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Factorise 3x + 6

Hcf=3
3(x+2)

Answered by Rumsha A. • Maths tutor

9959 Views

Solve 2^(3x-1) = 3

2^{3x - 1} = 3log₂(2^3x-1) = log₂(3)3x - 1 = log₂(3)3x = 1 + log₂(3)x = ¹/₃ + ¹/₃log₂(...

Answered by Jacob B. • Maths tutor

4781 Views

Express cos2x in the form a*cos^2(x) + b and hence show that the integral of cos^2(x) between 0 and pi/2 is equal to pi/a.

Apply the double angle formula to cos2x to yield the requested result.
cos2x = 2cos^2(x) - 1
Spot that the question asks us to prove the value of cos^2(x) when integrated, and that we can move t...

Answered by Louis P. • Maths tutor

4501 Views

Solve the differential equation dx/dt = -2(x-6)^(1/2) for t in terms of x given that x = 70 when t = 0.

First, manoeuvre variables so that we can integrate the equation.
1/(x-6)^(1/2) dx = -2 dt
Integrate the equation and add the constant.
2(x-6)^(1/2) = -2t +c
Solve for t.
t = -(x-...

Answered by Louis P. • Maths tutor

5011 Views