#$&* course Mth 164 09/10/10 10:48 &&& query modeling exercise
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Given Solution: ** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t. If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **
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15:10:20
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&* &&&& 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: To find the center of the circle you would add up the values and divide by two. To determine the radius you would first have to find the diameter which is the difference between the maximum and minimum values and then if you divide by two you would have the radius. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The center of the circle will be halfway between the max and min values, which can be found by averaging the two values (i.e., add and divide by 2). The diameter will be the difference between the max and min values and the radius will be half of the diameter. **
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15:22:16 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&* &&&& 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: The vertical coordinate for the center of the circle would be 12 because it is the average between the minimum day length (9) and the maximum day length (15). The angular velocity of the reference point for the daylight model would be pi/6 cycles per month. 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 coordinates for the center of the circle would be the average of the maximum value (75) and the minimum value (35) which would be at the vertical coordinate of 55. The angular velocity would be pi/26 cycles per period. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. The vertical coordinate of the center will be the temperature midway between the min and max temperatures.**
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15:58:33 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I put radians per period when it should have been radians per week. I understand my mistake. ------------------------------------------------ Self-critique rating #$&*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 coordinate of the center of the circle would be the average of the maximum point (12) and the minimum point (2) which would be at the vertical coordinate of 7. The angular velocity would be pi/5 radians per hour. confidence rating #$&* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If you have a cycle in 10 hours then you have 2 pi rad in 10 hours, or 2 pi / 10 = pi/5 rad / hour. The vertical coordinate of the center will be the water level midway between the min and max water levels. **
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15:58:35 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&* &&&& 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 of the center of the circle would be the average of the maximum point (40) and the minimum point (36) which would be at the vertical coordinate of 38. The angular velocity would be 10 pi radians per minute. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The center will lie halfway between the highest and lowest levels. At 5 waves per minute the angular frequency would be 5 periods / minute * 2 pi rad / period = 10 pi rad / min. **
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&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&* &&&& 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: If a tire has a radius of 15 and the angular velocity is 3 rev/ sec then the speed of the vehicle would be about 283 inch/sec. or 16 mph. ???Where did you get 905 pi rad/sec I only had 90 rad/sec was it a typo???
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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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