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Best_Mathematician

calculus help...plz explain and answer question...i totally dont know what they are...studying on my own

  • 11 months ago
  • 11 months ago

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  1. phi
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    r is a position vector... the position of a point that changes with time. it has components in the x direction (the "ith" component) and y direction the velocity of the point is dr/dt (derivative with respect to time) you take the derivative of each component separately.... you get a new vector that represents the velocity in the x and y dimensions...

    • 11 months ago
  2. phi
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    it is not obvious, but they mean v is the velocity vector and a is the acceleration vector (2nd derivative of r, and the 1st derivative of v)

    • 11 months ago
  3. Best_Mathematician
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    (t-sint)i = (1-cost)i = (sint)i (1-cost)j = (sint)j = (cost)j f(x) f'(x) f''(x)

    • 11 months ago
  4. Best_Mathematician
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    now??

    • 11 months ago
  5. phi
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    r= (t-sin t) i + (1-cos t) j v= dr/dt = (1-cos t) i + sin t j or v= < (1-cos t, sin t> the magnitude of v is found by doing the dot product |v|^2 = v dot v and |v| = sqrt( v dot v)

    • 11 months ago
  6. Best_Mathematician
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    what is dot product

    • 11 months ago
  7. phi
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    Khan has videos on vectors. See http://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/vector-dot-product-and-vector-length Here is one from the physics playlist http://www.khanacademy.org/science/physics/electricity-and-magnetism/v/the-dot-product which might be better. But the dot product is the sum of the product of corresponding elements. In this case < (1-cos t, sin t> dot < (1-cos t, sin t> = (1-cos t)^2 + (sin t)^2 which simplifies to |v| = 2(1- cos t)

    • 11 months ago
  8. Best_Mathematician
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    ohk got it...so how to get minimum nd maximum values

    • 11 months ago
  9. phi
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    we know cos t has a max of +1 and a min of -1, so |v| ranges between 2(1-1) and 2(1 - (-2)) or 0 and 4

    • 11 months ago
  10. Best_Mathematician
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    agree

    • 11 months ago
  11. phi
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    ** 2(1 - (-1)) or 0 and 4

    • 11 months ago
  12. Best_Mathematician
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    plz carry on

    • 11 months ago
  13. phi
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    a= < sin t , cos t> can you find its dot product (that gives you |a|^2 )

    • 11 months ago
  14. Best_Mathematician
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    yes it is 1

    • 11 months ago
  15. Best_Mathematician
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    sin^2t+cos^2t = 1

    • 11 months ago
  16. Best_Mathematician
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    1^2 = 1

    • 11 months ago
  17. Best_Mathematician
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    am i on track?

    • 11 months ago
  18. phi
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    yes

    • 11 months ago
  19. Best_Mathematician
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    ok so min and max for velocity is 0 and 4 repectively and min and max for acceleration is 1 and 1...correct?

    • 11 months ago
  20. phi
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    the magnitude of the acceleration is always 1, but its direction is changing.

    • 11 months ago
  21. Best_Mathematician
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    oh ya but we do not need to care about direction...right?

    • 11 months ago
  22. phi
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    you might care if you were trying to analyze what is going on... but you don't need the direction if all you care about is the magnitude.

    • 11 months ago
  23. Best_Mathematician
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    ok so how to do rest of the part

    • 11 months ago
  24. phi
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    I am not sure what they want for a plot... for the smaller hoop, make the frequency twice as fast. that means in sin t and cos t replace t with 2t this will make the hoop spin twice as fast.

    • 11 months ago
  25. Best_Mathematician
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    ok so what is the vector function that models the behavior

    • 11 months ago
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