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In order to find the points where these functions meet, we can equate them to get 3x-2 = x^2+4x-8 .

Subtraction (3x-2) from both sides, we get x^2+x-6 =0 which we can factorise to get (x+3)(x-2)=0<...

We have a "fraction" which we wish to differentiate, so we use the quotient rule with u=sin(x) and v=cos(x).

This means that d/dx of u/v = (vdu/dx - udv/dx)/(v^2).

y = cos(x)/sec²(x) = cos³(x)

y = cos(x)(1-sin²(x)) = cos(x) - cos(x) sin²(x)

-> sin(x) - sin³(x)/3 + c

This isn't a trick so much as a way to let you show you can think for yourself. You might be thrown off initially if a quadratic equation is in a format that you don't recognise, but usually all it takes ...

To work out how many litres of white and blue paint is needed, use the ratio 3:2. To find the specifc ratio for 18 litres, of paint: 2+3=5, 18/5=3.6 so (3:2)3.6 becomes 10.8:7.2 (check 10.8+7.2=18). S...