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a) This is no standard differentiate question. You will need identify the fact that the equation contains both x and y terms and thus you will need to differentiate with respect to both. This involves ap...

Subtract 2y from both sides:4y = 12Divide by 4:y = 3

3x + 5y = 14 (times this entire equation by 3) --> 9x + 15y = 42 4x + 3y = 4 (times this entire equation by 5) --> 20x + 15y = 20Now both of the simultaneous equations have 15y, so you can subtract ...

we first remember the double angle formula, a really important formula. cos(2x) = cos²(x) - sin²(x).We know that sin²(x) + cos²(x) = 1, therefore, cos(2x) = cos...

dy/dx = 3x² - 8x - 3
when dy/dx = 0 , 0 = 3x² - 8x - 3
Factorise : 0= (3x + 1)(x - 3)
when 3x+1 =0 , x = -1/3when x-3=0 , x =3
so x = -1/3 , 3co-ordinates are : (...