ElectricPavlov

8 8 12

9 9 10

10 10 8

11 11 6

12 12 4

13 13 2

Re-write as   x^2 + 10x = 0

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

Image below

Use cosine law     BC^2 = 8^2 + 13^2 - 2 ( 8)(13) cos 30         You can finish.... remember : this is to find BC²

re-write as

x^2 - kx + 8 = 0          discriminant of Quadratic Formula must be < 0 for no real roots

b^2 - 4ac < 0

k^2 - 4(1)(8) < 0

k^2 < 32

k  <   sqrt 32         sqrt 32 = 5.65    so largest integer would be 5

Taking a really long time to download the diagram........

distance / rate = time

upriver    11 / (r-c)  = 4.4 hr         r = speed if paddling in still water         c = current speed

             re-arrange to     c = (11-2r)/2

    downriver  11/ (r+c) = 2     sub in the red equation then sovle for r

                    r = 4 km/hr     

Use this result in either of the upstream or downstream equations to find c = 1.5 km/hr

If no current    :   11 km / 4 km/hr = 2.75 hrs       2 hrs 45 min

x = money at 5% interest

10000 -x    = money at 16%

.05 x  +  .16 ( 10000 - x ) = 775

x = 7500 at 5%        then 2500 at 16 %

Their differnce in speed is   2 mph

1/6 hr * 18 m/hr = 3 miles to go when Anna finishes

Anna gets ahead 2 miles every hour          3 miles /2m/hr = 1.5 hr for anna to finish       1.5 hr x 20 m/hr = 30 mile bike race

Take 1/2 of the x coefficient ....then square it

5/4 * 1/2 = 5/8         square it:   25 / 64

x^2 + 5/4 x + 25 / 64                is equal to   (x + 5/8)²

m/n   *    n/p   * p/q      =   15  * 1/3 * 1/10                   See how things 'cancel out' and you are left with  m/q  ? 

m/q = 1/2