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To start with, try and spot whether or not two of the coeffecients (numbers next to the letters) are the same for either question (i.e. could be a 3x in one equation and a 3x in the other). This also work...

The mixture has a ratio of 3:2, white to blue paint. 
3+2=5 so there are 5 parts to the mixture, 3 white and 2 blue.
We know the cost of 1 litre of each, so first we can work out the cost of 1...

Beth gets: £48 x 3/8 = £18 The remaining money is: £48 - £18 = £30  (Alternate method: £48 x 5/8 = £30. This eliminates the need for the first step) The ratio is 3:2 so this is the same as fracti...

Unit circle: x² + y² = 1 when x = sqrt(3)/2:  y² = 1 - (sqrt(3)/2)²  y² = 1 - 3/4  y² = 1/4  y = 1/2 or -1/2 (first quadrant, so y is posi...

Set f(x)= (x^4)-14x. f’(x)=4(x^3)-14=2(2(x^3)-7). Thus we can write (2(x^3)-7)/((x^4)-14x)=(1/2)f’(x)/f(x). The integral of f’(x)/f(x)=ln|f(x)|+c. Thus the integral of (2(x^3)-7)/((x^4)-14x) is (1/2)(ln|f...