A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h is the height of the ball above the ground, measured in feet. Write an inequality to model when the height of the ball is at least 36 feet above the ground. For how long is the ball at or above 36 feet?​

Given:

The given equation is:

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

The height of the ball is at least 36 feet above the ground. It means .

Splitting the middle term, we get

The critical points are:

These two points divide the number line in 3 intervals .

Intervals      Check point                     Result

              0                               False

                   4                                   True

                 8                                False

The inequality is true for (2,6) and the sign of inequality is . So, the ball is above 36 feet between 2 to 6 seconds.

Therefore, the required inequality is and the ball is 36 feet above for 4 seconds.

c-4 is the final answer! : )

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.