course Mth 163 I think I sent this one already but I am not sure. I am sending it this time to be on the safe side. v֧P݃xß{vassignment #001
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14:00:37 `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: 2
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14:02:23 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 --> 4 meters times 3 meters equals 12 meters squared. It is squared because you are multiplying meters times meters. self critique assessment: 2
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14:04:24 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> The area is 6m^2. confidence assessment: 2
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14:05:47 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 --> You can look at a right triangle as half of a rectangle and figure up what the rectangle would be and then divide it in half to get a right triangle. self critique assessment: 2
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14:06:56 `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 --> The area is 10m^2. confidence assessment: 3
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14:08:00 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 --> A parallelogram can be reconstructed to look like a retangle. You can use the rectangle to help figure out the answer for the parallelogram. self critique assessment: 3
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14:09:12 `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 --> The area is 5m^2. confidence assessment: 3
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14:10:25 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 --> A parallelogram cut in half is a triangle and you can take the answer of the parallelogram and cut in half to find the areas of a triangle. Instead is meters it should cm^2. self critique assessment: 3
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14:12:26 `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 --> The area is 20km^2. confidence assessment: 2
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14:13:46 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 --> you can reconstruct a rectangle that has the width as a trapazoid and use the same formula to come up with the area of a trapezoid. self critique assessment: 2
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14:16:03 `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 --> The area is 96cm^2. confidence assessment: 3
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14:17:49 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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RESPONSE --> Instead of just working the problem straight out you have to find the average altitude and divide by 2. Then multiply that answer by the width in order to find the correct answer. self critique assessment: 3
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14:19:20 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> The area of a circle is 28.26cm^2. confidence assessment: 3
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14:21:17 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 --> To find the area of a circle you need to take the radius and square it and then multiply by pi which is 3.14. Then with the decimal number you need to round it in order to get the answer 28.3cm^2. self critique assessment: 3
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14:23:36 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> The circumference is 18.8cm^2. confidence assessment: 3
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14:25:00 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 --> You don't have to square the cm because it is meansured in the same units and only mentioned once. Since the problem says exact then you do not round the decimal. self critique assessment: 3
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14:26:09 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> The area is 113.04m. confidence assessment: 3
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14:28:28 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 don't understand why you would have to use a 5-significant figuration of pi. Pi is equal to 3.14. The more places that you use the more the decimal changes. self critique assessment: 2
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14:31:05 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> The area is 153.86m^2. confidence assessment: 2
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14:35:19 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 --> Since we already know what the answer for pi is we need to find the radius. In order to do that we have to take pi which is 14 in this problem and put it over 2 and then put pi over pi in order to arrive at the answer 7 times 1 equals 7 meters. We still have to find the area so we leave pi as pi and input 7 for the radius. Since the radius is squared we get 49 pi m^2. self critique assessment: 3
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14:38:56 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> The area is 24.84076433m^2. confidence assessment: 2
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14:44:19 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 --> Since we know the area and we know what pi is we have to divide them by each other in order to find the radius. Since r^2 we have to find the square root of the numbers that we divided. In doing this we find that the square root of 24.84076433 is 4.98 which is then rounded to 5meters. self critique assessment: 3
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14:47:37 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 --> We can see the rectangle being covered by rows of 1-unit squares. Then we multiply the number of them by the nuber of rows. We use the formula A=L*W. self critique assessment: 3
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14:49:15 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> We can visualize the area of a triangle by thinking of a right triangle as half of a rectangle. The formaula that we would use is A=1/2*L*W or A=1/2*B*H. confidence assessment: 3
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14:50:12 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 --> Two right triangles make one rectangle. We can figure out the answer by multiplying the base times the height and then dividing that answer by 2 to get the final answer. self critique assessment: 3
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14:51:03 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> We can reconstruct it to look like a retangle. In doing so we move the parts of it around until we have a rectangle. We use the formula A=B*H. confidence assessment: 3
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14:53:45 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 --> You can find the area of a parallelogram by looking at the base and the height and figure the answer to it when it is multiplied. self critique assessment: 3
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14:55:00 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> A trapezoid can recontructed to look like a rectangle by moving the end triangle around. The to find the area we use the formula A=1/2*B*H. confidence assessment: 3
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14:56:13 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 --> If there is more than one width we have to find the average by adding them together and dividing them in half. Then we take the formual and take that number and multiply it by the base. self critique assessment: 3
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14:57:40 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> To find the area of the circle we use the formual A=pi*r^2. The reason we square r is because r is just half way across the center of the circle and we want to know the area of the whole circle. confidence assessment: 3
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14:58:14 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> The formula A=pi*r^2 gives us the answer to the area of the circle. self critique assessment: 3
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14:59:42 `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 --> To find the circumference of the circle we use the formula C=pi*d. In the circumferenceof a circle we use the diameter because it goes all the way across and when finding the area we use the radius squared because it goes half way across. confidence assessment: 3
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15:00:48 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 --> When finding the circumference we are not squaring the radius but use the diameter which goes all the way across the middle of the circle. self critique assessment: 3
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15:02:33 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> As I have went along I have made notes and wrote down every problem. I have visualized the shapes and reconstructed them on paper to help me better understand what it is talking about and for future reference. confidence assessment: 3"