Results 1 to 3 of 3

Math Help - Hyperbolic Function Question

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    34

    Hyperbolic Function Question

    Not sure how to go about this question...

    How many solutions does the equation -6 sinh(x) = 9 have?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    56
    Quote Originally Posted by mr_motivator View Post
    Not sure how to go about this question...

    How many solutions does the equation -6 sinh(x) = 9 have?

    Thanks.
    Easiet way is to graph y = \sinh x\;\;\; \text{and}\;\;\; y = -\frac {3}{2} and look for intersection points. To find them, replace

    \sinh x = \frac{e^x - e^{-x}}{2}

    so

     \frac{e^x - e^{-x}}{2} = -\frac{3}{2}

    or

     e^x + 3 - e^{-x} = 0

    or

     \left(e^x\right)^2 + 3 e^x - 1 = 0

    Now this is a quadratic in e^x. Yours from here.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Quote Originally Posted by mr_motivator View Post
    Not sure how to go about this question...

    How many solutions does the equation -6 sinh(x) = 9 have?

    Thanks.
    Trivial Question. This is a thought problem.

    f(x) = -6sinh(x) is an odd function - frankly, monotonic decreasing.

    f(x) = 9 is constant

    There is 1 solution.

    Done. Reach out and grab easy ones. You still have to explain it for your final grade. Good luck with that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 20th 2011, 02:29 AM
  2. Hyperbolic function question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 3rd 2010, 11:21 PM
  3. Hyperbolic function question
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 23rd 2010, 05:46 AM
  4. hyperbolic function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 14th 2009, 02:37 PM
  5. Hyperbolic function?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 17th 2009, 08:57 AM

Search Tags


/mathhelpforum @mathhelpforum