Consider the given vector equation. r(t) = (2t – 5, t2 + 4) (a) Find r'(t)....
t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that they are fundamental solution set of a linear 2 x 2-system 1c) and t interval I-(-5,16)? If yes, find the related linear system (c) The same question from (b) but on the interval 1 = (1,00). t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that...
Find the unit tangent vector for the given vector function. r(t)=< 3+t2 ,t4, 6>
Q6. The set B = {1+t2, t+t, 1+2t+t2} is a basis for P2. Find the coordinate vector of p(t) = 3+t-6t2 relative to B.
(1 point) Given the acceleration vector a(t) = (-4 cos (2t))i + (-4 sin (2t))j + (-3t) k , an initial velocity of v (0) =i+ k, and an initial position of r (0)=i+j+ k, compute: A. The velocity vector v (t) = j+ . B. The position vector r(t) = j+ k
Question 9 Let r(t)={cos 2t, sin 2t, V5t) a) Find the unit tangent vector and the unit normal vector of r(t) at += TI (Round to 2 decimal places) TE)= NG) = < b) Find the binormal vector of r(t) at t = TT 2 (Round to 2 decimal places) BC) =< A Moving to another question will save this response.
Find the curvature and radius of curvature of the curve r(t) =<2t+5, ln(t2+16) > at the point (1, In(20)). Round only the final answers to four decimal places. Find the curvature and radius of curvature of the curve r(t) = at the point (1, In(20)). Round only the final answers to four decimal places.
Find the curvature of the space curve. r(t) = -21 + (7 + 2t)j + (t2 + 5)k Ok=- 1 2012 Ver I 1 K= 2(2 + 1)3/2 Ok= 1 (2 + 1) 3/2 Oku- 1 2012-132
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
For the curve r(t), find an equation for the indicated plane at the given value of t. 55) r(t) (3 sint+6i+ (3 cos 20t) - 1j+ 12tk; osculating plane at t 2.5m. 12 12 60 +1) + 13 B) y-1) + 169 =0 13 169 12 -6) +. 60 9131)+30) 0 =0 (206-2 56) rt) (t2-6)i+ (2t-3)j+9k; osculating plane at t A) x+y+ (z+9)-0 C) x+ y+(z-9) 0 6. B) z =9 D) z =-9 For the curve r(t), find...
Edit: Please provide the points of intersection so I can see the methodology. Thanks! (1 point) Consider the curve defined by r()-(--t2, 1 -2t (a) The maximum curvature is max κ = (b) Consider two particles: one with position r(t) and the other with position S(t) -r e-πιν). Then The two particles A. do not collide and their paths do not intersect. B. collide C. do not collide, but their paths intersect. (1 point) Consider the curve defined by r()-(--t2,...