Aball is thrown into the air with an upward velocity of 24 ft/s. its height h in feet after t seconds is given by the function h=-16t+24t+7. in how many seconds does the ball reach its maximum height? round to the nearest hundredth if necessary. what is the ball’s maximum height?

The line of symmetry for the parabola described by

... y = ax²+bx+c

is given by

... x = -b/(2a)

That line for your parabola is

... t = -24/(2×(-16)) = 24/32 = 3/4 = 0.75

The vertex (maximum) lies on this line. The value of h at that point is

... h = -16(3/4)² + 24(3/4) + 7 = -9 + 18 + 7 = 16

The ball reaches its maximum height in 0.75 seconds.

The ball's maximum height is 16 ft.

table 3 represents a direct variation function. : )

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240