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Find the general solution of the equation tan(2x + pi/2) = SQRT(3), giving your answer for x in terms of π in a simplified form.

Assume y = 2x + pi/2, Since the period of 'tangent' is pi, the general solution of 'y' to valid the equation of tan(y) = SQRT(3) is the form of y = n pi+pi/3 where 'n' is any positive or negative integer and...
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Answered by Chunlong H. • Maths tutor
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Tom drink drives two days a week, the chance of him being caught per day is 1 in 100. What is the chance he will not be driving after a) one week? b) one year?

a) In one week he will drive drive twice, each day the probability of getting caught is 1/100 and not getting caught is 99/100. using a probability tree diagram, we can see there is only one possible outcome...
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Answered by Nils B. • Maths tutor
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Use integration by parts to find ∫ (x^2)sin(x) dx. (A good example of having to use the by parts formula twice.)

Before we blindly start using the integration by parts formula, we can see that no matter how many times we differentiate or integrate sin(x) we will still have a trigonometric function. The aim of the 'by p...
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Answered by Jack C. • Maths tutor
7330 Views

Find the intergal of 2x^5 -1/(4x^3) -5 giving each term in its simplest form.

When integrating, we raise the power by 1 and divide by the new powerSo, 2x 5 becomes 2x 6 /6 which simplified down as the question asks is x^6/3-1/(4x 3 ) is -(1/4)x^ -3 using indices laws, raising the powe...
EW
Answered by Emily W. • Maths tutor
3699 Views

The functions f and g are defined by f : x → 2x + ln 2, g : x → e^(2x). Find the composite function gf, sketch its graph and find its range.

Composition of functions is when one function is inside of another function. That is, we replace each occurrence of x found in the outside function with the inside function. In our example, we start by writi...
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Answered by Anna S. • Maths tutor
14674 Views