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3 years ago

Find the volume of the cylinder.

Mathematics

2 answers:

ValentinkaMS [17]3 years ago

8 0

Answer:

144π

Step-by-step explanation:

V=πr^2h=π·6^2·4≈144π

monitta3 years ago

6 0

Answer:

the answer is 144 pi

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Can someone help me with 19 and 20 plsss

SCORPION-xisa [38]

20. $158, 400 - multiply 40 by 22 to get the total square footage(880), then multiply 880 by 15 to get they total for the month, which is 13,200. lastly, you take 13,200 multiplied by 12(for each month in a year), and you get $157,400.

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2 years ago

How many times greater is 130,000,000 than 64,800,000?

insens350 [35]

$\frac{130,000,000}{64,800,000} = \frac{1,300}{648} =\boxed {2.00617283951}$

4 0

3 years ago

Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find

Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk $x^2+y^2\le3$ , I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere $x^2+y^2+z^2=3$ .

a. Let $C$ denote the hemispherical <u>c</u>ap $z=\sqrt{3-x^2-y^2}$ , parameterized by

$\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to $C$ to be

$\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k$

Then the upward flux of $\vec F=(2z+2)\,\vec k$ through $C$ is

$\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du$

$\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du$

$=\boxed{2(3+2\sqrt3)\pi}$

b. Let $D$ be the disk that closes off the hemisphere $C$ , parameterized by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le\sqrt3$ and $0\le v\le2\pi$ . Take the normal to $D$ to be

$\vec s_v\times\vec s_u=-u\,\vec k$

Then the downward flux of $\vec F$ through $D$ is

$\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv$

$=\boxed{-6\pi}$

c. The net flux is then $\boxed{4\sqrt3\pi}$ .

d. By the divergence theorem, the flux of $\vec F$ across the closed hemisphere $H$ with boundary $C\cup D$ is equal to the integral of $\mathrm{div}\vec F$ over its interior:

$\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV$

We have

$\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2$

so the volume integral is

$2\displaystyle\iiint_H\mathrm dV$

which is 2 times the volume of the hemisphere $H$ , so that the net flux is $\boxed{4\sqrt3\pi}$ . Just to confirm, we could compute the integral in spherical coordinates:

$\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi$

4 0

3 years ago

Draw the meaning of bar diagram

gladu [14]

Draw a bar and draw little squares inside the box not the bar and then shade the boxes this will represent the number

8 0

3 years ago

Plssss help with all thiss

allsm [11]

Step-by-step explanation:

8, 12(3-x)=48

36-12x=48

-12x=48-36

-12x=12 both side divideos by -12

-12x/-12=12/-12

x= 1

9, x/7=4.5 cris cross

x=31.5

10,5(x-3)=45

5x-15=45

5x=45+15

5x=60 both side divided by 5

5x/5=60/5

x=12

11,-3(x-3)=45

-3x+3=45

-3x=45-3

-3x=42 both side divided by -3

-3x/-3=42/-3

x=14

12,14y-8=13

14y=13+8

14y=21 both side divided by 14

14y/14=21/14

y=1.5

13,3m=5m-8/5

3m-5m=-8/5

-2m=-8/5 cris cross

-10m=-8 both side divided by -10

-10m/-10=-8/-10

x=0.8

4 0

3 years ago

Read 2 more answers