#$&*
course Phy 241
06/25/2013 4:43 pm
Question: `q001. There are 12 questions in this document.
The graph of a certain function is a smooth curve passing through the points (3, 5), (7, 17) and (10, 29).
Between which two points do you think the graph is steeper, on the average?
Why do we say 'on the average'?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The two points that produce the steeper graph are (10, 29) and (7, 17).
confidence rating #$&*: 3
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2. Answer without using a calculator: As x takes the values 2.1, 2.01, 2.001 and 2.0001, what values are taken by the expression 1 / (x - 2)?
1. As the process continues, with x getting closer and closer to 2, what happens to the values of 1 / (x-2)?
2. Will the value ever exceed a billion? Will it ever exceed one trillion billions?
3. Will it ever exceed the number of particles in the known universe?
4. Is there any number it will never exceed?
5. What does the graph of y = 1 / (x-2) look like in the vicinity of x = 2?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
x = 2.1 x = 2.01 x = 2.001 x = 2.0001
1/(2.1 - 2) 1/(2.01 - 2) 1/(2.001 - 2) 1/(2.0001 - 2)
= 10 = 100 = 1,000 =10,000
1. As the x gets closer and closer to 2, the values of 1/(x - 2) increase 10 times.
2. The value can exceed a billion and even higher as long as the right amount of zero is used for the reciprocal.
3. It can exceed the number of particles in the known universe since we can add as many zeros after the decimal point as we want.
4. No.
5. The graph will have a positive curve that will stop rising at 2 in the x-axis.
confidence rating #$&*: 2
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Question: `q004. If f(x) = x^2 (meaning 'x raised to the power 2') then which is steeper, the line segment connecting the x = 2 and x = 5 points on the graph of f(x), or the line segment connecting the x = -1 and x = 7 points on the same graph? Explain the basis of your reasoning.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The line segment connected between the x = 2 and x = 5 points is steeper than the line segment connected between the x = -1 and x = 7 because according to the slopes of the two line segments, the first segment’s slope is one unit higher than the other line segment’s slope.
confidence rating #$&*: 3
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Question: `q005. Suppose that every week of the current millennium you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time ( this is so), that the the gold remains undisturbed (maybe, maybe not so), that no other source adds gold to your backyard (probably so), and that there was no gold in your yard before..
1. If you construct a graph of y = the number of grams of gold in your backyard vs. t = the number of weeks since Jan. 1, 2000, with the y axis pointing up and the t axis pointing to the right, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
Your solution:
1. The graph will produce a rising straight line.
2. The graph will produce a line which rises faster and faster
3. The graph will produce a line which rises but more and more slowly
confidence rating #$&*: 3
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Question: `q006. Suppose that every week you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time, that the the gold remains undisturbed, and that no other source adds gold to your backyard.
1. If you graph the rate at which gold is accumulating from week to week vs. the number of weeks since Jan 1, 2000, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a straight line that neither rises nor descends.
2. The graph will produce a rising straight line.
3. The graph will produce a line that rises more slowly than the second graph.
confidence rating #$&*: 3
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``q007. If the depth of water in a container is given, in centimeters, by 100 - 2 t + .01 t^2, where t is clock time in seconds, then what are the depths at clock times t = 30, t = 40 and t = 60? On the average is depth changing more rapidly during the first time interval or the second?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The depths at the clock times of 30 sec, 40 sec, and 60 sec are 49 cm, 36 cm, and 16 cm respectfully.
t = 30 t = 40 t = 60
100 - 2(30) +.01(30)^2 100 - 2(40) +.01(40)^2 100 - 2(60) +.01(60)^2
= 100 - 60 + .01(900) = 100 - 80 +.01(1600) = 100 - 120 +.01(3600)
= 100 - 60 + 9 = 100 - 80 + 16 = 100 - 120+ 36
= 100 - 51 = 100 - 68 = 100 - 84
= 49 cm = 36 cm = 16 cm
The depth changed more rapidly during the second time interval.
First time interval = 49 cm - 36 cm = 13 cm
Second time interval = 36 cm - 16 cm = 20 cm
confidence rating #$&*: 3
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Question: `q008. If the rate at which water descends in a container is given, in cm/s, by 10 - .1 t, where t is clock time in seconds, then at what rate is water descending when t = 10, and at what rate is it descending when t = 20? How much would you therefore expect the water level to change during this 10-second interval?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The rate in which water is descending in 10 seconds is 9cm/s and the rate in which water is descending in 20 seconds is 8 cm/s. From the two rates, I believe that the water level will decrease by 1 cm/s during the 10-second interval.
t = 10 t = 20
10 - .1(10) 10 - .1(20)
=10 - 1 =10 - 2
= 9 = 8
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Question: `q009. Sketch the line segment connecting the points (2, -4) and (6, 4), and the line segment connecting the points (2, 4) and (6, 1). The first of these lines if the graph of the function f(x), the second is the graph of the function g(x). Both functions are defined on the interval 2 <= x <= 6.
Let h(x) be the function whose value at x is the product of the values of these two functions. For example, when x = 2 the value of the first function is -3 and the value of the second is 4, so when x = 2 the value of h(x) is -3 * 4 = -12.
What is the value of h(x) when x = 6?
Is the value of h(x) ever greater than its value at x = 6?
What is your best description of the graph of h(x)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The value of h(x) when x = 6 is 4
2. The value of h(x) = 4 is lower than its value x = 6
3. The graph will produce a line that falls more and more quickly.
confidence rating #$&*: 3
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Question: `q010. A straight line segment connects the points (3,5) and (7,9), while the points (3, 9) and (7, 5) are connected by a curve which decreases at an increasing rate. From each of the four points a line segment is drawn directly down to the x axis, so that the first line segment is the top of a trapezoid and the second a similar to a trapezoid but with a curved 'top'. Which trapezoid has the greater area?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The bottom trapezoid has the greater area since it have more horizontal space than the top trapezoid.
confidence rating #$&*:
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Question: `q011. Describe the graph of the position of a car vs. clock time, given each of the following conditions:
• The car coasts down a straight incline, gaining the same amount of speed every second
• The car coasts down a hill which gets steeper and steeper, gaining more speed every second
• The car coasts down a straight incline, but due to increasing air resistance gaining less speed with every passing second
Describe the graph of the rate of change of the position of a car vs. clock time, given each of the above conditions.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a rising straight line with the slope of 1.
2. The graph will produce a line that rises faster than the first graph.
3. The graph will produce a line that rises but more and more slowly.
confidence rating #$&*: 3
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Question: `q012. If at t = 100 seconds water is flowing out of a container at the rate of 1.4 liters / second, and at t = 150 second the rate is 1.0 liters / second, then what is your best estimate of how much water flowed out during the 50-second interval?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
My best estimate of how much water flowed out during the 50-second interval is 13 L because when I solve the amount of water flowed out for both the rates of 1.4 L/ second and 1.0 L/ second with the respective t values, I found there was a 1 L difference between the two.
t = 100 t =150
100 sec * (1.4L/sec) 150 sec * (1.0L/sec)
= 14L = 15L
confidence rating #$&*: 3
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Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course Phy 241
06/25/2013 4:43 pm
Question: `q001. There are 12 questions in this document.
The graph of a certain function is a smooth curve passing through the points (3, 5), (7, 17) and (10, 29).
Between which two points do you think the graph is steeper, on the average?
Why do we say 'on the average'?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The two points that produce the steeper graph are (10, 29) and (7, 17).
confidence rating #$&*: 3
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2. Answer without using a calculator: As x takes the values 2.1, 2.01, 2.001 and 2.0001, what values are taken by the expression 1 / (x - 2)?
1. As the process continues, with x getting closer and closer to 2, what happens to the values of 1 / (x-2)?
2. Will the value ever exceed a billion? Will it ever exceed one trillion billions?
3. Will it ever exceed the number of particles in the known universe?
4. Is there any number it will never exceed?
5. What does the graph of y = 1 / (x-2) look like in the vicinity of x = 2?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
x = 2.1 x = 2.01 x = 2.001 x = 2.0001
1/(2.1 - 2) 1/(2.01 - 2) 1/(2.001 - 2) 1/(2.0001 - 2)
= 10 = 100 = 1,000 =10,000
1. As the x gets closer and closer to 2, the values of 1/(x - 2) increase 10 times.
2. The value can exceed a billion and even higher as long as the right amount of zero is used for the reciprocal.
3. It can exceed the number of particles in the known universe since we can add as many zeros after the decimal point as we want.
4. No.
5. The graph will have a positive curve that will stop rising at 2 in the x-axis.
confidence rating #$&*: 2
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Question: `q004. If f(x) = x^2 (meaning 'x raised to the power 2') then which is steeper, the line segment connecting the x = 2 and x = 5 points on the graph of f(x), or the line segment connecting the x = -1 and x = 7 points on the same graph? Explain the basis of your reasoning.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The line segment connected between the x = 2 and x = 5 points is steeper than the line segment connected between the x = -1 and x = 7 because according to the slopes of the two line segments, the first segment’s slope is one unit higher than the other line segment’s slope.
confidence rating #$&*: 3
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Question: `q005. Suppose that every week of the current millennium you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time ( this is so), that the the gold remains undisturbed (maybe, maybe not so), that no other source adds gold to your backyard (probably so), and that there was no gold in your yard before..
1. If you construct a graph of y = the number of grams of gold in your backyard vs. t = the number of weeks since Jan. 1, 2000, with the y axis pointing up and the t axis pointing to the right, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
Your solution:
1. The graph will produce a rising straight line.
2. The graph will produce a line which rises faster and faster
3. The graph will produce a line which rises but more and more slowly
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q006. Suppose that every week you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time, that the the gold remains undisturbed, and that no other source adds gold to your backyard.
1. If you graph the rate at which gold is accumulating from week to week vs. the number of weeks since Jan 1, 2000, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a straight line that neither rises nor descends.
2. The graph will produce a rising straight line.
3. The graph will produce a line that rises more slowly than the second graph.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
``q007. If the depth of water in a container is given, in centimeters, by 100 - 2 t + .01 t^2, where t is clock time in seconds, then what are the depths at clock times t = 30, t = 40 and t = 60? On the average is depth changing more rapidly during the first time interval or the second?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The depths at the clock times of 30 sec, 40 sec, and 60 sec are 49 cm, 36 cm, and 16 cm respectfully.
t = 30 t = 40 t = 60
100 - 2(30) +.01(30)^2 100 - 2(40) +.01(40)^2 100 - 2(60) +.01(60)^2
= 100 - 60 + .01(900) = 100 - 80 +.01(1600) = 100 - 120 +.01(3600)
= 100 - 60 + 9 = 100 - 80 + 16 = 100 - 120+ 36
= 100 - 51 = 100 - 68 = 100 - 84
= 49 cm = 36 cm = 16 cm
The depth changed more rapidly during the second time interval.
First time interval = 49 cm - 36 cm = 13 cm
Second time interval = 36 cm - 16 cm = 20 cm
confidence rating #$&*: 3
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Question: `q008. If the rate at which water descends in a container is given, in cm/s, by 10 - .1 t, where t is clock time in seconds, then at what rate is water descending when t = 10, and at what rate is it descending when t = 20? How much would you therefore expect the water level to change during this 10-second interval?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The rate in which water is descending in 10 seconds is 9cm/s and the rate in which water is descending in 20 seconds is 8 cm/s. From the two rates, I believe that the water level will decrease by 1 cm/s during the 10-second interval.
t = 10 t = 20
10 - .1(10) 10 - .1(20)
=10 - 1 =10 - 2
= 9 = 8
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Question: `q009. Sketch the line segment connecting the points (2, -4) and (6, 4), and the line segment connecting the points (2, 4) and (6, 1). The first of these lines if the graph of the function f(x), the second is the graph of the function g(x). Both functions are defined on the interval 2 <= x <= 6.
Let h(x) be the function whose value at x is the product of the values of these two functions. For example, when x = 2 the value of the first function is -3 and the value of the second is 4, so when x = 2 the value of h(x) is -3 * 4 = -12.
What is the value of h(x) when x = 6?
Is the value of h(x) ever greater than its value at x = 6?
What is your best description of the graph of h(x)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The value of h(x) when x = 6 is 4
2. The value of h(x) = 4 is lower than its value x = 6
3. The graph will produce a line that falls more and more quickly.
confidence rating #$&*: 3
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Question: `q010. A straight line segment connects the points (3,5) and (7,9), while the points (3, 9) and (7, 5) are connected by a curve which decreases at an increasing rate. From each of the four points a line segment is drawn directly down to the x axis, so that the first line segment is the top of a trapezoid and the second a similar to a trapezoid but with a curved 'top'. Which trapezoid has the greater area?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The bottom trapezoid has the greater area since it have more horizontal space than the top trapezoid.
confidence rating #$&*:
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Question: `q011. Describe the graph of the position of a car vs. clock time, given each of the following conditions:
• The car coasts down a straight incline, gaining the same amount of speed every second
• The car coasts down a hill which gets steeper and steeper, gaining more speed every second
• The car coasts down a straight incline, but due to increasing air resistance gaining less speed with every passing second
Describe the graph of the rate of change of the position of a car vs. clock time, given each of the above conditions.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a rising straight line with the slope of 1.
2. The graph will produce a line that rises faster than the first graph.
3. The graph will produce a line that rises but more and more slowly.
confidence rating #$&*: 3
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Question: `q012. If at t = 100 seconds water is flowing out of a container at the rate of 1.4 liters / second, and at t = 150 second the rate is 1.0 liters / second, then what is your best estimate of how much water flowed out during the 50-second interval?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
My best estimate of how much water flowed out during the 50-second interval is 13 L because when I solve the amount of water flowed out for both the rates of 1.4 L/ second and 1.0 L/ second with the respective t values, I found there was a 1 L difference between the two.
t = 100 t =150
100 sec * (1.4L/sec) 150 sec * (1.0L/sec)
= 14L = 15L
confidence rating #$&*: 3
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"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!
#$&*
course Phy 241
06/25/2013 4:43 pm
Question: `q001. There are 12 questions in this document.
The graph of a certain function is a smooth curve passing through the points (3, 5), (7, 17) and (10, 29).
Between which two points do you think the graph is steeper, on the average?
Why do we say 'on the average'?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The two points that produce the steeper graph are (10, 29) and (7, 17).
confidence rating #$&*: 3
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2. Answer without using a calculator: As x takes the values 2.1, 2.01, 2.001 and 2.0001, what values are taken by the expression 1 / (x - 2)?
1. As the process continues, with x getting closer and closer to 2, what happens to the values of 1 / (x-2)?
2. Will the value ever exceed a billion? Will it ever exceed one trillion billions?
3. Will it ever exceed the number of particles in the known universe?
4. Is there any number it will never exceed?
5. What does the graph of y = 1 / (x-2) look like in the vicinity of x = 2?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
x = 2.1 x = 2.01 x = 2.001 x = 2.0001
1/(2.1 - 2) 1/(2.01 - 2) 1/(2.001 - 2) 1/(2.0001 - 2)
= 10 = 100 = 1,000 =10,000
1. As the x gets closer and closer to 2, the values of 1/(x - 2) increase 10 times.
2. The value can exceed a billion and even higher as long as the right amount of zero is used for the reciprocal.
3. It can exceed the number of particles in the known universe since we can add as many zeros after the decimal point as we want.
4. No.
5. The graph will have a positive curve that will stop rising at 2 in the x-axis.
confidence rating #$&*: 2
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Question: `q004. If f(x) = x^2 (meaning 'x raised to the power 2') then which is steeper, the line segment connecting the x = 2 and x = 5 points on the graph of f(x), or the line segment connecting the x = -1 and x = 7 points on the same graph? Explain the basis of your reasoning.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The line segment connected between the x = 2 and x = 5 points is steeper than the line segment connected between the x = -1 and x = 7 because according to the slopes of the two line segments, the first segment’s slope is one unit higher than the other line segment’s slope.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Question: `q005. Suppose that every week of the current millennium you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time ( this is so), that the the gold remains undisturbed (maybe, maybe not so), that no other source adds gold to your backyard (probably so), and that there was no gold in your yard before..
1. If you construct a graph of y = the number of grams of gold in your backyard vs. t = the number of weeks since Jan. 1, 2000, with the y axis pointing up and the t axis pointing to the right, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
Your solution:
1. The graph will produce a rising straight line.
2. The graph will produce a line which rises faster and faster
3. The graph will produce a line which rises but more and more slowly
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q006. Suppose that every week you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time, that the the gold remains undisturbed, and that no other source adds gold to your backyard.
1. If you graph the rate at which gold is accumulating from week to week vs. the number of weeks since Jan 1, 2000, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a straight line that neither rises nor descends.
2. The graph will produce a rising straight line.
3. The graph will produce a line that rises more slowly than the second graph.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
``q007. If the depth of water in a container is given, in centimeters, by 100 - 2 t + .01 t^2, where t is clock time in seconds, then what are the depths at clock times t = 30, t = 40 and t = 60? On the average is depth changing more rapidly during the first time interval or the second?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The depths at the clock times of 30 sec, 40 sec, and 60 sec are 49 cm, 36 cm, and 16 cm respectfully.
t = 30 t = 40 t = 60
100 - 2(30) +.01(30)^2 100 - 2(40) +.01(40)^2 100 - 2(60) +.01(60)^2
= 100 - 60 + .01(900) = 100 - 80 +.01(1600) = 100 - 120 +.01(3600)
= 100 - 60 + 9 = 100 - 80 + 16 = 100 - 120+ 36
= 100 - 51 = 100 - 68 = 100 - 84
= 49 cm = 36 cm = 16 cm
The depth changed more rapidly during the second time interval.
First time interval = 49 cm - 36 cm = 13 cm
Second time interval = 36 cm - 16 cm = 20 cm
confidence rating #$&*: 3
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Question: `q008. If the rate at which water descends in a container is given, in cm/s, by 10 - .1 t, where t is clock time in seconds, then at what rate is water descending when t = 10, and at what rate is it descending when t = 20? How much would you therefore expect the water level to change during this 10-second interval?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The rate in which water is descending in 10 seconds is 9cm/s and the rate in which water is descending in 20 seconds is 8 cm/s. From the two rates, I believe that the water level will decrease by 1 cm/s during the 10-second interval.
t = 10 t = 20
10 - .1(10) 10 - .1(20)
=10 - 1 =10 - 2
= 9 = 8
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Question: `q009. Sketch the line segment connecting the points (2, -4) and (6, 4), and the line segment connecting the points (2, 4) and (6, 1). The first of these lines if the graph of the function f(x), the second is the graph of the function g(x). Both functions are defined on the interval 2 <= x <= 6.
Let h(x) be the function whose value at x is the product of the values of these two functions. For example, when x = 2 the value of the first function is -3 and the value of the second is 4, so when x = 2 the value of h(x) is -3 * 4 = -12.
What is the value of h(x) when x = 6?
Is the value of h(x) ever greater than its value at x = 6?
What is your best description of the graph of h(x)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The value of h(x) when x = 6 is 4
2. The value of h(x) = 4 is lower than its value x = 6
3. The graph will produce a line that falls more and more quickly.
confidence rating #$&*: 3
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Question: `q010. A straight line segment connects the points (3,5) and (7,9), while the points (3, 9) and (7, 5) are connected by a curve which decreases at an increasing rate. From each of the four points a line segment is drawn directly down to the x axis, so that the first line segment is the top of a trapezoid and the second a similar to a trapezoid but with a curved 'top'. Which trapezoid has the greater area?
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Your solution: The bottom trapezoid has the greater area since it have more horizontal space than the top trapezoid.
confidence rating #$&*:
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Question: `q011. Describe the graph of the position of a car vs. clock time, given each of the following conditions:
• The car coasts down a straight incline, gaining the same amount of speed every second
• The car coasts down a hill which gets steeper and steeper, gaining more speed every second
• The car coasts down a straight incline, but due to increasing air resistance gaining less speed with every passing second
Describe the graph of the rate of change of the position of a car vs. clock time, given each of the above conditions.
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Your solution:
1. The graph will produce a rising straight line with the slope of 1.
2. The graph will produce a line that rises faster than the first graph.
3. The graph will produce a line that rises but more and more slowly.
confidence rating #$&*: 3
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Question: `q012. If at t = 100 seconds water is flowing out of a container at the rate of 1.4 liters / second, and at t = 150 second the rate is 1.0 liters / second, then what is your best estimate of how much water flowed out during the 50-second interval?
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Your solution:
My best estimate of how much water flowed out during the 50-second interval is 13 L because when I solve the amount of water flowed out for both the rates of 1.4 L/ second and 1.0 L/ second with the respective t values, I found there was a 1 L difference between the two.
t = 100 t =150
100 sec * (1.4L/sec) 150 sec * (1.0L/sec)
= 14L = 15L
confidence rating #$&*: 3
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Self-critique (if necessary):
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Self-critique rating:
#*&!#*&!
#$&*
course Phy 241
06/25/2013 4:43 pm
Question: `q001. There are 12 questions in this document.
The graph of a certain function is a smooth curve passing through the points (3, 5), (7, 17) and (10, 29).
Between which two points do you think the graph is steeper, on the average?
Why do we say 'on the average'?
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Your solution: The two points that produce the steeper graph are (10, 29) and (7, 17).
confidence rating #$&*: 3
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2. Answer without using a calculator: As x takes the values 2.1, 2.01, 2.001 and 2.0001, what values are taken by the expression 1 / (x - 2)?
1. As the process continues, with x getting closer and closer to 2, what happens to the values of 1 / (x-2)?
2. Will the value ever exceed a billion? Will it ever exceed one trillion billions?
3. Will it ever exceed the number of particles in the known universe?
4. Is there any number it will never exceed?
5. What does the graph of y = 1 / (x-2) look like in the vicinity of x = 2?
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Your solution:
x = 2.1 x = 2.01 x = 2.001 x = 2.0001
1/(2.1 - 2) 1/(2.01 - 2) 1/(2.001 - 2) 1/(2.0001 - 2)
= 10 = 100 = 1,000 =10,000
1. As the x gets closer and closer to 2, the values of 1/(x - 2) increase 10 times.
2. The value can exceed a billion and even higher as long as the right amount of zero is used for the reciprocal.
3. It can exceed the number of particles in the known universe since we can add as many zeros after the decimal point as we want.
4. No.
5. The graph will have a positive curve that will stop rising at 2 in the x-axis.
confidence rating #$&*: 2
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Question: `q004. If f(x) = x^2 (meaning 'x raised to the power 2') then which is steeper, the line segment connecting the x = 2 and x = 5 points on the graph of f(x), or the line segment connecting the x = -1 and x = 7 points on the same graph? Explain the basis of your reasoning.
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Your solution: The line segment connected between the x = 2 and x = 5 points is steeper than the line segment connected between the x = -1 and x = 7 because according to the slopes of the two line segments, the first segment’s slope is one unit higher than the other line segment’s slope.
confidence rating #$&*: 3
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Question: `q005. Suppose that every week of the current millennium you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time ( this is so), that the the gold remains undisturbed (maybe, maybe not so), that no other source adds gold to your backyard (probably so), and that there was no gold in your yard before..
1. If you construct a graph of y = the number of grams of gold in your backyard vs. t = the number of weeks since Jan. 1, 2000, with the y axis pointing up and the t axis pointing to the right, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
Your solution:
1. The graph will produce a rising straight line.
2. The graph will produce a line which rises faster and faster
3. The graph will produce a line which rises but more and more slowly
confidence rating #$&*: 3
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Question: `q006. Suppose that every week you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time, that the the gold remains undisturbed, and that no other source adds gold to your backyard.
1. If you graph the rate at which gold is accumulating from week to week vs. the number of weeks since Jan 1, 2000, will the points on your graph lie on a level straight line, a rising straight line, a falling straight line, a line which rises faster and faster, a line which rises but more and more slowly, a line which falls faster and faster, or a line which falls but more and more slowly?
2. Answer the same question assuming that every week you bury 1 more gram than you did the previous week.
3. Answer the same question assuming that every week you bury half the amount you did the previous week.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a straight line that neither rises nor descends.
2. The graph will produce a rising straight line.
3. The graph will produce a line that rises more slowly than the second graph.
confidence rating #$&*: 3
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``q007. If the depth of water in a container is given, in centimeters, by 100 - 2 t + .01 t^2, where t is clock time in seconds, then what are the depths at clock times t = 30, t = 40 and t = 60? On the average is depth changing more rapidly during the first time interval or the second?
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Your solution: The depths at the clock times of 30 sec, 40 sec, and 60 sec are 49 cm, 36 cm, and 16 cm respectfully.
t = 30 t = 40 t = 60
100 - 2(30) +.01(30)^2 100 - 2(40) +.01(40)^2 100 - 2(60) +.01(60)^2
= 100 - 60 + .01(900) = 100 - 80 +.01(1600) = 100 - 120 +.01(3600)
= 100 - 60 + 9 = 100 - 80 + 16 = 100 - 120+ 36
= 100 - 51 = 100 - 68 = 100 - 84
= 49 cm = 36 cm = 16 cm
The depth changed more rapidly during the second time interval.
First time interval = 49 cm - 36 cm = 13 cm
Second time interval = 36 cm - 16 cm = 20 cm
confidence rating #$&*: 3
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Question: `q008. If the rate at which water descends in a container is given, in cm/s, by 10 - .1 t, where t is clock time in seconds, then at what rate is water descending when t = 10, and at what rate is it descending when t = 20? How much would you therefore expect the water level to change during this 10-second interval?
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Your solution: The rate in which water is descending in 10 seconds is 9cm/s and the rate in which water is descending in 20 seconds is 8 cm/s. From the two rates, I believe that the water level will decrease by 1 cm/s during the 10-second interval.
t = 10 t = 20
10 - .1(10) 10 - .1(20)
=10 - 1 =10 - 2
= 9 = 8
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Question: `q009. Sketch the line segment connecting the points (2, -4) and (6, 4), and the line segment connecting the points (2, 4) and (6, 1). The first of these lines if the graph of the function f(x), the second is the graph of the function g(x). Both functions are defined on the interval 2 <= x <= 6.
Let h(x) be the function whose value at x is the product of the values of these two functions. For example, when x = 2 the value of the first function is -3 and the value of the second is 4, so when x = 2 the value of h(x) is -3 * 4 = -12.
What is the value of h(x) when x = 6?
Is the value of h(x) ever greater than its value at x = 6?
What is your best description of the graph of h(x)?
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Your solution:
1. The value of h(x) when x = 6 is 4
2. The value of h(x) = 4 is lower than its value x = 6
3. The graph will produce a line that falls more and more quickly.
confidence rating #$&*: 3
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Question: `q010. A straight line segment connects the points (3,5) and (7,9), while the points (3, 9) and (7, 5) are connected by a curve which decreases at an increasing rate. From each of the four points a line segment is drawn directly down to the x axis, so that the first line segment is the top of a trapezoid and the second a similar to a trapezoid but with a curved 'top'. Which trapezoid has the greater area?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The bottom trapezoid has the greater area since it have more horizontal space than the top trapezoid.
confidence rating #$&*:
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Question: `q011. Describe the graph of the position of a car vs. clock time, given each of the following conditions:
• The car coasts down a straight incline, gaining the same amount of speed every second
• The car coasts down a hill which gets steeper and steeper, gaining more speed every second
• The car coasts down a straight incline, but due to increasing air resistance gaining less speed with every passing second
Describe the graph of the rate of change of the position of a car vs. clock time, given each of the above conditions.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
1. The graph will produce a rising straight line with the slope of 1.
2. The graph will produce a line that rises faster than the first graph.
3. The graph will produce a line that rises but more and more slowly.
confidence rating #$&*: 3
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Question: `q012. If at t = 100 seconds water is flowing out of a container at the rate of 1.4 liters / second, and at t = 150 second the rate is 1.0 liters / second, then what is your best estimate of how much water flowed out during the 50-second interval?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
My best estimate of how much water flowed out during the 50-second interval is 13 L because when I solve the amount of water flowed out for both the rates of 1.4 L/ second and 1.0 L/ second with the respective t values, I found there was a 1 L difference between the two.
t = 100 t =150
100 sec * (1.4L/sec) 150 sec * (1.0L/sec)
= 14L = 15L
confidence rating #$&*: 3
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Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!#*&!#*&!
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