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MAXImum [283]
3 years ago
11

Evaluate the spherical coordinate integral

Mathematics
1 answer:
expeople1 [14]3 years ago
5 0

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}

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Maurinko [17]

Answer:

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Step-by-step explanation:

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A rideshare service charges a flat fee of $6.00, plus $1.50 for every mile driven. Let t represent the total cost of the ride, a
galina1969 [7]

Answer:

The independent variable is m, while the dependent variable is t.

Step-by-step explanation:

  • What is the independent variable?

An independent variable is a variable that does not rely on another variable to change its outcome. In this case, the variable 'm' does not rely on the ride's total cost.

  • What is the dependent variable?

The dependent variable is a variable that depends on another variable to give its amount. In this case, 't' is the dependent variable, because it depends on how many miles were driven, in order to provide the correct answer.

  • Write an equation representing this relationship:

t = $6 + ($1.50 x m)

  • Complete the table to show the total cost for riding 3 to 10 miles:

3 miles: t = $6 + ($1.50 x m) or $10.50 = $6 + ($1.50 x 3)

4 miles: t = $6 + ($1.50 x m) or $12 = $6 + ($1.50 x 4)

5 miles: t = $6 + ($1.50 x m) or $13.50 = $6 + ($1.50 x 5)

6 miles: t = $6 + ($1.50 x m) or $15 = $6 + ($1.50 x 6)

7 miles: t = $6 + ($1.50 x m) or $16.50 = $6 + ($1.50 x 7)

8 miles: t = $6 + ($1.50 x m) or $18 = $6 + ($1.50 x 8)

9 miles: t = $6 + ($1.50 x m) or $19.50 = $6 + ($1.50 x 9)

10 miles: t = $6 + ($1.50 x m) or $21 = $6 + ($1.50 x 10)

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2 years ago
Nevaeh went shopping for a new phone because of a discount sale. She multiplied the price of the phone by 0.95 to find the price
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Answer:

95% off

Step-by-step explanation:

because the percent u times by the actual price is the percent u have off

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fomenos
They are different the fraction 3/5 is 0.6 in decimal,and the fraction 6/15 is 0.4 in decimal.
Wish that helped.

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