The position of the particle at time tis given by s(t) =ť² –&t +15. The particle is moving from left to right at t = seconds %3D ut O 3.5 3.0 0.0 1.5 6.0

Q: y" + y = d(t – 27) sin(t); y(0) = 0, y'(0) = 1. %D %3D -

A: Given,      y''+y=δt-2πsin(t);      y(0)=0, y'(0)=1.

Q: The position of the particle at time t is given by s(t) = t² – 6t + 8. The particle is moving from…

A: Option c is correct.

Q: Solve D.E using Exact from first order 2.xy dx +(x² +3y²)dy

A: To solve the given differential equation.

Q: 1 dx dy A point is moving along the graph of the functiony = such that = 4 centimeters per second.…

A:

Q: The acceleration of a particle moving back and forth on a lineis a = d2s/dt2 = π2 cos pt m/sec2 for…

A:

Q: The position of the particle at timet is given by s(t) = t² – 16t + 63. - The particle is moving…

A: Given data: The position of particle is given by, st=t2-16t+63

Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

A:

Q: The position of the particle at time t is given by s(t) = t² – 12t + 35. - The particle is moving…

A: Velocity and position

Q: Find the initial value problem of: dy/dx +(2/t)y = cos(t)/(t^2) given that y(pi) = 0 and t>0

A: Given

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

A:

Q: Solve the following second order ODE dy dy + 2x dx? = 0 || dx with the initial conditions y(0) = 2…

A: The given 2nd order ODE is d2ydx2+2xdydx2=0, with initial conditions y0=2 and y'0=-1. The main…

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

A:

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: A particle was following the trajectory r(t) = (e', sin (2t), t), but it starts flying tangentially…

A: SolutionGivenA particle was following the trajectory r(t)= (et,sin(2t),t) , but it starts flying…

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: Q3) Find dy/dt of the function y = cos (5sin (t/3))

A:

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: Compute dy/dx using the chain rule in formula. State your answer in terms of x only.  y = u3&gt;2, u…

A: Given equations - y = u3+2           .....(1)                                                  In…

Q: The position of the particle at time t is given by s(t) = t2 – 8t + 15. The particle is moving from…

A:

Q: The position of the particle at time t is given by s(t) = t² – 8t + 15. %3D The particle is moving…

A: Given that       The position of the particle at time t is given by  s(t) = t2 -8t + 15. Here we…

Q: Use RK 4 with h = 0.05 to approximate in four decimal places the value of y(1) by solving the…

A: To find- Use RK4 with h=0.05 to approximate in four decimal places the value of y1 by solving the…

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: Compute for the initial velocity of 3÷(cos(45)×38. Show your complete solution

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Q: Let y = tan(3r + 4). Find the differential dy when T = 4 and da 0.4 Find the differential dy when x…

A: Given: Differentiate the above expression of 'y' with respect to 'x'.

Q: Solve the initial-value problem for yy as a function of x. (x2+49)dy/dx=1,y(7)=0.

A:

Q: Let y = y(t) be the solution to the initial value problem dy y = e' cos t; dt y(0) = 1. - Find the…

A: Given: Initial value problem dydt-y=et cost,   y(0)=1

Q: Find dy/dt. y= cos ~ 10t + 11)

A:

Q: Suppose that the position of a body moving along a coordinate line at time t is a. s = a cos kt + b…

A: Part (a):Part (a):Given,Given,

Q: d?y dz? Find the two real root second order differential with for 6- + 5 dy = 6y dx O C1*e^(2x/3) +…

A: Solution:-  Given differential equation            6d2ydx2+5dydx=6y     Firstly rearrange  this as…

Q: Solve the initial-value problem using the undetermined coefficients at the condition, y(0) = 2,…

A:

Q: Consider the following. dy dx ex — У, (0, 1) %3D y | || 5+\/|| -4 ///+1 | 4 I| |-3+ (a) Find the…

A: dydx=ex-y ,   0, 1 On simplification, we get dydx+y=ex Now comparing with dydx+Py=Q, we get P=1…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

A:

Q: The acceleration of a particle moving back and forth on a line is a = d2s/dt2 = pai ^2 cos pai t…

A: Given information:

Q: B) Find the distance traveled by the particle P (x.y) between t = 0 and t 4 if the position at time…

A:

Q: Find dy at the point t = 5. c(t) = (t4, t³ – 3) * (at t = 5) = dy dx

A: Given that, c(t) = (t4, t3, -3) To find dcdt t = 5

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: A particle moves along the x-axis so that at time t >0 its position is given by r(t) = t - 7t + 13.…

A: Given: t≥0xt=t2-7t+13

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: Find 4 at the point t = 5. dy dx c(t) = (t^, t³ – 3) dy dx (at t = 5) = ||

A:

Q: (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the parameter t 6. dt TO -/-

A:

Q: The position of the particle at time t is given by s(t) = t2 - 6t + 8. %3D The particle is moving…

A: To find the value of t particle moves from left to right

Q: Solve the initial-value problem for x as a function of t. dx (t – 12t + 35) dt 1, (t > 7, x(9) = 0)…

A: The given initial value problem is as below.

Q: Find the L{y(t)}, given the initial value proble y" - 3y' + 2y = t - 2;

A:

Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: dy Find the solution of = y (8 – ) satisfying the initial condition y(0) = 144.

A:

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

A:

Q: Find the particular solution if dy/dt=sin(t) and y(2)=2.

A: Topic:- application of integration

Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…

Q: the given velocity v(t) = e2ti– sin tk and r(0) = (1,2,0) to find the position at time t = 1.

A: