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3 years ago

Which of the following show a geometric series? Select all that apply.

Mathematics

2 answers:

dedylja [7]3 years ago

7 0

Answer:

only A. and E.

Step-by-step explanation:

Vilka [71]3 years ago

3 0

The choices
A, D, and E, are geometric series

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Karina wants to fill the base so that it is 85% full. What is the volume of the base that she is filling? (Find 85% of the volum

Mazyrski [523]

Question:

Karina has recently begun kickboxing and purchased training equipment as modeled in the diagram below. The cylindrical base is 15 inches tall with a diameter of 22 inches.

Karina wants to fill the base so that it is 85% full. What is the volume of the base that she is filling? (Find 85% of the volume).

Answer:

$Section = 4847.3205\ in^3$

Step-by-step explanation:

Given

$h = 15in$ -- height

$d = 22in$ -- diameter

Required

85% of the volume

First, calculate the radius

$r = \frac{1}{2} * d$

$r = \frac{1}{2} * 22= 11in$

The volume (V) is then calculated using:

$V = \pi r^2h$

$V = 3.142* 11^2 * 15$

$V = 5702.73\ in^3$

85% of the volume is:

$Section = 85\% * V$

$Section = 85\% * 5702.73\ in^3$

$Section = 4847.3205\ in^3$

3 0

3 years ago

Which numbers should be multiplied to obtain 175^2 − 124^2?

Tomtit [17]

Hi There! :)

Which numbers should be multiplied to obtain 175^2 − 124^2?

51 and 299

7 0

3 years ago

Read 2 more answers

The mean of 2.7, 3.6 and 1.8

kolezko [41]

Set them up from least to greatest..
The mean is the average of all the data so..
The answer is 2.7

8 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 cap $z=\sqrt{3-x^2-y^2}$ , 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

4 years ago

Plz solve i need this done today

garik1379 [7]

D,A,B,C i think this is correct !

3 0

3 years ago