# Geometric/ Sigma Problems

• May 11th 2010, 09:31 PM
TeriyakiDonnQ
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 • May 11th 2010, 09:40 PM pickslides Quote: Originally Posted by TeriyakiDonnQ 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 $t = 7$
• May 12th 2010, 01:01 AM
downthesun01
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?
• May 12th 2010, 02:19 AM
TeriyakiDonnQ
I'm not sure myself. Dx
I checked the answer and its 150
• May 12th 2010, 03:22 AM
downthesun01
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.
• May 12th 2010, 03:37 AM
TeriyakiDonnQ
Oh okay. (:
haha. My calculus is pretty bad xD
I won't go near that xD