-7.5 is the answer to the question you were looking for
Answer:
hello your question is incomplete here is the complete question
Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81
Answer : ![\frac{4 \pi }{3} [729 - 65\sqrt{65} ]](https://tex.z-dn.net/?f=%5Cfrac%7B4%20%5Cpi%20%7D%7B3%7D%20%5B729%20-%2065%5Csqrt%7B65%7D%20%5D)
Step-by-step explanation:
The given data
cylinder = x^2 + y^2 = 16
sphere = x^2 + y^2 +z^2 = 81
from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then multiply the sesult by 2
Note : we are restricting our attention to the cylinder x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well
the r parameter goes from 0 to 4
ATTACHED IS THE REMAINING PART OF THE SOLUTION
showing the integration
The best method would be to cross-multiply. Multiply the figure on the top left with the bottom right. Then set it equal to the multiplication of the bottom left with the top right.
This would turn into:
-1(x-1)=2(x+3) Then distribute the multiplication through the parentheses.
-x+1=2x+6 Next, get all the variables on one side, and the integers on another.
2x+x=1-6
3x= -5
x= -5/3
4b+1 equivalent to -2(b+4)+3
Answer:
a
Step-by-step explanation:
its obvious