Question

1) An apple drops off the apple tree from a height of 8 feet. How long does it take the apple to reach the ground? Use the function f(x) = -16x^2 + c, where c is the initial height of a falling object, to find the answer.

2) Trinette cut a square tablecloth into 4 equal pieces that she used to make two pillow covers. The area of the tablecloth was 3600 square inches. What is the side length of each piece Trinette used to make the pillow covers?

3) Elton earns x dollars per hour at the bookstore. His mother, Evelyn, earns x^2 dollars per hour as a career counselor. Twice Evelyn's wage equals $84.50. What is Elton's hourly wage? Round you answer to the nearest cent.​

Answer 1

Part 1)
`(√(2))/(2)\ sec` or
`0.7\ sec`

Part 2) The side length of each piece Trinette used to make the pillow covers is
`30 in`

Part 3) Elton's hourly wage is
`\$6.50`

Explanation:

Part 1)

Let

x------> the time in seconds

we have

`f(x)=-16x^(2)+c`

In this problem the initial height is 8 ft

so

`f(x)=-16x^(2)+8`

To find how long does it take the apple to reach the ground, equate the function to zero and solve for x

`0=-16x^(2)+8`

`16x^(2)=8`

`x^(2)=1/2`

`x=(√(2))/(2)\ sec`

`x=0.7\ sec`

Part 2)

step 1

The area of a square tablecloth is

`A=3,600\ in^(2)`

Divided by 4

`3,600/4=900\ in^(2)`

step 2

Find the length of each piece

`A=b^(2)`

so

`900=b^(2)`

`b=30 in`

Part 3)

we know that

`2x^(2) =84.50`

solve for x

`x^(2) =42.25`

`x=√(42.25)`

`x=\$6.50`