Tractrix A person moves from the origin along the positive y-axis pulling a weight at the end of a 12-meter rope (see figure). Initially, the weight is located at the point (12, 0).
(a) Show that the slope of the tangent line of the path of the weight is
(b) Use the result of part (a) to find the equation of the path of the weight. Use a graphing utility to graph the path and compare it with the figure.
(c) Find any vertical asymptotes of the graph in part (b).
(d) When the person has reached the point (0, 12), how far has the weight moved?
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Chapter 8 Solutions
EBK CALCULUS
- Graph y=log2(x+3) 10+ 9 8 7- 6 5 4 3 3 2 1 10 -9 -8 -7 -6 -5 -4 -3-2-1 1 2 3 4 5 6 7 8 7 8 9 10 -1 -2 -3 -4 -5 -6 -7- -8 -9 -10 Clear All Drawarrow_forwardWrite an equation for the graph below. +10+ 9 10 -9 -8 -7 -6 -5 -4 -3-2-1 8 7 6 5 4 3 2 1 1 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 f(x) = 9 -9 -10-arrow_forward3. Solve the inequality and give your answer in interval notation. Be sure to show all your work, and write neatly so your work is easy to follow. (4 points) 2|3x+12 ≥ 18arrow_forward
- - 2. In words, interpret the inequality |x8|> 7 the same way I did in the videos. Note: the words "absolute value" should not appear in your answer! (2 points)arrow_forwardFind the tangential and normal components of the acceleration vector for the curve (t) = (2t, -3t5,-3+4) at the point t = 1 ā(1) = T + N Give your answers to two decimal placesarrow_forwardA gun is fired with muzzle velocity 1152 feet per second at a target 4150 feet away. Find the minimum angle of elevation necessary to hit the target. Assume the initial height of the bullet is 0 feet, neglect air resistance, and give your answer in degrees.arrow_forward
- "Use the Opposite Method to solve the following differential equation:" 4'"""" + 34" + 34 + 4 = xarrow_forwardFor the curve defined by (t) = (e cos(t), et sin(t)) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at πT t = 3 П I(3) 丌_3_3 N (1) ат aN || = = =arrow_forwardFind the velocity vector for the position vector (t) = (sin(9+), 9t10, e¯7). x component = y component = Z component =arrow_forward
- In the xy-plane, an angle 0, in standard position, has a measure of the following is true? T. Which of 3 A The slope of the terminal ray of the angle is 1. B The slope of the terminal ray of the angle is 1. C D 3 The slope of the terminal ray of the angle is ✓ 2 The slope of the terminal ray of the angle is √3.arrow_forwardy'''-3y''+4y=e^2x Find particular solutionarrow_forward1 -1- Ο Graph of f y = + y = 1 + 1/2 ·2· x Graph of g y = 1- 플 The figure gives the graphs of the functions f and g in the xy-plane. The function of is given by f(x) = tan¹ x. Which of the following defines g(x)? A tan 1 x + 1 B - tan 1 x + П 2 C tan-1 (2/2) + 1 D tan-1 (2/2) + 1/1arrow_forward
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