All categories

3 years ago

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

Mathematics

1 answer:

kherson [118]3 years ago

7 0

Answer:

$=\frac{364\pi}{3}$ cubic units

Step-by-step explanation:

We are to find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

f(x)=2x+1, y=0, x=0, x=4.

The picture is given as shaded region.

This is rotated about x axis

Limits for x are already given as 0 and 4

f(x) is a straight line

The solid formed would be a cone

Volume = $\pi \int\limits^a_b {(2x+1)^2} \, dx \\= \pi \int\limits^4_0 {(4x^2+4x+1)} \, dx \\=\pi [\frac{4x^3}{3} +2x^2+x]^5_0\\\\=\pi[\frac{4*4^3}{3}+2*4^2+4-0]\\=\frac{364\pi}{3}$

You might be interested in

This is an isosceles trapezoid. R. s 75 X Y У T U

LekaFEV [45]

Answer:

S=R

75+75=150

360-150=210

210/2=105

y=105

5 0

3 years ago

Read 2 more answers

What is the length of segment AB?

AlekseyPX

Answer:

length of segment AB is 13

AB = 13

Step-by-step explanation:

Use the Pythagorean Theorem with c being the length of segment AB.

a^2 + b^2 = c^2

5^2 + 12^2 = c^2

169 = c ^2 (square root both sides to get c by itself)

13 = c

5 0

3 years ago

Solve for .

bezimeni [28]

Answer:

smaller x =-1/2

larger x = 7

Step-by-step explanation:

(x-7)(-4x - 2) = 0

Using the zero product property

(x-7)=0 (-4x - 2) = 0

x-7+7 = 0+7 -4x-2-2 =0+2

x=7 -4x =2

-4x/-4 = 2/-4

x = -1/2

4 0

3 years ago

Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the

Lera25 [3.4K]

Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given $h=1+2s$ where $h$ is the hypotenuse and $s$ is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with $h$ , "is" with $=$ , "1 foot more than" with $1+$ and finally "twice the length of the shorter leg" with $2s$ .

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with $L$ .

I'm going to replace "is" with $=$ .

I'm going to replace "7 feet longer than the shorter leg" with $7+s$ .

So we have the equation $L=7+s$ .

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: $s^2+L^2=h^2$ .