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Solve 2^(3x-1) = 3

2 3x - 1 = 3log 2 (2 3x-1 ) = log 2 (3)3x - 1 = log 2 (3)3x = 1 + log 2 (3)x = 1 / 3 + 1 / 3 log 2 (3)
JB
Answered by Jacob B. • Maths tutor
5742 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 the variables ...
LP
Answered by Louis P. • Maths tutor
5902 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-6)^(1/2) - c Substitute x = ...
LP
Answered by Louis P. • Maths tutor
5994 Views

If y = sec(z)tan(z)/sqrt(sec(z)) then find the indefinite integral of y with respect to z.

Using the substitution u = sec(z)=> du = sec(z)tan(z) dz.So, the integral ∫ y dz = ∫ sec(z)tan(z)/sqrt(sec(z)) dz=> ∫ y dz = ∫ 1/sqrt(u) du = 2sqrt(u) + C = 2sqrt(sec(z)) + C.
JM
Answered by Jordan M. • Maths tutor
7493 Views

Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

First, you will need to differentiate the function with respect to x. Finding dy/dx.For polynomials, this is done by taking one away from the old power and multiplying the coefficient by the old power and re...
LH
Answered by Laurence H. • Maths tutor
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