Consider the following parametric equations.
x=2t-3, y = 8t3 ;- 2 ≤ t ≤ 2
Consider the following parametric equations. x=2t-3, y = 8t3 ;- 2 ≤ t ≤ 2
Consider the parametric curve given by x(t) = t^2 − 2, y(t) = 2t^3 + 3, What is the length of the arc from the point (−1, 1) to the point (2, −13)
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,...
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...
Consider the following parametric equations. x = √1 + 2 , y = 2√t; 0 ≤ t ≤ 16 a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation.
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent vector for the curve with the parametric equations above B) Find the length function s (t) for the curve C) write the position vector as a function of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
Question 8 (10 points) Consider the following parametric curve: æ(t) = ť- 2t+2, y(t) = ť- 2+ + 2t - 3 In the FIRST answer box, write the SLOPE of the tangent line at t-2 and in the SECOND answer box, write the EQUATION of the tangent line at t-2. You do NOT need to show work. -
Question 8 (10 points) Consider the following parametric curve: æ(t) = ť- 2t+2, y(t) = ť- 2+ + 2t - 3 In the FIRST answer box, write the SLOPE of the tangent line at t-2 and in the SECOND answer box, write the EQUATION of the tangent line at t-2. You do NOT need to show work. -
QUESTION 6 Define a set of parametric equations as X=2-2t and y=12-4 on the interval -2 ts2, where t represents time. a. The graph with respect to time is b. The direction of the graph with respect to time is c. The y-intercept is (0, d. The smaller x-intercept is e. The larger x-intercept is ( ,0).
Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation. x = (t + 3)2. y=t+5; -10 ≤ t ≤ 10