Recent content by newchie

Would like to see a proof for the following question. Let p be a prime number. Define a set interesting if it has p+2 (not necessarily distinct) positive integers such than the sum of any p numbers is a multiple of each of the other two. Find all interesting sets.

Gr 10, this is a challenge problem. However I know a lot of advanced material, but not calculus, so that won't be helpful :/

Yes my error, Do you have any ideas on how to maximize this I really am stumped o.op

yes it would be h,k/2 But you get the vertex to be (-97/2,-7/2) So the radius would just be half the y coordinate, but it doesent really fit the condition of the sqrtp and such part. I think the maximization case i picked is wrong

Homework Statement A circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r where, p, q and r are integers and are relatively prime.What is p+q+r Homework Equations Vertex form...

ah yes woops, i misread hehe, anyways do you have an approach on this problem

Homework Statement consider the function f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/)cosx+cos2x+cos3x+...+cos(n-1)x+cosnx) Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200 Homework Equations you get obviously tanx+tan2x...

I see, but would another valid solution be listing the powers of 2 so x^1 x^2 x^4 x^8 x^16 x^32 x^64,x^128 x^256 x^512 x^1024 Then you see if you add 1024 512 256 128 64 16 8 and 4 it sums to 2012, you are left with x^1 x^2 and x^32 So the number of ways would be 1*2*32 so 64 or 2^6 which...

If you multiply everything in p2 by x^8 you simply get all the terms in P3. Also for the first is you multiply it by x^4 you get the first four terms of the next.

Yes it is 6, it was on question 20 on amc 12 exact question mabye you got the pattern wrong the next one is x^16 + 16, x^32+32 etc Yes i get the pattern the first two coefficients will start off as one, as in the highest two, then the next two will have a coefficient of 2, then the next 2 4 all...

Yes you would just add all the exponents with each other. I got it but i don't get how that helps me find the coefficient, becuase wouldn't the coefficient be one

Homework Statement Given that p(x) is a polynomial defined by (x+1)(x^2+2)(x^4+4)(x^8+8)...(x^1024+1024) and knowing that the coefficient on x^2012 can be written as 2^a, find a. Homework Equations Binomial thereom mabye idk The Attempt at a Solution Tried grouping up terms that...

Defining the boxes into n-2k+1 elements, then the general choosing statement, i get the first part, but the second part is a bit opaque

http://www.artofproblemsolving.com/Wiki/index.php/2006_AMC_12A_Problems/Problem_25 I don't understand the solution

If we have ways are there to choose k elements from an ordered n element set without choosing two consecutive members