The number, if we make a tree that displays all monotonically increasing subsequences of 4 , 7 , 3 , 9 , 5 , 1 , 8 .

Question

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Answer 1

Question

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

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Problem 11 (a) A tank is discharging water through an orifice at a depth of T meter below the surface of the water whose area is A m². The following are the values of a for the corresponding values of A: A 1.257 1.390 x 1.50 1.65 1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 Using the formula -3.0 (0.018)T = dx. calculate T, the time in seconds for the level of the water to drop from 3.0 m to 1.5 m above the orifice. (b) The velocity of a train which starts from rest is given by the fol- lowing table, the time being reckoned in minutes from the start and the speed in km/hour: | † (minutes) |2|4 6 8 10 12 14 16 18 20 v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0 Estimate approximately the total distance ran in 20 minutes.

- Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., p-1 2 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). 23 32 how come? The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. The set T is the subset of these residues exceeding So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1.

Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

Answer 2

Question

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

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Answer 3

Question

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

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Answer 4

Question

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

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Answer 5

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

Answer 6

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

Answer 7

Chapter 12, Problem 1RE

To determine

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Answer 8

Expert Solution & Answer

Explanation of Solution

We have seen in the text that to find all possible sub-sequences of a given sequence, we represent the problem in the form of a tree. We pull a tree from the root. The nodes of this root are the terms of the sequence given in the given order. Now, we have to draw the nodes of these nodes as well.

Therefore, we consider the first note. Since we need to find monotonically increasing followings for the nodes of the first node, we add the next terms in the same order that appear in the original sequence. We do this for all nodes and then their nodes, until we are exhausted (because the conditions will certainly do for us). The end result is the following tree.

Now, to calculate the total number of the latter, we simply calculate the total number of possible paths from root to leaf. These are the total nodes in a given tree (including trees). Since each node is viewed from the root through a unique path and for a write relative to a given path, we list only the nodes seen in order.

Hence, there are 22 such subsequences in all.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Ch. 12.1 - Prob. 1TFQ Ch. 12.1 - Prob. 2TFQ Ch. 12.1 - Prob. 3TFQ Ch. 12.1 - Prob. 4TFQ Ch. 12.1 - Prob. 5TFQ Ch. 12.1 - Prob. 6TFQ Ch. 12.1 - Prob. 7TFQ Ch. 12.1 - Prob. 8TFQ Ch. 12.1 - Prob. 9TFQ Ch. 12.1 - Prob. 10TFQ

The number, if we make a tree that displays all monotonically increasing subsequences of 4 , 7 , 3 , 9 , 5 , 1 , 8 .

The number, if we make a tree that displays all monotonically increasing subsequences of 4,7,3,9,5,1,8.

Explanation of Solution

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