A pumpkin is launched from the top of a 20 foot tall platform at an initial velocity of 84 feet per second. The height, h, of the pumpkin at time t seconds after the launch can be modeled by the equation h(t) = −16t 2 + 84t + 20. Find the maximum height reached by the pumpkin

In this problem we have a pumpkin is launched from the top of a 20 foot tall platform at an initial velocity of 84 feet per second. So the height, h, of the pumpkin at time t seconds after the launch can be modeled by the equation:

So this is the equation of a parabola. The maximum of this parabola occurs at its vertex. So let's find this vertex:

Finally, the maximum occurs at time 2.625 seconds when the height is 130.25m

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

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

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)