Replace $\tan w$ by $\frac{\sin w}{cos w}$.

Since $u \sim \tan u$, then $y \sim \arctan y$, so $x^2 \sim \arctan (x^2)$.

This means that $$\lim_{x \to 0} \frac{x \sin 3x}{\arctan x^2} = \lim_{x \to 0} \frac{x3x}{x^2} = 3$$

• This feels unsatisfactory, as you are still using the derivatives of the functions in the numerator and denominator. – Simon S Nov 3 '14 at 23:42

Using the Asymptotic expansion:
$\sin(x)\approx_0 x$
$\arctan(x^2) \approx_0 x^2$
So $$\lim _{x\rightarrow \:0}\:\frac{x\sin \:3x}{\arctan \:x^2}=\lim \:_{x\rightarrow 0}\:\frac{3x^2}{x^2}=\color{red}{3}$$


text:
## Ending a sentence in ぞと

1

One of the people I follow on twitter sometimes ends his sentences in ぞと. Is this just a more polite form of ぞ？

Here's an example:

ブログUPしましたぞと♪(´ε｀ )

1Can you give an example or two? – Louis – 2011-07-30T16:05:48.257

6

This ぞと should be broken down into two particles:

• ...ぞ: reinforces and reminds one's decision or will to oneself
• ex. さあ、やるぞ。Here I go.
• ...と: light declaration
• ex. いつか行こうっと。I'll visit there one day.

So your example roughly means, "There, I've posted a new blog article." And no, it doesn't add any politeness to the sentence.

The same と is discussed in this board (Japanese), which cites 明鏡国語辞典 {めいきょうこくごじてん} (Meikyo Japanese Dictionary):

（「・・・っと」の形で）軽く言い放つのに使う。 (In the form of ...っと) used to declare something lightly.

The preceding sentence is usually in volitional form, like  もう寝ようっと. Or, as in the case of ...ぞ, expresses volition in some other way.

Note: depending on the context, there are cases that ぞと should be parsed as 「...ぞ」と, as explained in istrasci's answer.

2

I would split the example sentence into two parts:

ブログUPしましたぞ / と

Unfortunately, I cannot explain how the と affects the other part well, but as far as I can say as a Japanese, the と is a kind of like an interjection and its effect is vanishingly small, at least not making the sentence more polite.

FYI, Reno, a Final Fantasy 7 character, often ends his words with 〜ぞ、と。 or 〜だぞ、と。 the same way as the example. The person may perhaps just imitate this habit.

2

The only thing I can think of (without any context provided) is that this would be used when quoting what someone else said. Like:

みんなでどうしたらいいかについて彼は意見を言った。心斎橋へ行くぞと　【He gave his opinion about what we should all do together. "Let's all go to Shinsaibashi!"】　→　The fact that he said something was previously known. Now it's being made known what he said.

1I'm annoyed that I often answer questions with no examples, and then the poster edits the OP with examples, and then my answer is no longer (or only slightly) relevant. – istrasci – 2011-08-01T14:21:44.403


text:
# Bevel tool not working properly

I'm new to blender and i'm having a problem, the bevel tool is not behaving like i want when i press ctrl+b

• Are you mixing trianlges and quads? – susu Jan 29 at 19:05
• Nope, only quads – Sandy Jan 29 at 19:06
• Try applying scale, then bevel. To apply scale: ctrl + a. Then choose scale. – SaladHead Jan 30 at 3:48
• hard to see what's happening, maybe share the part of the mesh where you try to bevel: pasteall.org/blend – moonboots Jan 30 at 5:44


text:
# System of differential equation with alternative variables

Let us suppose a system of linear differential equations

\begin{align} \frac{d}{d t}x_1(t)&= -\lambda x_2 (t) \\ \frac{d}{d t}x_2(t)&= \lambda x_1 (t) \end{align}

How this system could be solve analytically ? Because they refer to each other.

-

This can be solved very much like you solve a system of algebraic linear equations with two variables. In such a system, you would multiply the equations with appropriate numbers so that one variable has the same coefficient in both equations, and then subtract the two equations to eliminate that variable. Here, multiplication by a constant alone would not work. Let's rewrite the system as:

$\dfrac{d}{dt}x_1(t) + \lambda x_2(t) = 0\\ \lambda x_1(t) - \dfrac{d}{dt}x_2(t) = 0$

Even if we multiply the first equation by $\lambda$, the "coefficients" of $x_1$ will not be same in the two equations. This is because in the first, $x_1$ is differentiated once. So let us do the same in the second as well:

$\lambda \dfrac{d}{dt}x_1(t) + \lambda^2 x_2(t) = 0\\ \lambda \dfrac{d}{dt}x_1(t) - \dfrac{d^2}{dt^2}x_2(t) = 0$

Now, if we subtract the second equation from the first:

$\dfrac{d^2}{dt^2}x_2(t) + \lambda^2 x_2(t) = 0$

This is a second-order homogeneous linear differential equation, and the solution is $x_2(t) = c_1\cos(\lambda t) + c_2\sin(\lambda t)$. Now from the second equation,

\begin{align*} \lambda x_1(t) & = \dfrac{d}{dt}x_2(t)\\ & = \dfrac{d}{dt}[c_1\cos(\lambda t) + c_2\sin(\lambda t)]\\ & = c_2\lambda\sin(\lambda t) - c_1\lambda\cos(\lambda t) \Rightarrow \end{align*}\\ x_1(t) = c_2\sin(\lambda t) - c_1\cos(\lambda t)\\

Note that it is important not to do another elimination from the original equations to obtain another second-order equation with $x_1(t)$ and solve that, as this would give a solution with two new constants. The two solutions $x_1(t)$ and $x_2(t)$ with four different constants would not satisfy the original system. Similarly, after finding $x_2(t)$, one should not substitute it in the first equation to find $x_1(t)$. The first equation involves a derivative of $x_1(t)$, thus again giving rise to a (first-order) differential equation whose solution will contain a new constant, leading to the same problem as before.

-
To make the notation less cumbersome, I would suggest that you write $\dfrac{d}{dt}$ as the operator $D$, as there is no other differentiation involved. $\dfrac{d^2}{dt^2}$ would then be $D^2$, etc. The original system can then be written as $Dx_1 + \lambda x_2 = 0\\ \lambda x_1 - Dx_2 = 0\\$. Now differentiation indeed becomes similar to "multiplying" by $D$ (but always remember that you are actually differentiating). – M. Vinay May 30 '14 at 2:35

This equation is $$\frac{d}{dt}\left[\begin{array}{cc}x_{1} \\ x_{2}\end{array}\right] = \lambda\left[\begin{array}{cc}0 & -1 \\ 1 & 0 \end{array}\right] \left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right]$$ The $2\times 2$ coefficient matrix $A$ is an orthogonal matrix, so that $A^{T}=-A$ is the inverse of $A$. Thus $A^{2}=-I$. The powers of $A$ are $$A^{0}=I, A^{1}=A, A^{2}= -I, A^{3}=-A, A^{4}=I, A^{5}=A, \cdots.$$ Therefore, $$e^{tA} = I+tA-\frac{t^{2}}{2!}I-\frac{t^{3}}{3!}A+\frac{t^{4}}{4!}I+\frac{t^{5}}{5!}A+\cdots = \cos(t)I+\sin(t)A.$$ The solution of the equation is $$\frac{d}{dt}\left(e^{-\lambda t A}\left[\begin{array}{c}x_{1}\\x_{2}\end{array}\right]\right)=\left[\begin{array}{c}0 \\ 0\end{array}\right],\\ \left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right]= e^{\lambda t A}\left[\begin{array}{c}x_{1}(0)\\x_{2}(0)\end{array}\right] = \left[\begin{array}{c}x_{1}(0)\cos(\lambda t)\\x_{2}(0)\cos(\lambda t)\end{array}\right] +\left[\begin{array}{c}-x_{2}(0)\sin(\lambda t)\\x_{1}(0)\sin(\lambda t)\end{array}\right].$$ That is, $$x_{1}(t) = x_{1}(0)\cos(\lambda t)-x_{2}(0)\sin(\lambda t),\\ x_{2}(t) = x_{2}(0)\cos(\lambda t)+x_{1}(0)\sin(\lambda t).$$ Check that $x_{1}'(t) = -\lambda x_{2}(t)$ and $x_{2}'(t)= \lambda x_{1}(t)$. The constants $x_{1}(0)$ and $x_{2}(0)$ are arbitrary.

-


text:
# 3 variable system of equations activity

Therefore, the solution to the system of equations is $(1,2,1)$. These exercises will help to check how you are able to solve linear equations with 3 variables. Then, take over duties and write a random algebraic equation in each of the 81 spaces. Get the free "3 Equation System Solver" widget for your website, blog, Wordpress, Blogger, or iGoogle. Take the quiz. \left\{\begin{matrix} \begin {align} 2x + y - 3z &= 0 \\ 4x + 2y - 6z &= 0 \\ x - y + z &= 0 \end {align} \end{matrix} \right.. 3x3 System of equations solver. This set is often referred to as a system of equations. System of Three Equations. Solving a dependent system by elimination results in an expression that is always true, such as $0 = 0$. So x plus 2x is 3x. For example, consider this system of equations: Since the coefficient of z is already 1 in the first equation, solve for z to get: Substitute this expression for z into the other two equations: $\left\{\begin{matrix} -2x+2y+(3x+2y-6)=3\\ x+y+(3x+2y-6)=4\\ \end{matrix}\right. The substitution method involves solving for one of the variables in one of the equations, and plugging that into the rest of the equations to reduce the system. Recall that a solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. And if we want to eliminate the y's, we can just add these two equations. Gimme a Hint . Steps to Solve Systems of Equations by Addition or Elimination 1. These unique features make Virtual Nerd a viable alternative to private tutoring. Students need to learn and practice three main techniques for solving systems of linear equations: graphing, addition ... graphing, addition and substitution. Systems of Three Variables Example: Solve this system x + y - 3z = -10 x - y + 2z = 3 2x + y - z = -6 Example 4. Attention!!! Dependent systems have an infinite number of solutions. Welcome to the movement. 4. Using the elimination method for solving a system of equation in three variables, notice that we can add the first and second equations to cancel [latex]x$: \begin {align}(x - 3y + z) + (-x + 2y - 5z) &= 4+3 \\ (x - x) + (-3y + 2y) + (z-5z) &= 7 \\ -y - 4z &= 7 \end {align}. Example 3. Systems of equations in three variables are either independent, dependent, or inconsistent; each case can be established algebraically and represented graphically. System Of Equations 3 Variables - Displaying top 8 worksheets found for this concept.. System of Equations in Three Variables 5. Exercise. 3.4 Solving Systems of Linear Equations in Three Variables A system of linear equations is any system whose equations only contain constant or linear terms. And that is going to be equal to 3 plus negative 6 is negative 3. Graphically, a system with no solution is represented by three planes with no point in common. In a system of equations in three variables, you can have one or more equations, each of which may contain one or more of the three variables, usually x, y, and z. 2x ∙ 3y ∙ 2z ∙ ∙1 x ∙ 5y ∙ 9 4z ∙ 5x ∙ 4 1 4 6 10 Step 1 Choose equation ˚. (b) Two of the planes are parallel and intersect with the third plane, but not with each other. 5. Examples, videos, worksheets, solutions, and activities to help Algebra students learn how to solve systems of equations involving three variables. So the new system of equations, in just two variables, is. Or two of the equations could be the same and intersect the third on a line (see the example problem for a graphical representation). If you do not follow these steps…you will NOT receive full credit. Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1 2x - y + z = 3 5x + 2y - 3z = 1 2x + y - z = 2 Mission. (adsbygoogle = window.adsbygoogle || []).push({}); A system of equations in three variables involves two or more equations, each of which contains between one and three variables. If we were to graph each of the three equations, we would have the three planes pictured below. We really hope you can easily accept it as one of your reference and many thanks for your effort for exploring our website. Solve system of 3 variable equations. The graphof an equation in three variables is the graph of all its solutions. Elimination by judicious multiplication is the other commonly-used method to solve simultaneous linear equations. Systems Of Equations By Substitution Worksheets Math Go Linear Answers Second Grade Worksheet My Answer Generator … A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations. 3.5 Solving Systems of Three Linear Equations in Three Variables The Elimination Method SPI 3103.3.8 Solve systems of three linear equations in three variables… Students are to find the cards that correctly identify the variable and have a system of equations that represents each of the application problems. NCERT Class 10 Maths Lab Manual – Linear Equations Objective To verify the conditions for consistency of a system of linear equations in two variables by graphical representation. Write answers in word form!!! Graphically, the solution is where the functions intersect. The calculator will use the Gaussian elimination or Cramer's rule to generate a step by step explanation. While textbooks often chunk the idea of solving systems into discrete, almost unconnected mini-lessons (first let's learn about guess and check, now let's learn about solving systems by elimination, etc. We can solve this by multiplying the top equation by 2, and adding it to the bottom equation: \begin {align} 2(-y-4z) + (2y + 8z) &= 2(7) -12 \\ (-2y + 2y) + (-8z + 8z) &= 14 - 12 \\ 0 &= 2 \end {align}. These exercises will help to check how you are able to solve linear equations with 3 variables. Solving Systems of Three Equations in Three Variables In order to solve systems of equations in three variables, known as three-by-three systems, the primary tool we will be using is called Gaussian elimination, named after the prolific German mathematician Karl Friedrich Gauss. Worksheet will open in a new window. Next, multiply the first equation by $-5$,  and add it to the third equation: \begin {align} -5(x - 3y + z) + (5x - 13y + 13z) &= -5(4) + 8 \\ (-5x + 5x) + (15y - 13y) + (-5z + 13z) &= -20 + 8 \\ 2y + 8z &= -12 \end {align}. System Of Linear Equations Worksheets Katyphotoart Com . Displaying top 8 worksheets found for - Systems Of Equations With 3 Variables. Solve for x. This set of 3 mazes gets students solving a system of equations in a variety of ways. As the equations grow simpler through the elimination of some variables, a variable will eventually appear in fully solvable form, and this value can then be “back-substituted” into previously derived equations by plugging this value in for the variable. (c) All three planes are parallel, so there is no point of intersection. Get the free "3 Equation System Solver" widget for your website, blog, Wordpress, Blogger, or iGoogle. 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stu 30, 2020


text:
# The unit of resistance is

This question was previously asked in
ISRO (VSSC) Technician (Electrician) Sept 2016 Official Paper
View all ISRO Technical Assistant Papers >
1. Ohm
2. Mho
3. Coulomb
4. Henry

Option 1 : Ohm
Free
Subject Test 1: Electrical Basics
3012
20 Questions 80 Marks 30 Mins

## Detailed Solution

Electrical Resistance:

• The property of any conductor that opposes the flow of electric current through it is called resistance.
• It is denoted by R and the SI unit is the ohm (Ω).

The resistance is given by:

$$R=\rho \frac{l}{A}$$

Where ρ is resistivity, L is the length and A is the area of the cross-section.

EXPLANATION:

• The SI unit of electrical resistance is Ohm (Ω) and it is the SI derived unit of electrical resistance, named after German physicist, Georg Simon Ohm.


text:
Does spaghettification occur around a super massive black hole?

I heard recently that a supermassive black hole would not tear you apart like a smaller black hole would, that you would simply “flow into it never knowing that you are doomed until it is too late”. Is this true and if so why?

phinds
Gold Member
I don't know whether that's true or not but it certainly could be.

spaghettification is the result in a gravity differential between your head and your feet (well, all along your body, actually). In a supermassive BH, I guess the radius could be large enough that the differential would be small enough before you hit the surface that it wouldn't and you just be smeared into it.

Once you hit the event horizon (which is not there as far as you are concerned) you are doomed no matter what size the BH is, but with smaller BHs, you get spaghettified before hitting the EH and with large ones you get it afterwards or never.

Bill_K
The tidal forces are proportional to the Riemann tensor, which is like M/r3. For constant r it gets bigger as you increase the mass, but near the horizon where r = 2M it appears to go the other way.

pervect
Staff Emeritus
For small black holes you'll be torn apart earlier, before you can even cross the event horizon. For a larger hole, you'll still be torn apart after eventually, you won't avoid it, but you cross the event horizon first.

Matterwave
Gold Member
Although you wouldn't get spaghettified, I doubt that the experience would be "normal". All light signals that reach you inside a BH would necessarily have to come from a radius greater than the radius you are currently inhabiting. You would see everything kind of inverted at least. If you fell in feet first, beyond the EH, you would see your feet as they were at a farther out radius than your head. The nerve impulses must also be similarly screwed up, so I don't really know if you would still feel "normal"...

So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

PAllen
So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

The spaghettification simply comes from there being a large curvature over, say, 6 feet, creating a large tidal tension on your body. Remember, the event horizon is not a physical singularity - it is invisible to a body passing through it (in particular, they can still see light coming in from outside). Thus, for a small black hole you would feel extreme tension before even reaching the event horizon. For bigger, it might be at the event horizon. For a billion star black hole (believed to exist in some large galaxies), it would be way inside the horizon before the curvature became extreme over 6 feet.

[edit: correction pointed out by phinds: black hole where I meant event horizon]

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phinds
Gold Member
So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

Negen, Pallen's explaination is correct and complete, but I believe that in his last sentence "For a billion star black hole (believed to exist in some large galaxies), it would be way inside the black hole before the curvature became extreme over 6 feet." He meant to say "... way inside the EVENT HORIZON ... " not " ... way inside the black hole".

It took me a while to get this also when I first started reading about it, but as he said the EH is not physical barrier of any kind. The gravity just slightly outside the EH is only slightly different than the gravity inside the EH, it's just that just outside the EH it is still theoretically possible for things to escape and inside it is not. The closer you get to the EH, the more energy it would take to escape from the BH's gravity.

To people OUTSIDE the EH, it does appear that something happens at the EH, but that is in THEIR frame of reference, not in the frame of reference of the object AT the EH.

DaveC426913
Gold Member
So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

As PAllen points out, the spaghettification occurs because of a large difference in forces between your head and your feet. In a supermassive BH, the gradient is smaller, therefore even though the absolute value is still huge, the relative value is small.

There are analogies - such as density of an atmosphere - that might make it easier to understand.

Earth has an atmopshere that goes from 0 to 1 atmo in the space of about 100 miles.
Jupiter, while it might ultimately have a much higher pressure of hundreds or thousands of atmospheres, has a flux (change over distance) that is smaller than Earth's. It might go from 0 atmo to 1 atmo over a thousand miles (It might go from 10 atmo to 11 atmo over a thousand miles too).

So you can see that the gradient or flux or change-over-distance is much lower, even if the actual absolute values are much higher.

Back to black holes and gravity. High flux/gradient/change-over-distance is what results in spaghettification.

tom.stoer
You can callculate this rather easily for large black holes and the Newtonian limit. Using

r_s = 2GM

and

F(r) = GmM/r²

one finds

F(r_s) = m/4GM

i.e.

F(r_s) ~ 1/M

stevebd1
Gold Member
You can also use the following equations to see how big a black hole needs to be in order to at least reach the event horizon in one piece-

Tidal forces (change in gravity)-

$$dg=\frac{2Gm}{r^3}dr$$

and set r=rs where rs is the Schwarzschild radius $(r_s=2Gm/c^2)$.

If we assume that the maximum change in gravity a body can tolerate from head to toe is 1g then dg=9.81, dr=2 and you can rearrange the equation for dg relative to m. You can also consider a max of 5 or 10g (depending on how much the body can tolerate) from head to toe to see what size the (static) black hole needs to be to at least reach the EH.

You can also consider the 'ouch' radius-

$$r_{ouch}=\left(\frac{2Gm}{g_E}dr\right)^{1/3}$$

where gE is Earth gravity and rouch is the radius at which you will begin to feel pain (based on the idea that pain will be felt for a dg greater than 1g from head to toe). You'll be able to see that for small black holes, this radius is some way from the EH.

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# Using LaTeX in Sage

## 2149 days ago by kcrisman

First things first.  Do you remember how to open a new text cell?  Do you remember how to edit this one?

Here is a nasty integral - so nasty that Sage can't even compute it partially.

integrate(sin(x^2)/e^(2^x^2),x)
 integrate(e^(-2^(x^2))*sin(x^2), x) integrate(e^(-2^(x^2))*sin(x^2), x)

How can I insert this in my text, though?  For that, we just need dollar signs and the latex() command.

latex(integrate(sin(x^2)/e^(2^x^2),x))
 \int e^{\left(-2^{\left(x^{2}\right)}\right)} \sin\left(x^{2}\right)\,{d x} \int e^{\left(-2^{\left(x^{2}\right)}\right)} \sin\left(x^{2}\right)\,{d x}

This looks forbidding!  But let's do it.

\$\int e^{\left(-2^{\left(x^{2}\right)}\right)} \sin\left(x^{2}\right)\,{d x}\$

\int e^{\left(-2^{\left(x^{2}\right)}\right)} \sin\left(x^{2}\right

If I cut and paste that in this cell, I get:

$\int e^{\left(-2^{\left(x^{2}\right)}\right)} \sin\left(x^{2}\right)\,{d x}$

Wow!

Such mathematical typesetting is the beginnings of what we call LaTeX (pronounced "lah-tech" or "lay-tech", hard ch).  LaTeX is one of the best ways to do mathematically typesetting, and is very powerful.

• Today, we'll see how to do math itself in LaTeX.
• Next time, we'll start seeing how to organize thoughts using LaTeX.

But it is nice that Sage can do the hard part for us to make it look nice.

f(x) = e^(-x^2+sin(abs(x)))*sinh(x^2+1) latex(f(x)); latex(derivative(f(x)))
 e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) {\left(\frac{x \cos\left({\left| x \right|}\right)}{{\left| x \right|}} - 2 \, x\right)} e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) + 2 \, x e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \cosh\left(x^{2} + 1\right) e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) {\left(\frac{x \cos\left({\left| x \right|}\right)}{{\left| x \right|}} - 2 \, x\right)} e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) + 2 \, x e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \cosh\left(x^{2} + 1\right)

The derivative of $e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right)$ is ${\left(\frac{x \cos\left({\left| x \right|}\right)}{{\left| x \right|}} - 2 \, x\right)} e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) + 2 \, x e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \cosh\left(x^{2} + 1\right)$.

Hmm, maybe those are long enough that they need their own lines.  If I use \$\$ on each side, I get that.  Like \$\$x^2\$\$ becomes $$x^2\; .$$

e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right)

e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right)
{\left(\frac{x \cos\left({\left| x \right|}\right)}{{\left| x \right|}} - 2 \, x\right)} e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) + 2 \, x e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \cosh\left(x^{2} + 1\right)

The derivative of $$e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right)$$ is $${\left(\frac{x \cos\left({\left| x \right|}\right)}{{\left| x \right|}} - 2 \, x\right)} e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \sinh\left(x^{2} + 1\right) + 2 \, x e^{\left(-x^{2} + \sin\left({\left| x \right|}\right)\right)} \cosh\left(x^{2} + 1\right)$$.

Note how there is a trailing period, because I did like \$\$x^2\$\$. instead of \$\$x^2 .\$\$.  We'll get there!

But there is a lot more we can do.  So let's play around a little - try to figure out what you want to typeset, maybe from some of your "exploration" problems (!) and then we'll get going.


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# A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45^{\circ}$, and $40$ times per minute where the dip is $30^{\circ}$. If $B_{1}$ and $B_{2}$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_{1}/B_{2}$ is best given by : Option 1) $2.2$ Option 2) $0.7$ Option 3) $1.8$ Option 4) $3.6$

Compass needle 1 $\rightarrow$

Compass needle 2$\rightarrow$

$I_{1}=\frac{1}{2\pi}\sqrt{\frac{rB_{1}\cos45^{\circ}}{I}}$

$I_{2}=\frac{1}{2\pi}\sqrt{\frac{rB_{2}\cos30^{\circ}}{I}}$

$\Rightarrow \frac{I_{1}}{I_{2}}=\sqrt{\frac{B_{1}\cos45^{\circ}}{B_{2}\cos30^{\circ}}}$

$\Rightarrow \frac{B_{1}}{B_{2}}=0.7$

Option 1)

$2.2$

Option 2)

$0.7$

Option 3)

$1.8$

Option 4)

$3.6$

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# Does a phase rotation introduce a delay?

Suppose I have 2 complex time series, $$x_1$$ and $$x_2$$.

If I measure the delay between $$x_1$$ and $$x_2$$, I get $$t$$.

If I make $$x_2 = x_2 e^{-j 2 \pi 10}$$, and measure the delay between $$x_1$$ and $$x_2$$, do I still get $$t$$?

if your signal is a tone, phase rotation and time delay do the same thing.

In general, a rotation of a complex signal isn’t equivalent to a time delay.

A good portion of the beamforming literature uses the “narrow band” assumption and if the travel time of a wavefront over an array is small compared the inverse bandwidth of the envelope of the tone, beam steering (delay) is well approximated by phase multiplication.

• Do you have a source you can recommend which goes over this material? – Isaac Gerg Apr 17 at 21:40
• Optimum Array Processing Vol 4 by Harry Van Trees covers it. Most books on beam forming will have something on narrow band processing. This is not an esoteric subject – Stanley Pawlukiewicz Apr 17 at 21:45

I would assume a discrete-time context (though your notation suggests continuous-time).

Then you have a misunderstanding of the relation between the "delay" and "phase". Delay is measured in time-domain whereas the phase rotation is defined in frequency-domain.

So if there was a delay $$\pm d$$ between $$x_1[n]$$ and $$x_2[n]$$, then $$y_1[n]$$ (defined as the inverse DTFT of $$Y_1(\omega)$$ defined below) will have zero delay wrt $$x_2[n]$$ in time:

$$Y_1(\omega) = e^{ \mp j \omega d } X_1(\omega)$$

• I can measure phase rotation in time domain. Think of a QPSK modulated signal which I rotate slightly by pi/eps. I can measure this rotation by looking at the constillation in time domian. – Isaac Gerg Apr 17 at 21:36
• so you don't have a misunderstanding of phase and delay then... :-) sorry. – Fat32 Apr 17 at 22:03