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3 years ago

Plz help I have a time limit

Mathematics

1 answer:

vivado [14]3 years ago

3 0

Answer:

Area 108cm2

Step-by-step explanation:

triangle =1/2 ×base× height

rectangle =length × width

then add the area of each shape

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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

3 years ago

Why are these triangles similar?

Nezavi [6.7K]

The answer is AA

good luck

3 0

2 years ago

Subtract. 7 4/10−1 2/10 Write your answer in simplest terms.

Stolb23 [73]

The answer is 6 1/5.

7 0

2 years ago

Read 2 more answers

Whats the slope of (-8,-1) and (-6,-2)

STatiana [176]

Answer: -1/2 or -0.5.
Explanation: -2- -1, -6- -2= -0.5

5 0

2 years ago

a single die is rolled one time. Find the probability of rolling a number greater than 4 or less than 3.

Fynjy0 [20]

Answer

The probability of rolling a number of 2 is 1/6 (16.667%)

The probability of rolling a number of 3 is 2/6 (33.33%)

The probability of rolling a number 4 is 3/6 (50%)

The probability of rolling a number 5 is 4/6 (66.667%)

Explanation:
I’m not sure what you were trying to look for. So I put the probability for numbers 2,3,4, and 5. Your welcome, have a great day/night!.

6 0

2 years ago