ElectricPavlov

tan 30 =  opposite side / adjacent side

1/sqrt3  = 9 sqrt3 / PQ         SOLVE for PQ            (  1/sqrt3  is tan 30 )

Here is one way to find the quadratic

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)   =  (7+- sqrt23i)/2        so  a  =1   and b = -7

x^2 -7x + c              to find c      sqrt(  -7^2-4(1)(c))  = sqrt 23i        

                                  solving for c = 18

x^2-7x+18 =0                            

.075 km / (x -6) = 15

x = 24 k/hr  is the speed of the train

If the person was standing still

  the time required would be     .075/24 x 3600 = 11.25 seconds    so for the train to pass in 7.5 seconds, the person must be walking TOWARD the train

    so walking the same direction as the train at 6 k/hr   takes 15 seconds

        standing still takes  11.25 seconds

            the second person has to be walking TOWARD the train for the train to pass in 7.5 seconds

                and they have to be walking at a rate of   .075/(24+x ) = 7.5/3600    x=12 km/hr    TOWARD the train !!!!

(110 m + 240m) = 350 miles

3 hours + 240m / 60m/hr = 7 hrs total       350 m/ 7hr = ......... m/hr

1 nickel   + 1 dime + 1 quarter  = 40 cents

how many ways can you make 35 cents with n d q

1 q   2n

1 q   1 d

2 d  3 n

3 d   1 n

5 n    1 d

7 n

    I think that is it.....  6 ways

Slope is defined as   rise / run         1/x = .45

 x = 1/.45  = 2.22 units

cos = -1/2    at   120^o

^{120 -30 = 90     sin 90 = 1}

Multiply bottom equation by 3 to get

9x+3y=21   now add the top equation to get

17x= 51

x = 3                   You can now solve for y....take it away ....

Since we are looking for 'h' , let's put dimensions in terms of 'h'

h    

l = h-3

l = 2w    or   1/2 l = w     so w = 1/2(h-3)

surface area =   2 (lh) + 2 wh + 2 wl

                           2 ((h-3)(h)    + 2(1/2h-1.5)(h)   +  2 (1/2h-1.5)(h-3)

                            2 h^2  - 6h   + h^2- 3h           + h^2-6h+9

                            4 h^2 -15h+9    = 100

                             4 h^2 -15h-91 = 0              Quadratic formula shows h = 7    

Easiest to look at it on a graph   then     11+0i     and  5  - 10 i    look to be solutions

https://www.desmos.com/calculator/dtvkny3kpe