ElectricPavlov

y = 110

110 = -16t^2 + 26t + 105

0 = -16t^2 + 26t -5                     Now use Quadratic Formula to calcualte 't' values,,,

                                                        the smaller t will be on the way up...the larger will be on the way down

a = -16  b = 26  c = -5

\(t = {-26 \pm \sqrt{26^2-4(-16)(-5)} \over 2(-16)}\)

Here is what I think is the answer

p = k / d^4

35 = k / (375⁴)

k = 6.92 x 10 ^11 m⁴ - uW

1.5 km = 1500 m

p = 6.92 x 10 ^11 m⁴ - uW  / (1500 m)⁴  = 1.37 x 10^-1 uW

(This applies to radar waves returning to the reciever/transmitter.....I believe wave power diminishes inversely to the SQUARE of the distance.....so this may not be the answer you are looking for.....it may be   p = k / d^2

     in this case the answer would be 2.187 uW )

The Quadratic Formula is a method of calculating the value(s) of 'x' that solve the quadratic of form

y = a x²  + b x   + c      the x values can be found by plugging   a ,  b and c into the formula and computing:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

60 - 46 = 14 dollars to buy data

14/3 = 3 2/3     since he can only buy whole gigabytes, he can only buy  ~ 3 Gb data

 = x^2 + 10x   = 0

     x ( x + 10)     = 0      x = 0    or  -10  

x = 3.333333...

y = x^2 + 23x -3        complete the square for 'x'

y =   (x+11.5)^2  - 132.25  -3

y =   (x+11.5)² - 135.25     <===== finish from here !

= t^2 +2t + 9             bowl shaped parabola ....   minumum value will be at  t = -b/2a   =  - 2 / (2*1)  = -1    

Use Vieta's calcs

ab = -5/7

a+b = -1/7

1/a + 1/b      multiply first term by b/b    second term by  a/a

b/ab  +  a/ab  =  ( b + a )/ab    sub in the red values above

1/a + 1/b   =  (-1/7) / (-5/7 ) =  1/5

30 * x = 120     divide both sides of the equation by '30' to find 'x'