CPhill

Are we supposed to see an image, NSS??

Thanks, hectictar, for catching that mis-type.  I fixed it ...and you're correct.....perfect fit....!!!

Look at the graph of the data points, here :

https://www.desmos.com/calculator/o7kuhjqe3b

Neither "C" nor "D"   [ both linear ]  will model the data

It appears from the graph that  "B" is the best choice

Note  .......derivative of arctan (u)  =   1 / ( 1 + u^2) * du  .....so......

f(x)  =   arctan (sin (5x))   =   [  1 /  [ 1 + (sin(5x) )^2]  * 5 cos (5x)  =

[ 5 cos (5x) ]  /  [ 1 + sin²(5x) ]

y  =  0^(-5)   =  1 / 0^5   =  1 / 0    =  undefined

30 days / 16.8 inches  ≈  1.786 inches per day

1. (  [ 8 - 6] / 8 * 100)% =   ( 2 / 8 * 100)%  = ( 1/4 * 100)%  = 25% discount

2.  45.50 + .20*45.50  =  $54.60

3. 150* (.300  =  $45 savings

4. 200000 * .03   =  $6000  commission

5. Basketball 18 - .20*18  =  $14.40

    Baseball  =  30  - 30*.30  =  $ 21       the basketball is cheaper

The new area will be [ scale factor]^2 times the old area

Old Area  =  2 * 3  = 6 inches^2

New Area  =  6 * [ 3 ]^2   =  6 * 9   = 54 inches^2

[35 + .20 (35) ] / 2  =  [ 35 + 7 ] / 2   =  42 / 2  =  $21 each

The increase is given by

(4/3) pi [ 9^3 - 3^3 ]  ≈  2940.53  cu ft