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First step is to realise that as x=3 is a root of f(x)=0, then we can use (x-3) as a factor of f(x). A really good method to use to find what (fx)/(x-3) gives is Synthetic Division. Using this method we t...

Given the equation of the straight line is: x+y=9 and the equation of the circle is: (x-2)²+(y-3)²=16 , find the point or points of intersection? The equation x+y=9 can be rearranged...

Start the integration by parts process

|udv = uv - |vdu

  u = (ln x)²             dv = x⁷ dx

du = 2(ln x)/x dx         v = 1/8 x⁸

A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding ...

(a) There is a quadratic equation which should e solved using the delta andthe roots formulas.

delta=a²-4ab

delta=144-4(k+1)(k-4)

delta=-4k²+12k+160

Becau...