Concept explainers
Stability of equilibrium points Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to indicate only whether solutions are increasing or decreasing on either side of the equilibrium solution.
18.
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- d. Example: Give the positions s f(t) of a body moving on a line, with s in meters and t In second. Find the body's displacement and average velocity for the given time interval. Also, find the body's speed and acceleration at the endpoints of the interval. During the given interval, when docs the body change direction 2. a= -t+ 3t2 - 3t, Osts3 3. 8 (t/4)-+t², %3D 4. 8 = 145 - 4SISOarrow_forwardA stone thrown vertically on Mars Suppose a stone is thrownvertically upward from the edge of a cliff on Mars (where theacceleration due to gravity is only about (2 ft/s2) with an initialvelocity of 64 ft>s from a height of 192 ft above the ground. Theheight s of the stone above the ground after t seconds is given bys = -6t2 + 64t + 192.a. Determine the velocity v of the stone after t seconds.b. When does the stone reach its highest point?c. What is the height of the stone at the highest point?d. When does the stone strike the ground?e. With what velocity does the stone strike the ground?arrow_forwardMotion in a gravitational field An object is fired vertically upward with an initial velocity ν(0) = ν0 from an initial position s(0) = s0.a. For the following value of ν0 and s0 , find the position and velocity functions for all times at which the object is above the ground (s = 0).b. Find the time at which the highest point of the trajectory is reachedand the height of the object at that time. ν0 = 29.4 m/s, s0 = 30 marrow_forward
- Please eliminate the arbitrary constants of the equation below, where β is a parameterarrow_forwardA mass weighting 40 lbs stretches a spring 8 inches. The mass is in a medium that exerts a viscous resistance of 11 lbs when the mass has a velocity of 2 ft/sec. Suppose the object is displaced an additional 5 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t)= Show Transcribed Textarrow_forwardDirection: Eliminate the following arbitrary constants to obtain the DE. = (4) + bx аarrow_forward
- Find the equilibrium point of this equationarrow_forwardK ds The accompanying figure shows the velocity v = = f(t) (m/sec) of a body moving along a dt coordinate line. a. When does the body reverse direction? b. When is it moving at a constant speed? c. Graph the body's speed for 0 st≤ 10. d. Graph the acceleration, where defined. Av (m/sec) 5- 0- -5- v = f(t) s 6 8 (sec) 10arrow_forwardVelocity and acceleration from position Consider the following position function.a. Find the velocity and speed of the object.b. Find the acceleration of the object. r(t) = ⟨2 + 2t, 1 - 4t⟩, for t ≥ 0arrow_forward
- C An object travels with velocity function given by v (t) = 3t + 5. The next three questions refer to this object.arrow_forwardThe gas equation for one mole of oxygen relates its pressure, P (in atmospheres), its temperature, T (in K), and its volume, V (in cubic decimeters, dm³): dT T 16.574. = 1 V 0.52754. 1 V2 (a) Find the temperature T and differential dT if the volume is 34 dm³ and the pressure is 0.75 atmosphere. T = 0.3879 P + 12.187 V P. (b) Use your answer to part (a) to estimate how much the pressure would have to change if the volume increased by 2.5 dm³ and the temperature remained constant. change in pressure =arrow_forwardIf z = 5x2 + y2 and (x, y) changes from (1, 3) to (0.95, 3.1), compare the values of Az and dz. (Round your answers to four decimal places.) dz = Az = Need Help? Talk to a Tutor Read It Watch Itarrow_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