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Math Help - Review questions (conics, etc.)

  1. #1
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    Question Review questions (conics, etc.)

    Hello all,

    Just reviewing for the finals and stumbled upon some questions I'm having issues with. Conics mostly (I literally failed that chapter way back when).

    1) "Find the focus of the graph y = 1/8(x-2)+3

    2) "Find the sum of the series: -1 + 2 + 5 + 8... +56" (for this one, I resulted with S(19.3333) = 531.6657. Which is not one of the multiple choice answers).

    3) "f(x) = x-4 and g(x) = x^2, find g(f(3))"

    4) "Find the foci of the ellipse x^2+9y^2=81"

    5) "Find the verticle asymptotes f(x) = x-1/x^2-25"

    Thanks in advance!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mulya66 View Post
    2) "Find the sum of the series: -1 + 2 + 5 + 8... +56" (for this one, I resulted with S(19.3333) = 531.6657. Which is not one of the multiple choice answers).
    This is an arithmatic series
    a_n = a_0 + nd
    with
    a_0 = -1
    d = 3

    The sum of this series is:
    S = \sum_{n = 0}^N (-1 + 3n) = \sum_{n = 0}^N (-1) + 3 \sum_{n = 0}^N n

     = -(N + 1) + 3 \cdot \frac{N(N + 1)}{2}

    So what's N?
    a_N = 56 = -1 + 3N \implies N = 19

    Thus
    S = -20 + 3 \cdot \frac{19(20)}{2} = 550

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mulya66 View Post
    3) "f(x) = x-4 and g(x) = x^2, find g(f(3))"
    f(3) = 3 - 4 = -1
    g(f(3)) = g(-1) = (-1)^2 = 1

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mulya66 View Post
    5) "Find the verticle asymptotes f(x) = x-1/x^2-25"
    I presume this is:
    f(x) = \frac{x - 1}{x^2 - 25}

    Then
    f(x) = \frac{x - 1}{(x + 5)(x - 5)}

    Thus the function goes to infinity (ie. is undefined) at two x values, x = -5 and x = 5. These are your vertical asymptotes.

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    f(3) = 3 - 4 = -1
    g(f(3)) = g(-1) = (-1)^2 = 1

    -Dan
    I just got that, too. But I'm perplexed on the answer choices provided by the book. The choices are 144, -1, 1, and 5. Obviously, it's either B) -1 or C) 1. What should I do in a case like this? My instincts are going with C) 1...

    Thanks.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mulya66 View Post
    I just got that, too. But I'm perplexed on the answer choices provided by the book. The choices are 144, -1, 1, and 5. Obviously, it's either B) -1 or C) 1. What should I do in a case like this? My instincts are going with C) 1...

    Thanks.
    I'm confused about your confusion. If the answer is 1 then it must be answer C. Or am I missing something here?

    -Dan
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  7. #7
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    Quote Originally Posted by topsquark View Post
    I'm confused about your confusion. If the answer is 1 then it must be answer C. Or am I missing something here?

    -Dan
    And then I confused myself... haha. You're not missing anything, I realized that I misunderstood our answers, sorry.

    Thank you, though.
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