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Concept explainers
Tractrix A person moves from the origin along the positive y-axis pulling a weight at the end of a 12-meter rope. Initially, the weight is located at the point (12.0).
(a) In Exercise 61 of Section 8,4, it was shown that the path of the weight is modeled by the rectangular equation
where
(b) Use a graphing utility to graph the parametric equations
where
(c) Use the parametric equations for the tractrix to verify that the distance from the v-intercept of the tangent line to the point of tangency is independent of the location of the point of tangency.
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Chapter 10 Solutions
Calculus of a Single Variable
- Number 4 plsarrow_forwardGood Day, Would appreciate any assistance with this query. Regards,arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage