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2 years ago

????????? Help pls & thanks

Mathematics

1 answer:

mina [271]2 years ago

7 0

Top left is the right answer hope this helps <3

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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

30 = −5(6n + 6) multi step equation show all steps pls

lora16 [44]

Step-by-step explanation:

30=-5(6n+6)

30=-5×6n-5×6

30=-30n-30

30+30=-30n

60=-30n

60/-30=-30n/30

-2=n

5 0

3 years ago

Read 2 more answers

Calculate limits x>-infinity<br> -2x^5-3x+1

Lera25 [3.4K]

Given:

The limit problem is:

$\lim_{x\to -\infty}(-2x^5-3x+1)$

To find:

The value of the given limit problem.

Solution:

We have,

$\lim_{x\to -\infty}(-2x^5-3x+1)$

In the function $-2x^5-3x+1$ , the degree of the polynomial is 5, which is an odd number and the leading coefficient is -2, which is a negative number.

So, the function approaches to positive infinity as x approaches to negative infinity.

$\lim_{x\to -\infty}(-2x^5-3x+1)=\infty$

Therefore, $\lim_{x\to -\infty}(-2x^5-3x+1)=\infty$ .

3 0

2 years ago

What is the measure for the following angle?<br>AOC

anygoal [31]

Answer:

40 degrees

cuz 40+40=80

7 0

3 years ago

Keelah's clothing store buys coats for $50 and then sells them for $80 .what is the percent of mark up on the price of the coat

meriva

I would say 10% but I'm not really sure

3 0

3 years ago