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3 years ago

Solve for x in the equation x squared + 2 x + 1 = 17.

Mathematics

1 answer:

PtichkaEL [24]3 years ago

5 0

Step-by-step explanation:

quadratic formula

-b+-√b^2

2a

-2+-√2^2-4×1×-16

2×1

-2+-√68

either

x= 3.125

x= -5.125

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

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Because I've gone ahead with trying to parameterize $S$ directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over $S$ straight away, let's close off the hemisphere with the disk $D$ of radius 9 centered at the origin and coincident with the plane $y=0$ . Then by the divergence theorem, since the region $S\cup D$ is closed, we have

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so the flux over the closed region is

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$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv$

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