Homework Homework Assignment #20 Review Section 3.11

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Homework Homework Assignment #20 Review Section 3.11 Page 204, Exercises: 1 – 37 (EOO) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 Consider a rectangular bathtub whose base is 18 ft2. 1. How fast is the water level rising if water is filling the tub at a rate of 0.7 ft3/min? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 Assume the radius r of a sphere is expanding at a rate of 14 in/min. 5. Determine the rate at which the volume is changing with respect to time when r = 8 in. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 9. A road perpendicular to a highway leads to a farmhouse located 1 mile away. A car travels past the farmhouse at 60 mph. How fast is the distance between the farmhouse and car changing when the car is 3 miles past the intersection of the highway and road? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 13. Sonya and Isaac are in boats at the center of a lake. At t = 0, Isaac takes off, heading east at 27 mph. At t = 1 min, Sonya begins heading south at 32 mph. a) How far have Isaac and Sonya traveled at t = 12? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 13. b) At what rate is the distance between them increasing at t = 12? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 17. A hot air balloon rising vertically is tracked by an observer located 2 mi from the lift-off point. At a certain moment, the angle between the observer’s line of sight and the horizontal is π/5, and it is changing at a rate of 0.2 rad/min. How fast is the balloon rising at that moment? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 Consider a 16-ft ladder sliding down a wall. The variable h is the height of the ladder’s top at time t and x is the distance from the wall to the ladder’s base. 21. Suppose h(0) = 12 and the top slides down the wall at a rate of 4 ft/s. Calculate x and dx/dt at t = 2s. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 25. Suppose that both the radius r and the height h of a circular cone are changing at the rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 29. A plane traveling at 20,000 ft passes directly overhead at time t = 0. One minute later you observe the angle between the vertical and your line of sight to the plane is 1.14 rad and that the angle is changing at the rate of 0.38 rad/min. Calculate the velocity of the airplane. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 Assume that the pressure P (in kilopascals) and volume V (in cm3) of an expanding gas are related by PVb = C, where b and C are constants. 33. Find dP/dt if b = 1.2, P = 8 kPa, V = 100cm3, and dV/dt = 20 cm3/min. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 204 37. A water tank in the shape of a right circular cone of radius 300 cm and height 500 cm leaks water from the vertex at the rate of 10 cm3/min. Find the rate at which the water level is decreasing when it is 200 cm. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework Homework Assignment #21 Review Sections 3.1 – 3.11 Page 207, Exercises: 1 – 121 (EOO) Chapter 3 Test next time Rogawski Calculus Copyright © 2008 W. H. Freeman and Company