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konstantin123 [22]
3 years ago
12

What is the average rate of change for the relation shown below between x = -2 and x = 2?

Mathematics
1 answer:
victus00 [196]3 years ago
7 0
Between x=-2 and x=2 is 5/2

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I need help with these problems please
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Step-by-step explanation:

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Vesnalui [34]

Step-by-step explanation:

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6 0
2 years ago
ILL GIVE BRAINLIEST<br><br> Combine like terms.<br> 4x – 7y + 2x – 4 = [ ? ]x + [ ]y + [ ]
maxonik [38]

Answer:

[6x] + [-7y] + [-4]

Step-by-step explanation:

There are only two like terms in this expression "4x" and "2x." Since they are like terms we can combine them by adding the coefficients and keeping the variable attached. Therefore we can combine 4x and 2x into 6x. Since there are no more like terms, this expression can be simplified to 6x - 7y - 4.

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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
Tomtit [17]

Apparently my answer was unclear the first time?

The flux of <em>F</em> across <em>S</em> is given by the surface integral,

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S

Parameterize <em>S</em> by the vector-valued function <em>r</em>(<em>u</em>, <em>v</em>) defined by

\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k

with 0 ≤ <em>u</em> ≤ π/2 and 0 ≤ <em>v</em> ≤ π/2. Then the surface element is

d<em>S</em> = <em>n</em> • d<em>S</em>

where <em>n</em> is the normal vector to the surface. Take it to be

\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}

The surface element reduces to

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv

so that it points toward the origin at any point on <em>S</em>.

Then the integral with respect to <em>u</em> and <em>v</em> is

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS

=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS

=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}

4 0
4 years ago
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