57. Given the model d- 20e 0 cos 2 71, for an object in damped harmonic motion, a. Determine the initial displacement, d (in centimeters). b. Graph the model on a graphing utility. c. Determine the time t (in seconds) between two consecutive relative maxima. d. By what percentage is the displacement of the object decreased with each successive oscillation between consecutive maxima? Round to the nearest tenth of a percent.

Q: Find the solution of the initial value problem y" + 4y + 5y = 0, 3) = 0, y = 6. Y (7) تھی y(t) = -6…

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Q: (d): dT %3D dr 10(T - 71) (Newton's Law of Cooling - T is temperature and t is time) 1 dl (e): + 10/…

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A: The velocity of the particle is given by: v(t)=(t2.5+4t)cos(3t)

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A: y''+4y=0m2+4=0m2=-4m=-4m=±2i Complementary solution:The equation of roots are imaginary…

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A: p(t)=4048-1250 cos(2π9t)t=0P(0)=4048-1250P(0)=2798P(t)=4700t=?4700=4048-1250 cos(2π9t)652=1250…

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A: We will use second derivative test to find time at which maximum veolcity achieved

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Q: 1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) = 23,000 –…

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Q: 17. An initial population, p, of 10000 bacteria grows in number according to the equation 4t p(t) =…

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Q: 11. An object moves along the x-axis so that at any time t > 0, its velocity is given by v(t) = 4 –…

A: Given,               Velocity V (t) = 4 – 3.8 cos (0.7t)

Q: Q 5: (a) Assume that after w months, butterflies' populace in 1000 is calculated as: f(w) = 12w +…

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Q: 4. (а) Solve the IVP for y(t): y" + 4y = 3 8(t – n), y(0) = 0, y' (0) = 0 (b) 2n. Be sure to label…

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A: Given: Differential equation y''+100y=9cos(10t), with initial conditions y(0)=0 and y'(0)=0.

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