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step 1 remember than the a and b terms locate the centre of the circle on the axis so we can substitute in the centre values for a and b. (x-5)^2 + (y-(-3))^2 = k. (x-5)^2 + (y+3)^2 = k.

Step 2. k ...

(i): 15x^(2)+7 --- in order to arrive at this answer, we can divide the equation into 3 separate parts: 5x^(3) and 7x and 3. For the first part, you would multiply the first number, 5 by the power, in thi...

3

By differentiating with respect to x, 3x^2+6x(dy/dx)+6y+2y(dy/dx)=0 So, dy/dx(6x+2y)=-3x^2-6y so dy/dx = -(3x^2+6y)/(2(3x+y))

Imagine the function f(x) as a black box which takes in any value x and produces an output y. The black box acts on its input according to a rule which produces a unique value of y for a given x. If the b...