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It is given f(x)=(19x-2)/((5-x)(1+6x)) can be expressed A/(5-x)+B/(1+6x) where A and B are integers. i) Find A and B ii) Show the integral of this from 0 to 4 = Kln5

Firstly, we are given that f(x) can be expressed in the above form, so we write this out: (19x-2)/((5-x)(1+6x)=A/(5-x)+B/(1+6x) We then multiply by the denominator of f(x): 19x-2=A(1+6x)+B(5-x) Now we can ch...
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Answered by Mike W. • Maths tutor
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Find the possible values of x for x^2 = 36-5x.

While this question may appear unfamiliar at first, it is just a quadratic equation in disguise. Rearranging such that it equals 0: x^2 + 5x - 36 = 0 Now this equation is ready to be solved! We can approach ...
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Answered by Ben H. • Maths tutor
10032 Views

How do I simplify fully (p^3 x p^4)/p^2?

At first this looks quite daunting as it combines a number of different indices (powers) and a fraction. The rules for indices are just something that you have to learn - so don't worry if you don't know the...
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Answered by Emily R. • Maths tutor
15055 Views

Solve simultaneously: x + y + 3 = 0 and y = 2x^2 +3x - 1

First Step: I believe here it is important to firstly look at each equation on its own and just try to think how the examiner would want you to answer this type of question. Second Step: Recognise that both ...
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Answered by Jamie S. • Maths tutor
5198 Views

Solve the equation; 4 cos^2 (x) + 7 sin (x) – 7 = 0, giving all answers between 0° and 360°.

4 cos 2 (x) + 7sin (x) – 7 = 0 (1) Using the identity sin 2 (x) + cos 2 (x) = 1, rearrange to give; cos 2 (x) = 1 - sin 2 (x) (2) Sub (2) into (1) ... Giving; 4 ( 1 - sin 2 (x) ) + 7sin (x) - 7 = 0 Expand br...
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Answered by Connor S. • Maths tutor
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