course Mth 158 ???????{??N???assignment #001
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13:49:43 `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 --> The area is 12 meters confidence assessment: 3
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13:50:45 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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RESPONSE --> I know that the area of a rectangle is length times width. self critique assessment: 2
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13:56:51 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> First you must find the height using pythagorean theorem. I did 4^2 + 3^2 = h^2. I found the height to be 5. Then I used the formula for area of a triangle. A=1/2 (b) (h). A=1/2(3)(5). A=7.5 meters confidence assessment: 2
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14:00:31 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 found the height using the pythagorean theorem. I understand now that how you got the triangles from the rectangle. self critique assessment: 2
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14:06:21 `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 --> A=bh. A=5 ( 2). Area equals 10 meters ^2 confidence assessment: 3
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14:07:37 A parallelogram is easily rearranged into a rectangle by 'cutting off' the protruding end, turning that portion upside down and joining it to the other end. Hopefully you are familiar with this construction. In any case the resulting rectangle has sides equal to the base and the altitude so its area is A = b * h. The present rectangle has area A = 5.0 m * 2.0 m = 10 m^2.
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RESPONSE --> I didn't cut of the end. I just used the formula for area of a parallelogram and got the same answer. self critique assessment: 2
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14:09:25 `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 --> Area for a triangle is 1/2 base times the height. A=1/2 ( 5) (2). A=1/2(10). Area equals 5 cm^2. confidence assessment: 3
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14:10:23 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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RESPONSE --> I just used the formula for area of a triangle. I still got the correct answer. self critique assessment: 2
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14:16:44 `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 --> I don't have any idea how to find the area of a trapezoid. confidence assessment: 0
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14:18:23 Any trapezoid can be reconstructed to form a rectangle whose width is equal to that of the trapezoid and whose altitude is equal to the average of the two altitudes of the trapezoid. The area of the rectangle, and therefore the trapezoid, is therefore A = base * average altitude. In the present case this area is A = 4.0 km * 5.0 km = 20 km^2.
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RESPONSE --> I understand how a trapezoid can be made into a rectangle. I know how to find the area of a rectangle, so now I will be able to find the area of a trapeziod. self critique assessment: 2
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14:21:24 `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 --> First you must find the average altitude. 3 ( 8) is 24. 24/ 2 is 12. Next you multiply the width by the average altitude. A= 4*12. A=48 cm^2. confidence assessment: 2
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14:23:00 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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RESPONSE --> I multipied 3 and 8 instead of adding. I understand my mistake. I would've gotten the question right since I knew the formula, but I multiplied the two numbers instead of adding. self critique assessment: 2
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14:30:16 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> A=pie (radius^2). A= pie ( 3^2). A=pie (9). Area equals about 28.3 cm^2. confidence assessment: 2
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14:31:31 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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RESPONSE --> I didn't use significant figures but I still got the right answer. self critique assessment: 2
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14:32:53 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> C= 2 * pi * r. C=2 * 3.14 * 3. The circumference is 18.84 cm. confidence assessment: 2
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14:33:27 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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RESPONSE --> I got it. self critique assessment: 3
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14:35:14 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> First you must convert the diameter to the radius. The radius is half the diameter, therefore the radius is 6. A= pi * r^2. A= 3.14 * 6^2. Area equals 113.04 m^2. confidence assessment: 2
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14:37:20 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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RESPONSE --> I just used three significant figures. How do you know how many significant figures to use. I used three significant figures in previous questions and got the correct answer. Why do you use 5 in this question? self critique assessment: 2
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14:40:29 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> C=2*pi*r. If the circumference is 14 *pi. then r must equal 7 because 7*2 is 14. Area= pi* (r^2). A= pi * (7^2). A= pi* 49. Area equals 3.14 *49. A=153.86 m^2. confidence assessment: 2
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14:41:53 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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RESPONSE --> I went a step further and found hat 49 pi is 153.86. Why did you stop at the step before this? self critique assessment: 2
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14:44:37 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> I set 78 equal to pi*r^2. Then I divided 78 by pi and I got 25. Then I used the equation 25=r^2. then I took the square root of 25 and got that the radius equals 5. confidence assessment: 2
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14:45:52 Knowing that A = pi r^2 we solve for r. We first divide both sides by pi to obtain A / pi = r^2. We then reverse the sides and take the square root of both sides, obtaining r = sqrt( A / pi ). Note that strictly speaking the solution to r^2 = A / pi is r = +-sqrt( A / pi ), meaning + sqrt( A / pi) or - sqrt(A / pi). However knowing that r and A are both positive quantities, we can reject the negative solution. Now we substitute A = 78 m^2 to obtain r = sqrt( 78 m^2 / pi) = sqrt(78 / pi) m.{} Approximating this quantity to 2 significant figures we obtain r = 5.0 m.
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RESPONSE --> I forgot about the possibilty of a negitive solution, but I understand that the answer must be positive. self critique assessment: 2
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14:46:47 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> We visualize the area of a rectangle as two widths and two height multipied together. confidence assessment: 3
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14:47:38 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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RESPONSE --> I forgot about the squares, when I think about a rectangle I think about the outside demensions rather than the inside. self critique assessment: 2
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14:49:50 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> We view the area of a right triangle a the triangle and a copy of itself that form a rectangle. Then we can visualize the rows of squares. confidence assessment: 2
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14:50:53 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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RESPONSE --> I see how you can view the length as equal to the base and the width as being equal to the altitude. self critique assessment: 2
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14:54:03 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> We calculat the area of a parallelogram by multiplying the base times the height. confidence assessment: 3
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14:54:20 The area of a parallelogram is equal to the product of its base and its altitude. The altitude is measured perpendicular to the base.
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RESPONSE --> I got it. self critique assessment: 3
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14:58:27 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> the area of a trapezoid is calculated by cuting of the triangle on the end and adding it to the other side to form a rectangle. The base of the trapezoid is equal to the length of the rectangle, and the height of the trapezoid is equal to the width of the rectangle. Then you cn multipy l * w to find the area. confidence assessment: 2
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14:59:22 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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RESPONSE --> I got the trapezoid and the parallelogram mixed up. I remember about the average altitude now. self critique assessment: 2
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14:59:47 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> The area of a circle is equal to pi* r^2. confidence assessment: 3
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15:00:09 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> I got it. self critique assessment: 3
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15:01:01 `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 --> The circumference is 2*pi*r. The area is measured in square units and the circumference is not. confidence assessment: 3
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15:01:13 We use the formula C = 2 pi r. The formula for the area involves r^2, which will give us squared units of the radius. Circumference is not measured in squared units.
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RESPONSE --> I got it right. self critique assessment: 3
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15:02:57 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I organized my knowledge as formulas for the various shapes. Also, I know that you can use one shape and transform it into another either by copying the shape or adding a piece to it. confidence assessment: 3
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