Question

Help someone plz

A student needs to make a rectangular cardboard piece that is 12 inches long. The area of the cardboard piece should be between 60 square inches to 300 square inches. The function f(w) relates the area of the cardboard, in square inches, to the width w in inches. Which of the following shows a reasonable domain for f(w)?

A: 2 ≤ w ≤ 5

B: 5 ≤ w ≤ 25

C: 25 ≤ w ≤ 60

D: 60 ≤ w ≤ 300

Answer 1

Option B

`5 \leq w \leq 25`

Explanation:

Let

L------> the long of the cardboard piece

W-----> the width of the cardboard piece

The area of cardboard piece is equal to

`A=L*W`

In this problem we have

`L=12\ in`

so

`A=12W`

`f(W)=12W`------> equation A

`f(W)\geq 60\ in^(2)` ------> inequality B

`f(W)\leq 300\ in^(2)` ------> inequality C

Substitute equation A in the inequality B

`12W\geq 60\ in^(2)`

`W\geq 60/12`

`W\geq 5\ in`

Substitute equation A in the inequality C

`12W\leq 300\ in^(2)`

`1W\leq 300/12`

`1W\leq 25\ in`

The domain for the function f(W) is equal to the interval------>
`[5,25]`

Answer 2

area = L x w

60 = 12 x w

w=60/12 = 5

300 = 12 x w

w = 300/12 = 25

so B is the correct answer