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Further Mathematics
A Level

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(Sinhx)2 - 5Coshx = 5 . Hmm, we don't really like to do maths w...

2472 Views

Are the integers a group under addition? How about multiplication?

There are 4 things we need for a group: associativity, the existence of an identity, inverses in the group and closure. The integers are definitely associative under this operation as addition is associat...

Answered by Damon C. Further Mathematics tutor
4422 Views

The ODE mx'' + cx' + kx = 0 is used to model a damped mass-spring system, where m is the mass, c is the damping constant and k is the spring constant. Describe and explain the behaviour of the system for the cases: (a) c^2>4mk; (b) c^2=4mk; (c) c^2<4mk.

In the case c2>4mk, the characteristic equation has two distinct real roots; this represents overdamping. The system does not oscillate, and x approaches zero as time approaches infinity.In ...

Answered by Oliver G. Further Mathematics tutor
10437 Views

How do I determine whether a system of 3 linear equations is consistent or not?

First, form the system into a 3x3 matrix using the coefficients. Find the determinant of this matrix.If the determinant =/= 0, then the matrix is singular and has a unique solution. The system is consiste...

16743 Views

Prove by induction that f(n) = 2^(k + 2) + 3^(3k + 1) is divisible by 7 for all positive n.

First we establish our base case: f(0) = 22 + 31 = 4 + 3 = 7, so clearly f(0) is divisible by 7.Now. by the inductive hypothesis. we assume that f(k) is divisible by 7, and attempt t...

Answered by William P. Further Mathematics tutor
2320 Views

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