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Simplify the expression: (x^2 + x - 6)/(3x^2 + 9x)

Factorise the numerator: x^2 + x - 6 = (x+3)(x-2) Factorise the denominator: 3x^2 + 9x = 3x(x+3) Cancel '(x+3)' Answer: (x-2)/3x
RD
Answered by Richard D. • Maths tutor
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sin(x)/(cos(x)+1) + cos(x)/(sin(x)+1) = 1

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1 (sin^2(x) + cos^2(x) =1) Therefore; 1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1 Cancelling out on both sides cos(x)sin(x) =...
JO
Answered by James O. • Maths tutor
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What is the indefinite integral of cos^2x?

List Trigonmetric identities which could help to simpilfy integral Use cos(2x)= Cos 2 x-sin 2 x and sin 2 x=1-cos 2 x Sub identity 2 into 1 and rearrange to show Cos 2 x=(1+cos2x)/2 and integrate to find the...
JM
Answered by Jake M. • Maths tutor
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Solve 3x^2 + 6x – 2 = 0 Give your solutions correct to 2 decimal places.

3x 2 + 6x - 2 = 0 When we have a polynomial with powers of x up to 2 (a quadratic equation) we can apply the quadratic formula : -b ± root(b 2 -4ac)/2a where your equation is in the form ax 2 + bx + c 0 so a...
MS
Answered by Maya S. • Maths tutor
9831 Views

Given y = x^3 + 4x + 1, find the value of dy/dx when x=3

To differentiate this equation, you must bring the power of each x term down to the front and reduce the power of x by 1, with constants disappearing: dy/dx = 3 x 3-1 + (4 1)*x 1-1 = 3x 2 + 4 To find the val...
FH
Answered by Florence H. • Maths tutor
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