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Prove that the square of an odd number is always 1 more than a multiple of 4

We start off by defining what an odd number is. We take a general letter, say the letter n, to represent any number. If we multiple it by 2 we are sure no matter what number we enter as n the answer will...

Answered by Tanmayi M. • Maths tutor

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A circle C has centre (-5, 12) and passes through the point (0,0) Find the second point where the line y=x intersects the circle.

The equation of a circle comes in a standard format of (x-a)² + (y-b)² = r² where (a, b) are the coordinates of the centre of the circle and r is the radiusFrom the inform...

Answered by • Maths tutor

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Solve the equation sec^2(x) - 4tan(x)= -3 , 0 ≤x≤ 2π

To solve this problem, we have to look at some trig. identities that will help us simplify the problem.The formula booklet is always a great place to start! You can find that sec^2(x) = 1 + tan^2(x). Subs...

Answered by Patrick H. • Maths tutor

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Show algebraically that (4n-3)^2 - (2n+5)^2 is always a multiple of n-4

First we expand the brackets by squaring each side(4n-3)² = (4n-3)(4n-3)= 16n² - 24n + 9(2n+5)² = (2n+5)(2n+5)= 4n²+ 20n + 25Remember the expression i...

Answered by Ella B. • Maths tutor

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Put the following in order of size, smallest first: 8/sqrt3, sqrt6*sqrt2, sqrt48-sqrt27

First part of the question is to recognise that these are surds and we will need to simplify them. Then it is asking to place the values from smallest to highest. In order to simplify the surds we have t...

Answered by Sandeep S. • Maths tutor

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