A boat on the ocean is 2 mi from the nearest point on a straight shoreline; that point is 11 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? miles from the restaurant. To minimize the total travel time, the boat should land (Type an exact answer, using radicals as needed.)
A boat on the ocean is 2 mi from the nearest point on a straight shoreline; that point is 11 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? miles from the restaurant. To minimize the total travel time, the boat should land (Type an exact answer, using radicals as needed.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:**Problem Description:**
A boat on the ocean is 2 miles from the nearest point on a straight shoreline; that point is 11 miles from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below.
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**Part (a):**
*If she walks at 3 miles per hour and rows at 2 miles per hour, at which point on the shore should she land to minimize the total travel time?*
To minimize the total travel time, the boat should land \(\_\) miles from the restaurant.
(Type an exact answer, using radicals as needed.)
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**Instructions:**
1. Determine the point on the shore where the woman should land the boat to minimize her total travel time.
2. Consider her rowing speed (2 mi/hr) and walking speed (3 mi/hr).
3. Use calculus or optimization techniques to find the precise landing point.
(Note: There's no graph or diagram provided in the text to explain further.)
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Step 1: Introduce to the given information
VIEWStep 2: Draw the figure and define the variables
VIEWStep 3: Determining the equation of total travel time
VIEWStep 4: Differentiating the T(x) and finding the critical point
VIEWStep 5: Verifying the total travel time is minimum at the critical point
VIEWStep 6: Finding the distance woman lands from the restaurant
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I am having trouble understanding your answer. How many miles should the boat land from the resturant?
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