course Phy 201 assignment #001001. Areas
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03:54:13 `q001. There are 11 questions and 7 summary questions in this assignment. What is the area of a rectangle whose dimensions are 4 m by 3 meters.
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RESPONSE --> 4*3=12m confidence assessment: 3
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03:56:19 02-06-2009 03:56:19 A 4 m by 3 m rectangle can be divided into 3 rows of 4 squares, each 1 meter on a side. This makes 3 * 4 = 12 such squares. Each 1 meter square has an area of 1 square meter, or 1 m^2. The total area of the rectangle is therefore 12 square meters, or 12 m^2. The formula for the area of a rectangle is A = L * W, where L is the length and W the width of the rectangle. Applying this formula to the present problem we obtain area A = L * W = 4 m * 3 m = (4 * 3) ( m * m ) = 12 m^2. Note the use of the unit m, standing for meters, in the entire calculation. Note that m * m = m^2.
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NOTES -------> I forgot to use the square my meters
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03:57:02 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> 4.0m*3.0m=12m^2 confidence assessment: 3
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03:58:38 A right triangle can be joined along its hypotenuse with another identical right triangle to form a rectangle. In this case the rectangle would have dimensions 4.0 meters by 3.0 meters, and would be divided by any diagonal into two identical right triangles with legs of 4.0 meters and 3.0 meters. The rectangle will have area A = L * W = 4.0 m * 3.0 m = 12 m^2, as explained in the preceding problem. Each of the two right triangles, since they are identical, will therefore have half this area, or 1/2 * 12 m^2 = 6.0 m^2. The formula for the area of a right triangle with base b and altitude h is A = 1/2 * b * h.
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RESPONSE --> I misread this problem I thougth i was still dealing with the rectangle instead of the triangle. self critique assessment: 3
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03:59:38 `q003. What is the area of a parallelogram whose base is 5.0 meters and whose altitude is 2.0 meters?
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RESPONSE --> 5.0m*2.0m=10.0m^2 confidence assessment: 3
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04:02:34 `q004. What is the area of a triangle whose base is 5.0 cm and whose altitude is 2.0 cm?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. The area of the triangle would be 1/2 the area of the parallelogram so 10m^/2=5m^2 confidence assessment: 3
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04:03:30 02-06-2009 04:03:30 It is possible to join any triangle with an identical copy of itself to construct a parallelogram whose base and altitude are equal to the base and altitude of the triangle. The area of the parallelogram is A = b * h, so the area of each of the two identical triangles formed by 'cutting' the parallelogram about the approriate diagonal is A = 1/2 * b * h. The area of the present triangle is therefore A = 1/2 * 5.0 cm * 2.0 cm = 1/2 * 10 cm^2 = 5.0 cm^2.
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NOTES -------> Be careful with your measurements m vs cm etc.
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04:04:40 `q005. What is the area of a trapezoid with a width of 4.0 km and average altitude of 5.0 km?
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RESPONSE --> 4.0km*5.0km=20.0km^2 confidence assessment: 2
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04:07:12 `q006. What is the area of a trapezoid whose width is 4 cm in whose altitudes are 3.0 cm and 8.0 cm?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. 4cm*3.0cm=12.0cm^2 and 4cm*8.0cm=32cm^2 Then add the two together to get 12cm+32cm=44cm^2 confidence assessment: 2
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04:08:49 02-06-2009 04:08:49 The area is equal to the product of the width and the average altitude. Average altitude is (3 cm + 8 cm) / 2 = 5.5 cm so the area of the trapezoid is A = 4 cm * 5.5 cm = 22 cm^2.
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NOTES -------> Should have added the two sides together first then divided them by 2 to get 5.5 cm then did the multiplication by the 4cm to get the 22 cm
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04:10:12 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> 3.0^2=9.00cm^2 confidence assessment: 1
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04:13:05 02-06-2009 04:13:05 The area of a circle is A = pi * r^2, where r is the radius. Thus A = pi * (3 cm)^2 = 9 pi cm^2. Note that the units are cm^2, since the cm unit is part r, which is squared. The expression 9 pi cm^2 is exact. Any decimal equivalent is an approximation. Using the 3-significant-figure approximation pi = 3.14 we find that the approximate area is A = 9 pi cm^2 = 9 * 3.14 cm^2 = 28.26 cm^2, which we round to 28.3 cm^2 to match the number of significant figures in the given radius. Be careful not to confuse the formula A = pi r^2, which gives area in square units, with the formula C = 2 pi r for the circumference. The latter gives a result which is in units of radius, rather than square units. Area is measured in square units; if you get an answer which is not in square units this tips you off to the fact that you've made an error somewhere.
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NOTES -------> I forgot how to get the area of a circle always A=pi*r^2.
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04:14:24 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> 3cm*2=6cm confidence assessment: 0
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04:15:41 02-06-2009 04:15:41 The circumference of this circle is C = 2 pi r = 2 pi * 3 cm = 6 pi cm. This is the exact area. An approximation to 3 significant figures is 6 * 3.14 cm = 18.84 cm. Note that circumference is measured in the same units as radius, in this case cm, and not in cm^2. If your calculation gives you cm^2 then you know you've done something wrong.
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NOTES -------> c=2 pi r
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04:17:09 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> a=pi*d a=3.14*12m=37.68m confidence assessment: 1
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04:18:47 02-06-2009 04:18:47 The area of a circle is A = pi r^2, where r is the radius. The radius of this circle is half the 12 m diameter, or 6 m. So the area is A = pi ( 6 m )^2 = 36 pi m^2. This result can be approximated to any desired accuracy by using a sufficient number of significant figures in our approximation of pi. For example using the 5-significant-figure approximation pi = 3.1416 we obtain A = 36 m^2 * 3.1416 = 113.09 m^2.
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NOTES -------> Ok remember to break the diameter down into the radius before you do your calculations and use the a=pe * r^2 formula.
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04:23:52 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> take 14/3.14=4.458598then divide that by 2=2.229299 to get the radius then a=pi*r^2 so a=3.14*2.2292^2=4.96977*3.14=15.605m^2 confidence assessment: 1
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04:25:41 02-06-2009 04:25:41 We know that A = pi r^2. We can find the area if we know the radius r. We therefore attempt to use the given information to find r. We know that circumference and radius are related by C = 2 pi r. Solving for r we obtain r = C / (2 pi). In this case we find that r = 14 pi m / (2 pi) = (14/2) * (pi/pi) m = 7 * 1 m = 7 m. We use this to find the area A = pi * (7 m)^2 = 49 pi m^2.
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NOTES -------> remember to use your formulas to backtrack and solve these problems.
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04:29:32 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> use the forumla A=pi*r^2 so 78m^2=3.14*r^2=78/3.14=r^2 rounding you get 25=r^2 and if you take the square root of 25 you get 5m confidence assessment: 1
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04:32:19 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. All of the space inside the rectangle. Like having two triangles attached together. confidence assessment: 3
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04:33:00 02-06-2009 04:33:00 We visualize the rectangle being covered by rows of 1-unit squares. We multiply the number of squares in a row by the number of rows. So the area is A = L * W.
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NOTES -------> visualize them being covered by 1 unit squares
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04:34:30 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> The area of a right triangle is 1/2 the l*w or a rectangle. confidence assessment: 2
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04:35:45 02-06-2009 04:35:45 We visualize two identical right triangles being joined along their common hypotenuse to form a rectangle whose length is equal to the base of the triangle and whose width is equal to the altitude of the triangle. The area of the rectangle is b * h, so the area of each triangle is 1/2 * b * h.
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NOTES -------> whoops not 1/2 the l*w but 1/2 the b*h
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04:36:02 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> A=b*h confidence assessment: 3
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04:37:05 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. area of a trapezoid is area= base * height confidence assessment: 3
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04:37:43 02-06-2009 04:37:43 We think of the trapezoid being oriented so that its two parallel sides are vertical, and we multiply the average altitude by the width.
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NOTES -------> trapezoid should be the length * width
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04:38:04 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> A= pi *r^2 confidence assessment: 3
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04:40:11 `q017. Summary Question 6: How do we calculate the circumference of a circle? How can we easily avoid confusing this formula with that for the area of the circle?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. C=2pi*r the circumference is 2pi r where the area is pi *r^2. in area you square your radius and in circ you take 2 times your pi multiplied by your radius. confidence assessment: 3
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04:41:54 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. This was a refresher for me I could not remember much of this without this assignment. Its been awhile. I have taken notes on all the formulas and saved some of my notes so I can refere back to them later if needed. confidence assessment: 3
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