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4 years ago

15

What is x minus 3 over x^2 minus 25 over x^2 minus 9 over x minus 5?

1 answer:

hichkok12 [17]4 years ago

6 0

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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

The function f(x) = 1.50x – 30 gives the amount of money Amelia has to spend each week for x school lunches, after taking money

Naya [18.7K]

To find the inverse, switch the x and y, and then solve for y (f(x) is the same as y)

So we get:
x=1.50y-30 (add 30 to both sides)
x+30=1.50y (divide both sides by 1.5)
x/1.5+30/1.5=y
y=x/1.5+20

Hope this helps

7 0

3 years ago

A home file is the place where you should keep financial records that you may need to access regularly? True or False

alex41 [277]

True! we have an excel file called moneydoc.xls

6 0

3 years ago

Read 2 more answers

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!

Juli2301 [7.4K]

Answer:

QPN and TSU

Step-by-step explanation:

They're both exterior angles and they are both alternate to each other.

4 0

3 years ago

9 - x = 6; x = 15 6x = 24; x = 6 35 = 5x; x = 7 x + 10 = 21; x = 31 <br> which one is right

ycow [4]

Answer:

35 = 5x ; x = 7

Step-by-step explanation:

plug 7 in for x

35 = 5(7)

35 = 35

hope this helps!!!

6 0

3 years ago

Read 2 more answers