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Math Help - Geometric/ Sigma Problems

  1. #1
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    Geometric/ Sigma Problems

    Okay so I'm having trouble with these questions.


    1. If ...

    Σ (sinx)^ k-1 =6 determine x to the nearest degree. (0 ≤ x ≤ 90
    k=1

    2. Suppose that you drop a ball from a window 50 meters above the ground. The ball bounces to 50% of its previous height with each bounce. If the ball continues to bounce in this manner, how far will it have traveled, up and down, from the time it was dropped from the window?

    3. Solve for x:
    8
    Σ (ix-3) =76
    i=4

    4. A new $12,000 automobile decreases in value by 25% each year. What will be its value 7 years from now?




    I've tried everything and i'm still getting the wrong answer.
    Thanks in advance! <3
    Last edited by TeriyakiDonnQ; May 11th 2010 at 08:39 PM. Reason: The spacing is off for my equation
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  2. #2
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    Quote Originally Posted by TeriyakiDonnQ View Post
    4. A new $12,000 automobile decreases in value by 25% each year. What will be its value 7 years from now?

    Use this model

    V = value, t = years

    V = 12,000(0.75)^t

    Find V when t = 7
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  3. #3
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    Problem 2 interests me. I would've thought that that it'd simply be 50+ \sum^{\infty}_{i=1}\frac{50}{i} because after the first bounce, the ball would've traveled 50m, after the second bounce 50m (25m up and 25m down), after the third 25m (12.5m up and 12.5m down), etc..

    However the problem that I see is that the ball never stops bouncing. As i approaches infinity, \frac{50}{i} gets smaller and smaller. However, it never reaches 0 and therefore never stops bouncing.

    Is there more to the problem (like calculate to the nearest centimeter or millimeter or something) or am I just missing something?
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  4. #4
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    I'm not sure myself. Dx
    I checked the answer and its 150
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  5. #5
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    Hmm.. I just did the summation up to 20 and I'm 151.4515m. I think my way of going about it may be correct but I'm just missing something.

    Nevermind, the answer is \approx 150m if you work the summation out you'll see that it'll approach 150m meters but it'll never quite get to it.

    You can use calculus to show that as n approaches \infty the limit equals 150. My calculus is rusty, so I'd have to do some reviewing to prove it.
    Last edited by downthesun01; May 12th 2010 at 02:35 AM.
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  6. #6
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    Oh okay. (:
    haha. My calculus is pretty bad xD
    I won't go near that xD
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