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2 years ago

Can someone help me?

Mathematics

1 answer:

galina1969 [7]2 years ago

8 0

Answer:

What are you trying to do you have not Explained to us

Step-by-step explanation:

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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

3 years ago

What is the mean of the data ?

julia-pushkina [17]

Answer:

maryland

Step-by-step explanation:

3 0

3 years ago

What is the answer for this

Leviafan [203]

I think that
the triangle is 6
the square is -5
and the star is -20
but i would get a second answer bc i cant certainly say that<span />

6 0

3 years ago

Please helpppp meeeee

aalyn [17]

Answer:

Step-by-step explanation: d I think

7 0

3 years ago

Read 2 more answers

Filip is inviting 6 friends to a party. Each friend wants 5 cookies and each box has 8 cookies. How many boxes should Filip get?

Alecsey [184]

Flip should get 4 boxes.

6*5=30
30/8=3.75
round up for 4.

3 0

1 year ago