Geometric/ Sigma Problems

Jan 2010
22
0
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:

pickslides

MHF Helper
Sep 2008
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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

\(\displaystyle V\) = value, \(\displaystyle t \) = years

\(\displaystyle V = 12,000(0.75)^t\)

Find \(\displaystyle V\) when \(\displaystyle t = 7\)
 
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Oct 2009
303
33
Problem 2 interests me. I would've thought that that it'd simply be \(\displaystyle 50+ \sum^{\infty}_{i=1}\frac{50}{i}\) 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, \(\displaystyle \frac{50}{i}\) 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?
 
Oct 2009
303
33
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 \(\displaystyle \approx 150m\) 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 \(\displaystyle \infty\) the limit equals 150. My calculus is rusty, so I'd have to do some reviewing to prove it.
 
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Jan 2010
22
0
Oh okay. :)
haha. My calculus is pretty bad xD
I won't go near that xD