Question

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)?

2 ≤ w ≤ 5

5 ≤ w ≤ 25

25 ≤ w ≤ 60

60 ≤ w ≤ 300

Answer 1

Not sure, I think it's the last

Answer 2

Even if I'm right can someone explain

Answer 3

Okay, we have piece of cardboard that's \(\underline{definitely}\) going to be 12 inches long, right?

So the only unknown is its width...

Answer 4

Ok

Answer 5

If we let its unknown width be w, what's the area of the rectangle?

Answer 6

Area between 60 and 300

Answer 7

area = lxw

Answer 8

Don't take this the wrong way, but I'm really not interested in your guesses... trust me, it's easier than you might make it out to be ^_^

Answer 9

5x12=60, 25x12=300

Answer 10

Length is 12, width is w
area is....?

Answer 11

a=12xw

Answer 12

That's right. 12w is the area.
And the area has to be between 60 and 300
\[\Large 60 \le 12w \le300\]

Answer 13

so then you divide them both by 12

Answer 14

Yup. Then you get?

Answer 15

5<=12<=25

Answer 16

So it's B... ?

Answer 17

It's not *12* in the middle after you divide all sides by 12 XD

Answer 18

I mean w not 12 sorry

Answer 19

Better. Yes, it's the second choice.

Both of your guesses were wrong, so, avoid guessing ^_^

Answer 20

I've had like 3 hours sleep I apologize

Answer 21

Thanks for the help!

Answer 22

No problem.