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Further Mathematics

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Prove by induction that for all positive integers n , f(n) = 2^(3n+1) + 3*5^(2n+1) , is divisible by 17.

Prove the base caseFor n=0, f(0)= 2 + 15 = 17Therefore, when n=0, f(n) is divisible by 17, base case is true2. Assume true for any integerAssume for n=k, f(k) is divisible by 17f(k)= 2^3k+1
Answered by Salma E. • Further Mathematics tutor
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explain the eigenvalue problem

The eigenvalue problem is how we can find non-trivial solutions where x does not equal zero to the matrix equation;AX=LX (L=lambda)Values of the scalar L for which non-trivial solutions exist are calle...

Answered by Kedar D. • Further Mathematics tutor

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Unfortunately this box is to small to contain the question so please see the first paragraph of the answer box for the question.

Question: A smooth conical shell with its axis aligned to the vertical and apex pointing downwards has its surface at an angle of 30 degrees to the horizontal. A ball of mass m = 1kg moves in circular mot...

Answered by Jack N. • Further Mathematics tutor

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Whats the derivative of sin(3x)?

3*cos(3x)

Answered by Tomas A. • Further Mathematics tutor

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A particle is undergoing circular motion in a horizontal circle, that lies within the smooth surface of a hemispherical bowl of radius 4r. Find the distance OC (explained in diagram) if the angular acceleration of the particle is equal to root (3g/8r).

Resolve the reaction force caused by the weight, mg, of the particle horizontally and vertically. Rsin(theta) = mg Rcos(theta)=m(CP)w^2 where w = root (3g/8r).thus tan(theta) = 8r/3CPconsider the right an...

Answered by Ed B. • Further Mathematics tutor

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