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Solve the following simultaneous equations: y-3x+2=0, y^2-x-6x^2=0

(1) y-3x+2=0 (2) y 2 -x-6x 2 =0 Using (1): y=3x-2 Sub y value into (2): (3x-2) 2 -x-6x 2 =0 Expand the brackets: 9x 2 -13x+4-x-6x 2 =0 Group terms: 3x 2 -13x+4=0 Factorise: (3x-1)(x-4)=0 Find roots (set brac...
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Answered by Phoebe A. • Maths tutor
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Prove that cos(4x) = 8(cos^4(x))-8(cos^2(x)) + 1

cos(4x) = cos(2(2x)) = 2(cos^2(2x)) - 1 = 2 (cos^2(x) - 1)^2 - 1 = 8(cos^4(x)) - 8(cos^2(x)) + 1
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Answered by Harry T. • Maths tutor
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How would you integrate (4x+1)^1/3 ?

Firstly, increase the power outside the brackets by 1 and divide the whole thing by the new power. This gives 3/4(4x+1) 4/3 Next, divide the whole thing by the derivative of the bracket. The derivative of (4...
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Answered by Nicholas G. • Maths tutor
7995 Views

How many roots does the equation x^2 = x + 12 have and what are they?

x 2 -x -12 = 0. Here we have rearranged the equation so that we have 0 on one side of the equation, allowing us to now factorise. (x - 4)(x+3) = 0. By looking at the equation we can see that the number 12 ha...
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Answered by Juzer E. • Maths tutor
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Find the gradient of the line Y = X^3 + X + 6 when X = 4

Step 1: Differentiate the equation Y = X^3 + X + 6 to find the gradient of the line at any point. To do this, multiply each term of X by the old power and -1 from that power. This makes dy/dx = 3X^2 + 1.Step...
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Answered by Henry O. • Maths tutor
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