Top answers

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
4301 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...
5815 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...
3772 Views

Integrate tan(x) wrt x

Use substitutionlet u = cos(x)du = - sin(x)dxint(tan(x)) dx = int(sinx/cosx) dx = - int(1/u) du = - ln(u) + c= ln(secx) + c
MH
4747 Views

Find a vector that is normal to lines L1 and L2 and passes through their common point of intersection where L1 is the line r = (3,1,1) + u(1,-2,-1) and L2 is the line r = (0,-2,3) + v(-5,1,4) where u and v are scalar values.

We will use the cross product of these two vectors to help us find the perpendicular vector. The cross product works by finding a vector which has no effect on the position of a point with respect the the di...
AR
3771 Views