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(a) Suppose that a spherical snowball melts so that its surface area decreases at a constant rate of 1 cm²/min. At what rate is the radius of the snowball decreasing when the radius is 5 cm? Note: the surface area of a sphere of radius r is 4ñr².

(a) Suppose that a spherical snowball melts so that its surface area decreases at a constant rate of 1 cm²/min. At what rate is the radius of the snowball decreasing when the radius is 5 cm? Note: the surface area of a sphere of radius r is 4ñr².

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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(a) Suppose that a spherical snowball melts so that its surface area decreases at a constant rate of 1 cm²/min. At what rate is the radius of the snowball decreasing when the radius is 5 cm? Note: the surface area of a sphere of radius r is 4πr². (b) A weather balloon is rising vertically from a launching pad on the ground. A technician standing 300 feet from the launching pad watches the balloon rise. At what rate is the balloon rising at the instant when the angle between the ground and the technician's line of sight is radians and is increasing at a rate of 4 radian per second? (Disregard the height of the technician.) 1 120 (c) Two straight roads meet at right angles at an intersection. A car is traveling due south towards the intersection at a constant speed of 60 miles per hour. A second car is traveling due west towards the same intersection at a constant speed of 70 miles per hour. How fast is the distance between the cars changing at the instant when the southbound car is 30 miles from the intersection and the westbound car is 40 miles from the intersection? (d) Boyle's Law states that when a sample of gas is compressed at a constant temper- ature, the pressure P and volume V are related by the equation PV = c, where c is a constant. Suppose that at a certain instant the volume of the gas is 600 cm³, the pressure is 150 kPa and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?
Transcribed Image Text:(a) Suppose that a spherical snowball melts so that its surface area decreases at a constant rate of 1 cm²/min. At what rate is the radius of the snowball decreasing when the radius is 5 cm? Note: the surface area of a sphere of radius r is 4πr². (b) A weather balloon is rising vertically from a launching pad on the ground. A technician standing 300 feet from the launching pad watches the balloon rise. At what rate is the balloon rising at the instant when the angle between the ground and the technician's line of sight is radians and is increasing at a rate of 4 radian per second? (Disregard the height of the technician.) 1 120 (c) Two straight roads meet at right angles at an intersection. A car is traveling due south towards the intersection at a constant speed of 60 miles per hour. A second car is traveling due west towards the same intersection at a constant speed of 70 miles per hour. How fast is the distance between the cars changing at the instant when the southbound car is 30 miles from the intersection and the westbound car is 40 miles from the intersection? (d) Boyle's Law states that when a sample of gas is compressed at a constant temper- ature, the pressure P and volume V are related by the equation PV = c, where c is a constant. Suppose that at a certain instant the volume of the gas is 600 cm³, the pressure is 150 kPa and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?
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