We can use the fact that, for
,

Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)



By the ratio test, this series converges if

so the series has radius of convergence
.
Answer:
j. Pam, Tia, Veronica, Lily (if it's youngest to oldest)
Step-by-step explanation:
If Tia is 8 yrs old and she's 2 yrs older than Pam, then Pam must be 6 yrs old. Pam si 5 yrs younger than Veronica who must be 11 + 4 = 15.
Tia: 8 yrs.
Veronica: 11 yrs
Pam: 6 yrs.
Lily: 15
Answer:
the equation is 2p-7=25 // p = 16
I assume the cone has equation
(i.e. the upper half of the infinite cone given by
). Take

The volume of the described region (call it
) is

The limits on
and
should be obvious. The lower limit on
is obtained by first determining the intersection of the cone and sphere lies in the cylinder
. The distance between the central axis of the cone and this intersection is 1. The sphere has radius
. Then
satisfies

(I've added a picture to better demonstrate this)
Computing the integral is trivial. We have

Answer:
About 14 - 15 Minutes!
Step-by-step explanation:
24 cents x $12.32 = 295.68 (Multiplication)
295.68/20.00 (Division.)
14.784 (Answer and Estimated.)