A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 9 miles down the shore from P in the least time? Let x be the distance (in miles) between point P and where the boat lands on the lakeshore. (a) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x. T(x) = (include units) (b) What is the distance x = c that minimizes the travel time? c= (include units) (c) What is the least travel time? The least travel time is (include units)
A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 9 miles down the shore from P in the least time? Let x be the distance (in miles) between point P and where the boat lands on the lakeshore. (a) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x. T(x) = (include units) (b) What is the distance x = c that minimizes the travel time? c= (include units) (c) What is the least travel time? The least travel time is (include units)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Transcribed Image Text:A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 9 miles down the shore from Pin
the least time? Let x be the distance (in miles) between point P and where the boat lands on the lakeshore.
(a) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x.
T(x) =
(include units)
(b) What is the distance x = c that minimizes the travel time?
(include units)
C =
(c) What is the least travel time?
The least travel time is
(include units)
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