Please help me. You work every Sunday in the yard from 8:00 A.M. To 11:30 A.M. Draw a diagram that shows the rotation completed by the hour hand of a clock during this time. Find the measure of the angle generated by the hour hand in both degrees and radians. Compare this angle with the angle generated by the minute hand from 8:00 A.M. To 11:30 A.M
Ah, time-related questions! Well, let me put on my clown makeup and tackle this one for you.
Now, let's start with the hour hand. During the time from 8:00 A.M. to 11:30 A.M., the hour hand goes through a rotation of 270 degrees (3/4 of a full rotation). In radians, that's about 4.71 radians, which is a pretty rad number.
Now, let's clown around with the minute hand. From 8:00 A.M. to 11:30 A.M., the minute hand completes a full rotation of 360 degrees. In radians, that's about 6.28 radians. The minute hand sure loves going in circles.
Comparing the two angles, we can see that the minute hand covers a larger angle than the hour hand during that time interval. This is because the minute hand completes a full rotation while the hour hand only goes through 3/4 of a rotation. So, the minute hand is the real showstopper in this time act.
I hope that brings some humor to your time-related question! If you have any more questions or need some more laughs, feel free to ask!
To draw the diagram, we must first understand the rotation completed by the hour hand of a clock during the given time.
The hour hand of a clock completes one full rotation, which is 360 degrees or 2π radians, in 12 hours. Since we are interested in the time from 8:00 A.M. to 11:30 A.M, which is a total of 3 hours and 30 minutes, we need to find the fraction of the full rotation completed during this time.
Step 1: Convert 3 hours and 30 minutes to decimal form:
3 hours = 3
30 minutes = 30/60 = 0.5 hours
So, the total time is 3 + 0.5 = 3.5 hours.
Step 2: Find the fraction of the full rotation completed:
Fraction = (Time / Total hours) * Full rotation
= (3.5 / 12) * 360 degrees
= 105 degrees
Therefore, the hour hand completes a rotation of 105 degrees or 105π/180 radians during the time from 8:00 A.M. to 11:30 A.M.
Now, let's compare this angle with the angle generated by the minute hand during the same time period.
The minute hand of a clock completes one full rotation in 60 minutes, which is equal to 60 degrees or π radians.
Step 1: Calculate the total time from 8:00 A.M. to 11:30 A.M. in minutes:
3 hours = 3 * 60 = 180 minutes
30 minutes = 30
So, the total time is 180 + 30 = 210 minutes.
Step 2: Find the fraction of the full rotation completed:
Fraction = (Time / Total minutes) * Full rotation
= (210 / 60) * 360 degrees
= 1260 degrees
Therefore, the minute hand completes a rotation of 1260 degrees or 1260π/180 radians during the time from 8:00 A.M. to 11:30 A.M.
In conclusion, the hour hand generates an angle of 105 degrees or 105π/180 radians, while the minute hand generates an angle of 1260 degrees or 1260π/180 radians during the time from 8:00 A.M. to 11:30 A.M.
To draw a diagram that shows the rotation completed by the hour hand of a clock from 8:00 A.M. to 11:30 A.M., we need to visualize a clock face and mark the positions of the hour hand at the beginning and end times.
1. Start by drawing a circle to represent the clock face.
2. Draw a straight line from the center of the circle to the edge, representing the hour hand. Label the starting point as "8:00 A.M." and the ending point as "11:30 A.M."
3. Connect the starting and ending points with an arc, representing the rotation completed by the hour hand.
To find the measure of the angle generated by the hour hand in both degrees and radians, we need to calculate the fraction of a full rotation covered during the given time span.
1. Calculate the total number of hours between 8:00 A.M. and 11:30 A.M. The difference is 3.5 hours.
2. Determine the fraction of the full hour represented by 3.5 hours. Divide 3.5 by 12 (total hours on a clock face) to find the fraction: 3.5/12 = 0.2917.
3. Multiply the fraction by the full angle covered in a clock face (360 degrees) to find the angle generated by the hour hand: 0.2917 * 360 = 105 degrees.
4. To convert the angle to radians, multiply it by π/180: 105 * π/180 = approximately 1.833 radians.
To compare this angle with the angle generated by the minute hand from 8:00 A.M. to 11:30 A.M., we need to calculate the rotation completed by the minute hand during the same time interval.
1. Calculate the total number of minutes between 8:00 A.M. and 11:30 A.M. The difference is 210 minutes.
2. Determine the fraction of the full hour represented by 210 minutes. Divide 210 by 60 (total minutes in an hour) to find the fraction: 210/60 = 3.5.
3. Multiply the fraction by the full angle covered in a clock face (360 degrees) to find the angle generated by the minute hand: 3.5 * 360 = 1260 degrees.
4. To convert the angle to radians, multiply it by π/180: 1260 * π/180 = approximately 22 radians.
Therefore, the angle generated by the hour hand from 8:00 A.M. to 11:30 A.M. is 105 degrees (1.833 radians), while the angle generated by the minute hand during the same time interval is 1260 degrees (approximately 22 radians).
hour hand:
8:00 am to 11:30 am is 3.5 hours.
on the face of a standard clock this is 3.5/12 or 7/24 of a rotation, thus
105° or 7π/12 radians
minute hand from 8:00 am to 11:30 am
the minute hand will have made 3.5 rotations or
gone through
1260° or 7π radians