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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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A curve has equation y = ax^2 + 3x, when x= -1, the gradient of the curve is -5. Work out the value of a.

The gradient of a curve at a point is given by dy/dxDifferentiate the equationplug in the valuesdy/dx = 2ax + 3x = -1, dy/dx = -5-5 = 2a*-1 + 38 = 2aa = 4

Answered by Salma E. • Further Mathematics tutor

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Solve x^(-1/4) = 0.2

Get both sides in similar forms to make it easier to solve.1/x^1/4 = 1/5x^1/4 = 5x = 5⁴ = 625

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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