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D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 3ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4ft above the ground?

D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 3ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4ft above the ground?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Question 6D
D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 3ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4ft above the ground? E. If y = x3 – 2x and d = -3, find 4 when r = x- and y- variables depend on t. 4. Note that, in this case, both F. Finally, a light is mounted at the top of a 12 ft pole. A person 5 ft tall walks away from the pole with a speed of 4 ft/s in a straight line. How fast do you think the tip of his shadow moves when he is 35 ft away from the pole? You must explain your work step by step in order to receive credit.
Transcribed Image Text:D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 3ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4ft above the ground? E. If y = x3 – 2x and d = -3, find 4 when r = x- and y- variables depend on t. 4. Note that, in this case, both F. Finally, a light is mounted at the top of a 12 ft pole. A person 5 ft tall walks away from the pole with a speed of 4 ft/s in a straight line. How fast do you think the tip of his shadow moves when he is 35 ft away from the pole? You must explain your work step by step in order to receive credit.
6. The following set of problems concern applications of Calculus to real life situations. Think about the following points when solving each such problem: i) What quantities are given in the problem? ii) What is the unknown? iii) Draw a picture of the situation for any time t. iv) Write an equation that relates the quantities involved. v) Finish solving the problem. A. If r = r(t) represents the position function at time t of a certain particle, then what do you think would be the interpretation of the derivative r'(t)? B. The position of a particle moving along a horizontal line is given by a(t) = t3-6t2+9t, where t>0 is measured in seconds and s is in meters. a) Find the velocity function at time t. b) When is the particle stopped? When is the particle moving forward? Explain. C. Two cars start moving from the same point. One travels east at 55mi/h and the other travels south at 65mi/h. At what rate is the distance between the two cars increasing three hours later?
Transcribed Image Text:6. The following set of problems concern applications of Calculus to real life situations. Think about the following points when solving each such problem: i) What quantities are given in the problem? ii) What is the unknown? iii) Draw a picture of the situation for any time t. iv) Write an equation that relates the quantities involved. v) Finish solving the problem. A. If r = r(t) represents the position function at time t of a certain particle, then what do you think would be the interpretation of the derivative r'(t)? B. The position of a particle moving along a horizontal line is given by a(t) = t3-6t2+9t, where t>0 is measured in seconds and s is in meters. a) Find the velocity function at time t. b) When is the particle stopped? When is the particle moving forward? Explain. C. Two cars start moving from the same point. One travels east at 55mi/h and the other travels south at 65mi/h. At what rate is the distance between the two cars increasing three hours later?
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