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All 3 of her children will receive 133,333.3333
Check the picture below.
so by graphing those two, we get that little section in gray as you see there, now, x = 6 is a vertical line, so we'll have to put the equations in y-terms and this is a washer, so we'll use the washer method.

the way I get the radii is by using the "area under the curve" way, namely, I use it to get R² once and again to get r² and using each time the axis of rotation as one of my functions, in this case the axis of rotation will be f(x), and to get R² will use the "farthest from the axis of rotation" radius, and for r² the "closest to the axis of rotation".

now, both lines if do an equation on where they meet or where one equals the other, we'd get the values for y = 0 and y = 1, not surprisingly in the picture.
![\displaystyle\pi \int_0^1\left( 3y-3y^2-\cfrac{y^2}{16}+\cfrac{y^4}{16} \right)dy\implies \pi \left( \left. \cfrac{3y^2}{2} \right]_0^1-\left. y^3\cfrac{}{} \right]_0^1-\left. \cfrac{y^3}{48}\right]_0^1+\left. \cfrac{y^5}{80} \right]_0^1 \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{59\pi }{120}~\hfill](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%20%5Cint_0%5E1%5Cleft%28%203y-3y%5E2-%5Ccfrac%7By%5E2%7D%7B16%7D%2B%5Ccfrac%7By%5E4%7D%7B16%7D%20%5Cright%29dy%5Cimplies%20%5Cpi%20%5Cleft%28%20%5Cleft.%20%5Ccfrac%7B3y%5E2%7D%7B2%7D%20%5Cright%5D_0%5E1-%5Cleft.%20y%5E3%5Ccfrac%7B%7D%7B%7D%20%5Cright%5D_0%5E1-%5Cleft.%20%5Ccfrac%7By%5E3%7D%7B48%7D%5Cright%5D_0%5E1%2B%5Cleft.%20%5Ccfrac%7By%5E5%7D%7B80%7D%20%5Cright%5D_0%5E1%20%5Cright%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20%5Ccfrac%7B59%5Cpi%20%7D%7B120%7D~%5Chfill)
Answer:
At 10:30 A.M.
Step-by-step explanation:
A college offers shuttle service from Dickson Hall or Lot B to its campus quad.
At 9:10 A.M the first shuttle leaves from their locations for the campus.
If the shuttles leave from Lot B every 10 minutes and leave from Dickson Hall every 12 minutes, then both the shuttles will leave their origin at the same time after 60 minutes.
This is because 60 is the smallest multiple of 10 and 12 which is common for them.
Therefore, 10:30 A.M. is the next time when both shuttles will depart for the campus at the same time. (Answer)