The velocity (in m/s) of a moving particle is a function of time (in seconds). The table below summarizes the velocity at specific time intervals.Itv(t)022152418372225Use the Direct Method to interpolate a cubic polynomial for the velocity of the particle. Use the resulting polynomial to approximate the total distance travelled by the particle over the period from t=11 secods to 1=15 secods.75.4201O 92.3391O none of the choicesO 40.0251O 88.4841

Given Data: Let us consider the given table, t 0 15 18 22 v(t) 22 24 37 25

Answered: The velocity (in m/s) of a moving…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate of 10 gal/min and the resulting uniform mixture is removed from the tank at the same rate.a. Derive an expression for the amount of dye in the tank as a function of time.b. Find the time t at which the tank contains 25% dye solution
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Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 90 95 35 188 212 238 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. f(хо + Дх, Уо) -f (хо- Уo) if,(xo, yo) = lim Ay-0 f (x0, Yo + Ay) – f (xo. Yo) Ay f. (xo, Yo) = lim Ax-) Ax Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of r with respect to v when v = 85ft/s and 0 = 45°. dr i dv (b) Estimate the partial derivative of r with respect to 0 when v = 85ft/s and e = 45°. dr ANGLE O (degrees)
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