2y Suppose f(x, y) = sin X in the direction of (1, 2). Then, 2y 2y i (a) ▼ f(x, y) = cos(2)21 +21) X (b) ▼ ƒ(6, π) = COS and u is the unit vector 1/2 ( - 1 3 ² + 1) i 18 3 (c) fu (6, π) = Du ƒ(6, π) = in 36 + 6
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- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) xFind the velocity vector v(t), given the acceleration vector a(t) = (3e¹, 7, 10t +9) and the initial velocity v(0) = (8,-5,3). (Use symbolic notation and fractions where needed. Give your answer in the vector form.) v(t) = 2(e' - 2)i + (3t-2)j + (3r² +9r+2)k IncorrectThe motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(t) =
- Create the vector & parametric equations for the line that passes through the point L₁ x 3- 2t (0, 1, -2) and is parallel to the line y z = = - 5t - 1-t.The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function F(t) = 4(26t – sin(26t))i + 4(1 – cos(26t))3 Find the velocity vector of the point. ü(t) = | 4(26 – 26 cos(26t))i + 4(26 sin( 26t ))j Find the acceleration vector of the point. ä(t) = | 2704 sin(26t )i + 2704 cos( 26t)j v| Find the speed of the point. s(t) = 2704 sin(26t)i+ 2704 cos( 26t)j x syntax error. Check your variables - you might be using an incorrect one.Find the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy) at the point (1,5). Give your answer as a unit vector. (sin(5) + 5 cos(5))i + cos(15) i 1+ (5 cos (5))² + 10 sin(5) - cos (5) x Invalid notation. syntax incomplete.
- The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the vector function F(t) = 5(24t - sin(24t))i +5(1 - cos(24t))j Find the velocity vector of the point. v(t) Find the acceleration vector of the point. ä(t) 2880 sin (24t)i + 2880 cos (24t)j✔ CABAME 120(1- cos (24t) )i + 120 sin (24t)j✔ Find the speed of the point. s(t) 240 sin (12t) wwwww Submit Question X Q Search EO HDefine two vector functions (t) 9 sin(t)+7 cos(t)] + (t³ - 15) k = = (t) 7 sin(t)+9 cos(t)] + tk = . Compute (t) (t) =6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of the unit vector u = cos i+sinj. (b) What is the maximum value of the directional derivative of w = ²y at (1,-3) and it what direction is it attained? Q Search A
- Consider the vector 212 +1 (2t, 2, 1) The derivative of y with respect to t is (2-4t,-2t,-2t) T (1- 2t, 2t, 21) O None of these options are true O (2, 4t, 0) O (1 2t, 2t,- 2t) O (2-4t, 2t.-2t)a) Find F‘(0) for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find 3a +2b Note: an arrow representing direction should be on the alphabetsCalculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect