Answer:
The volume is:
Step-by-step explanation:
See the sketch of the region in the attached graph.
We set the integral using washer method:
Notice here the radius of the washer is the difference of the given curves:
So the integral becomes:
We solve it:
Factor 
out and distribute the exponent (you can use FOIL):
Notice: 
So the integral becomes:
Then using the basic rule to evaluate the integral:
Simplifying a bit:
Then plugging the limits of the integral:
![\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cleft%5B%5Cfrac%7B4%5E3%7D%7B3%7D-%5Cfrac%7B4%284%29%5E%7B5%2F2%7D%7D%7B5%7D%2B%5Cfrac%7B4%5E2%7D%7B2%7D-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B4%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cright%5D)
Taking the root (rational exponents):
![\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cleft%5B%5Cfrac%7B4%5E3%7D%7B3%7D-%5Cfrac%7B4%282%29%5E%7B5%7D%7D%7B5%7D%2B%5Cfrac%7B4%5E2%7D%7B2%7D-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B4%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cright%5D)
Then doing those arithmetic computations we get:
Answer and Step-by-step explanation:
The answer is H.
When 4 is brought to the power of a number it gets multiplied to the numerator of 1/3. When inputting those numbers for x in this function, the result is what is shown on the table, meaning the function is correct.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>
Answer:91
Step-by-step explanation:
If the best grade is 100,91 is it.
Answer:
Step-by-step explanation:
Parameterize the ellipse as (acos∙,bsin∙). Take points P:=(acosp,bsinp) and Q:=(acosq,bsinq) on the ellipse, with midpoint M:=(P+Q)/2.
If |PQ|=2k, then
a2(cosp−cosq)2+b2(sinp−sinq)2=4k2
The coordinates of M are
xy==a2(cosp+cosq)b2(sinp+sinq)
