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# Calculus Week 7 MA 1713

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This 16 page Class Notes was uploaded by Katerina Kushla on Thursday September 29, 2016. The Class Notes belongs to MA 1713 at Mississippi State University taught by Robert Banik in Fall 2016. Since its upload, it has received 5 views. For similar materials see Calculus I in Math at Mississippi State University.

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Date Created: 09/29/16

Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Ex. 5: The height, in meters, or a projectile shot vertically upward from a point 2 meters above ground level with an initial velocity of 24.5 m/s is h = 2 +24.5t – 4.9t 2 ****A problem like this will be on the final!!!**** Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 If a snowball melts so that its surface area decreases at a rate of 1 cm /min, find the rate at which the diameter decreases when the diameter is 10 cm. Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 The height of a triangle is increasing at a rate of 1 cm/min while the area of the 2 triangle is increasing at a rate of 2 cm /min. At what rate is the base of the triangle changing when the height is 10 cm and the area is 100 cm ? 2 Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 meter higher than the bow of the boat. If the rope is being pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 meters from the dock? Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 3 Gravel is being dumped from a conveyor belt at a rate of 30 ft /min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 feet high? Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 A kite 100 feet above the ground moves horizontally at a speed of 4 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 feet of string has been let out? Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 feet from the wall? How fast is the angle between the ground and ladder changing? Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom of the ladder is 3 meters from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is the ladder? Chapter 2: Sections 2.7 & 2.8 Week 7 9/27-29/16 A camera is located 30 feet from a straight road along which a car is traveling at 150 feet per second. The camera rotates so that it will always be pointed at the traveling car at all times. In radians per second, how fast is the camera turning as the car passes closest to the camera?

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