course Mth 151 ͮJy}Ҫassignment #007
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13:27:00 `q001. Note that there are 7 questions in this assignment. Sketch three points A, B and C forming an equilateral triangle on a piece of paper, with point A at the lower left-hand corner, point B at the lower right-hand corner and point C at the top. Sketch the segments AB and AC. Now double the lengths of AB and AC, and place a point at each of the endpoints of these segments. Connect these new endpoints to form a new equilateral triangle. Two sides of this triangle will have three points marked while the new side will only have its two endpoints marked. Fix that by marking that middle point, so all three sides of your new triangle are marked the same. How many marked points were there in the original triangle, and how many are there in the new triangle?
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RESPONSE --> There are three marked points in the original triangle (A, B, C) and five marked points in the new triangle. confidence assessment: 0
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13:27:55 The original triangle had the three points A, B and C. When you extended the two sides you marked the new endpoints, then you marked the point in the middle of the third side. So you've got 6 points marked. Click on 'Next Picture' to see the construction. The original points A, B and C are shown in red. The line segments from A to B and from A to C have been extended in green and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and an equally spaced point has been constructed at the midpoint of that side. Your figure should contain the three original points, plus the three points added when the new side was completed.
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RESPONSE --> I did not count the point in the center between the double length of AC and AB (the new triangle) self critique assessment: 2
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13:31:02 `q002. Extend the two sides that meet at A by distances equal to the distance original lengths AC and AB and mark the endpoints of the newly extended segments. Each of the newly extended sides will have 4 marked points. Now connect the new endpoints to form a new right triangle. Mark points along the new side at the same intervals that occur on the other two sides. How many marked points are on your new triangle, and how many in the whole figure?
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RESPONSE --> 5 points on the new triangle and 11 in the whole figure. confidence assessment: 0
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13:31:39 You added the two new endpoints when you extended the sides. You then should have marked two new points on the new third side, so that each side contains 4 points including its endpoints. Your figure will now contain 10 marked points.
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RESPONSE --> I added an extra unnecessary point to get 5/11. self critique assessment: 2
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13:32:26 `q003. Continue the process for another step-extend each side by a distance equal to the original point-to-point distance. How many points do you have in the new triangle?
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RESPONSE --> 14 points in the new triangle. confidence assessment: 0
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13:32:50 You will add an endpoint to each newly extended side, so each of the new sides will contain 5 points. You will then have to add 3 equally spaced points to the new side, giving you a total of 13 points on the new triangle. In addition there are two marked points inside the triangle, for a total of 15 points. Click on 'Next Picture' to see the construction. The line segments along two sides of the triangle have again been extended and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and equally spaced points have been constructed along that side.
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RESPONSE --> Here I've forgotten a point. self critique assessment: 0
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13:33:25 `q004. Continue the process for one more step. How many points do you have in the new triangle?
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RESPONSE --> 21 points in the new triangle. confidence assessment: 1
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13:34:39 You will add an endpoint to each newly extended side, so each of the new sides will contain 6 points. You will then have to add 4 equally spaced points to the new side, giving you a total of 15 points on the new triangle. There are also 5 marked points inside the triangle for a total of 21 marked points.
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RESPONSE --> The triangle grows larger diagonally by a sequence of 1, 2, 3, 4, 5, so the next step is logically to add 6 points to the previous total of 15 to arrive at 21 points. self critique assessment: 2
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13:35:52 `q005. The sequence of marked points is 3, 6, 10, 15, 21. What do expect will be the next number in this sequence?
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RESPONSE --> 28 should be the next number in the sequence given that the pattern seems to be going (3, 4, 5, 6, ...) so 7 should be added to 21 to obtain 28. confidence assessment: 2
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13:37:39 `q006. How can you tell, in terms of the process you used to construct these triangles, that the next number should be 7 greater?
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RESPONSE --> The same way that the triangle appears to grow diagonally in a pattern of 1, 2, 3, 4, 5 for the marked points, the sequence of numbers also grows by 3, 4, 5, 6. confidence assessment: 1
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13:38:52 `q007. How do you know this sequence will continue in this manner?
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RESPONSE --> The sequence will continue in this manner because the triangle will cease to be an equal triangle if it does not. confidence assessment: 1
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13:39:38 Each time you extend the triangle, each side increases by 1. All the new marked points are on the new side, so the total number of marked points will increase by 1 more than with the previous extension.
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RESPONSE --> By extending the triangle each side increases by 1, therefore keeping the equality of the newly formed 'big' triangle. self critique assessment: 2
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}XV assignment #007 007. Triangular, Square, Pentagonal Numbers Liberal Arts Mathematics I 02-15-2009"
course Mth 151 ͮJy}Ҫassignment #007
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13:27:00 `q001. Note that there are 7 questions in this assignment. Sketch three points A, B and C forming an equilateral triangle on a piece of paper, with point A at the lower left-hand corner, point B at the lower right-hand corner and point C at the top. Sketch the segments AB and AC. Now double the lengths of AB and AC, and place a point at each of the endpoints of these segments. Connect these new endpoints to form a new equilateral triangle. Two sides of this triangle will have three points marked while the new side will only have its two endpoints marked. Fix that by marking that middle point, so all three sides of your new triangle are marked the same. How many marked points were there in the original triangle, and how many are there in the new triangle?
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RESPONSE --> There are three marked points in the original triangle (A, B, C) and five marked points in the new triangle. confidence assessment: 0
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13:27:55 The original triangle had the three points A, B and C. When you extended the two sides you marked the new endpoints, then you marked the point in the middle of the third side. So you've got 6 points marked. Click on 'Next Picture' to see the construction. The original points A, B and C are shown in red. The line segments from A to B and from A to C have been extended in green and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and an equally spaced point has been constructed at the midpoint of that side. Your figure should contain the three original points, plus the three points added when the new side was completed.
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RESPONSE --> I did not count the point in the center between the double length of AC and AB (the new triangle) self critique assessment: 2
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13:31:02 `q002. Extend the two sides that meet at A by distances equal to the distance original lengths AC and AB and mark the endpoints of the newly extended segments. Each of the newly extended sides will have 4 marked points. Now connect the new endpoints to form a new right triangle. Mark points along the new side at the same intervals that occur on the other two sides. How many marked points are on your new triangle, and how many in the whole figure?
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RESPONSE --> 5 points on the new triangle and 11 in the whole figure. confidence assessment: 0
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13:31:39 You added the two new endpoints when you extended the sides. You then should have marked two new points on the new third side, so that each side contains 4 points including its endpoints. Your figure will now contain 10 marked points.
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RESPONSE --> I added an extra unnecessary point to get 5/11. self critique assessment: 2
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13:32:26 `q003. Continue the process for another step-extend each side by a distance equal to the original point-to-point distance. How many points do you have in the new triangle?
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RESPONSE --> 14 points in the new triangle. confidence assessment: 0
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13:32:50 You will add an endpoint to each newly extended side, so each of the new sides will contain 5 points. You will then have to add 3 equally spaced points to the new side, giving you a total of 13 points on the new triangle. In addition there are two marked points inside the triangle, for a total of 15 points. Click on 'Next Picture' to see the construction. The line segments along two sides of the triangle have again been extended and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and equally spaced points have been constructed along that side.
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RESPONSE --> Here I've forgotten a point. self critique assessment: 0
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13:33:25 `q004. Continue the process for one more step. How many points do you have in the new triangle?
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RESPONSE --> 21 points in the new triangle. confidence assessment: 1
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13:34:39 You will add an endpoint to each newly extended side, so each of the new sides will contain 6 points. You will then have to add 4 equally spaced points to the new side, giving you a total of 15 points on the new triangle. There are also 5 marked points inside the triangle for a total of 21 marked points.
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RESPONSE --> The triangle grows larger diagonally by a sequence of 1, 2, 3, 4, 5, so the next step is logically to add 6 points to the previous total of 15 to arrive at 21 points. self critique assessment: 2
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13:35:52 `q005. The sequence of marked points is 3, 6, 10, 15, 21. What do expect will be the next number in this sequence?
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RESPONSE --> 28 should be the next number in the sequence given that the pattern seems to be going (3, 4, 5, 6, ...) so 7 should be added to 21 to obtain 28. confidence assessment: 2
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13:37:39 `q006. How can you tell, in terms of the process you used to construct these triangles, that the next number should be 7 greater?
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RESPONSE --> The same way that the triangle appears to grow diagonally in a pattern of 1, 2, 3, 4, 5 for the marked points, the sequence of numbers also grows by 3, 4, 5, 6. confidence assessment: 1
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13:38:52 `q007. How do you know this sequence will continue in this manner?
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RESPONSE --> The sequence will continue in this manner because the triangle will cease to be an equal triangle if it does not. confidence assessment: 1
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13:39:38 Each time you extend the triangle, each side increases by 1. All the new marked points are on the new side, so the total number of marked points will increase by 1 more than with the previous extension.
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RESPONSE --> By extending the triangle each side increases by 1, therefore keeping the equality of the newly formed 'big' triangle. self critique assessment: 2
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}XV assignment #007 007. Triangular, Square, Pentagonal Numbers Liberal Arts Mathematics I 02-15-2009"