In a "WEIRD" Mathematical system, the following is true: 11+1=1 11+2=2 5+2=2 3+5=8 5+10=4 12+9=10 9+8=6 18+28=2 27+13=7 10+9=8 11+11=11 33+7=7 22+16=5 15+12=5 15+7=11 23+10=11 22+1=1 35+12=3 These are clues! After figuring out the system answer this problem: 152+46=? It can be a combination of anything, ...continues
What is a Pythagorean Triple and what is the Pythagorean Triples Theorem?
What are Pythagorean triple? What are primitive Pythagorean triples? What is the Pythagorean triples theorem?
Prove the associative law for matrix multiplication.
Prove the associative law for matrix multiplication: (AB)C = A(BC)
1. (i) Find the gcd (210, 48) using factorizations into primes (ii)Find (1234, 5678) 2. Prove that there are no integers x, y, and z such that x^2 + y^2 + z^2 = 999 keywords: greatest comon divisor
A simple pendulum and its period in different planets
When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of time called the period. One period is the amount of time required for the mass to swing all the way to the other side and then swing back to its staring point. we are maki ...continues
Problem 1: Prove that there are no integers x, y, and z such that x^2 +y^2 + z^2 = 999 Problem 2: Show that square root of 2 cubed is an irrational number. Problem 3: For each of the following pairs a and b, use the division algorithm to find quotient q and remainder r. (a) b=189, a=17 ...continues
Need detailed instruction on how to work Use mathematical induction to prove that : 1*2+2*3+3*4+....+n(n+1)(n+2)/3 for all n >_1 and (2) Find d=gcd (721 , 448), find integers s and t with d=721s + 448t, and put the fraction 448/721 in lowest terms.
(1) What is the remainder after dividing 10^2006 by 7? and (2) Use factorizations into primes to find gcd (105, 30) and lcm (105, 30)?
Homomorphism and First Isomorphism Theorem
Let R>0 be the group of positive real numbers under multiplication. Let CX be the group of nonzero complex numbers under mu!tiplication. Let S1 = {a + bi such that a^2 + b^2 = 1) be the subgroup of C consisting of all complex numbers of absolute value 1. Note that is normal in Cx since Cx is abelian. Prove that CX/S1 is isomorph ...continues
Prove that is p is prime, we have: n choose m is congruent to [floor(n/p) choose floor(m/p)]*[(n mod p) choose (m mod p)] (mod p) Hint: show that (1+x)^(pq+r) is congruent to (1+x)^r * (1+x^p)^q (mod p) If you can point me to a book or website explaining how to do this type of problem, and give a sketch of the proof, ...continues
