9. An object moving along a curve in the xy-plane has position (x(t),y(t)) at dy dx :=1+ tan(r²) and = 3e" . Find the acceleration dt time t2 0 with dt vector and the speed of the object when t = 5. plane so that the position of the particle is given by

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

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A: The distance of a point (x, y) and the origin can be calculated as follows.

Q: dy Find at x = dt dy dt || 4 if y = 3x² + 5 and dx dt = 1.

A: Let's find dy/dt value at x=4.

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A: Given: y=4x2+4

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A: I have appended the formula used in the solution part

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Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

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A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

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A: Given  By chain rule of differentiation , we have

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A:

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: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

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A: Given parametric functions are: dxdt=3t+2dydt=t2-4

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Q: At any point (x,y), If dy/dt=D0 and dx/dt is non zero then curve has no tangent none of these…

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Q: dy dt 1 Find if 4y°t + t°y = 2 and dx dx cos t dy dx

A: To find dydx here we need to use both chain rule and product rule of differentiation.

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Q: y = tan (5t - 21 +1)

A:

Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

A:

Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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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: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

A:

Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

A:

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: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

A:

Q: Given xy+x 2y =2 such that dx/dt = 2in/sec. Find dy/dt for x=1.

A:

Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

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Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

A:

Q: A particle is moving along the curve y=x- 2 where x and y are functions of t. Find dx/dt if dy/dt =…

A: From the given problem:   y2=x3-2 ....(1)dydt=4.   Now differentiate the function with respect to x.…

Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

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Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

A:

Q: Can i get help step by step please

A: To find dx/dt when y = 2 and dy/dt = 5

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: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…