The denominator of a fraction cannot be zero.Therefore in h(x) = f(x)/g(x), g(x) cannot equal zero, x + 6 cannot equal zero, x cannot equal -6. The domain of h(x) is ℜ - {-6}.
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Remember that transformation between Cartesian and polar system are:
x=r*cos(α)
y=r*sin(α)
From this we can conclude that:
r=√(x^2 + y^2)
Using trigonometry transformations we can write:
r=sin(2α) = 2sin(α)cos(α)
Now we can multiply both sides with r^2:
r^3 = 2(r*sin(α))*(r*cos(α))
Now using some replacements we can write:
(x^2 + y^2)^(3/2) = 2*x*y
3 x 7 because three, seven times is 21
