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3 years ago

0.86 is 3.06 % of what number (Round to the nearest hundredth.)

Mathematics

1 answer:

polet [3.4K]3 years ago

4 0

Answer:

Let the number be x

3.06% = 0.0306

The above statement is written as

0.0306x = 0.86

Divide both sides by 0.0306

x = 0.86/0.0306

Hope this helps you

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Solve for 43.<br> 43 = [?]<br> 58°<br> 139° 41°<br> 43

Dovator [93]

Answer:

∠3 = 81

Step-by-step explanation:

Interior angles in a triangle add up to equal 180°

Hence, 58° + 41° + ∠3 = 180

58 + 41 = 99

99 + ∠3 = 180

* subtract 99 from each side *

99 - 99 cancels out

180 - 99 = 81

we're left with ∠3 = 81°

4 0

3 years ago

For how many weeks would the class need to have car washes to earn $5000.

nikdorinn [45]

The correct answer would be for 29 weeks.
Its because if for 4 weeks the profit is $700, divide 700 and 4 which gives you $175 per week. Then divide 5000 and 175 which gives you 28.5714286. So all you have to do is round it up to the nearest whole which gives you the answer: 29 weeks.
Hope that helps. :)

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4 years ago

PLS HELP ILL GIVE U POINTS :)

denpristay [2]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Given:<br> f(x)=x^2<br> g(x)=x-1<br> Find f(g(2))+g(f(-1))

Marina CMI [18]

Answer:

-1

Step-by-step explanation:

First, we need to work out the left-hand side.

find g(2) → g(2) = 2 - 1 which is 1
next, find f(1) → f(1) = 1³ which is 1

Now, we can work out the right hand side.

find f(-1) → f(-1) = -1³ which is -1
then, find g(-1) → g(-1) = -1 - 1 = -2

Finally we can work out the full sum: 1 + -2 = -1.

Hope this helps!

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2 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

4 years ago