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From an Algebra Magazine. 1.Find the consecutive integers whose product is 156. Find two consecutive integers whose product is 156. Find two consecutive even integers whose product is 288. Find two consecutive odd integers whose product is 783.
I also have some word problems Michelle is 5 years younger than Cindy.Janet is years less than twice Cindy`s age.Kenny is 10 years old.The ratio of Janet`s age to Cindy`s age equals the ratio of Michelle`s age to Kenny`s age.How old are Cindy,Michelle and Janet.
A rectangular poster has an area of 190 square inches.The height of the poster is 1 inch less than twice it`s width.Find the dimensions of the poster.
Daryl earns twice as much per hour as Andy,and John earns 6 dollars more per hour than Andy.June earns 16 dollars per hour.The ratio of John`s hourly earnings to Andy`s hourly earnings is the same as the ratio of John`s hourly earnings to Andy`s hourly earnings is the same as the ratio of Daryl`s hourly earnings to June`s hourly earnings.How much does Daryl earn per hour.
A small rocket is launched upward from ground level.The height of the pocket from the ground is given by the quadratic equation h=-16t2 plus 144t where h is the height of the rocket in feet and t is the number of seconds since the rocket was launched.How many seconds will it take for the rocket to return to the ground.
given by the quadratic equation h0 —Preceding unsigned comment added by Yeats30 ( talk • contribs) 00:13, 4 February 2008 (UTC)
It's possible to write the set of complex numbers in decimal-like form using a complex base, like 2i, and the appropriate number of digits, in that case 0, 1, 2, and 3. Given a base, how do you determine whether it will produce a consistent number system in that way? Black Carrot ( talk) 00:52, 4 February 2008 (UTC)
I'm not sure you actually read my question. Black Carrot ( talk) 07:34, 4 February 2008 (UTC)
Not sure if I understood - but if the base is a+ib where a and b are integers then the new number system will be workable - ? (it's just solving linear equations of order 2)
87.102.90.249 (
talk) 12:57, 4 February 2008 (UTC) Don't ask me how to find out how many digits to use...
87.102.90.249 (
talk) 13:11, 4 February 2008 (UTC)
Here's an attempt at an answer. Let b be the base and say |b| > 1. Because we can always move the "decimal" point around (i.e. scale by powers of the base) it suffices to consider points inside a shape of our choice which contains a neighborhood of the origin. The fundamental reason why base 2i with digits 0,1,2,3 works is that there exists such a shape which can be covered by four copies of itself scaled down by 2i and translated by 0,1,2,3: namely the rectangle defined by and . In general, since the unit disc (for example) can be covered by finitely many scaled copies of itself regardless of the scaling factor, any base b with |b| > 1 can be used, but the minimum number of digits for arbitrary b looks like it might be a difficult geometric covering problem. We can get a lower bound of from area alone, though. -- BenRG ( talk) 18:30, 4 February 2008 (UTC)
i visted clay mathematics institute web site and i read this, Euclid gave the complete solution for that equation,(x^2+y^2=z^2).my question is how could we give such solution?by picking up an arbitrary values? or by finding operators, like we put,y=(a+s),x=(b+s),then z=(b+a+2s),where,a,b are constants and s,is variable.then we fixed a,and ,b,and start chossing differents value of ,s? is that how we find the solutions?or the general way is different? 209.8.244.39 ( talk) 12:01, 4 February 2008 (UTC)
Insert non-formatted text here
The article Digital Signature Algorithm contains the line: Choose g, a number whose multiplicative order modulo p is q. This may be done by setting g = h(p–1)/q for some arbitrary h (1 < h < p-1), and trying again if the result comes out as 1. Here p-1 is a multiple of q. I am translating this as follows: If q|(p-1) then h(p–1)/q generates the multiplicative subgroup of of order q provided it is not 1. Can someone give me the proof for this fact. Thanks.-- Shahab ( talk) 15:34, 4 February 2008 (UTC)
Recently, I've done a poll on an online forum asking other users what their Top Ten favorite The Land Before Time characters are (the list is in a hierarchy, meaning #10 on their list is their 10th most favorite, and #1 is their favorite character. The positions are not equal). I've recieved about 30 replies. Now, I want to calculate the Top Ten favorite characters overall. What would be the best way to calculate the popularity of each individual character? I'll add that I have ample time to go through each poll and check each character one-by-one, if need be. -- Ye Olde Luke ( talk) 23:57, 4 February 2008 (UTC)
I like the 2nd and 3rd options. I might do one of those.
One other thing. Since the main characters appear in all 13 movies, while most guest stars only appear in one, the recurring characters have a bit of an advantage, seeing as more people are likely to have seen them. Should this be factored in? -- Ye Olde Luke ( talk) 00:52, 5 February 2008 (UTC)
Wait, there is one problem with your #2 solution. You're assuming there are only ten characters to choose from. Since there are many, many characters, I can't rate the lowest score as the most popular. Some character who's #1 on a single person's list would beat a character who is #2 on five different lists, even though the latter character is obviously more popular. -- Ye Olde Luke ( talk) 00:58, 5 February 2008 (UTC)
Mathematics desk | ||
---|---|---|
< February 3 | << Jan | February | Mar >> | February 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. |
From an Algebra Magazine. 1.Find the consecutive integers whose product is 156. Find two consecutive integers whose product is 156. Find two consecutive even integers whose product is 288. Find two consecutive odd integers whose product is 783.
I also have some word problems Michelle is 5 years younger than Cindy.Janet is years less than twice Cindy`s age.Kenny is 10 years old.The ratio of Janet`s age to Cindy`s age equals the ratio of Michelle`s age to Kenny`s age.How old are Cindy,Michelle and Janet.
A rectangular poster has an area of 190 square inches.The height of the poster is 1 inch less than twice it`s width.Find the dimensions of the poster.
Daryl earns twice as much per hour as Andy,and John earns 6 dollars more per hour than Andy.June earns 16 dollars per hour.The ratio of John`s hourly earnings to Andy`s hourly earnings is the same as the ratio of John`s hourly earnings to Andy`s hourly earnings is the same as the ratio of Daryl`s hourly earnings to June`s hourly earnings.How much does Daryl earn per hour.
A small rocket is launched upward from ground level.The height of the pocket from the ground is given by the quadratic equation h=-16t2 plus 144t where h is the height of the rocket in feet and t is the number of seconds since the rocket was launched.How many seconds will it take for the rocket to return to the ground.
given by the quadratic equation h0 —Preceding unsigned comment added by Yeats30 ( talk • contribs) 00:13, 4 February 2008 (UTC)
It's possible to write the set of complex numbers in decimal-like form using a complex base, like 2i, and the appropriate number of digits, in that case 0, 1, 2, and 3. Given a base, how do you determine whether it will produce a consistent number system in that way? Black Carrot ( talk) 00:52, 4 February 2008 (UTC)
I'm not sure you actually read my question. Black Carrot ( talk) 07:34, 4 February 2008 (UTC)
Not sure if I understood - but if the base is a+ib where a and b are integers then the new number system will be workable - ? (it's just solving linear equations of order 2)
87.102.90.249 (
talk) 12:57, 4 February 2008 (UTC) Don't ask me how to find out how many digits to use...
87.102.90.249 (
talk) 13:11, 4 February 2008 (UTC)
Here's an attempt at an answer. Let b be the base and say |b| > 1. Because we can always move the "decimal" point around (i.e. scale by powers of the base) it suffices to consider points inside a shape of our choice which contains a neighborhood of the origin. The fundamental reason why base 2i with digits 0,1,2,3 works is that there exists such a shape which can be covered by four copies of itself scaled down by 2i and translated by 0,1,2,3: namely the rectangle defined by and . In general, since the unit disc (for example) can be covered by finitely many scaled copies of itself regardless of the scaling factor, any base b with |b| > 1 can be used, but the minimum number of digits for arbitrary b looks like it might be a difficult geometric covering problem. We can get a lower bound of from area alone, though. -- BenRG ( talk) 18:30, 4 February 2008 (UTC)
i visted clay mathematics institute web site and i read this, Euclid gave the complete solution for that equation,(x^2+y^2=z^2).my question is how could we give such solution?by picking up an arbitrary values? or by finding operators, like we put,y=(a+s),x=(b+s),then z=(b+a+2s),where,a,b are constants and s,is variable.then we fixed a,and ,b,and start chossing differents value of ,s? is that how we find the solutions?or the general way is different? 209.8.244.39 ( talk) 12:01, 4 February 2008 (UTC)
Insert non-formatted text here
The article Digital Signature Algorithm contains the line: Choose g, a number whose multiplicative order modulo p is q. This may be done by setting g = h(p–1)/q for some arbitrary h (1 < h < p-1), and trying again if the result comes out as 1. Here p-1 is a multiple of q. I am translating this as follows: If q|(p-1) then h(p–1)/q generates the multiplicative subgroup of of order q provided it is not 1. Can someone give me the proof for this fact. Thanks.-- Shahab ( talk) 15:34, 4 February 2008 (UTC)
Recently, I've done a poll on an online forum asking other users what their Top Ten favorite The Land Before Time characters are (the list is in a hierarchy, meaning #10 on their list is their 10th most favorite, and #1 is their favorite character. The positions are not equal). I've recieved about 30 replies. Now, I want to calculate the Top Ten favorite characters overall. What would be the best way to calculate the popularity of each individual character? I'll add that I have ample time to go through each poll and check each character one-by-one, if need be. -- Ye Olde Luke ( talk) 23:57, 4 February 2008 (UTC)
I like the 2nd and 3rd options. I might do one of those.
One other thing. Since the main characters appear in all 13 movies, while most guest stars only appear in one, the recurring characters have a bit of an advantage, seeing as more people are likely to have seen them. Should this be factored in? -- Ye Olde Luke ( talk) 00:52, 5 February 2008 (UTC)
Wait, there is one problem with your #2 solution. You're assuming there are only ten characters to choose from. Since there are many, many characters, I can't rate the lowest score as the most popular. Some character who's #1 on a single person's list would beat a character who is #2 on five different lists, even though the latter character is obviously more popular. -- Ye Olde Luke ( talk) 00:58, 5 February 2008 (UTC)