Arrange the fractions from the largest to the smallest.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify y

Drupady [299]

Answer:

$V = \frac{\pi^2}{8}$

$V = 1.23245$

Step-by-step explanation:

Given

$y = \cos 2x$

$y = 0; x = 0; x = \frac{\pi}{4}$

Required

Determine the volume of the solid generated

Using the disk method approach, we have:

$V = \pi \int\limits^a_b {R(x)^2} \, dx$

Where

$y = R(x) = \cos 2x$

$a = \frac{\pi}{4}; b =0$

So:

$V = \pi \int\limits^a_b {R(x)^2} \, dx$

Where

$y = R(x) = \cos 2x$

$a = \frac{\pi}{4}; b =0$

So:

$V = \pi \int\limits^a_b {R(x)^2} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {(\cos 2x)^2} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx$

Apply the following half angle trigonometry identity;

$\cos^2(x) = \frac{1}{2}[1 + \cos(2x)]$

So, we have:

$\cos^2(2x) = \frac{1}{2}[1 + \cos(2*2x)]$

$\cos^2(2x) = \frac{1}{2}[1 + \cos(4x)]$

Open bracket

$\cos^2(2x) = \frac{1}{2} + \frac{1}{2}\cos(4x)$

So, we have:

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {[\frac{1}{2} + \frac{1}{2}\cos(4x)]} \, dx$

Integrate

$V = \pi [\frac{x}{2} + \frac{1}{8}\sin(4x)]\limits^{\frac{\pi}{4}}_0$

Expand

$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})] - [\frac{0}{2} + \frac{1}{8}\sin(4*0)])$

$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})] - [0 + 0])$

$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})])$

$V = \pi ([{\frac{\pi}{8} + \frac{1}{8}\sin(\pi)])$

$\sin \pi = 0$

So:

$V = \pi ([{\frac{\pi}{8} + \frac{1}{8}*0])$

$V = \pi *[{\frac{\pi}{8}]$

$V = \frac{\pi^2}{8}$

or

$V = \frac{3.14^2}{8}$

$V = 1.23245$

4 0

3 years ago

Evaluate 6t-20-32u when t=6 and u=1/4

ankoles [38]

Answer:

8

Step-by-step explanation:

6t - 20 - 32u = ?

t = 6 u = 1/4 [.25]

6*(6) - 20 - 32*(1/4)

36 - 20 - 8 = ?

? = 8

i hope this helps!

:)

it would mean a lot if you marked as brainliest :)

4 0

3 years ago

-x+y-z=17, 4x+3y+z=-10, 2x+y+3z=0

mario62 [17]

Answer:

x = -11, y = 10, z = 4

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

5 0

3 years ago

A recipe for 1 batch of spice mix says, “Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of sa

otez555 [7]

Answer:

There is no diagram for our observation. Please refine your question next time.

Step-by-step explanation:

7 0

3 years ago

Please answer this for me. i have no idea :( please please please, i am desperate.

marysya [2.9K]

<h3>Answer: B) 60</h3>

================================================

Explanation:

Whenever the angle theta is between 0 and 90, the reference angle is exactly that value.

It's only when you get to other quadrants is when things get a bit tricky. Right now we're in quadrant 1, often written as Q1.

-------------------

Extra info:

If theta is between 90 and 180, then the reference angle is 180-theta. This region is Q2
If theta is in quadrant 3, between 180 and 270, then the reference angle is theta-180. The order of subtraction is important since x-y is the not the same as y-x.
Lastly, if theta is between 270 and 360 (in Q4), then the reference angle is 360-theta.
As you can see, we have four quadrants starting with Q1 in the upper right corner. Then we move counterclockwise to get Q2,Q3 and Q4.

7 0

3 years ago

Read 2 more answers