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By multiplying everything in equation 2 by 2, you get 2x + 8y = 34. If you then subtract equation 1 from this you get 5y = 15. Thus y = 3, going back to equation two, and subbing y back in, x + 12 = 17, t...

First differentiate 2x² - 5x - 3 to get 4x -5. At x = 3, the gradient of the tangent must be 7, and we know it goes through (3, 0) Plug the values into y = mx + c to get the equation of the lin...

f(x) = 7e^2x sin(3x) Chain rule: f(x) = uv → f'(x) = u'v + uv' u = 7e^2x u' = 14e^2x v = sin(3x) v' = 3cos(3x) f'(x) = 14e^2xsin(3x) + 7e^2x 3cos(3x) f'(x...

Dy/dx=3x²+7

In order to prove this we can write a general expression of an odd number in terms of n, e.g - 2n+1Square this 'odd number': (2n+1)^2, therefore you can write it as (2n+1)(2n+1), then expand (multiply out...