Answer:

Step-by-step explanation:
This problem can be solved by using the expression for the Volume of a solid with the washer method
![V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_a%5Eb%5BR%28x%29%5E2-r%28x%29%5E2%5Ddx)
where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).
Before we have to compute the limits of the integral. We can do that by taking f=g, that is

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)
x1=0.14
x2=8.21
and because the revolution is around y=-5 we have

and by replacing in the integral we have
![V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_%7Bx1%7D%5E%7Bx2%7D%5B%28lnx%2B5%29%5E2-%28%5Cfrac%7B1%7D%7B2%7Dx%2B3%29%5E2%5Ddx%5C%5C)
and by evaluating in the limits we have

Hope this helps
regards
Answer:
z=1.96
Step-by-step explanation:
Using normal distribution table or technology, 97.5% corresponds to z=1.959964, generally denoted z=1.96, or 1.96 standard deviations above the mean.
(above value obtained from R)
Answer:
Step-by-step explanation:
12.
the formula for the volume of a cone is V=1/3hπr²
549.5 = 1/3(21)(3.14)(x)^2
549.5 = 7(3.14)(x)^2
549.5 = 21.98(x)^2
549.5 = 21.98(x)^2
divide by 21.98 on both sides
25 = (x)^2
sqrt 25 = sqrt x^2
5 = x
13.
the formula for the volume of a sphere is V=4/3πr^3
v=4/3(3.14)9^3
v=4/3(3.14)729
v=(4.186)729
v=3052.08
14.
the formula for the volume of a sphere is V=4/3πr^3
523=4/3(3.14)r^3
523=4/3(3.14)r^3
523=(4.186)r^3
divide by 4.186 on both sides
124.92=r^3
cube root on both sides
4.998=r
round
5=r
<em><u>Please mark brainliest this took me a while</u></em>
Answer:
56
Step-by-step explanation:
for this problem you would first figure out what 1/8 of 64 is. 1/8 of 64 is 8.so we do 7*8 to get 56 so 56 of the 64 houses have been sold