Answer:
2x-y-13=0
Step-by-step explanation:
You can see how the difference between two consecutive terms is constantly increasing:




So, for the next terms we'll have to add +9, +11, +13 and so on.
Also, note that
is obtained by adding the 2nd odd number to
,
is obtained by adding the 3rd odd number to
, and so on.
So, the recursive formula is

For the explicit formula, recall that the sum of the first n odd numbers is n squared. Taking into account the fact that we're not starting from 1, we have

Answer:
a) 7.79%
b) 67.03%
c) Cumulative Distribution Function

Step-by-step explanation:
We are given the following in the question:

where x is the duration of a call, in minutes.
a) P( calls last between 2 and 3 minutes)
![=\displaystyle\int^3_2 p(x)~ dx\\\\= \displaystyle\int^3_20.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^3_2\\\\=-\Big[e^{-0.3}-e^{-0.2}\Big]\\\\= 0.0779\\=7.79\%](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint%5E3_2%20p%28x%29~%20dx%5C%5C%5C%5C%3D%20%5Cdisplaystyle%5Cint%5E3_20.1e%5E%7B-0.1x%7D~dx%5C%5C%5C%5C%3D%5CBig%5B-e%5E%7B-0.1x%7D%5CBig%5D%5E3_2%5C%5C%5C%5C%3D-%5CBig%5Be%5E%7B-0.3%7D-e%5E%7B-0.2%7D%5CBig%5D%5C%5C%5C%5C%3D%200.0779%5C%5C%3D7.79%5C%25)
b) P(calls last 4 minutes or more)
![=\displaystyle\int^{\infty}_4 p(x)~ dx\\\\= \displaystyle\int^{\infty}_40.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^{\infty}_4\\\\=-\Big[e^{\infty}-e^{-0.4}\Big]\\\\=-(0- 0.6703)\\= 0.6703\\=67.03\%](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_4%20p%28x%29~%20dx%5C%5C%5C%5C%3D%20%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_40.1e%5E%7B-0.1x%7D~dx%5C%5C%5C%5C%3D%5CBig%5B-e%5E%7B-0.1x%7D%5CBig%5D%5E%7B%5Cinfty%7D_4%5C%5C%5C%5C%3D-%5CBig%5Be%5E%7B%5Cinfty%7D-e%5E%7B-0.4%7D%5CBig%5D%5C%5C%5C%5C%3D-%280-%090.6703%29%5C%5C%3D%200.6703%5C%5C%3D67.03%5C%25)
c) cumulative distribution function

Answer is lots of god Which equation is the inverse of <em>y </em>= 100 – <em>x</em>2?




Answer:
So the radius is increasing at
.
This is approximately 0.00497 cm/min that the radius is increasing.
Step-by-step explanation:

The volume and radius are both things that are changing with respect to time.
So their derivatives will definitely not be 0.
Let's differentiate:

I had to use constant multiple rule and chain rule.
We are given
and
.
We want to find
.
Let's plug in first:



Multiply both sides by 3:


Divide both sides by
:


So the radius is increasing at
.
This is approximately 0.00497 cm/min that the radius is increasing.