CPhill

Pure ethanol  couldn't have a concentration of "95%"....if it's pure, it's 100% ethanol....!!!!

And pure water has a concentration of  0%  ethanol  .......so.....let the amount of pure ethanol to be mixed = x

And....the amount of pure water = 500 - x .......and we have....

100x + 0 (500 - x)  = 70 (500)

100x  = 35000    divide both sides by  100

x = 350 ml  of pure ethanol 

And the amount of water  = 500 - 350  = 150 ml

cos (3z + pi) = 0      using a trig identity, we have :

cos(3z)cos(pi)  - sin(pi)sin(3z)     =  0

-cos(3z)  = 0

cos(3z)  = 0

cos(z)  = 0   at   pi/2 + n*pi

So

3z  = pi/2 + n*pi       divide both sides by 3

z = pi/6  + n* (pi/3)   where n is any integer

The general "formula"  for the nth term is :

(n + 2)^2     for n >= 1

Using

Vf  = Vi  -9.8t       where Vi  is the initial velocity  [ = 0]   and Vf is the final velocity = -112m/s

So we have

-112 = -9.8t         divide both sides by -9.8

-112 / -9.8   = t  ≈  11.429 s

Just multiply   .14 x 80

(2x+2)/(-1x+3)  = .3       multiply both sides by (-1x + 3)

2x + 2  =  .3(-1x + 3)      simplify

2x + 2  = -.3x + .9       subtract 2 from both sides.....add .3x to both sides

2.3x   =  -1.1      divide both sides by 2.3

x = -1.1 / 2.3   = -11/23

Hey, rarinstraw......I'm fine......

Just type in the fractions that you want to add, subtract, etc.

The shaded area xan be represented as :

Total area - Area of Path =

[x(x + 4)  -  1x] m^2  =

[x^2 + 4x - 1x ] m^2 =

[ x^2 + 3x ] m^2

Type  1.07     hit the x^y  key     type 30      hit   =