Explanation Calculation: Consider the differential equation of terminal velocity. m d v d t = m g − k v Here, k is a positive constant, g acceleration due to gravity, v is the velocity of a body of mass m falling under the gravity from a great height. Rewrite the above differential equation is, d v d t = 1 m ( m g − k v ) d v d t = g − k m v Write the normal form of the above differential equation. f ( v ) = g − k m v Substitute 0 for f ( v ) to find the critical points of the differential equation

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 2.1, Problem 40E

To determine

The limiting velocity of the body.

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Chapter 2.1, Problem 39E

Chapter 2.1, Problem 41E

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| Without evaluating the Legendre symbols, prove the following. (i) 1(173)+2(2|73)+3(3|73) +...+72(72|73) = 0. (Hint: As r runs through the numbers 1,2,. (ii) 1²(1|71)+2²(2|71) +3²(3|71) +...+70² (70|71) = 71{1(1|71) + 2(2|71) ++70(70|71)}. 72, so does 73 – r.)

By considering the number N = 16p²/p... p² - 2, where P1, P2, … … … ‚ Pn are primes, prove that there are infinitely many primes of the form 8k - 1.

(c) (i) By first considering the case where n is a prime power, prove that n μ² (d) = ø(n) (d)' n≥ 1. d\n (ii) Verify the result of part (c)(i) when n = 20.

Chapter 2 Solutions

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The limiting velocity of the body.

Solution Summary: The author explains that the limiting velocity of the body is mgk.

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Chapter 2 Solutions