Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Assuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone.

A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Assuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CR: Chapter Review
Problem 14CC
See similar textbooks
icon
Related questions
Question

Answer question 3

3:51 Search Done Written Assignment 3-1 (1... •.. 2. The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of Newton's Law of Cooling is dT 2 of 2 = kS(T – Tm), dt 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 200° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 120° F. If Tm = 70° F, then what is the temperature of the coffee in cup B after 30 min? (Turn Over) 3. A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. ASsuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone. 4. The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming that the carrying capacity for the world population is 50 billion, the logistic differential equation dP = kP(50 – P) dt models the population of the world P(t) (measured in billions), where t is the number of years after 1990. Solve this differential equation for P(t) and use this solution to predict what the population will be in 2050 according to this model.
Transcribed Image Text:3:51 Search Done Written Assignment 3-1 (1... •.. 2. The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of Newton's Law of Cooling is dT 2 of 2 = kS(T – Tm), dt 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 200° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 120° F. If Tm = 70° F, then what is the temperature of the coffee in cup B after 30 min? (Turn Over) 3. A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. ASsuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone. 4. The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming that the carrying capacity for the world population is 50 billion, the logistic differential equation dP = kP(50 – P) dt models the population of the world P(t) (measured in billions), where t is the number of years after 1990. Solve this differential equation for P(t) and use this solution to predict what the population will be in 2050 according to this model.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS