A IS ATTACHED FOR REFERENCE. PLEASE HELP WITH C CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 81c. Now, rather than walking due east or due north, let's suppose that theperson is walking with velocity given by the vector v = (3, 4), where timeis measured in seconds. Note that the person's speed is thus |v| = 5 feetper second. Find parametric equations for the person's path; that is,parametrize the line through (2, 1) using the direction vector v = (3,4).Let x(t) denote the x-coordinate of the line, and y(t) its y-coordinate.Make sure your parametrization places the walker at the point (2, 1) whent = 0.d. With the parametrization in (c), we can now view the temperature fas not only a function of x and y, but also of time, t. Hence, use thechain rule to determine the value of to. What are the units on youranswer? What is the practical meaning of this result?dt t=0 10.6 Directional Derivatives and the GradientPreview Activity 10.6.1 Let's consider the function f defined by1f(x, y) 30 - x²and suppose that ƒ measures the temperature, in degrees Celsius, at a givenpoint in the plane, where x and y are measured in feet. Assume that thepositive x-axis points due east, while the positive y-axis points due north. Acontour plot of f is shown in Figure 10.6.1654321-yX12 3 4 5Figure 10.6.1 A contour plot of f(x, y) = 30 — x² – ¹⁄y².6a. Suppose that a person is walking due east, and thus parallel to the x-axis.At what instantaneous rate is the temperature changing with respect tox at the moment the walker passes the point (2, 1)? What are the unitson this rate of change?b. Next, determine the instantaneous rate of change of temperature withrespect to distance at the point (2, 1) if the person is instead walking duenorth. Again, include units on your result.

c. Now, rather than walking due east or due north, let's suppose that the person is walking with velocity given by the vector v = (3,4), where time is measured in seconds. Note that the person's speed is thus |v| = 5 feet per second. Find parametric equations for the person's path; that is, parametrize the line through (2, 1) using the direction vector v = (3,4). Let x(t) denote the x-coordinate of the line, and y(t) its y-coordinate. Make sure your parametrization places the walker at the point (2, 1) when t = 0.

c. Now, rather than walking due east or due north, let's suppose that the person is walking with velocity given by the vector v = (3,4), where time is measured in seconds. Note that the person's speed is thus |v| = 5 feet per second. Find parametric equations for the person's path; that is, parametrize the line through (2, 1) using the direction vector v = (3,4). Let x(t) denote the x-coordinate of the line, and y(t) its y-coordinate. Make sure your parametrization places the walker at the point (2, 1) when t = 0.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter10: Radical Functions And Equations

Section: Chapter Questions

Problem 15CT

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