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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

We know that the equation of the area of a rectangle is width times by length. Therefore:

8=(3x+1)(2x+5)

If we multiply out the brackets we get:

8=(6x²+2x+15x+5), thus, 8=6...

Sin x is equal to the length of the opposite side divided by the length of the hypotenuse. So, the length of the opposite side is Sin x multiplied by the length of the hypotenuse