Search over 10,000 free study notes

First, let's think of how many different possibilities we have to seat 6 people at a 'normal' table, i.e. in a straight line. Let's call the people A, B, C, D, E, F. We now have 6 seats: __ __ __ __ __ When ...

(bx+d)(bx-d)=b^2x^2-d^2(ax-c)(bx+d)(bx-d)=(ax-c)(b^2x^2-d^2)=ab^2x^3-ad^2x-b^2cx^2+cd^2ab^2=3b^2c=2ad^2=147-cd^2=98From equations:a=3/b^2c=2/b^2d^2=49b^2Since a, b, c, d are positive integers, b must be 1. T...

The procedure of mathematical induction is as following: Firstly prove the base case is true i.e. when n=1, the statement is true. Then assume for some integer n=k the statement is true, and then prove the c...

Here we are examining the imaginary number ‘i’, defined as the square root (sqrt) of ‘-1’.We begin by using Euler’s identity:e^(i π)+1=0e^(i π)=-1Since sqrt(x) is the same as x^(1/2):(e^(i π))^(1/2)=sqrt(-1)...

When differentiating cos inverse x, the typical method is to make y equal to cos inverse x.By taking cos of both sides: x = cosy.You can then differentiate with respect to y, obtaining that: (dx/dy) = - siny...