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Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 14.5 - Problem 23
Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 14.5 - Problem 23

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# Solved: 2326. Curl of a rotational field Consider the

ISBN: 9780321947345 167

## Solution for problem 23 Chapter 14.5

Calculus: Early Transcendentals | 2nd Edition

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Problem 23

2326. Curl of a rotational field Consider the following vector fields, where r = 8x, y, z9. a. Compute the curl of the field and verify that it has the same direction as the axis of rotation. b. Compute the magnitude of the curl of the field. F = 81, 0, 09 * r

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Calculus notes of 9/26/16 3.11 Related Rates Suppose a spherical weather balloon is filled with gas at a rate of 150 ft /min. What is the rate of change of its radius when the radius is 20 ft We are given / = 150: Volume increases by 150 ft /min. 3 dt dr We want / whedtr = 20 We need an equation relating V to r. 3 For a sphere, V = 4/3ᴨr dv 2 dr Different Rating time / = 4/3dt* 3r / (implicitdtifferentiation) 2 Or V’ = 4/3ᴨ * 3r r’ Solving for / , dt = dt(4ᴨr ) * /2 dvdt = 1/(4ᴨ * 20 ) * 150 = (3/32ᴨ) ft/min = 0.02984 ft/min Procedure: 1. Identify known rates and desired rates. Label what you alread

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