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A particle A rests on a smooth inclined plane, it is connected to a particle B by a light inextensible string that is passed over a fixed smooth pulley at the top of the plane. B hangs freely. Find the acceleration of the system and tension in the string.

Full Question: A particle A of mass 2.5kg is at rest on a smooth inclined plane at an angle of 25 degrees, it is connected to a particle B of mass 1.5kg by a light inextensible string which lies along a l...

Answered by Kyle W. • Maths tutor

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Edexcel C3 June 2015 Q1: tan(x)=p, where p is a constant. Using standard trigonometric identities, find the following in terms of p. a) tan(2x). b) cos(x). c) cot(x-45).

a) tan(A+B)=(tanA+tanB)/(1-tanAtanB) So, tan(2x)=[tan(x)+tan(x)]/[1-(tanx)(tanx)]. Therefore, tan(2x)=[2tan(x)]/[1-tan^2(x)] = 2p/(1-p^2). b) cos(x)=1/sec(x). Using other trigonometric identities, we know...

Answered by Liam R. • Maths tutor

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When do I use the chain rule and when do I use the product rule in differentiation?

These are two really useful rules for differentiating functions. We use the chain rule when differentiating a 'function of a function', like f(g(x)) in general. We use the product rule when differentiatin...

Answered by Michael O. • Maths tutor

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Express 6cos(2x) + sin(x) in terms of sin(x), hence solve the equation 6cos(2x) + sin(x) = 0 for 0<x<360

For the 1st part of the question: use the double angle formula to rewrite cos(2x) = cos^2(x) - sin^2(x). Then use the basic identity to write cos^2(x) = 1-sin^2(x), hence cos(2x) = 1-2sin^2(x). Plug the r...

Answered by Gwen F. • Maths tutor

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How do you do integration by parts?

Split the equation into two : one that you are going to integrate, and the other one you want to differentiate. then, apply formula uv - integral(v * du)

Answered by Harvin I. • Maths tutor

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