Recent content by timjones007

Find a primitive root modulo 101. What integers mod 101 are 5th powers? 7th powers? -I tested 2. -2 and 5 are the prime factors dividing phi(101)=100 so i calculated 2^50 is not congruent to 1 mod 101 and 2^20 is not congruent to 1 mod 101. -Therefore 2 is a primitive root modulo 101 I guess...

yes that's the all that's give in the problem. there's no boundary conditions

solve the heat equation ut = kuxx -infinity < x < infinity and 0 < t < infinity with u(x,0)= x2 and uxxx(x,0)= 0 first i showed that uxxx(x,t) solves the equation (easy part) the next step is to conclude that u(x,t) must be of the form A(t)x2 + B(t)x + C(t). i...

ah thank you that works

how do you integrate 1/(x2 + 1)2 ? i have tried integration by partial fractions but when you set 1 equal to (Ax +B)(x2+1) + (Cx + D) this leads to A=B=C=0 and D=1 which just gives you the original equation

Let me just say this in response to post number 17 by csproof2000. Suppose there are two pieces of string forming the legs of an isosceles right triangle and each string measures 1 meter in length. Now suppose that I ask you to cut a string of sqrt(2) meters to complete the triangle. Even if...

no, i don't think sqrt(2) exists. This is my reason: sqrt(2) is just a symbol for it's decimal representation which is 1.414213562..., and the decimal places continue on infinitely. So, if we will never reach the last digit in the decimal places for sqrt(2), how can we multiply it by itself...

why do irrational numbers exist? I am well familiar with the proof that irrational numbers exist, but why do they?

How does a gust of wind affect the direction and motion of light according to wave theory and the particle theory?