Explanation Given information: Radius of the earth = 3960 miles Formula used: For a function f ( x ) , the linear approximation is, Δ f ≈ f ′ ( a ) Δ x for Δ x is small . Calculation: The function from the given Newton’s Law of Gravitation is, W ( x ) = w R 2 x 2 , for x ≥ R Differentiate the above expression. W ′ ( x ) = − 2 w R 2 x 3 Substitute R for x in the expression W ′ ( x ) = − 2 w R 2 x 3 and simplify. W ′ ( R ) = − 2 w R 2 R 3 = − 2 w R Use the formula of linear approximation for W ′ ( x ) To determine (b) To calculate: The value of the weight lost.

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 4.1, Problem 35E

To determine

(a)

To prove:

That the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

To determine

(b)

To calculate:

The value of the weight lost.

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Chapter 4.1, Problem 34E

Chapter 4.1, Problem 36E

Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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(a) To prove: That the weight lost at altitude h miles above the earth’s surface is approximately Δ W ≈ − ( 0.0005 w ) h .

Solution Summary: The author demonstrates that the weight lost at altitude is approximately Delta Wapprox -left.

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(a)

To prove:

That the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

(b)

To calculate:

The value of the weight lost.

Want to see the full answer?

Chapter 4 Solutions

(a) To prove: That the weight lost at altitude h miles above the earth’s surface is approximately Δ W ≈ − ( 0.0005 w ) h .

Solution Summary: The author demonstrates that the weight lost at altitude is approximately Delta Wapprox -left.

Videos

(a) To prove: That the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

(b) To calculate: The value of the weight lost.

Want to see the full answer?

Chapter 4 Solutions

(a)

To prove:

That the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

(b)

To calculate:

The value of the weight lost.