37–38 Compare the curves represented by the parametric equations. How do they differ?
(a)
(b)
(c)
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Chapter 10 Solutions
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- consider the curve represented by the parametric equations: x=2t-10*sin((pi/6)*t), y=t. (a) Sketch the curve by making a table of values for -5 t 5 (b) Find an equation of the tangent line to the curve at the point corresponding to t=-3 (c) Find all values of the parameter (t) for which the curve has a horizontal tangent line. You may approximate your t values to two decimal places. Only consider -5 5 for this question. (d) Find all values of the parameter (t) for which the curve has a vertical tangent line. You may approximate your t values to two decimal places. Only consider -5 t 5 for this question. VI VI VIarrow_forward(b) The following shows the graph of the parametric equations: x = 3t² + t² + 1, y = t³ - 2t 1 y ₁-2 + Figure 1 Determine the derivative not defined. x = 3² + ² + 1₁ y = {-21 dy and the real values of t where this derivative is dz (c) Let y = x. Determine 10 dy dz Page 420arrow_forwardd) Find the slope of the parametric equations x=2+3sin 0 and y=0-cose at 0=arrow_forward
- PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric equations given. 4) x=√1-t₁y = t³ - 3t 5) x 1 1/t, y = 6-7/t + 2/t² -arrow_forwardConsider the following information. Parametric Equations x = 6t, y = 1 - 4t² (a) Use a graphing utility to graph the curve represented by the parametric equations. y dx dt dy dt dy dx -10 y = -10 10 -5 5 10 Ñ -5 -10 y 10 5 5 X لدينا 10 (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the parameter t = - 2 -10 -10 (c) Find an equation of the tangent line to the curve at the parameter t = - HIN -5 1 y -5 10 -5 -10 y 10 5 -5 -10 5 5 10 10arrow_forwardDetermine any differences between the curves of the parametric equations (a) x = t + 1, y = t3 (b) x = −t + 1, y = (−t)3 . Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain.arrow_forward
- The parametric equations of four plane curves are given (a) x = t and y = t2 - 4. (b) x = t2 and y = t4 - 4, (c) x = cos t and y = cos2 t - 4, (d) x = et and y = e2t - 4. Graph each plane curve and determine how they differ from each other.arrow_forwardFind parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 1 + 127, y = t3 - t, z = t3 + t; (13, 0, 2) Your answerarrow_forwardconsider the curve represented by the parametric equations: x=2t-10*sin((pi/6)*t), y=t. (a) Sketch the curve by making a table of values for -5t5 (b) Find an equation of the tangent line to the curve at the point corresponding to t=-3 (c) Find all values of the parameter (t) for which the curve has a horizontal tangent line. You may approximate your t values to two decimal places. Only consider -5 is less than or equal ,t is less than or equal 5 for this question. (d) Find all values of the parameter (t) for which the curve has a vertical tangent line. You may approximate your t values to two decimal places. Only consider -5arrow_forward
- consider the curve represented by the parametric equations: x=2t-10*sin((pi/6)*t), y=t. (a) Sketch the curve by making a table of values for -5t5 (b) Find an equation of the tangent line to the curve at the point corresponding to t=-3 (c) Find all values of the parameter (t) for which the curve has a horizontal tangent line. You may approximate your t values to two decimal places. Only consider -5t5 for this question. (d) Find all values of the parameter (t) for which the curve has a vertical tangent line. You may approximate your t values to two decimal places. Only consider -5t5 for this question. Please help me with this! Thanksarrow_forwardA wheel with radius 2 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 790 cm long, and 250 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale). P 790 cm 250 cm Write parametric equations for the position of the point P as a function of t, time in seconds after the ball starts rolling up the ramp. Both x and y are measured in centimeters. I = y = You will have a radical expression for part of the horizontal component. It's best to use the exact radical expression even though the answer that WAMAP shows will have a decimal approximation.arrow_forwardFind parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 2et, y = te4t, z = tet6, (2, 0, 0)arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning