To calculate the centripetal force needed for Nan to stay on the merry-go-round, you convert the rotational speed to radians per second and use the centripetal force formula, factoring in the radius and angular velocity. ;
To find the equation representing the given situation, we need to write the number of times Nan rode the roller coaster in terms of the number of times she rode the Ferris wheel. Nan rode the Ferris wheel 4 times, and the equation representing the situation is 2x = 8. ;
The equation to represent how many times Nan rode the roller coaster compared to the Ferris wheel is 2f = 8, where 'f' represents the number of times she rode the Ferris wheel. Solving this gives us that she rode the Ferris wheel 4 times. Therefore, Nan rode the roller coaster 8 times, which is twice the number of times she rode the Ferris wheel.
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