Question

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 7 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?
Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?
Show all work.

Answer 1

Answer:

Let r represent the radius of the smaller circle and R the radius of the larger circle.

Apply ratios: the radius of smaller circle to radius of larger circle, i.e.

r: R = 3 : 7.

I complete rotation = 360 degrees.

Part 1:

For one complete rotation of the smaller circle, the larger circle is rotated through: (3/7)*(360) = 154.3 degrees

Part 2:

For one complete rotation of the larger circle, the larger circle is rotated through: (7/3)*(360) = 840.0 degrees

This is equivalent to (840/360) = 2.3 rotations

Alternatively, use the ratios:

The number of rotations = R/r = 7/3 = 2.3 rotations  

BRAINLIEST PLEASE??

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

for smaller gear circumference=2π×2=4π inches

for larger gear

l=4π

θ=l/r

θ=(4 ×180)/7=720/7=102 .9°

for larger gear circumference=2π×7=14π

number of rotations=(14π)/4π=7/2=3.5 rotations or 3 1/2 rotations.