# Slow and steady wins the race

Find the equation of cross-section of a circularly symmetrical bowl shaped racetrack such that the time of completing a lap in it is inversely proportional to the square of velocity of a race car by a constant of proportionality $$K$$ .

If the equation is given by:

$$y=-\frac { a }{ b } \times \frac { { K }^{ c } }{ { \pi }^{ d }{ g }^{ e }{ x }^{ f } }$$

where $$g$$ is the acceleration due to gravity and $$x$$ is the distance from centre of the racetrack.

find,

$$\left| a \right| +\left| b \right| +\left| c \right| +\left| d \right| +\left| e \right| +\left| f \right|$$

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