A soccer player uses her head to hit a ball up in the air from a height of 1 meters with an initial vertical velocity of 5 meters per second. The height h in meters of the ball is given by h = −4.9t2 + 5t + 1, where t is the time elapsed in seconds. How long will it take the ball to hit the ground if no other players touch it? Enter the time to two decimal places.

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Step-by-step explanation:

The height of the ball after t seconds is given by the following equation:

How long will it take the ball to hit the ground if no other players touch it?

This is t when h(t) = 0. So

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

In this question:

So

So

Since we want a time measure, the answer cannot be negative.

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

that there are 12 data points

step-by-step explanation:

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.