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In Topic 5 (Statistics and Probability) what is the difference between mutually exclusive events and independent events?

Put simply, mutually exclusive events cannot occur at the same time, e.g when tossing a coin, the result can either be heads or tails but cannot be both. Independence of events means the occurrence of one ev...
MS
Answered by Meghna S. • Maths tutor
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Given that sin(x) + cos(x) = 2/3, find cos(4x)

It is not clear what to do when starting, but we realise that by making both sides to the power of two, will lead to have an expression containing sin^2(x) + cos^2(x), which is equal to one (which will proba...
FR
Answered by Felipe R. • Maths tutor
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Find integer solutions for m - n(log3(2)) = 10(log9(6)).

From the properties of logarithms (log b a = log c a / log c b), 10log 9 6 can be rewritten as 10(log 3 6 / log 3 9). Since log 3 9 = 2, 10log 9 6 = 5log 3 6. We then bring both log terms to the same side of...
TK
Answered by Tristan K. • Maths tutor
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Solve the differential equation csc(x)*dy/dx=exp(-y), given that y(0)=0. (Typical Math HL paper 3 question, Calculus optional topic)

Firstly, we need to grasp the problem, and understand what the question is asking us to do. We are given a differential equation, and we are required to solve for y, i.e. write y as a function of x: y(x)=......
KG
Answered by Khariton G. • Maths tutor
2125 Views

How to prove that Integral S 1/(a^2+x^2) dx= 1/a arctan(x/a) + C ?

In order to answer this question, at first we need to use the method of substitution. That means, we're trying to replace x with a different variable u. Lets use the substitution of x = a tan u, then du/dx =...
JW
Answered by Judyta W. • Maths tutor
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