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Masja [62]
3 years ago
14

Taylor completed the problem below. describe and correct the error in the problem. 2^(-4) = -2*-2*-2*-2=16

Mathematics
1 answer:
valina [46]3 years ago
3 0
I am looking at ur first answer choice.....but something is off..
2^-4 = 1/(2^4) = 1/(2*2*2*2) = 1/16...this is correct

but ur answer choice says 2^-4 = 1/(2^-4)...and its supposed to equal 1/(2^4).
But I still think ur answer choice is A
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I gather you're supposed to compute the integral of G(x,y,z)=z over a surface S that is the part of the parabolic cylinder y=z^2 with 0\le x\le2 and 0\le z\le\frac{\sqrt{15}}2.

We can parameterize S by

\vec s(x,z)=x\,\vec\imath+z^2\,\vec\jmath+z\,\vec k

with the given constraints on x and z. Take the normal vector to S to be

\vec s_x\times\vec s_z=-\vec\jmath+2z\,\vec k

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\mathrm dS=\|\vec s_x\times\vec s_z\|\,\mathrm dx\,\mathrm dz=\sqrt{1+4z^2}\,\mathrm dx\,\mathrm dz

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\displaystyle\iint_Sz\,\mathrm dS=\int_0^2\int_0^{\sqrt{15}/2}z\sqrt{1+4z^2}\,\mathrm dz\,\mathrm dx=\boxed{\frac{21}2}

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Step-by-step explanation:

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