2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
- A vector tangent to the parametric curve given by r (t) = <cos (4t); sin (4t); e^(t^2)> at the point (0; 1; e^((pi/8)^2)) is a) (0; 1; e^((pi/8)^2)) b) (0; 4; e^((pi/8)^2)) c) (4; 0; e^((pi/8)^2)) d) (4; 4; e^((pi/8)^2)) e) None of the above - The curve c (t) = (cost, sint ,t) lies on which of the following surfaces: (a) cone (b) cylinder (c) sphere (d) plane (e) none of the above
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
Find the curvature of the curve r(t) = (3 cos(4t), 3 sin(4t), t) at the point t = 0 Give your answer to two decimal places Preview
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) (4t, 2 sin(t), cos(2t)) 5(0) (0, 5,5) r(t) Preview Preview Preview The position of an object at time t is given by the parametric equations Find the horizontal velocity, the vertical velocity, and the speed at the moment wheret - 4. Do not worry about units in this problem. Horizontal Velocity - Preview Vertical Velocity- Preview Preview peed- Find the position vector for...
2t from Find the length of the parametric curve given by r(t) = 2 – logt and y(t) t=l to t= e.