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:
7,000 is the answer
Step-by-step explanation:
Answer:
73 and 113 / 144 ft^2
Step-by-step explanation:
Lets convert everything into pure feet.
10ft 5in = 10 and 5/12 feet = 125/12 feet
14ft 2in = 14 and 1/6 feet = 85/6
Now lets calculate area:
1/2 * 125/12 * 85/6 = 125*85 / 144 = 73 and 113/144
If you multiply all the square inches, you would get 15,015
Two inequalities are equivalent if they have the same set of solutions.
x - 5 ≤ 6 - 5
x - 5 ≤ 1 |add 5 to both sides
x ≤ 6