[Wind-Chill Index] [C] [S] The wind-chill index is given by W(Tv) = 13.12 +0.6215T-11.370.16 +0.3965Tv0.16, where T is the temperature in Celsius and v is the wind speed in km/h. The temperature is currently 12°C and the wind speed is 15 km/hr. (a) Calculate the current wind-chill index. (b) Calculate the current value for Wand W and interpret their meaning. (c) Approximate what the wind-chill index will be if the temperature increases to 14°C but the wind speed decrease to 10 km/hr.
[Wind-Chill Index] [C] [S] The wind-chill index is given by W(Tv) = 13.12 +0.6215T-11.370.16 +0.3965Tv0.16, where T is the temperature in Celsius and v is the wind speed in km/h. The temperature is currently 12°C and the wind speed is 15 km/hr. (a) Calculate the current wind-chill index. (b) Calculate the current value for Wand W and interpret their meaning. (c) Approximate what the wind-chill index will be if the temperature increases to 14°C but the wind speed decrease to 10 km/hr.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Wind-Chill Index Calculation and Analysis**
The wind-chill index is given by the formula:
\[ W(T, v) = 13.12 + 0.6215T - 11.37v^{0.16} + 0.3965T v^{0.16}, \]
where \( T \) is the temperature in Celsius and \( v \) is the wind speed in km/h.
The current temperature is 12°C and the wind speed is 15 km/h.
Tasks:
(a) **Calculate the current wind-chill index.**
(b) **Calculate the current values of** \(\frac{\partial W}{\partial T}\) **and** \(\frac{\partial W}{\partial v}\) **and interpret their meaning.**
(c) **Approximate the wind-chill index if the temperature increases to 14°C and the wind speed decreases to 10 km/h.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbc1f6b1-9cf7-4fb9-9628-525fb0fcd15f%2Fc386b6c9-c2bf-4dfa-b103-deff4a13b7bf%2F2o04t8_processed.png&w=3840&q=75)
Transcribed Image Text:**Wind-Chill Index Calculation and Analysis**
The wind-chill index is given by the formula:
\[ W(T, v) = 13.12 + 0.6215T - 11.37v^{0.16} + 0.3965T v^{0.16}, \]
where \( T \) is the temperature in Celsius and \( v \) is the wind speed in km/h.
The current temperature is 12°C and the wind speed is 15 km/h.
Tasks:
(a) **Calculate the current wind-chill index.**
(b) **Calculate the current values of** \(\frac{\partial W}{\partial T}\) **and** \(\frac{\partial W}{\partial v}\) **and interpret their meaning.**
(c) **Approximate the wind-chill index if the temperature increases to 14°C and the wind speed decreases to 10 km/h.**
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