Evaluate the expression for x=2 and y=4. (x5y?)/(x3y5)

Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

4 0

4 years ago

Find all missing angles I need help please

aksik [14]

Answer:

1) 34º

2) 52º

3) 56º

4) 94º

Step-by-step explanation:

let 3 be x

let 1 be y

let 2 be z

let 4 be j

180=86+38+x 56=x

90=56+y 34=y

180=86+j 94=j

180=34+z+94 52=z

4 0

2 years ago

NEED ANSWER ASAP . Which table represents a linear function?

alexira [117]

Answer:

Step-by-step explanation:

Answer choice C would be correct since both sides are increasing at a set rate, x is increasing by one while y is increasing by 2 every time. Hope this helps :)

6 0

3 years ago

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function f(

alekssr [168]

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−

Answer:

vertex = (-4, -5)

Axis of symmetry = -4

use the (-4, -5) to find the minimum value

$Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5$