Suppose that a baseball is thrown upward with an initial velocity of 132 feet per second (90 miles per hour) and it is released 4 feet above the ground. its height h after t seconds is given by hequalsminus16tsquaredplus132tplus4 . after how many seconds does the baseball reach a maximum height?

it will take 8.25 seconds to reach maximum height

Step-by-step explanation:

Initial velocity, u of baseball = 132 feet per second. The height of the baseball, h in feet after t seconds is given by the function h = −16t^2 + 132t + 4

The given function is a quadratic equation. If values of height attained is plotted against time, the graph will take the shape of a parabola whose vertex corresponds to the maximum height attained by the baseball

Vertex of the parabola = -b/2a

a = - 16

b = 132

Vertex = - 132/-16× 2 = -132/32

Vertex = 4.125

The maximum height is 4.125 feets

To determine the time it will take to reach the maximum height of 4.125 feets, we will substitute h = 4.125 in the equation

4.125 = −16t^2 + 132t + 4

−16t^2 + 132t - 0.125 = 0

Applying the general formula for quadratic equations,

t = [- b ± √b^2 - (4ac)]/2a

a = -16

b = 132

c = -0.125

t = [- 132 ± √132^2 - 4(-16 × - 0.125)]/2× -16

t = [- 132 ± √17424 - 8)]/-32

t = [- 132 ± √17416]/-32

t = (-132 ± 132)/-32

t = (-132 + 132)/-32 or (-132 -132)/-32

t = 0 or -264/-32

t = 8.25 seconds

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )