word problem and interval notation

rj2001 · #1 $Old$ April 14th, 2007, 09:33 PM

I never liked wp's

the perimeter of a standard rug is 44ft the length is 2ft longer than the width find the dimensions width and length anyone please?

interval notation of the set {xl -2 > x > 6}

is it (-6 -2) ?

Jhevon · #2 $Old$ April 14th, 2007, 10:05 PM

Quote:

Originally Posted by rj2001 $View Post$

I never liked wp's

the perimeter of a standard rug is 44ft the length is 2ft longer than the width find the dimensions width and length anyone please?

interval notation of the set {xl -2 > x > 6}

is it (-6 -2) ?

Are you sure this is the right question? to have an interval for such a question, we need an inequality. there's no inequality here.

let width = x
=> length = x + 2
=> Perimeter = 2x + 2(x + 2) = 44
=> 2x + 2x + 4 = 44
=> 4x + 4 = 44
=> 4x = 40
=> x = 10

so the width is 10 and the length is 12

so the rug is a 10 x 12 rug

EDIT: oh, the interval thing is for the second question, ok i'll do that...what is xl?

Jhevon · #3 $Old$ April 15th, 2007, 02:38 AM

ok, so {x| -2> x > 6} makes no sense. what you are actually saying is x is less than -2 but greater than 6. I think it should be {x| -2 < x < 6}, that is, x is greater than -2 but less than 6.

so in interval notation that would be (-2,6). we use parenthesis as oppsosed to square brackets since x cannot be equal to either of the values at the end points.

Soroban · #4 $Old$ April 15th, 2007, 06:46 AM

Hello, rj2001!

Is that interval problem stated correctly?
If it is, it's not the way we should write it.

Quote:

interval notation of the set {x l -2 > x > 6}

It says: x > 6 . (x is greater than 6)
. . and: -2 > x . (x is less than -2)

This is clearly impossible; a number cannot be greater than 6 and less than -2.

The intent could have been: .x < -2 .or .x > 6

And the interval would be: .(-∞, -2) U (6, ∞)

rj2001 · #5 $Old$ April 15th, 2007, 08:04 AM

hi yeah sorry for not making it clear that was 2 problems in one post

but yeah the second one is on our online homework (mymathlab) multiple choice

Write interval notation for the set

{ x l -2 > x >-6 } the l = absolute value bar? but just one no close

answers are
(-6,-2)
[-6,-2]
[-6,-2)
(-6,-2]

this is a review from a chapter wayy back and I think he read it x is such that? something dunno if that will help

janvdl · #6 $Old$ April 15th, 2007, 10:33 AM

x is between -2 and -6, but neither of the two numbers is included.
Which means that x is not equal to either -2 or -6, but lies between them.

For the rug:
Perimeter = 2L + 2B
But L = (x + 2)
B = (x)

44 = 2(x + 2) + 2(x)
44 = 4x + 4
x = 10

Thus B = 10
And L = 10 + 2 = 12