I need help with Question 9 ?

Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

Jenna found three solution to a linear equation she graphed them, but they don't lie in a straight line. What errors could jenna

steposvetlana [31]

Answer:

A system of linear equation could only have 1 solution. This is because the straight lines will only have to meet, cross, or intersect each other once.

There are many different methods in arriving to the final answer. However, errors cannot be perfectly avoided. One of these errors to mistakenly identify equations as linear. It is important that we know that the equations we are dealing with are of exact or correct characteristics.

Also, if she had used substitution method, she might have mistakenly taken the value of one variable for the other.

5 0

3 years ago

Liam is making barbecue ribs over a fire. The internal temperature of the ribs when he starts cooking is 40°F. During each hour

Soloha48 [4]

Answer: You need to wait at least 6.4 hours to eat the ribs.

t ≥ 6.4 hours.

Step-by-step explanation:

The initial temperature is 40°F, and it increases by 25% each hour.

This means that during hour 0 the temperature is 40° F

after the first hour, at h = 1h we have an increase of 25%, this means that the new temperature is:

T = 40° F + 0.25*40° F = 1.25*40° F

after another hour we have another increase of 25%, the temperature now is:

T = (1.25*40° F) + 0.25*(1.25*40° F) = (40° F)*(1.25)^2

Now, we can model the temperature at the hour h as:

T(h) = (40°f)*1.25^h

now we want to find the number of hours needed to get the temperature equal to 165°F. which is the minimum temperature that the ribs need to reach in order to be safe to eaten.

So we have:

(40°f)*1.25^h = 165° F

1.25^h = 165/40 = 4.125

h = ln(4.125)/ln(1.25) = 6.4 hours.

then the inequality is:

t ≥ 6.4 hours.

4 0

3 years ago

Calculate the area of the square shown on the xy-plane in the diagram. Your answer

nikdorinn [45]

Answer: 50

Find the area of the triangles then multiply by 2.

1/2 x 5 x 10 = 25

25 x 2 = 50

6 0

3 years ago

You have 6 reindeer, Rudy, Jebediab, Ezekiel, Lancer, Gloopin, and Balthazar, and you want to have 5 fly your sleigh. You always

Anna71 [15]

You can arrange your reindeer 30 different ways.

5 0

3 years ago