ElectricPavlov

x = x0 + vot + 1/2 a t^2         In this instance x0 = original position = 0   vo = original velocity = 0

so you are left with  x = 1/2 a t^2  = 1/2 (32) (1.4)^2 = 16 ( 1.96) = 31.36 ft deep  (using 'a' = 32)

Divie by 3 to get   3:4:7

Least Common Multiple ????   966,000

$ 450,000 worth of pencils is a LOT of pencils !

Markup 9 % = .09         450,000 (1.09) = $ 490500. 

If he sold them all and got this much money, that is a HUGE profit because he spent only  3600 + 450,000

Profit = GROSS income - costs =    490500  - (450,000 + 3600)  = $ 36,900.

SECOND question:

x = the number

2x = twice the number

-2x =two times the  opposite of number

so:  (2x) = 16 + (-2x)

        2x = 16 -2x

        4x = 16

           x = 4

Let x=full mug

1/2 x  = half full     2/3 x = 2/3 full

1/2 x + 4dl  = 2/3 x     Solve for 'x'

4 = 2/3 x - 1/2 x

4 = 1/6 x

24 dl = x      Which is 2.4 liter

NOT SURE, but if you simplify it and do some 'completing of the squares', you will get

16(x-2)^2 - 9(y-1)^2 = 145

A graphing calculator will show this to be a hyperbola with axes of symmetry  x = 2    y = 1

Here is what you are given:      v = k  1/p     Where 'k' is a constant

84 = k (1/16)      Yields k = 1344

v = 1344 (1/p)     Now substitute for the new 'p'      v = 1344 (1/12) = 112 liters

ANOTHER way     p1/p2 = v2/v1   (they are inverse)       p1/p2 x v1 = v2     16/12  x 84 = 112

You are describing:

.34 (x) = 16.32      Divide both sides by .34

x = 16.32/.34 = 48

Not sure what you are trying to accomplish.

If you MULTIPLY both sides by 't'

(n)(t) = ms            

The ARC LENGHT will be a fraction of the CIRCUMFERENCE of the circle

Angle/ 360  x Circumference = ARC LENGTH