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Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 3.11 - Problem 48
Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 3.11 - Problem 48

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# Solved: Oblique tracking A ship leaves port traveling

ISBN: 9780321947345 167

## Solution for problem 48 Chapter 3.11

Calculus: Early Transcendentals | 2nd Edition

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Problem 48

Oblique tracking A ship leaves port traveling southwest at a rate of 12 mi>hr. At noon, the ship reaches its closest approach to a radar station, which is on the shore 1.5 mi from the port. If the ship maintains its speed and course, what is the rate of change of the tracking angle u between the radar station and the ship at 1:30 p.m. (see figure)? (Hint: Use the Law of Sines.) Southwest course 458 1.5 mi Radar station Port Point of closest approach to radar station N

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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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