05:53Parametric Equations Introduction, Eliminating The Paremeter t, Graphing Plane Curves, PrecalculusThe Organic Chemistry Tutor454views
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 95views
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 113views
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 = 1234views
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 = 1160views
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 = 2230views
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 = 2146views
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/2167views
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 = π168views
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 = 2163views
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 ≤ 3189views
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 < ∞211views
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 < ∞166views
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 = 2t179views
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 − 1169views
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 < 2π226views
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 ≥ 0173views
Textbook QuestionIn Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = 4x − 3181views
Textbook QuestionIn Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = x² + 4179views
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 − 4213views
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 = 2t173views
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 < ∞175views
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 < 2π199views
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 (― ∞ , ∞)18views
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 t14views
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 t18views
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 t18views
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 ― 120views
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