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Stuck on cone maxvolume (picture)A cone is going to be build with 6m long sticks as the picture shows, what is the maximum volume of the cone? http://hem.bredband.net/nimkam/cone.jpg #2 20060418 00:43:07
Re: Stuck on cone maxvolume (picture)Just to make sure I understand the problem... "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060418 00:52:18
Re: Stuck on cone maxvolume (picture)I'm going to assume that you are in Calculus, as that seems the easiest way to do the problem. This just uses simple trig. Ah, now all we have to do is substitute it in: And now we have a function of one variable. Take the derivative, find the zeros, and then find the max. Last edited by Ricky (20060418 00:53:25) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20060418 00:58:43
Re: Stuck on cone maxvolume (picture)Thank you! Yes I´m in calculus, yet we haven`t studies cos , tan and sin yet so I assumed there`d be a solution without involving those in this problem. But yes, you assume right, those two sticks are to build the cone. Thank you yet again #5 20060418 01:23:30
Re: Stuck on cone maxvolume (picture)Without trignometry? Let me try... Substituting the value of h from the above equation, Now there is only one variable, use the condition for maximum value, and the problem is solved! Character is who you are when no one is looking. #6 20060418 02:02:45
Re: Stuck on cone maxvolume (picture)Thank you Ricky and Ganesh, I looked the basics of sin, tan and cos up after Ricky's through answer and learned a few things but still haven't learned to derive those 3 so I´ll have to go with Ganes method. Amazing that it can be solved in at least 2 presented ways. Thank you yet again. Keep up the good work, your help is invaluable to many! #8 20060418 04:59:13
Re: Stuck on cone maxvolume (picture)
am I the only one who doesnt get this? Is it a joke, or? #9 20060418 05:04:38
Re: Stuck on cone maxvolume (picture)No Patrick, we`re in the same boat on that one. :S #10 20060418 13:17:15
Re: Stuck on cone maxvolume (picture)The angle is not 45 degrees because a 3,4,5 triangle cone has a larger volume. Last edited by John E. Franklin (20060418 13:17:46) igloo myrtilles fourmis #11 20060418 14:45:59
Re: Stuck on cone maxvolume (picture)John, you get the maximum of the function by taking the derivative and setting it to 0. You end up with 4.8989 if you use ganesh's, and 0.6154 if you use mine. But remember, 6cos(0.6154) = 4.8989. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #15 20060418 15:50:34
Re: Stuck on cone maxvolume (picture)you can plot "y=x*x*sqrt(36x*x)" for xMin=0 to xMax=6 and parameters none at this site: Last edited by George,Y (20060418 15:52:38) X'(yXβ)=0 #16 20060428 00:15:41
Re: Stuck on cone maxvolume (picture)Is the number [(44+\sqrt{1996})^{100}] odd or even? #17 20060428 00:24:23
Re: Stuck on cone maxvolume (picture)Mozartmoses, Since 1996 is not a perfect square, the value of square root of 1996 is an irrational number. Hence, the resultant is neither even nor odd, it is an irrational number. The expansion of would contain 101 terms, many of the terms would be irrational numbers. For example, the second term of the expansion would be which is an irrational number! Character is who you are when no one is looking. #18 20060428 00:29:41
Re: Stuck on cone maxvolume (picture)The root of 1996 is irrational, and the entire expression will be as well. Even and odd don't make any sense when you are talking about something with a decimal place. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #19 20060502 22:33:27
Re: Stuck on cone maxvolume (picture)Hey !! #20 20060502 23:14:22
Re: Stuck on cone maxvolume (picture)Victoria woke up in the middle of the night and looked at her digital clock, it said 2:58, then she saw it change to 2:59 and then 3:00. Bored she began adding up the digit as they changed 15,16.3. Hmmmm #22 20060502 23:55:23
Re: Stuck on cone maxvolume (picture)Hi !! #23 20060503 07:26:37
Re: Stuck on cone maxvolume (picture)And on a 24 hour clock you get two uniques: 0:00 gives 0, and 19:59 gives 24 "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #24 20060504 05:01:21
Re: Stuck on cone maxvolume (picture)The 12hour clock has 2 solutions as well. 1:00 is the only time that gives a sum of 1. Why did the vector cross the road? It wanted to be normal. #25 20060509 03:34:59
Re: Stuck on cone maxvolume (picture)What is the difference between sequence and pattern? Can any one help me to get a clear picture? Last edited by Mozartmoses (20060509 03:52:54) 