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Math Help - Stuck on a few multi choice...

  1. #1
    Member classicstrings's Avatar
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    Stuck on a few multi choice...

    The number of solutions to the equation x = 5cos2x where x is a subset of the R is?

    If tan(x) = 1/a
    sin^2(x) = 1/b
    cos(x) = ?

    I tried using the identities but I cant seem to get right answer.

    The intensity, I, of a light bumb is I = k/(x^2) where x = distance from bulb. THe rate at which the intensity changes with respect to distance when x = 5 is?

    THis one is dI/dx right? So I get -2k/5, which is wrong.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by classicstrings View Post
    The intensity, I, of a light bumb is I = k/(x^2) where x = distance from bulb. THe rate at which the intensity changes with respect to distance when x = 5 is?

    THis one is dI/dx right? So I get -2k/5, which is wrong.
    dI/dx = -2k/(x^3)

    so dI/dx at x=5 is: -2k/5^3 = -2k/225.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by classicstrings View Post
    The number of solutions to the equation x = 5cos2x where x is a subset of the R is?

    If tan(x) = 1/a
    sin^2(x) = 1/b
    cos(x) = ?

    I tried using the identities but I cant seem to get right answer.
    I'm not quite sure what the question is here. The number of solutions of:

    x= 5 cos(2x) (or is that x = 5 cos^2 (x) ?)

    is not related as far as I can see to your list of candidate solutions.

    RonL
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  4. #4
    Member classicstrings's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    I'm not quite sure what the question is here. The number of solutions of:

    x= 5 cos(2x) (or is that x = 5 cos^2 (x) ?)

    is not related as far as I can see to your list of candidate solutions.

    RonL
    Oops sorry they are 2 different questions!

    For the first the solns are 3,5,7,9 but i am not sure how to work out the answer.

    Then the 2nd q, I can't do either. Thanks CB!
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  5. #5
    Member Glaysher's Avatar
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    Quote Originally Posted by classicstrings View Post

    If tan(x) = 1/a
    sin^2(x) = 1/b
    cos(x) = ?
    \tan x =\frac{\sin x}{\cos x}

    \sin x = \frac{1}{\sqrt{b}} if x is acute or obtuse (case i)

    or \sin x = -\frac{1}{\sqrt{b}} otherwise (case ii)

    Case i
    So  \frac{1}{a} = \frac {\frac{1}{\sqrt{b}}}{\cos x}

    \cos x = \frac {a}{\sqrt{b}}

    Case ii
    \cos x = -\frac {a}{\sqrt{b}}
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by classicstrings View Post
    Oops sorry they are 2 different questions!

    For the first the solns are 3,5,7,9 but i am not sure how to work out the answer.

    Then the 2nd q, I can't do either. Thanks CB!
    As 5 cos(2x) lies between +/-5, all the roots of x=5 cos(2x) lie between
    +/-5. So if you graph the two function you can just count the roots.

    See attachment (looks like 7 roots to me).

    RonL
    Attached Thumbnails Attached Thumbnails Stuck on a few multi choice...-gash.jpg  
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  7. #7
    Member classicstrings's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    dI/dx = -2k/(x^3)

    so dI/dx at x=5 is: -2k/5^3 = -2k/225.

    RonL

    Dang, my brain is fried, such a silly error. Thanks for the help Glaysher too!
    Last edited by ThePerfectHacker; October 22nd 2006 at 07:36 AM.
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