A ball is thrown into the air with an upward velocity of 44 ft/s. It’s height h in feet after t seconds is given by the function h=-16t^2 +44t+5. How long does it take the ball to reach its maximum height? What is the balls maximum height?

9514 1404 393

1.375 seconds35.25 feet

Step-by-step explanation:

A quadratic function y=ax^2 +bx +c is symmetric about the vertical line x=-b/(2a). That is the x-coordinate of the vertex (maximum or minimum).

Here, we have ...

  h = -16t^2 +44t +5

  t = -44/(2(-16)) = 11/8 = 1.375

It takes 1.375 seconds for the ball to reach its maximum height.

The height at that time is ...

  h = (-16(11/8) +44)(11/8) +5 = (-22 +44)(11/8) +5 = 121/4 +5 = 141/4 = 35.25

The maximum height is 35.25 feet.

To find the area of the triangle, you will need to know the length of the base and there length of the height.

You can find both of these by using the circles that are given.

If the total length of the circles is 35 cm, then each circle has a length of 7 cm. If these are circles, then each circle has a height of 7 cm also.

A = 1/2 x b x h
1/2 x (4x7) x (2x7)
A = 196 square cm