05:53Parametric Equations Introduction, Eliminating The Paremeter t, Graphing Plane Curves, PrecalculusThe Organic Chemistry Tutor436views
Multiple ChoiceGraph the plane curve formed by the parametric equations and indicate its orientation. x(t)=−t+1x\left(t\right)=-t+1; y(t)=t2y\left(t\right)=t^2−2≤t≤2-2\le t\le2 80views
Multiple ChoiceGraph the plane curve formed by the parametric equations and indicate its orientation.x(t)=2t−1x(t)=2t-1; y(t)=2ty(t)=2\sqrt{t}t≥0t≥0 96views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 3 − 5t, y = 4 + 2t; t = 1216views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 7 − 4t, y = 5 + 6t; t = 1148views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = t² + 1, y = 5 − t³; t = 2220views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = t² + 3, y = 6 − t³; t = 2137views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 4 + 2 cos t, y = 3 + 5 sin t; t = π/2155views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 2 + 3 cos t, y = 4 + 2 sin t; t = π157views
Textbook QuestionIn Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = (60 cos 30°)t, y = 5 + (60 sin 30°)t − 16t²; t = 2151views
Textbook QuestionIn Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = t − 2, y = 2t + 1; −2 ≤ t ≤ 3176views
Textbook QuestionIn Exercises 15–16, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. _ x = √t , y = t + 1; −∞ < t < ∞200views
Textbook QuestionIn Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 2t, y = |t − 1|; −∞ < t < ∞154views
Textbook QuestionIn Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = t, y = 2t167views
Textbook QuestionIn Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. _ x = √t, y = t − 1153views
Textbook QuestionIn Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = 1 + 3 cos t, y = 2 + 3 sin t; 0 ≤ t < 2π210views
Textbook QuestionIn Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = 2ᵗ, y = 2⁻ᵗ; t ≥ 0161views
Textbook QuestionIn Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = 4x − 3166views
Textbook QuestionIn Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = x² + 4166views
Textbook QuestionIn Exercises 57–58, the parametric equations of four plane curves are given. Graph each plane curve and determine how they differ from each other. x = t and y = t² − 4199views
Textbook QuestionIn Exercises 59–62, sketch the plane curve represented by the given parametric equations. Then use interval notation to give each relation's domain and range. x = t² + t + 1, y = 2t160views
Textbook QuestionIn Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. x = 2t − 1, y = 1 − t; −∞ < t < ∞161views
Textbook QuestionIn Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. x = 3 + 2 cos t, y = 1+2 sin t; 0 ≤ t < 2π185views
Textbook QuestionFor each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. See Examples 1 and 2.x = t + 2 , y = t ―4 , for t in (― ∞ , ∞)3views
Textbook QuestionGraph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.x = 2 cos t , y = 2 sin t5views
Textbook QuestionGraph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.x = 4 sin t , y = 3 cos t6views
Textbook QuestionGraph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.x = 2 + sin t , y = 1 + cos t6views
Textbook QuestionGraph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.x = 1 + cos t , y = sin t ― 15views
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