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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.
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- Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for fa(t)=-2-t ly(t) = 19 - 3t The Cartesian equation is y= T ? FE 2016 EXPRES 2015- 201 144 2017 10-01- 1000046arrow_forwarddNo linearlfemential Find tovo to equation and als. thearrow_forwardThe motion of an oscillating weight suspended from a spring was measured by a motion detector. The data were collected, and the approximate maximum displacements from equilibrium (y = 3) are labeled in the figure. The distance y from the motion detector is measured in centimeters, and the time t is measured in seconds. (0.125, 3.32) 4 (a) Is y a function of t? O Yes ○ No (0.375, 2.68) 0.9 Explain. ○ For some value of t there is more than one value of y. ○ For some value of y there is more than one value of t. OFor each value of t there corresponds one and only one value of y. For each value of y there is some value of t. ◇ For each value of y there corresponds one and only one value of t. (b) Approximate the amplitude and period. amplitude period cm S (c) Find a model for the data. y = (d) Use a graphing utility to graph the model in part (c). Compare the result with the data in the figure.arrow_forward
- Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan ²t-sec c²t₁ y₂ = 6 Select the correct choice below and, if necessary, fill in the answer box within your choice. © A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 Y₂ on (0,1), the functions are linearly dependent on (0,1). Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).arrow_forwardHow do I solve in steps? What are the main equations that I use?arrow_forwardHand written plzarrow_forward
- Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y1 =sint cos t, y, = 5 sin 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = y, on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O B. Since y, =O2 on (0,1), the functions are linearly independent on (0,1) (Simplify your answer.) O C. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).arrow_forwardDirection: Refer to the given worded problem below and answer the question provided. A man is suspended from a bungee rope and moving according to the equation. Where h(t) feet is directed distance of the weight from its equilibrium position at tseconds, and the positive distance means above its equilibrium position. 1. At what time is the displacement of theMan 5 feet below its equilibrium positionfor the first time?arrow_forwardCLO 5 Find the gradient of the scalar function V=p2 cos²o at P(2,3.62,3). а. 1.63 ар -3.15 аф b. 1.58 ap - 0.82 ad с. 3.15 ар- 1.63 аф d. -3.55 ap 0.82 ad e. None of the choicesarrow_forward
- Determine whether the functions y, and y₂ are linearly dependent on the interval (0,1). y₁ = sint cost, y₂ = 5 sin 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 10 Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). y₂ on (0,1), the functions are linearly dependent on (0,1).arrow_forwardFind the directions of maximum and minimum change of fat the given point, and the values of the maximum and minimum rates of change. f(x, y)=9y²ex, (3, 1) O The maximum change is 18e¹8 √10; in the direction (-54e¹8, -18e¹8); The minimum change is-18e¹8 √10; in the direction (54e18, 18e¹8). The maximum change is 18e-18 √10; in the direction (-54e-18, -18e-18); The minimum change is-18e-18 √10; in the direction (54e-18, 18e-18). O The maximum change is 18e¹8 √10; in the direction (54e¹8, 18e¹8); The minimum change is-18e¹8 √10; in the direction (-54e18, -18e¹8). The maximum change is 18e-18 √10; in the direction (54e-18, 18e-18); The minimum change is-18e-18 √10; in the direction (-54e-18, -18e-18).arrow_forwardpls input letter of final answerarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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