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Step One: stationary/turning points are points on the curve where the gradient equals 0 (i.e. a point at which the slope changes from negative to positive, or vice versa). So we ne...

a) Using log rules, a^x=b becomes log(a)b=x. If we take ln of both sides, we get ln(e^(3x-9))=ln8. ln(e) =1, so we just get 3x-9=ln8. Now we can simply manipulate this to get x=(9+ln8)/3=3+(1/3)ln8. Anoth...

Start with a). Looking at this equation, the trig identity screaming out is cosx^2+sinx^2=1--> cosx^2=1-sinx^2. Substituting this into the LHS of the equation, and with a bit of algebraic rearrangement...

The key to solving simultaneous equations is trying to reduce them into one equation. You can see that one of these equations is quadratic, so you should be thinking there will be 2 answers for x and y. Y...

eq.1 4x+3y=7eq.2 3x+7y=16
You want to eliminate one of the variables (either x or y) reducing the problem to just one equation with one variable which can be solved. This can be done by multiplying e...