1)Convert 1/20 of a circle to both degrees and radians.
All I have is 9/180 is what I come up with.
2) what fraction of a circle does 3pi/4 represent?
Is 1/4 correct?
3) a ferries wheel has cars which move at 1.5mph. If the diameter of the wheel is 600 ft, how long will it take to complete one revolution? I use v=rw and get 11rev/50pi min I think I did it right but it wants 1rev/ min?
360/20 = 18 deg and 2pi/20 = 0.1 pi
3 pi/4 / 2 pi = 3/8
1.5 (5280 ft/3600 seconds) = 2.2 feet/second
r = 300 feet (not likely ferris wheel radius is the length of a football field but anyway)
circumference = 2 pi r = 600 pi
time to do 2 pi radians = 600 pi/2.2 = 857 seconds
857 seconds / 60 = 14.3 minutes
This must be the world's biggest and slowest ferris wheel. Are you sure the diameter is not 60 feet?
mouu
1) To convert 1/20 of a circle to degrees, we need to find what fraction of 360 degrees it represents:
1/20 * 360 degrees = 18 degrees
To convert 1/20 of a circle to radians, we need to find what fraction of 2π radians it represents:
1/20 * 2π radians = π/10 radians
So, 1/20 of a circle is equivalent to 18 degrees and π/10 radians.
2) To find the fraction of a circle represented by 3π/4, we need to divide it by 2π:
(3π/4) / (2π) = 3/8
Therefore, 3π/4 represents 3/8 of a circle.
3) To find the time it takes to complete one revolution of a ferris wheel, we can use the formula v = rw, where v is the linear velocity, r is the radius, and w is the angular velocity (in radians per minute).
Given that the diameter of the wheel is 600 ft (radius = 600/2 = 300 ft) and the cars move at 1.5 mph, we need to convert the units to be consistent:
1.5 mph * 5280 ft/mile = 7920 ft/hour
7920 ft/hour / 60 min/hour = 132 ft/min
Now we can use the formula:
v = rw
132 ft/min = (300 ft) * w
Solving for w:
w = 132 ft/min / 300 ft
w = 11/25 radians per minute
Therefore, it takes 25/11 minutes (or approximately 2.27 minutes) to complete one revolution of the ferris wheel.
1) To convert a fraction of a circle to degrees, you need to know that a complete circle is divided into 360 degrees. So, to convert 1/20 of a circle to degrees, you can multiply 1/20 by 360:
1/20 * 360 = 18 degrees.
To convert the same fraction to radians, you need to know that there are 2π radians in a complete circle. So, multiply 1/20 by 2π:
1/20 * 2π = π/10 radians.
Therefore, 1/20 of a circle is equal to 18 degrees and π/10 radians.
2) To determine the fraction of a circle that 3π/4 represents, we need to compare it to a complete circle. A complete circle is represented by 2π radians or 360 degrees.
Since 3π/4 is less than 2π, it represents less than a complete circle. To express it as a fraction, we can divide it by 2π:
(3π/4) / 2π = 3/8.
Therefore, 3π/4 represents 3/8 of a circle, not 1/4.
3) To calculate the time it takes to complete one revolution on the ferris wheel, you correctly used the formula v = rw, where v is the speed, r is the radius, and w is the angular velocity.
Given that the diameter of the wheel is 600 ft, the radius is half of the diameter, which is 300 ft. Let's assume the ferris wheel completes one revolution in T minutes. The angular velocity can be expressed as 2π radians per T minutes.
Using the formula v = rw, we have:
1.5 mph = 300 ft * (2π/T) (since the speed is given in mph)
We need to convert 1.5 mph to ft/min by multiplying it by 5280 ft/1 mile and dividing by 60 min/1 hr:
1.5 mph * (5280 ft/1 mile) / (60 min/1 hr) = 88 ft/min.
Substituting this value into the equation, we have:
88 ft/min = 300 ft * (2π/T)
To solve for T, we can rearrange the equation as follows:
T = 300 ft * (2π) / 88 ft/min
Simplifying this expression gives us:
T ≈ 21.5 min
Therefore, it will take approximately 21.5 minutes to complete one revolution on the ferris wheel.