On a given dive, a platform diver’s body follows a path that can be modeled by the equation d = −4t^2 + 2t + 6, where d represents the diver’s distance above the water after t seconds. Use this information to determine how long it will take a diver to reach the water’s surface.

t = 1.5 seconds

Step-by-step explanation:

Given that d = −4t^2 + 2t + 6,

where d = distance above the water and

t = seconds.

Let assume that it's a perfect parabola

At the symmetry

t = -b/2a

Where a = -4, b = 2

t = -2/2(-4)

t = 1/4

To determine how long it will take a diver to reach the water’s surface

d = −4t^2 + 2t + 6

At water surface d =0

4t^2 - 2t - 6 = 0

Factorizing the above equation leads to

4t^2 + 4t - 6t - 6 = 0

4t(t + 1) -6(t + 1) = 0

4t - 6 =0

4t = 6

t = 6/4= 3/2 = 1.5 seconds

Since t can't be negative so we ignore the second factor.

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.