For the drop down boxes the options are \"equal to\", \"less than\", \"more than
ID: 2912414 • Letter: F
Question
For the drop down boxes the options are "equal to", "less than", "more than", and "not enough info"
4 points) A bug rests at the end of a fan blade, 34 cm from the center of the fan. The bug is in the 3 o'clock position on the fan's circle of rotation when the fan begins to turn counter clockwise. (Click on the graph to get a larger version.) a) If the bug travels 55 cm around the circle from the 3 o'clock position, what angle measured in radians did the fan turn? Round to the nearest hundredth. b) If the fan rotates 5.3 radians, how many cm does the bug travel along the arc? Give an exact result. c) A fly lands on the same fan blade as the bug, but closer to the center of the fan than the bug. The bug and fly maintain their positions as the fan rotates for an interval of time. During that time intervalâ the radius length associated with the fly is the number of radians swept out by the fly is v the radius length associated the bug. v the number of radians swept out by the bug. the number of cm the fly travels along its arc is v the number of cm the bug travels along its arc.Explanation / Answer
55 cm from 3 o clock in counterclockwise.
r = 34 cm
Circumference = 2pi*34 = 68pi cm, i.e 213.6283004441059402 cm
So, fraction of circumference covered is :
(55 / 213.6283004441059402) i.e 0.2574565255898306902
So, the approx radians covered =
0.2574565255898306902 * 2pi
1.6176470588235294116744 radians
1.62 radians -----> ANS
----------------------------------------------------------------
b)
5.3 radians
5.3/(2pi) * circumference
0.8435211983870453 * (2pi * 34)
180.2 cm -----> ANS
----------------------------------------------------------------
c)
Fly is closer to the center than the bug
So, radius length of fly IS LESS THAN that of the bug
Number of radians swept is EQUAL TO that of the bug
number of cm the fly travels is LESS THAN that of the bug
cuz its closer and therefore has a smaller radius length