a. Explanation Given information: The point to determine linearization is ( 50 , − 20 ) . The point to determine wind chill is ( 49 , − 22 ) . The wind chill formula is given below: W = W ( v , T ) = 35.74 + 0.6215 T − 35.75 v 0.16 + 0.4275 T ⋅ v 0.16 Here, v is wind speed in mph and T is air temperature in ° F . Calculation: Show the wind chill formula as follows: W = W ( v , T ) = 35.74 + 0.6215 T − 35.75 v 0.16 + 0.4275 T ⋅ v 0.16 (1) Find the value of W ( 50 , − 20 ) : Substitute 50 mph for v and − 20 ° F for T in Equation (1). W ( 50 , − 20 ) = 35.74 + 0.6215 ( − 20 ) − 35.75 ( 50 ) 0.16 + 0.4275 ( − 20 ) ⋅ ( 50 ) 0.16 = − 59.5298 ° F Differentiate Equation (1) with respect to v as follows: ∂ W ∂ v = 0 + 0 − 35.75 ( 0.16 ) v 0.16 − 1 + 0.4275 T ⋅ ( 0.16 ) v 0.16 − 1 = − 5.72 v 0.84 + 0.0684 T v 0.84 For the given point ( 50 , − 20 ) : Substitute 50 mph for v and − 20 ° F for T. ( ∂ W ∂ v ) ( 50 , − 20 ) = − 5.72 ( 50 ) 0.84 + 0.0684 ( − 20 ) ( 50 ) 0.84 = − 0.2651 Differentiate Equation (1) with respect to T as follows: ∂ W ∂ T = 0 + 0.6215 − 0 + 0.4275 v 0.16 = 0.6215 + 0.4275 v 0.16 Substitute 50 mph for v b. To determine Find the wind chill value W ( 53 , − 19 ) . bc. To determine Find the wind chill value W ( 60 , − 30 ) .

Pearson eText for Thomas' Calculus -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137442997

Author: Joel Hass, Christopher Heil

Publisher: PEARSON+

See similar textbooks

Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

Videos

Question

Chapter 14.6, Problem 34E

To determine

Find the wind chill value W(49,−22).

To determine

Find the wind chill value W(53,−19).

bc.

To determine

Find the wind chill value W(60,−30).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.6, Problem 33E

Chapter 14.6, Problem 35E

Students have asked these similar questions

i don't understand how to get these answers please help!

Enter your answer in interval notation. No decimal entries allowed. Type oo (lower case o) for ∞ and -oo for -∞ if needed. Domain: Question Help: Message instructor

Write a formula for the function g that results when the graph of the function f(x) = = 4 X is reflected about the y-axis, horizontally compressed by a factor of 2, shifted 7 units left, reflected about the x-axis and shifted 3 units up. g(x): = Question Help: Message instructor

Chapter 14 Solutions

Pearson eText for Thomas' Calculus -- Instant Access (Pearson+)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Find the wind chill value W ( 49 , − 22 ) .

Concept explainers

Videos

Find the wind chill value W(49,−22).

Find the wind chill value W(53,−19).

Find the wind chill value W(60,−30).

Want to see the full answer?

Chapter 14 Solutions