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3 years ago

14

Jacelin was paid $50 after a day of babysitting. She watched the children from 8am until 4pm. What is the unit rate of her earni

ngs

1 answer:

taurus [48]3 years ago

5 0

Answer:

The unit rate of her earnings is 12.5

Step-by-step explanation:

50 divided by 9 = 12.5

She makes $12.50 an hour.

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2) Use spherical coordinates to find the integral of f(x,y,z) = z over x^2 + y^2 + z^2 < 4 and x,y,z < 0

777dan777 [17]

1. Denote by $\mathcal D$ the region bounded by the cylinder $x^2+y^2=9$ and the planes $z=0$ and $z=6$ . Converting to cylindrical coordinates involves setting

$\begin{cases}x=r\cos u\\y=r\sin u\\z=v\end{cases}$

and $\mathcal D$ is obtained by varying the parameters over $0\le r\le3$ , $0\le u\le2\pi$ , and $0\le v\le6$ . The volume element is

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm du\,\mathrm dv$

so the integral becomes

$\displaystyle\iiint_{\mathcal D}xz\,\mathrm dV=\int_{v=0}^{v=6}\int_{u=0}^{u=2\pi}\int_{r=0}^{r=3}r^2v\cos u\,\mathrm dr\,\mathrm du\,\mathrm dv=0$

2. Now let $\mathcal D$ denote the region bounded by the sphere $x^2+y^2+z^2=4$ and the coordinate planes in the octant in which each coordinate of the point $(x,y,z)$ is negative.

Converting to spherical coordinates, we set

$\begin{cases}x=\rho\cos u\sin v\\y=\rho\sin u\sin v\\z=\rho\cos v\end{cases}$

where we obtain $\mathcal D$ by varying over $0\le\rho\le2$ , $\pi\le u\le\dfrac{3\pi}2$ , and $\dfrac\pi2\le v\le\pi$ . The volume element is now

$\mathrm dV=\rho^2\sin v\,\mathrm d\rho\,\mathrm du\,\mathrm dv$

so the integral becomes

$\displaystyle\iiint_{\mathcal D}z\,\mathrm dV=\int_{v=\pi/2}^{v=\pi}\int_{u=\pi}^{u=3\pi/2}\int_{\rho=0}^{\rho=2}\rho^3\cos v\sin v\,\mathrm d\rho\,\mathrm du\,\mathrm dv=-\pi$

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3 years ago

How to calculate the height of an object using trigonometry

Harrizon [31]

Answer:

${a}^{2} + {b}^{2} = {c}^{2}$

Step-by-step explanation:

a is the height

b is the base

c is the hypotenuse

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3 years ago

Read 2 more answers

Write a word problem with 1/2 as the dividend and 3 as the divisor. Then find the quotient.

Ivenika [448]

Answer: Kaylie has 1/2 of a bottle of soda left. Her 2 friends come over to her house so she gives her and each of them an equal amount. How much soda does each girl get (1/6)

Step-by-step explanation:

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3 years ago

When 334 college students are randomly selected and surveyed, it is found that 103 own a car. Find a 99% confidence interval for

NemiM [27]

Answer:

(.24329, .3734)

Step-by-step explanation:

1-propzint

n=334

x=103

c level .99

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3 years ago

What is the slope and y-intercept of the following equation:<br> = 13 − 4 (show your work pls)

Colt1911 [192]

Answer:

Slope is 1/3

Y intercept is -4

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