Concept explainers
(a)
To find: The slope of the path of the particle at time
(a)
Answer to Problem 48RE
The slope of the path of the particle at time
Explanation of Solution
Given:
The parametric equations are
Calculation:
The slope of the particle is given by,
Differentiate the equation
Differentiate the equation
Find the slope of the path of the particle at time
Therefore, the slope of the path of the particle at time
(b)
To find: The speed of the particle when
(b)
Answer to Problem 48RE
The speed of the particle when
Explanation of Solution
Given:
The parametric equations are
Calculation:
Find the velocity
Find the magnitude of the velocity vector as follows.
Find the speed of the particle when
Therefore, the speed of the particle when
(c)
To find: The distance traveled by the particle along the path from
(c)
Answer to Problem 48RE
The distance traveled by the particle along the path from
Explanation of Solution
Given:
The parametric equations are
Calculation:
Find distance traveled by the particle along the path from
Therefore, the distance traveled by the particle along the path from
Chapter 11 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (4th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
Precalculus
Elementary Statistics: Picturing the World (7th Edition)
Algebra and Trigonometry (6th Edition)
- 2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.arrow_forwardwrite it down for better understanding pleasearrow_forward1. Suppose F(t) gives the temperature in degrees Fahrenheit t minutes after 1pm. With a complete sentence, interpret the equation F(10) 68. (Remember this means explaining the meaning of the equation without using any mathy vocabulary!) Include units. (3 points) =arrow_forward
- 2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below. a. Evaluate f(-3). If you have multiple steps, be sure to connect your expressions with EQUALS SIGNS. (3 points)arrow_forward4c Consider the function f(x) = 10x + 4x5 - 4x³- 1. Enter the general antiderivative of f(x)arrow_forwardA tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 11 L/min. Let y be the number of kg of salt in the tank after t minutes. The differential equation for this situation would be: dy dt y(0) =arrow_forward
- • • Let > be a potential for the vector field F = (−2 y³, −6 xy² − 4 z³, −12 yz² + 4 2). Then the value of sin((-1.63, 2.06, 0.57) – (0,0,0)) is - 0.336 -0.931 -0.587 0.440 0.902 0.607 -0.609 0.146arrow_forwardThe value of cos(4M) where M is the magnitude of the vector field with potential ƒ = e² sin(лy) cos(π²) at x = 1, y = 1/4, z = 1/3 is 0.602 -0.323 0.712 -0.816 0.781 0.102 0.075 0.013arrow_forwardThere is exactly number a and one number b such that the vector field F = conservative. For those values of a and b, the value of cos(a) + sin(b) is (3ay + z, 3ayz + 3x, −by² + x) is -0.961 -0.772 -1.645 0.057 -0.961 1.764 -0.457 0.201arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning