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How can I find the arguments of two functions, where the value of the first function is a multiple of the value of the second function? To better illustrate what I mean, I will provide an example.
Suppose we are given the following two simple functions
with
I want to find those arguments, where the value of is a multiple of the value of . How could I do this? Toshio Yamaguchi ( talk) 14:02, 25 September 2011 (UTC)
Hi. In some calc textbooks if you have a separable differential equation of the form it recommends multiplying both sides by the differential dx and then separating and integrating. Is this a valid step? Is it ever valid to split up the ? Since you're actually just integrating both sides wrt x but using substitution to integrate the lhs wrt y by grabbing the aren't you? THanks. 41.234.205.210 ( talk) 14:12, 25 September 2011 (UTC)
Hi, I recently found the symbol ⊙ (represented in LaTeX as \odot), and I am not familiar with it. Wikipedia does not appear to have an article on the subject, and a Google Search comes up with absolutely nothing. What does it do, and what is its formal name?--82.113.103.164 (talk) 16:40, 25 September 2011 (UTC) — Preceding unsigned comment added by 82.113.103.164 ( talk)
Note for those replying: Original post is at WP:HD#What does the mathematical symbol ⊙ represent?, where I posted a link to a Unicode conversion and a document mentioning this symbol. You might be able to better explain for what it is used than the people at the help desk, though. Regards Toshio Yamaguchi ( talk) 17:46, 25 September 2011 (UTC)
hello. I've seen this problem countless times and still have not figured out how to do it. Consider a regular polygon, such as a pentagon, with diagonals drawn such that each vertex is connected to each other vertex (or equivalently, that a pentagram is inscribed such that each convex vertex of the pentagram coincides with a vertex of the pentagon). How many triangles are in the interior? The problem is that there are triangles made of many little triangles. How do I do this analytically? There is also the form where a rectangle is divided except not just at the vertices, with a bunch of random lines, I assume it is solved the same way? muchas gracias.
A problem with Bkell's answer is that it works separately in individual cases, but if n is the number of vertices, it doesn't say in what way the answer depends on n. For example, how fast does it grow as n grows?
Another question is: What if it's slightly irregular? Look at the case of the hexagon, with three concurrent lines meeting at the center. As soon as they're not quite concurrent, some more triangles appear. Michael Hardy ( talk) 17:27, 27 September 2011 (UTC)
Hi, this is explicitly a homework question, but I just need a push in the right direction. There's a game where you can choose between a nickel and dime, if the dime is chosen the game ends, if you choose the nickel you are presented with the same choice.
"Consider a variant of the game in which if the dime is taken the game stops, but if the nickel is taken then the game is repeated with probability p. Assume that p < 1, so the game will eventually stop. What is the optimal strategy?"
I'm just confused about how to go about solving such a problem. Any advice? 209.6.54.248 ( talk) 20:12, 25 September 2011 (UTC)
Mathematics desk | ||
---|---|---|
< September 24 | << Aug | September | Oct >> | September 26 > |
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. |
How can I find the arguments of two functions, where the value of the first function is a multiple of the value of the second function? To better illustrate what I mean, I will provide an example.
Suppose we are given the following two simple functions
with
I want to find those arguments, where the value of is a multiple of the value of . How could I do this? Toshio Yamaguchi ( talk) 14:02, 25 September 2011 (UTC)
Hi. In some calc textbooks if you have a separable differential equation of the form it recommends multiplying both sides by the differential dx and then separating and integrating. Is this a valid step? Is it ever valid to split up the ? Since you're actually just integrating both sides wrt x but using substitution to integrate the lhs wrt y by grabbing the aren't you? THanks. 41.234.205.210 ( talk) 14:12, 25 September 2011 (UTC)
Hi, I recently found the symbol ⊙ (represented in LaTeX as \odot), and I am not familiar with it. Wikipedia does not appear to have an article on the subject, and a Google Search comes up with absolutely nothing. What does it do, and what is its formal name?--82.113.103.164 (talk) 16:40, 25 September 2011 (UTC) — Preceding unsigned comment added by 82.113.103.164 ( talk)
Note for those replying: Original post is at WP:HD#What does the mathematical symbol ⊙ represent?, where I posted a link to a Unicode conversion and a document mentioning this symbol. You might be able to better explain for what it is used than the people at the help desk, though. Regards Toshio Yamaguchi ( talk) 17:46, 25 September 2011 (UTC)
hello. I've seen this problem countless times and still have not figured out how to do it. Consider a regular polygon, such as a pentagon, with diagonals drawn such that each vertex is connected to each other vertex (or equivalently, that a pentagram is inscribed such that each convex vertex of the pentagram coincides with a vertex of the pentagon). How many triangles are in the interior? The problem is that there are triangles made of many little triangles. How do I do this analytically? There is also the form where a rectangle is divided except not just at the vertices, with a bunch of random lines, I assume it is solved the same way? muchas gracias.
A problem with Bkell's answer is that it works separately in individual cases, but if n is the number of vertices, it doesn't say in what way the answer depends on n. For example, how fast does it grow as n grows?
Another question is: What if it's slightly irregular? Look at the case of the hexagon, with three concurrent lines meeting at the center. As soon as they're not quite concurrent, some more triangles appear. Michael Hardy ( talk) 17:27, 27 September 2011 (UTC)
Hi, this is explicitly a homework question, but I just need a push in the right direction. There's a game where you can choose between a nickel and dime, if the dime is chosen the game ends, if you choose the nickel you are presented with the same choice.
"Consider a variant of the game in which if the dime is taken the game stops, but if the nickel is taken then the game is repeated with probability p. Assume that p < 1, so the game will eventually stop. What is the optimal strategy?"
I'm just confused about how to go about solving such a problem. Any advice? 209.6.54.248 ( talk) 20:12, 25 September 2011 (UTC)