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x - 2y = 1 , x^2 + y^2 = 13 find the solutions to this quadratic equation

equation 1) x - 2y = 1equation 2) x 2 + y 2 = 13 Rearrange equation 1 to: x = 1+2ysubstitute into equation 2: (1+2y) 2 + y 2 =13expand first bracket: (1+2y)(1+2y) +y 2 =13(1+4y+4y 2 ) +y 2 = 13Collect like t...
CS
Answered by Caitlin S. • Maths tutor
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solve y=3x+4, x=y+1

Equation 1) y=3x+4Equation 2) y=x+1 Rearrange equation 2 into terms of x as this is the simplest: x= y-1 (We do this by subtracting 1 off of each side to get X by itself)Substitute new equation 2 into 1: y=3...
CS
Answered by Caitlin S. • Maths tutor
3502 Views

Factorise x 2 − x − 12

X 2 - X -12 look at what numbers will add together and make 12. (2x6) or (3x4)Then see what of these combinations, when added together, makes -1. you have to consider that one of these values will be negativ...
VV
Answered by Vicky V. • Maths tutor
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What actually IS 'differentiation'?

Differentiation is a really common technique in a branch of maths called calculus. The idea is that you have a line on a graph (or a 'function') and we want to know the gradient - the steepness - of that cur...
BT
Answered by Ben T. • Maths tutor
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Consider an isosceles triangle ABC, where AB=AC=1, M is the midpoint of BC, and <BAM=<CAM=x. Use trigonometry to find an expression for BM and by finding BC^2, show that cos2x = 1 - 2(sinx)^2.

Consider the right-angled triangle BAM. We have the hypotenuse and an angle, and want to find the opposite side. Therefore, using SOHCAHTOA, sinx = BM/1, hence BM = sinx. Because M is the midpoint of BC, BC ...
BS
Answered by Blessie S. • Maths tutor
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