Results 1 to 9 of 9

Thread: Polynomial inequality

  1. #1
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    288
    Thanks
    2

    Question Polynomial inequality

    Hi,

    I hope someone can help. I'm trying to solve 11b and 11c:
    Polynomial inequality-screen-shot-2017-04-13-4.18.39-pm.png

    For 11b - I don't understand why the solution is only 0 < 154.75 Celsius. I see other parts of this graph where v > 0, namely on the left-hand side of the y-axis, so I'm curious why this is not included in the solution. For example, I see v > 0, when x < -6.676 and in between -2.42 < x < 3.095 - this is without the 50 Celsius conversion. Can someone please provide clarification on this?

    For 11c - I just don't know where to start in order to find this solution, so guidance would be appreciated. The solution is 133.78 degrees celsius to 139.56 degrees celsius.

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

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    Re: Polynomial inequality

    For 11b - I don't understand why the solution is only 0 < 154.75 Celsius. I see other parts of this graph where v > 0, namely on the left-hand side of the y-axis, so I'm curious why this is not included in the solution. For example, I see v > 0, when x < -6.676 and in between -2.42 < x < 3.095 - this is without the 50 Celsius conversion. Can someone please provide clarification on this?
    the function is a mathematical model for viscosity for realistic temperatures (not all real values of $t$) ... the negative value where $v$ changes from positive to negative is $\approx -334^\circ \, C$ ... fyi, absolute zero is $\approx -273^\circ \, C$.

    For 11c - I just don't know where to start in order to find this solution, so guidance would be appreciated. The solution is 133.78 degrees celsius to 139.56 degrees celsius.
    graph y=15 and y=20 on the calculator and determine the intersections (see screenshots) ... multiply both x-values by 50
    Attached Thumbnails Attached Thumbnails Polynomial inequality-temp1.png   Polynomial inequality-temp2.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,577
    Thanks
    1711

    Re: Polynomial inequality

    Hey otownsend.

    Hint - Can you find the roots of the function along the derivatives at each root?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    288
    Thanks
    2

    Re: Polynomial inequality

    Why isn't anything before 0 not a "realistic temperature"?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,770
    Thanks
    2417

    Re: Polynomial inequality

    Quote Originally Posted by otownsend View Post
    Why isn't anything before 0 not a "realistic temperature"?
    I believe he meant anything below $-273^\circ C$ is unrealistic as absolute zero is as cold as is theoretically possible. (even in Canada!)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    Re: Polynomial inequality

    Quote Originally Posted by otownsend View Post
    Why isn't anything before 0 not a "realistic temperature"?
    I didn't say that ... you did. I said the value of $t = -6.676$ was not realistic.

    coldest-temperature-recorded-earth-antarctica-guinness-book

    What value of $t$ would this correspond to in your given model?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    288
    Thanks
    2

    Re: Polynomial inequality

    okay I understand now why -6.676 would not be realistic as this above be below the temperature of absolute zero. So then why doesn't the ranges between -2.42 < x < 3.095 work?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    Re: Polynomial inequality

    $-2.42 < t < 3.095$ corresponds to the temperatures between $-121.99^\circ \, C$ and $154.77^\circ \, C$

    the question asks for the temperature range where viscosity is positive ... your stated solution gives the upper bound as $154.77^\circ \, C$ (close).

    I do not know why the answer cuts it off at zero for the lower bound. Clearly, $-121.99^\circ \, C$ is colder than the lowest temperature ever recorded on Earth.

    You'll just have to ask your instructor why the lower bound was zero. Maybe the graph represents a climate where it doesn't get below freezing.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    288
    Thanks
    2

    Re: Polynomial inequality

    Okay sounds good. Thanks for your help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polynomial Inequality
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Mar 22nd 2016, 06:27 PM
  2. [SOLVED] polynomial inequality
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 6th 2010, 05:23 PM
  3. Polynomial Inequality
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Nov 30th 2008, 08:26 AM
  4. Polynomial inequality
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Apr 30th 2008, 06:44 AM
  5. Polynomial inequality
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Oct 28th 2007, 10:39 PM

Search Tags


/mathhelpforum @mathhelpforum