ElectricPavlov

K =   9x         and    9x-5 is a multiple of 8

   9x-5  multiple of 8

   9-5    no

   18-5

    27-5

   36-5    no but getting close

   45-5 = 40       yes!                    x = 5         9x = 45    9x-5 = 40  

She could also be 117      but unlikely !  

1/x   + 1/(2x)  = 1/ 4

solve for x  = 6 hours for the faster 

m = 7c-1

c = m-29 =  (7c-1) - 29 

c = 7c -1   -29                    solve for c   

x^2 = 84 + 5x

x^2 -5x-84 = 0     Use quadratic formula to find value(s) of 'x'  

4x^2 + 20x + 4y^2 - 24y + 21

Divide thrugh by 4

x^2 +5x +y^2-6y = -21/4      ' complete the square '   for x and y

(x+2.5)^2    +   (y-3)^2  = -21/4  + 6.25  + 9 

                                      =  -21/4  + 25/4 + 36/4 = 40/4 = 10

10 = r^2     r = sqrt 10

y= -2x +8      slope = -2     perpindicular slope =  -1 / -2 = 1/2

y = 1/2 x +b     sub in the given point

2 = 1/2 (9) + b     b= -2.5

y = 1/2 x -2.5

1/2 (12-p) *2 =   12-p  unit²

35 x   +   15 (55-x)   = 1325       solve fo x, the gallons used by the 35 mpg car.... then the other is   55-x

Amplitude is 13    so the wave goes from 13   to  -13     AND it is shifted UP by 24

    so max height will be   13 + 24 = 37ft       min height will be   -13 + 24 = 11 ft

Min height will be when the cos fxn = 1     

   when    cos (............) = -1     (0 degrees)

       pi x /60 - 5pi/12 = 0

          x = 25 min    or   8:25

Max height will occur   when    -13 ( cos ( pix/60 - 5pi/12) = 13

        or in other words, when      cos ( pi x / 60 - 5pi/12)   = -1      pi x/60 - 5pi/12 =   pi       x = 85 minutes =  9: 25