The equation p(x)=−x2+50x+500 models the height of a projectile, in feet, after x seconds. after how many seconds will the projectile reach its maximum height?

25 seconds

Step-by-step explanation:

we have

This is the equation of a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum height of the projectile

The x-coordinate of the vertex is the time in seconds that the projectile takes to reach its maximum height.

Convert the quadratic equation in vertex form

we have

Factor -1

Complete the square

Rewrite as perfect squares

The vertex is the point (25,1,125)

therefore

The maximum height of the projectile is 1,125 feet

The time in seconds that the projectile takes to reach its maximum height is 25 seconds

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft