40:1,2,4,5,8,10,20,40
60:1,2,3,4,5,6,10,12,15,20,30,60
The GCF between 40 and 60 is 20
Answer:
The answer is 1
Step-by-step explanation:
-50+50=1
Answer:
V = 8.06 cubed units
Step-by-step explanation:
You have the following curves:

In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:
(1)
To determine the limits of the integral you equal both curves f=g and solve for x:

Then, the limits are a = -1 and b = 1
You replace f(x), g(x), a and b in the equation (1):
![V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_%7B-1%7D%5E%7B1%7D%5B%28%5Cfrac%7B13%7D%7B9%7D-x%5E2%29%5E2-%28%5Cfrac%7B4%7D%7B9%7Dx%5E2%29%5E2%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2Bx%5E4-%5Cfrac%7B16%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%20%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2B%5Cfrac%7B65%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5B%5Cfrac%7B169%7D%7B81%7Dx-%5Cfrac%7B26%7D%7B27%7Dx%5E3%2B%5Cfrac%7B65%7D%7B405%7Dx%5E5%5D_%7B-1%7D%5E1%5C%5C%5C%5CV%5Capprox8.06%5C%20cubed%5C%20units)
The volume of the solid of revolution is approximately 8.06 cubed units
for 2a, use the theorems of geometry and such to look at the area of the square as 16 squares total, then use the lengths and Sim/cos rule for the triangular area, then subtract and you have you shaded area.
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
x = 5 x = 4
Step-by-step explanation: