Question 6:a) Give a formula for triangular numbers (show first 7 elements of triangular numbers withexplanation).b) Give a formula for Fibonacci numbers (show first 5 elements with explanation).c) How does Hanoi Tower work? (explain).d) Give a pseudocode for factorial (show how it works).Question 7:d) Show that 5x² + 25x - 9 is 0(x²).e) Suppose a computer can perform 10¹2 bit operations per second. Find the largest problemsize that could be solved in 1 second if an algorithm requires: n³ and 3¹.f)Suppose a computer can perform 10¹2 bit operations per second. Find the time it wouldtake an algorithm that requires n³ + logn operations with a problem size of: n = 3000 andn = 10⁹.Question 8:Calculate time and space complexity for given algorithms.a) procedure function(){answer = 0for i=1 to nfor j = 1 to log(i)answer += 1print(answer) }b) {int i;for (i=1;i

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a) Give a formula for triangular numbers (show first 7 elements of triangular numbers with explanation). b) Give a formula for Fibonacci numbers (show first 5 elements with explanation). c) How does Hanoi Tower work? (explain).

a) Give a formula for triangular numbers (show first 7 elements of triangular numbers with explanation). b) Give a formula for Fibonacci numbers (show first 5 elements with explanation). c) How does Hanoi Tower work? (explain).

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter4: Selection Structures

Section: Chapter Questions

Problem 14PP

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Starting with the first Fibonacci number, Fib(1) = 1, and the second Fibonacci number, Fib(2) = 1, what is the sum of Fib(8) and Fib(10)?
Summary: Given integer values for red, green, and blue, subtract the gray from each value. Computers represent color by combining the sub-colors red, green, and blue (rgb). Each sub-color's value can range from 0 to 255. Thus (255, 0, 0) is bright red, (130, 0, 130) is a medium purple, (0, 0, 0) is black, (255, 255, 255) is white, and (40, 40, 40) is a dark gray. (130, 50, 130) is a faded purple, due to the (50, 50, 50) gray part. (In other words, equal amounts of red, green, blue yield gray). Given values for red, green, and blue, remove the gray part. Ex: If the input is: 130 50 130 the output is: 80 0 80 Find the smallest value, and then subtract it from all three values, thus removing the gray.
Summary: Given integer values for red, green, and blue, subtract the gray from each value. Computers represent color by combining the sub-colors red, green, and blue (rgb). Each sub-color's value can range from 0 to 255. Thus (255, 0, 0) is bright red, (130, 0, 130) is a medium purple, (0, 0, 0) is black, (255, 255, 255) is white, and (40, 40, 40) is a dark gray. (130, 50, 130) is a faded purple, due to the (50, 50, 50) gray part. (In other words, equal amounts of red, green, blue yield gray). Given values for red, green, and blue, remove the gray part. Ex: If the input is: 130 50 130 the output is: 80 0 80 Find the smallest value, and then subtract it from all three values, thus removing the gray. Note: This page converts rgb values into colors. 461710.3116374.qx3zqy7 LAB ACTIVITY 1 111 4.10.1: LAB: Remove gray from RGB Type your code here. 111 main.py 0/10 Load default template...
Summary: Given integer values for red, green, and blue, subtract the gray from each value. Computers represent color by combining the sub-colors red, green, and blue (rgb). Each sub-color's value can range from 0 to 255. Thus (255, 0, 0) is bright red, (130, 0, 130) is a medium purple, (0, 0, 0) is black, (255, 255, 255) is white, and (40, 40, 40) is a dark gray. (130, 50, 130) is a faded purple, due to the (50, 50, 50) gray part. (In other words, equal amounts of red, green, blue yield gray). Given values for red, green, and blue, remove the gray part.
The Fibonacci sequence is listed below: The first and second numbers both start at 1. After that, each number in the series is the sum of the two preceding numbers. Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, ... If F(n) is the nth value in the sequence, then this definition can be expressed as F(1) = 1 F(2) = 1 F(3) = 2 F(4) = 3 F(5) = 5 F(6) = 8 F(7) = 13 F(8) = 21 F(n) = F(n - 1) + F(n - 2) for n > 2 Example: Given n with a value of 4F(4) = F(4-1) + F(4-2)F(4) = F(3) + F(2)F(4) = 2 + 1F(4) = 3 The value of F at position n is defined using the value of F at two smaller positions. Using the definition of the Fibonacci sequence, determine the value of F(10) by using the formula and the sequence. Show the terms in the Fibonacci sequence and show your work for the formula.
Rahul is a maths genius so he came up with a game and as raj is Rahul's best friend so Rahul decided to play the game with raj. Rahul gives raj two numbers LL and RR and asks raj to find the count of numbers in the range from LL to RR (LL and RR inclusive) which are a digit palindromic. A number is a digit palindromic if its first digit is the same as its last digit. As raj is not very good at maths so your task is to help Raj find out how many numbers are a digit palindromic in the range LL to RR. For example if LL = 88 and RR = 2525 .The following numbers are a digit palindromic in the range of LL to RR: 8, 9, 11, and 22. If LL = 12511251 and RR = 12661266. The digit palindromic numbers are 1251 and 1261. Input format The first line contains an integer denoting the number of test cases. Each test case is described by a single line that contains two integers LL and RR. Output format For each test case output, an integer denoting how many a digit palindromic numbers are there in the…
Your objective is to write the solution to the 9 × 9 sudoku puzzle below. You must write in the digits 1 through 9 in each row such that no digit is repeated vertically, horizontally and in each box. In your solution, write each row on itsown line; and for each row, write each digit enclosed in square braces. For instance, if the row is (1, 2, 3, 4, 5, 6, 7, 8, 9), then you would type [1][2][3][4][5][6][7][8][9] for that row.
We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits" {0,1, ...,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0, 1,...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. Assume that digits and letter can be repeated. a. How many 4-digit hexadecimals are there in which the first digit is E or F? b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?
We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits" {0, 1,...,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0, 1, ...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. a. How many 4-digit hexadecimals are there in which the first digit is E or F? 8192 b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? c. How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?
A provable formula B is denoted by (you can write the answer in the paper and picture that answer upload it here).
Consider the given alorithm where A(1:n) is an array of n integers... A) What does the program do? What are the interpretations of B and C? B) What is the EXACT number comparisons in the best case in terms of n? C) What is the EXACT number comparisons in the worst case in terms of n?
Growing Triangles, cont. 1 2 3 The first figure is made up of three line segments of equal length. You can think of the second figure as made of nine segments of that same length, and so on. 5. Find the number of segments of the given length that would be needed for the tenth figure in this sequence. 6. Explain how you would find the number of segments of the given length that would be needed for the 100th figure in this sequence. 7. Write a rule for determining the number of segments of the given length for any figure in this sequence. Explain why your rule works. This activity was adapted from Driscoll, M. Fostering Algebraic Thinking, Heinemann 1999.