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How do you simplify something of the form Acos(x) + Bsin(x) ?

This sort of question is quite common, and a little bit complicated, so the explanation is quite long! But it's a great one to understand. There are a few tricks you need to know to be able to do it. The fir...
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Answered by Jack M. • Maths tutor
15962 Views

f(x) = (4x + 1)/(x - 2) with x > 2. Find a value for 'x' such that f'(x) (first derivative of f(x) with respect to x) is equal to -1.

Re-write f(x) using indicies, so that the use of the product rule becomes more clear => f(x) = (4x + 1) *(x - 2)^-1 where ^ means 'raised to the power of' and * means 'multiplied by'. use the product rule...
ZS
Answered by Zak S. • Maths tutor
5321 Views

Find the exact solutions for 4 − x^2 = |2x − 1|

x=-1 x=-1+6 0.5
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Answered by Shroya V. • Maths tutor
6256 Views

What is a confidence interval?

Using the normal distribution, we can estimate a range of values which we expect to contain the mean. For example, if we take a sample of 30 students height, we can estimate the mean height of students in th...
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Answered by Alexander R. • Maths tutor
4985 Views

i) Simplify (2 * sqrt(7))^2 ii) Find the value of ((2 * sqrt(7))^2 + 8)/(3 + sqrt(7)) in the form m + n * sqrt(7) where n and m are integers.

i) (2 sqrt(7)) 2 = 2 2 sqrt(7) 2 = 4 * 7 = 28 (1 mark) ii) First of all substitute the answer from above. ((2 * sqrt(7)) 2 + 8) / (3 + sqrt(7)) = (28 + 8) / (3 + sqrt(7)) = 36 / (3 + sqrt(7)) Multiply by (3 ...
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Answered by Andrew B. • Maths tutor
8096 Views