course MTH 164 1/24/10 8:30 p.m. If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: ** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t. If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **
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15:10:20
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?
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15:22:13 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The diameter would be 8 given the min and max of 6 and 14 the circle would lie on the center axis of 10 confidence rating #$&*: 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The center of the circle will be halfway between the max and min values, which can be found by averaging the two values (i.e., add and divide by 2). The diameter will be the difference between the max and min values and the radius will be half of the diameter. **
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15:22:16 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2pi/12 months angular velocity day varies from 9 to 15 the mid point vertical coordinate would be 12 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. If the period is in months then you have 2 pi / 12 cycles per month, or pi/6 cycles per month. The vertical coordinate of the center will be the day length midway between the min and max day lengths, which is 12 hours.**
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?......!!!!!!!!................................... 15:55:04 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The vertical coordiante would be 55 which is half way between 75 and 35 The angular velocity will be 2pi/52 weeks confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. The vertical coordinate of the center will be the temperature midway between the min and max temperatures.**
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15:58:33 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the tide model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Midpoint would be -5 halfway between -12 and 2 the angular velocity would be 2pi/10hours confidence rating #$&*: 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If you have a cycle in 10 hours then you have 2 pi rad in 10 hours, or 2 pi / 10 = pi/5 rad / hour. The vertical coordinate of the center will be the water level midway between the min and max water levels. **
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15:58:35 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the ocean wave model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The vertical coordinate would be 38 and you would have 5cycles per/min which would be 5*2pi = 10pi/minute confidence rating #$&*: 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The center will lie halfway between the highest and lowest levels. At 5 waves per minute the angular frequency would be 5 periods / minute * 2 pi rad / period = 10 pi rad / min. **
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?
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YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 15pi *3 rev/sec 45pi in/sec 141.37in/sec 141.37/12 = 11.78 ft/sec 5280/11.78 = 448.218 secs to travel a mile = 7.47 min per mile 60/7.47= 8.03 mph confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If 15 inches is the diameter of the wheel then the radius is 15 inches. The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec. 905 pi rad / sec. If you approximate this you get around 280 in/sec. This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx. A mile is 5280 ft and an hour is 3600 sec so this is 23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. ** Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I'm not sure where I went wrong at the beginning of this problem, I thought you could just get the circumfrence of the wheel by taking pi*d then multiply by the 3 rev/sec and thats how many in the wheel would have gone per second. ------------------------------------------------ Self-critique rating #$&*:
course MTH 164 1/24/10 8:30 p.m. If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: ** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t. If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **
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15:10:20
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?
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15:22:13 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The diameter would be 8 given the min and max of 6 and 14 the circle would lie on the center axis of 10 confidence rating #$&*: 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The center of the circle will be halfway between the max and min values, which can be found by averaging the two values (i.e., add and divide by 2). The diameter will be the difference between the max and min values and the radius will be half of the diameter. **
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15:22:16 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2pi/12 months angular velocity day varies from 9 to 15 the mid point vertical coordinate would be 12 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. If the period is in months then you have 2 pi / 12 cycles per month, or pi/6 cycles per month. The vertical coordinate of the center will be the day length midway between the min and max day lengths, which is 12 hours.**
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?......!!!!!!!!................................... 15:55:04 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The vertical coordiante would be 55 which is half way between 75 and 35 The angular velocity will be 2pi/52 weeks confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. The vertical coordinate of the center will be the temperature midway between the min and max temperatures.**
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15:58:33 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the tide model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Midpoint would be -5 halfway between -12 and 2 the angular velocity would be 2pi/10hours confidence rating #$&*: 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If you have a cycle in 10 hours then you have 2 pi rad in 10 hours, or 2 pi / 10 = pi/5 rad / hour. The vertical coordinate of the center will be the water level midway between the min and max water levels. **
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15:58:35 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the ocean wave model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The vertical coordinate would be 38 and you would have 5cycles per/min which would be 5*2pi = 10pi/minute confidence rating #$&*: 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The center will lie halfway between the highest and lowest levels. At 5 waves per minute the angular frequency would be 5 periods / minute * 2 pi rad / period = 10 pi rad / min. **
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*: &&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?
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YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 15pi *3 rev/sec 45pi in/sec 141.37in/sec 141.37/12 = 11.78 ft/sec 5280/11.78 = 448.218 secs to travel a mile = 7.47 min per mile 60/7.47= 8.03 mph confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If 15 inches is the diameter of the wheel then the radius is 15 inches. The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec. 905 pi rad / sec. If you approximate this you get around 280 in/sec. This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx. A mile is 5280 ft and an hour is 3600 sec so this is 23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. ** Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I'm not sure where I went wrong at the beginning of this problem, I thought you could just get the circumfrence of the wheel by taking pi*d then multiply by the 3 rev/sec and thats how many in the wheel would have gone per second. ------------------------------------------------ Self-critique rating #$&*: