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Homework Help: Can you help me graph this inequality?

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    The possible solution to a problem I've been working on is this:
    note that all the < are actually less than or equal to.
    could someone show me exactly how to get this graph and/or what it looks like? I would really appreciate it :)
  2. jcsd
  3. Nov 22, 2009 #2


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    Staff: Mentor

    Welcome to the PF. Your notation seems a little off to me. f(x) does not equal what you have shown as the right hand side(s) (RHS). If you take away the f(x)=, then you have an inequality that you can plot and find the solution for.

    So if you take a piece of xy graph paper (or a graphing calculator or Excel or whatever), and graph the 5 functions:

    f(x) = 100

    f(x) = 200/(3x+300)

    f(x) = 500

    f(x) = 200*sin(2x)+300

    f(x) = 33.33333x+600

    What is the region that satisfies the inequalities?
  4. Nov 22, 2009 #3
    Thanks berkeman :)

    I'm not sure if I'm doing this right at all anymore. The idea was supposed to be to have a function that started at 300 and gradually increasing to 500 so the peak would be (3,500). Then it was supposed to fluctuate up and down rapidly as it approached y=100 at x=15.

    So, my thought was that if the function was linear until (3,500) and became sinusoidal (I thought about it last night and it will probably have to be a cos, whatever) from there on out, it could "bounce" off the lines y=33.333x+600 and y=100, making it so it would fluctuate more and more as it approached (15,100). Is there a way to make it do this and not have a piecewise function? Part of my assignment is to have it be a single formula, hence all the inequalities together. :)

    Would this be better described as an affine transformation or something else using matrices?

    Thank you again :)
    Last edited: Nov 22, 2009
  5. Nov 22, 2009 #4


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    Staff: Mentor

    Can you please post the original question in its entirety? A lot is being lost in the translation and transcription.

    It now sounds like you are given a piecewise function (not an inequality), and asked to formulate a single equation representing the same? That can be done using step funtions with offsets on the horizontal axis, if needed.
  6. Nov 27, 2009 #5
    Oops, sorry that it took so long to reply (thanksgiving craziness...you know)

    anyways, the question is this:
    design a new thermal cycle for a heat treatment system using processes such as annealing, quenching, and tempering. This treatment must fit the following requirements:
    Last 15 hours
    Oven starts at 300 degrees C
    Oven ends at 100 degrees C
    The temperature must gradually increase for the first few hours until it reaches 500 degrees
    Then it must dramatically and rapidly go up and down in temperature.
    Finally, it must gradually cool for several hours and smoothly approach 100 degrees.
    Note that it can only increase in temperature at a rate of 3 degrees per minute, and it can cool at 5 degrees per minute BUT the rate of change should not be above 4 degrees per minute per 10 minutes.

    does what I suggested make sense with this? Have the function start out linearly and then become sinusoidal at 3 hours and then have this sinusoidal line reflect between the line sloped to equal 100 degrees at 15 hours and a horizontal line on the bottom that is equal to 100? Or more importantly, is there any way to make a sinusoidal line that kind of "bounces" off other lines kind of like how the absolute value of a line gets to zero and then "bounces" in a perpendicular slope?
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