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A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures

Break the solution down into small logical steps, outlining thought process in each one to make it clear to the examiner what it is you are try to do. Emphasise the importance of a clear and neat layout of t...
SF
4140 Views

How do I apply mathematical induction to answer questions

If you are familiar with induction but unsure how to answer the types of questions that require it, a structure can be useful. Even when confident, it will help an examiner to see where to award you marks if...
OM
3091 Views

z = -2 + (2root3)i. Find the modulus and argument of z.

The first step to answering this question is to pinpoint exactly what it means. We remind ourselves that when we are given a number in the form of a + bi, we are dealing with a complex number . A complex num...
MS
12601 Views

Find the Taylor Series expansion of tan(x) about π/4 up to the term in terms of (x-π/4)^3.

Firstly, set f(x) = tan(x). We can then differentiate this 3 times in order to find f'(x), f''(x) and f'''(x). This will require use of the chain rule and the product rule. We can find:f'(x) = sec 2 xf''(x) ...
JM
55981 Views

find all the roots to the equation: z^3 = 1 + i in polar form

1st write 1+ i in polar form, sketch a diagram to find the angle ( =pi/4) and find the modulus ( sqrt(2))z^3 = Sqrt(2) E^ipi/4This is true for all equivalent solutions (add 2kpi) z^3 = sqrt(2)e^(pi/4 +2kpi)i...
RM
11155 Views