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Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.

Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.

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Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.

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Mastering presents homework items assigned by your instructor and works with you to answer them. Homework items typically have an introduction, possibly figures, and one or more parts for you to answer. Part A What is the magic number in (Figure 1)? You could try to guess the magic number but you would probably use up all your tries before getting the correct answer. Notice the View Available Hint(s) link underneath the question statement for this part. Selecting this link will open up a list of hints that will guide you to the correct number. Hint 1 for Part A. How to approach the problem Notice that there are two hints for this question. You are not required to use all of the hints or to use them in order. Each hint has a tagline that describes its contents. Based on the tagline you can decide whether or not a particular hint will be useful to you. Your instructor may choose to give you a bonus for not using hints or to deduct a small penalty for using hints. If you are stuck, using the hints will usually result in a higher score than simply trying to guess because you may lose fewer points for opening a hint than for getting the answer to the main question incorrect. To help you, the magic number is equal to 10⋅x, where x is a number between 1 and 8. Now, open up the second hint to uncover the value of x. Hint 2for Part A. What is x? You are told from the previous hint that the magic number is equal to 10⋅x. For this problem, x is equal to 6. Use this to compute the magic number and enter it below. magic number Part B Multiple-choice questions have a special grading rule determined by your instructor. Assume that your instructor has decided to grade these questions in the following way: If you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n-1) of the credit for that question. Just like the similar multiple-choice penalty on most standardized tests, this rule is necessary to prevent random guessing. If a multiple-choice question has five answer choices and you submit one wrong answer before getting the question correct, how much credit will you lose for that part of the question? 100% 50% 33% 25% 20%

Mastering presents homework items assigned by your instructor and works with you to answer them. Homework items typically have an introduction, possibly figures, and one or more parts for you to answer. Part A What is the magic number in (Figure 1)? You could try to guess the magic number but you would probably use up all your tries before getting the correct answer. Notice the View Available Hint(s) link underneath the question statement for this part. Selecting this link will open up a list of hints that will guide you to the correct number. Hint 1 for Part A. How to approach the problem Notice that there are two hints for this question. You are not required to use all of the hints or to use them in order. Each hint has a tagline that describes its contents. Based on the tagline you can decide whether or not a particular hint will be useful to you. Your instructor may choose to give you a bonus for not using hints or to deduct a small penalty for using hints. If you are stuck, using the hints will usually result in a higher score than simply trying to guess because you may lose fewer points for opening a hint than for getting the answer to the main question incorrect. To help you, the magic number is equal to 10⋅x, where x is a number between 1 and 8. Now, open up the second hint to uncover the value of x. Hint 2for Part A. What is x? You are told from the previous hint that the magic number is equal to 10⋅x. For this problem, x is equal to 6. Use this to compute the magic number and enter it below. magic number Part B Multiple-choice questions have a special grading rule determined by your instructor. Assume that your instructor has decided to grade these questions in the following way: If you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n-1) of the credit for that question. Just like the similar multiple-choice penalty on most standardized tests, this rule is necessary to prevent random guessing. If a multiple-choice question has five answer choices and you submit one wrong answer before getting the question correct, how much credit will you lose for that part of the question? 100% 50% 33% 25% 20%

Mastering presents homework items assigned by your instructor and works with you to answer them. Homework items typically have an introduction, possibly figures, and one or more parts for you to answer. Part A What is the magic number in (Figure 1)? You could try to guess the magic number but you would probably use up all your tries before getting the correct answer. Notice the View Available Hint(s) link underneath the question statement for this part. Selecting this link will open up a list of hints that will guide you to the correct number. Hint 1 for Part A. How to approach the problem Notice that there are two hints for this question. You are not required to use all of the hints or to use them in order. Each hint has a tagline that describes its contents. Based on the tagline you can decide whether or not a particular hint will be useful to you. Your instructor may choose to give you a bonus for not using hints or to deduct a small penalty for using hints. If you are stuck, using the hints will usually result in a higher score than simply trying to guess because you may lose fewer points for opening a hint than for getting the answer to the main question incorrect. To help you, the magic number is equal to 10⋅x, where x is a number between 1 and 8. Now, open up the second hint to uncover the value of x. Hint 2for Part A. What is x? You are told from the previous hint that the magic number is equal to 10⋅x. For this problem, x is equal to 6. Use this to compute the magic number and enter it below. magic number Part B Multiple-choice questions have a special grading rule determined by your instructor. Assume that your instructor has decided to grade these questions in the following way: If you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n-1) of the credit for that question. Just like the similar multiple-choice penalty on most standardized tests, this rule is necessary to prevent random guessing. If a multiple-choice question has five answer choices and you submit one wrong answer before getting the question correct, how much credit will you lose for that part of the question? 100% 50% 33% 25% 20%
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Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.

Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.
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Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. (i) A bird with these tendencies is released from an island that is 3 km from the nearest point B on a straight shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Points B and D are 10 km apart. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. (Round your answers to two decimal places.) (a) In general, if it takes 1.2 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure is minimized, determine a function for the ratio WL in terms of x, the distance from B to C. W/L = (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 2 km from B, how many times more energy does it take a bird to fly over water than land?
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