Particle MotionA particle moves in the xy-plane along the curve represented by the
(a) Use a graphing utility to graph r. Describe the curve.
(b) Find the minimum and maximum values of
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- Header & Footer Text Consider the vector-valued function = ( 4 cos(t) + 2 sin(t), -cos(t) + V5 4 sin(t), V105 f(t)%3D 20 V105 VI05 sin(e) (a) Compute the first derivative and the nmagnitude of the first derivative. (Hint: Make sure to simplify your answer for the magnitude as much as possible! There will be magic cancellations.) (b) Are ^r(t) and ^r0°(t) perpendicular for all t? (Hint: You do not need to compute the second derivative. Use the formula (1*OF)' = (*"(t) · (1) = 26"(1) · i'(1) and your answer from part a.) (c) Use your answer from part b. to compute the principal normal vector in termns of the second derivative r00(E). (Hint: Your answer should involve the symbol r 0t). Do not compute the second derivative).arrow_forwardDetermine the domain of the vector function r(t) = cos(4t) i + 7In(t - 5) j - 10 k Evaluate if the vector function is possible at the value of t=8, round to two tenths Find the derivative of the vector function r(t)arrow_forwardshow solution in a paperarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage