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How would I find the path of the particle that is described by 1 = _______________? A screenshot of the given equation is attached.

How Would I Find The Path Of The Particle That Is Described By 1 A Screenshot Of The Given Equation Is Attached class=

Sagot :

Sqdancefanidn

Answer:

  graph the equation (see attached)

Step-by-step explanation:

You want to find the path of a particle defined by the vector equation ...

  r = 4cos(3t)i +6sin(3t)j

Path

When t=0, the position is ...

  r = 4(1)i +6(0)j = 4i

When t=π/6, the position is ...

  r = 4(0)i +6(1)j = 6j

You can continue to evaluate r for different values of t, and you will find the points form an ellipse centered at the origin. Its major axis extends from y=-6 to y=6, and its minor axis extends from x=-4 to x=4. The graph is attached. Motion is counterclockwise from the +x axis.

It works nicely to let a graphing calculator plot the points.

View image Sqdancefan
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