asst_1_query

course Mth 164

The pendumlum I constructed was about 16 inches long with a 5.020 angular velocity.

??r???????}?assignment #001

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001.

Precalculus II

01-26-2007

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16:11:31

What is the distance between the peaks of the graph for which the angular velocity of the reference point is 3 rad / sec, and what are the maximum and minimum vertical coordinates if the circle is centered at vertical coordinate 12?

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RESPONSE -->

The distance between peaks is about 4 seconds. The maximum vertical is 13 and the minimum is 11 if the radius of the circle is 1 unit.

confidence assessment: 2

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16:12:34

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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RESPONSE -->

The maximum value is the highest point on the graph and the minimum number is the lowest point. The radius is found by subtracting the two values and divide it by two. The center point is found by adding the radius to the lowest point or subtracting it from the highest point, is centered on the y axis.

confidence assessment: 2

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16:13:45

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?

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RESPONSE -->

The vertical coordinate of the circle's center is y = 12. Found by 15hr-9hr = 6 / 2 = 3 units of radius So 9+3 = 12 center.

The angular velocity is 2pi/12 rad/month = pi/6 rad/month.

confidence assessment: 2

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16:14:51

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?

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RESPONSE -->

The vertical coordinate of the circle's center of the circle is y = 55. Found by 75-35 = 40 / 2 = 20 units of radius, then 35+20 = 55 center.

The angular velocity is 2pi/52 rad/week = pi/26 rad/week.

confidence assessment: 2

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16:16:37

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?

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RESPONSE -->

The vertical coordinate of the circle's center is y = -5, found by -12-2 = -14 / 2 = -7 units of radius, then 2-7 = -5 center.

The angular velocity is 2pi/10 rad/hr = pi/5 rad/hr.

confidence assessment: 2

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16:17:53

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?

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RESPONSE -->

The vertical coordinate of the circle's center is y = 38, found by 40-36 = 4/2 = 2 units of radius, then 36+2 = 38 center.

The angular velocity is 2pi/12 rad/sec = pi/6 rad/sec.

confidence assessment: 2

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16:20:38

query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

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RESPONSE -->

With a radius = 15 in at 3 rev/sec.

omega = 3 rev/sec * 2pi rad/rev = 6pi rad/sec

linear speed = r(omega) = 15 in(6pi rad/sec)= 90pi in/sec = approx. 282.743 in/sec / 17.6 = 16.065 mph

confidence assessment: 1

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16:22:24

Explain your solution to this problem.

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RESPONSE -->

Given the radius and rev/sec, find the angular velocity (6pi rad/sec) now the linear speed can be found with v=rw giving value 282.743 in/sec which is divided by 17.6 (conversion factor of in/sec to mi/hr = 63360/3600 = inches in mile/ sec in an hour) to get the value of 16.065 mph.

confidence assessment: 1

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Excellent work. Let me know if you have questions.