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The set of midpoints of the parallel chords of an ellipse with gradient, constant 'm', lie on a straight line: find its equation; equation of ellipse: x^2 + 4y^2 = 4

// Allow me to make the question more explicit: we have a set of lines of equal gradients ‘m’. We need to find a line through which the midpoints of the intersections of these lines with the ellipse; a...

Answered by Drew P. • Further Mathematics tutor

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Prove by induction that n^3+5n is divisible by 3 for every natural number.

Proof by induction has three core elements to it. To start with you must prove that the statement is true for the 'basic case'. For the most part this is 1, but some questions state it is higher.

Answered by Philip D. • Further Mathematics tutor

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Find the square root of i

When dealing with powers of complex numbers, always start by putting the quantity into exponential form.

i has a magnitude of 1 and an ...

Answered by Jamie L. • Further Mathematics tutor

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Find arsinh(x) in terms of x

let y=arsinh(x)x=sinh(y)=(e^y - e^-y)/22x=e^y- e^-y2x*e^y=e^y-1 (multiply bye^y)0=(e^y)²-2xe^y-1This i...

Answered by Joe B. • Further Mathematics tutor

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Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.

We don't know what type of a triangle we're considering here. Therefore the universal and quickest solution to the first problem is use of the cosine rule, which states that for a triangle with sides a,b ...

Answered by Szymon K. • Further Mathematics tutor

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