Math

CalculusQ&A LibraryA visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. The island is 7 miles due south of the shoreline. The visitor plans to travel from the cottage to the island by running and swimming. If the visitor runs at a rate of 5 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the island?Question

Asked Apr 12, 2019

124 views

A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. The island is 7 miles due south of the shoreline. The visitor plans to travel from the cottage to the island by running and swimming. If the visitor runs at a rate of 5 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the island?

Step 1

The distance of the visitor’s cottage is 10 miles east of the closest point on a shoreline to an island. The distance between the island and the shoreline is 7 miles south of the shoreline. The visitor runs at a speed of 5 mph and swims at a speed of 3 mph.

If the visitor runs 10 miles at 5 mph, the time taken is

Step 2

If the visitor swims 7 miles at 3 mph, the time taken is

Step 3

Maximum time would be 4 h 20 m, unfortunately, the minimum time is required.

...Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: 1. Given the function f(x) x-4x (a) Determine if the function x) defined on Theorem. If so, find the...

A: a) To check whether the given function satifies the Rolle\\\\\\'s theorem over the interval [0, 4] o...

Q: The heat flow vector field for conducting objects is F=−k∇T, where T(x,y,z) is the temperature in t...

A: Assume k = 1.Then the vector field becomes, F = −∇T.Find ∇T as follows.

Q: How do you solve the limit of this graph?

A: x->-1^- means x is slightly less than -1.

Q: 8xy′+4(ln x)y)(4) +5x3 y′=−6x4 y−9xy″ What is the order of the differential equation shown above?

A: The given differential equation is, 8xy′ +4(lnx)y4 +5x3y′ = -6x4y - 9xy″.The order of the highest d...

Q: find the domain and range of f(x)=X5+x (the last x is supposed to be squared) and domain and range o...

A: Given information:The given function is f(x)=X5+x^2 and g(y)=1/y-2.

Q: Find the volume of the solid generated when R (shaded region) is revolved about the given line. 28- ...

A: Consider a shaded disc as shown in the diagram on the white board.Radius, R = 14 - y; thickness = dx...

Q: Please sketch this by hand! And show all your steps as im doing my best to fully understand the proc...

A: (A) The function has an absolute maximum but no local maximum. This means the graph is strictly incr...

Q: If f(x) 3x-2then f(x) = x 2x+ 2x5/3 2x 2x-1 12 1+5x8/3 3x2 2x-53-3x-3/2 x2 none of the above

A: The given function is,

Q: Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following: a) Give the domain of the function ...

A: a) First obtain the singularity for the given function as follows.The denominator of the given fract...