Top answers

Prove that 27(23^n)+17(10^2n)+22n is divisible by 11 for n belongs to the natural numbers

Proofs come in many shapes and sizes but this one is done via induction. When doing proof by induction, examiners love a list of a clear definite list of steps, the first being the base case, in this case it...
3334 Views

The point D has polar coordinates ( 6, 3π/4). Find the Cartesian coordinates of D.

We know that r= 6 and θ = 3π/4 as it is given in the question. We can then use the identities: x= rcosθ and y= rsinθ to find the x and y coordinates which are the Cartesian coordinates. So, x= rcosθ = 6cos(3...
MB
4320 Views

In the expansion of (x-7)(3x**2+kx-3) the coefficient of x**2 is 0. i) Find the value of k ii) Find the coefficient of x. iii) write the fully expanded equation in terms of x

i) multiply out: 3x 3+kx 2-3x-21x 2-7kx+21 simplify: 3x 3+(k-21)x 2+(-7k-3)x+21 the coefficient of x 2 is 0 and therefore k-21=0 k=21. ii)from i) the coefficient of x is (-7k-3) k=21 and therefore the requir...
2842 Views

Prove by induction that 2^(6n)+3^(2n-2) is divsible by 5. (AS Further pure)

For this question I would heavily emphasise layout as these questions are very strict. Base n=1 simply plug n=1 into the equation and you will find you end up with 65 which is divisble by 5 Assumption n=k pl...
5829 Views

Solve the differential equations dx/dt=2x+y+1 and dy/dt=4x-y+1 given that when t=0 x=20 and y=60. (A2 Further pure)

These questions are really mean but if given in the exam give ALOT of marks and whilst scary at first follow a very general pattern. First I would take either equation and re-arrange for the lone variable. T...
3782 Views