Question 448887
y = -0.042x^2+5x [you left out the 2]
a) The maximum height reached will be the height at which dy/dx = 0
dy/dx = 0 = (2)(-0.042)x + 5
Solve for x:
0 = -0.084x + 5
x = 59.52 ft. along the ground.
Therefore, the maximum height is:
y = -0.042*(59.52)^2 + 5*59.52 = 148.81 ft.
b) We need to set y=0 and solve for x:
0 = -0.042x^2 + 5x
0 = x(-0.042x + 5)
This gives x = 0 [the starting point]
and x = -5/-0.042 = 119.05 ft.
The graph is below:
{{{graph(400,400,-200,200,-200,200,x*(-0.042x+5))}}}