Results 1 to 2 of 2

Thread: Polynomial inequality - word problem

  1. #1
    Junior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    48

    Question Polynomial inequality - word problem

    Hi,

    I hope someone can help. I'm trying to solve for the following question:

    Polynomial inequality - word problem-screen-shot-2017-04-13-4.29.12-pm.png
    <= "less than or equal to"
    >= "greater than or equal to"

    These are my steps:
    1. I know that the volume of a rectangle is l x w x h - therefore the inequality to the equation must be x(50 - 2x)(30 - 2x) <= 4000, where x represents the height, 50 - 2x represents the width, and 30 - 2x represents the length.
    2. Find the roots to the inequality: x = 0, x = 25, and x = 15
    3. Create intervals for the corresponding roots: x <= 0, 0 <= x <= 15, 15 <= x <= 25, x >= 25
    4. Identify values within those intervals, then sub those intervals within the inequality equation. If the outcome is less than or equal to 4000, then consider this a range of the side lengths. These ranges would represent my solution(s) to this question.

    The textbook solution 5 < x < 7.19. My solution is wrong so I would appreciate some guidance on where I went wrong in my steps.

    Sincerely,
    Olivia
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,687
    Thanks
    3469

    Re: Polynomial inequality - word problem

    2. Find the roots to the inequality: x = 0, x = 25, and x = 15
    the correct inequality is $x(50 - 2x)(30 - 2x) > 4000$

    roots of the inequality are where $x(50-2x)(30-2x) - 4000 = 0$

    the values of $5 < x < 7.19$ yield a volume $\ge 4000 \, cm^3$
    Attached Thumbnails Attached Thumbnails Polynomial inequality - word problem-vol1.png   Polynomial inequality - word problem-vol2.png  
    Last edited by skeeter; Apr 13th 2017 at 01:19 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inequality Word Problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Dec 20th 2016, 05:12 PM
  2. inequality word problem
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Jul 18th 2013, 07:57 AM
  3. Inequality word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 7th 2012, 08:34 PM
  4. Inequality word problem!
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Aug 21st 2012, 09:34 PM
  5. Inequality Word Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Feb 14th 2008, 01:34 AM

Search Tags


/mathhelpforum @mathhelpforum