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miv72 [106K]
3 years ago
11

How to do the monomials

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
8 0

<u>Given</u>:

The given monomial expression is \frac{16 y^{8}}{4 y^{2}}

We need to simplify the given monomial expression.

<u>Simplification:</u>

Let us simplify the given expression.

Dividing the numbers 16 and 4, we get;

\frac{4 y^{8}}{y^{2}}

Let us apply the exponent rule  \frac{x^{a}}{x^{b}}=x^{a-b} in the above expression.

Thus, we get;

4 y^{8-2}

Subtracting the numbers in the numerator of the above expression, we get;

4 y^{6}

Thus, the simplified expression is 4 y^{6}

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By inspecting the integrand, the "obvious" choice for substitution would be

<em>u</em> = <em>y</em> + <em>x</em>

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<em />

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J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12

The trapezoid <em>R</em> has two of its edges on the lines <em>x</em> + <em>y</em> = 8 and <em>x</em> + <em>y</em> = 9, so right away, we have 8 ≤ <em>u</em> ≤ 9.

Then for <em>v</em>, we observe that when <em>x</em> = 0 (the lowest edge of <em>R</em>), <em>v</em> = <em>y</em> ; similarly, when <em>y</em> = 0 (the leftmost edge of <em>R</em>), <em>v</em> = -<em>x</em>. So

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-<em>u</em> + <em>v</em> ≤ 2<em>v</em> ≤ <em>u</em> + <em>v</em>

-<em>u</em> ≤ <em>v</em> ≤ <em>u</em>

<em />

So, the integral becomes

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I think the answers would be B) 17
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