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Eliminate the parameter in the parametric equations x(t) = 6t + 4 and y(t) = -24t + 5 to identify a Cartesian form of the equations. Provide your answer below:
Question 3 (1 point) Consider the lines: L1: x=-6t, y=1+9t, z=-3t L2: x=1+2s, y=4-3s, z=s Choose their intersection point from below (0,0,1) none (1,2,1) (0,1,0)
3) Givenr"(t) = (6t + 4)+(-sint)i + (-4cos(2t))k, and r'O) = 0 and r(0) = 41 -1+k a) find r(t). 4) Givenf (x,y) = 6xły – yex-1 a) Find Vf(x,y). Show all support work! b) Find the direction of maximum increase of f(x,y) at the point (1,-1).
x = t^2 - 2t + 4, y = t^3 - 6t^2
8. a) Set up the integral you would need to evaluate to find the length of the curve given in #3 if Osts 10. b) Set up the integral you would need to evaluate to find the arclength of the curve r = 4sin(30), traced out once. 3
Express x = 5t-1, y = 2t-2 in the form y = f(x). (Express numbers in exact form. Use symbolic notation and fractions where needed.) y(x) =
(0) 3 -1 (a) ynt X(t) Y(E) ( Express y(t) as a function x(+). (b) verify your result by creeking at least 3 point In time to X (A 2 1 1
1) Given parametric equations x(t) = 2 + t and y(t) = 2-1, determine the rectangular form by eliminating the parameter. I Determine the equation of the given graph of the ellipse: (-2,8) (-2,5+15) (-4,5) (0,5) (-2,5) (-2,5-15) (-2, 2) +X
Given y(t) = 3 + cos(6t) - ecos(6t) and Y(s) defined as a Y(s) = hs + s²+k + s+p s2 + qs+t s+b match variables to correct values that make Laplace transform correct. Laplace transform table handout may be used as reference, a [Choose] b [Choose h [Choose) k [Choose] р [Choose 9 [Choose [Choose)
(1 point) Consider the function f(t) = 10 sec?(t) – 6t". Let F(t) be the antiderivative of f(t) with F(0) = 0. Find F(t).
1. A LTI system has the frequency response function 0, all other o Compute the output y(t) resulting from the in put x(t) given by (a) x(t) -2-5cos(3t)+10sin(6t-jx/3)+4cos(12t-x/4) (b) x(t) = 1 + Σ- cos(2kt ) k-l (c) x(t) is the periodic pulse train signal shown below (repeats beyond the graph) 0.5 0.5 5 t (second) Hint: Refer to lecture 10 note. For (c), find the Fourier series coefficients of x(t) first.
1. A LTI system has the frequency response...