Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = t v(t) (-1,1) a(t) (-1) | %3D |v(t)| V2 II

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

A: We have to find the

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Q: Use this order-three version of variation of parameters to find the general solution: y" + 2y" – y –…

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A: Given exy + y = x - 1 is a solution of given differential equation.

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A: According to the given information, it is required to find equilibria.

Q: g(x) = Vx is reflected over the y-axis and vertically compressed by a factor of ¼ %3|

A: Given function is gx=x We have to find the transformed function which is reflected over the y-axis…

Q: 5. Find a solution f(x) to the equation (D3 – D² + D – 1)f(x) = 0 %3D such that f(0) = 1, f'(0) = 0,…

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Q: Find the critical numbers of the function.…

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Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

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A: Givenx(t)=t3-6t+9t     0≤t≤5

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Q: The orthogonal trajectories of the family of curves y = cx2 is A x=ky? B x²=ky² © 2x2+y²=k D…

A: Solution

Q: Find values of m so that the function y = e"™x is a solution of the given D а) y' + 2y = 0 b) y" –…

A: Using differential equations ,

Q: The orthogonal trajectories of the family of curves y= cx2 is A 2x²+y²=k B x²+2y²=k © x=ky? D x²=ky²

A: Given family of curves is y = cx2 We have to find the orthogonal trajectories.

Q: Solve the problem. Given the velocity and initial position of a body moving along a coordinate line…

A: Given: Velocity at time t is V=-6t+4 Initial position is s(0)=6

Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 7. x = 3(y – c);

A: Here we have to find the orthogonal trajectories of the given family of curves.    x3 = 3(y-c)

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Q: ) Find the maxima and the minima of z=f(x,y) under the condition y=2x. (d) Find the maxima and the…

A: Max or  Min f(x,y)=(3x2+5y2)e-x2-y2subject to    y=2x

Q: The orthogonal trajectories of the family of curves y= cx² is A x=ky? B 2x2+y2 = k © x2 = ky? x2…

A: The given family of curve y=cx2

Q: (b) Consider the IVP, test whether it is exact and solve it. x(x – y)dy = -(3xy – y²)dx y(-1) = 1

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Q: The position of a particle moving along the x - axis at time t is given by x(t) = ecos2t, 0<ts . For…

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Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

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A: Given query is to find the initial vertical velocity and horizontal velocity.

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Q: Jester Sports manufactures tennis rackets. The total cost of producing a rackets per hour is given…

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Q: The position of a particle on the x-axis is given by x(t) = t – 4t + 3. At what time is the…

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Q: Find the Orthogonal Trajectories: a.) y6 = C (x2 + 1)

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Q: sive a particular solution for y" - 2y' + y = z 1+x2

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Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

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Q: The relationship between total capacitance C and the three capacitors C1, C2 and C3 is shown below:…

A: We can solve the question as below

Q: Mathematically, what is the total (or net) effects of an increase of the wealth of households on Y?…

A: Answer : C dYdA = 11-CY+V(i)YV'(i)

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A: The objective is to find when the velocity of the body is increasing.

Q: (b) Classify the equation t - 2ty +2y =t, t> 0. What order is it? Is it linear or nonlinear? Is it…

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Q: Q-1 Find the orthogonal trajectories of y = ea" where a be the arbitrary constant. [

A: Given curve is y=eax

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Q: Maximise Z = 3 a + 2 b S.T. la - 1 b s 1 l a + lb 2 3 and both x and y are > 0

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Q: h34. Find the general solution of the FOLDE, (x + 3y)dx- xdy 0. a. y = -2x + Cx³ b. Сх3 3 2х + у c.…

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Q: Find the relative maximum and minimum values. f(x,y) = x° +y° - 3xy

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Q: The orthogonal trajectories of the family of curves y= cx² is A x² = ky? x² +2y² =k В © x=ky? D 2x2+…

A: In this question we have to find the orthogonal trajectories of the family of the curves y=cx2

Q: t = x+ y Use the substitutions : to solve the S = x ди ди PDE : -2y 0, u(x,2x+1) = e. -- дх ду

A: Given PDE, ∂u∂x-∂u∂y-2y=0,   ux,2x+1=ex To find the solution of the PDE.

Q: The position of a particle moving along the x- axis at time t is given by x(t) = ecos2f, 0stS T. For…

A: Given that: Position, x(t)=ecos2t

Q: The maximm rate of change of the finction /(x.y,2) x In(yz) at (1:2;5 is equal to: V17/2 V17/4 O…

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Q: 4 Use global extrema to find constants m and M such that m < dx < M. x3-2 1.5

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Q: Given f (x, y)=x e*(y+1); x20, y 20. Find the regression curve of Yon X.

A: Answer: For the given data,