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Arada [10]
3 years ago
6

Evaluate the expression when c=3 and y=-4. 8c-y

Mathematics
1 answer:
Savatey [412]3 years ago
3 0

Answer:

28

Step-by-step explanation:

8c - y

8( 3) - (- 4)

24 + 4

28

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Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and
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Call the surface S; then the area of S is given by the surface integral

\displaystyle\iint_S\mathrm d\mathbf S

Parameterize the surface by

\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}

with 2\le u\le4 and 0\le v\le2\pi. The surface element is given by

\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv
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So the area is

\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv
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where w=1+4u^2\implies\mathrm dw=8u\,\mathrm du

=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}
=\dfrac\pi6\left(65^{3/2}-17^{3/2}\right)\approx237.69
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Solve the equation.
Gelneren [198K]

Answer:

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Step-by-step explanation:

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or

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Step-by-step explanation:


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