Answer:
A) 150
B)30
Step-by-step explanation:
Answer:
y = (-13/11)x - 5/11
Step-by-step explanation:
Where's the list of equations from which you're to choose?
The line that connects points (-8 ,9) and (3, -4) has the following slope:
9 - (-4)
m = ----------------- = -13/11
-8 - 3
Then the new line with this slope is y = (-13/11)x + c
and because (-8, 9) satisfies this equation, 9 = (-13/11)(-8) + c, and we need to calculate c from this. 9 = 104/11 + c, or
-c = 104/11 - 99/11, or - 5/11
Then the desired equation is y = (-13/11)x - 5/11
Answer:
Step-by-step explanation:
For this case we are interested on the region shaded on the figure attached.
And we can find the volume with the method of rings.
The area on this case is given by:
![A(x) = \pi [f(x)]^2 = \pi r^2 = \pi [3x]^2 = 9\pi x^2](https://tex.z-dn.net/?f=%20A%28x%29%20%3D%20%5Cpi%20%5Bf%28x%29%5D%5E2%20%3D%20%5Cpi%20r%5E2%20%3D%20%5Cpi%20%5B3x%5D%5E2%20%3D%209%5Cpi%20x%5E2)
And the volume is given by the following formula:

For our case our limits are x=0 and x=2 so we have this:

And if we solve the integral we got this:
![V= \pi [\frac{x^3}{3}]\Big|_0^{2}](https://tex.z-dn.net/?f=%20V%3D%20%5Cpi%20%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5D%5CBig%7C_0%5E%7B2%7D)
And after evaluate we got this:
![V=\pi [(\frac{8}{3} )-(\frac{0}{3} )]](https://tex.z-dn.net/?f=%20V%3D%5Cpi%20%5B%28%5Cfrac%7B8%7D%7B3%7D%20%29-%28%5Cfrac%7B0%7D%7B3%7D%20%29%5D)
3 plus 5 equal 2 and minus 60