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What is Pythagoras's theorem?

Pythagoras's theorem is used to calculate the lengths of the sides of right-angled triangles. The theorem can be used to find the length of the third side of a right-angled triangle, as long as the lengths o...
SJ
Answered by Samuel J. • Maths tutor
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How do you find the maximum and minimum value of a quadratic function with no use of calculus?

By completing the square, since this makes you see that the square will always be >= 0 and the other part allows you to calculate the minima or maxima depending on the sign in front of x 2 . E.g. x 2 +4x=...
AO
Answered by Alexander O. • Maths tutor
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Prove that 1/sin(2theta) - cos(2theta)/sin(2theta) = tan(theta)

Before we begin to approach this question, we first write down all the relevant formulae for this trigonometry question. We can see that we will need the double angle formulae (on account of the presence of ...
CM
Answered by Colin M. • Maths tutor
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Solve for y: 5(y – 2) + 2(y – 3) = 19

Most important thing is to do the same thing to both sides of the equation. 5(y – 2) + 2(y – 3) = 19 Step 1. Multiply out the brackets: 5y - 10 + 2y - 6 = 19 Step 2. Collect like terms & Simplify: 5y + 2...
RJ
Answered by Rahul J. • Maths tutor
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Solve the following simultaneous equations: 3x + 2y = 16 2x + 3y = 14

Answer: x = 4, y = 2 Method: Eq 1) 3x + 2y = 16 Eq 2) 2x + 3y =14 Eq 1 x 2) 6x + 4y = 32 Eq 2 x 3) 6x + 9y = 42 New Eq 2 - New Eq 1) 5y = 10, so y = 2 Sub y into Eq 1) 3x + 4 = 16, 3x = 12, so x = 4
EO
Answered by Elizabeth O. • Maths tutor
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