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2 years ago

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Ella's family took a road trip to Niagara Falls. Ella slept through the last 14% of the trip. If Ella fell asleep after they had

travelled 602 miles, what was the total length of the trip?

1 answer:

egoroff_w [7]2 years ago

4 0

X= 4300

14%xx=602

i think that is the answer, i tried helppoo

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If C is the path the particle follows, then work done is $\int_{C}^{}F.dx$ .

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therefore, if S is the at surface with boundary C, so that S is the portion of the plane $z=\frac{1}{4}y$ over the rectangle D=[0,2]\times [0,4].

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$curlF=\begin{vmatrix}i &j &k \\ \frac{\partial }{\partial x}&\frac{\partial }{\partial y} &\frac{\partial }{\partial z} \\ z^{2}&5xy &4y^{2} \end{vmatrix}=8yi+2zj+5yk$

By the Stoke's theorem:

$\int_{C}^{}F.dx=\iint_{s}^{}curlF.dS\\\\=\iint_{D}^{}[-8y(0)-2z\left ( \frac{1}{4} \right )+5y]dA\\\\=\iint_{D}^{}\left ( -\frac{1}{2}z+5y \right )dA$

$=\iint_{D}^{}\left ( \frac{39}{8}y \right )dA\, \, \, \, \, \, \, \, \, Since\, \, z=\frac{1}{4}y\\\\=\int_{0}^{2}\int_{0}^{4}\frac{39}{8}y\, \, \, dy\, dx\\\\$

$\int_{0}^{2}\left [ \frac{39}{16}y^2 \right ]_{0}^{4}dx\\\\=\int_{0}^{2}39\, \, dx\\\\=39\times 2\\\\=78 \, N$

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