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Evgesh-ka [11]
3 years ago
11

Expand the expression and combine like terms

Mathematics
1 answer:
____ [38]3 years ago
4 0
But what is the expression, you have to tell me so I can do it.
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Evaluate the spherical coordinate integral
expeople1 [14]

Rewrite the equations of the given boundary lines:

<em>y</em> = -<em>x</em> + 1  ==>  <em>x</em> + <em>y</em> = 1

<em>y</em> = -<em>x</em> + 4  ==>  <em>x</em> + <em>y</em> = 4

<em>y</em> = 2<em>x</em> + 2  ==>  -2<em>x</em> + <em>y</em> = 2

<em>y</em> = 2<em>x</em> + 5  ==>  -2<em>x</em> + <em>y</em> = 5

This tells us the parallelogram in the <em>x</em>-<em>y</em> plane corresponds to the rectangle in the <em>u</em>-<em>v</em> plane with 1 ≤ <em>u</em> ≤ 4 and 2 ≤ <em>v</em> ≤ 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
Brainliest for correct answer! :)
professor190 [17]

Answer:

Mode: 44 (mode is biggest number)

Mean: 30 (the average between numbers)

Step-by-step explanation:

Calculating the Mean

44 + 43 = 87

25 + 8 = 33

87 + 33 = 120

120 + 30 = 150

150/5 = 30

3 0
2 years ago
If you owe your friend $3 and you have $15, which expression would help you find out how much money you would have left?
gizmo_the_mogwai [7]
The answer is B because your subtracting it
7 0
3 years ago
Read 2 more answers
A sphere has a radius of 3 and a different sphere has a radius of 6. Compare the ratio of the volume of the smaller sphere to th
SSSSS [86.1K]
Since we are dealing with a volume problem (3 dimensions) when you increase the radius by a factor of 2, you increase the volume by a factor of 2^3 or 8
So, the larger sphere has a volume 8 times greater than the smaller sphere.


5 0
3 years ago
Find the area of the shape shown below. Please help
Eduardwww [97]

4,800

Step-by-step explanation:

3 0
2 years ago
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