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A piece of wire of length k cm is bent to from a sector. Find the maximum area of the sector.
There has given some equations, please use these equations to slove my question.
Let r be the radian, A be the area, y be the arcs.
k=2r+y.....(1) y=2πr* x/360.....(2) A=πr^2 (x/360) ....(3) -- Dansonncf ( talk) 11:10, 4 May 2009 (UTC)
The length of the circular arc is k − 2r. The circumference of the whole circle is 2πr. The fraction of the circle's area is therefore (k − 2r)/(2πr). The area of the whole circle is πr2. The area of the sector is therefore
You don't need differentiation to find the value of r that maximizes this, since is just a quadratic polynomial in r, so it's just a matter of finding the vertex of a parabola by completing the square. You already know how to do that before you take calculus. But you can do it by differentiation. Michael Hardy ( talk) 14:40, 4 May 2009 (UTC)
Okay, just read Penney's game, and it makes exactly zero sense to me.
Probability of getting a specified particular result in a fair coin toss: 1/2. Probability of getting any specified sequence of three: 1/2^3 = 1/8. Probability of getting any one specified sequence before any one other specified sequence: 1/2. Each sequence has an equal probability of occurring. I have no idea what the linked Java simulation is doing, but I coded up a trial ( here) and the result is a pretty clear 1/2.
Can someone explain what this article is talking about?
Thanks a lot, Aseld talk 19:07, 4 May 2009 (UTC)
What is the largest decimal number that will spell an English word in HEX? Is it 251636973? 65.121.141.34 ( talk) 20:09, 4 May 2009 (UTC)
Mathematics desk | ||
---|---|---|
< May 3 | << Apr | May | Jun >> | May 5 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
A piece of wire of length k cm is bent to from a sector. Find the maximum area of the sector.
There has given some equations, please use these equations to slove my question.
Let r be the radian, A be the area, y be the arcs.
k=2r+y.....(1) y=2πr* x/360.....(2) A=πr^2 (x/360) ....(3) -- Dansonncf ( talk) 11:10, 4 May 2009 (UTC)
The length of the circular arc is k − 2r. The circumference of the whole circle is 2πr. The fraction of the circle's area is therefore (k − 2r)/(2πr). The area of the whole circle is πr2. The area of the sector is therefore
You don't need differentiation to find the value of r that maximizes this, since is just a quadratic polynomial in r, so it's just a matter of finding the vertex of a parabola by completing the square. You already know how to do that before you take calculus. But you can do it by differentiation. Michael Hardy ( talk) 14:40, 4 May 2009 (UTC)
Okay, just read Penney's game, and it makes exactly zero sense to me.
Probability of getting a specified particular result in a fair coin toss: 1/2. Probability of getting any specified sequence of three: 1/2^3 = 1/8. Probability of getting any one specified sequence before any one other specified sequence: 1/2. Each sequence has an equal probability of occurring. I have no idea what the linked Java simulation is doing, but I coded up a trial ( here) and the result is a pretty clear 1/2.
Can someone explain what this article is talking about?
Thanks a lot, Aseld talk 19:07, 4 May 2009 (UTC)
What is the largest decimal number that will spell an English word in HEX? Is it 251636973? 65.121.141.34 ( talk) 20:09, 4 May 2009 (UTC)