Question

The function
`h(t) = -16t^2 + 75t + 25` shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by
`g(t) = 5 + 5.2t`, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 2 through 5 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know?

Part B: Explain what the solution from Part A means in the context of the problem.

Answer 1

Step-by-step explanation:Part A:

To find the solution to H(t) = g(t), we need to compare the height function H(t) to the height function g(t) and determine when they are equal. Let's create a table using the integers 2 through 5 for both functions:

| t | H(t) | g(t) |

|------|--------|--------|

| 2 | ? | ? |

| 3 | ? | ? |

| 4 | ? | ? |

| 5 | ? | ? |

To fill in the table, we need the specific functions for H(t) and g(t) provided in the question.

Once we have the values of H(t) and g(t) for each second from 2 to 5, we can compare them to find the solution to H(t) = g(t). The solution will be the time interval between two consecutive seconds when H(t) is equal to g(t).

Part B:

The solution from Part A, which represents the time interval between two seconds when H(t) = g(t), has a specific meaning in the context of the problem. Since H(t) represents the height of one baseball and g(t) represents the height of another object, finding the solution to H(t) = g(t) indicates the moments when both baseballs are at the same height.

In other words, the solution represents the points in time when the two objects are level with each other vertically. It could be interpreted as the instances when the baseballs could potentially collide or cross paths in the air.

By determining the time interval between two seconds when H(t) = g(t), we can identify the specific moments when the heights of the baseballs align and analyze their potential interactions or relationship during those instances.

Answer 2

Look below:

Explanation:

Part A:

To create a table for the functions H(t) and g(t), we need to substitute the values 2 through 5 for t in both functions.

For example, let's calculate the values for H(t) and g(t) when t = 2:

- Substitute t = 2 into the function H(t): H(2) = ?

- Substitute t = 2 into the function g(t): g(2) = ?

Repeat this process for t = 3, t = 4, and t = 5 to complete the table.

Once you have the table with the corresponding values for H(t) and g(t), find the interval where the solutions to H(t) = g(t) are located. Look for the rows in the table where the values of H(t) and g(t) are equal.

Part B:

The solution to H(t) = g(t) represents the time(s) when the height of the baseball given by the function H(t) is equal to the height of the object given by the function g(t).

In the context of the problem, finding the solution tells us the specific time(s) when both the baseball and the object are at the same height. This can be used to determine if the baseball will hit the object or if they will pass each other at different times.

By analyzing the table and identifying the interval where the solutions are located, you can determine the time range when the baseball and the object will have the same height.