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4 years ago

72 pint = ? Gallons. How much is the gallon?

Mathematics

1 answer:

Zarrin [17]4 years ago

5 0

8 pints = 1 gallon
so divide it by 8
72 pints ÷ 8 = 9 gallons

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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

4 years ago

What is the equation of the line that passes through the points (-2,2) and (0,5)

gregori [183]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -2}}\quad ,&{{ 2}})\quad 
% (c,d)
&({{ 0}}\quad ,&{{ 5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-2}{0-(-2)}\implies \cfrac{5-2}{0+2}
\\\\\\
\cfrac{3}{2}$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=\cfrac{3}{2}(x-(-2))\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-2=\cfrac{3}{2}(x+2)\implies y-2=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x+3+2
\\\\\\
y=\cfrac{3}{2}x+5$

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3 years ago

Anyone Need Help Urgent

Leviafan [203]

Answer:

Step-by-step explanation:

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3 years ago

DESPERATE PLZ HELP NOW find a slope of the two numbers (-4,-5) (2,10)

MrRissso [65]

Answer:

The slope is 2.5

Step-by-step explanation:

y = 2.5x + 5 or

y = 5/2x + 5

When x=0, y = 5

When y=0, x = -2

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3 years ago

Read 2 more answers

Circumference C=25 units.

Allisa [31]

The answer is 50. I have the same question and it makes no sense. The r= and the d= are supposed to have answers, but I’m not sure how you get them

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3 years ago