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Three forces, (15i + j) N, (5qi – pj) N and (–3pi – qj) N, where p and q are constants, act on a particle. Given that the particle is in equilibrium, find the value of p and the value of q. (Mechanics 1 June 2017)

As the particle is at rest, the net force acting on the particle must be equal to zero, i.e. Fres = 0Therefore, (15i + j) + (5qi - pj) + (-3pi - qj) = 0Collating 'i' terms: 15 + 5q - 3p = 0 (Equation 1)Colla...
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Answered by Idris K. • Maths tutor
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Find dy/dx if y=(x^3)(e^2x)

Use product rule. Set u=x^3 and v=e^2x. Differentiate u and v. Then dy/dx = uv'+vu' = (3x^2)*(e^(2x))+(2x^3)(e^(2x)). This problem is best explained written on a whiteboard (it's difficult to give an explana...
JM
Answered by Joseph M. • Maths tutor
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What is the moment about the pivot C

Uniform rod AB of weight 5g (g being 9.8) and length 4 metres rested on a pivot C which is 1.5m from B. Calculate the moments about the point C. sketch diagram of information provided weight is acting left o...
TZ
Answered by Talal Z. • Maths tutor
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Use integration to find I = ∫ xsin3x dx

Use integration by parts, let U = x, the derivative of U = 1, let the derivative of V = sin3x and intergrate the derivative of V to arrive at V = (-1/3)(cos3x). Substitute the value into the formula uv − ∫ v...
ZL
Answered by Zifeng L. • Maths tutor
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Find a solution to sec^(2)(x)+2tan(x) = 0

This question is a quadratic equation in hiding. The first step to solving this would be to expand sec^(2)(x) into 1 + tan^(2)(x) as they are equivalent. This can be derived by dividing sin^(2)(x) + cos^(2)(...
MB
Answered by Mohamed B. • Maths tutor
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