Mountain RangesA mountain range is a series of mountains connected by high ground. Consider the followingfictional mountain range with 10 peaks which are ordered in a line, from 1 to 10.1. First Mountain - 3500 ft.2. Second Mountain - 3300 ft.3. Giant Mountain - 5000 ft.4. Giant's Nephew - 4600 ft.5. Old Giant Mountain - 4950 ft.6. Old Giant's Cane Mountain - 4600 ft.7. Mt. Discrete Structures - 4200 ft.8. Mt. Noname - 4800 ft.9. Mt. Runningoutofnames - 4725 ft. 10. Last Mountain - 4650 ftWe call a subset of peaks consecutive if they include all of the peaks from į toj (1si A. You want to hike an entire subrange. Assuming you summit exactly one mountain with eachhike, what is the fewest number of hikes necessary to hike an entire subrange? Briefly justify theanswer.B. Your friend wants to hike all 10 mountains. To decide the order, they will pick a new mountainof a hat each week (they don't replace the mountain, once it is hiked they move on to a new oneuntil they get all 10). After how many hikes will they be guaranteed to hike an entire subrange?Justify your answer. Hint: It may help to first determine the subranges.Answer:

Name: Mountain RangesA mountain range is a series of mountains connected by
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Description: Mountain RangesA mountain range is a series of mountains connected by high ground. Consider the followingfictional mountain range with 10 peaks which are ordered in a line, from 1 to 10.1. First Mountain - 3500 ft.2. Second Mountain - 3300 ft.3. Gia

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You want to hike an entire subrange. Assuming you summit exactly one mountain with each hike, what is the fewest number of hikes necessary to hike an entire subrange? Briefly justify the answer. Your friend wants to hike all 10 mountains. To decide the order, they will pick a new mountain of a hat each week (they don't replace the mountain, once it is hiked they move on to a new one until they get all 10). After how many hikes will they be guaranteed to hike an entire subrange? Justify your answer. Hint: It may help to first determine the subranges.

You want to hike an entire subrange. Assuming you summit exactly one mountain with each hike, what is the fewest number of hikes necessary to hike an entire subrange? Briefly justify the answer. Your friend wants to hike all 10 mountains. To decide the order, they will pick a new mountain of a hat each week (they don't replace the mountain, once it is hiked they move on to a new one until they get all 10). After how many hikes will they be guaranteed to hike an entire subrange? Justify your answer. Hint: It may help to first determine the subranges.

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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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

Mountain Ranges
A mountain range is a series of mountains connected by high ground. Consider the following
fictional mountain range with 10 peaks which are ordered in a line, from 1 to 10.
1. First Mountain - 3500 ft.
2. Second Mountain - 3300 ft.
3. Giant Mountain - 5000 ft.
4. Giant's Nephew - 4600 ft.
5. Old Giant Mountain - 4950 ft.
6. Old Giant's Cane Mountain - 4600 ft.
7. Mt. Discrete Structures - 4200 ft.
8. Mt. Noname - 4800 ft.
9. Mt. Runningoutofnames - 4725 ft. 10. Last Mountain - 4650 ft
We call a subset of peaks consecutive if they include all of the peaks from į toj (1si<js 10). For
example, First, Second, and Giant Mountain are consecutive, as are Old Giant Mountain and Old Giant's
Cane Mountain.
We will define a subrange as a maximal subset of three or more consecutive peaks in the range whose
elevations are all within 500 feet of each other. Maximal means that a subrange can not be a proper
subset of another subrange (e.g. if {1,2,3,4} were a subrange, then {1,2,3} is not a subrange because
{1,2,3} C {1,2,3,4}).

A. You want to hike an entire subrange. Assuming you summit exactly one mountain with each
hike, what is the fewest number of hikes necessary to hike an entire subrange? Briefly justify the
answer.
B. Your friend wants to hike all 10 mountains. To decide the order, they will pick a new mountain
of a hat each week (they don't replace the mountain, once it is hiked they move on to a new one
until they get all 10). After how many hikes will they be guaranteed to hike an entire subrange?
Justify your answer. Hint: It may help to first determine the subranges.
Answer:

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