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
I’m sure it’s the last one D
#1. look at the individual probability first.
A dice has 6 sides. The numbers > 2 are {3, 4, 5, 6}. So the chance of rolling a number > 2 is 4/6 or 2/3 simplified.
Multiples of 3 on a dice are {3, 6}. So the chance of rolling a multiple of 3 is 2/6 or 1/3 simplified.
Rolling a dice is an independent event, like flipping a coin the previous roll does not have an effect on the outcome of the next roll. So when you see the word AND connecting the outcomes, you multiply them.
Prob of rolling >2 AND then multiple of 3 = (2/3)*(1/3)
= 2/9
#2. The total socks in the drawer: 8+8+4= 20 socks
The probability of first drawing a blue sock is 8/20 or 2/5 simplified.
Since the question does not say the socks are put back in the drawer, the total number of socks and number of blue socks decrease by 1 after the first draw. This makes the next draw dependent on the first.
The probability of drawing a blue sock is then: 7/19
because there's a blue sock missing.
Probability of drawing blue sock AND then a blue sock (without replacement)
= (2/5)*(7/19)
= 14/95
Answer:
Rotation
Step-by-step explanation:
The third one is true
because 3 is subtracted from a number.if you say that a number subtract from 3 it will be:
3–x
good luck
