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)
![V=\pi [28x+\frac{1}{x}+xln^2x-12xlnx-6lnx]](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5B28x%2B%5Cfrac%7B1%7D%7Bx%7D%2Bxln%5E2x-12xlnx-6lnx%5D)
and by evaluating in the limits we have
Hope this helps
regards
Answer:
6.5in
Step-by-step explanation:
find the area of the shaded regions
fine the surface area of the square
A = 2×2
A = 4
find the area of the triangle
A = 1/2bh
A = 1/2×2×2.5
A = 2.5
add the areas
2.5+4 = 6.5
The answer to this one will be C
Hope this helps :)
Answer:3/7
Step-by-step explanation:
3 * 1/7 is
3 * 1 = 3
Divided by 7 = 3/7
There’s nothing to simply, as that fraction cannot be reduced
First we have to know the formula of the volume f each of the solids,
<span>V of sphere = 4/3 pi r^3
</span><span>Volume of Cylinder = pi r^2(2r)=2pi r^3
</span><span>Volume of cone = 1/3 pi r^2(r)=1/3 pi r^3
</span>
The surest and easiest way we can answer this is actually assigning values. We first assign values to r hence we would get the volume of the sphere and rest of the solids (cylinder and cone). You then compare your answers to that of the sphere, and you should get your answer.
