Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Solve 1,2,3 1. A rectangular piece of cardboard, 8 inches by 14 inches, is used to make an open top box by cutting out a

Solve 1,2,3

1. A rectangular piece of cardboard, 8 inches by 14 inches, is used to make an open top box by cutting out a small square from each corner and bending up the sides. What size square should be cut from each corner for the box to have the maximum volume?

2. Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have the largest possible volume, what fraction of the volume of the larger cone does it occupy? (Let H and R be the height and radius of the large cone, let h and r be the height and radius of the small cone. Use similar triangles to get an equation relating h and r. (The formula for the volume of a cone is V = 1/3 pi r^2h.)

3. You're sunbathing on the island shown on the map below. The island is six miles from shore at the closest point, and the nearest store is a convenience store seven miles down the beach. If you can row at 4 miles an hour, and you can walk at 5 miles an hour, where should you land to get a bag of tortilla chips in the least possible time? (Ignore tides, currents, and sharks. No fair renting a helicopter.)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image_2

Step: 3

blur-text-image_3

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Bicomplex Holomorphic Functions The Algebra, Geometry And Analysis Of Bicomplex Numbers

Authors: M Elena Luna Elizarrarás, Michael Shapiro, Daniele C Struppa, Adrian Vajiac

1st Edition

3319248685, 9783319248684

More Books

Students also viewed these Mathematics questions