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3 years ago

9

To observe a session of the state senate, 18 students are visiting the state capitol. They will tour the capital in groups with

x chaperones.
Complete the table. How many students will be in each group if x = 9?

1 answer:

inysia [295]3 years ago

6 0

Answer:9

Step-by-step explanation:

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Simple interest on a bank loan can be calculated by multiplying the principal times the interest rate times the time. In the for

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I = interest/simple interest

So your answer is D.

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A sphere of radius r is cut by a plane h units above the equator, where

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Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

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3 years ago

NEED THIS ASAPWrite the standard form of the equation of each line given the slope and y-intercept

Mama L [17]

<em>Note:</em>

<em>Your first question is missing the y-intercept, so I am solving the 2nd question. You would still get your concept clear because the procedure to solve each of the questions is the same.</em>

Question 2

Answer:

The equation in the standard form is:

2/3x + y = -4

Please also check the attached graph.

Step-by-step explanation:

We know that the equation in the standard form is

Ax + By = C

where x and y are variables and A, B and C are constants

Given

Slope m = -2/3

y-intercept = -4

To determine

Write the equation in the standard form

We know that the slope-intercept form of the line equation

$y = mx+b$

where

m is the slope

b is the y-intercept

In our case:

Slope m = -2/3

y-intercept = -4

substituting m = -2/3 and y-intercept b = -4 in the slope-intercept of the line equation

y = mx+b

y = -2/3x + (-4)

y = -2/3x - 4

Writing the equation in the standard form

2/3x + y = -4

Therefore, the equation in the standard form is:

2/3x + y = -4

Please also check the attached graph.

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3 years ago

What is 9-3y=x I don't know this one

torisob [31]

The answer is
y= - x-9/3 I believe.
1- Subtract 9 from both sides.
-3y = x - 9
2- Divide both sides by -3
y = - x-9/3

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devlian [24]

No i don’t think so

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