$48.47. $33.20 + $18.33= $51.53
$51.53 - $100.00= $48.47
Keisha ran 2.4 miles more than Jamal.
Keisha ran 8.5 miles, how many miles did Jamal run?
m = the number of miles Jamal ran
2.4 + m = 8.5
[Keisha ran 2.4 more miles than Jamal(m), she ran a total of 8.5 miles]
2.4 + m = 8.5 Subtract 2.4 on both sides
m = 6.1
Jamal ran 6.1 miles (Your answer is the 2nd option)
In 2 weeks and it will be 60 minions
Answer:
About the x axis
![V = 4\pi[ \frac{x^5}{5}] \Big|_0^2 =4\pi *\frac{32}{5}= \frac{128 \pi}{5}](https://tex.z-dn.net/?f=%20V%20%3D%204%5Cpi%5B%20%5Cfrac%7Bx%5E5%7D%7B5%7D%5D%20%5CBig%7C_0%5E2%20%3D4%5Cpi%20%2A%5Cfrac%7B32%7D%7B5%7D%3D%20%5Cfrac%7B128%20%5Cpi%7D%7B5%7D)
About the y axis
![V = \pi [4y -y^2 +\frac{y^3}{12}] \Big|_0^8 =\pi *\frac{32}{3}= \frac{32 \pi}{3}](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cpi%20%5B4y%20-y%5E2%20%2B%5Cfrac%7By%5E3%7D%7B12%7D%5D%20%5CBig%7C_0%5E8%20%3D%5Cpi%20%2A%5Cfrac%7B32%7D%7B3%7D%3D%20%5Cfrac%7B32%20%5Cpi%7D%7B3%7D)
About the line y=8
![V = \pi [64x -\frac{32}{3}x^3 +\frac{4}{5}x^5] \Big|_0^2 =\pi *(128-\frac{256}{3} +\frac{128}{5})= \frac{1024 \pi}{5}](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cpi%20%5B64x%20-%5Cfrac%7B32%7D%7B3%7Dx%5E3%20%2B%5Cfrac%7B4%7D%7B5%7Dx%5E5%5D%20%5CBig%7C_0%5E2%20%3D%5Cpi%20%2A%28128-%5Cfrac%7B256%7D%7B3%7D%20%2B%5Cfrac%7B128%7D%7B5%7D%29%3D%20%5Cfrac%7B1024%20%5Cpi%7D%7B5%7D)
About the line x=2
![V = \frac{\pi}{2} [\frac{y^2}{2}] \Big|_0^8 =\frac{\pi}{4} *(64)= 16\pi](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5B%5Cfrac%7By%5E2%7D%7B2%7D%5D%20%5CBig%7C_0%5E8%20%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%20%2A%2864%29%3D%2016%5Cpi)
Step-by-step explanation:
For this case we have the following functions:

About the x axis
Our zone of interest is on the figure attached, we see that the limit son x are from 0 to 2 and on y from 0 to 8.
We can find the area like this:

And we can find the volume with this formula:


![V = 4\pi [\frac{x^5}{5}] \Big|_0^2 =4\pi *\frac{32}{5}= \frac{128 \pi}{5}](https://tex.z-dn.net/?f=%20V%20%3D%204%5Cpi%20%5B%5Cfrac%7Bx%5E5%7D%7B5%7D%5D%20%5CBig%7C_0%5E2%20%3D4%5Cpi%20%2A%5Cfrac%7B32%7D%7B5%7D%3D%20%5Cfrac%7B128%20%5Cpi%7D%7B5%7D)
About the y axis
For this case we need to find the function in terms of x like this:

but on this case we are just interested on the + part
as we can see on the second figure attached.
We can find the area like this:

And we can find the volume with this formula:


![V = \pi [4y -y^2 +\frac{y^3}{12}] \Big|_0^8 =\pi *\frac{32}{3}= \frac{32 \pi}{3}](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cpi%20%5B4y%20-y%5E2%20%2B%5Cfrac%7By%5E3%7D%7B12%7D%5D%20%5CBig%7C_0%5E8%20%3D%5Cpi%20%2A%5Cfrac%7B32%7D%7B3%7D%3D%20%5Cfrac%7B32%20%5Cpi%7D%7B3%7D)
About the line y=8
The figure 3 attached show the radius. We can find the area like this:

And we can find the volume with this formula:


![V = \pi [64x -\frac{32}{3}x^3 +\frac{4}{5}x^5] \Big|_0^2 =\pi *(128-\frac{256}{3} +\frac{128}{5})= \frac{1024 \pi}{5}](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cpi%20%5B64x%20-%5Cfrac%7B32%7D%7B3%7Dx%5E3%20%2B%5Cfrac%7B4%7D%7B5%7Dx%5E5%5D%20%5CBig%7C_0%5E2%20%3D%5Cpi%20%2A%28128-%5Cfrac%7B256%7D%7B3%7D%20%2B%5Cfrac%7B128%7D%7B5%7D%29%3D%20%5Cfrac%7B1024%20%5Cpi%7D%7B5%7D)
About the line x=2
The figure 4 attached show the radius. We can find the area like this:

And we can find the volume with this formula:


![V = \frac{\pi}{2} [\frac{y^2}{2}] \Big|_0^8 =\frac{\pi}{4} *(64)= 16\pi](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5B%5Cfrac%7By%5E2%7D%7B2%7D%5D%20%5CBig%7C_0%5E8%20%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%20%2A%2864%29%3D%2016%5Cpi)