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
Answer:
x = 33.33 kilometers
Step-by-step explanation:
you could make use of the percent, base, and rate formula here. we know that 15% is the rate, 5 kilometers is the percent, therefore what we are looking for is our base.

; cross multiply.
15x = 500
x = 33.33 kilometers
therefore, the race is 33.33 kilometers.