course Mth 271 wΏމKassignment #001
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18:22:54 `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 --> it would be 12 meters 4 * 3 = 12 confidence assessment: 3
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18:23:27 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 should have written down square meters, i only said 12 meters, so that is not exactly right. self critique assessment: 2
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18:26:14 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> i think this is the right formula 1/2 (4 * 3) so 1/2 * 12 = 6 confidence assessment: 1
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18:26:37 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 had it right again, but did not metion the square meter part self critique assessment: 2
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18:27:47 `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 so 5 * 2 = 10^2 square meters confidence assessment: 2
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18:28:23 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 --> need to get my symbols straight still, i answered mine a little off. had right number, but had symbols in wrong place self critique assessment: 2
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18:29:36 `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 --> 1/2 (5 * 2) 1/2 (10) = 5cm^2 confidence assessment: 3
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18:29:44 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 --> ok self critique assessment: 2
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18:31:28 `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 --> because we already have average altitude, we can simply use a=4(5) a=20 km^2 confidence assessment: 2
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18:31:36 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 --> ok self critique assessment: 3
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18:33:21 `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 --> similar to last one except we need to figure out the averag altitude. so 3+8=11 11/2= 5.5 average altitdue so for area, A=4 (5.5)= 22 cm^2 confidence assessment: 2
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18:33:26 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 --> ok self critique assessment: 3
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18:34:41 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> area = r^2 *pi so 3^2 * pi = 9 * pi = 28.27cm^2 confidence assessment: 2
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18:35:40 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 --> mine was slightly off, by .01, but otherwise i had it right. self critique assessment: 2
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18:37:42 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> circumferance = pi * 3cm so circumferance = 9.4 confidence assessment: 1
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18:38:49 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 did not due the multiple of 2 part, so i had only have the circumferance. i needed to figure out diameter, since i only had radius self critique assessment: 2
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18:41:57 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> i do not understand how to figure it out using diameter confidence assessment: 0
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18:42:40 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 dont' really know what i was thinking, i know that diameter is half the radius, so i should have been able to figure it out self critique assessment: 2
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18:45:07 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> im not really clear on this one either confidence assessment: 0
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18:46:36 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 --> geometry is something i need to brush up on to get all this straight. i can understand the simple concepts but this one got a little beyond me. self critique assessment: 2
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18:57:58 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> well area = r^2 * pi so 78 = r^2 * pi if you 78/pi = 24.82 so you need the ^2 of something to get that number. 5 is close but not exact. i dont' see how to get the exact number without trial and error on my calculator, which i know does not really help me any but you can go for the square root of 24.82 = 4.98 confidence assessment: 1
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18:58:35 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 --> ok, i would have had right answer with the rounding, but i wasn't sure how close to get and out of habit tried to get it exact. i should have rounded self critique assessment: 2
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19:00:02 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> i am not sure if you are asking me to describe a rectangle or something else. confidence assessment: 0
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19:00:30 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 --> ok, i see now how you meant for it to be described, by breaking it up into squares. self critique assessment: 2
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19:01:48 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> i visualize it as a right angle with the ends of the angles forming a straight line to connect. since it is a right angle, the corner will equal 90 degrees, always confidence assessment: 1
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19:02:17 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 --> this would have been a lot easier to do then how i attempted. this also makes a bit more sense self critique assessment: 2
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19:03:04 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> you calculate area by multiplying the base * height A=bh confidence assessment: 3
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19:03:13 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 --> ok self critique assessment: 2
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19:04:37 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> area is calculated: A= h((a+b)/2) so you add the two sides and divide by 2. you then multiply this number by h to get your area confidence assessment: 3
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19:04:42 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 --> ok self critique assessment: 2
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19:05:21 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> to get area, you square the radius then multiply that by pi A=r^2 * pi confidence assessment: 2
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19:05:27 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> ok self critique assessment: 2
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19:06:42 `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 --> usually you do C=d * pi area is different since you are using radius then confidence assessment: 2
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19:07:09 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 --> that is true, circumference is not squared self critique assessment: 2
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19:08:07 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> i still have to study a bit to remind myself how circles work exactly, but i pretty much think i have everything else straight in my head. confidence assessment: 1
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