The data given for a football kicked from the field follows a quadratic model, h(x) = - 3x2 + 18x +7 . where h(t) is the height in feet and t is the in seconds. using this model, at what time will the ball reach its maximum height

The time at which the ball will reach its maximum height is t= 3 seconds.

Step-by-step explanation:

To find the the time at which the ball will reach its maximum height,  we need to solve the model given - 3x2 + 18x +7

since h(t) is the height given we can re-write the equation as:

h(t)= -3(t)² + 18t +7

Differentiating the above equation

When the ball is at maximum height

0=-6t+18

-18 = -6t

=> t= -18/-6

=> t= 3

the time at which the ball will reach its maximum height is t= 3 seconds.

We can find the maximum height by putting value of t in equation:

h(3) = -3(3)²+ 18(3) +7

h(3)= -27 + 54 + 7

h(3)= 34 ft

\frac{\sqrt{3} }{2}  - .75

Step-by-step explanation:

cot Θ = Sqrt (3)

SinΘ = 1/2                         CscΘ = 2

CosΘ = Sqrt3 /  2              SecΘ = 2Sqrt3 / 3

TanΘ = Sqrt3 / 3               CotΘ = Sqrt (3)

Cotangent is Adjacent over Opposite

Adjacent = Sqrt 3

Opposite = 1

That means the Hyp = 2 (Pythag Theorem)

Sin Θ * Cot Θ - CosΘ ² =

1/2 * Sqrt 3 - .75 = (Sqrt3 / 2) - .75

Sqrt3 / 2 - .75 is as far as I can get.