Can y’all help me on question 39?!

Pllsss help

torisob [31]

Answer:

[8.6,oo)

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

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

Is (0,0) a solution to this system? y ≤ x^2 + x - 4 y < x^2 + 2x + 1

yaroslaw [1]

( 0,0 ) is not the solution of the first inequality y≤x² +x-4 but ( 0,0) is the solution for the second inequality y <x²+2x+1.

<h3>What is inequality?</h3>

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than’

Finding the solution for the inequality is as follows:-

y ≤ x² +x-4 by putting x and y equal to 0.

0 ≤ 0 + 0 -4

0 ≤ - 4

This is incorrect so (0,0) can not be the solution for this inequality.

y < x²+2x+1.

0 < 0 + 0 + 1

0 < 1

This inequality is showing the solution for (0,0)

Therefore ( 0,0 ) is not the solution of the first inequality y≤x² +x-4 but ( 0,0) is the solution for the second inequality y <x²+2x+1.

To know more about inequality follow

brainly.com/question/24372553

#SPJ1

5 0

2 years ago

Help Me Please.................(5)

just olya [345]

The answer is 5 you’re welcome

6 0

3 years ago

A sandwich shop offers the following toppings. How many two topping sandwiches can you make? -lettuce -tomato -bacon -cheese -mu

lina2011 [118]

Lettuce & tomato, lettuce & bacon , lettuce & cheese , lettuce & mustard
tomato & lettuce , tomato & bacon , tomato & cheese , tomato & mustard
bacon & lettuce , bacon & tomato , bacon & cheese , bacon & mustard
cheese & lettuce, cheese and tomato, cheese & bacon , cheese & mustard
mustard & luttuce , mustard & tomato , mustard & Bacon , mustard & cheese

THE ANSWER IS D.) 20
BECAUSE ITS PROPORTIONAL REALTIONSHIP TO FIND OUT MORE WHAT THE MEAN YOU MAY LOOK IT UP ON A SITE CALLED KHAN ACADEMY

8 0

4 years ago