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A particle P of mass 0.4 kg is moving under the action of a constant force F newtons. Initially the velocity of P is (6i – 27j) m s−1 and 4 s later the velocity of P is (−14i + 21j) m s−1 . Find, in terms of i and j, the acceleration of P.

On the whiteboard I would provide a brief drawing of the particle, and of all the information provided (force applied to P and its before and after velocity) as a visual aid for the student. I would ask/r...

Answered by Finn W. • Maths tutor

6918 Views

Factorise 3x + 6

Hcf=3
3(x+2)

Answered by Rumsha A. • Maths tutor

10657 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

5077 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

4909 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

5346 Views