(1 point) (a) Find dy du as a function of t for the given parametric equations....
(1 point) (a) Find as a function of t for the given parametric equations. dx x t-ps у 4 - 31 dy dx = (b) Find dy as a function of t for the given parametric equations. dx X 5 - 4 -1 у dy dx =
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
Find the ordered pair that corresponds to the given pair of parametric equations and value of t. x=4t+3, y=-2t+4;t=2 The ordered pair is:
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 In(t), y = 6/t, z = t4; (0,6, 1) x(t), y(t), z(t) = X
4. Find the parametric equations for a line through a point (0,1,2) that (a). parallel to the plane x + y + z = 2, and (b). perpendicular to the line T = 1+t, y = 1 –t, z = 2t (Answer: x = 3t, y=1-t, 2 = 2 - 2t)
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
Question: A dynamical system's equations of motion are given below: du)dut) dy(t) 1 2 80-5 to0 + 6y(et+) d2x(t) dx(t) Note: initial conditions are zeros, U(s) is an impulse function and Fs) is a step function. Hint: factor nicely the denominators. For each of the dynamical system, please: (a) Compute the transfer function U(s) (b) Find the inverse Laplace transform expression for y() and x(0) (c) Compute the final value of the system. (d) Compute the initial value of the...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (5+?) 1+ (2t - 1)]+(31') k, t=to = 3 What is the standard parameterization for the tangent line? X = y = ZE (Type expressions using t as the variable.)
(a) Given the parametric equations x = 5t2 −10t, y = t5 find dy/dx. (b) Find the (x,y) coordinate point(s) where the curve has a vertical tangent.