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 View Poll Results: Look at the two parts given below. Q: Math geniuses should solve the first part very easily, but not True.    1 100.00% False.    0 0% I don't know.    0 0% Voters: 1. You may not vote on this poll

March 7th, 2008, 05:47 PM   #1
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Difference in the subject of Mathematics

Here are two sets of mathematical problems, and see which one you like more:
Quote:
 The first hard part of mathematics (Rule on this part: You may use a pencil and a paper, possibly using geometric protractors etc., but possibly not an calculator.) A1. ABC is acute-angled. O is its circumcenter. X is the foot of the perpendicular from A to BC. Angle C ≥ angle B + 30deg. Prove that angle A + angle COX < 90deg. A2. a, b, c are positive reals. Let a' = √(a^2 + 8bc), b' = √(b^2 + 8ca), c' = √(c^2 + 8ab). Prove that a/a' + b/b' + c/c' ≥ 1. A3. Integers are placed in each of the 441 cells of a 21 x 21 array. Each row and each column has at most 6 different integers in it. Prove that some integer is in at least 3 rows and at least 3 columns. B1. Let n_1, n_2, ... , n_m be integers where m is odd. Let x = (x_1, ... , x_m) denote a permutation of the integers 1, 2, ... , m. Let f(x) = x_1n_1 + x_2n_2 + ... + x_mn_m. Show that for some distinct permutations a, b the difference f(a) - f(b) is a multiple of m!. B2. ABC is a triangle. X lies on BC and AX bisects angle A. Y lies on CA and BY bisects angle B. Angle A is 60deg. AB + BX = AY + YB. Find all possible values for angle B. B3. K > L > M > N are positive integers such that KM + LN = (K + L - M + N)(-K + L + M + N). Prove that KL + MN is composite.
and
Quote:
 The second hard part of Mathematics (Rule on this part: Solve the following stuff in your head. Don't use paper and pencil, or calculators.) A1. Simplify (a + 2b + 3c - 6c)^5 - d^3/dx^3[sin(x^2 + x + 1)]. A2. Find the 10th derivative of y = cos(sin(2x^2)). A3. Simplify (x - y + z)^6 + d^9/dx^9[cos(sec(x^2))]. B1. What is the area of the circle with the radius of r = x^5 + x^4 + 3x^3 + x + 24, where x > 0. Express the area in terms of pi and x variable. B2. Find the area under the curve of y = x^2 from x = k + k^2 + k^3 to x = k^5 + 6k^9 + k^15 + 8k^27, where k > 0. Express the area under the curve in terms of k. B3. What's the 20th derivative of sin(cos(x))? March 7th, 2008, 05:49 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 I think it's true, in my opinion. Tags difference, mathematics, subject Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Battler. Abstract Algebra 4 February 19th, 2014 01:09 PM TheGoofster Algebra 5 December 28th, 2012 01:04 AM fiw Physics 2 February 4th, 2011 08:40 PM Majestic_Q Algebra 5 September 24th, 2008 03:48 PM johnny New Users 2 December 7th, 2007 04:13 AM

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