Add & give answer in lowest (reduced) form: 1/6 + 3/8
2 answers:
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Answer:
1. The fan blade makes 112.3 revolutions in 1.4 minutes
2. The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute ⇒ B
Step-by-step explanation:
1.
∵ The angular velocity of a fan blade is 8.4 radians per second
∴ ω = 8.4 rad/sec
- The revolution = the product of angular velocity and the time
of revolution ÷ 2π
∵ Revolutions = (ω . t)/2π
∵ The fan blade makes x revolutions in 1.4 minutes
∴ t = 1.4 minutes
- Change it to seconds
∵ 1 minute = 60 seconds
∴ 1.4 minutes = 1.4 × 60 = 84 seconds
- Substitute ω and t in the rule of revolutions
∴ Revolutions =
∴ Revolutions ≅ 112.2997278
∴ Revolutions ≅ 112.3
- Round it to the nearest tenth
∴ The fan blade makes 112.3 revolutions in 1.4 minutes
2.
∵ The radius of the larger gear is 8 centimeters
∵ The radius of the small gear is 3 centimeters
∵ The two gears are connected by a chain
- That means the move the same distance together
∴ , where n is the number of revolution for each
gear and C is the circumference of each gear
The formula of the circumference of a circle is C = 2πr
∵ = 2π(3) = 6π
∵ = 2π(8) = 16π
∵ The smaller gear completes 24 revolutions in 20 seconds
∴ = 24
- Substitute them in the rule above to find
∵ 24 × 6π = × 16π
∴ 144π = × 16π
- Divide both sides by 16π
∴ 9 =
∴ The larger gear completes 9 revolutions in 20 seconds
The linear velocities of the two gears are equal because they move together and make the same distance in the same time
∵ The linear velocity = Distance ÷ Time
∵ Distance which each gear makes = C × n
∴ V =
Let us use the smaller gear to find the linear velocity
∵ C = 6π centimeters
∵ n = 24 revolution
∵ t = 20 seconds
- Change it to minutes
∴ 20 seconds = 20 ÷ 60 = minute
∴ V =
∴ V = 432π cm/min
Let us check the answer by find the linear velocity fro the larger gear
∵ C = 16π centimeters
∵ n = 9 revolution
∵ t = minute
∴ V =
∴ V = 432π cm/min
The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute