ElectricPavlov

the only way the line can intersect this sideways parabola is if it is at the apex     - b/2a = 3/-4  = - .75

   Sub this value of y into the equation to calculate 'k'

Another way

  the discriminant must = 0 for only one intersection

k = -2y^2-3y+5

0 = -2y^2-3y+ ( 5-k)

    b^2 - 4ac   = 0

    (-3)^2 - 4(-2)(5-k) = 0

     9 +40 - 8k = 0

     49 = 8k

      k = 49/8 = 6 1/8    or   6.125

Use law of sines to find missing side length   then use Heron's Rule to find ara of triangle given 3 sides,

Use law of cosines to find missing side length

   then use   Heron's Rule to find area of triangle given 3 sides

One revolution would be 2pi

7 revolutions would be   14 pi  R

Time in MINUTES   would be      14 pi R    /   32pi/9 rev/min    x  60 s/min  = 236.3 seconds

x^2 + 4x             +   y^2 -6y            = -4

x^2 + 4x + 4     +     y^2 -6y+9      = -4 +4 + 9

(x+2)^2            +     (y-3)^2           = 9

I think you meant    7pi /15    rahter than   7 pi 15 ?

Total circle circumference would be     pi d  =   28 pi

this arc is a fraction of the total

7 pi/15   /   28 pi      x  2pi   =   pi/30 R

When the ball hits the ground   h = 0

sooo   h(t) = 0 = -16t^2 + 93t+3         Use QUadratic formula to find value of 't'

b.       130 = -16t^2 + 93t +3               again use quadratic formula  to find 't' ....there will be TWO of them

                                                                          ....one when ball is going up and one when it is coming down

c.     Put in '4' for   't' and calculate    h(4)    the height of the ball at t = 4 sec

             maximum height will occur at   t = -b/2a     if  4  is less than this value the ball is still going up....

                              if 4 = this value it is at maximum (not going up or down)     if 4 is > than this  , ball is coming down

Use distruibutive property to expand

-2/5 (15)    +  -2/5(-20d)    +  -2/5 (5c)     and simplify

-6               +   8d               -   2c         re-arange to get 

-2c             +8d                  -6                and  factor out  - 2 to get

-2 (3          - 4d                  + c)            

https://web2.0calc.com/questions/please-help_86509#r1

Just use pythagorean theorem

d^2 = 47^2 + 28^2     solve for 'd'   km