14)NO..... -2x+5y=10.....-2(-3)+5(2)=10.....6+10 is not =10
15)YES......-2x+5y=10....-2(-10)+5(-2)=10.....20-10=10
16)YES......-2x+5y=10.....-2(5)+5(4)=10......-10+20=10
Answer:


Step-by-step explanation:
Given


Required
Determine the volume of the solid generated
Using the disk method approach, we have:

Where


So:

Where
So:
Apply the following half angle trigonometry identity;
![\cos^2(x) = \frac{1}{2}[1 + \cos(2x)]](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5B1%20%2B%20%5Ccos%282x%29%5D)
So, we have:
![\cos^2(2x) = \frac{1}{2}[1 + \cos(2*2x)]](https://tex.z-dn.net/?f=%5Ccos%5E2%282x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5B1%20%2B%20%5Ccos%282%2A2x%29%5D)
Open bracket

So, we have:
![V = \pi \int\limits^{\frac{\pi}{4}}_0 {[\frac{1}{2} + \frac{1}{2}\cos(4x)]} \, dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Cint%5Climits%5E%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D_0%20%7B%5B%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5Ccos%284x%29%5D%7D%20%5C%2C%20dx)
Integrate
![V = \pi [\frac{x}{2} + \frac{1}{8}\sin(4x)]\limits^{\frac{\pi}{4}}_0](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5B%5Cfrac%7Bx%7D%7B2%7D%20%2B%20%5Cfrac%7B1%7D%7B8%7D%5Csin%284x%29%5D%5Climits%5E%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D_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)])](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%28%5B%5Cfrac%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B1%7D%7B8%7D%5Csin%284%2A%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5D%20-%20%5B%5Cfrac%7B0%7D%7B2%7D%20%2B%20%5Cfrac%7B1%7D%7B8%7D%5Csin%284%2A0%29%5D%29)
So:
or

Answer:
The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two.