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- The motion of a point on the circumference of a rolling wheel of radius 2 feet is described by the vector function r(t) = 2(23t sin (23t))i + 2(1 - cos(23t))j - 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) =(1n |t – 1], e', vî ) 1. Let 7(t) = (a) Express the vector valued function in parametric form. (b) Find the domain of the function. (c) Find the first derivative of the function. (d) Find T(2). (e) Find the vector equation of the tangent line to the curve when t=2. 2. Complete all parts: (a) Find the equation of the curve of intersection of the surfaces y = x? and z = x3 (b) What is the name of the resulting curve of intersection? (c) Find the equation for B the unit binormal vector to the curve when t= 1. Hint: Instead of using the usual formula for B note that the unit binormal vector is orthogonal to 7 '(t) and 7"(t). In fact, an alternate formula for this vector is ア'(t) × ア"(t) ア(t) ×デ"(t)| B(t) =Find the second derivative of the vector-valued function 7(t) = (6t + 4 sin(t))i + (5t + 7 cos(t))j 7(t) = %3D
- Suppose we do not know the path of a hang glider, but only its acceleration vector a(t) = -(3 cos t)i - (3 sin t)j + 2k. We also know that initially (at time t = 0) the glider departed from the point (4, 0, 0) with velocity v(0) = 3j. Find the glider’s position as a function of t.Find the domain of the vector function r(t)= <e-t , (t-5)1/2 , (7-t)1/2.3, Let u(t) = 2t°i+ (t- 1)j- 8k. Compute the derivative of the following function. (118 + 7t) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. The derivative is the vector-valued function ( Di+ ( Di+ ( k. O B. The derivative is the scalar function
- Let u(t) = 2t°i+ (ť - 1)j-8k. Compute the derivative of the following function. (1" +71) u(1) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function ()i+ (Dj+ ( k. Click to select and enter your answer(s) and then click Check Answer. Clear All All parts showingFind the domain of the vector function r(t) =(t-1)/(t+1)i + sin(t) j + ln(9 − t2) kThe motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j 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) = =