Explanation Given: The cabin of the hunter is located 19 miles north and 8 miles west from the point along the river bank. The speed of the hunter along the river bank is 5 mph. The speed of the hunter on the rocky land is 2 mph. Calculation: Let 8 − x be the distance that the hunter travel along the river bank. Then x is the distance that he does not travel along river bank. The cabin is at 19 miles north. From Figure 1, it is observed that triangle APB is a right angled triangle. Applying Pythagorean Theorem for the given figure, The distance that he travel on land is 19 2 + x 2 = 361 + x 2 The formula for time taken is t = d r where d is distance and r is rate of speed. The time taken by him to travel along the river is 8 − x 5 The time taken by him to travel on the land is 361 + x 2 2 The total time is, T ( x ) = 8 − x 5 + 361 + x 2 2 = 8 5 − 1 5 x + 1 2 ( 361 + x 2 ) 1 2 Find the critical points by evaluating T ′ ( x ) and equating to 0. T ′ ( x ) = − 1 5 + 1 2 ( 1 2 ) ( 2 x ) ( 361 + x 2 ) − 1 2 = − 1 5 + x 2 ( 361 + x 2 ) − 1 2 Equate T ′ ( x ) to 0. − 1 5 + x 2 ( 361 + x 2 ) − 1 2 = 0 x 2 ( 361 + x 2 ) − 1 2 = 1 5 x 2 = ( 361 + x 2 ) 1 2 5 x = 2 (

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 6.2, Problem 50E

To determine

To find: The distance that the hunter should travel along the river in order to reach his cabin in minimum time.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.2, Problem 49E

Chapter 6.2, Problem 51E

Students have asked these similar questions

please solve with full steps please

4. Identify at least two mistakes in Francisco's work. Correct the mistakes and complete the problem by using the second derivative test. 2f 2X 2. Find the relative maximum and relative minimum points of f(x) = 2x3 + 3x² - 3, using the First Derivative Test or the Second Derivative Test. bx+ bx 6x +6x=0 12x- af 24 = 0 x=0 108 -2 5. Identify at least three mistakes in Francisco's work. Then sketch the graph of the function and label the local max and local min. 1. Find the equation of the tangent line to the curve y=x-2x3+x-2 at the point (1.-2). Sketch the araph of y=x42x3+x-2 and the tangent line at (1,-2) y' = 4x-6x y' (1) = 4(1) - 667 - 2 = 4(-2)4127-6(-2) 5-8-19-20 =

۳/۱ R2X2 2) slots per pole per phase = 3/31 B=18060 msl Ka, Sin (1) Kdl Isin ( sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 120*50 5) Synchronous speed, 120 x 50 S1000-950 1000 Copper losses 5kw 50105 Rotor input 5 0.05 loo kw 6) 1 1000rpm اذا ميريد شرح الكتب فقط Look = 7) rotov DC ined sove in peaper PU + 96er Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 3" 6" Σ=1 (2-1) π X9

Chapter 6 Solutions

Calculus with Applications (11th Edition)

Ch. 6.1 - YOUR TURN 1 Find the absolute extrema of the...Ch. 6.1 - Prob. 2YT Ch. 6.1 - Prob. 1WE Ch. 6.1 - Prob. 2WE Ch. 6.1 - Prob. 1E Ch. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.