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Further Mathematics
A Level

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...

Answered by Aengus R. Further Mathematics tutor
2401 Views

Find the general solution of the differential equation d^2y/dx^2 - 2(dy/dx) = 26sin(3x)

2 Parts to this question - requires a complimentary function (treating equation as if right-hand side (RHS) = 0) and a particular integral (the general solution for where the RHS = 26sin(3x) )
1) The...

Answered by Matt P. Further Mathematics tutor
4560 Views

A tank contains 500L of salty water. Pure water is pumped in at a rate of 10 L/sec, and the the mixture is pumped out at a rate of 15L/ sec. If the concentration of salt is 5g/L initially, form an equation of amount of salt, s, at t seconds.

This is a word problem with the task of forming a first order differential equation (or DE), and involves two major aspects that need to be worked out: the volume of water in the tank at any given point, ...

2571 Views

Find the volume of revolution about the x-axis of the curve y=1/sqrt(x^2+2x+2) for 0<x<1

The volume of revolution is given by integrating Piy2 dx from 0 to 1.Squaring, y2=1/(x2+2x+2)Completing the square, we see that y=1/((x+1)2+1)Make the subst...

Answered by Harry G. Further Mathematics tutor
1821 Views

Particles P and Q move in a plane with constant velocities. At time t = 0 the position vectors of P and Q, relative to a fixed point O in the plane, are (16i - 12j) m and -5i + 4j) m respectively. The velocity of P is (i + 2j) m/s and the velocity of Q

is (2i + j) m/s. Find the shortest distance between P and Q in the subsequent motion. This is an m4 question from the edexcel June 2015 paper. First I would explain to the student that I would form an equ...

2007 Views

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