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Solve the simultaneous equations: y = x - 2 and y^2 + x^2 = 10

y = x - 2 y 2 + x 2 = 10 Subsitutute the top equation into the second equation: (x-2) 2 + x 2 = 10 Expand out the brackets and simplify: x 2 - 4x + 4 + x 2 = 10 2x 2 - 4x - 6 = 0 x 2 - 2x - 3 = 0 Factorise t...
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Answered by Iman R. • Maths tutor
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What is a derivative - Introduction to Calculus

Strictly speaking, the derivative is the rate of change of a function, process or pattern. So far, to calculate the gradient of a given function we always computed the change in the y coordinates divided by ...
GM
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How do I differentiate (2x+1) / (3x^2 - 5)?

This is a typical example where the quotient rule is required to answer the question. This is clear because the function is made up of two other functions of x, one is the numerator and the other is the deno...
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Answered by Sophie T. • Maths tutor
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In an arithmetic sequence, the first term is 2, and the fourth term is 14. a) Find the common difference, d. b) Calculate the sum of the first 14 terms, S14.

a) We have that a 1 = 2 and a 4 = 14, so the first thing that we can conclude is that the common difference, d, is positive, and that a 2 and a 3 are in between 2 and 14. We know that a 1 + 3d = 14. Substitu...
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Answered by Zhihong Z. • Maths tutor
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Solve the simultaneous equations 2x - 3y = 7 and 3x + 4y = 2. Do not use trail and improvement.

[ 2x - 3y = 7 ] *3 = [ 6x - 9y = 21 ] [ 3x + 4y = 2 ] *2 = [ 6x + 8y = 4 ] [ 6x + 8y = 4 ] - [ 6x - 9y = 21 ] = [ 17y = -17 ] Therefore, y = -1. Substituting y = -1 into the original equations and solving fo...
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Answered by Elizabeth H. • Maths tutor
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