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There are 10 balls in a bag. The balls are the same apart from their colour. Of the 10 balls, 3 are black, 5 white, 2 red. What is the probability of picking a white ball from the bag.

To calculate the probability assume it is equally likely to choose any of the 10 balls. This is reasonable as we are told that the balls are the same apart from their colours. If we label each ball by number...
AS
Answered by Alvin S. • Maths tutor
8435 Views

Express (3+ i)(1 + 2i) as a complex number in the form a+bi where a and b are real numbers.

One can treat complex multiplication as polynomial multiplication, but remembering i^2 = -1. To perform polynomial multiplication, multiply each term one by one, then add them together. Hence (3+i)(1+2i) = 3...
AS
Answered by Alvin S. • Maths tutor
10500 Views

When integrating by parts, how do I decide which part of the integrand is u or f(x) and which dv or g'(x)?

Integration by parts is not only a very useful techinque for integrating, but it is also one of the techinques that appears more in the IB Mathematics exams. The most important step is to choose the part of ...
XB
Answered by Xell B. • Maths tutor
2668 Views

(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

This question is a typical example aimed to test the student's understanding of the quotient rule, a technique which is used very often in calculus problems. Answer: For a function f(x) = cosx/sinx = u/v, le...
MH
Answered by Mark H. • Maths tutor
18658 Views

Find the integral of xe^(-2x) between the limits of 0 and 1 with respect to x.

We can identify xe^(-2x) as a product and hence we will most probably need to use integration by parts. We then set u = x and v' = x^(-2x). It is important to do it this way round so that when we differentia...
TB
Answered by Tom B. • Maths tutor
8311 Views