Only answer if you know please

Mathematics

1 answer:

SpyIntel [72]3 years ago

5 0

Again, we use the Pythagorean theorem:

x^2 = 13^2(hypotenuse) - 12^2(side)

x^2 = 169 - 144

x^2 = 25

x = square root of 25

x = 5

The correct answer is B. 5.

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Use stoke's theorem to evaluate∬m(∇×f)⋅ds where m is the hemisphere x^2+y^2+z^2=9, x≥0, with the normal in the direction of the

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We can check this result by evaluating the equivalent surface integral. We have

$\nabla\times\mathbf f=\langle1,0,0\rangle$

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where $0\le v\le\dfrac\pi2$ and $0\le u\le2\pi$ . Then,

$\displaystyle\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S=\int_{v=0}^{v=\pi/2}\int_{u=0}^{u=2\pi}9\cos v\sin v\,\mathrm du\,\mathrm dv=9\pi$

as expected.

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