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temperature is 0sv< 1.79 (10.45 + 10Vv - v)(33 – t) W = { 33 - 1.79 s v s 20 22.04 33 1.5958 (33 - t) v > 20 where v represents the wind speed (in meters per second) and t represents the air temperature (°C). Compute the wind chill for the following: (a) An air temperature of 10°C and a wind speed of 1 meter per second (m/sec)

temperature is 0sv< 1.79 (10.45 + 10Vv - v)(33 – t) W = { 33 - 1.79 s v s 20 22.04 33 1.5958 (33 - t) v > 20 where v represents the wind speed (in meters per second) and t represents the air temperature (°C). Compute the wind chill for the following: (a) An air temperature of 10°C and a wind speed of 1 meter per second (m/sec)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(e) Construct a function C = C(s),where Cisthe loan-level price adjustment (LLPA) and s is the credit score of an individual who wishes to borrow $300,000 with an 80% (b) An air temperature of 10°C and a wind speed of 5 m/sec (c) An air temperature of 10°C and a wind speed of 15 m/sec LTV ratio. ) What is the LLPA on a $300,000 loan with an 80% LTV ratio for a borrower whose credit score is 725? (e) What is the LLPA on a $300,000 loan with an 80% LTV ratio for a borrower whose credit score is 670? (d) An air temperature of 10°C and a wind speed of 25 m/sec (e) Explain the physical meaning of the equation corresponding to 0 s v < 1.79. () Explain the physical meaning of the equation corresponding to v > 20. 0 Minimum Payments for Credit Cards Holders of credit cards issued by banks, department stores, oil companies, and so on, receive bills each month that state minimum amounts that must be paid by a certain due date.The minimum due depends on the total amount owed. One such credit card company uses the following rules: For a bill of less than $10, the entire amount is due. For a bill of at least $10 but less than $500, the minimum due is $10. A minimum of $30 is due on a bill of at least $500 but less than $1000, a minimum of $50 is due on a bill of at least $1000 but less than $1500, and a minimum of $70 is due on bills of $1500 or more. Find the function f that describes the minimum payment due on a bill of x dollars. Graph f. 61. Wind Chill The wind chill factor represents the air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is 62. Wind Chill Redo Problem 61(a)-(d) for an air temperature of – 10°C. 63. First-class Mail In 2018 the U.S. Postal Service charged $1.00 postage for certain first-class mail retail flats (such as an 8.5" by 11" envelope) weighing up to 1 ounce, plus $0.21 for each additional ounce up to 13 ounces. First-class rates do not apply to flats weighing more than 13 ounces. Develop a model that relates C, the first-class postage charged, for a flat weighing x ounces. Graph the function. Source: United States Postal Service 64. Challenge Problem Pool Depth Develop a model for the depth of the swimming pool shown below as a function of the distance from the wall on the left. 16 ft 6 ft 8 ft++8 ft 3 ft 3 ft 0sv< 1.79 8 ft 8 ft (10.45 + 10Vv – v)(33 – t) W = { 33 1.79 s v s 20 22.04 33 – 1.5958 (33 - t) v > 20 65. Challenge Problem Find the sum function (f + g) (x) if if x < 2 where v represents the wind speed (in meters per second)itnde f(x) = and t represents the air temperature (°C). Compute the wind chill for the following: S2r + 3 x² + 5x _if x 2 and (a) An air temperature of 10°C and a wind speed of 1 meter per second (m/sec) (-4x + 1 if x50 x-7 g(x) = if x > 0 Expiaining Concepts: Discussion and Writing In Problems 66-73, use a graphing utility. 71. Exploration Graph y = x'. Then on the same screen 66. Exploration Graph y = x². Then on the same screen olgraph y = (x – 1)³ + 2. Could you have predicted the result? graph y = x² + 2, followed by y = x² + 4, followed by y = x - 2. What pattern do you observe? Can you predict the graph of y = x² – 4? Of y = x² + 5? 67. xploration Graph y = x². Then on the graph y = (x – 2)2, followed by y = (x – 4)², followed by y = (x + 2)². What pattern do you observe? Can you Predict the graph of y = (x + 4)2? Of y = (x – 5)²? 08. Exploration Graph y = |x|. Then on the same screen 72. Exploration Graph y = x², y = x*, and y = x° on the same screen. What do you notice is the same about each graph? What do you notice is different? screen 73. Exploration Graph y = x', y = x’, and y = x’ on the same screen. What do you notice is the same about each graph? What do you notice is different? 74. Consider the equation if x is rational 0 ifx is irrational graph y = 2|x|, followed by y = 4|x|, followed by y = |x\. y = What pattern do you observe? Can you predict the graph of Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe its graph? 75. Define some functions that pass through (0,0) and (1, 1) and are increasing for x 2 0. Begin your list with y = Vx, y = x, and y = x². Can you propose a general result about such functions? y=지? Ofy = 5제? . Exploration Graph y = x². Then on the same screen graph y = -x². Now try y = |x| and y = -x|. What do you conclude? . Exploration Graph y = Vx. Then on the same screen Braph y = V-x. Now try y = 2x + 1 and y = 2(-x) + 1. What do you conclude?
Transcribed Image Text:(e) Construct a function C = C(s),where Cisthe loan-level price adjustment (LLPA) and s is the credit score of an individual who wishes to borrow $300,000 with an 80% (b) An air temperature of 10°C and a wind speed of 5 m/sec (c) An air temperature of 10°C and a wind speed of 15 m/sec LTV ratio. ) What is the LLPA on a $300,000 loan with an 80% LTV ratio for a borrower whose credit score is 725? (e) What is the LLPA on a $300,000 loan with an 80% LTV ratio for a borrower whose credit score is 670? (d) An air temperature of 10°C and a wind speed of 25 m/sec (e) Explain the physical meaning of the equation corresponding to 0 s v < 1.79. () Explain the physical meaning of the equation corresponding to v > 20. 0 Minimum Payments for Credit Cards Holders of credit cards issued by banks, department stores, oil companies, and so on, receive bills each month that state minimum amounts that must be paid by a certain due date.The minimum due depends on the total amount owed. One such credit card company uses the following rules: For a bill of less than $10, the entire amount is due. For a bill of at least $10 but less than $500, the minimum due is $10. A minimum of $30 is due on a bill of at least $500 but less than $1000, a minimum of $50 is due on a bill of at least $1000 but less than $1500, and a minimum of $70 is due on bills of $1500 or more. Find the function f that describes the minimum payment due on a bill of x dollars. Graph f. 61. Wind Chill The wind chill factor represents the air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is 62. Wind Chill Redo Problem 61(a)-(d) for an air temperature of – 10°C. 63. First-class Mail In 2018 the U.S. Postal Service charged $1.00 postage for certain first-class mail retail flats (such as an 8.5" by 11" envelope) weighing up to 1 ounce, plus $0.21 for each additional ounce up to 13 ounces. First-class rates do not apply to flats weighing more than 13 ounces. Develop a model that relates C, the first-class postage charged, for a flat weighing x ounces. Graph the function. Source: United States Postal Service 64. Challenge Problem Pool Depth Develop a model for the depth of the swimming pool shown below as a function of the distance from the wall on the left. 16 ft 6 ft 8 ft++8 ft 3 ft 3 ft 0sv< 1.79 8 ft 8 ft (10.45 + 10Vv – v)(33 – t) W = { 33 1.79 s v s 20 22.04 33 – 1.5958 (33 - t) v > 20 65. Challenge Problem Find the sum function (f + g) (x) if if x < 2 where v represents the wind speed (in meters per second)itnde f(x) = and t represents the air temperature (°C). Compute the wind chill for the following: S2r + 3 x² + 5x _if x 2 and (a) An air temperature of 10°C and a wind speed of 1 meter per second (m/sec) (-4x + 1 if x50 x-7 g(x) = if x > 0 Expiaining Concepts: Discussion and Writing In Problems 66-73, use a graphing utility. 71. Exploration Graph y = x'. Then on the same screen 66. Exploration Graph y = x². Then on the same screen olgraph y = (x – 1)³ + 2. Could you have predicted the result? graph y = x² + 2, followed by y = x² + 4, followed by y = x - 2. What pattern do you observe? Can you predict the graph of y = x² – 4? Of y = x² + 5? 67. xploration Graph y = x². Then on the graph y = (x – 2)2, followed by y = (x – 4)², followed by y = (x + 2)². What pattern do you observe? Can you Predict the graph of y = (x + 4)2? Of y = (x – 5)²? 08. Exploration Graph y = |x|. Then on the same screen 72. Exploration Graph y = x², y = x*, and y = x° on the same screen. What do you notice is the same about each graph? What do you notice is different? screen 73. Exploration Graph y = x', y = x’, and y = x’ on the same screen. What do you notice is the same about each graph? What do you notice is different? 74. Consider the equation if x is rational 0 ifx is irrational graph y = 2|x|, followed by y = 4|x|, followed by y = |x\. y = What pattern do you observe? Can you predict the graph of Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe its graph? 75. Define some functions that pass through (0,0) and (1, 1) and are increasing for x 2 0. Begin your list with y = Vx, y = x, and y = x². Can you propose a general result about such functions? y=지? Ofy = 5제? . Exploration Graph y = x². Then on the same screen graph y = -x². Now try y = |x| and y = -x|. What do you conclude? . Exploration Graph y = Vx. Then on the same screen Braph y = V-x. Now try y = 2x + 1 and y = 2(-x) + 1. What do you conclude?
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