Explanation 1) Concept: Use the definition of partial derivative of f with respect to x at a , b and differentiate W partially with respect to T partially to find the apparent temperature W to drop, if the actual temperature decreases by 1 ° C , ∂ W ∂ T also differentiate W partially with respect to v partially to find the apparent temperature W to drop, if the wind speed increases by 1 k m / h , ∂ W ∂ v , substitute T = - 15 ℃ and v = 30 k m / h in ∂ W ∂ T and ∂ W ∂ v 2) Definition: Partial derivative of f with respect to x : f x a , b = g ' a where g x = f x , b 3) Given: The wind-chill index is modeled by the function W = 13.12 + 0.6215 T - 11.37 v 0.16 + 0.3965 T v 0.16 , where T is the temperature ℃ and v is the wind speed ( k m / h ) 4) Calculation: The wind-chill index is modeled by the function W = 13.12 + 0.6215 T - 11.37 v 0.16 + 0.3965 T v 0.16 , where T is the temperature ℃ and v is the wind speed ( k m / h ) By definition of partial derivative of f with respect to x Differentiate W partially with respect to T , ∂ W ∂ T = ∂ ∂ T 13.12 + 0.6215 T - 11.37 v 0.16 + 0.3965 T v 0.16 = ∂ ∂ T 13.12 + ∂ ∂ T 0.6215 T - ∂ ∂ T 11.37 v 0.16 + ∂ ∂ T 0.3965 T v 0.16 = 0 + 0.6215 - 0 + 0.3965 v 0.16 = 0.6215 + 0.3965 v 0.16 Therefore, ∂ W ∂ T = 0.6215 + 0.3965 v 0.16 … 1 Substitute T = - 15 ° C and v = 30 k m / h in 1 , ∂ W ∂ T = 0.6215 + 0.3965 30 0

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 14.3, Problem 90E

To determine

To find:

(a) The apparent temperature W to drop if the actual temperature decreases by 1°C

(b) The apparent temperature W to drop if the wind speed increases by 1 km/h, when T=-15℃ and v=30 km/h

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Chapter 14.3, Problem 89E

Chapter 14.3, Problem 91E

Chapter 14 Solutions

Calculus (MindTap Course List)

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One is for a function...Ch. 14.1 - Prob. 37E Ch. 14.1 - Prob. 38E Ch. 14.1 - The body mass index BMI of a person is defined by...Ch. 14.1 - Prob. 40E Ch. 14.1 - A contour map of a function is shown. Use it to...Ch. 14.1 - A contour map of a function is shown. Use it to...Ch. 14.1 - A contour map of a function is shown. Use it to...Ch. 14.1 - A contour map of a function is shown. 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T=v1+uvw Ch. 14.4 - Prob. 29E Ch. 14.4 - Find the differential of the function. L=xzey2z2 Ch. 14.4 - Prob. 31E Ch. 14.4 - Prob. 32E Ch. 14.4 - The length and width of a rectangle are measured...Ch. 14.4 - Use differentials to estimate the amount of metal...Ch. 14.4 - Use differentials to estimate the amount of tin in...Ch. 14.4 - Prob. 36E Ch. 14.4 - Prob. 37E Ch. 14.4 - The pressure, volume, and temperature of a mole of...Ch. 14.4 - If R is the total resistance of three resistors,...Ch. 14.4 - A model for the surface area of a human body is...Ch. 14.4 - In Exercise 14.1.39 and Example 14.3.3, the body...Ch. 14.4 - Prob. 42E Ch. 14.4 - Show that the function is differentiable by...Ch. 14.4 - Show that the function is differentiable by...Ch. 14.4 - Prob. 45E Ch. 14.4 - Prob. 46E Ch. 14.5 - Use the Chain Rule to find dz/dt or dw/dt....Ch. 14.5 - Use the Chain Rule to find dz/dt or dw/dt....Ch. 14.5 - Use the Chain Rule to find dz/dt or dw/dt....Ch. 14.5 - Use the Chain Rule to find dz/dt or dw/dt....Ch. 14.5 - Use the Chain Rule to find dz/dt or dw/dt....Ch. 14.5 - 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Find the local maximum and minimum values and...Ch. 14.7 - Prob. 6E Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Prob. 8E Ch. 14.7 - Prob. 9E Ch. 14.7 - Prob. 10E Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Prob. 14E Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Prob. 16E Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Find the local maximum and minimum values and...Ch. 14.7 - Prob. 19E Ch. 14.7 - Prob. 20E Ch. 14.7 - Prob. 21E Ch. 14.7 - Show that f(x,y)=x2yex2y2 has minimum values at...Ch. 14.7 - Prob. 23E Ch. 14.7 - Prob. 24E Ch. 14.7 - Use a graph or level curves or both to estimate...Ch. 14.7 - Prob. 26E Ch. 14.7 - Prob. 27E Ch. 14.7 - Use a graphing device as in Example 4 or Newtons...Ch. 14.7 - Prob. 29E Ch. 14.7 - Prob. 30E Ch. 14.7 - Find the absolute maximum and minimum values of f...Ch. 14.7 - Find the absolute maximum and minimum values of f...Ch. 14.7 - Find the absolute maximum and minimum values of f...Ch. 14.7 - Prob. 34E Ch. 14.7 - Prob. 35E Ch. 14.7 - Find the absolute maximum and minimum values of f...Ch. 14.7 - Find the absolute maximum and minimum values of f...Ch. 14.7 - Prob. 38E Ch. 14.7 - Prob. 39E Ch. 14.7 - Prob. 40E Ch. 14.7 - Find the shortest distance from the point (2,0,3)...Ch. 14.7 - Prob. 42E Ch. 14.7 - Prob. 43E Ch. 14.7 - Prob. 44E Ch. 14.7 - Find three positive numbers whose sum is 100 and...Ch. 14.7 - Find three positive numbers whose sum is 12 and...Ch. 14.7 - Find the maximum volume of a rectangular box that...Ch. 14.7 - Find the dimensions of the box with volume 1000...Ch. 14.7 - Prob. 49E Ch. 14.7 - Find the dimensions of the rectangular box with...Ch. 14.7 - Find the dimensions of a rectangular box of...Ch. 14.7 - The base of an aquarium with given volume V is...Ch. 14.7 - A cardboard box without a lid is to have a volume...Ch. 14.7 - A rectangular building is being designed to...Ch. 14.7 - If the length of the diagonal of a rectangular box...Ch. 14.7 - Prob. 56E Ch. 14.7 - The Shannon index sometimes called the...Ch. 14.7 - Prob. 58E Ch. 14.7 - Suppose that a scientist has reason to believe...Ch. 14.7 - Find an equation of the plane that passes through...Ch. 14.8 - Pictured are a contour map of f and a curve with...Ch. 14.8 - Prob. 2E Ch. 14.8 - Each of these extreme value problems has a...Ch. 14.8 - Prob. 4E Ch. 14.8 - Prob. 5E Ch. 14.8 - Prob. 6E Ch. 14.8 - Prob. 7E Ch. 14.8 - Prob. 8E Ch. 14.8 - Each of these extreme value problems has a...Ch. 14.8 - Prob. 10E Ch. 14.8 - Each of these extreme value problems has a...Ch. 14.8 - Prob. 12E Ch. 14.8 - Prob. 13E Ch. 14.8 - Each of these extreme value problems has a...Ch. 14.8 - The method of Lagrange multipliers assumes that...Ch. 14.8 - Find the minimum value of f(x,y,z)=x2+2y2+3z2...Ch. 14.8 - Prob. 17E Ch. 14.8 - Prob. 18E Ch. 14.8 - Prob. 19E Ch. 14.8 - Prob. 20E Ch. 14.8 - Find the extreme values of f on the region...Ch. 14.8 - Find the extreme values of f on the region...Ch. 14.8 - Find the extreme values of f on the region...Ch. 14.8 - Prob. 24E Ch. 14.8 - Consider the problem of minimizing the function...Ch. 14.8 - Prob. 26E Ch. 14.8 - The total production P of a certain product...Ch. 14.8 - Prob. 28E Ch. 14.8 - Use Lagrange multipliers to prove that the...Ch. 14.8 - Use Lagrange multipliers to prove that the...Ch. 14.8 - Use Lagrange multipliers to give an alternate...Ch. 14.8 - Prob. 32E Ch. 14.8 - Prob. 33E Ch. 14.8 - Prob. 34E Ch. 14.8 - Use Lagrange multipliers to give an alternate...Ch. 14.8 - Prob. 36E Ch. 14.8 - Prob. 37E Ch. 14.8 - Prob. 38E Ch. 14.8 - Prob. 39E Ch. 14.8 - Prob. 40E Ch. 14.8 - Prob. 41E Ch. 14.8 - Prob. 42E Ch. 14.8 - Prob. 43E Ch. 14.8 - Find the maximum and minimum volumes of a...Ch. 14.8 - The plane x+y+2z=2 intersects the paraboloid...Ch. 14.8 - The plane 4x3y+8z=5 intersects the cone z2=x2+y2...Ch. 14.8 - Prob. 47E Ch. 14.8 - Find the maximum and minimum values of f subject...Ch. 14.8 - a Find the maximum value of...Ch. 14.8 - a Maximize i=1nxiyi subject to the constraints...Ch. 14.R - Prob. 1CC Ch. 14.R - Prob. 2CC Ch. 14.R - Prob. 3CC Ch. 14.R - Prob. 4CC Ch. 14.R - Prob. 5CC Ch. 14.R - What does Clairauts Theorem say?Ch. 14.R - Prob. 7CC Ch. 14.R - Prob. 8CC Ch. 14.R - Prob. 9CC Ch. 14.R - Prob. 10CC Ch. 14.R - Prob. 11CC Ch. 14.R - Prob. 12CC Ch. 14.R - Prob. 13CC Ch. 14.R - aDefine the gradient vector f for a function f of...Ch. 14.R - Prob. 15CC Ch. 14.R - Prob. 16CC Ch. 14.R - Prob. 17CC Ch. 14.R - Prob. 18CC Ch. 14.R - Prob. 19CC Ch. 14.R - Prob. 1TFQ Ch. 14.R - Prob. 2TFQ Ch. 14.R - Prob. 3TFQ Ch. 14.R - Prob. 4TFQ Ch. 14.R - Prob. 5TFQ Ch. 14.R - Prob. 6TFQ Ch. 14.R - Prob. 7TFQ Ch. 14.R - Prob. 8TFQ Ch. 14.R - Prob. 9TFQ Ch. 14.R - Prob. 10TFQ Ch. 14.R - Prob. 11TFQ Ch. 14.R - Prob. 12TFQ Ch. 14.R - Prob. 1E Ch. 14.R - Prob. 2E Ch. 14.R - Prob. 3E Ch. 14.R - Prob. 4E Ch. 14.R - Prob. 5E Ch. 14.R - Prob. 6E Ch. 14.R - Make a rough sketch of a contour map for the...Ch. 14.R - The contour map of a function f is shown. a...Ch. 14.R - Prob. 9E Ch. 14.R - Prob. 10E Ch. 14.R - Prob. 11E Ch. 14.R - Prob. 12E Ch. 14.R - Prob. 13E Ch. 14.R - Prob. 14E Ch. 14.R - Prob. 15E Ch. 14.R - Prob. 16E Ch. 14.R - Prob. 17E Ch. 14.R - Prob. 18E Ch. 14.R - Prob. 19E Ch. 14.R - Prob. 20E Ch. 14.R - Prob. 21E Ch. 14.R - Prob. 22E Ch. 14.R - Prob. 23E Ch. 14.R - Prob. 24E Ch. 14.R - Prob. 25E Ch. 14.R - Prob. 26E Ch. 14.R - Prob. 27E Ch. 14.R - Find equations of a the tangent plane and b the...Ch. 14.R - Find equations of a the tangent plane and b the...Ch. 14.R - Prob. 30E Ch. 14.R - Find the points on the hyperboloid x2+4y2z2=4...Ch. 14.R - Prob. 32E Ch. 14.R - Prob. 33E Ch. 14.R - The two legs of a right triangle are measured as 5...Ch. 14.R - Prob. 35E Ch. 14.R - Prob. 36E Ch. 14.R - Suppose z=f(x,y), where x=g(s,t), y=h(s,t),...Ch. 14.R - Prob. 38E Ch. 14.R - Prob. 39E Ch. 14.R - Prob. 40E Ch. 14.R - Prob. 41E Ch. 14.R - Prob. 42E Ch. 14.R - Prob. 43E Ch. 14.R - Prob. 44E Ch. 14.R - Prob. 45E Ch. 14.R - Prob. 46E Ch. 14.R - Prob. 47E Ch. 14.R - Prob. 48E Ch. 14.R - The contour map shows wind speed in knots during...Ch. 14.R - Prob. 50E Ch. 14.R - Prob. 51E Ch. 14.R - Prob. 52E Ch. 14.R - Prob. 53E Ch. 14.R - Prob. 54E Ch. 14.R - Prob. 55E Ch. 14.R - Prob. 56E Ch. 14.R - Use a graph or level curves or both to estimate...Ch. 14.R - Use a graphing calculator or computer or Newtons...Ch. 14.R - Prob. 59E Ch. 14.R - Prob. 60E Ch. 14.R - Prob. 61E Ch. 14.R - Prob. 62E Ch. 14.R - Prob. 63E Ch. 14.R - A package in the shape of a rectangular box can be...Ch. 14.R - A pentagon is formed by placing an isosceles...Ch. 14.P - A rectangle with length L and width W is cut into...Ch. 14.P - Marine biologists have determined that when a...Ch. 14.P - Prob. 3P Ch. 14.P - For what values of the number r is the function...Ch. 14.P - Prob. 5P Ch. 14.P - Prob. 6P Ch. 14.P - If the ellipse x2/a2+y2/b2=1 is to enclose the...Ch. 14.P - Show that the maximum value of the function...

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(a) The apparent temperature W to drop if the actual temperature decreases by 1 ° C (b) The apparent temperature W to drop if the wind speed increases by 1 k m / h , when T = - 15 ℃ and v = 30 k m / h

Solution Summary: The author explains that the wind-chill index is modeled by the function W=13.12+0.6215T-11.37v0.16+0.3965

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To find:

(a) The apparent temperature W to drop if the actual temperature decreases by 1°C

(b) The apparent temperature W to drop if the wind speed increases by 1 km/h, when T=-15℃ and v=30 km/h

Want to see the full answer?

Chapter 14 Solutions

(a) The apparent temperature W to drop if the actual temperature decreases by 1 ° C (b) The apparent temperature W to drop if the wind speed increases by 1 k m / h , when T = - 15 ℃ and v = 30 k m / h

Solution Summary: The author explains that the wind-chill index is modeled by the function W=13.12+0.6215T-11.37v0.16+0.3965

Videos

To find: (a) The apparent temperature W to drop if the actual temperature decreases by 1°C (b) The apparent temperature W to drop if the wind speed increases by 1 km/h, when T=-15℃ and v=30 km/h

Want to see the full answer?

Chapter 14 Solutions

To find:

(a) The apparent temperature W to drop if the actual temperature decreases by 1°C

(b) The apparent temperature W to drop if the wind speed increases by 1 km/h, when T=-15℃ and v=30 km/h