Question

The height of an object can be modeled by the function H(t)=-8t^(2)+48t+40, where H(t) is the height in feet after t seconds.

Answer 1

To find the height of the object after 5 seconds, we need to substitute t = 5 into the equation.

Here are the steps:

1. Replace t with 5 in H(t) = -8t^2 +48t + 40.
- H(5) = -8*(5^2) + 48*5 + 40

2. Follow the order of operations, which is parentheses, exponents, multiplication and division, and addition and subtraction. This is often remembered by the acronym PEMDAS.

3. Square 5 (because of the exponent 2) in -8*(5^2):
- H(5) = -8*25 + 48*5 + 40

4. Multiply -8 with 25:
- H(5) = -200 + 48*5 + 40

5. Multiply 48 with 5:
- H(5) = -200 + 240 + 40

6. Add the three numbers together:
- H(5) = 80

So, the height of the object after 5 seconds would be 80 feet.