text:
# Guessing the solution

1. Jan 1, 2006

### twoflower

Hi all,

I found this problem on web and though we haven't encountered this kind of problem in class I wonder how could it be done. Here it is:

Guess solution of the problem

$$x' = t + \frac{x}{1+x^2},\mbox{ x(0) = 0}$$

ie. find functions $\omega(t) \leq x(t) \leq \phi(t)$ for each $t$ from domain of solution.

Well, I have no clue. I have the results here if anyone tries...

Thank you for hints!

2. Jan 1, 2006

### Tide

HINT: What are the largest and smallest possible values of the real function

$$\frac {x}{1+x^2}$$
?

3. Jan 1, 2006

### twoflower

$$\frac{1}{2}$$

and

$$-\frac{1}{2}$$ ?

4. Jan 1, 2006

### HallsofIvy

Yes, and if you replace the "x" in the right hand side of the equation by those, can you then solve for x(t)?

5. Jan 2, 2006

### twoflower

Thank you HallsofIvy, so I wrote the bounds

$$x \leq \frac{t^2}{2} + \frac{t}{2}$$

and

$$x \geq \frac{t^2}{2} - \frac{t}{2}$$

It's ok, isn't it? Anyway, the official results say something slightly different...

6. Jan 2, 2006

### twoflower

Ok, I have it. In the results, there is

$$\frac{t^2}{2} - t \leq x(t) \leq \frac{t^2}{2} + t$$

which is just result of rougher bounds.

7. Jan 2, 2006

### saltydog

So can someone suggess a method for solving the original ODE analytically? I can't.

8. Jan 2, 2006

### HallsofIvy

Non-linear differential equations, such as this one, tend NOT to have solutions that can be found exactly.

9. Jan 2, 2006

### saltydog

Hello Hall. How are you? May I say I'm not satisfied by this outcome? I know what you're thinkin': "why do I even bother; he's a pain in the . . .". Tell you what, suppose an asteriod was heading here and we had to find some analytical expression for this ODE in order to successfully deflect it. What progress could the combined intellect of the world muster to do so? I bet a whole dollar something could be done.


text:
# Elevator

The panel house has ten over-ground stories and four underground. The lift goes from the ground floor to the 2nd floor, then down to the 3rd underground floor, nine floors up, and finally four floors down. To what floor elevator arrive? How many floors did it pass over?

a =  2
b =  20

### Step-by-step explanation:

$a=-3+9-4=2$
$b=0+2+\left(2+3\right)+9+4=20$

Did you find an error or inaccuracy? Feel free to write us. Thank you!

## Related math problems and questions:

• Running
Joanne ran 8 1/2 Kyleigh 1 2/3 and John 6 3/4 miles in one day. How many miles did the girls run in 3 days?
• Pedestrian up-down hill
Pedestrian goes for a walk first at the plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back, and goes downhill at speed 6 km/h. The total walk was 6 hours. How many kilometers went pedestrian?
• Dog II
The journey from a rangers' home to the town is 6 km. Mr. ranger started from his home and went 3 km per hour. His women came from the town and also went 3 km per hour. With ranger started dog and runs in 12 km in 1 hour. The dog went to the ranger's woma
• Donuts 3
You pick up donuts for a party. You have 3 and 4/12 boxes of donuts. Roy picks up donuts too. He has 2 and 9/12 boxes of donuts. How many boxes of donuts do you have in all?
• The tourist
The tourist has walked 3/4 of the route. The destination is 12.5 km away. How many kilometers did the route measure?
• Play tennis
Peter and Jirka agreed to go play tennis. Peter's path to the tennis court is 800 meters longer and leads around Jirka's house. Peter comes out first and then picks up Jirka. Together they go at the same average speed as Peter went, so they reach the plac
• The Tunnel
The Tunnel of Fear ride climbs straight up to its peak 50 meters above the ground. Then, it drops 65 meters into an underground tunnel. What is the elevation of the tunnel relative to the ground?
• The book 4
Mr. Kinion read 3 3/4 chapters in his book on Monday. He then read 2 4/6 more chapters on Tuesday. How many chapters has he read so far?
• Cottage house
The village is 28 km from the cottage. Father goes from village to cottage. Son goes from the cottage to the village. They meet 10 km further behind the cottage. How much did dad walk?
• Trolleybus
Trolleybus line No. 206 measured 24 km. If the trolleybus goes faster by 5 km/h, the way there and back would is shorter by 33 minutes. Calculate the trolleybus speed and how much time it takes a return trip.
• On the floor
You enter the room and there are 2 dogs, 4 horses, 1 giraffe and one duck on the bed, 3 chickens are flying over the chair. How many feet are on the floor?
• Evaluate expr with 2 vars
If a=6 and x=2, find the value of (2ax + 7x- 10) /(4ax-3a-2)

format: plain


text:
# Extracting angular observables without a likelihood and applications to rare decays

Beaujean, Frederik; Chrząszcz, Marcin; Serra, Nicola; van Dyk, Danny (2015). Extracting angular observables without a likelihood and applications to rare decays. Physical Review D (Particles, Fields, Gravitation and Cosmology), 91:114012.

## Abstract

Our goal is to obtain a complete set of angular observables arising in a generic multibody process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events. Instead, we apply the method of moments that relies both on the orthogonality of angular functions and the estimation of integrals by Monte Carlo techniques. The big advantage of this method is that the joint distribution of all observables can be easily extracted, even for very few events. The method of moments is shown to be robust against mismodeling of the angular distribution. Our main result is an explicit algorithm that accounts for systematic uncertainties from detector-resolution and acceptance effects. Finally, we present the necessary process-dependent formulas needed for direct application of the method to several rare decays of interest.

## Abstract

Our goal is to obtain a complete set of angular observables arising in a generic multibody process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events. Instead, we apply the method of moments that relies both on the orthogonality of angular functions and the estimation of integrals by Monte Carlo techniques. The big advantage of this method is that the joint distribution of all observables can be easily extracted, even for very few events. The method of moments is shown to be robust against mismodeling of the angular distribution. Our main result is an explicit algorithm that accounts for systematic uncertainties from detector-resolution and acceptance effects. Finally, we present the necessary process-dependent formulas needed for direct application of the method to several rare decays of interest.

## Statistics

### Citations

Dimensions.ai Metrics
26 citations in Web of Science®
22 citations in Scopus®


text:
# $G$ connected planar graph, less than 12 vertices, then $\chi (G) \leq 4$

The problem is:

Let $G$ be a connected planar graph with less than 12 vertices. a) Prove that G has a vertex with degree $\leq 4$. b) Prove that $\chi (G) \leq 4$. (Do not use the Four Color Theorem)

I did prove part a) satisfactorily I think at least =/

My question is about part b).

I am thinking showing part b) by contradiction may work. I am thinking perhaps something concerning a particular vertex with degree at most $4$, deleting this vertex, showing a $4$ coloring is still possibly, any hints? =/

I am also thinking I could use Euler's Formula but I am not sure of how I would relate $n+r-e=2$ back to the chromatic number.

(I should have stated it said to do the problem without the four color theorem)

-

I think you can change the standard proof of "any planar graph is 5 colorable" to this case.

Assume by contradiction that this is not true. Pick a planar graph which is not $4$ colorable, and has at most 12 vetices, with the smallest number of vertices

Now, by the previous part, this graph has a vertex of degree $4$. Remove that vertex. The smaller graph is 4 colorable.

Add the vertex back in. It is connected to 4 vertices. If two have the same color, you are done. If all four vertices have different colors, repeat the argument from the 5 color theorem to recolor the four neighbours..

-
Ok thank you very much. I have been behind in this class and I am trying to get caught up to save my grade, if the gods shall be it so lol –  Starlight Dec 7 '12 at 3:15
Two bugs: (a) "at most 12 vetices" -> "at most 11 vertices". (E.g. the icosahedron is an example of a 5-regular 12-vertex planar graph.) (b) "has a vertex of degree $4$" -> "has a vertex of degree at most $4$". –  Douglas S. Stones Aug 18 '13 at 7:08


text: dc.contributor.advisor Andersen, Jens Oluf dc.contributor.author Pedersen, Alf-Håkon dc.date.accessioned 2017-06-12T14:00:35Z dc.date.available 2017-06-12T14:00:35Z dc.date.created 2017-05-15 dc.date.issued 2017 dc.identifier ntnudaim:14362 dc.identifier.uri http://hdl.handle.net/11250/2445854 dc.description.abstract We begin by deriving the Einstein equation from the Einstein-Hilbert action integral using variational methods; Variation with respect to the metric and the Palatini variation. The vacuum solution (Schwarzschild solution) is then presented and derived. Weak field approximation is introduced, and the vacuum solution is derived again in this framework. Higher-order Lagrangians and their effects on the gravitational potential is investigated, but found to not be of particular significance to the quantization procedure that follows. The quantization of the theory is accomplished through the use of the background field method, and therefore applies for any background space-time. dc.language eng dc.publisher NTNU dc.subject Physics (MSPHYS) dc.title Linearized general relativity and its quantization dc.type Master thesis


text:
# Axes¶

## Introduction¶

An Axis labels a dimension of a tensor. The op-graph uses the identity of Axis objects to pair and specify dimensions in symbolic expressions. This system has several advantages over using the length and position of the axis as in other frameworks:

1. Convenience. The dimensions of tensors, which may be nested deep in a computation graph, can be specified without having to calculate their lengths.

2. Safety. Axis labels are analogous to types in general-purpose programming languages, allowing objects to interact only when they are permitted to do so in advance. In symbolic computation, this prevents interference between axes that happen to have the same lengths but are logically distinct, e.g. if the number of training examples and the number of input features are both 50.

3. Generic. The order of axes for multi-dimensional tensors do not imply a specific data layout or striding, making the graph specification compatible across different hardware with different constraints.

## Core concepts¶

### Axis and Axes¶

The Axis object represents one dimension of a tensor, and can be created with the ng.make_axis method.

H = ng.make_axis(length=3, name='height')
W = ng.make_axis(length=4, name='width')

For tensors with multiple dimensions, we create an Axes passing in a list of individual Axis objects. Note that the ordering does not matter in specifying the axes, and has no bearing on the eventual data layout during execution. See Properties for a full description of axes properties.

axes = ng.make_axes([H, W])

We use Axes to define the shape of tensors in ngraph. For example,

image = ng.placeholder(axes)

We can also delay the specification of the axis length.

H = ng.make_axis(length=3, name='height')
W = ng.make_axis(length=4, name='width')
image = ng.placeholder([H, W])
H.length = 3
W.length = 4

## Semantics¶

In the nervana graph, our axis design is very flexible. Axes can be given arbitrary names and the ordering of the axes does not matter. Sometimes, however, axes need to have additional semantic information provided to operations.

### AxisRole¶

For example, convolution kernels need to know which axes correspond to the channel, height, width, and/or depth, in order to assemble the feature map. For this reason, we can attach AxisRole types to any axis by using ng.make_axis_role(). For example, to create an axis with the Channel role:

role_channel = ng.make_axis_role(name="Channel")
axis_channel = ng.axis(length=3, roles=[role_channel], name="my_axis")

The neon frontend relies on several axis roles, specified by its name: Height, Width, Depth, Channel, Channelout, and Time. These roles are primarily used for automatic axes inference. For example, a convolution kernel can examine the input feature maps’AxisRole to determine whether a dimshuffle shall be applied prior to convolution.

### DualAxis¶

When two tensors are provided to a multi-axis operation, such as ng.dot(), we need to indicate the corresponding axes that should be paired together. We use “dual offsets” of +/- 1 to mark which axes should be matched during a multi-axis operation.

For example, if you have two tensors to dot together, other approaches may rely on the user to make sure the right-most axis of the first tensor matches the left-most of the second tensor. (e.g. (N x M) dot (M x K) = (N x K)). Instead we have semantic axis, so we can create two tensors:

A = ng.placeholder([ax.C, ax.H, ax.W, ax.N])
B = ng.placeholder([ax.K, ax.C-1, ax.H-1, ax.W-1])

The -1 offset signifies that during a ng.dot(A, B) operation, the ax.C, ax.H, ax.W axes should be matched and cancelled out, leaving the unmatched axes in the result – a tensor with axes [ax.K, ax.N].

Here are some more examples of using DualAxis in dot products that illustrate its properties

# 2d dot
(H, W - 1) • (W, N) -> (H, N)
(H, W) • (W + 1, N) -> (H, N)

# 4d dot
(M, C - 1, H - 1, W - 1)  • (C, H, W, N) -> (M, N)
(M, C, H, W)  • (C + 1, H + 1, W + 1, N) -> (M, N)

# swapping the order of the axes is allowed
(M, C - 1, H - 1, W - 1)  • (C, H, W, N) -> (M, N)
(M, W - 1, H - 1, C - 1)  • (C, H, W, N) -> (M, N)

We can also use ng.cast_axis to recast the axes of an already defined tensor into the same dimensions, but using different offsets, to specify which dimensions should be reduced.

## Properties¶

1. The order of Axes does not matter.
• Two tensors x and y are considered having the same type if

• x and y have the same number of axes and same set of axes
• After shuffling of y‘s axes to be the same order of x‘s, the underlying values are the same.
• We can check element-wise tensor equality using ng.equal().

import numpy as np
import ngraph as ng

H = ng.make_axis(length=2)
W = ng.make_axis(length=3)
np_val = np.random.rand(2, 3)
x = ng.constant(np_val, [H, W])
y = ng.constant(np_val.T, [W, H])
z = ng.equal(x, y)

trans = ng.NumPyTransformer()
comp = trans.computation([z])
z_val = comp()[0]
print(z_val)
# [[ True  True  True]
#  [ True  True  True]]

1. An axis can occur at most once in the axes of a tensor.

For example:

H = ng.make_axis(length=2)
W = ng.make_axis(length=2)
x = ng.constant(np.ones((2, 2)), [H, H])  # throws exception
x = ng.constant(np.ones((2, 2)), [H, W])  # good

1. Axes have context

A set of standard neon axes are defined for neon frontends.

• Axes roles
ar = ng.make_name_scope(name="ar")
ar.Height = ng.make_axis_role()
ar.Width = ng.make_axis_role()
ar.Depth = ng.make_axis_role()
ar.Channel = ng.make_axis_role()
ar.Channelout = ng.make_axis_role()
ar.Time = ng.make_axis_role()

• Image / feature map
ax = ng.make_name_scope(name="ax")
ax.N = ng.make_axis(batch=True, docstring="minibatch size")
ax.C = ng.make_axis(roles=[ar.Channel], docstring="number of input feature maps")
ax.D = ng.make_axis(roles=[ar.Depth], docstring="input image depth")
ax.H = ng.make_axis(roles=[ar.Height], docstring="input image height")
ax.W = ng.make_axis(roles=[ar.Width], docstring="input image width")

• Filter (convolution kernel)
ax.R = ng.make_axis(roles=[ar.Height], docstring="filter height")
ax.S = ng.make_axis(roles=[ar.Width], docstring="filter width")
ax.T = ng.make_axis(roles=[ar.Depth], docstring="filter depth")
ax.J = ng.make_axis(roles=[ar.Channel], docstring="filter channel size (for crossmap pooling)")
ax.K = ng.make_axis(roles=[ar.Channelout], docstring="number of output feature maps")

• Output
ax.M = ng.make_axis(roles=[ar.Depth], docstring="output image depth")
ax.P = ng.make_axis(roles=[ar.Height], docstring="output image height")
ax.Q = ng.make_axis(roles=[ar.Width], docstring="output image width")

• Recurrent
ax.REC = ng.make_axis(roles=[ar.Time], recurrent=True, docstring="recurrent axis")

• Target
ax.Y = ng.make_axis(docstring="target")

## Elementwise Binary Ops¶

• When matches, output the same axis.

(H,) + (H,) -> (H,)
(H, W) + (H, W) -> (H, W)

• Automatic broadcasting / dim shuffle, the output axis order determined by input axis order of the left and right operands.

(H, W) + (H,) -> (H, W)
(H, W) + (W,) -> (H, W)
(H, W) + (W, N) -> (H, W, N)
(H, W) + (N, W) -> (H, W, N)
(C, H) + (W, H, N) -> (C, H, W, N)

• Commutative property is as usual, though axis order of the equivalent tensors can be different.

(H,) + (W,) -> (H, W)
(W,) + (H,) -> (W, H)
(C,) + (H, W) -> (C, H, W)
(H, W) + (C,) -> (H, W, C)

In the following example, z from left and right are equivalent, although the axis orders are different.

x = ng.constant(np.ones((2, 3)), [H, W]) | x = ng.constant(np.ones((2, 3)), [H, W])
y = ng.constant(np.ones((3, 2)), [W, H]) | y = ng.constant(np.ones((3, 2)), [W, H])
z = x + y                                | z = y + x  # <== changed order
|
trans = ng.NumPyTransformer()            | trans = ng.NumPyTransformer()
comp = trans.computation([z])            | comp = trans.computation([z])
z_val = comp()[0]                        | z_val = comp()[0]
print(z_val)                             | print(z_val)
print(z_val.shape)                       | print(z_val.shape)
-----------------------------------------------------------------------------
Output:                                  | Output:
[[ 2.  2.  2.]                           | [[ 2.  2.]
[ 2.  2.  2.]]                         |  [ 2.  2.]
(2, 3)                                   |  [ 2.  2.]]
| (3, 2)

• Associative property is as usual.

((H,) + (W,)) + (N,) -> (H, W) + (N,) -> (H, W, N)
(H,) + ((W,) + (N,)) -> (H,) + (W, N) -> (H, W, N)

• Distributive property is as usual.

(H,) * ((W,) + (N,)) = (H,) * (W, N) = (H, W, N)
(H,) * (W,) + (H,) * (N,) = (H, W) * (H, N) = (H, W, N)

## Axes Reduction¶

• We specify the reduction axes in reduction_axes. Reduction operations can have arbitrary number of reduction axes. The order of the reduction axes can be arbitrary.
• When reduction_axes is empty, reduction is performed on NONE of the axes.

Examples:

from ngraph.frontends.neon.axis import ax
x = ng.placeholder([ax.C, ax.H, ax.W])
ng.sum(x, reduction_axes=[])            -> [ax.C, ax.H, ax.W]
ng.sum(x, reduction_axes=[ax.C])        -> [ax.H, ax.W]
ng.sum(x, reduction_axes=[ax.C, ax.W])  -> [ax.H]
ng.sum(x, reduction_axes=[ax.W, ax.C])  -> [ax.H]
ng.sum(x, reduction_axes=x.axes)        -> []

## Axes Casting¶

Use ng.cast_axes to cast at axes to targeting axes with the same dimensions. For example, we might want to sum two layer’s outputs, where they have the same dimensions but different axes. Examples:

# assume C1.length == C2.length == 100
hidden_1 = ng.constant(np.ones((100, 128)), [C1, N])
hidden_2 = ng.constant(np.ones((100, 128)), [C2, N])

# if we add directly without casting
sum_direct = hidden_1 + hidden_2  # sum_direct has axes: [C1, C2, N]

# cast before sum
hidden_2_cast = ng.cast_axes(hidden_2_cast, [C1, N])
sum_cast = hidden_1 + hidden_2_cast  # sum_cast has axes: [C1, N]

Use ng.broadcast to broadcast to new axes. The new axes must be a superset of the original axes. The order of the new axes can be arbitrary. Examples:
from ngraph.frontends.neon.axis import ax


text:
5

# (10 points) Show that the set {u1,4z,u3} is AI orthogonal column vectors U] basis for R% 3,0). 42 where the (2 2 Kr1) ad 43 7(5,23.1) as a linear 1,4); Also express...

## Question

###### (10 points) Show that the set {u1,4z,u3} is AI orthogonal column vectors U] basis for R% 3,0). 42 where the (2 2 Kr1) ad 43 7(5,23.1) as a linear 1,4); Also express x combination Of the orthogonal set {ue} k 2,3.

(10 points) Show that the set {u1,4z,u3} is AI orthogonal column vectors U] basis for R% 3,0). 42 where the (2 2 Kr1) ad 43 7(5,23.1) as a linear 1,4); Also express x combination Of the orthogonal set {ue} k 2,3.

#### Similar Solved Questions

##### Dtl 0 ( Le+l ~(on R=1 82 ereVo 9 k=2Conves (T4)
Dtl 0 ( Le+l ~(on R=1 82 ere Vo 9 k=2 Conves ( T4)...
##### Let n â‚¬ Z and let n = (-1)"2"p%1 Pf " be the canonical decomnposition of n with u = 0 Or 1; v 2 0, and each "j 0 when 21_ (i) If v is odd then let TLo In/2 and choose T â‚¬ N s0 that mn = 5 (mod 8) ald TnL = (Inod no)- Prove that=-1,If v is eve; but there is & j for which Uj is odd let Tlj In/2 and choose mn â‚¬ N s0 that In = (Inod (Anlj)) and Tn is QNR Inodulo Pj: Prove that(iii) If v is even, Uj is even fOr every and u = 1, choose Tn â‚¬ Ns0 that (Tl,; n) = 1 and mn
Let n â‚¬ Z and let n = (-1)"2"p%1 Pf " be the canonical decomnposition of n with u = 0 Or 1; v 2 0, and each "j 0 when 21_ (i) If v is odd then let TLo In/2 and choose T â‚¬ N s0 that mn = 5 (mod 8) ald TnL = (Inod no)- Prove that =-1, If v is eve; but there is & j f...
##### The reaction Aask + & Caiculate the With coumbium mnitiated concentration Toics 0f thc productIncle Uie
The reaction Aask + & Caiculate the With coumbium mnitiated concentration Toics 0f thc product Incle Uie...
##### 26. baton is composed of a thin rod of length L and mass m and two small masses each of mass mn at either end Due to the symmetry; the certer of mass of the baton passes exactly through the center of thc rod. If thc baton rotates around its center of mass with an angular velocity _, then what is the rotational kinetic energy of the baton?
26. baton is composed of a thin rod of length L and mass m and two small masses each of mass mn at either end Due to the symmetry; the certer of mass of the baton passes exactly through the center of thc rod. If thc baton rotates around its center of mass with an angular velocity _, then what is the...
##### 10 5 the G(x) be beohe , V onileer [ Explain your Trmllons of gas answer, approximately how used W car N were been dricqurea aideariveTI 1 NAME OR 1 PARILAL 2 CREDL 1 1 ofde
10 5 the G(x) be beohe , V onileer [ Explain your Trmllons of gas answer, approximately how used W car N were been dricqurea aidearive TI 1 NAME OR 1 PARILAL 2 CREDL 1 1 ofde...
##### 2. Seperation of Varlables for FDEs: Use separation of varlables (0 find, If possible, product solutions_ u(x,y) = X(x) . Y(y) , for the following first-order PDEs: Du Du du du =0 Ox 85 Dy
2. Seperation of Varlables for FDEs: Use separation of varlables (0 find, If possible, product solutions_ u(x,y) = X(x) . Y(y) , for the following first-order PDEs: Du Du du du =0 Ox 85 Dy...
##### 4.A professional football team has found that 35% of the new players it signs out of univetity actually play for more than one year; During recent year, I0 new players were signed contracts. Find the probability that: A.At least will play for more than one year: B. No more than. will play for more than one year: C.For the 20 players signed last year, exactly are still playing this second year: What the probability of this event?
4.A professional football team has found that 35% of the new players it signs out of univetity actually play for more than one year; During recent year, I0 new players were signed contracts. Find the probability that: A.At least will play for more than one year: B. No more than. will play for more t...
##### Find the_relationships_between the angular and linear quantities?Solve_the_following problems: A wheel rotates with constant angular acceleration of 35 rads . If the angular velocity of the wheel is 2 rad/s at t (a) What angle does the wheel rotate through in 2 s? (b) What is the angular velocity at t = 2 s?A turntable rotates initially at a rate of 33 revolutions/min and takes 20 t0 come t0 rest. (a) What is the angular acceleration of the turntable, assuming the acceleration is uniform? (b) Ho
Find the_relationships_between the angular and linear quantities? Solve_the_following problems: A wheel rotates with constant angular acceleration of 35 rads . If the angular velocity of the wheel is 2 rad/s at t (a) What angle does the wheel rotate through in 2 s? (b) What is the angular velocity a...
##### Am irection. The distance l = 64 cmOB, 0ISem(le4 crvi
am irection. The distance l = 64 cm OB, 0 ISem (le4 crvi...
##### 1/ Which of the following statement is true for the reaction below? (Spts) HF(aq) + HPO: X-aq) F(aq) + HpPO4 (aq) A- HF is the conjugate base C-F is the conjugate base B- HPO4?- is the acid D- HPO4" is the conjugate base
1/ Which of the following statement is true for the reaction below? (Spts) HF(aq) + HPO: X-aq) F(aq) + HpPO4 (aq) A- HF is the conjugate base C-F is the conjugate base B- HPO4?- is the acid D- HPO4" is the conjugate base...
##### Let R be the rotation around the origin clockwise by 5 Is R a linear transform from R? to R2? Write down the corresponding matrix Au = R(u). Compute R(u) with u = [-1,3] (3 pts)
Let R be the rotation around the origin clockwise by 5 Is R a linear transform from R? to R2? Write down the corresponding matrix Au = R(u). Compute R(u) with u = [-1,3] (3 pts)...
##### Find the absolute minimum and absolute maximum of f(z,y) = 22 2x + y? 4y on the triangle with vertices at (0,0), (4,4) , and (0,4)_
Find the absolute minimum and absolute maximum of f(z,y) = 22 2x + y? 4y on the triangle with vertices at (0,0), (4,4) , and (0,4)_...
##### Which of the following is TRUE about vapor pressure lowering?Select one: a, The higher the van Hoff factor of solvent, the higher the vapor pressure of the solvent b. The lower the van Hoff factor of solvent; the higher the vapor pressure of the solvent The higher the mole fraction of solute; the higher the vapor pressure of the solvent The higher the mole fraction of solute; the lower the vapor pressure of the solvent
Which of the following is TRUE about vapor pressure lowering? Select one: a, The higher the van Hoff factor of solvent, the higher the vapor pressure of the solvent b. The lower the van Hoff factor of solvent; the higher the vapor pressure of the solvent The higher the mole fraction of solute; the h...
##### Q2. At 259C, the following heats of reaction are known: AH"mxn 167.4 kJlmol 2CIFlg) Oz(g) ClzOlg) + FzOlg) AH?rxn " 341.4 klmol 2CIFa(g) 202(g) ClOlg) + 3F2O(g) AH?, -43.4 klmol Ozlg) 2F,O(g) rxn 2F2(g) use Hesss law to calculate AH"n for the reaction: At the same temperature, CIF(g) Fzlg) + CIFslg)
Q2. At 259C, the following heats of reaction are known: AH"mxn 167.4 kJlmol 2CIFlg) Oz(g) ClzOlg) + FzOlg) AH?rxn " 341.4 klmol 2CIFa(g) 202(g) ClOlg) + 3F2O(g) AH?, -43.4 klmol Ozlg) 2F,O(g) rxn 2F2(g) use Hesss law to calculate AH"n for the reaction: At the same temperature, CIF(g) ...
##### Television Advertising On a given weekend in the fall, a tire company can buy television advertising time for a college football game, a baseball game, or a professional football game. If the company sponsors the college football game, there is a 70% chance of a high rating, a 50% chance if they sponsor a baseball game, and a 60% chance if they sponsor a professional football game. The probabilities of the company sponsoring these various games are 0.5, 0.2, and 0.3, respectively. Suppose the co
Television Advertising On a given weekend in the fall, a tire company can buy television advertising time for a college football game, a baseball game, or a professional football game. If the company sponsors the college football game, there is a 70% chance of a high rating, a 50% chance if they spo...
##### $17-28$ Use cylindrical coordinates. $$\begin{array}{l}{\text { Find the mass of a ball } B \text { given by } x^{2}+y^{2}+z^{2} \leqslant a^{2} \text { if the }} \\ {\text { density at any point is proportional to its distance from the }} \\ {z \text { -axis. }}\end{array}$$
$17-28$ Use cylindrical coordinates. \begin{array}{l}{\text { Find the mass of a ball } B \text { given by } x^{2}+y^{2}+z^{2} \leqslant a^{2} \text { if the }} \\ {\text { density at any point is proportional to its distance from the }} \\ {z \text { -axis. }}\end{array} \end{eq...