Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

A child's mobile makes one full rotation every 15 seconds. Through what angles has the mobile rotated after 5 minutes? Options are below.?

a. 2pi radians

b. 20pi radians

c. 40pi radians

d. 0 pi radians

5 Answers

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  • 1 month ago

    5 min = 5 * 60 = 300 s

    300/15 = 20 rotations

    20 rotations * 2pi/rotation = 40pi radians

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  • 1 month ago

    A child's mobile makes one full rotation every 15 seconds.

    Through what angles has the mobile rotated after 5 minutes?

    The number of 15 seconds in 5 minutes is 20.

    Answer option:  

    c. 40pi radians  

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  • 1 month ago

    15 seconds = 1/4 minute

    5 minutes = 20 * 15 seconds

    so 20 revolutions

    1 revolution = 2pi radians

    so 40pi radians

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  • 1 month ago

    5 minutes x (60 seconds / 1 minute) = 300 seconds.

    300 / 15 = 20 rotations.

    1 rotation = 2π radians.

    20 rotations = 40π radians (c).

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  • 1 month ago

    1 full rotation is 360° or 2π radians.

    Intuitively:

    In 1/4 minute (15 seconds) --> 2π radians.

    In 1 minute --> 8π radians

    In 5 minutes --> 40π radians

    If you want to be a little more formal:

    2π radians / 15 seconds * 60 seconds / minute * 5 minutes

    = (2π * 60 * 5) / 15 radians

    = 2π * 4 * 5 radians

    = 40π radians

    Answer:

    c. 40π radians

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