Top answers

Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n

First I would do the base case (the first value):Test n=1,11 1 -6=5. 5 is divisible by 5 therefore true for n=1. Now we assume true for n=k,11 k -6 is divisible by 5.Next we test n=k+1,11 k+1 -6We can rearra...
4176 Views

Use differentiation to show the function f(x)=2x^3–12x^2+25x–11 is an increasing function for all values of x

Firstly, I would remember what differentiation shows - which is the rate of change of a function. I would think about how I could use this to show it's always increasing. Now the first derivative would show ...
9074 Views

A complex number z has argument θ and modulus 1. Show that (z^n)-(z^-n)=2iSin(nθ).

This problem wants you to use De Moivre's theorem to prove a trigonometric identity.We will tackle this problem by taking the left hand side and using theorems and manipulation to show it is equivalent to th...
GC
6958 Views

Find the reflection of point P(2,4,-6) in the plane x-2y+z=6

If the point P' is a refection of point P in any plane, then both P and P' line on the line perpendicular to that plane. The equation of such line is easy to find: all we need is a point and the direction ve...
26971 Views

Solve the equation 2(Sinhx)^2 -5Coshx=5, giving your answer in terms of natural logarithm in simplest form

It doesn't hurt to write down the equation again, so let's do so. Equation: 2(Sinh x ) 2 - 5Cosh x = 5 . Hmm, we don't really like to do maths with two different trig functions, why don't we see if we can re...
3627 Views