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Juli2301 [7.4K]

3 years ago

15

9. Waldo and Freddy caught fish one weekend. The dot plots show the lengths of the fish they caught. Length of Waldo's Fish + 16

15 17 18 19 20 21 22 Inches Length of Freddy's Fish

1 answer:

Licemer1 [7]3 years ago

6 0

The Range of the length of the fish caught by Freddy is Greater than the range of the length of the fish caught by Waldo.

Step-by-step explanation:

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Sidana [21]

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3 years ago

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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

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

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3 years ago

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marishachu [46]

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Step-by-step explanation:

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3 years ago

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masha68 [24]

Answer:

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Step-by-step explanation:

Since AB and CD are parallel lines, then

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x - 12 = 16 ( add 12 to both sides )

x = 28

Thus

3x - 12 = 3(28) - 12 = 84 - 12 = 72°

y and 3x - 12 are adjacent angles and supplementary, thus

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Vinvika [58]

Answer:

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Step-by-step explanation:

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