Question

A wire 24 inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of x. a. Express the area A of the rectangle as a function of x. b. Determine the domain of of the function

Answer 1

since the shortest side is x, do you know what is the length of the other side?

Answer 2

24-x?

Answer 3

close but it is actually (12-x).... do you know why?

Answer 4

for a. I got 12-x^2 but I don't know how to get b

Answer 5

ohhh

Answer 6

(shortest side) + (other side) = 12

since the perimeter is 24, then:
2(shortest side) + 2(other side) = 24

Answer 7

so now, to get the area, just multiply: Area = (shortest side) * (other side)
what u got now?

Answer 8

x(12-x)=12x-x^2

Answer 9

how do i find the domain?

Answer 10

good...
Area = 12x - x^2

Answer 11

now, what do you think is the domain?

Answer 12

here's a hint...
what can x be?

Answer 13

uhhh how would you solve it? would it be all real numbers because i plugged it into my graphing calculator and it looks like it is

Answer 14

definitely not... x cannot be 30 because the wire is 24 inches long.....

Answer 15

so x cannot be all real numbers...

Answer 16

remember what x represents?

Answer 17

the shorter side of the rectangle

Answer 18

and how long can that be?

Answer 19

ohhh so would that mean that its like less than 12

Answer 20

so would it be like [1,12)

Answer 21

correct...:) but what?

Answer 22

oops (0,12) ?

Answer 23

not [1, 12)

Answer 24

i agree with the left part of (0, 12)... but not that right part "12)"... do you know why it cant be something like 8?

Answer 25

OHHHHHH BECAUSE THERES TWO SIDES

Answer 26

SO ITS LESS THAN SIX?

Answer 27

very good!!!

Answer 28

GODDAMMIT RECTANGLES SUCK

Answer 29

so what's the domain?

Answer 30

(0,6)

Answer 31

nicely done... :)

Answer 32

omg thanks

Answer 33

yw....:)