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3 years ago

9

30% of ________is $75?

1 answer:

Helga [31]3 years ago

4 0

The answer to this is 250.

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Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =

Strike441 [17]

Answer:

The volume is:

$\displaystyle\frac{37\pi}{10}$

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

$\displaystyle\int_a^b\pi r^2dx$

Notice here the radius of the washer is the difference of the given curves:

$x-\sqrt{x}$

So the integral becomes:

$\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx$

We solve it:

Factor $\pi$ out and distribute the exponent (you can use FOIL):

$\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx$

Notice: $x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}$

So the integral becomes:

$\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx$

Then using the basic rule to evaluate the integral:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{2x^{5/2}}{5/2}+\frac{x^2}{2}\right|_1^4$

Simplifying a bit:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4$

Then plugging the limits of the integral:

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Taking the root (rational exponents):

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Then doing those arithmetic computations we get:

$\displaystyle\frac{37\pi}{10}$

6 0

2 years ago

What is the area of a bedroom thats 12 ft in length and 10 ft in width?

ludmilkaskok [199]

Answer:

120 sq ft.

Step-by-step explanation:

REMEMBER: Area is found by multiplying one side, by the other side that isn't the same length as it.

Multiply 12 by 10 to get 120

120 is the area of the bedroom

3 0

2 years ago

-3(5n-8)=-8(n-3)<br><br> Please Hurry

BartSMP [9]

Answer:

$- 3(5n - 8) = - 8(n - 3)$

$- 15n + 24 = -8 n + 24$

$- 15n + 8n = 24 - 24$

$- 7n = 0$

$n = \frac{0}{ - 7}$

$n = 0$

6 0

2 years ago

The numbers in this sequence increase by the same amount each time.

PilotLPTM [1.2K]

Answer:

2, 4, 6, 8 , 10

Step-by-step explanation:

7 0

2 years ago

What is the value of x in the function f (x)=4/3x+6 when f (x) = 22?<br> x=?

mamaluj [8]

Answer:

$x=12\\$

Step-by-step explanation:

$f(x)=22\\\\\frac{4}{3}x +6=22\\\\\frac{4}{3}x=16\\\\x= 12$

8 0

2 years ago