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Find an expression for y
y = 3 - x
sub this into the second equation
x^2 + (3 - x)^2 = 5
then expand the brackets
x^2 + x^2 - 6x + 9 = 5
simplify
2(x^2 - 3x + 2) = 0<...

First differentiate the function to obtain
dy/dx = 6x^2 + 30x + 24
Then set this equal to 0 and solve to find the x values of the stationary points
6x^2 + 30x + 24 = 0
6(x^2 + 5x + 4) ...

£29.40 represents 4/5 of xThus to find x, we must multiply 29.40 by 5/4:
29.40/4 = 7.35 (this is 1/5) 7.35 x 5 = 36.75 (this is 5/5, the original price)
Original price = £36.75

First, take the side of the equation that looks most complicated because it often needs simplifying. This is the LHS in this case. The LHS has cos(2x) twice - therefore the double angle formula probably a...

This term cannot be integrated in the form that it is in. We will have to do some algebraic manipulation to rewrite it. The term can be split into partial fractions because the denominator of the term has...