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Maths
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How do I solve the equation "2cos(x) = sin(2x), for 0 ≤ x ≤ 3π"?

The key to solving this equation is realizing that sin(2x) can be written in terms of sin(x) and cos(x) using a double-angle formula. (With trigonometric problems similar to this one, you...

Answered by Sanveer R. Maths tutor
32226 Views

How do you calculate the probability P(X < x) for a normally distributed random variable X?

If the details of the distribution - its mean and standard deviation are known, the following transformation applies Z = (X - mean) / stdev where Z is now a random variable distributed as normal(0, 1). No...

Answered by Jonas P. Maths tutor
3834 Views

Solve the equation log(1-x) - log(x) = 1 where log() is the logarithmic function, base 10.

From the rules of logarithms, we know that:

log(A) - log(B) = log(A/B)

and thus:

log(1-x) - log(x) = log[(1-x)/x]

...

Answered by Joshua D. Maths tutor
21337 Views

Differentiate y = e^(x^2 - 3x).

This question is an example of the chain rule for differentiating. 

Firstly, identify the inner function. In this case, it is x- 3x. This function must be differentiated firs...

Answered by Ellie S. Maths tutor
11445 Views

Find cos4x in terms of cosx.

As with any question involving sines and cosines, consider complex numbers as a likely way to find the answer. For this particular kind of question, where sin/cos of a multiple of x is needed in terms ...

Answered by Ellie S. Maths tutor
18501 Views

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