Answer:
28.25 square units
Step-by-step explanation:
A circumference of the circle is

where r is the radius of the circle.
So,

The area of the circle is

Substitute the value of the radius:
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:
1.4
Step-by-step explanation:
Probability of selecting a red counter :
Number of red counter / total number of counters
5 / (5 + 3) = 5 /8 = 0.625
Probability of selecting a blue counter = 0.375
Let number of red counters :
0, 1 or 2
0 red counters :
Expected value = x * p(x)
0 + (0.625*1) + (0.390625 * 2)
0 + 0.625 + 0.78125 = 1.40625
Expected number of red counters = 1.4
Answer:
slope = -1
Step-by-step explanation:
y2-y1 divided by x2-x1
3-7= -4
2-(-2) = 4
-4 divided by 4 = -1
The answer to -3-8+(-4) is -15