17. Cowboy Clint wants to build a dirt road from his ranch to the highway so that he can drive to the city in the shortest amount of time. The perpendicular distance from the ranch to the highway is 4 miles, and the city is located 9 miles down the highway. Where should Clint join the dirt road to the highway if the speed limit is 20 mph on the dirt road and 55 mph on the highway? Ranch City 9 - x 9 3 Calculus 1 HW Assignment #3 Spring 2022 Hint: Minimize the total number of hours for the trip, which is /16+ x² 9 T (x) 20 55 16 Answer: x = V105 - 1.56 (miles). 18. A rectangular storage container with an open top is to have a volume of 10 m³. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.
17. Cowboy Clint wants to build a dirt road from his ranch to the highway so that he can drive to the city in the shortest amount of time. The perpendicular distance from the ranch to the highway is 4 miles, and the city is located 9 miles down the highway. Where should Clint join the dirt road to the highway if the speed limit is 20 mph on the dirt road and 55 mph on the highway? Ranch City 9 - x 9 3 Calculus 1 HW Assignment #3 Spring 2022 Hint: Minimize the total number of hours for the trip, which is /16+ x² 9 T (x) 20 55 16 Answer: x = V105 - 1.56 (miles). 18. A rectangular storage container with an open top is to have a volume of 10 m³. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:17. Cowboy Clint wants to build a dirt road from his ranch to the highway so that he can
drive to the city in the shortest amount of time. The perpendicular distance from the ranch to
the highway is 4 miles, and the city is located 9 miles down the highway. Where should Clint
join the dirt road to the highway if the speed limit is 20 mph on the dirt road and 55 mph on
the highway?
Ranch
City
9 - x
9
3
Calculus 1
HW Assignment #3
Spring 2022
Hint: Minimize the total number of hours for the trip, which is
/16+ x²
9
T (x)
20
55
16
Answer: x =
V105 - 1.56 (miles).
18. A rectangular storage container with an open top is to have a volume of 10 m³. The length
of its base is twice the width. Material for the base costs $10 per square meter. Material for
the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.
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