please tell me not only answers,but also explanationsa. Factor pol.pdf

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please tell me not only answers,but also explanations a. Factor polynomial P(X) = x^5 - 256x into linear and irreducible quadratic factor with real coefficients. b. find the polynomial with real coefficients of the smallest possible degree where \'i\' and \'1+i\' are zeros and the coefficient of the highest power is 1 Solution a. p(x)=x*(x^4-256)=x*(x^2+16)(x^2-16)=x*(x^2+16)*(x+4)*(x-4) b. Since i and (i+1) are zeros so -i and -i+1 will also be zeros. Polynomial will be P(x) = (x-i)(x+i)(x-i-1)(x+i-1) P(x) = (x-i)(x+i)(x-1-i)(x-1+i) P(x) = (x^2 - i^2)((x -1)^2 -i^2) P(x) = (x^2 +1)((x -1)^2 +1) P(x) = (x^2 +1)(x^2 -2x+1 +1) P(x) = (x^2 +1)(x^2 -2x+2) P(x) = x^4 - 2x^3 + 3x^2 -2x + 2 Answer: P(x) = x^4 - 2x^3 + 3x^2 -2x + 2.

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Please write in C++ and should be able to compile and debug.Thank you Create a class called BinaryTreeDeque. This binary tree implements all of the functionality of the BinaryTree class, but instead of storing its values in a tree structure, the element values are stored in a deque, using pointers to maintain the relationship between the binary tree and its node values. Additionally: deque * getValues() - returns a copy of the deque the current array of values (which should be in insertion order). Solution Following are steps to insert a new node in Complete Binary Tree. 1. If the tree is empty, initialize the root with new node. 2. Else, get the front node of the queue. …….If the left child of this front node doesn’t exist, set the left child as the new node. …….else if the right child of this front node doesn’t exist, set the right child as the new node. 3. If the front node has both the left child and right child, Dequeue() it. 4. Enqueue() the new node. Code :- ------------------------- binarytreedequeue.h #ifndef BINARYTREEDEQUE_H #define BINARYTREEDEQUE_H // Program for linked implementation of complete binary tree #include #include // For Queue Size #define SIZE 50 // A tree node struct node { int data; struct node *right,*left; }; // A queue node struct Queue { int front, rear; int size; struct node* *array; }; class BinaryTreeDeque { public: BinaryTreeDeque(); struct node* newNode(int data); struct Queue* createQueue(int size); int isEmpty(struct Queue* queue); int isFull(struct Queue* queue); int hasOnlyOneItem(struct Queue* queue); void Enqueue(struct node *root, struct Queue* queue); struct node* Dequeue(struct Queue* queue); struct node* getFront(struct Queue* queue); int hasBothChild(struct node* temp); void insert(struct node **root, int data, struct Queue* queue); void display(struct Queue* queue); node * getValues(struct Queue* queue); }; #endif // BINARYTREEDEQUE_H binarydequeue.cpp --------------------------------------- #include \"binarytreedeque.h\" BinaryTreeDeque::BinaryTreeDeque() { } // A utility function to create a new tree node struct node* BinaryTreeDeque::newNode(int data) { struct node* temp = (struct node*) malloc(sizeof( struct node )); temp->data = data; temp->left = temp->right = NULL; return temp; } // A utility function to create a new Queue struct Queue* BinaryTreeDeque::createQueue(int size) { struct Queue* queue = (struct Queue*) malloc(sizeof( struct Queue )); queue->front = queue->rear = -1; queue->size = size; queue->array = (struct node**) malloc(queue->size * sizeof( struct node* )); int i; for (i = 0; i < size; ++i) queue->array[i] = NULL; return queue; } // Standard Queue Functions int BinaryTreeDeque::isEmpty(struct Queue* queue) { return queue->front == -1; } int BinaryTreeDeque::isFull(struct Queue* queue) { return queue->rear == queue->size - 1; } int BinaryTreeDeque::hasOnlyOneItem(struct Queue* queue) { return queue->front == queue->rear; } void BinaryTreeDeque::Enqueue(struct node *root, s.

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Please verify if the statement is true or false (I had to submit to answer for this question) A saddle point is a point on a surface that is not necessarily a maxima or minima in the graph. The term \"saddle point\" refers to the physical look of the surface. The surface of the graph resembles the shape of a saddle. The saddle point lies on the surface where one side of the graph curves up and the other side curves downward. Thank you Solution true.

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Please write clearly 6. Briefly define the terms Linear, Homogeneous, and Isotropic. Give an example of a material that is homogeneous and a material that is inhomogeneous. Give an example of a material that is isotropic and a material that is anisotropic. Solution A transmission medium can be classified as a: Free space is isotropic medium Example for anisotropic medium is GAS, CONUCTOR, ELECTRON BEAM etc.

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Please use Best Buy Solution Roe = Annual net income / Shareholder Equity The amount of net income returned as a percentage of shareholders equity. Return on equity measures a corporation\'s profitability by revealing how much profit a company generates with the money shareholders have invested. Roe = $1277 /6602 = 19.34 % This is telling me that almost 20% of the companies profit is been generated due to shareholders equity Roa = Net Income / Average Total Assets The return on assets formula, sometimes abbreviated as ROA, is a company\'s net income divided by its average of total assets. The return on assets formula looks at the ability of a company to utilize its assets to gain a net profit. Roa = $1277 / 10473 = 12.19% Information from page 121 and 123 from Best Buy.

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Please tell me the definition of polynomial function and when it is continuous? Solution A polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x^2 - 4x + 7 is a polynomial. polynomial functions are continuous everywhere (for all real numbers).

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Please think of an employment occupation that utilizes theoretical probability; and please write in detail. Thank you! Solution Statisticians: The profession exists in both the public and private sectors. Statisticians work with theoretical or applied statistics. The field shares much common history with positivist social science, but often with a greater emphasis on advanced mathematical methods. For example, in engineering statisticians collect and analyze mathematical data to solve problems. In manufacturing (they often are employed to support managerial decisions or to supervise quality control in manufacturing). In government, science and public health, statisticians make predictions on future such as forecasts on population growth, economic conditions and the outcome of elections; the core of that work is to measure, interpret, and describe the world and human activity patterns within it. Using statistical techniques, statisticians can make some statisticians work to develop the theories on which statistical techniques are based Thus, they apply their knowledge to many different fields..

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Please solve and explain: 1. You toss a coin 270 times. Find the probability that exactly 135 of the 270 tosses will be heads. 2. About 4% of the scientists in the National Academy of Sciences believe in PSI (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 144 members show up. Let X be the number of scientists at the convention who believe in PSI. You may assume for the following questions that X is binomially distributed with parameters n=144 and p=0.04. (a) How many scientists at the convention do you expect do believe in PSI? (b) What are the chances that none of the scientists at the convention believes in PSI? (c) What are the chances that at least 4 scientists at the convention believe in PSI? (d) What is the standard deviation of X? Solution a)scientists at the convention do you expect do believe in PSI=mean=140*4/100=6(approx of 5.6); b)134; c)134.4 d)5.76.

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Please solve problem. Thanks. Suppose that you toss a coin and roll a die. The sample space is shown in the figure below. (a) What is the probability of obtaining tails and a five? (Enter the probability as a fraction.) (b) What is the probability of obtaining tails or a five? (Enter the probability as a fraction.) (c) What is the probability of obtaining heads and a two? (Enter the probability as a fraction.) Solution 1. sample space , S = 12 so P(obtaining tails and a five) = 1/12 2 . P(obtaining tails or a five) = 1/2 + 1/6 = 2/3 3. P(obtaining heads and a two) = 1/2 * 1/6 = 1/12.

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