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43. One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is π/6? 5

43. One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is π/6? 5

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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2z = 4 n degrees ds is mea- S ture erage mate C/year also 2 ction, salinity 16D is the ow the y dive ng O of by the (min) ing as how the current I is changing at the moment when R 400 2, = -0.01 V/s, and dR/dt = 0.03 /s. IR, to find 1 = 0.08 A, dv/dt 41. The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is increasing at a rate of 0.15 K/s. Use the equation PV = 8.31T in Example 2 to find the rate of change of the volume when the pressure is 20 kPa and the temperature is 320 K. 42. A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65 K0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Suppose that when L= 30 and K = 8, the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of $500,000 per year. Find the rate of change of production. 43. One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is π/6? 48. If z = 44. A sound with frequency f, is produced by a source traveling along a line with speed vs. If an observer is traveling with speed v, along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is fo= = 49-54 Assum second-order 49. Show tha -[f is a solu [Hint: 50. If u = c + vo C - Vs where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 34 m/s and accelerating at 1.2 m/s². A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.4 m/s², and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear and how fast is it changing? 51. If z (Con 52. If z (a) 53. If a 54. S C
Transcribed Image Text:2z = 4 n degrees ds is mea- S ture erage mate C/year also 2 ction, salinity 16D is the ow the y dive ng O of by the (min) ing as how the current I is changing at the moment when R 400 2, = -0.01 V/s, and dR/dt = 0.03 /s. IR, to find 1 = 0.08 A, dv/dt 41. The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is increasing at a rate of 0.15 K/s. Use the equation PV = 8.31T in Example 2 to find the rate of change of the volume when the pressure is 20 kPa and the temperature is 320 K. 42. A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65 K0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Suppose that when L= 30 and K = 8, the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of $500,000 per year. Find the rate of change of production. 43. One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is π/6? 48. If z = 44. A sound with frequency f, is produced by a source traveling along a line with speed vs. If an observer is traveling with speed v, along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is fo= = 49-54 Assum second-order 49. Show tha -[f is a solu [Hint: 50. If u = c + vo C - Vs where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 34 m/s and accelerating at 1.2 m/s². A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.4 m/s², and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear and how fast is it changing? 51. If z (Con 52. If z (a) 53. If a 54. S C
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