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Multiply out brackets
x² = 4(x² - 6x + 9)x² = 4x² - 24x + 36
Minus x² from both sides 3x² -24x + 36 = 0
Divide equation by ...

These are a pair of simultaneous equations.First, we can equate two of the coefficients in each equation (let's choose x) by multiplying each equation respectively.With our first equation, multiply it by ...

The probability that the first sweet is orange is 6/n, as 6 of the n number of sweets are orange. After an orange sweet is eaten, there are 5 orange sweets left and n-1 total sweets in the bag. This means...

The general equation of a circle takes the form (x - A)^2 + (y - B)^2 = r^2 where (A,B) is the centre of the circle with radius r. Thus, we aim to rearrange the equation in the question to match this form...

Use the cosine trig identity, cos(a-b)=cos(a)cos(b)+sin(a)sin(b) ,to write Rcos(x-a) as R(cos(x)cos(a)+sin(x)sin(a)).Now we can equate the coefficients of the sines and cosins on either side of the equati...