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Express x^2+3x+2 in the form (x+p)^2+q, where p and q are rational numbers.

x 2 +3x+2 = (x+p) 2 +q (x+3/2) 2 = x 2 +3x+9/4 x 2 +3x+2 = (x+3/2) 2 -9/4+2 x 2 +3x+2 = (x+3/2) 2 -1/4
RI
Answered by Ross I. • Maths tutor
8409 Views

How can I remember how to differentiate and integrate cos and sin?

I find it is best whenever you open your maths paper to draw this diagram to help you remember: Sin(X) -> cos(X)-> -sin(X) -> -cos(X)-----> {Drawn in a circle on the board} To differentiate you f...
HM
Answered by Hannah M. • Maths tutor
6936 Views

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...
CH
Answered by Chunlong H. • Maths tutor
5009 Views

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...
NB
Answered by Nils B. • Maths tutor
3542 Views

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...
JC
Answered by Jack C. • Maths tutor
7323 Views