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
Multiply 3.3 by everything in the parenthesis.
3.3x - 26.4 - x = 1.2
Combine like terms.
2.3x - 26.4 = 1.2
Add 26.4 to both sides.
2.3x = 27.6
Divide 2.3 on both sides.
x = 12
Hope this helps!
<span>D) perpendicular bisector <em>I believe.
</em></span>
Answer:
Step-by-step explanation:
2. area of a triangle is 1/2 b h
1/2 (5 * 2) = 5 yd squared
area of the circle is pi r squared
you only need 1/2 of this area
find all these areas and add them together.
6. this is just a square sitting on a rectangle.
36 x 36 for the square
36 x 60 for the rectangle
add these together.
8. this a 1/2 circle and a triangle.
area of a circle is pi r squared
r is 7 in this problem
the area of a triangle is 1/2 b h
height is 7x2 here or 14
add the two together.
