BigBrainOnBrad

Given the equation x^3 + (m - 5)x^2 + (9 - 5m)x + 6(m - 1) = 0, where m is a real parameter find:

1) how many roots are independent of m

2) the values of m for which all roots are real

3) the integer values of m for which all rots of the equation are integer

Show your work and thank you!

Find limit when n-->infinity of I_n(a) where 0 < a < 1 and I_(a) = integral[arctan(x) / (x^2 + 2ax + 1)]dx with lower limit of the integral is 1/n and the upper limit of the integral is n.

Show your work, and thank you!

Let p/q be the reduced form of 1 - 1/2 + 1/3 - 1/4 + ... +1/1339 - 1/1340

Which of the statements below are true?

a) p is divisible by 2011

b) q is divisible by 2011

c) (p+q) is divisible by 2011

d) q^p is divisible by 2011

e) (p*q + 1) is divisible by 2011

I just don't find how to crack this... Help me please!!!

Thank you!

Let ABC be a right triangle in C. [AD is the angle bisector of <BAC where D is inside (BC) such that DC = 3

The hypotenuse AB is of length 10. Inside (AB) we choose a point E such that EB/AE = 1/4

Find the area of EBD!

Thank you!

Let ABC be an isosceles triangle with AB = AC and m(<BAC) = 20 degrees.

The point D is inside (AB) such that m(<ACD) = 10 degrees

What is the value of AD/BC ???

Thank you!

What is the probability for the following event: take a random natural number (greater than 2 if you prefer) and that number to be "free of squares"?

"Free of squares" means that it the number does not divide any perfect square.

Examples of square-free numbers: 2, 3, 5, 6 = 2*3 , 7, 10 = 2*5 , 11, 13, 14 = 2*7 , 15 = 3*5 , 17, 19, 21 = 3*7 , 22 = 2*11, 23, 26 = 2*13 , and so on...

Counterexamples of square-free numbers: 4 = 2^2, 8 = (2^2)*2, 9 = 3^2, 12 = (2^2) * 3 , 16 = (2^2)*(2^2) , 18 = (3^2)*2 , 20 = (2^2)*5 , 24 = (2^2)*2*3 , and so on...

Can you generalize?

When is the best time to have unprotected sex with a woman between two periods?

Show sources please, or explain...

Find all functions f:R-->R that satisfy:

2*f(x) = f(x+y) + f(x+2y)

for all real x ; and all y >= 0 (positive real numbers y).

Let there be n people, each speaking at most 3 languages. In every 3-person group there exist at least 2 persons that speak one common language.

a) If n <= 8 prove that this is possible: no language is spoken by more than 2 persons.

b) If n >= 9 prove that there exists a language spoken by at least 3 persons.

A special category of natural numbers are those that have the same number of digits as the number of distinct prime factors. (I don't know if they have a name in English... a rough translation from Romanian would be "balanced numbers").

Examples: 34 = 2*17 ; 99 = (3^2)*11 ; 385 = 5*7*11 ; 572 = (2^2)*11*13 ; and so on...

Counterexamples: 275 = (5^2)*11 = 5*5*11 ; 847 = 7*(11^2) = 7*11*11 ; ...

Prove that there exist a finite number of such numbers.

First of all I wouldn't write all this if I didn't know for sure that my friend will never ever read it!

I have a buddy who graduated 3 years ago and since then he is a teacher... He teaches to 5th, 6th, 7th and 8th graders. Until this school year his only concerns were about how to teach better, what teaching strategies to use best and so on... This year he has another issue... He suspects that a 8th grade girl (about 14 or 15 years old) is in love with him because she's always smiling to him, sometimes blushing, always trying to get around him... even gave him a small present, some small joke book...

That wouldn't be a problem, because students fall in love all the time with their teachers... But I think he's in love with her to.... He told me he misses her (they're in Easter vacation now), he thinks about her... he even watched a romance called Roxanne... The girl's name is Roxanne....

He knows that any relations between them would be trouble... He's not an idiot (I HOPE!!!!)... But I don't know anymore what to tell him to keep his cool... The main problem here is that he's in love with her to! It's a good thing that she doesn't have internet at home and that they cannot keep in touch...

The question is: do you have some words of wisdom, maybe some cool life stories that will help with this buddy of mine????

Thanks!

First of all I wouldn't write all this if I didn't know for sure that my friend will never ever read it!

I have a buddy who graduated 3 years ago and since then he is a teacher... He teaches to 5th, 6th, 7th and 8th graders. Until this school year his only concerns were about how to teach better, what teaching strategies to use best and so on... This year he has another issue... He suspects that a 8th grade girl (about 14 or 15 years old) is in love with him because she's always smiling to him, sometimes blushing, always trying to get around him... even gave him a small present, some small joke book...

That wouldn't be a problem, because students fall in love all the time with their teachers... But I think he's in love with her to.... He told me he misses her (they're in Easter vacation now), he thinks about her... he even watched a romance called Roxanne... The girl's name is Roxanne....

He knows that any relations between them would be trouble... He's not an idiot (I HOPE!!!!)... But I don't know anymore what to tell him to keep his cool... The main problem here is that he's in love with her to! It's a good thing that she doesn't have internet at home and that they cannot keep in touch...

The question is: do you have some words of wisdom, maybe some cool life stories that will help with this buddy of mine????

Thanks!

Limit challenge: Find the following limit involving a fractional part.

limit when n-->infinity of { 5 + 3sqrt(2) }^[1 / (5 - 3sqrt(2))]

where { 5 + 3sqrt(2) } means the fractional part of 5 + 3sqrt(2)

Today (8th of February 2011) I eat 1 candy. The following two days I eat 2 candies each day. The following 3 days I eat 3 candies each day. The following 4 days I eat 4 candies each day. And so on until I run out of candies.

a) How many candies will I eat in the last day?

b) What is the date I eat my last candy?

Arithmetic sequence with a twist: Let (a_n), n>0 be an arithmetic sequence such that (a_1)^2, (a_2)^2, (a_3)^2 are all terms in the sequence. Prove that all the terms of the sequence are integers.

I want to gather up all the cool ideas that you have. Please don't send me links or "I don't know" answers.

Whether the answer is "3 cm has more points" or "20 cm has more points" or "they have the same number of points" you have to prove it!!! Use whatever field of mathematics you're most comfortable in to prove the answer.

This is not a "how do I do my homework, because I'm lazy or incapable" type of question; I just want to know what potential is on this site... I've seen some potential and I want to confirm it.

Turkey meat is much healthy than the pork meat,and turkey does not give you the sensation of being to full,oh and it is delicious.You should try it.In stead of pork ham you should try turkey rolls,or turkey meat balls.Don t worry because you don t loose weight but really don t gain any weight to.It s Christmas time,and the next day,after eating pork ham,you feel like you have a giant ball in your belly.But after turkey you will feel fit.Sound like a deal?You can always try...

I am sick of all that green in yahoo answers home page.They should change it being the holidays and all,and evan after holidays,they should rally change the color.I would go for a dark purple,you?

Why is it the green light the one you can safely cross the street and when it s red you halt?Who came up whit it?We have to have red alert and when invasion is over we say we have green light.Why?Thank you!

Where you can volunteer to go whit other people to nursing homes,hospitals evan churches to bring the Christmas joy and to sing a Christmas Carol?I am a student at Oxford,soft ball year,and could not find any program like that for Christmas.So do you know if someone is doing something like this this year?Thanks!