A rock climber climbs 90 feets of steep rock face in teh first half-hour of climbing. In each succeeding 30 minutes, the climber acheive only 80% of the height achieved in the previous half-hour. Find the total height climbed. Can you help me?
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2007-05-17 15:26:49 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
If you were asking the total amount of time the rock climber climbed in one hour, the answer from the above person for 172 ft. would be correct. But since you say "each succeeding time step" I'm assuming this means it continues to infinity. So I too would use the infinite series formula.
Step 1: Write down the equation and your given information.
The infinite geometric series formula is A/(1-R), where A is the initial condition in this problem (90 feet), and R is the common ratio (80% = 0.8).
Step 2: Plug it in.
Total Height = 90 ft./(1-0.8) = 450 ft.
As the above user said, it would actually approach 450 feet but mathematically never reach it (e.g., 449.9999999999). But for all practical purposes it is 450 feet.
2007-05-17 15:41:15 · answer #1 · answered by JoeSchmo5819 4 · 0⤊ 0⤋
This is almost as easy as falling off a cliff.
In the first half-hour, he climbs 90 feet.
In the next 30 minutes (also a half-hour) he climbs 80 percent of 90 feet [72 feet]
That's as far as he has gone. So he has climbed 90+72 feet or 162 feet. If he has been climbing longer, let me know.
2007-05-17 15:35:40 · answer #2 · answered by cattbarf 7 · 1⤊ 0⤋
You need the total hours climed
TH=
hlf hr = 90ft
1hr = 90ft(80%) + 90
72+90 = 162ft
1 1/2 hr = 72(80%) + 162
57.6 + 162 = 219.6
The formula is right check my math
2007-05-17 15:43:08 · answer #3 · answered by Me 4 · 0⤊ 0⤋
I think you mean the time is infinite? This resembles the geometric infinite series. There is a sum formula for that and it is T1/1-R. T1 is term 1 and R is common ratio. Replace T1 with 90 and R with 4/5. 30 minutes isn't needed because the time is infinite, but the sum is not. 90/1-4/5=90/1/5 90*5
450 feet is your answer. If you constantly add, you should get 449.999999999999... and the 9 never ends because your adding infinitely and you can't reach the next whole number.
2007-05-17 15:33:22 · answer #4 · answered by UnknownD 6 · 0⤊ 1⤋
90+(90 x 0.8)=162
The 90 x 0.8 = 72, so 90 + 72 = 162
2007-05-17 15:36:29 · answer #5 · answered by Aliz 6 · 0⤊ 0⤋
where i come from, there is no math
2007-05-17 15:29:49 · answer #6 · answered by Anonymous · 0⤊ 1⤋
how long?
2007-05-17 15:31:38 · answer #7 · answered by Chris K 2 · 0⤊ 1⤋