A particle is moving with acceleration a(t) = 6t + 4. its position at time t = 0 is s(0) = 14 and its velocity at time t = 0 is v(0) = 16. What is its position at time t = 6?

Q: In Exercises 27-30, find the differential. 27. d(Vī-x) 28. d(e* + x) 29. d(arctan 4x) 30. d(8" + x)

A: 27. d1-x2 Ans.  ddx1-x2 =ddx(1-x2)12                         =  121-x212-1× ddx(1-x2)…

Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: Solve the differential eqyations (3x +5y +4)dx + (5x +3y +6)dy =0

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Q: A mass-spring system is modelled by the differential equation u" + 16 u = 0 , and the motion starts…

A: Given that u''+16u=0   with   u0=7   and  u'0=4. Its auxiliary equation is m2+16=0. Solve as…

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: How does the Fundamental Theorem provide a solution to the initial value problem dy/dx = ƒ(x), y(x0)…

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Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

Q: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.04. y = V3x – 2 A. 0.01…

A: Given that: y=3x-2x=2 to x=2.04

Q: A mass-spring system is modelled by the differential equation u' + 16 u = 0, and the motion starts…

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Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: Suppose we have a velocity function and an initial condition for position: 1 1 2t v (t) = r (1) =…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: 4. A 2 kg mass is attached to a spring whose constant is 6 N/m, and the entire system is submerged…

A: Given: X(0)=2-4 ∴2-4=C1-11+C2-131 2=-C1-C23,    -4=C1+C2 The required solution is…

Q: Find dt y = 6t + /9+ 7-t dy dt |3|

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Q: The maximum acceleration attained on the interval 0 <t < 3 by the particle whose velocity is v(t) =…

A: Given Data: Interval: 0≤t≤3 Velocity: v(t)=t3-3t2+12t+4 The acceleration can be obtained by…

Q: Suppose that we are interested in the amount of salt (in kg) at a certain moment in time, denoted by…

A: To solve the given statements

Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: find dy/dt. y = (esin (t/2))3

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Q: find dy&gt;dt.…

A: Given function, y=ecos2pt−1

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

Q: Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use…

A: Given dydx=x(y-8)2-6 We know that slope of linear equation id the it's derivative So, m=dydx

Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: The differential equation is dydx=0.8y, y(0)=4. Solve the equation as follows.…

Q: If y = x - 4x and x = V2r + 1, find dy/dt when t = 1= V2.

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Q: Estimate Ay using differentials. 1/33x-1, y = x ¹/3 e³x-1. a = 1, dx = 0.1

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Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

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Q: ,dz Find ifz = xy2 +x²y, y = ln x - dt

A: We are given : z=xy2+x2y and y=ln x⇒z=x(ln x)2+x2 ln x

Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: 2(y-4x2) dx + x dy

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Q: Given a particle is moving in a curve r(t) = cos 7t i + sin 7t j + 6t k. Find the tangential…

A: Given a particle is moving in a curve rt=cos 7t i^+sin 7t j^+6t k^to find the tangential and normal…

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

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Q: Find dy/dt. 13) y - cos (πt - 19) 14) y = 4t(5t + 2)4

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Q: Use the fourth-order Runge Kutta method to solve for the velocity and position of the free-falling…

A: Given:- t=0 , x=v=0  t=4s

Q: Solve the initial value dy/dx = 1/x2 + 1 - 1, y(0) = 1

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Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

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Q: Find the solution of the differential equatlor dy 3xeY, y(0) = 0 dx %3D

A: Consider the equation

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: tion of the separable equation dy 23 3 +2)³ + 2)?

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Q: Find the linearization of x = -1 f(x) = 3+ S sec(t – 1)dt at

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Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: dy dy + 7 dt + 10y = e-t dt2

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Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

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Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A: From the given problem, we considered m= 1 kg,  k= 16 N/m, β=10 SO, the mass is released from the…