please its due in few minutes Suppose r(t) = (cos(t), sin(t)). For each of the following,...
2 (7 points each) Consider the circle parametrized by r(t) 3,6 cos t, 6 sin t). (a) Compute its are length over the interval 0 < wfind an are leugth pi of the circle. 2 (7 points each) Consider the circle parametrized by r(t) 3,6 cos t, 6 sin t). (a) Compute its are length over the interval 0
Please help solve the following question with steps. Thank you! 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done. 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
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 at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning 2. A dragon is flying around in a pattern given by the parametric curve r(t)...
Question 7 Suppose vx-2t2 and vy-12 t + sin(t) + cos(t) + et. If the initial position at t-0 is x-0, y-o, what is the final x position after 2 seconds? Select the correct answer CHECK ANSWER 0 of 1 attempts used LAST ATTEMPT O Between 0 and2 O Between 8 and 10 O Between 4 and 6 O Between 6 and O Between 2 and 4
QUESTION 4 Suppose a fourth field and path: F= <cos(z), sin(z), xy > and r= <sin(t), cos(t), t-> when Osts 21 What does this field look like? What does the path look like? Find ff. dr (use a calculator), what does it represent? Explain.
Please show work. Choose the correct general solution of the with r(t) = { a, cos (nt), [w] + 1, 2, ..,N. y= mnozcos (nt) y = c cos (@f) + C2 sin (m) y = c cos (@t) + C2 sin (61) + imz " cos (nt) T y = c cos (t) + c2 sin (ot) + Ime cos (nt) y = cj cos (ot) + C2 sin (01) + " ,cos (nt)
3. If T2 = r3 cos(0) sin(d) and v2 = sin(0) cos(O)f + r sin(0)θ + r2 sin(d)φ compute the following (a) ▽T, (b) ▽.
1) For this problem use the following space curve: r(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
1) For this problem use the following space curve: r(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
1of 1 attempts used Question 7 Suppose v-2t2 and vy-12t+sin(t)+ cos(t)+ et. If the initial position at t-0 is x-0, y-0, what is the final x position after 2 seconds? Select the correct answer O Between 8 and 10 O Between D and 2 O Between 6 and 8 O Between 2 and 4 O Between 4 and 6 SONY 血ね F9 F10 5 6