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2 years ago

MNOP is a trapezoid with median QR. Find x

Mathematics

1 answer:

nikitadnepr [17]2 years ago

5 0

$\bf \large \rightarrow \: \:2x \: + \: 8 \: = \: 0$

$\bf \large \rightarrow \: \:x \: = \: \frac{8}{2} \\$

$\bf \large \rightarrow \: \:x \: = \: \cancel\frac{ 8}{ 2} \: \: ^{4} \\$

$\bf \large \rightarrow \: \:x \: = \: 4$

Option ( A ) is the correct answer.

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<h3>Answer:</h3>

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Parameterize $S$ by

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with $0\le u\le1$ and $0\le v\le1$ . Take the normal vector to $S$ to be

$\vec s_v\times\vec s_u=(20v,8v,4v)$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^1\int_0^1\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv$

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3 years ago