Given the vector function: *(t) = (1+ sin (3t), tan (2t), t) Relate the vector functions to the velocity function, the acceleration function, and the speed of (-9 cos (3t), 8 sec? (2t) tan (2t), 0) Choose. 9 cos2 (3t) + 4 sec (2t) + 1 Choose. (3 cos (3t), 2 sec? (2t), 1) Choose.

Q: 12 of 17 > Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point…

A: We have to find equation of tangent plane for the given Curve.

Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

A:

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A:

Q: first and second at point x=3 of the given function the value of its derivatives, a) Calculate…

A: Given a function: fx=2ex+cosx-5x2+7x (a) To find the first and second derivatives of the function…

Q: 6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of…

A:

Q: T = [ Cos(a)+Sin(a).Cos(b) ] A-) Find function's gradient vector B-) Find function's Laplace…

A: We have to solve given problem:

Q: The function y = 2x – cos x have two variables (x and y), these variables called

A: Here, the given equation is y=2x-cosx , which is a function of two variables(x and y). The name of…

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A: we are given the curve r(t)=3ti+e4tj+6e-tk we have to find the velocity vector , acceleration vector…

Q: A golfer hits a golf ball at an angle of 0 = 22° with initial velocity v = 120 ft/s. (a) Estimate As…

A: given angleθ=22∘initial velocityv=120 ft/s we will use the formula  s=v2sin2θghere g=32.17

Q: If a ball is thrown vertically upward with a velocity of 144 ft/s, then its height after t seconds…

A: Given s = 144 t - 16 t^2 a.Take the derivative with respect to t:ds/dt = 144 - 32 tAt the maximum…

Q: A hamster runs at a speed of 12 centimeters per second in a wheel of radius 15 centimeters. a) What…

A:

Q: bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 sec me t…

A: We know position vector of bee if it has a velocity vector  is We are given

Q: use the following fact derived from Newton's Laws: An object released at an angle 0 with initial…

A:

Q: The equation below defines y implicitly as a function of x: 2x2 + xy = 3y2 Use the equation to…

A:

Q: The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the…

A:

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A:

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an…

A: