Please help with D. The function is in the first photo 5-4f3.2+412 35 6Figure 10.6.1 A contour plot of f(x, y) = 30-1²-². CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONSc. 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 r(t) denote the z-coordinate of the line, and y(t) its y-coordinate.Make sure your parametrization places the walker at the point (2, 1) whent=0.+ = 2² (+₁4) =(²11) Whent=02 = ²+² +²²³(ky) = (2₂1) + (3,4)(x,y) = (2, 1) + (3=14€)(x47) = (2+ 3+₁ 1+4)x=2+3ty=1+4681EQN=X(t) = 2+ 3ty (=/+4td. With the parametrization in (c), we can now view the temperature fas not only a function of z and y, but also of time, t. Hence, use thechain rule to determine the value of 0 What are the units on youranswer? What is the practical meaning of this result?

A graph of contour plot is given as f(x, y)=30-x2-12y2. The parametric equations obtained in part…

d. With the parametrization in (c), we can now view the temperature f as not only a function of z and y, but also of time, t. Hence, use the chain rule to determine the value of What are the units on your answer? What is the practical meaning of this result?

d. With the parametrization in (c), we can now view the temperature f as not only a function of z and y, but also of time, t. Hence, use the chain rule to determine the value of What are the units on your answer? What is the practical meaning of this result?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 20E

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Question

Please help with D. The function is in the first photo

5-
4f
3.
2+
4
1
2 3
5 6
Figure 10.6.1 A contour plot of f(x, y) = 30-1²-².

CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS
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 r(t) denote the z-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.
+ = 2² (+₁4) =(²11) Whent=0
2 = ²+² +²²³
(ky) = (2₂1) + (3,4)
(x,y) = (2, 1) + (3=14€)
(x47) = (2+ 3+₁ 1+4)
x=2+3t
y=1+46
81
EQN=
X(t) = 2+ 3ty (=/+4t
d. With the parametrization in (c), we can now view the temperature f
as not only a function of z and y, but also of time, t. Hence, use the
chain rule to determine the value of 0 What are the units on your
answer? What is the practical meaning of this result?

Expert Solution

Step 1

A graph of contour plot is given as $f (x, y) = 30 - x^{2} - \frac{1}{2} y^{2}$ .

The parametric equations obtained in part (c) as

$x (t) = 2 + 3 t y (t) = 1 + 4 t$

The aim is to find the derivative ${\frac{d f}{d t}}_{t = 0}$ using chain rule.

Let $x (t)$ and $y (t)$ are differentiable functions in $t$ , $f (x, y)$ is a differentiable function in $x and y$ . Then $f (x (t), y (t))$ is a differentiable function in $t$ and the chain rule of derivative states that $\frac{d f}{d t} = \frac{\partial f}{\partial x} \cdot \frac{d x}{d t} + \frac{\partial f}{\partial y} \cdot \frac{d y}{d t}$ .