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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...

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 ...

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...

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...

First we must ensure that the differential is i the standard form of y' + p(x) y = f(x)The we use the integration factor I(x) = e to the integral of p(x)we then realise that if we differentiate this we wi...