A tool is programmed to move, such that x=2cos3t and y=cos2t. Find the velocity of the tool when t=4.1s.

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The velocity of the machine can be divided into two components, x and y.

It moves at x = 2 cos 3t in the x-direction.

Therefore the x component of the velocity is dx/dt = -2*3 sin 3t.

At t = 4.1, this is equal to 1.5793.

In the y-...

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The velocity of the machine can be divided into two components, x and y.

It moves at x = 2 cos 3t in the x-direction.

Therefore the x component of the velocity is dx/dt = -2*3 sin 3t.

At t = 4.1, this is equal to 1.5793.

In the y- direction it moves at y = cos 2t.

dy/dt = -2* sin 2t

At t = 4.1, this is equal to -1.8814

The direction of the velocity is at angle of -0.8724 radians to the x-axis.

Therefore the magnitude of the velocity at t = 4.1 is sqrt ( 1.5793^2 + 1.8814^2) = 2.4563.

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