An orange is shot up into the air with a catapult. The function h given by h (t) = 15+60t-16t^2 models the orange's height, in feet, t seconds after it was launched select all the true statements about the situation.

Complete question is:An orange is shot up into the air with a catapult. The function h given by h (t) = 15 + 60t - 16t² models the orange's height, in feet, t seconds after it was launched.

Select all the true statements about the situation.

Options:

1. The domain of function h only contains values greater than or equal to 0.

2. The orange is at the same height 1 second after launch and 2 seconds after launch.

3. After 3 seconds, the orange has hit the ground.

4. The orange is 15 feet above the ground when it is launched.

5. The value t = 10 does not belong to the domain of h.

Answer:

Option 1 - True

Option 2 - False

Option 3 - False

Option 4 - True

Option 5 - True

Step-by-step explanation:

Looking at the options,

-The domain is the x or t value and it is time. Now, time can only be positive or greater than or equal to zero i. e. t ≥ 0. Thus, option 1 is true.

- At t = 1 second;

h = 15 + 60 (1) - 16 (1) ²

h = 15 + 60 - 16 = 59 ft

Also, at t = 2 seconds;

h = 15 + 60 (2) - 16 (2) ²

h = 15 + 120 - 64 = 71 ft

So, value of h is not the same at t = 1 and t = 2. Thus, option 2 is not true.

- The orange will hit the ground when h (t) = 0.

However, at t = 3;

h (t) = 15 + 60 (3) - 16 (3) ²

h (t) = 51 ft

h (t) is not equal to zero at t = 3, so option 3 is false

- when the orange is launched it is at time t = 0.

Thus,

h (0) = 15 + 60 (0) - 16 (0) ²

h (0) = 15 ft

So option 4 is true.

- At t=10, h (t) = 15 + 60 (10) - 16 (10) ²

h (10) = - 985

This means the orange would be below ground level and thus doesn't belong to the domain of h, so option 5 is true.