CPhill

-16t^2 + 80t =  36

-16t^2 + 80t  - 36 =  0          divide through by -4

4t^2  -20t + 9  = 0

(2t -1) (2t - 9)  = 0

The first factor set =  0  is what we need

2t -  1 =  0

2t =1

t =  1/2 sec =  .5 sec

Rule for rounding to  nearest 10th.....look at the 100ths place....if its  4 or less keep the 10ths digit

If it's   5  or greater  round the 10ths place up by 1

So.....using this rule :

A =  14.5

B =  14.5

C =  14.4

D =  14.6

cos X  =  sqrt (13^2 -3^2)  /13  =  sqrt (160) / 13  =  (4/13)sqrt (10)

Multiply through by  2004x  and we  have

2003x^2  + 2004x + 2004   =  0

Call the roots  a, b

The sum of the reciprocals =   1/a + 1/b  =  (a + b)  / (ab)

The sum of the roots =  -2004/2003   = a+ b

The product of the  roots  = 2004/2003

So....the sum of the reciprocals =   (-2004 /2003) / ( 2004 /2003 )  =   -1    !!!!!

17/5 < x <  17+ 1/5

3.4 < x < 17.2

Sum  =  [ 4 + 5 + 6 + .... + 17 ]  =

Sum of first 17 positive integers  - Sum of first 3 positive integers

[(17 ) (18) / 2]  -  6   =  17*9 - 6  =    147

Sum of first n odd integers  = n^2  where n is the number of odd integers

Sum =  2021^2

Mean  =    2021^2  / 2021  =   2021

jaz^2   = (4) (a+7) (a + 5)^2  =

4 ( a + 7) (a^2 + 10a + 25)  =

(4a + 28) (a^2 + 10a + 25) =

4a^3  + 40a^2  + 100a

+          28a^2   + 280a  + 700

_________________________

4a^3 + 68a^2 + 380a + 700

Geometric Sum  where  r = 1.12   

   9 [ 1 - (1.12)^5] /  [ 1 -  1.12 ]  ≈  57 miles

8 /125 * blank =  5/2     multiply both sides by 125 / 8

blank =   (5/2) (125/8)  =  625 / 16

The form is x^2  + bx + c

Sum of the roots = 11 =  -b   →  b  = -11

Product of the roots =  c = 28

The quadratic  is     x^2  -11x + 28