Solve the simultaneous equations xy=2 and y=3x+5.

x=1/3 and y=6 or x=-2 and y=-1

SS

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A ladder of length 2L and mass m is placed leaning against a wall, making an angle t with the floor. The coefficient of friction between all surfaces is c. At what angle t does the ladder begin to slip?


x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).


f(x) = 2x^3+6x^2-18x+1. For which values of x is f(x) an increasing function?


The curve C is given by the equation x^4 + x^2y + y^2 = 13. Find the value of dy/dx at the point (-1,3). (A-level)