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In order to solve this question we simply must substitute x=1 into f(x).

If we carry out this substitution we see that

f(1) = 2(1^3) + (1^3) -5(1) + c = 2(1) + (1) -5(1) + c = 2 + 1  - 5 + c...

Let's reorgansie the information we've been provided with in the question: Colour of marble - number of marbles in the bag Blue - 2x Green - 7 Red - 7x + 5 Orange - 4x - 3 Probability of the green marble ...

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

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 b...

List Trigonmetric identities which could help to simpilfy integral

Use cos(2x)= Cos²x-sin²x and sin²x=1-cos²x

Sub identity 2 into 1 and rearrange ...