ElectricPavlov

You are describing    a = k b/c       where k is some constant (often '1')

a = 12 =  k 4/5      yields k = 15  

so   a = 15 b/c

15% off leaves 85 %

400 (.85) = 340 

Kinetic ENergy = 1/2 m v^2        200 kg ?   REALLY?  that is almost 440 lbs !

= 1/2 (200) (8^2) = 6400 j

First, multiply both sides of the equation by 3 to get:

3V = Bh      then divide both sides by h

3V/h = B

To calculate the VOLUME of a cube , realize that  volume is given by Length x Width x Height     ( L x H x W)

However, for a CUBE   L = W = H    so the volume is give by

L^3       or     W^3      or     H^3

Not EXACTLY sure I understand  'from the horizon of the Earth'  , but I assume it is referring to a tangential line from the satellite to the earths surface.   In this case we have a RIGHT triangle with hypoteneuse equal to the distance we are looking for....

Pythagorean theorem  :    13200^2 + 4000^2 = d^2      d = 13792.75 miles

This 'd' is to the CENTER of the Earth....we must subtract the RADIUS to find the distance to the SURFACE
13792.75 - 4000 =  9792.75 Miles

2.5 R  /   (2 x pi )/360  radians/circle  = 143.23944degrees   = 143 Degrees 14 minutes  (and 22 seconds)

A Quadratic EQUATION is generally of the form  ax^2 + bx + c = 0

The QUADRTIC FORMULA can be used to solve quadratic EQUATIONS in this form for 'x'

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

Break them up into their prime factors and take the common ones to get the HCF

32  =  2 x 2 x 2 x 2 x 2

40  =  2 x 2 x 2 x 5                 2 x 2 x 2  are common factors = 8

Seems we go through this every few weeks

(-4)^2 =16

-4^2  =  -(4^2) = -16    as explained by Alan