anonymous
  • anonymous
calculus help...plz explain and answer question...i totally dont know what they are...studying on my own
Differential Equations
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
http://assets.openstudy.com/updates/attachments/517d65e4e4b0be6b54ab31bc-best_mathematician-1367172592503-3.png
phi
  • phi
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...
phi
  • phi
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)

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anonymous
  • anonymous
(t-sint)i = (1-cost)i = (sint)i (1-cost)j = (sint)j = (cost)j f(x) f'(x) f''(x)
anonymous
  • anonymous
now??
phi
  • phi
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)
anonymous
  • anonymous
what is dot product
phi
  • phi
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)
anonymous
  • anonymous
ohk got it...so how to get minimum nd maximum values
phi
  • phi
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
anonymous
  • anonymous
agree
phi
  • phi
** 2(1 - (-1)) or 0 and 4
anonymous
  • anonymous
plz carry on
phi
  • phi
a= < sin t , cos t> can you find its dot product (that gives you |a|^2 )
anonymous
  • anonymous
yes it is 1
anonymous
  • anonymous
sin^2t+cos^2t = 1
anonymous
  • anonymous
1^2 = 1
anonymous
  • anonymous
am i on track?
phi
  • phi
yes
anonymous
  • anonymous
ok so min and max for velocity is 0 and 4 repectively and min and max for acceleration is 1 and 1...correct?
phi
  • phi
the magnitude of the acceleration is always 1, but its direction is changing.
anonymous
  • anonymous
oh ya but we do not need to care about direction...right?
phi
  • phi
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.
anonymous
  • anonymous
ok so how to do rest of the part
phi
  • phi
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.
anonymous
  • anonymous
ok so what is the vector function that models the behavior

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