#$&* course Mth 164 February 7 11:06 PM &&&& query modeling exercise
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Given Solution: ** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t. If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **
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15:10:20
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): 3 ------------------------------------------------ Self-critique Rating: 3 &&&& Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?
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15:22:13 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: YOu would find the average of the maxium and minium values and place the circle in the center. The radius is half of the diameter and the diameter is the difference of the max and min values. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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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): OK ------------------------------------------------ Self-critique Rating: 3 &&&& 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: If you are looking at weeks there are 52 weeks in a year, so you would have 2pi/52 cycles in a week. You would look at the hours in a day which is 24 hours and to find the vertical coordinate you would divide 24 by 2 which is 12 hours. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. If the period is in months then you have 2 pi / 12 cycles per month, or pi/6 cycles per month. The vertical coordinate of the center will be the day length midway between the min and max day lengths, which is 12 hours.**
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?......!!!!!!!!................................... 15:55:04 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The vertical is the halfway point between the max and min tem. The max is 75 and min is 35 so our average would be 55. The angular velocity could be based on 52 weeks per year which would be 2pi/52cycles per week or pi/26cycles per week. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 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. 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): OK ------------------------------------------------ Self-critique Rating: 3 &&&& 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: The vertical would be the halfway point between 12 feet and 2 feet which is 12+2 = 14/2= 7 feet. The angular velocity would be 2pi rad/10 cycles or pi/5rad/hour. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: ** If you have a cycle in 10 hours then you have 2 pi rad in 10 hours, or 2 pi / 10 = pi/5 rad / hour. The vertical coordinate of the center will be the water level midway between the min and max water levels. **
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15:58:35 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): 2 I didn't add the radius in to the answer until I read the given solution. ???Why would you put the radius in the answer???
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Given Solution: ** The center will lie halfway between the highest and lowest levels. At 5 waves per minute the angular frequency would be 5 periods / minute * 2 pi rad / period = 10 pi rad / min. **
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 &&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?
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YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Radius and diameter of the wheel are the same at 15 in. The angular velocity is 2pi rad/rev * 3/rev = 6pi rad/sec. At this point I am lost. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 1
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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. Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So 6 pi rad / sec * 15 inches / radian = 90 pi inches / second. 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 understand the angular velocity of 6pi rad/sec and after reading the given solution I understand how you have 90 pi inches/sec, ???but I didn't understand how you got 280 inches/sec???