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ABC are points on a circle, centre O. AO=9cm, OC=9cm and AC=15cm. Find the angle ABC.

Diagrams would be used to help visualise the answer. To find the angle OAC, the cosine rule needs to be used: cosA = (b 2 + c 2 - a 2 )/2bc. Therefore, looking at the diagram, (15 2 + 9 2 - 9 2 )/2x15x9 = co...
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Answered by Imogen P. • Maths tutor
4453 Views

Calculate the integral of (3x+3)/(2x^2+3x) between the limits 39 and 3

The first step is to split the fraction into 2 separate fractions using partial fractions techniques. Write 3x+3/2x^2+3x as A/x + B/2x+3 and solve to get A = 1, B = 1. We have now converted 3x+3/2x^2+3x into...
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Answered by Oliver W. • Maths tutor
3528 Views

Where do the graphs of y=3x-2 and y=x^2+4x-8 meet?

In order to find the points where these functions meet, we can equate them to get 3x-2 = x^2+4x-8 . Subtraction (3x-2) from both sides, we get x^2+x-6 =0 which we can factorise to get (x+3)(x-2)=0 Therefore ...
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Answered by Helen S. • Maths tutor
4049 Views

Given that z=sin(x)/cos(x), show that dz/dx = sec^2(x).

We have a "fraction" which we wish to differentiate, so we use the quotient rule with u=sin(x) and v=cos(x). This means that d/dx of u/v = (v du/dx - u dv/dx)/(v^2). We have u=sin(x) so du/dx= cos(...
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Answered by Gabriela G. • Maths tutor
5075 Views

Integrate y with respect to x, where y = cos(x)/[1+tan^2(x)]

y = cos(x)/sec 2 (x) = cos 3 (x) y = cos(x)(1-sin 2 (x)) = cos(x) - cos(x) sin 2 (x) -> sin(x) - sin 3 (x)/3 + c
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Answered by Daniel C. • Maths tutor
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