A bug is stuck on a fan blade as it rotates in a counter-clockwise direction. Th

Question

A bug is stuck on a fan blade as it rotates in a counter-clockwise direction. The function f gives the angle measure swept out by the bug (in radians) in terms of the number of seconds since he was at ti 3 o'clock position. The function g gives the height of the bug (in radi) above the horizontal diameter of the fan in terms of the angle measure swept out by the bug (in radians) from the 3 o'clock position The function h gives the height of the bug (in feet) above the horizontal diameter of the fan in terms of the height of the bug (in radii) above the horizontal diameter of the fan. The function ke gives the height of the bug (in feet) above the table in terns of the height of the bug (in feet) above the horizontal diameter of the fan. The function m gives the angle measure swept out by the bug (in radians) in terms of the number of feet the bug has traveled along the circular path traced out by the fan blade Match the following expressions with the appropriate quantity

Explanation / Answer

e-h(g(f(x)))

height in feet in terms of time

d-g(f(x))

height in radii in terms of time

g-g(f(h(x)))

f is function of times,where h(x) is distance in feet

b-f-1(m(x))

time elapsed in terms of number of feet the bug travelled along circular path traced out by the fan blade

c- m-1(x)

number of feet the bug travelled along circular path traced out by the fan blade in terms of angle swept out by bug

b -f-1(g-1(x))

time elapsed in terms of radii

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