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# MATH
Write an equation that represents away to break down the number.
1. 60
2. 54
3. 32
1. 👍 0
2. 👎 0
3. 👁 79
1. What number? I would guess A since it's a set of ten and could've been rounded, but cannot tell without seeing the number.
1. 👍 0
2. 👎 0
posted by Jen
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Awesome Open Source
Awesome Open Source
## Data Structure and Algorithms Problems
Current Status Stats
Total C++ Problems 188
Total Python Problems 15
Current Daily Streak 11
Last Streak 06/20/2019 - 06/21/2019
Current Streak 06/23/2019 - 07/03/2019
Note: Some of the code here is old and was written when I was learning C++. It might be possible that code is not safe or making wrong assumptions. Please use with caution. Pull requests are always welcome.
Problem Solution
Find the nth node of linked list from last. nthToLastNode.cpp, nth_to_last_node.py
Swap nodes of a linkedlist without swapping data. swapNodesWithoutSwappingData.cpp, swap_nodes_without_swapping_data.py
Given a linked list, reverse alternate nodes and append at the end. reverseAlternateNodes.cpp
Only given a node pointer, delete the node from the linked list. deleteNode.cpp
Print middle node of linkedlist without iterating twice. printMiddleNode.cpp
Determine if a linked list is a pallindrome. listPallindrome.cpp
Determine the intersection(merging) point of two given linked list. findIntersectionPointOfLists.cpp, intersection_of_lists.py
Clone a linkedlist which has next and an random pointer, Space Complexity - O(1). cloneListWithRandomPtr.cpp, clone_list_with_random_ptr.py
Given a sorted linked list with duplicates, remove duplicates in one iteration. removeDuplicatesFromSortedList.cpp
Using Floyd's cycle finding algorithm, detect if a linkedlist contain cycle, if it does contain cycle, remove the loop floyedCycleDetection.cpp
Sort a linked list using merge sort merge_sort.cpp
Given a singly linked list L0 -> L1 -> … -> Ln-1 -> Ln. Rearrange the nodes in the list (in place) so that the new formed list is : L0 -> Ln -> L1 -> Ln-1 -> L2 -> Ln-2 .... rearrange_list.cpp
### Include
Include contains single header implementation of data structures and some algorithms.
Data Structure/Algorithm Implementation
Generic Macros and Algorithms like swap, random number generation generic.h
Generic Stack Implementation stack.h
Generic Queue Implementation queue.h
Generic List Implementation list.h
Binary Search Tree Implementation binarySearchTree.h
Quick Sort Implementation quickSort.h
Merge Sort Implementation mergeSort.h
Selection Sort Implementation selectionSort.h
Bubble Sort Implementation bubbleSort.h
Generic Graph Implementation (Adjacency List) graph.h
Heap Sort Implementation heap_sort.h
My own string library implementation pstring.h pstring.cpp
### Bit Manipulation Problems
Problem Solution
Determine if a number is a power of 2. power_of_2.cpp
Determine the next power of 2 for a given number. next_power_of_2.cpp
Using bit manipulation determine if a number is multiple of 3. multiple_of_3.cpp
Determine endianess of the machine, print a number in reverse Endianess. reverseEndianness.cpp
Find the parity of given number. find_parity.cpp
Implement fast multiplication of a number to 7 using bit manipulation. multiply_by_7.cpp
Reverse bits of unsigned integer (two methods - Reversing bit by bit & divide and conquer). reverseBitsOfAnInteger.cpp
Small function to determine position of right most set bit in a given integer. right_most_set_bit.cpp
Given a vector of numbers, only one number occurs odd number of times, find the number. find_odd_one_out.cpp
Given two integers, determine if their sum would be interger overflow. integerOverflow.cpp
How many bit flip operation would require to convert number A to B. countNumberOfBitFlips.cpp
Given a number x and two positions (from right side) in binary representation of x, write a function that swaps n right bits at given two positions and returns the result. It is also given that the two sets of bits do not overlap. swapSetOfBits.cpp
Louise and Richard play a game. They have a counter set to N. Louise gets the first turn and the turns alternate thereafter. In the game, they perform the following operations:
• If N is not a power of 2, reduce the counter by the largest power of 2 less than N.
• If N is a power of 2, reduce the counter by half of N.
The resultant value is the new N which is again used for subsequent operations.The game ends when the counter reduces to 1, i.e., N == 1, and the last person to make a valid move wins.
• Given N, your task is to find the winner of the game. If they set counter to 1, Richard wins, because its Louise' turn and she cannot make a move.
• Input Format : -The first line contains an integer T, the number of testcases. T lines follow. Each line contains N, the initial number set in the counter.
counter_game.cpp
Determine if two integers are of opposite signs. check_opposite_signs.cpp
Swap two bits at position p and q of a given integer. swapBits.cpp
Check if a number is power of 4. check_if_power_of_4.cpp
### Cracking the coding interview problems
Problem Solution
Problem 1-1 : Edition 6: Write an algorithm to determine whether a string has unique characters or not. Can we do it without using additional data structures? 1-1-hasUniqueChars.cpp, 1-1-hasUniqueChars.py
Problem 1-2 : Edition 5: Reverse a string when you are a pass a null terminated C string. 1-2-edi5-reverseString.cpp
Problem 1-2 : Edition 6: Given two strings, determine if one is permutation of other. 1-2-perm-strings.cpp, 1-2-perm-strings.py
Problem 1-3 : Edition 5: Write an algorithm to remove duplicate chars from a string. 1-3-edi5-removeDuplicates.cpp
Problem 1-3 : Edition 6: URLify: Replace all the spaces in a string with '%20'. Preferebly Inplace 1-3-URLify.cpp
Problem 1-4 : Edition 6: Given a string, write a function to check if it is a permutation of a pallindrome. 1-4-pallindrome-permutations.cpp
Problem 1-5 : Edition 6: There are three possible edits that can be performed on a string - Insert a char, Delete a char, Replace a char. Given two strings, determine if they are one or 0 edit away. 1-5-one-edit-away.cpp
Problem 1-6: Implement a method to perform basic string compression. Example string aabcccccaaa should be compressed to a2b1c5a3, however if compressed string is bigger than original string, return original string 1-6-string-compression.cpp
Problem 1-7: Rotate the matrix clockwise( & anticlockwise) by 90 degrees 1-7-matrix-rotation.cpp
Problem 1-8: Write an algorithm such that if an element of MxN matrix is 0, its entire row and column is set to 0. 1-8-zero-matrix.cpp
Problem 1-9: Given two strings s1 and s2, determine s2 is rotation of s1 using only one call to a function which checks whether one string is rotation of another. 1-9-string-rotation.cpp
Problem 2-1: Remove duplicates from an unsorted linked list. What if no temporary buffer is allowed. 2-1-remove-dups.cpp
Problem 2-2: Determine kth node from the last of a singly linked list. (Iterative and Recursive Approaches) 2-2-kthToLast.cpp
Problem 2-3: Implement an algorithm to delete a node in the middle of a singly linked list 2-3-delete-middle-node.cpp
Problem 2-4: Partition a linked list around a value x, all the nodes smaller than x come before all the nodes greater than equal to x 2-4-partition.cpp
Problem 2-5: You have two numberse represented by a linked list where each node contains a single digit. The digits are stored in reversed order, such that 1's digits are at the head of the list. Write a function that adds the two numbers and returns the sum as a linked list.Example:
• Input: ( 7 --> 1 --> 6 ) + ( 5 --> 9 --> 2 ) that is 617 + 295
• Output: ( 2 --> 1 --> 9 ) i.e. 912.
• FOLLOW UP : Suppose the lists are stored in forward order, Repeat the above problem.
• Input: ( 6 --> 1 --> 7 ) + ( 2 --> 9 --> 5 ) i.e. 617 + 295
• Output: ( 9 --> 1 --> 2 ) i.e. 912.
• Implement it recursively and iteratively.
Problem 2-6: Determine if linked list is palindrome( 2 iterative and one recursive approach 2-6-palindrome.cpp
Problem 2-7: Determine if two singly linked list intersect, if yes, return the intersecting node. The intersection is defined based on reference not on values 2-7-intersection.cpp
Problem 2-8: Detect if the linked list have a loop, Find the start node of the loop and remove the loop 2-8-loop-detection.cpp
### Dynamic Programming Problems
Problem Solution
Nth Fibonacci term using different memoization techniques fibonacci.cpp
Longest Common Subsequence Problem lcs.cpp, longest_common_subsequence.py
Maximum Value Contigous Subsequence Problem wiki max_subsequence.cpp
Catalan number - Count the number of possible Binary Search Trees with n keys catalan_number.cpp
Calculate the number of unique paths from source origin (0, 0) to destination (m-1, n-1) in a m x n grid. You can only move either in down or right direction. unique_paths.cpp
0-1 Knapsack Problem: Imagine you are a thief and you want to steal things with room full of things. You have a knapsack which can handle maximum capacity of weight W, and you want to fill it up such that it's worth is maximum. Being an intelligent thief, you know weights and values of each item in room. How would you fill your knapsack, such that you get the maximum possible value, such that you can only fill upto capacity W. 0_1_knapsack_problem.cpp
### Tree Problems
Problem Solution
Iterative Level order traversal of Tree using queue levelOrderTraversalIterative.cpp, level_order_tree_traversal_iterative.py
Recursive Level order traveral of Tree levelOrderTraversalRecursive.cpp, level_order_tree_traversal_recursive.py
ZigZag Traversal of Tree zigZagTraversal.cpp, zig_zag_traversal.py
Predecessor and Successor of a given node in Binary Search Tree predecessorSuccessor.cpp
Given values of two nodes in a Binary Search Tree, find the Lowest Common Ancestor (LCA). Assume that both the values exist in the tree. lowest-common-ancestor.cpp, lowest_common_ancestor.py
Given a binary tree (unlike binary search tree), find the Lowest Common Ancestor (LCA). lowest-common-ancestor-binary-tree.cpp
Given a binary tree, print out all of its root-to-leaf paths one per line. printAllRootToLeafPath.cpp
Determine if a tree is sum tree. A SumTree is a Binary Tree where the value of a node is equal to sum of the nodes present in its left subtree and right subtree. An empty tree is SumTree and sum of an empty tree can be considered as 0. A leaf node is also considered as SumTree. sumTree.cpp
Convert a tree to sumTree, such that each node is sum of left and right subtree of the original tree. convert_to_sum_tree.cpp, convert_to_sum_tree.py
Convert a sorted array to balanced binary search tree. sortedArrayToBST.cpp
Given a binary tree, generate sum of each vertical column. verticalSum.cpp
Given a binary tree and key, node with key exists in tree. Find all the ancestors of the node with key, ancestor here are the nodes which are in straight path from node to root. node_ancestors_in_root_path.cpp
Given a binary tree and key, return the level of the node with key. Root is at level 1, and if node with key does not exists in tree, return 0 level_of_node.cpp
Given a binary tree, find all the paths from root to nodes, whose sum is k. k_sum_paths.cpp
Given a binary tree, print its nodes level by level in reverse order. i.e. all nodes present at last level should be printed first followed by nodes of second-last level and so on.. All nodes for any level should be printed from left to right. reverseLevelOrderTraversal.cpp
Invert a binary tree, recursively and iteratively. invert_a_tree.cpp
Given a Binary Search Tree, find ceil and floor of a given key in it. If the given key lie in the BST, then both floor and ceil is equal to that key, else ceil is equal to next greater key (if any) in the BST and floor is equal to previous greater key (if any) in the BST floor_ceil_bst.cpp
Find kth smallest element in a binary search tree kth_smallest.cpp
Validate if a given binary tree is a binary search tree. validate_bst.cpp
Given a Binary Search Tree and a target number, return true if there exist two elements in the BST such that their sum is equal to the given target. find_target_k.cpp
Given a non-empty binary search tree and a target value, find the value in the BST that is closest to the target. Also, to note that the target value is a floating point. There will be only one unique value which is closest to the target. closest_bst_value.cpp, closest_bst_value.py
Given a binary tree, traversing preorder, construct a string output containing node values and parenthesis. The null node needs to be represented by empty parenthesis pair "()". And you need to omit all the empty parenthesis pairs that don't affect the one-to-one mapping relationship between the string and the original binary tree. Examples in code file string_from_tree.cpp
### String Problems
Problem Solution
Implementation of Robin-Karp algorithm for string search robinKarpStringMatching.cpp
Find next permutation of a given string, ie. rearrange the given string sucht a way that is next lexicographically greater string than given string next_permutation.cpp
Implementation of Z algorithm for pattern matching z.cpp
Test cases for self created string library pstring_test.cpp
Get the length of the last word in a string. length_of_last_word.cpp
Find the difference between two string. String t is generated by random shuffling string s and then add one more letter at a random position. Determine the character which is different in t find_difference.cpp
### Common Data Structure and logic problems
Problem Solution
Print the contents of matrix in a spiral order matrix_spiral_print.cpp
Given a M x N matrix, rotate it by R rotations anticlockwise, and show the resulting matrix. rotate_matrix.cpp
Rotate an array by r elements ( left or right ) array_rotation.cpp
Given an array of repeating/non-repeating intergeres, determine the first non-repeating int in this array first_non_repeating_int.cpp
In Quantumland, there are n cities numbered from 1 to n. Here, ci denotes the ith city. There are n−1 roads in Quantumland. Here, ci and ci+1 have a bidirectional road between them for each i < n.There is a rumor that Flatland is going to attack Quantumland, and the queen wants to keep her land safe. The road between ci and ci+1 is safe if there is a guard in ci or ci+1. The queen has already placed a few guards in some of the cities, but she is not sure if they are enough to keep the roads safe. She wants to know the minimum number of new guards she needs to hire. See comments in solution for input/output details. save_quantamland.cpp
You are given an integer N. Find the digits in this number that exactly divide N (division that leaves 0 as remainder) and display their count. For N=24, there are 2 digits (2 & 4). Both of these digits exactly divide 24. So our answer is 2. See more details in header comment of the solution file. findDigits.cpp
Encrypt and then decrypts a text using Caeser Cipher. caeser_cipher.cpp
Encrypt and then decrypts a text using Vigenère cipher. vigenere_cipher.cpp
Generate binary numbers between 1 to N efficiently. n_binary.cpp
Implement power function power_function.cpp
### Math Problems
Problem Solution
Print all the permutations of a string. Example: Permutations of ABC are ABC, ACB, BCA, BAC, CAB, CBA string_permutations.cpp
Euclidean algorithm to find greatest common divisor of two numbers. (Iterative and recursive) gcd.cpp
Implement pow(x,y) using divide and conquer approach. Try implementing it in O(logn) pow.cpp
Calculate factorial of large number, say 100 (it will have 158 digits) factorial_of_large_num.cpp
Generate all possible words from a number entered on a traditional mobile keypad phone_digits.cpp
Given a string representation of a number, remove n characters from the string such that number representation is lowest possible. lowest_possible_number.cpp
Detect if a number is a happy number. A number is happy number if sequence of operations where number is replaced by sum of square of its digits leads eventually to 1. A number is not a happy number if we are in an infinite loop when above operations are performed. happy_number.cpp
### Stack Problems
Problem Solution
We have series of n daily price quotes for a stock. We need to calculate span of stock's price for all n days. Span for ith day is defined as maximum number of consecutive days, for which the price of the stock was less than or equal to ith day. For stock quotes {100, 60, 70, 65, 80, 85} span will be {1, 1, 2, 1, 4, 5}. Span for day 1 is always 1, now for day 2 stock is at 60, and there is no day befor it when stock was less than 60. So span remains 1. For day 3, the stock is priced at 70, so its span is 2, as previous day it was 60, and so on. stock_span_problem.cpp
Given an infix expression, convert it to postfix expression, Example (A+B)*C --> AB+C* infix_to_postfix.cpp
Given a string containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.The brackets must close in the correct order, "()" and "()[]{}" are all valid but "(]" and "([)]" are not. valid_parenthesis.cpp
### Sort and Search Problems
Problem Solution
Given a sorted vector, return first index of the occurrence of a value in vector, if number does not exist, return -1 first_occurrence_binary_search.cpp
Find the first repeating element in an array of integers. Given an array of integers, find the first repeating element in it. We need to find the element that occurs more than once and whose index of first occurrence is smallest. firstRepeatingElement.cpp
Given a list of unsorted integers, A={a1,a2,…,aN}, Find the pair of elements that have the smallest absolute difference between them? If there are multiple pairs, find them all. closest_numbers.cpp
Given a sorted array, determine index of fixed point in this array. If array does not have a fixed point return -1. An array has a fixed point when index of the element is same as index i.e. i == arr[i], Expected time complexity O(logn) fixedPoint.cpp
Find the maximum element in an array which is first increasing and then decreasing. Input: arr[] = {8, 10, 20, 80, 100, 200, 400, 500, 3, 2, 1}, output : 500. Array may be strictly increasing or decreasing as well. ExpectedTime complexity is O(logn). findMaximum.cpp
Given an array of positive and/or negative integers, find a pair in the array whose sum is closest to 0. findClosestPairToZero.cpp
Numeros, the Artist, had two lists A and B, such that B was a permutation of A. Numeros was very proud of these lists. Unfortunately, while transporting them from one exhibition to another, some numbers were left out of A. Can you find the missing numbers? Notes:
• If a number occurs multiple times in the lists, you must ensure that the frequency of that number in both lists is the same. If that is not the case, then it is also a missing number.
• You have to print all the missing numbers in ascending order.
• Print each missing number once, even if it is missing multiple times.
• The difference between maximum and minimum number in B is less than or equal to 100.
.
• There will be four lines of input: n - the size of the first list, This is followed by n space-separated integers that make up the first list. m - the size of the second list. This is followed by m space-separated integers that make up the second list. Output the missing numbers in ascending order.
missingNumbers.cpp
Find the closest pair from two sorted arrays. Given two sorted arrays and a number x, find the pair whose sum is closest to x and the pair has an element from each array. We are given two arrays ar1[0…m-1] and ar2[0..n-1] and a number x, we need to find the pair ar1[i] + ar2[j] such that absolute value of (ar1[i] + ar2[j] – x) is minimum. closestPairSorted.cpp
Given an array A of n elements, find three indices i, j and k such that A[i]^2 + A[j]^2 = A[K]^2. O(n2) time complexity and O(1) space complexity squareSum.cpp
Given an unsorted array arr[0..n-1] of size n, find the minimum length subarray arr[s..e] such that sorting this subarray makes the whole array sorted. minLengthUnsortedArray.cpp
Find the missing number in Arithmetic Progression missingNumber2.cpp
Find the common elements in 3 sorted vectors commonIn3Arrays.cpp
Find all the pairs with a given sum in an unsorted array/vector find_pairs_with_sum.cpp
Given an array, find peak element in it. A peak element is an element that is greater than its neighbors. peak_element.cpp
Given a sorted array of distinct non-negative integers, find smallest missing element in it. smallest_missing.cpp
Move all zeros in the vector to the end move_zeros.cpp
### Graph Problems
Problem Solution
Depth First Traversal of a Graph dfsDemo.cpp
Breadth First Traversal of a Graph bfsDemo.cpp
calculate the shortest distance from the start position (Node S) to all of the other nodes in the graph using Dijkstra algorithm. dijkstra-shortest-reach.cpp
Calculate total weight of Minimum Spanning Tree of a given graph ( sum of weights of edges which forms MST) using Prim's algorithm primsMST.cpp
Print Minimum Spanning Tree( MST ) of a given graph using Kruskal's algorithm. kruskalMST.cpp
Create a program to generate a Huffman encoding for each character as a table. huffman_encoding.cpp
Search a given word in a 2D board containing letters. The word can be constructed by sequentially traversing adjacent horizontal or vertical cells. In a sequence to form word, letter on same position can not be used more than once. (Check top of file for examples.) grid_word_search.cpp
Given a 2D screen, location of the pixel and new value of the color to fill, replace the color of the pixel and all the adjacent(up, below, left, right) same colored pixel with new color. This is same as flood fill (remember the bucket symbol) a region in MS-PAINT. flood_fill.cpp
### Greedy Problems
Problem Solution
Given two integer arrays, A and B, each containing N integers. You are free to permute the order of the elements in the arrays. Is there an permutation A', B' possible of A and B, such that, A'i+B'i ≥ K for all i, where A'i denotes the ith element in the array A' and B'i denotes ith element in the array B'. two_arrays.cpp
John is taking orders. The ith order is placed by the ith customer at ti time and it takes di time to procees. What is the order in which the customers will get their orders? (see more details in solutions's comments) orders_order.cpp
### Backtracking Problems
Problem Solution
You are given a digit string (e.g "1234", "567" etc), provide all possible letter combinations we could generate from this digit string, based on the mapping we see on the telphone/mobile dialpad. If you have typed SMS in old style phones, you would know. For e.g. "1" is mapped to "abc", 2 is mapped to "def". You can refer to the image..
• Example: "34" will give output: {"dg","dh","di","eg","eh","ei","fg","fh","fi"}
Note that order does not matter in result set.
Implement wildcard pattern maching with support for '?' & ''.
• '?' Matches any single character.
• '
' Matches any sequence of character.. Checkout examples in file for more details.
wild_card_matching.cpp
Given a 2D board and list of words from a dictionary, find all the possible words on board fromt the list. (Check example in the solution) word_search.cpp
### Leet code Problems
Problem Solution
Given a sorted integer array without duplicates, return the summary of its ranges. For example, given [0,1,2,4,5,7], return ["0->2","4->5","7"]. summary_ranges.cpp
Given a 2D matrix, with following properties
• Integers in each row are sorted in ascending from left to right.
• Integers in each column are sorted in ascending from top to bottom.
search2DII.cpp
Given an unsorted integer array, find the first missing positive integer.Example: [1,2,0] should return 3 and [3,4,-1,1] should return 2. Expected time complexity O(n) and solution should use constant space firstMissingPositiveNum.cpp
Given an unsorted array of integers, find the length of the longest consecutive elements sequence. For example: Given [100, 4, 200, 1, 3, 2]. The longest consecutive elements sequence is [1, 2, 3, 4]. Return its length: 4. Algorithm should run in O(n) complexity. longestConsecutiveSeq.cpp
Given two sorted integer arrays nums1 and nums2, merge nums2 into nums1 as one sorted array.You may assume that nums1 has enough space (size that is greater or equal to m + n) to hold additional elements from nums2. The number of elements initialized in nums1 and nums2 are m and n respectively. mergeArrays.cpp
Given an array of non-negative integers, you are initially positioned at the first index of the array. Each element in the array represents your maximum jump length at that position. Determine if you are able to reach the last index. For example:
• A = [2,3,1,1,4], return true.
• A = [3,2,1,0,4], return false.
jumpGame.cpp
Given a positive integer, return its corresponding column title as appear in an Excel sheet. For example 1 -> A, 2 -> B,...26 -> Z, 27 -> AA, 28 -> AB, ...705 -> AAC excelColSheetTitle.cpp
Given an array nums, write a function to move all 0's to the end of it while maintaining the relative order of the non-zero elements. For example, given nums = [0, 1, 0, 3, 12], after calling your function, nums should be [1, 3, 12, 0, 0]. moveZeroes.cpp
Given an array of integers, find if the array contains any duplicates. Function should return true if any value appears at least twice in the array, and it should return false if every element is distinct. containsDuplicate.cpp
Given a list, rotate the list to the right by k places, where k is non-negative. For example:
• Given 1->2->3->4->5->NULL and k = 2, return 4->5->1->2->3->NULL
rotateList.cpp
Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.). You have the following 3 operations permitted on a word:
• Insert a character
• Delete a character.
• Replace a character
.
editDistance.cpp
Given a binary tree, Populate each next pointer to point to its next right node. If there is no next right node, the next pointer should be set to NULL. Initially, all next pointers are set to NULL.You may only use constant extra space.You may assume that it is a perfect binary tree (ie, all leaves are at the same level, and every parent has two children). connectNextPointers.cpp
Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses. For example, given n = 3, a solution set is "((()))", "(()())", "(())()", "()(())", "()()()" generate_parenthesis.cpp
Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array.For example, Given nums = [0, 1, 3] return 2. missing_number.cpp
Suppose a sorted array is rotated at some pivot unknown to you beforehand. (i.e., 0 1 2 4 5 6 7 might become 4 5 6 7 0 1 2). Find the minimum element. You may assume no duplicate exists in the array. find_min_rotated.cpp
Given an array S of n integers, find three integers in S such that the sum is closest to a given number, target. Return the sum of the three integers. You may assume that each input would have exactly one solution. threeSumClosest.cpp
Given n non-negative integers a1, a2, ..., an, where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of line i is at (i, ai) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water. Note: You may not slant the container. maxArea.cpp
Given a binary tree containing digits from 0-9 only, each root-to-leaf path could represent a number. An example is the root-to-leaf path 1->2->3 which represents the number 123. Find the total sum of all root-to-leaf numbers. Example in solution comments sumRootToLeafNumbers.cpp
Say you have an array for which the ith element is the price of a given stock on day i. If you were only permitted to complete at most one transaction (ie, buy one and sell one share of the stock), design an algorithm to find the maximum profit. maxProfitStock.cpp
Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path. Note: You can only move either down or right at any point in time. minPath.cpp
Count the number of prime numbers less than a non-negative number, n. countPrimes.cpp
Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers. Ensure that numbers within the set are sorted in ascending order. Example : for k = 3, n = 9 result would be [[1,2,6], [1,3,5], [2,3,4]], similarly for k = 3, n = 7, result would be [[1,2,4]]. combinationSum3.cpp
Given a non-negative integer num, repeatedly add all its digits until the result has only one digit. For example: Given num = 38, the process is like: 3 + 8 = 11, 1 + 1 = 2. Since 2 has only one digit, return it. Follow up: Could you do it without any loop/recursion in O(1) runtime? addDigits.cpp
Given a matrix with cell values 0 or 1. Find the length of the shortest path from (a1, b1) to (a2, b2), such that path can only be constructed through cells which have value 1 and you can only travel in 4 possible directions, i.e. left, right, up and down. shortest_path_maze.cpp
The Hamming distance between two integers is the number of positions at which the corresponding bits are different. Given two integers x and y, calculate the Hamming distance. hamming_distance.cpp
Given two binary trees and imagine that when you put one of them to cover the other, some nodes of the two trees are overlapped while the others are not. You need to merge them into a new binary tree. The merge rule is that if two nodes overlap, then sum node values up as the new value of the merged node. Otherwise, the NOT null node will be used as the node of new tree. merge_trees.cpp
Write a function that takes a string as input and reverse only the vowels of a string. reverse_vowels.cpp
Given a string, sort it in decreasing order based on the frequency of characters.For example:
• Input: cccbbbbaa Output: bbbcccaa
sortCharByFrequency.cpp
Product of Array Except Self. Given an array of n integers where n > 1, nums, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i]. product_except_self.cpp
Given a sorted array, remove duplicates in place and return the new length. It doesn't matter what is in array beyond the unique elements size. Expected O(1) space and O(n) time complexity. remove_duplicates.cpp
Count the number of islands in a grid. Given a grid representing 1 as land body, and 0 as water body, determine the number of islands (more details in problem comments) count_islands.cpp
Find median from a data stream. Design a data structure that supports addNum to add a number to the stream, and findMedian to return the median of the current numbers seen so far. Also, if the count of numbers is even, return average of two middle elements, return median otherwise. median_stream.cpp
Remove the minimum number of invalid parentheses in order to make the input string valid. Return all possible results. Note: The input string may contain letters other than the parentheses ( and ) remove_invalid_parenthesis.cpp
Given an array and a value, remove all instances of that value in-place and return the new length. Do not allocate extra space for another array, you must do this by modifying the input array in-place with O(1) extra memory. The order of elements can be changed. It doesn't matter what you leave beyond the new length. remove_element.cpp
Find intersection of two arrays/vectors, Given two vectors find the result of their interaction. The result should only contain unique characters and can be in any order intersection_of_array.cpp
Given a pattern and a string str, find if str follows the same pattern. Here follow means a full match, such that there is a bijection between a letter in pattern and a non-empty word in str. example:
pattern = "abba", str = "dog cat cat dog" should return true.
pattern = "abba", str = "dog cat cat fish" should return false.
pattern = "aaaa", str = "dog cat cat dog" should return false.
pattern = "abba", str = "dog dog dog dog" should return false. word_pattern.cpp
You are provided a vector of numbers, where each number represents
price of a stock on ith day. If you are permitted to only complete
one transaction per day (i.e buy one and sell one stock), design
an algorithm to find the maximum profit. best_time_to_buy_sell.cpp
Given a sentence, reverse the order of characters in each word within a sentence while still preserving whitespace and initial word order.
Example:
Input: She loves chocolate
Output: ehs sevol etalocohc reverse_words.cpp
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Select Page
# Number Sense Series
Math Whisperer materials are dedicated to each person who wants to be successful in math, including those who have struggled in the past. Our goal for our students is that they know the math they need to lead the lives they want.
Grade 6 and above: Understanding negative numbers.
Grade 8 and above: Calculating with positive and negative numbers using a powerful model.
Math Whisperer materials are dedicated to each person who wants to be successful in math, including those who have struggled in the past. Our goal for our students is that they know the math they need to lead the lives they want.
Grades 2 and above: Our numbers are based on “tens.” While this seems obvious to most adults, many students do not actually understand this fundamental way our numbers are constructed. This book uses a popsicle stick model and game to help students understand numbers through the hundreds.
Fractions are critical to success in algebra. In this book, fractions will make sense to you and you will never have to learn them again.
Grades 6 and above: Fractions are important in their own right, and essential for Algebra. To be successful in Algebra, students must understand what fractions are all about, and how to multiply them. In this book, multiplying fractions and reducing fractions actually make sense, so that students can understand and remember how to do those problems.
Fractions are critical to success in algebra. In this book, fractions will make sense to you and you will never have to learn them again.
Grades 7 and above: Fractions are important in their own right, and essential for Algebra. To be successful in Algebra, students must be able to subtract, add and divide fractions. In this book, those fraction operations actually make sense, so that students can understand and remember them.
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Physics
kyraketen2:
A car covers 72 kilometers in the first hour of its journey. In the next hour, it covers 90 kilometers. What is the amount of work done by the car? The total mass of the car, including its passengers, is 2.5 × 103 kilograms.
SmokeyBrown:
Hi, and welcome to QuestionCove! This is a question involving calculating work, which we can find by taking the force exerted multiplied by the displacement over which the force was exerted. The displacement part is simple to calculate, since we are told how much distance the car travels. As for the force exerted by the car, we know the mass of the car... any idea how we can calculate force based on that information?
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# CBSE Class 9 Mathematics Quadrilaterals Assignment Set B
## Quadrilaterals Assignment for Class 9
Class 9 Quadrilaterals students should refer to the following printable assignment in Pdf in standard 9. This test paper with questions and answers for Grade 9 Quadrilaterals will be very useful for exams and help you to score good marks
### Class 9 Quadrilaterals Assignment Pdf
Q 1 Name a quadrilateral whose each pair of opposite sides is equal.
Q 2 What is the sum of two consecutive angles in a parallelogram?
Q 3 The angles of quadrilateral are respectively 100 , 30 , 92 and x. Find the value of x.
Q 4 The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.
Q 5 Thee sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.
Q 6 In a triangle ABC, P,Q and R are the mid – points of sides BC, CA and AB respectively.
If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.
Q 7 Find the four angles P, Q, R and S in the parallelogram PQRS as shown below.
Q 8 Two opposite angles of a parallelogram are (5x + 1)° and (49 – 3x)°. Find the measure of these opposite angles of the parallelogram.
Q 9 Prove that each of the four sides of a rhombus is of the same length.
Q 10 ABCD is a rhombus. Show that diagonals AC bisects angle A as well as angle C.
## Tags:
Click to View or Download pdf file
Click for more Quadrilaterals Study Material
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Read the latest news and announcements from NCERT and CBSE below. Important updates relating to your studies which will help you to keep yourself updated with latest happenings in school level education. Keep yourself updated with all latest news and also read articles from teachers which will help you to improve your studies, increase motivation level and promote faster learning
### Celebration of Matribhasha Diwas Mother Language day
UNESCO has declared 21st February of every year to be celebrated as International Mother Language day to promote dissemination of Mother Language of all, create awareness of linguistic and cultural traditions and diversity across the world and to inspire solidarity...
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### Board Exams Date Sheet Class 10 and Class 12
Datesheet for CBSE Board Exams Class 10 (Scroll down for Class 12 Datesheet) Datesheet for CBSE Board Exams Class 12
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# Number 3009770 facts
The even number 3,009,770 is spelled 🔊, and written in words: three million, nine thousand, seven hundred and seventy, 3.0 million. The ordinal number 3009770th is said 🔊 and written as: three million, nine thousand, seven hundred and seventieth. The meaning of the number 3009770 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 3009770. What is 3009770 in computer science, numerology, codes and images, writing and naming in other languages
## What is 3,009,770 in other units
The decimal (Arabic) number 3009770 converted to a Roman number is (M)(M)(M)(IX)DCCLXX. Roman and decimal number conversions.
#### Time conversion
(hours, minutes, seconds, days, weeks)
3009770 seconds equals to 1 month, 6 days, 20 hours, 2 minutes, 50 seconds
3009770 minutes equals to 6 years, 2 months, 2 weeks, 4 days, 2 hours, 50 minutes
### Codes and images of the number 3009770
Number 3009770 morse code: ...-- ----- ----- ----. --... --... -----
Sign language for number 3009770:
Number 3009770 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
## Share in social networks
#### Is Prime?
The number 3009770 is not a prime number.
#### Factorization and factors (dividers)
The prime factors of 3009770 are 2 * 5 * 300977
The factors of 3009770 are 1, 2, 5, 10, 300977, 601954, 1504885, 3009770.
Total factors 8.
Sum of factors 5417604 (2407834).
#### Powers
The second power of 30097702 is 9.058.715.452.900.
The third power of 30097703 is 27.264.650.008.674.832.384.
#### Roots
The square root √3009770 is 1734,868871.
The cube root of 33009770 is 144,381352.
#### Logarithms
The natural logarithm of No. ln 3009770 = loge 3009770 = 14,917374.
The logarithm to base 10 of No. log10 3009770 = 6,478533.
The Napierian logarithm of No. log1/e 3009770 = -14,917374.
### Trigonometric functions
The cosine of 3009770 is 0,144444.
The sine of 3009770 is -0,989513.
The tangent of 3009770 is -6,850491.
## Number 3009770 in Computer Science
Code typeCode value
3009770 Number of bytes2.9MB
Unix timeUnix time 3009770 is equal to Wednesday Feb. 4, 1970, 8:02:50 p.m. GMT
IPv4, IPv6Number 3009770 internet address in dotted format v4 0.45.236.234, v6 ::2d:ecea
3009770 Decimal = 1011011110110011101010 Binary
3009770 Decimal = 12122220121222 Ternary
3009770 Decimal = 13366352 Octal
3009770 Decimal = 2DECEA Hexadecimal (0x2decea hex)
3009770 BASE64MzAwOTc3MA==
3009770 MD5f5c491a6e572496dbe59790a575ec4ef
3009770 SHA189e8b6959c4ccca04293b4789a4d79d51e6591ce
More SHA codes related to the number 3009770 ...
If you know something interesting about the 3009770 number that you did not find on this page, do not hesitate to write us here.
## Numerology 3009770
### Character frequency in the number 3009770
Character (importance) frequency for numerology.
Character: Frequency: 3 1 0 3 9 1 7 2
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 3009770, the numbers 3+0+0+9+7+7+0 = 2+6 = 8 are added and the meaning of the number 8 is sought.
## № 3,009,770 in other languages
How to say or write the number three million, nine thousand, seven hundred and seventy in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 3.009.770) tres millones nueve mil setecientos setenta German: 🔊 (Nummer 3.009.770) drei Millionen neuntausendsiebenhundertsiebzig French: 🔊 (nombre 3 009 770) trois millions neuf mille sept cent soixante-dix Portuguese: 🔊 (número 3 009 770) três milhões e nove mil, setecentos e setenta Hindi: 🔊 (संख्या 3 009 770) तीस लाख, नौ हज़ार, सात सौ, सत्तर Chinese: 🔊 (数 3 009 770) 三百万九千七百七十 Arabian: 🔊 (عدد 3,009,770) ثلاثة ملايين و تسعة آلاف و سبعمائة و سبعون Czech: 🔊 (číslo 3 009 770) tři miliony devět tisíc sedmset sedmdesát Korean: 🔊 (번호 3,009,770) 삼백만 구천칠백칠십 Danish: 🔊 (nummer 3 009 770) tre millioner nitusinde og syvhundrede og halvfjerds Hebrew: (מספר 3,009,770) שלושה מיליון ותשעת אלפים שבע מאות ושבעים Dutch: 🔊 (nummer 3 009 770) drie miljoen negenduizendzevenhonderdzeventig Japanese: 🔊 (数 3,009,770) 三百万九千七百七十 Indonesian: 🔊 (jumlah 3.009.770) tiga juta sembilan ribu tujuh ratus tujuh puluh Italian: 🔊 (numero 3 009 770) tre milioni e novemilasettecentosettanta Norwegian: 🔊 (nummer 3 009 770) tre million ni tusen syv hundre og sytti Polish: 🔊 (liczba 3 009 770) trzy miliony dziewięć tysięcy siedemset siedemdziesiąt Russian: 🔊 (номер 3 009 770) три миллиона девять тысяч семьсот семьдесят Turkish: 🔊 (numara 3,009,770) üçmilyondokuzbinyediyüzyetmiş Thai: 🔊 (จำนวน 3 009 770) สามล้านเก้าพันเจ็ดร้อยเจ็ดสิบ Ukrainian: 🔊 (номер 3 009 770) три мільйони дев'ять тисяч сімсот сімдесят Vietnamese: 🔊 (con số 3.009.770) ba triệu chín nghìn bảy trăm bảy mươi Other languages ...
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# A lateral-thinking puzzle
I came up with a nice little lateral-thinking exercise.
Note that puzzles like these are inherently unfair, because you have to think outside the box, without breaking out of the (ill-defined and completely unrealistic) world model. But usually, once you see the solution, you'll know that it's the correct one.
Beware of spoilers in the comments.
Here we go:
You are a medical doctor working under rather chaotic conditions. Somebody turns up with three unconscious patients and their papers, and promptly disappears again. The patients have lost a lot of blood, and you realise that they're all going to die soon unless they get blood transfusions. From the papers, you can see that one patient has blood type A, another has blood type B, and the last one has blood type O. However, the papers are all mixed up, and you cannot tell which patient has which blood type.
If you do nothing, all three are going to die. Thus, you find it morally justifiable to take any risk that improves the odds of survival of at least one patient.
To clarify the rules of the game:
1. Patient A will live after receiving a transfusion of Patient O's blood.
2. Patient B will live after receiving a transfusion of Patient O's blood.
3. Patient A's blood will instantly kill Patient B and/or Patient O.
4. Patient B's blood will instantly kill Patient A and/or Patient O.
5. The only way you can learn something about the blood type of a patient is by giving them a transfusion and seeing whether they die.
For instance, if we refer to the patients as 1, 2 and 3, one strategy might be to perform the transfusions 1→2 and 1→3. With 1/3 probability, Patient 1 has blood type O, and Patients 2 and 3 live. Otherwise, everybody dies. The expected number of people saved is thus 1/3 * 2 + 2/3 * 0 = 2/3.
Your own blood is of type AB and therefore useless.
Find the best strategy.
(If your strategy is expected to save 1 person, then good job, but there's an even better approach!)
Posted Saturday 19-Sep-2015 09:35
Disclaimer: I am not responsible for what people (other than myself) write in the forums. Please report any abuse, such as insults, slander, spam and illegal material, and I will take appropriate actions. Don't feed the trolls.
Jag tar inget ansvar för det som skrivs i forumet, förutom mina egna inlägg. Vänligen rapportera alla inlägg som bryter mot reglerna, så ska jag se vad jag kan göra. Som regelbrott räknas till exempel förolämpningar, förtal, spam och olagligt material. Mata inte trålarna.
Anonymous
Sat 19-Sep-2015 14:22
(No spoilers) I've got 4/3. Is a better solution possible?
lft
Linus Åkesson
Sun 20-Sep-2015 14:03
The intended solution is indeed 4/3. Well done! I haven't found a better way, but who knows.
Anonymous
Mon 21-Sep-2015 14:12
I'll give the first "hint". For my solution to give an expected value of 4/3, I assumed that a patient doesn't immediately die when donating blood.
Anonymous
Tue 22-Sep-2015 03:00
Draw a small amount of blood from two of them and give the blood to the other. ⅓ of the time you will have drawn from A and B and everyone will die. Otherwise, you will have drawn from O and one other. O will die but the other will still be alive, and you can use O's blood for the other two. This assumes that the small amount mixed into O's bloodstream now won't kill the third one upon receiving more blood from O though.
Vale
Valentino Miazzo
Tue 29-Sep-2015 08:09
I assume Hr doesn't matter and the amount of blood removed and necessary to save one patient doesn't kill immediately the donor.
Solution: Pick two patients randomly. Spill from the receiver a transfusion and keep the blood aside. Transfuse from donor to receiver. 1/3 of times the donor is O and receiver doesn't die immediately. Restore the receiver blood and do another transfusion from the donor to the other patient. You saved 2 people.
2/3 of times the donor is A or B and the receiver dies immediately. Reverse the transfusion.
In 1/2 of times the receiver was O. The corpe contains compatible blood and the reverse transfusion saves the original donor. The blood aside is O and useful to save the other patient.You saved 2 people.
In the other 1/2 of times the receiver is not O and all the patients die.
Therefore: 1/3*2 + 2/3*1/2*2 + 2/3*1/2*0=4/3
By the way, your projects are marvelous and very inspiring. Thanks!
lft
Linus Åkesson
Thu 1-Oct-2015 21:13
Vale wrote:
Solution: Pick two patients randomly. Spill from the receiver a transfusion and keep the blood aside. Transfuse from donor to receiver. 1/3 of times the donor is O and receiver doesn't die immediately. Restore the receiver blood and do another transfusion from the donor to the other patient. You saved 2 people.
2/3 of times the donor is A or B and the receiver dies immediately. Reverse the transfusion.
In 1/2 of times the receiver was O. The corpe contains compatible blood and the reverse transfusion saves the original donor. The blood aside is O and useful to save the other patient.You saved 2 people.
In the other 1/2 of times the receiver is not O and all the patients die.
Therefore: 1/3*2 + 2/3*1/2*2 + 2/3*1/2*0=4/3
That is exactly the solution I had in mind! Well done!
By the way, your projects are marvelous and very inspiring. Thanks!
Thank you!
Anonymous
Mon 30-Nov-2015 20:37
Is the assumption that other blood is not available? That is not spelt out. Why would you not give just O blood to everyone. DOes not matter who has what blood type. If the requirement is to transfuse from one to the other then that should be spelt out in the question. Otherwise my solution will save all three.
lft
Linus Åkesson
Tue 1-Dec-2015 23:00
A fair point. Yes, that assumption should have been spelt out.
Anonymous
Thu 10-Dec-2015 16:49
I reached 5/3, assuming that drawing blood enough to give transfusion to 2 persons does not kill patient immediately.
Define patients 1, 2 and 3. Draw and store blood from each of them. Give blood of patient 1 to 2, and if he survives, also to patient 3. If patient 2 does not survive, give his stored blood to patient 3. If patient 3 does not survive, give his stored blood to patient 1, but if patient 3 survives, give patient 2's blood also to patient 1.
List of scenarios with (1,2,3) marking blood types of each patient:
(o,a,b),(o,b,a): Patients 2 and 3 both survive, 1/3 cases.
(a,b,o),(b,a,o): Patient 1 survives, 1/3 cases.
(a,o,b),(b,o,a): Patients 1 and 3 both survive, 1/3 cases.
1/3*2+1/3*1+1/3*2=5/3
lft
Linus Åkesson
Fri 11-Dec-2015 14:38
That's an interesting approach! But I'm not entirely convinced about the third case. Let's assume (a,o,b). In the beginning, each patient lacks 1 transfusion's worth of blood. After the initial drawing, each patient lacks 3 units of blood. You use one of the stored units of Type A blood, giving it to Patient 2. Then you give one unit of Type O blood to Patient 3. Finally, you give the remaining unit of Type O blood to Patient 1. At this point, I assume that any leftovers are given back to the respective patient, so the two stored units of Type B blood are given to Patient 3. But you only have one unit left of Type A blood, so Patient 1 would still end up lacking one unit of blood. You'd have to transfuse some of the blood from Corpse 2 back to Patient 1. That may or may not work in real life (please don't try it), but it's lateral thinking all right. If it was part of the intended solution, then I think it would have been good to spell it out. Otherwise; did I miss something?
Anonymous
Fri 11-Dec-2015 14:54
Hi Linus,
You're right about giving leftover blood back to donor, and the needed assumption I missed to state is actually based on original rules:
Patient A's blood will instantly kill Patient B and/or Patient O.
Patient B's blood will instantly kill Patient A and/or Patient O.
So, we can assume that virtually a drop of blood is enough to see the potential negative effect, and transfusion can be stopped without consuming any significant amount of blood. We need to draw blood from everyone just to avoid contaminating patient O's blood with even a single drop of wrong type.
-Pets
lft
Linus Åkesson
Fri 11-Dec-2015 16:40
All right, then I follow you. Good work there!
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# Newton’s 2nd law
Acceleration is caused by a net/resulting force, $\sum \vec F$; and vice versa, a net force causes acceleration $\vec a$. This acceleration is “dampened” or resisted by the mass $m$.
$$\sum \vec F=m\vec a$$
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Posted on
# What’s your alternative solution? Challenge #29
This is series of daily JavaScript coding challenges... for both beginners and advanced users.
Each day I’m gone present you a very simple coding challenge, together with the solution. The solution is intentionally written in a didactic way using classic JavaScript syntax in order to be accessible to coders of all levels.
Solutions are designed with increase level of complexity.
## Today’s coding challenge
``````Create a function that will receive an array of numbers as argument and will return a new array with distinct elements
``````
(scroll down for solution)
## Code newbies
If you are a code newbie, try to work on the solution on your own. After you finish it, or if you need help, please consult the provided solution.
You can solve it using functional concepts or solve it using a different algorithm... or just solve it using the latest ES innovations.
By providing a new solution you can show code newbies different ways to solve the same problem.
## Solution
``````// Solution for challenge27a
var ar = getDistinctElements([1, 2, 3, 6, -1, 2, 9, 7, 10, -1, 100]);
println(ar);
function getDistinctElements(ar)
{
var ar2 = [];
for(let i = 0; i < ar.length; i++)
{
if (!isInArray(ar[i], ar2))
{
ar2.push(ar[i]);
}
}
return ar2;
}
function isInArray(n, ar)
{
for(let i = 0; i < ar.length; i++)
{
if (ar[i] === n)
return true;
}
return false;
}
``````
To quickly verify this solution, copy the code above in this coding editor and press "Run".
Note: The solution was originally designed for codeguppy.com environment, and therefore is making use of `println`. This is the almost equivalent of `console.log` in other environments. Please feel free to use your preferred coding playground / environment when implementing your solution.
Chris McKay • Edited
So, here's my solution:
``````var ar = getDistinctElements([1, 2, 3, 6, -1, 2, 9, 7, 10, -1, 100]);
println(ar);
function getDistinctElements(ar = []) {
return [...new Set(ar)];
}
``````
So, just by way of explanation, Set is an object that only accepts distinct values. Using the spread operator (...) inside array brackets converts the set back into an array.
Tomas Fernandez
With a reduce
``````function distinct(list = []){
const reduced = list.reduce((acc, curr) => {
acc[curr] = curr;
return acc;
}, {})
return Object.values(reduced)
}
``````
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# Vector topology cleaning
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Introduction
Q: What would be the 'recommended' way of dealing with the 'errors' found in vector data which were created with zero topological restrictions (and saved as .shp?)
A: For import, try to find a snapping threshold for v.in.ogr that produces an error-free output (during import the module suggests a threshold). Ideally the output would not only be error-free, but the number of centroids would match the number of input polygons (both are reported by v.in.ogr). The min_area option of v.in.ogr could also help. The bulk of the cleaning should be done by v.in.ogr. After that, removing small areas with v.clean ... tool=rmarea, threshold in square meters, could help.
Example: For data which are mainly based on Landsat data, a threshold of 10 square meters could remove artefacts and preserve valid areas (Landsat pixel size is about 90 square meters). The threshold needs to be empirically determined.
Note: there might not be a standard procedure that works for all data sources.
### A strategy to find a viable snapping threshold
A hint for snapping: v.in.ogr suggest for vector data with topological errors a range of [1e-08, 1] for suitable snapping values. The exponent thus ranges from -8 to 0. Testing all possible values in this range obviously takes a lot of time.
Strategy: You could set low = -8 , high = 0, and set mid to (low + high) / 2 = -4 and test v.in.ogr with snap=1e\$mid.
• If you still get errors, increase: set low to mid, get new mid with (low + high) / 2
• else, decrease: set high to mid, get new mid with (low + high) / 2
Continue this until you found the threshold were these warnings just disappeared.
Note: Snapping is slow and uses quite a bit of memory because it needs a spatial search tree.
## Cleaning large network datasets
Q: How can I speed up topologial cleaning (v.clean) in GRASS 6 for large network datasets (for example OpenStreetMap data)?
A: The improved v.clean version in GRASS 7 is way faster. Here some hints though:
GRASS 6: When breaking lines it is recommended to
• split the lines first in smaller segments with v.split using the vertices option. Then,
• run v.clean with 'tool=break'. After that,
• use v.build.polylines to merge lines again.
GRASS 7: Here this has become much easier. Use v.clean with the -c flag and 'tool=break' and 'type=line'. The 'rmdupl' tool is then automatically added, and the splitting and merging is done internally.
## Cleaning zero length lines
In order to remove all lines with zero length, run
``` v.clean type=line tool=rmline
```
## Cleaning patched polygons
Q: How can I patch to fitting area maps with have been digitized separately and correct the topology? I observe that the shared polygon boundaries do not perfectly match... I need to clean topology.
Polygon vector map with topology problems (click to see)
A: You can use v.clean for this.
Tools to consider:
• snap,bpol,rmdupl,break,rmdupl,rms
• the threshold (in map units) should be very small
Example (Lat-Long):
``` v.in.ogr natural_earth/ne_110m_admin_0_countries.shp out=country_boundaries snap=0.0001 TODO: FIX THIS
```
## Polygon import from SHAPE file
Overlayed polygons after import from SHAPE file (Simple Features
v.clean applied:
Overlayed polygons topologically cleaned. Note the double categories.
### Hints
• In recent GRASS GIS 7 versions, snapping thresholds for unclean polygons are suggested to the user when using v.in.ogr.
• Note that the snap threshold is given in map units, e.g. meters. To select a reasonable value consider the distance of vertices in the map, i.e. the level of detail in order to avoid that either the entire geometry is getting "ruined" by an aggressive snapping nor that nothing happens if the snap threshold is magnitudes lower than the map unit (e.g. trying to fix cadastral maps at pico-meter level will not change much).
• If the input polygons are supposed to not overlap each other, the number of centroids should be identical to the number of input polygons. If not the case, more topological cleaning is needed.
• If the input polygons have logical errors, for example when the same landuse polygon is present more than once, this can not be cleaned automatically with v.in.ogr or v.clean. You can investigate overlapping areas in the imported vector with 'd.vect yourmap type=area layer=2' (only overlapping areas have a category in layer 2 after import). Additionally you may show the centroids of layer=2 to easier find tiny overlapping areas with 'd.vect yourmap type=centroid layer=2'
Q: How about self-intersecting lines and boundaries?
A: In the GRASS GIS topological model self-intersecting lines are allowed, self-intersecting boundaries are not. Self-intersecting lines are ok e.g. for v.net modules, e.g. to represent a bridge of a secondary road over a highway.
Note: There are some modules that do not like self-intersecting lines, e.g with v.buffer problems are expected.
Q: I've imported a shapefile with 6842 input polygons and after importing (with 1e-12 snapping threshold) there are 6800 centroids. Further cleaning does not change the topology. Why?
A: It could be that some of the input polygons are exact duplicates. v.clean can remove them.
Q: Can I ignore the areas without centroids?
A: Yes, these are typically holes in polygons (islands).
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https://www.ato.gov.au/forms-and-instructions/depreciating-assets-guide-2005/low-value-pools/working-out-the-decline-in-value-of-depreciating-assets-in-a-low-value-pool
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Search Suggestion:
# Working out the decline in value of depreciating assets in a low-value pool
Last updated 7 April 2020
Once you allocate an asset to a low-value pool, it is not necessary to work out its adjustable value or decline in value separately. Only one annual calculation for the decline in value for all of the depreciating assets in the pool is required.
You work out the deduction for the decline in value of depreciating assets in a low-value pool using a diminishing value rate of 37.5%.
For the income year you allocate a low-cost asset to the pool you work out its decline in value at a rate of 18.75% or half the pool rate. Halving the rate recognises that assets may be allocated to the pool throughout the income year. This eliminates the need to make separate calculations for each asset based on the date it was allocated to the pool.
To work out the decline in value of the depreciating assets in a low-value pool, add:
18.75% of:
• the taxable use percentage of the cost of low-cost assets you have allocated to the pool for the income year, and
• the taxable use percentage of any amounts included in the second element of cost for the income year of:
• all assets in the pool at the end of the previous income year, and
• low-value assets allocated to the pool for the income year,
and
37.5% of:
• the closing pool balance for the previous income year, and
• the taxable use percentage of the opening adjustable value of any low-value assets allocated to the pool for the income year.
Start of example
Example: working out the decline in value of depreciating assets in a low-value pool - ignoring any GST impact
During the 2004-05 income year, John bought a printer for \$990. John allocated low-cost assets to a low-value pool in the 2003-04 income year so he had to allocate the printer to the pool because it too was a low-cost asset. He estimated that only 60% of its use would be for taxable purposes. He therefore allocated only 60% of the cost of the printer to the pool - that is, \$594.
Assume that at the end of the 2003-04 income year, John had a low-value pool with a closing pool balance of \$5,000. John's deduction for the decline in value of the assets in the pool for the 2004-05 income year would be \$1,986. This is worked out as follows:
18.75% of the taxable use percentage of the cost of the printer allocated to the pool during the year (18.75% × \$594) \$111 Plus 37.5% of the closing pool balance for the previous year (37.5% × \$5,000) \$1,875
End of example
The closing balance of a low-value pool for an income year is:
• the closing pool balance for the previous income year
plus
• the taxable use percentage of the cost of any low-cost assets allocated to the pool for the income year
plus
• the taxable use percentage of the opening adjustable value of any low-value assets allocated to the pool for the income year
plus
• the taxable use percentage of any amounts included in the second element of cost for the income year of:
• assets in the pool at the end of the previous income year, and
• low-value assets allocated for the income year
less
• the decline in value of the assets in the pool for the income year.
Start of example
Example: Working out the closing balance of a low-value pool - ignoring any GST impact
Following on from the previous example above, assuming that John made no additional allocations to or reductions from his low-value pool, the closing balance of the pool for the 2004-05 income year would be \$3,608:
Closing pool balance for the 2003-04 income year \$5,000 plus the taxable use percentage of the cost of the printer \$594 less the decline in value of the assets in the pool for the income year (\$1,986)
End of example
QC27597
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# Skydiving Article - Ram Air Flight
Dynamics of the Ram Air Canopy
## Brian Germain
www.bigairsportz.com
If we achieve and cultivate a higher understanding of skydiving equipment, we will increase the. margin of safety in the sport.
The purpose of the following seminar is to examine and discuss the dynamic relationships of the ram air canopy in order to achieve a functional understanding of the modern parachute.
By "functional", I mean useful understanding that can help us in the real world.
By "dynamic", I mean the net result of two or more interactive variables, resulting in a phenomenon that would be otherwise unachievable but for the cooperative and complimentary forces joining to achieve a new level of possibility.
"Things derive their being and nature by mutual dependence and are nothing in themselves." Nagarjuna, Second century Buddhist philosopher
"An elementary particle is not an independently existing, analysable entity. It is, in essence, a set of relationships that reach outward to other things." H. P. Stapp, Twentieth century physicist
In order to fully understand the dynamics of the ram air parachute, one must consider all of the "players":
1) The parachute (the wing) Definitions of Orientation: (attitude)(axis of movement, relative to horizon)
a) Roll
b) Pitch
c) Yaw
2) The Pilot (Suspended Weight) ("G" Forces)
3) The Relative Wind Relationship of the Wing to the Wind ie., where you are Actually Going
One cannot understand flight in a comprehensive, synergistic manner without intimately lacing the actions of the wing to the air in which it is flying.
## Full Glide (static)
Angle of Incidence: Established by "Trim"
Airfoil Aspect Ratio Airspeed and "Glide Ratio effected by wing loading, trim, airfoil, and aspect ratio, and planform.
Similar size canopies will fly at about the same speed
## Braked Flight (static)
Depending on the design and wing loading, canopy may sink or glide flatter, decrease it's descent rate or increase it.
Braked Flight (dynamic characteristics):
## Slow Flare:
Phase 1: Initial Input (pitching) Airspeed diminishes slowly
"G's" stay near One "G" Descent rate decreases, but does not reach zero Angle of attack is not changed significantly, therefore minimal dynamic forces are exhibited.
Phase ll: Canopy reaches level flight below half brakes, or not at all. Usually ends in a hard touchdown, with no time for choices prior to actual landing.
## Quicker Flare(optimal dynamic pitch):
Phase 1: (initial Input) Airspeed diminishes somewhat
### Riggers Manual - Community Centre - Job Opportunities - Indoor Skydiving
E-Mail Skydive Safety
"G's" increase above One "G" Descent rate reaches zero, level flight before reaching the half brake position.
The "Sweet Spot: The part of the toggle stroke at which the parachute transitions it's airspeed into lift, sufficient to stop descending. The Sweet spot is generally higher at higher airspeeds, and lower when flying at low airspeeds. {It is not a location; it is a phenomenon.}
Phase II: Once in level flight at a high airspeed, the pilot is afforded the opportunity to change direction, as well as choose foot placement. As airspeed diminishes, more and more angle of attack (i.e., pitch change) is necessary to maintain level flight. The absence of more brakes as speed diminishes yields increased descent rate and a premature landing. Discussion of "Foot Skiing": diminishes stall speed "Arrested Progression" Technique (pop up)
## Stabbing Flare (flaring too hard):
Phase 1: (initial Input) Airspeed diminishes abruptly "G"s increase sharply and dramatically. Canopy climbs for a short time
Phase ll: Airspeed approaches zero, risking a stall. Releasing the brakes slightly and slowly is the only hope, but the chance of a soft landing are very low unless canopy is flown at a very low wing loading. Re flare is not usually an option, as airspeed is already gone.
## Turning:(No Brakes)
Asymmetric drag causes Roll axis change (bank) Roll creates Yaw "G" forces determine stability "G's" are dependant on angle of attack. Abrupt application of a single toggle often results in line twists. Likewise, abrupt reversal of the turn can an easily induce line twists. Pausing between turns will give the canopy a chance to "catch up" to coordinated flight and positive "G's", reducing the chances of line twists.
## Turning:(Brakes)
Low Speed, low line tension: Consider the possibility of line twists is quick turns. Maintain coordination to the relative wind. Turn slowly.
High Speed: Usually heavier toggle pressure and "G" forces, so risk of line twists is generally lower. Canopy is capable of level flight turns (no altitude loss), or even climbing turns. Many possibilities. (turn and flare, flare and turn...
## Rear Risers:
Lower drag method of increasing Angle of Attack High risk of stall, as angle of attack is being changed without the need for pilot position change, Swinging the Pitch)This results in a higher risk of high speed stall. Pushing out vs. Pulling Down.
## Weight Shift:
(works better with elliptical canopies) Pilot can accentuate or ameliorate the over steer tendency of the parachute lean into the turn to increase the over steer and recovery arc lean to the outside of the turn to decrease the over steer and dive tendency. Application during openings: Flying the canopy with weight shift prior to unstowing the toggles affords the pilot a chance to immediately steer the canopy following the opening. Over use of this technique too early in the opening can actually induce off heading openings and/or fine twists. Application for swooper's: If turn is too low: finish with weight shift.
## Flying in Unstable Conditions:
Concept One: Airspeed creates internal pressure. Higher pressure in the canopy yields a more stable wing. Concept Two: High angle of attack flight increases "G" forces and line tension. Higher line tension increases stability.
## Never:
Abruptly release control inputs in turbulence: (surge to line slack) Fly in deep brakes in turbulence. (not enough airspeed) Abruptly apply the front risers in turbulence. Continue a front riser turn if the front riser goes slack:
(apply brakes quickly) Fly behind large objects near the ground.
## Always:
Maintain a high airspeed when flying in turbulence. Release control inputs smoothly and slowly, or positively maintain angle of attack through positive pitch input when reversing direction. Notice line tension and "G" loading, and be prepared to apply brakes when wing surges forward and decreases in angle of attack.
In the event of canopy collapse:
1) Aggressively maintain heading with opposite toggle input.
2) Pull or pump the toggle on the collapsed side to re inflate it, if it has not already inflated.
## Airspeed: "Energizing the System"
Quickens all canopy responses to input. Parachute performs more like an airplane. More lift at the pilot's disposal.
More descent rate at the pilot's disposal
More "Response ability": The pilot has the ability to respond immediately with the appropriate control input.
When the pilot is over stimulated by the circumstances, he or she is less capable of performing complex tasks. If under stimulated, he or she is less capable due to lack of interest, and learns less from the experience.
Psychological Factors that may diminish pilot performance:
2) Canopy design too high performance for "Perceived Ability".
3) Too many new variables to process:
4) Skydive was too stimulating, and pilot is still recovering.
5) Flying technique is too aggressive for experience level.
6) Trying to execute a Preconceived Notion about how the landing will occur, rather than responding to the sensory input regarding the Actual Situation. Conditions Change. Response ability includes a malleable mind set, ready to adapt to the changing environment. Response ability requires the pilot to remain at the "Optimal Arousal level" at all times.
1.0 <100
1.1 100-199
1.2 200-299
1.3 300-399
1.4 400-499
1.5 500-599
1.6 600-699
1.7 700-799
1.8 800-899
1.9 900-999
2.0 1000+.
## Learn Through Experience:
1) Pull Higher! 2000 feet is just not enough time to learn
2) look at your canopy! l'
3) Try new things.
4) "Call Your Pocket" (decide where you are going to land and how prior to getting in the plane)
5) Fly Relative
## "Canopy Freeflying"
If we do not expect to be able to learn how to freefall without a reference with which to fly relative, why do we attempt to do so with our canopy piloting skills?
Skydiving is the least dangerous thing we do at the drop zone. It is canopy flight that matters most. Just look at the statistics...
## Manoeuvres to Practice:
1) Basic Proximity and Stillness (all speeds)
2) Slot swapping
a. Over and under
b. Behind the back
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# How to Build and Use a Pendulum
Co-authored by wikiHow Staff
Updated: June 6, 2019
A pendulum is a device that uses gravity to swing a weight back and forth. Because of their consistent and measurable swings, or oscillations as they’re called, pendulums have been used for hundreds of years to keep time. Part of the beauty of a pendulum is its simplicity. With a few supplies, you can build and use your own pendulum to try out different experiments to see how the physics of a pendulum work.
### Method 1 of 3: Making a Simple Pendulum
1. 1
Tape a pencil horizontally to the top of a table. Lay a pencil on its side and use clear tape to firmly fasten it to a tabletop. Leave about 12 inch (1.3 cm) of the pencil hanging over the edge. The pencil will anchor your pendulum and keep it from falling down, so be sure to use enough tape to secure it and keep it from moving around.[1]
• Test the pencil by flicking it with your finger. It should stay stuck to the tabletop.
2. 2
Tie a loop about 1 inch (2.5 cm) in diameter at one end of a string. Take a length of string 2–3 feet (0.61–0.91 m) long and curl one end to form a loop. The loop needs to fit around the pencil, but not too tight or it won’t swing properly. Tie a knot with the loop to keep it from coming undone.[2]
• Slide the loop onto the pencil and slide it off to make sure it’s not too tight.
3. 3
Make a small 12 inch (1.3 cm) hook with a metal wire. Take a 2 in (5.1 cm) length of metal wire and curl one end of it into a “J” shape to form your hook. The hook will hold the weight that swings the pendulum so shape your hook so it’s easy to attach and remove nuts onto it to alter the weight of the pendulum.[3]
• You can use pliers to curl the metal wire.
4. 4
Slide a 14 inch (0.64 cm) nut onto the end of the hook. Use a standard metallic nut as the weight for your pendulum. The hole in the center makes a nut ideal for sliding onto the hook, and you can easily add or remove nuts to experiment with different weights. Slide the nut onto the hook so that it’s not able to fall or slide off when the pendulum swings.[4]
• Do not close the hook around the nut.
Tip: Use nuts of the same size and weight so you can experiment with changing the weight to see how it affects the swing of the pendulum.
5. 5
Tape a piece of paper on a wall or table behind the hook. You can use the paper to mark where you release the pendulum each time so you can see the way the pendulum behaves and swings based on where you release it. Tape the paper so that it is a backdrop behind the hook with the nut on it.[5]
• Any color paper is fine, as long as you can see the pencil markings.
### Method 2 of 3: Experimenting with the Pendulum
1. 1
Pull the hook with the nut on it back about 20 inches (51 cm). Before you release it, use your pencil to mark on the paper taped behind the pendulum where you release it from. That way, you can repeat the experiment by letting the pendulum go from the same place each time.[6]
• You need to have a consistent release point for accurate results in your experiments!
2. 2
Release the pendulum and start a stopwatch. When you release the pendulum, count the number of oscillations, or the number of times it swings back and forth, for 1 minute. Repeat the process 5 times, releasing the pendulum from the same spot on the paper each time.[7]
• Let the pendulum fall on its own; don’t swing or push it.
• Write down the number of oscillations so you can calculate an average.
3. 3
Calculate the average of the oscillations. Take the number of oscillations from each time you released the pendulum, add them all together, then divide the number by 5. This is the average number of oscillations the pendulum completes from that distance and at that weight.[8]
For example: If you release the pendulum 5 times, and the number of oscillations you get are 9, 7, 8, 10, and 7, add up all of the numbers to get 41. Divide 41 by 5 to get 8.2 as an average number of oscillations for that experiment.
### Method 3 of 3: Testing the Physics of a Pendulum
1. 1
Add a nut to the hook to see what difference the mass makes. Add a second nut to the hook and bring the pendulum back to where you marked on the paper the first time. When you release the pendulum, start a stopwatch and count the number of oscillations for 1 minute. Repeat the process 5 times, then calculate your average.
• Notice the difference in the number of oscillations and the average between 1 nut on the hook and 2 nuts on the hook.
• Add another nut and repeat the experiment to see if even more mass will affect the pendulum’s oscillations.[9]
Spolier: Adding weight changes the mass of the pendulum, but mass doesn’t affect the swing rate of a pendulum, so your average number of oscillations should be almost the same, no matter the weight!
2. 2
Change the distance to see how it affects the oscillations. Go back to just 1 nut on the hook, bring the string back about 10 inches (25 cm), and make a mark on the paper taped behind it so you can repeat the experiment from the same distance. Release the pendulum and count the number of oscillations for 1 minute. Repeat the process 5 times and calculate an average.[10]
• You may be surprised to learn that the distance (also called amplitude) does not affect the swing rate, or number of oscillations.
• Try the experiment again from 5 inches (13 cm) and find the average number of oscillations to see how much of a difference the distance makes.
3. 3
Cut off 10 inches (25 cm) of the string to see the effects. Slide the look off of the pencil and cut off 10 inches (25 cm) of string, tie another loop, and put it back on the pencil. Then bring the pendulum back about 10 inches (25 cm) and mark on the paper where you release it from. Repeat the experiment 5 times and find the average number of oscillations to see how the length of the string affects the pendulum.
• Cut off another 10 inches (25 cm) of string to see the difference it makes on the average number of oscillations.
• The length from which a pendulum is suspended helps determine the speed and regularity of the swings, which is why pendulums have been used to keep time.[11]
## Community Q&A
Search
• Question
What's the swinging mass at the end of a pendulum?
Donagan
It's called a "bob."
• Question
What is the type of pendulum used to communicate with ghosts? Is there an article on that?
Tivababe77
Yes, several. You can search for "Use a Pendulum for Divination," "Use a Pendulum," and "Do a Spirit Guide Communication With a Pendulum" in WikiHow's search bar, or search for pendulums in a normal search engine to bring up results.
200 characters left
## Things You’ll Need
• A length of string about 2–3 feet (0.61–0.91 m) long
• 1 piece of metal wire 2 inches (5.1 cm) long
• 3-4 nuts 14 inch (0.64 cm) in size
• 1 piece of paper
• Pencil
• Clear tape
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# Scale diagram troubles!
1. Jul 11, 2004
### Physicshelpneeded
hey all...
Im having trouble with a question here that asks when only 2 forces act on an object (1: 8.0 to the right, 2: 12.0 N to the left) draw a scale diagram to determine the magnitude and direction of the resulting NET force.
anyone know how to do this?
anyone know how to draw a scale diagram PERIOD?
My professor forgot to explain this part but of course expects me to know the answer and do the homework correctly
anyways, thanks guys
2. Jul 11, 2004
### Staff: Mentor
He wants you to add those force vectors graphically: draw the first vector, then draw the second vector by placing its tail at the tip of the first vector, the sum is a vector from the tail of the first to the tip of the second. (Check your book if that's not clear.)
To add them properly, make sure that each vector is drawn to scale: that just means the length of the arrow should be proportional to the magnitude of the vector. For example: if you represent the 8 N force with an arrow 2 inches long, then the 12 N force better be an arrow 3 inches long.
3. Jul 11, 2004
### Physicshelpneeded
wow, thanx alot Doctor Al....that really helped me alot! ill do everything u suggested and see how it works out - thanx again
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## Determinant Modules
We will describe another construction for the Schur module.
Introduce variables $z_{i,j}$ for $i\ge 1, j\ge 1$. For each sequence $i_1, \ldots, i_p\ge 1$ we define the following polynomials in $z_{i,j}$:
$D_{i_1, \ldots, i_p} := \det{\small \begin{pmatrix} z_{1, i_1} & z_{1, i_2} & \ldots & z_{1, i_p} \\ z_{2, i_1} & z_{2, i_2} & \ldots & z_{2, i_p} \\ \vdots & \vdots & \ddots & \vdots \\ z_{p, i_1} & z_{p, i_2} & \ldots & z_{p, i_p}\end{pmatrix}}.$
Now given a filling T of shape λ, we define:
$D_T := D_{\text{col}(T, 1)} D_{\text{col}(T, 2)} \ldots$
where $\text{col}(T, i)$ is the sequence of entries from the i-th column of T. E.g.
Let $\mathbb{C}[z_{i,j}]$ be the ring of polynomials in $z_{ij}$ with complex coefficients. Since we usually take entries of T from [n], we only need to consider the subring $\mathbb{C}[z_{i,1}, \ldots, z_{i,n}]$.
Let $\mu = \overline \lambda.$ Recall from earlier that any non-zero $GL_n\mathbb{C}$-equivariant map
$\displaystyle \bigotimes_j \left(\text{Alt}^{\mu_j} \mathbb{C}^n\right) \longrightarrow \bigotimes_i \left(\text{Sym}^{\lambda_i} \mathbb{C}^n \right)$
must induce an isomorphism between the unique copies of $V(\lambda)$ in the source and target spaces. Given any filling T of shape $\lambda$, we let $e^\circ_T$ be the element of $\otimes_j \text{Alt}^{\mu_j} \mathbb{C}^n$ obtained by replacing each entry k in T by $e_k$, then taking the wedge of elements in each column, followed by the tensor product across columns:
Note that the image of $e^\circ_T$ in $F(V)$ is precisely $e_T$ as defined in the last article.
Definition. We take the map
$\displaystyle \bigotimes_j \left(\text{Alt}^{\mu_j} \mathbb{C}^n\right) \longrightarrow \bigotimes_i \left(\text{Sym}^{\lambda_i} \mathbb{C}^n \right), \quad e_T^\circ \mapsto D_T$
where $z_{i,j}$ belongs to component $\text{Sym}^{\lambda_i}.$
E.g. in our example above, $D_T$ is homogeneous in $z_{1,j}$ of degree 5, $z_{2,j}$ of degree 4 and $z_{3,j}$ of degree 3. We let $g \in GL_n\mathbb{C}$ act on $\mathbb{C}[z_{i,j}]$ via:
$g = (g_{i,j}) : z_{i,j} \mapsto \sum_k z_{i,k}g_{k,j}.$
Thus if we fix i and consider the variables $\mathbf z_i := \{z_{i,j}\}_j$ as a row vector, then $g: \mathbf z_i \mapsto \mathbf z_i g^t$. From another point of view, if we take $z_{i,1}, z_{i,2},\ldots$ as a basis, then the action is represented by matrix g since it takes the standard basis to the column vectors of g.
Proposition. The map is $GL_n\mathbb{C}$-equivariant.
Proof
The element $g = (g_{i,j})$ takes $e_i \mapsto \sum_j g_{j,i} e_j$ by taking the column vectors of g; so
$\displaystyle e_T \mapsto \sum_{j_1, \ldots, j_d} g_{j_1, i_1} g_{j_2, i_2} \ldots g_{j_d, i_d} e_{T'}$
where T’ is the filling obtained from T by replacing its entries $i_1, \ldots, i_d$ with $j_1, \ldots, j_d$ correspondingly.
On the other hand, the determinant $D_{i_1, \ldots, i_p}$ gets mapped to:
$\det{\small \begin{pmatrix} z_{1, i_1} & z_{1, i_2} & \ldots & z_{1, i_p} \\ z_{2, i_1} & z_{2, i_2} & \ldots & z_{2, i_p} \\ \vdots & \vdots & \ddots & \vdots \\ z_{p, i_1} & z_{p, i_2} & \ldots & z_{p, i_p}\end{pmatrix}} \mapsto \det{\small \begin{pmatrix} \sum_{j_1} z_{1,j_1} g_{j_1, i_1} & \ldots & \sum_{j_p} z_{1, j_p}g_{j_p i_p}\\ \sum_{j_1}z_{2, j_1} g_{j_1, i_1} & \ldots & \sum_{j_p} z_{2, j_p}g_{j_p, i_p} \\ \vdots & \ddots & \vdots \\ \sum_{j_1} z_{p, j_1} g_{j_1, i_1} & \ldots & \sum_{j_p} z_{p, j_p} g_{j_p, i_p} \end{pmatrix}}$
which is $\sum_{j_1, \ldots, j_d} g_{j_1, i_1} \ldots g_{j_d, i_d} D_{T'}$. ♦
Since $\otimes_j \text{Alt}^{\mu_j} \mathbb{C}^n$ contains exactly one copy of $V(\lambda)$, it has a unique $GL_n\mathbb{C}$-submodule Q such that the quotient is isomorphic to $V(\lambda).$ The resulting quotient is thus identical to the Schur module F(V), and the above map factors through
$F(V) \to \otimes_i \text{Sym}^{\lambda_i} \mathbb{C}^n, \quad e_T \mapsto D_T.$
Now we can apply results from the last article:
Corollary 1. The polynomials $D_T$ satisfy the following:
• $D_T = 0$ if T has two identical entries in the same column.
• $D_T + D_{T'} = 0$ if T’ is obtained from T by swapping two entries in the same column.
• $D_T = \sum_S D_S$, where S takes the set of all fillings obtained from T by swapping a fixed set of k entries in column j’ with arbitrary sets of k entries in column j (for fixed j < j’) while preserving the order.
Proof
Indeed, the above hold when we replace $D_T$ by $e_T.$ Now apply the above linear map. ♦
Corollary 2. The set of $D_T$, for all SSYT $T$ with shape λ and entries in [n], is linearly independent over $\mathbb{C}.$
Proof
Indeed, the set of these $e_T$ is linearly independent over $\mathbb{C}$ and the above map is injective. ♦
### Example 1.
Consider any bijective filling T for $\lambda = (2, 1)$. Writing out the third relation in corollary 1 gives:
$\left[\det\begin{pmatrix} a & c \\ b & d\end{pmatrix}\right] x = \left[\det\begin{pmatrix} x & c \\ y & d\end{pmatrix}\right] a + \left[ \det\begin{pmatrix} a & x \\ b & y\end{pmatrix}\right] c.$
More generally, if $\lambda$ satisfies $\lambda_j = 2$ and $\lambda_{j'} = 1$, the corresponding third relation is obtained by multiplying the above by a polynomial on both sides.
### Example 2: Sylvester’s Identity
Take the $2 \times n$ SYT by writing $1,\ldots, n$ in the left column and $n+1, \ldots, 2n$ in the right. Now $D_T = D_{1,\ldots, n}D_{n+1, \ldots, 2n}$ is the product:
$\det \overbrace{\begin{pmatrix} z_{1,1} & z_{1,2} & \ldots & z_{1,n} \\ z_{2,1} & z_{2,2} &\ldots & z_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ z_{n,1} & z_{n,2} & \ldots & z_{n,n} \end{pmatrix}}^M \det \overbrace{\begin{pmatrix} z_{1,n+1} & z_{1,n+2} & \ldots & z_{1,2n} \\ z_{2,n+1} & z_{2,n+2} &\ldots & z_{2,2n} \\ \vdots & \vdots & \ddots & \vdots \\ z_{n,n+1} & z_{n,n+2} & \ldots & z_{n,2n} \end{pmatrix}}^N.$
In the sum $D_T = \sum_S D_S$, each summand is of the form $D_S= \det M' \det N'$, where matrices M’N’ are obtained from MN respectively by swapping a fixed set of k columns in N with arbitrary sets of k columns in M while preserving the column order. E.g. for n=3 and k=2, picking the first two columns of N gives:
\begin{aligned} \det ( M_1 | M_2 | M_3) \det(N_1 | N_2| N_3) &= \det(N_1 | N_2 | M_3) \det(M_1 | M_2 | N_3) \\ +\det(N_1 | M_2 | N_2) \det(M_1 | M_3 | N_3) &+ \det(M_1 | N_1 | N_2) \det(M_2 | M_3 | N_3).\end{aligned}
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# Quick Answer: How Do You Calculate Price Per Gallon?
## How much is 1.30 per Litre in gallons?
As a rough guide £1.00 per litre is £4.56 per gallon, £1.09 per litre is £5.00 per gallon, £1.15 per litre is £5.25 per gallon, £1.20 per litre is £5.47 per gallon and £1.32 per litre is £6.00 gallon, £1.43 per litre is £6.50 per gallon and £1.54 per litre is £7.00 per gallon.
(1 litre = 0.219 969 248 3 gallon.).
## How many miles can you drive with 12 gallons of gas?
For example, if your car averages 25 miles per gallon on the highway and has a 12-gallon fuel tank, its range is 25 x 12 = 300 miles.
## What is 30 miles per gallon in Litres?
Convert MPG to Litres/100 km We have converted 30 Miles per Gallon to 9.4 Litres per 100 kilometres.
## Is 3 liters more than a gallon?
Not to any current gallon, though possibly there was once a gallon corresponding to 3 litres. Current Gallons – Wikipedia are: US gallon (about 3.785 l) US dry gallon (about 4.405 l)
## How many Litres of fuel does a car hold?
Most average tank size of a car can carry something between 45 and 65 liters. However, SUVs and trucks have larger tanks while the size is smaller for the Nano cars. Some vehicles have a secondary fuel tank called the reserve tank, which contains approximately 15% of the capacity of the primary chamber.
## What is good miles per gallon?
Don’t expect to attain higher than 20 mpg overall with a non-hybrid, and most offer less than 30 mpg on the highway. The best fuel-efficient non-electric vehicles get the following EPA-estimated combined numbers: Small Pickup: Chevrolet Colorado 2WD Diesel and GMC Canyon 2WD Diesel get 23 mpg.
## How much does it cost to fill up your car?
Smaller cars generally have gas tanks that hold 12 gallons worth of gas, while larger cars can hold 15 or 16 gallons. For the purpose of this story, let’s say gas costs \$3.85 a gallon. A car with a 12-gallon tank costs \$46.20 to fill up while a larger car with a 15-gallon tank costs \$57.75.
## How many gallons of gas can you get for \$10?
4 gallons1 Expert Answer Best way to start this is to figure out how much gas you can get for that \$10. Since gas is \$2.50/gallon and you buy \$10 worth, that says you’ll get 4 gallons of gas (\$2.50 * 4 = \$10).
## Does 4 liters equal 1 gallon?
An easy way to figure from liters to gallons, for example, is that a quart is a little less than a liter and 4 liters is a little more than 1 gallon. To be exact, 1 liter is 0.264 gallon (a little more than a quart), and 4 liters is 1.06 gallons.
## How many 1 liter bottles are in a gallon?
3.8A 1 liter bottle of water is approximately 33.8 ounces, so approximately 3.8 of these bottles make up a gallon.
## How do you calculate fuel?
How fuel consumption is calculatedDivide the distance by the litres used to get the km/litre.Convert the km/litre to L/100 km i.e. divide 100 by km per litre.Convert km/litre to miles per gallon i.e. multiply km/litre by 2.825.
## How many gallons of gas is \$20?
a little over 10 gallons. A little over 10 gallons. Just over half of a tank.
## How do you calculate cost per Litre?
To estimate the fuel cost for a trip you must know the trip distance, the average per litre cost of fuel and the vehicle’s fuel consumption.Divide the trip distance by 100.Multiply the result of this by the fuel consumption.Then multiply this figure by the cost of fuel/litre.
## HOW FAR CAN 4 gallons of gas take you?
As a general rule, most cars have about 2.5 gallons left in the tank when the gas light comes on. So depending on how many miles you get per gallon, you can probably go anywhere between 30-60 miles.
## How much is a 1 gallon?
The US liquid gallon (frequently called simply “gallon”) is legally defined as 231 cubic inches, which is exactly 3.785411784 litres. A US liquid gallon of water weighs about 8.34 pounds or 3.78 kilograms at 62 °F (17 °C), making it about 16.6% lighter than the imperial gallon.
## How far can you go with 1 Litre of petrol?
Anything that is listed as less than 6-litres/100km or more than 16.5km/1-litre is considered to be pretty good. The first (and most common) reference is litres per 100km (litres/100km). This is how many litres of fuel the car needs in order to travel 100km. You’ll often see it referred to as ‘fuel economy’.
## How do you convert price per Litre to price per gallon?
Divide the gas price (per U.S. gallon) by the number of liters in a gallon, 3.78541. The result is the gas price per liter.
## How far can 20 dollars worth of gas get you?
You mean how far does 20 bucks get ME? Right around 150-170 miles.
## Is a gallon more than 2 liters?
1 US fluid gallon is equal to 3.785411784 liters and 1 Imperial gallon is equal to 4.54609 liters. The symbol is “gal”. The US fluid gallon is defined as 231 cubic inches (3.785411784 liters), the US dry gallon is defined as 1⁄8 US bushel (4.4048838 liters) and the imperial gallon is defined as 4.54609 liters.
## How many Litres is 4 gallons of water?
Converting US Gallons and LitersUS GallonsLiters1 US Gallon3.78541 Liters2 US Gallons7.57082 Liters3 US Gallons11.35624 Liters4 US Gallons15.14165 Liters16 more rows
## How do you figure out how much a gallon of gas cost?
Add up Your Trip Cost Take the mileage of the total distance of your trip and divide it by your miles per gallon to get the number of gallons of gas you will need on your trip. Then multiply that figure by the current price of gas, and the result is the estimated cost of gas for your road trip.
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# JAM 2022 [ 41 -50]
Let X and Y be two independent and identically distributed random variables having U(0,1) distribution. Then P(X^2 < Y < X equals _________________ (round off to 2 decimal places)
Since whenever, 0< x < 1 , x^2 < x
\begin{align*}
P (X^2 < Y < X) &= \int_{0}^{1} \int_{x^2}^{x} dy dx \\
&= \int_{0}^{1} (x-x^2) dx \\
&= \left[ \frac{x^2}{2} - \frac{x^3}{3} \right]_{0}^{1} \\
&= \frac{1}{6} = 0.1667
\end{align*}
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# Averages
In these notes, we will learn the basic of averages, median and mode. To begin with, first
please note that Arithmatic mean, average, or simply the mean have same definition, meaning
these are different words for same concept.
Definition:
Arithmatic mean, or the average of a certain set of N numbers is simply equal to the sum of
those numbers divided by N.i.e
Average of N numbers =
And that is all. So, to find average of 4 numbers, we will first add (+) all the four numbers, and
then divide the result by 4. This will be equal to their Mean, Arithmatic mean or Average.
## Next thing to understand is that average of some
numbers is somewhat Central or Middle Value of all the numbers. In other words, it lies in
the centre of the set of numbers. See the example below to understand:
Q:1
Q.1 If the average of 5,6,7 and w is 8. What is the value of w?
A. 8
B. 12
C. 14
D. 16
E. 24
Solution:
As we studied above, just apply formula of average and put average = 8, As there are 4
numbers (5,6,7 and w), so N=4 here.
Average of N numbers =
8=
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Move 4 to left side: 8x4 = 5+6+7+w
OR: 32=18+w
OR: 32-18 = w
## Remember: Average is the middle value or central value of a data set.
Here Average should be 8, but all the 3 numbers given are 5,6 and 7 which are smaller than 8,
so to make the middle value equal to 8, the fourth number (.i.e w) should be much greater
than 8. To cover the effect of 3 numbers, it should be like 14 or 16. So, just looking at options,
you must know that option A can never be the answer. Similarly E is just too big.
Q:2
Q.2 The average of five numbers is 54. If three of the numbers are 26, 28 and 30,
then what is the average of other two?
A. 91
B. 93
C. 54
D. 186
Solution:
Before solving, just think, if first 3 numbers are 26,28 and 30, then what should be the last two
to make overall average equal to 54. As average is central value of a data set, therefore, the last
numbers (or their average) should be much higher than 54 to balance these smaller numbers.
Looking at options, I guess answer is option A or B. Option C is impossible, option D is just
too big.
Now apply formula of average on all the five numbers, letting last two unknown numbers are
M and N.
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Average of N numbers =
54 =
## Move 5 to left side: 54x5 = 26+28+30+M+N
OR: 270=84+M+N
OR: M+N=270-84=186
## Finally: Average of M and N = 186/2
= 93 (Option B)
Remember: Answer what is being asked in the question and NOT what do you think should
Here what was asked was AVERAGE of last two numbers, NOT SUM of last two numbers. If
you just find M+N=186, and mark answer (D) (=186), it would be foolishly wrong. So, tip is to
calculations like we did here.
Q:3
Q.3 Ahmad took 5 Chemistry tests during the semester and average of his test scores
was 85. If his average after first three tests was 83, what was the average of his
fourth and fifth test?
A. 83
B. 85
C. 87
D. 88
E. 90
Solution:
Before solving, just think, if the total average of 5 tests is 85, and average of first three tests is
83, then the average of last two tests must be greater than 85 so that NET average of 5 tests
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becomes equal to 85. Moreover, as first 3 tests average is 2 less than final average (85-83=2),
the average of last two tests should be greater than 85 even more than 2!! Because there are 3
tests on 83, and here are only two tests to Balance those 3 tests, so their average should be
even greater. So, answers A, B and C are impossible (Got it??). Answer must be D or E.
## Now solving, for average of 5 tests = 85;
So, Total score of 5 tests = 85 x 5 = 425. [Average = Sum/5 - Sum = Average x 5]
Similarly, Score of first 3 tests = 83 x 3 = 249.
So, score of last 2 tests = score of total 5 tests Score of first 3 tests;
= 425 249 = 176.
So, average of last 2 tests = Score of last 2 tests / 2 = 176/2 = 88 (D).
Q:4
Q.4 If x + y = 6, y + z = 7 and z + x = 9. What is the average of x, y and z?
A. 11/3
B. 11/2
C. 22/3
D. 11
E. 22
Solution:
Average of x, y and z =
Remember: When you are given two equations in a questions, add (+) them or subtract (-)
them. When there are three equations, just add (+) them !! You will MOST PROBABLY get your
## Adding: 2x + 2y + 2z = 6+7+9 = 22.
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Dividing by 2:
Or: x + y + z = 11,
As we have to find (x+y+z)/3, so divide whole equation by 3 to get Average = 11/3 (A). Here
once again, if you had stopped at x+y+z=11 and marked answer = D, that would be wrong.
First carefully understand what is being asked!!
Q:5
Q.5 On Thursday, 20 of the 25 students took a Chemistry test and their average was
80. On Friday, the other 5 students took the test and their average was 90. What was
the average of entire class?
Solution:
Before solving, just think, if the average of 20 students is 80 and remaining 5 students is 90.
The overall average must be between 80 and 90. Next, as more students are towards 80 (Only 5
students are towards 90), so average is more close to 80 than 90.i.e answer must be something
between 80 and 85.
Now solving, for for first 20 students:
So, Total score of 20 students = 80 x 20 = 1600. [Average = Sum/20 - Sum = Average x 20]
And, Score of other 5 students = 90 x 5 = 450.
So, Total Score =1600+450 = 2050. .
So, Net average of whole (entire) class = 2050/25 = 410/5 = 82. (ANS).
Q:6
Q.6 What is the average of all positive integers from 1 to 100?
A. 49
B. 49.5
C. 50
D. 50.5
E. 51
Solution:
Average of 100 numbers = ;
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Now we can NOT add all numbers manually, so please remember the following formula to
find sum of n numbers in an Arithematic Sequence:
a1 + an]
Where:
S = Sum of N numbers.
N = Number of terms. (Here N = 100)
a1 = First term of sequence (Here a1 = 1)
an = Last term of sequence (Here an = 100).
So,
Sum = S = 100/2 x (1+100) = 50 x (101).
Or, Average = S/100 = 50/100 x 101 = 101/2 = 50.5 (D).
Median:
When a set of numbers is arranged in an order .i.e either Ascending order (from smallest
number to largest number) or Descending order (from largest number to smallest number), the
Middle number is called Median.
1. When total numbers in a data set are odd, then the data will have only 1 middle value
which will be its median. e.g for the following data set:
11,13,15,17,21,29,36.
There are total 7 numbers (hence odd), and all numbers are already arranged in
ascending order, so middle value is the median of this data which is 17. It is at the
centre of the data from either end.
2. When total numbers in a data set are even, then the data will have 2 middle values.
Median will then be equal to average of these two middle values. e.g for the following
data set:
11,13,15,17,21,29,36,39,40,45.
There are total 10 numbers (hence even), and all numbers are already arranged in
ascending order, so there are two middle values which are 21 and 29. They are at the
centre from both ends. So, Median of data set= (21+29)/2 = 50/2 = 25
## Remember: It is NECESSARY to arrange the data in Ascending or Descending order before
findng median, meaning you CAN NOT find median from an un-arranged data set.
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Mode:
The value which repeats most frequently in a data set is called MODE. So, mode is a value
which comes greatest number of times in a data set.
## 1. For example, in the data set:
11,13,11,17,21,13,25,13,25,36.
13 is repeated more than any other value (3 times), so mode = 13.
2. When two values repeat equal number of times, then the data will have 2 modes. e.g for
the following data set:
11,13,11,17,21,13,25,13,25,36,11
Both 11 and 13 are repeated 3 times, so data has 2 modes, 11 and 13.
Q:7
Q.7 During a ten day period, Azhar received following number of phone calls each
day, 2,3,9,3,5,7,7,10,6,7. What is the average of median and mode of this data?
A. 6
B. 6.25
C. 6.5
D. 6.75
E. 7
Solution:
Average of Median and Mode = (Median + Mode) / 2.
1. Median:
First arrange data in ascending order:
2,3,3,5,6,7,7,7,9,10.
As total values are even (.i.e.10), so median is average of two middle values which are
6 and 7. So median = (6+7)/2 = 6.5.
2. Mode:
In given data, 7 repeats more than any other value (3 times), so Mode = 7.
Finally: Ans = (Median + Mode) /2 = (6.5+7)/2 = 13.5/5 = 6.75 (D).
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EXERCISES
Q.1 What is the average of three interior angles of a triangle?
[HINT: From geometry, sum of interior angles of a triangle = S = 180 degree, so average = S/3 = 60 0]
ANS=600.
A. 0.75
B. 10.5
C. 12
D. 27
ANS=D
## Remember: To avoid calculation of decimal numbers, one way is to remove decimal
Point. For this, just write the number without decimal point and divide by number with
Zeros equal to number of digits AFTER decimal point. Then do cutting before
multiplication.e.g:
4.25 = 425/100 = 85/20 = 17/4
## Q. 3 If the average of 3,5,10 and S is 6. What is the value of S?
A. 4
B. 6
C. 12
D. 0
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[HINT: Average = S/n - 6 = (3+5+10+S)/ 4 - 6x4 = 24 = 18+S -S=24-18 =6]
ANS=B
A. 359
B. 39+319+329
C. 357
D. 311+321+331
## [HINT: Average = S/n - Mean = = + =
310-1+320-1+330-1= 39+319+329. For details on exponents and power rules, plz see the notes
Exponents. ]
ANS=B
## Q. 5 If 20x+20y=70, What is the average of x and y?
A. 7/2
B. 7
C. 7/4
D. 4/7
[HINT: Average of x and y = (x+y)/2; first divide whole given equation by 20 to get: x+y = 70/20 =
7/2, but we have to find (x+y)/2 , {not x+y}, so just divide whole equation by 2 again to get (x+y)/2 =
7/2 2 = 7/2x1/4 = 7/4]
ANS=C
## Q. 6 Which of the following is the average of x4 - 20, 40 - x4 and 3x + 4?
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A. X4 24
B. X+8
C. X4 + 3x +24
D. X + 24
## [HINT: As these are 3 polynomials, so average = S/3 = (x4 20 + 40 - x4 +3x + 4)/3 =
(3x+24)/3 = 3x/3 + 24/3 = x+8]
ANS=B
## Q. 7 If 10a+10b=35, What is the average of a and b?
[HINT: Just like question#5, divide whole equation by 10, a+b = 35/10 = 7/2, now divide by 2,
Average = (a+b)/2 = 7/4 = 1.75.]
ANS=7/4 or 1.75
A.
B.
C.
D.
E.
]
ANS=E.
## Q. 9 Find the average of 210 and 220 ?
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A. 215
B. 25+210
C. 29 +219
D. 229
E. 30
## [HINT: Average = S/n - Mean = = + =
210-1+220-1= 29+219. For details on exponents and power rules, plz see the notes Exponents.]
ANS=C
Q. 10:
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[HINT: Average = S/n, These are total 8 angles (a,b,c,d,e,f,g and h), so n = 8. From geometry, angles
around a complete circle is 360 degree, so a+b+c+d = 360 and also e+f+g+h = 360, So, average =
(a+b+c+d+e+f+g+h) / 8 = (360+360)/8 = 720/8 = 90]
ANS=C
Q. 11 Kashifs average score on first 4 tests is 80. What score should he get on fifth test to
make his overall average of five tests equal to 84?
A. 82
B. 84
C. 92
D. 96
E. 100
[HINT: To balance 4 tests on lower side of 84, answer must be much higher than 88. i.e Total score of
5 tests = 84x5 = 420. Score in first 4 tests = 80x4=320, so fifth tests score = 420-320=100]
ANS=E
Q. 12 Kashifs average score on first 4 tests is 80. If total score on each test is 100, then
what minimum score can he get on fifth test and still have a chance to make his average of
7 tests equal to 85?
A. 60
B. 70
C. 75
D. 80
E. 85
[HINT: Score in first 4 tests = 80x4 = 320, now to make average of 7 tests equal to 85, total score in
7 tests = 85x7 = 595. So, score in 5th + 6th+ 7th test (last 3 tests) = 595-320 = 275. Now if he wants
to score minimum (LEAST) on fifth test, he must get maximum on sixth and seventh test, i.e he should
get 100 marks each in 6th and 7th test, so MINIMUM score in 5th test = 275 100 100 = 75]
ANS=C
## Q. 13 The average of all even integers from 2 to 100 is?
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A. 50
B. 50.5
C. 49.5
D. 51
E. 100
[HINT: By arithmetic sum formula: S = n/2 x (2+100) = n/2 x (102) = nx51. So, average = Sum/n =
S/n = (nx51)/n = 51. n=50 here, but as you see, question can be solved even without the value of n]
ANS=D
Q. 14 Eight students in a class get 60% marks, 3 students get 75%, 2 get 80% and 7 get
45% in a test. What are the average marks of whole class?
A. 49%
B. 29%
C. 51%
D. 59%
## [HINT: Sum = 8x60% + 3x75% + 2x80% + 7x45% = 480%+225%+160%+315% = 1180%. Total
students = n = 8+3+2+7=20, So, average = Sum/n = 1180%/20 = 118%/2 = 59% ]
ANS=D
Q. 15 Salman is paid R rupees per hour for first 8 hours of job daily. For every hour after
the first 8 hours, he is paid S rupees per hour. If he works 12 hours in a daily, what is his
average hourly income of the day?
A.
B.
C.
D.
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[HINT: Total hours = 12, for first 8 hours, income = 8R and for last 4 hours, income = 4S, so total
income of 12 hours = (8R+4S), so average income = (8R+4S)/12 = (2R+S)/3 ]
ANS=D
Q. 16 Asim had an average of 60 on first 4 math tests. After taking fifth test, his average
dropped to 58. What was his fifth test score?
A. 32
B. 40
C. 48
D. 50
[HINT: 4 tests score = 60x4=240. Total 5 tests score = 58x5=290. So, fifth test score = 290-240=50]
ANS=D
## Q. 17 What is the average of interior angles of a pentagon?
[HINT: Remember a formula from geometry, for a polygon (any closed figure) of N sides:
x 1800
For example, for a triangle, N=3, so sum of interior angles = (3-2)x180 = 1800. Now a pentagon has 5
sides, so Sum of interior angles = (5-2)x1800 = 3x1800, so average = S/5 = 3x180/5 = 3x36 = 1080]
ANS=108 degrees
## Q. 18 Let M be the Median and m be the mode of following set of numbers:
10,70,20,40,70,90. What is the average of M and m?
A. 50
B. 55
C. 60
D. 62.5
E. 65
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# Math
1/x+1-1/x+2=1/6
Must have 2 solutions
1. 👍
2. 👎
3. 👁
1. 1 / x + 1 - 1 / x + 2 = 1 / 6
1 / x - 1 / x + 1 + 2 = 1 / 6
3 = 1 / 6
Makes no sense.
1. 👍
2. 👎
2. however,
1/(x+1) - 1/(x+2) = 1/6
can be solved by rewriting it as
6(x+2) - 6(x+1) = (x+1)(x+2)
6x + 12 - 6x - 6 = x^2 + 3x + 2
x^2 + 3x - 4 = 0
(x+4)(x-1) = 0
x = -4,1
Now you know how useful parentheses can be. Always use them when posting problems where it's not clear how to group the terms.
1. 👍
2. 👎
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How to
# 14 an inferior good is one for which an increase in income causes a(n) Tutorial
You are reading about an inferior good is one for which an increase in income causes a(n). Here are the best content from the team nguyendinhchieu.edu.vn synthesized and compiled from many sources, see more in the category How To.
### Price increase – inferior good
Price increase – inferior good
Price increase – inferior good
### Economics Help [1]
An inferior good occurs when an increase in income causes a fall in demand. An inferior good has a negative income elasticity of demand
For example, if average incomes rise 10%, and demand for holidays in Blackpool falls 2%. When income rises, people can afford to forego the cheap alternative and buy the higher quality good instead
But, when his income rises, he will afford better quality foods, such as fine bread and meat. When income rises you buy better quality, more expensive tea.
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An inferior good is one for which an increase in income causes a(n). If a small percentage increase in the price of a good greatly reduces the quantity demanded for that good, the demand for that good is
The law of supply states that an increase in the price of a good:. If the income elasticity of demand for a good is negative, it must be:
According to ———– when income increases by a small increment, it leads to increasing marginal utility of income. Which of the following would cause a demand curve for a good to be price inelastic?
### Inferior good [3]
This article needs additional citations for verification. In economics, an inferior good is a good whose demand decreases when consumer income rises (or demand increases when consumer income decreases),[1][2] unlike normal goods, for which the opposite is observed.[3] Normal goods are those goods for which the demand rises as consumer income rises.[2][4]
As a rule, these goods are affordable and adequately fulfill their purpose, but as more costly substitutes that offer more pleasure (or at least variety) become available, the use of the inferior goods diminishes. Direct relations can thus be drawn from inferior goods to socio-economic class
Depending on consumer or market indifference curves, the amount of a good bought can either increase, decrease, or stay the same when income increases.[2]. A number of economists have suggested that shopping at large discount chains such as Walmart and rent-to-own establishments vastly represent a large percentage of goods referred to as “inferior”
### Demand and Income [4]
Consumer income (Y) is a key determinant of consumer demand (Qd). The relationship between income and demand can be both direct and inverse.
For example, for most people, consumer durables, technology products and leisure services are normal goods.. In the case of inferior goods income and demand are inversely related, which means that an increase in income leads to a decrease in demand and a decrease in income leads to an increase in demand
It should be noted that ‘normal’ and ‘inferior’ are purely relative concepts. Any good or service could be an inferior one under certain circumstances
### Inferior good [5]
This article needs additional citations for verification. In economics, an inferior good is a good whose demand decreases when consumer income rises (or demand increases when consumer income decreases),[1][2] unlike normal goods, for which the opposite is observed.[3] Normal goods are those goods for which the demand rises as consumer income rises.[2][4]
As a rule, these goods are affordable and adequately fulfill their purpose, but as more costly substitutes that offer more pleasure (or at least variety) become available, the use of the inferior goods diminishes. Direct relations can thus be drawn from inferior goods to socio-economic class
Depending on consumer or market indifference curves, the amount of a good bought can either increase, decrease, or stay the same when income increases.[2]. A number of economists have suggested that shopping at large discount chains such as Walmart and rent-to-own establishments vastly represent a large percentage of goods referred to as “inferior”
### What is Inferior Goods? Definition of Inferior Goods, Inferior Goods Meaning [6]
Proposed definitions will be considered for inclusion in the Economictimes.com. Definition: An inferior good is a type of good whose demand declines when income rises
Description: For example, there are two commodities in the economy — wheat flour and jowar flour — and consumers are consuming both. Presently both commodities face a downward sloping graph, i.e
If the income of consumer rises, then he would be more inclined towards wheat flour, which is a little costly than jowar flour.. The mindset of the consumer behind this behavior is that now he can afford wheat flour because of his increase in income
### An inferior good is one for which an increase in income causes a(n) [7]
The buyers and sellers must trade an identical item. If there is no excess demand or excess supply, the market will be in equilibrium
There will be a fall in quantity supplied and a rise in quantity demanded. There will be a fall in quantity supplied and a rise in demand
There will be a fall in supply and a rise in demand
### What factors change demand? (article) [8]
– Substitution and income effects and the law of demand. – Lesson summary: Demand and the determinants of demand
Changes in factors like average income and preferences can cause an entire demand curve to shift right or left. This causes a higher or lower quantity to be demanded at a given price.
This article talks about what happens when other factors aren’t held constant.. We defined demand as the amount of some product a consumer is willing and able to purchase at each price
### Economics 504 [9]
The law of demand states that consumers will purchase more of a good at. The law of supply states that producers will sell less of a good at lower prices
When equilibrium exits, the quantity people plan to buy is equal to the. The laws of demand and supply cause the market to move to equilibrium.|
An increase in demand is depicted as a rightward shift of the demand. An increase in demand means that consumers plan to purchase more of
### Income Elasticity of Demand: Meaning & Calculation [10]
Would you afford to buy an item you wanted if your income increased by 20% in a particular month? The answer will differ from person to person because their incomes and preferences are different, and their consumption decisions react to changes differently. Eager to learn more? Let’s talk about the income elasticity of demand.Income elasticity of demand measures the responsiveness of…
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Eager to learn more? Let’s talk about the income elasticity of demand.. Income elasticity of demand measures the responsiveness of the quantity demanded to a change in consumer income.
### 3.1 Demand – Principles of Economics [11]
– Define the quantity demanded of a good or service and illustrate it using a demand schedule and a demand curve.. – Distinguish between the following pairs of concepts: demand and quantity demanded, demand schedule and demand curve, movement along and shift in a demand curve.
How many pizzas will people eat this year? How many doctor visits will people make? How many houses will people buy?. Each good or service has its own special characteristics that determine the quantity people are willing and able to consume
The number of pizzas people will purchase, for example, depends very much on whether they like pizza. It also depends on the prices for alternatives such as hamburgers or spaghetti
### [Solved] A good for which demand decreases with increase in income of [12]
A good for which demand decreases with increase in income of consumer is called. – As the income of the consumer increases, the demand for an inferior good falls, and as the income decreases, the demand for an inferior good rise.
– Inferior goods demand is inversely proportional to the income of consumers.. |Giffen goods||A Giffen good is a low income, non-luxury product for which demand increases as the price increases and vice versa||bread rising in price because people lacked the income to buy meat|
|Substitute Goods||Goods which are a substitute for each other||tea and coffee|. IB ACIO Notification 2023 is expected to be released soon
### Reading: Other Types of Elasticity [13]
The basic idea of elasticity—how a percentage change in one variable causes a percentage change in another variable—does not just apply to the responsiveness of supply and demand to changes in the price of a product. Recall that quantity demanded (Qd) depends on income, tastes and preferences, population, expectations about future prices, and the prices of related goods
Elasticity can be measured for any determinant of supply and demand, not just the price.. The income elasticity of demand is the percentage change in quantity demanded divided by the percentage change in income, as follows:
For most products, most of the time, the income elasticity of demand is positive: that is, a rise in income will cause an increase in the quantity demanded. This pattern is common enough that these goods are referred to as normal goods
### Difference Between Normal Goods and Inferior Goods (with Comparison Chart) [14]
The goods whose demand tends to increase as the income of the consumer rises are called normal goods. As against this, inferior goods are the goods which encounter a fall in demand as the income of consumer rises.
Therefore, the individuals who have higher disposable incomes spend the larger part of their incomes on consumer goods and services as compared to lower incomes.. Income elasticity of goods describes some significant characteristics of the demand for goods in question
When income elasticity is more than one, then there is an increase in quantity demanded. When income elasticity is less than one, then there is a decrease in quantity demanded
### Sources
1. https://www.economicshelp.org/concepts/inferior-good/#:~:text=An%20inferior%20good%20occurs%20when,negative%20income%20elasticity%20of%20demand.
2. https://mcqmate.com/discussion/59859/an-inferior-good-is-one-for-which-an-increase-in-income-causes-an
3. https://en.wikipedia.org/wiki/Inferior_good#:~:text=In%20economics%2C%20an%20inferior%20good,rises%20as%20consumer%20income%20rises.
4. https://www.economicsonline.co.uk/competitive_markets/demand_and_income.html/#:~:text=In%20the%20case%20of%20inferior,rice%20are%20often%20inferior%20goods.
5. https://en.wikipedia.org/wiki/Inferior_good
6. https://economictimes.indiatimes.com/definition/inferior-goods
7. https://mytutorialworld.com/objective-questions/single_question_view.php?table_name=gk-set-1-economics-micro-economics&uid=80
9. https://www3.nd.edu/~cwilber/econ504/504book/outln3a.html
10. https://www.studysmarter.co.uk/explanations/microeconomics/supply-and-demand/income-elasticity-of-demand/
11. https://open.lib.umn.edu/principleseconomics/chapter/3-1-demand/
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# Percentages as Fractions and Decimals (2)
In this worksheet, students recognise the percent symbol (%) and understand that percent relates to ‘number of parts per hundred’, writing percentages as fractions with denominator 100, and as a decimal.
Key stage: KS 2
Curriculum topic: Maths and Numerical Reasoning
Curriculum subtopic: Fractions
Difficulty level:
### QUESTION 1 of 10
The symbol % stands for 'per cent' or 'percent', which means 'out of a hundred'.
'Cent' is the French for 'hundred' and the % looks a bit like two zeros with a 1 through them.... 0|0.
We can easily convert between percentages, fractions and decimals.
45% (45 percent) is equal to 45/100 (45 hundredths) = 0.45
78% (78 percent) is equal to 78/100 (78 hundredths) = 0.78
5% (5 percent) is equal to 5/100 (5 hundredths) = 0.05
40% (40 percent) is equal to 40/100 (40 hundredths) = 0.40 = 0.4
Remember that:
50% (50 percent) is equal to 50/100 (50 hundredths) = 0.5 or a half
100% is equal to 1 or a whole
(Remember to change 0.40 to 0.4 in the last example as the final zero is not needed.)
Select all the answers which are equal to:
25%
2%
25/100
0.25
25/10
2.5
Select all the answers which are equal to:
64%
60%
6/100
64/100
64 hundredths
0.64
Select all the answers which are equal to:
10%
a half
10/100
one hundredth
0.10
0.1
Select all the answers which are equal to:
2%
1/2
2/100
two hundredths
0.2
0.02
Select all the answers which are equal to:
50%
1/2
50/100
fifty hundredths
0.5
0.50
Select all the answers which are equal to:
79%
80%
80/100
7.9
79/100
0.79
Select all the answers which are equal to:
90%
a ninth
90/100
90 hundredths
0.9
0.09
Select all the answers which are equal to:
9%
1/9
9/100
nine hundredths
0.9
0.09
Select all the answers which are equal to:
99%
1/99
99/100
ninety-nine hundredths
0.99
99
Select all the answers which are equal to:
100%
1/100
100/100
a whole
1
100
• Question 1
Select all the answers which are equal to:
25%
25/100
0.25
EDDIE SAYS
25% = 25 hundredths = 0.25
• Question 2
Select all the answers which are equal to:
64%
64/100
64 hundredths
0.64
EDDIE SAYS
64% = 64 hundredths = 0.64
• Question 3
Select all the answers which are equal to:
10%
10/100
0.10
0.1
EDDIE SAYS
10% = 10 hundredths = 0.10 = 0.1
• Question 4
Select all the answers which are equal to:
2%
2/100
two hundredths
0.02
EDDIE SAYS
2% = 2 hundredths = 0.02
• Question 5
Select all the answers which are equal to:
50%
1/2
50/100
fifty hundredths
0.5
0.50
EDDIE SAYS
50% = 50 hundredths = ½ = 0.50 = 0.5
• Question 6
Select all the answers which are equal to:
79%
79/100
0.79
EDDIE SAYS
79% = 79 hundredths = 0.79
• Question 7
Select all the answers which are equal to:
90%
90/100
90 hundredths
0.9
EDDIE SAYS
90% = 90 hundredths = 0.90 = 0.9
• Question 8
Select all the answers which are equal to:
9%
9/100
nine hundredths
0.09
EDDIE SAYS
9% = 9 hundredths = 0.09
• Question 9
Select all the answers which are equal to:
99%
99/100
ninety-nine hundredths
0.99
EDDIE SAYS
99% = 99 hundredths = 0.99
• Question 10
Select all the answers which are equal to:
100%
100/100
a whole
1
EDDIE SAYS
100% = 100 hundredths = 1.00 = 1 = a whole
---- OR ----
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# DLMF:13.19.E2 (Q4588): Difference between revisions
No description defined
Language Label Description Also known as
English
DLMF:13.19.E2
No description defined
## Statements
${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)\sim\frac{\Gamma\left% (1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}e^{\frac{1}{2}z}z^{-% \kappa}\*\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}-\mu+\kappa\right)_{s}}{% \left(\frac{1}{2}+\mu+\kappa\right)_{s}}}{s!}z^{-s}+\frac{\Gamma\left(1+2\mu% \right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{-\frac{1}{2}z\pm(\frac{1% }{2}+\mu-\kappa)\pi\mathrm{i}}z^{\kappa}\*\sum_{s=0}^{\infty}\frac{{\left(% \frac{1}{2}+\mu-\kappa\right)_{s}}{\left(\frac{1}{2}-\mu-\kappa\right)_{s}}}{s% !}(-z)^{-s},}}$
0 references
DLMF:13.19.E2
0 references
${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}}$
0 references
${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$
0 references
${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$
0 references
${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$
0 references
${\displaystyle{\displaystyle\sim}}$
0 references
${\displaystyle{\displaystyle\pi}}$
0 references
${\displaystyle{\displaystyle\mathrm{e}}}$
${\displaystyle{\displaystyle!}}$
${\displaystyle{\displaystyle\mathrm{i}}}$
${\displaystyle{\displaystyle\operatorname{ph}}}$
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If Blankenship Enterprises has to switch suppliers in the : GMAT Critical Reasoning (CR)
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# If Blankenship Enterprises has to switch suppliers in the
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If Blankenship Enterprises has to switch suppliers in the [#permalink]
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25 Sep 2005, 12:08
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If Blankenship Enterprises has to switch suppliers in the middle of a large production run, the company will not show a profit for the year. Therefore, if Blankenship Enterprises in fact turns out to show no profit for the year, it will also turn out to be true that the company had to switch suppliers during a large production run.
The reasoning in the argument is most vulnerable to criticism on which one of the following grounds?
(A) The argument is a circular argument made up of an opening claim followed by a conclusion that merely paraphrases that claim.
(B) The argument fails to establish that a condition under which a phenomenon is said to occur is the only condition under which that phenomenon occurs.
(C) The argument involves an equivocation, in that the word “profit” is allowed to shift its meaning during the course of the argument.
(D) The argument erroneously uses an exceptional, isolated case to support a universal conclusion.
(E) The argument explains one event as being caused by another event, even though both events must actually have been caused by some third, unidentified event.
If you have any questions
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25 Sep 2005, 13:02
B. the argument fails to show that reason of no profit is only the swith of suppliers.
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25 Sep 2005, 15:34
B. The argument fails to prove that replacing suppliers is the only reason of no profit.
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25 Sep 2005, 21:39
I think it is B
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26 Sep 2005, 04:25
B, clearly.
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26 Sep 2005, 06:05
B too - a classic in CR
A->B does not mean that in any cases B comes from A, B may also come from C
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26 Sep 2005, 06:42
IMO B
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26 Sep 2005, 07:10
It is a clear B for me.
What is the OA?
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26 Sep 2005, 07:23
A clear B.
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26 Sep 2005, 07:28
Clearly B. pure logic question for CR.
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26 Sep 2005, 12:01
B is OA. I leaned toward B as well, but couldn't effectively rule out A. Why isn't this circular?
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26 Sep 2005, 15:46
eastcoaster9 wrote:
B is OA. I leaned toward B as well, but couldn't effectively rule out A. Why isn't this circular?
IMO, a circular argument is something like "A is B because A is B".
However, what the author says in the article is ;
- Switching suppliers(A) => No profit(B)
- No profit(B) => suppliers(A)
Here, the author considers "A=B" as "B=A".
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27 Sep 2005, 02:20
gamjatang wrote:
eastcoaster9 wrote:
B is OA. I leaned toward B as well, but couldn't effectively rule out A. Why isn't this circular?
IMO, a circular argument is something like "A is B because A is B".
However, what the author says in the article is ;
- Switching suppliers(A) => No profit(B)
- No profit(B) => suppliers(A)
Here, the author considers "A=B" as "B=A".
Good explanation.
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Display posts from previous: Sort by
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https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(OpenStax)/10%3A_Exponential_and_Logarithmic_Functions/10.01%3A_Prelude_to_Exponential_and_Logarithmic_Functions
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$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
# 10.1: Prelude to Exponential and Logarithmic Functions
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As the world population continues to grow, food supplies are becoming less able to meet the increasing demand. At the same time, available resources of fertile soil for growing plants is dwindling. One possible solution—grow plants without soil. Botanists around the world are expanding the potential of hydroponics, which is the process of growing plants without soil. To provide the plants with the nutrients they need, the botanists keep careful growth records. Some growth is described by the types of functions you will explore in this chapter—exponential and logarithmic. You will evaluate and graph these functions, and solve equations using them.
10.1: Prelude to Exponential and Logarithmic Functions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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# What is an exponential
Definition/Summary
The exponential (the exponential function), written either $e^x$ or exp(x), is the only function whose derivative (apart from a constant factor) is itself.
It may be defined over the real numbers, over the complex numbers, or over more complicated algebras such as matrices.
Its value at 0 is 1, and its value at 1 is the exponential constant (or Euler's constant or Napier's constant), e = 2.71828...
Its value at pure imaginary numbers is a combination of cos and sin (and therefore it may be used to define them): exp(ix) = cosx + isinx (Euler's formula), and therefore exp($i\pi$) = -1 (Euler's indentity).
Its inverse (over real or complex numbers) is the natural logarithm, log(x) (often written ln(x), to distinguish it from the base-10 logarithm): if y = exp(x), then x = log(y).
Equations
Definitions:
$$\frac{de^x}{dx}\ =\ e^x\ \text{and}\ e^0\,=\,1$$
$$e^x\ =\ 1\ +\ x\ +\ \frac{x^2}{2} +\ \frac{x^3}{6} +\ \frac{x^4}{24} +\ \frac{x^5}{120}\ \dots\ = \sum_{n\,=\,0}^{\infty}\frac{x^n}{n!}$$
$$e^x\ =\ \lim_{n\rightarrow\infty}\left(1\ +\ \frac{x}{n}\right)^n$$
Euler's formula:
$$e^{ix}\ =\ cosx\ +\ i sinx$$
and so cos and sin may be defined:
$$cosx\ =\ \frac{1}{2}\left(e^{ix}\ +\ e^{-ix}\right)$$ and $$i sinx\ =\ \frac{1}{2}\left(e^{ix}\ -\ e^{-ix}\right)$$
Hyperbolic functions:
$$e^{x}\ =\ coshx\ +\ sinhx$$
$$coshx\ =\ \frac{1}{2}\left(e^{x}\ +\ e^{-x}\right)$$ and $$sinhx\ =\ \frac{1}{2}\left(e^{x}\ -\ e^{-x}\right)$$
$$tanhx\ =\ \frac{sinhx}{coshx}\ =\ \frac{e^x\ -\ e^{-x}}{e^x\ +\ e^{-x}}$$
$$tanh\frac{1}{2}x\ =\ \frac{e^x\ -\ 1}{e^x\ +\ 1}$$ and $$e^x\ =\ \frac{1\ +\ tanh\frac{1}{2}x}{1\ -\ tanh\frac{1}{2}x}$$
Logarithms:
$$y\ =\ e^x \Leftrightarrow\ x\ =\ ln(y) \Leftrightarrow\ \frac{dy}{dx}\ =\ y\ \text{and}\ y(0)\,=\,1\Leftrightarrow\ \frac{dx}{dy}\ =\ \frac{1}{x}\ \text{and}\ x(1)\,=\,0$$
$$e^{ln(x)}\ =\ x$$
$$a^x\ =\ \left(e^{ln(a)}\right)^x\ =\ e^{x\,ln(a)}$$
$$y\ =\ a^x \Leftrightarrow\ x\ =\ log_a(y)\ \equiv\ \frac{ln(y)}{ln(a)}$$
$$\frac{da^x}{dx}\ =\ ln(a)\,e^{x\,ln(a)}\ =\ ln(a)\,a^x$$
Extended explanation
"Exponentially" ("geometrically"):
A function is said to increase exponentially (or geometrically), or is O(ex), if it increases "as fast as" ex
So such a function increases faster than any fixed power of x.
(For example, 2x increases exponentially.
By comparison, a function increases arithmetically, or is O(x), if it increases "as fast as" x, and is O(xn) if it increases "as fast as" xn)
* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
Last edited by a moderator:
$$\left. \dfrac{d}{dx}\right|_{x=p}\left( f(x)\cdot g(x)\right) =\left(\left. \dfrac{d}{dx}\right|_{x=p} f(x)\right)\cdot g(x)+f(x)\cdot\left(\left. \dfrac{d}{dx}\right|_{x=p} g(x)\right)$$
$$\exp \circ \operatorname{ad} = \operatorname{Ad} \circ \exp$$
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# All About Shapes - What is a Rectangle?
Shapes are one of the first mathematical subjects introduced to kids. At around 18 months old, kids start to notice differences between shapes. At 2 years old, they begin to understand, recognize and name basic shapes such as circle, triangle, square, and rectangle. Rectangles are one of the most common shapes that form a part of our daily life. A rectangle is 2D shape that has 4 straight sides and 4 corners, and all 4 corners are vertical.
This worksheet is all about rectangles. It helps kids learn about the concepts of rectangles and how to recognize rectangles. A Rectangle is a four sided-polygon, with its parallel sides equal to each other and all four internal angles equal to 90 degrees. An interesting fact to know is that a square is a special type of rectangle, with 4 equal sides. Rectangles can be any size. Rectangles can be any color: yellow, green, red, and so on. Some real-life examples of rectangles are blackboards, notebooks, doors, dollar bills, computer screens, and bank cards. A simple exercise is provided at the end for kids to recognize rectangles. This could help kids reinforce their understanding of the concept of the rectangle shape.
Rectangles with Changing Dimensions in Width and Height
All About Shapes - What is a Square?
All About 3D Shapes - What is a Cube?
Squares and Circles with Changing Sizes
Number Blocks: Square Numbers
All About Shapes - What is a Hexagon?
All About Shapes - What is an Octagon?
All About Shapes - What is a Pentagon?
All About Shapes - What is a Triangle?
All About Shapes - What is a Circle?
Shapes with Happy Faces
High-Contrasting Black and White Flashcards for Newborn Babies
All About 3D Shapes - What is a Sphere?
All About 3D Shapes - What is a Cylinder?
Black and White Images of Fruits for Newborn Babies
All About 3D Shapes - What is a Cone?
High-Contrasting Black and White Images for Newborns
Twelve Irregular Figures of Shapes
Opposite Words Illustrated with Simple Shapes
Find and Count Basic Shapes in Compositions
Six Different Types of Triangles
Black and White Flashcards of Animals for Newborn Babies
Cylinders with Changing Dimensions in Diameter and Height
Exercise for Sorting Shapes by Coloring
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edHelper subscribers - Create a new printable
Math
Middle School Math
Name _____________________________ Date ___________________
Solving Equations
Solve each equation.
1.
119 = 31 + h
2.
59 = 65 - a
3.
e ÷ 3 = 2
4.
9g = 27
5.
u - 11 = 9
6.
21 + w = 30
7.
9 = x ÷ 8
8.
62 = z + 54
9.
m + 25 = 115
10.
36 = j - 32
11.
62 = 93 - d
12.
36 ÷ f = 6
13.
139 = b + 98
14.
q + 71 = 136
15.
56 = 7k
16.
39 - v = 25
17.
y - 25 = 17
18.
28 = 4t
19.
13 = h - 66
20.
36 + a = 99
21.
8 ÷ z = 4
22.
94 - b = 7
23.
25 = 5g
24.
127 = 90 + w
25.
32 ÷ j = 4
26.
75 = e + 37
27.
72 - f = 4
28.
67 = p + 62
29.
78 = s - 14
30.
20 = 4n
31.
u ÷ 9 = 2
32.
34 + v = 44
33.
24 = 3d
34.
7 + m = 103
35.
69 - q = 57
36.
39 = c - 10
37.
k - 22 = 12
38.
40 + x = 124
39.
86 = x + 64
40 * This is a pre-made sheet.Use the link at the top of the page for a printable page.
41 * This is a pre-made sheet.Use the link at the top of the page for a printable page.
42.
96 - b = 15
Sample
This is only a sample worksheet.
edHelper subscribers - Create a new printable
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Interpret the contents of a trading and profit and loss account of a food retailer.
Extracts from this document...
Introduction
Transfer-Encoding: chunked I am going to examine the financial statements of Alpha Ltd, a food retailer. I will be using ratios to measure solvency, profitability and efficiency of the company. Finally, I will analyse and interpret reasons for the performance of Alfa Ltd. Solvency ratio Solvency ratios measures the ability of Alpha Ltd to settle their short term debts. These ratios allow managers and other interested parties to monitor Alpha Ltd.’s cash position. 1. Current ratio measures the ability of Alpha Ltd. to meet its liabilities or debts over the next year or more. Formula: Current ratio = Current Assets Current Liabilities = £75000 £50000 = 1.5:1 Alpha Ltd.’s current ratio of 1.5:1 is very close to a representative current ratio of 1.6:1. This means that Alpha Ltd. are now in a position to settle their debts on time. This puts Alpha Ltd. in a positive position. Alpha Ltd. can improve their current ratio by raising more cash through the sale of fixed assets or the negotiation of long-term loans. ...read more.
Middle
are able to convert their stock into sales 15.5 times a year or every 23.55 days. This means that Alpha Ltd. are working efficiently; as a food retailer, they are able to sell their stock quickly before perishable items are no longer in date. They can improve their stock turnover ratio by holding lower levels of stock or to achieve higher sales without increasing stock levels. 1. Debtors’ collection period calculates the time typically taken by a business to collect the money that it is owned. Formula: Debtors’ collection period = Debtors X 365 Turnover = £5000 £1200000 = £1825000 £1200000 = 1.52 days Alpha Ltd. are able to gain their cash within 1.52 days which means they are running their business efficiently. They are able to gain from their debtors’ quickly because the majority of their customers pay by cash. Alpha Ltd. can improve their debtors’ collection period by reducing the credit period on offer to customers or by insisting on cash payment. ...read more.
Conclusion
= Operating Profit X 100 Capital Employed = 150000 X 100 275000 = 15000000 275000 = 54.55% Alpha Ltd.’s return on capital employed is 54.55% which is exceptional because a typical Ratio is between 20-30%. They have used the money very efficiently to generate profits. To improve their ROCE by increasing its operating profit without raising further capital or by reducing the amount of capital employed, for instance, paying off a long term debt. In conclusion, Alpha Ltd. have done very well. They are able to settle their debts on time, and also can settle these debts despite selling their stock. In addition, Alpha Ltd. are using their assets very efficiently to generate sales, are able to convert their stock into sales 15.5 times a year or every 23.55 days and are able to gain their cash within 1.52 days from their debtors. Lastly, for every £1 of sales they make a gross profit of 22.5p, every £1 of sales they make a net profit of 8.33p and their return on capital employed is 54.55% which means they have used the money very efficiently to generate profits. Reference – A2 business studies by Malcom Surridge and Andrew Gillespie Unit 2 M3 ...read more.
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## Thursday, January 21, 2021
### IAS PUZZLE QUESTION FOR GENIUS PEOPLE.
IAS PUZZLE QUESTION FOR GENIUS PEOPLE.
General Information (GK) is significant territory in all the serious test held in the nation. The majority of the applicants feel trouble in scoring great imprints in it. Presently a day, decent information on broad mindfulness is significant in clearing any serious test. To overcome this you ought to have a comprehension of the things occurring around you. Columbia College is one of the world's most significant focuses of exploration and simultaneously a particular and recognized learning condition for students and graduate understudies in numerous academic and expert fields.
The College perceives the significance of its area in New York City and tries to interface its examination and instructing to the huge assets of an incredible city. It tries to draw in an assorted and worldwide staff and understudy body, to help exploration and instructing on worldwide issues, and to make scholastic associations with numerous nations and locales. It anticipates that all zones of the College should propel information and learning at the most significant level and to pass on the results of its endeavors.
PUZZLE -3
After performing the multiplication, we reach the result by adding the individual numbers that make up the result.
If 12x12 = 144, then 1 + 4 + 4 = 9
If 23x23 = 529, then 5 + 2 + 9 = 16
If 34x34 = 1156, then 1 + 1 + 5 + 6 = 13
PUZZLE- 1
3+5+6=151872
5+5+6=253094
5+6+7=303585
5+5+3=251573
.........
........
9+4+7=?
Not long after these early beginning functions, classes were hindered by war. During World War I, the college permitted the U.S. military to utilize a portion of its justification for testing. In 1917, the U.S. military separated American College into two sections, Camp American College and Camp Drain.
IAS PUZZLE QUESTION FOR GENIUS PEOPLE.
1604656713249637-1
The answer for 9+4+7 is 366329
9+4+7=9×4+9×7
=36,63
first fours digits
for the last digit, we have to do
36+63-7=92
the reverse of 92 is 29
so 9+4+7=366329
Camp American College turned into the origin of the US's concoction weapons program and the site of substance weapons testing; this necessary a significant cleanup exertion during the 1990s. Camp Drain was home to cutting edge examination, improvement, and testing of present-day cover methods. Starting at 2014, the Military Corps of Specialists was all the while evacuating weapons including mustard gas and mortar shells.
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Ajuda do Scilab >> Biblioteca de Gráficos > 2d_plot > plot2d
# plot2d
2D plot
### Syntax
```plot2d() // example
plot2d(y)
plot2d(x, y)
plot2d(logflag, x, y)
plot2d(.., y, style)
plot2d(.., y, style, strf)
plot2d(.., y, style, strf, leg)
plot2d(.., y, style, strf, leg, rect)
plot2d(.., y, style, strf, leg, rect, nax)
plot2d(.., y, key1=value1, key2=value2, ..)```
### Arguments
x
a real matrix or vector of abscissae. If omitted, abscissae are assumed to be `1:n` for all curves, where `n` is the number of points in curves, as given by `y`.
y
real matrix or vector: Ordinates
key1=value1, key2=value2, ...
The following options `logflag`, `style`, `strf`, `leg`, `rect`, `nax`, `frameflag`, and `axesflag` described below can either be listed in the right order as listed in the synopses, or provided in any order after `y` as named arguments, for instance like in `plot(y, frameflag=3, leg="Curve 1@Curve 2")`.
logflag
Sets the linear or logarithmic scale for both X and Y axes. Possible values are `"nn"`, `"nl"` , `"ln"` or `"ll"`. `"n"` stands for normal scale ; `"l"` stands for logarithmic. The first letter set the X axis. The second one sets the Y axis.
style
Sets the respective line or mark styles of the curves. It is a vector of decimal integers with one element per curve:
• if `style(i)` is strictly positive, the curve is drawn as plain line and `style(i)` defines the index of the color used to draw the curve (see getcolor).
• if `style(i)` is negative or zero, the given curve points are drawn using marks. Then `abs(style(i))` is the mark's id.
Note that all curves properties -- like also their color, thickness, marks colors, etc -- can be set through their handles (see polyline_properties).
strf
3-character-long string `"abc"` specifying all together if legends must be displayed, and the values of `frameflag` and `axesflag`. By default, `strf= "081"`. "a", "b" and "c" are:
a : controls the display of captions:
a=0 : no caption. captions given by the optional argument `leg` are displayed.
b : `frameflag` integer code in [0,9], controlling the computation the actual coordinate ranges, as described below.
c : `axesflag` integer code in [0:5 9], controlling the display and position of X and Y axes, as described below.
leg
Single string `"leg1@leg2@...."` setting the legends leg1, leg2, etc for the respective curves #1, #2, etc. The default is `" "`. The block of legends is drawn on the bottom, below the x-axis.
After plotting, the handle of the block of legends can be retrieved with `gca().children(2)`. captions, legend or legends can also be used instead of `leg`.
rect
Vector of decimal numbers `[xmin, ymin, xmax, ymax]` setting the minimal bounds requested for the plot. `[xmin, xmax]` is the X-axis range, and `[ymin, ymax]` is the Y-axis one.
This argument works with the `frameflag` option to specify how the actual axes boundaries are computed. If the `frameflag` option is not given, it is supposed to be `frameflag=7`.
The axes boundaries can also be customized through the `gca().data_bounds` property of the axes (see axes_properties).
nax
Vector of decimal integers `[nx,Nx,ny,Ny]` specifying the numbers Nx and Ny of major ticks, and the numbers nx and ny of minor ticks between 2 majors, for both respective axes. To use autoticking on an axis, set Nx=-1 or Ny=-1.
If the `axesflag` option is not specified, using `nax` sets and uses `axesflag=9`.
frameflag
controls the computation of the actual coordinate ranges from the minimal requested values. The associated value should be an integer ranging from 0 to 8.
frameflagaxes bounds other actions
0 unchanged
1 from rect
2 from input x,y
3 from rect isometric axes
4 from input x,y isometric axes
5 from rect pretty axes
6 from input x,y pretty axes
7 from rect all replot with new scales
8 from input x,y all replot with new scales
9 from input x,y Pretty axes. All replot with new scales
The setting of axes boundaries can also be customized through the `gca().data_bounds`, `gca().tight_limits`, `gca().data_bounds`, and `gca().isoview` properties (see axes_properties).
axesflag
integer code in [0:5 9], controlling the display and position of X and Y axes.
The axes aspect can also be customized directly through the `gca().box`, `gca().axes_visible`, `gca().x_location`, and `gca().y_location`, properties (see axes_properties).
0"off"["off" "off"] Naked plot
1"on" ["on" "on"]
2"on" ["off" "off"] Naked box
3"off"["on" "on"] y_location="right"
4"off"["on" "on"] crossed @ middle
5"on" ["on" "on"] crossed @ middle
9"off"["on" "on"] (default setting)
### Description
`plot2d` plots a set of 2D curves. Piecewise linear interpolation is done between the given curve points.
Any point with `y(i)=Nan` is masked: no mark and no segment to its neighboors are displayed.
For any point with `y(i)=±Inf`, a vertical segment starting from each of its both neighboors is drawn in the ± direction, up to the current ceil or down to the current floor of the axes.
By default, successive calls to plot2d() overplots new curves over existing ones. Autoclearing for each new plot can be set using `gca().auto_clear="on"`. Please see axes properties. `clf` can also be used to manually clear the whole figure.
If you are familiar with Matlab `plot` syntax, you should use plot instead.
If `x` and `y` are vectors, plot2d(x,y,…) plots vector `y` versus vector `x`. `x` and `y` vectors should have the same number of entries.
If `x` is a vector and `y` a matrix plot2d(x,y,…) plots each columns of `y` versus vector `x`. The number of rows of `y` must be equal to the number of `x` entries.
If `x` and `y` are matrices, plot2d(x,y,…) plots each columns of `y` versus corresponding column of `x`. `x` and `y` must then have the same sizes.
If `y` is a vector, plot2d(y,…) plots vector `y` versus vector `1:size(y,'*')`.
If `y` is a matrix, plot2d(y,…) plots each columns of `y` versus vector `1:size(y,1)`.
Enter the command `plot2d()` to see a demo.
Other high level plot2d functions exist:
• plot2d2 same as `plot2d` but the curve is supposed to be piecewise constant.
• plot2d3 same as `plot2d` but the curve is plotted with vertical bars.
• plot2d4 same as `plot2d` but the curve is plotted with vertical arrows.
### Examples
```// x initialisation
x=[0:0.1:2*%pi]';
//simple plot
plot2d(sin(x));```
```clf();
x=[0:0.1:2*%pi]';
plot2d(x,sin(x));
//multiple plot```
```clf();
x=[0:0.1:2*%pi]';
plot2d(x,[sin(x) sin(2*x) sin(3*x)])```
```// multiple plot giving the dimensions of the frame
clf();
x=[0:0.1:2*%pi]';
plot2d(x,[sin(x) sin(2*x) sin(3*x)],rect=[0,0,6,0.5]);```
```//multiple plot with captions and given tics + style
clf();
x=[0:0.1:2*%pi]';
plot2d(x,[sin(x) sin(2*x) sin(3*x)],..
[1,2,3],leg="L1@L2@L3",nax=[2,10,2,10],rect=[0,-2,2*%pi,2]);```
```// isoview
clf();
x=[0:0.1:2*%pi]';
plot2d(x,sin(x),1,frameflag= 4);```
```// scale
clf();
x=[0:0.1:2*%pi]';
plot2d(x,sin(x),1,frameflag= 6);```
```// auto scaling with previous plots + style
clf();
x=[0:0.1:2*%pi]';
plot2d(x,sin(x),-1);
plot2d(x,2*sin(x),12);
plot2d(2*x,cos(x),3);```
```// axis on the right
clf();
x=[0:0.1:2*%pi]';
plot2d(x,sin(x),leg="sin(x)");
a=gca(); // Handle on axes entity
a.y_location ="right";```
```// axis centered at (0,0)
clf();
x=[0:0.1:2*%pi]';
plot2d(x-4,sin(x),1,leg="sin(x)");
a=gca(); // Handle on axes entity
a.x_location = "origin";
a.y_location = "origin";
// Some operations on entities created by plot2d ...
isoview
a=gca();
a.children // list the children of the axes.
// There are a compound made of two polylines and a legend
poly1= a.children(1).children(1); //store polyline handle into poly1
poly1.foreground = 4; // another way to change the style...
poly1.thickness = 3; // ...and the thickness of a curve.
poly1.clip_state='off'; // clipping control
leg = a.children(2); // store legend handle into leg
leg.font_style = 9;
leg.line_mode = "on";
isoview off```
• plot — Esboço 2d
• .polyline_style — description of the Polyline entity properties
• plot2d2 — esboço 2d (funções de degraus)
• plot2d3 — esboço 2d (barras veticais)
• plot2d4 — esboço 2d (setas)
• polarplot — Esboço de coordenadas polares
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## How many mg are in mM?
Therefore, there must be 1,000 milligrams in a milliliter, making the formula for mg to ml conversion: mL = mg / 1000 .
## What is 1mm in mg?
How do you Convert from Molarity (M) to Parts Per Million (ppm) and mg/L?
Molarity (moles/Liter = M) grams/L (g/L) miligrams/L (mg/L)
1 M 35.5 35,500
10-1 M 3.55 3,550
10-2 M 0.355 355.0
10-3 M 0.0355 35.5
How do you calculate concentration in mM?
Calculate concentration in millimolars using the formula: Molarity (millimolars)= Amount (in millimoles)/Volume of solution (in liters). In our example, the volume of the solution is 500 ml or 0.5 liters. The molarity of NaOH would be: Molarity (NaOH)= 12.5 millimoles/0.5 liters=25 millimolars.
### Is mg same as mM?
Note that 1 M = 1 mol/l and 1 mM = 1 mmol/l, where 1 mol = 1000 mmol. Milliliter and milligrams are not equivalent measures. A milliliter ( mL, or in some places ml) is a liquid measurement, and a miligram (mg) is a measurement of amount within a specific guideline for that substance.
### How do you convert mM to mg?
This is the weight in grams of 1 mole of the compound. 1 millimole Fe2O3 = 159.69 / 1000 = 0.1597 grams = 159.69 milligrams. Calculate the number of milligrams required for the chemical reaction by multiplying the number millimoles by the weight of one millimole of the compound.
Is mL L the same as mg L?
No – 10mL dissolved O2 /L is about 13.3 mg dissolved O2 /L. Here’s an explanation: The concentration unit ml/L is equivalent to parts per thousand; i.e. for every 1 mL of O2, there are 1000mL = 1000mg of water. So 10 mL dissolved oxygen/L water = 13.3 dissolved oxygen mg/L water.
## How do you calculate concentration in mg ml?
Divide the mass in milligrams by volume in milliliters to find concentration in mg/mL. For example, if you have 8,000 milligrams of sugar dissolved in 200 milliliters of water, work out 8,000 รท 200 = 40. The concentration of the solution is 40 mg/mL.
How much is 5 ml in mg?
How Many Milligrams are in a Milliliter?
Volume in Milliliters: Weight in Milligrams of:
Water Granulated Sugar
5 ml 5,000 mg 3,500 mg
6 ml 6,000 mg 4,200 mg
7 ml 7,000 mg 4,900 mg
### How do you convert mg to ML?
Find the density of the material you are measuring. Because you are trying to convert mass into volume,you need to know the density of the material.
• Check with your pharmacist for medication densities. If you are trying to convert amounts for a prescription,you should check with your pharmacist.
• Prepare to convert from mass to volume.
• ### How many MG is equal to 15 ml?
15 ml = 15000 mg: 1 ml = 1000 mg: 3 ml = 3000 mg: 5 ml = 5000 mg: 16 ml = 16000 mg How can 1 mg be equal to 0.001 ml? 1 mg of water is equal to 1 g of water or
How many mm are in a ML?
The answer is: The change of 1 ml ( milliliter ) unit for a volume and capacity measure equals = into 1,000.00 cu mm – mm3 ( cubic millimeter ) as per its equivalent volume and capacity unit type measure often used.
## How many mg to ML?
1 mg / (100 ml) to microgram / ml = 10 microgram / ml. 5 mg / (100 ml) to microgram / ml = 50 microgram / ml.
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HO24-PS3-Solutions
# HO24-PS3-Solutions - MS&E 352 Handout#23 Decision Analysis...
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MS&E 352 Handout #23 Decision Analysis II Mar 04, 2009 ______________________________________________________________________ ______________________________________________________________________ 03/07/06 Page 1 of 9 Problem Set #3 Problem Set #3 Solutions Grade Distribution 0% 5% 10% 15% 20% 25% 30% 35% 0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 76-80 81-85 86-90 91-95 96-100 Problem 1 – Discretization Practice [30 points] We designed this problem to give you practice in discretizing continuous distributions (here, a Gaussian or normal distribution), as well as to show you the accuracy of the different discretization methods. Willie Wafer, sole proprietor of Big Chip Little Chip Semi Conductors, faces an alternative whose net present value (NPV) has a normal distribution with mean of \$0 and standard deviation of 1 million dollars. Willie follows the delta property and has a risk tolerance of 5 million dollars. You will find the cumulative distribution for Willie's alternative on the attached page (You can generate this for yourself using the NORMDIST function in Excel). You will compare the distributions and certain equivalents, which result from the different discretization methods.
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MS&E 352 Handout #23 Decision Analysis II Mar 04, 2009 ______________________________________________________________________ ______________________________________________________________________ 03/07/06 Page 2 of 9 Problem Set #3 Question 1: [20 points] Fill out the table on the following page. If you want partial credit, show your work on the moment-matching discretizations on a separate page. Answer: See table on next page. Error Codes: [1.1.1] – 2 to 5 points – At least one PISP calculation is wrong. [1.1.2] – 1 to 7 points – Mistake in or missing results for one of the two methods. [1.1.3] – 1 point – Minor mistake in the PISP calculations, such as: a) wrong sign; or b) because you did not exactly compute the probabilities of each degree (e.g. typed 0.33 instead of 1/3 for 3 degrees), your PISP’s are slightly off; or c) used a probability distribution for the equal areas method that did not make sense; d) rounded off all the answers, so it was impossible to compare accuracy; e) used incorrect risk tolerance
MS&E 352 Handout #23 Decision Analysis II Mar 04, 2009 ______________________________________________________________________ ______________________________________________________________________ 03/07/06 Page 3 of 9 Problem Set #3 A closed form equation exists to find the certain equivalent of a normal distribution, given its mean and variance. ~ x x x = - 1 2 ( ρ where ~ x = certain equivalent x = mean ( x = variance ρ = risk tolerance As an aside, if you know the mean and variance of your distribution (even a non-normal distribution), this equation can serve as an approximation to the certain equivalent of that distribution.
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You may think that I am a real space cadet for talking about space today, but this is the way that I learn things and this post is not being written to make your heads explode. Space in Physics is a fundamental concept like time and mass. Space is where things happen, and spatial coordinates provide us with our reference system, they are necessary to define unique locations of any particular point or any object. At times it is hard to imagine space, I always tend to think about different shapes that relate to Geometry, and that makes sense as this subject is often defined as the mathematics of space. Space gives us the geometrical terms of distance or length, area and volume and this is sometimes called 1-dimensional, 2-dimensional or 3-dimensional space, however mathematicians often work in higher dimensional spaces. Terms for different types of space were developed to help us to understand complex phenomena. In mathematics, a space is a set (sometimes called a universe) with some added structure. Space is an abstract idea in math, it is extraordinarily general, but it is also a supremely important concept. In modern mathematics many different types of spaces are used, but the notion of “space” itself is not defined.
Space can be looked at as being a place for numerical variables, data structures or functions to exist and comprise points on a line, objects in a plane or in some higher dimensions of a universe. Space is a geometric structure, one that has its own mathematical entities and axioms that define it. Types of space include abstract space, affine space, ambient space, analytic space, anti-de Sitter space, Baire space, Banach space, Base space, Bergman space, Besov space, Borel space, Calabi-Yau space, Cartesian space, Cellular space, Chu space, compact space, connected space, configuration space, coordinate space, convex space, De Sitter space, Dirichlet space, Drinfeld’s Symmetric space, Eilenberg-Mac Lane space, Euclidean space, event space, feature space, Fiber space, Finsler space, First-Countable space, Fréchet space, function space, G-Space, Green space, Hardy space, Heisenberg space, Hilbert space, hyperbolic space, hypothetical space, Inner Product space, L2-Space, Lp space, Lens space, linear space, Liouville space, locally finite space, loop space, mapping space, measure space, metric space, minimal space, Minkowski space, moduli space, momentum space, Müntz space, noncommutative space, normed space, null space, outcome space, Paracompact space, phase space, physical space, planar space, Polish space, Poisson space, probability space, projective space, quotient space, real space, Riemannian space, sample space, Sobolev space, Standard space, State space, Stone space, subspace, Symplectic space, T2-Space, tangent space, Teichmüller space, Tensor Space, theory space, topological space, total Space, uniform space, vector space and virtual space. It is easy to get lost in a world that is comprised of so many exotic types of space, because math is often hidden in darkness, and obscured by an impenetrable cloud of symbols and jargon.
Space begins with the point, which is a 0-dimensional object that gives you a precise location or place on a plane. The most basic form of a space is a point and points can be combined or build up into a string of points which is where they eventually become lines, because lines are basically a series of points. Only a coherent arrangement of points makes up a space. Mathematics defines a space as being a set with some added structure. You could think of structures as places we do algebra, and spaces as places we do geometry in the same way that the human brain is split into an algebraic “left hemisphere” that thinks in logical sequences and a geometric “right hemisphere” that takes a more visual approach. Everything in the universe is part of a mathematical structure. All matter is made up of particles, which have properties and these properties are purely mathematical. Since space has properties such as dimensions, it is ultimately a mathematical structure. The everyday type of space familiar to most people is called Euclidean space. In Einstein’s theory of Special Relativity, Euclidean three-space plus time (the “fourth dimension”) are unified into the so-called Minkowski space. One of the most general type of mathematical spaces is the topological space.
## 12 thoughts on “About Space”
1. That’s an awful lot of space Jim. You just need to devise something to remember them all, just like the periodic table song. Over to you!
Liked by 1 person
2. Jim there wasn’t enough space in my mind to accommodate what you said here, sorry!
Liked by 1 person
1. More likely a fuse would blow and everything would be forgotten. Hey maybe not a bad idea…
Liked by 1 person
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# The initial rate for zero order reaction of the gaseous reaction $A(g)\rightarrow 4B(g)$ is $10^{-3}Msec^{-1}$. If the initial concentration of $A$ is $0.01\;M$ after $2\;sec$. Concentration of $B$ should be
$\begin{array}{1 1}(a)\;0.002M&(b)\;0.001M\\(c)\;0.008M&(d)\;0.004M\end{array}$
$[A]_t=[A_o]-kt$
$\;\;\;\;\;\;=0.01-10^{-3}(2)$
$\;\;\;\;\;\;=0.008M$
$[B]_t=4(0.002)M$
$\;\;\;\;\;\;=0.008M$
Hence (c) is the correct answer.
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## pls help to solve these problems...
Math Help on Cosine (cos), Sine (sin), Tangent (tan), Cotangent (cot), Cosecant (cosec), Secant (sec), Arccos, Arcsin, Arctan, Hypotenuse, Angles, Formulas, Trigonometric Circle, Unit Circles, Quadrants, Rotations; Triangles, Rectangles, Squares, Parallelograms, Quadrangles, Lozenges, Lines, Perpendicular, Parallel, Perpendicular, Parallel Lines, Bisector, Median, Gravity Center, Circumcenter, Circles, Pythagorean Theorem, Thales, Height, Side, Length, Ruler, Compass, Constructions, Formulas; Quadratic equations (Second degree equations), Absolute Values, Inequalities; Events, Random, Mean, Variance, Expectation, Wins, Losses, Bernoulli, Newton's Binomial Formula, Multinomial Formula, Tests, Samples on My Math Forum.
### pls help to solve these problems...
trapezoid01.JPG (66.67 KiB) Viewed 425 times
Last edited by MarkFL on Sun Feb 19, 2012 2:59 am, edited 1 time in total.
Reason: To resize and crop image
verynice2000
Newcomer
Posts: 2
Joined: Sun Feb 19, 2012 1:17 am
### Re: pls help to solve these problems...
and problem no. 2 please. TIA!
squares01.JPG (59.3 KiB) Viewed 425 times
Last edited by MarkFL on Sun Feb 19, 2012 3:02 am, edited 1 time in total.
Reason: To resize and crop image
verynice2000
Newcomer
Posts: 2
Joined: Sun Feb 19, 2012 1:17 am
### Re: pls help to solve these problems...
Here are some very rough sketches:
1:
trapezoid.jpg (8.55 KiB) Viewed 428 times
The parts are similar to the original with side lengths of 1/2 the original.
2:
squares.jpg (4.95 KiB) Viewed 428 times
Again, the parts are similar to the original with side lengths of 1/2 the original.
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)
MarkFL
Global Moderator
Posts: 11318
Joined: Thu Jul 01, 2010 3:14 am
Location: St. Augustine, FL., U.S.A.'s oldest city
### Re: pls help to solve these problems...
These are fascinating shapes.
A shape can be combined with its clones to make a larger (similar) model.
There were named "rep-tiles" by Martin Gardner.
Here is one more . . . called "The Sphinx".
Code: Select all
` * / \ / \ / \ / *---*-------* / / \ / \ *---* \ *---* \ / \ / \ *-----------*-----------*`
soroban
Super User
Posts: 2480
Joined: Sun Dec 10, 2006 9:37 am
Location: Lexington, MA
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# Q3 2011 GDP 3rd Revision: 1.8%
Q3 GDP 2011 was revised down another 0.2 percentage points to 1.8%.. Consumer spending was revised significantly downward due to a large downward revision to medical expenditures. GDP was initially reported to be 2.5% for the third quarter, then revised to 2.0% on the second estimate report and now a measly 1.8% for the final, 3rd revision. Here is the original BEA GDP report.
Q3 GDP had a sharp decrease in personal consumption, an upward revision in private inventories, a large increase in reported imports, which subtracts from gross domestic product and a bump up in fixed investment. The government is fairly D.O.A. in adding to economic growth now.
As a reminder, GDP is made up of: $Y=C+I+G+{\left(X-M\right)}$ where:
Y=GDP, C=Consumption, I=Investment, G=Government Spending, (X-M)=Net Exports, X=Exports, M=Imports*.
Below is the Q3 2011, third revision, breakdown of GDP by percentage point contributions. Without final rounding, Q3 GDP was 1.82%.
• C = +1.24
• I = +0.17
• G = –0.02
• X = +0.64
• M = –0.21
Here is the Q3 2011, second revision, breakdown of GDP by percentage point contributions. Without final rounding, Q3 GDP was 2.00%.
• C = +1.63
• I = –0.10
• G = –0.02
• X = +0.59
• M = –0.09
Below are the percentage point differences, or spread between the Q3 3rd revision and Q3 2nd revision GDP report components, by percent point contribution. The quarterly change in private inventories was revised up significantly, from a -1.55 to –1.35 percentage points. The change in private inventories revision alone added +0.20 percentage points to the 1.82% Q3 GDP reported in the 3rd revision.
• C = -0.39
• I = +0.27
• G = 0.00
• X = +0.05
• M = -0.12
Below the the St. Louis FRED graph for C of the above GDP equation, or real personal consumption expenditures, percentage change . As we can see from the above, PCE, or C in the above percentage point contribution, is the main reason for lower GDP growth in Q3.
Below is the breakdown in C or real PCE annualized percentage quarterly change. The third quarter PCE percentage point breakdown was a -0.43 downward revision from +1.33 to a +0.90 percentage point contribution in services. PCE goods was also revised up by +0.03 percentage points, from +0.30 to +0.33 with durable goods being revised up by +0.01 percentage points from the 2nd revision, from +0.41 to +0.42 of the +1.8 GDP. Notice when times are tough, durable goods (bright red) consumption drops. Where people spent their money in Q3 was personal household expenditures.
Personal household expenditures, which is part of services, was revised significantly down, from +1.32 to +0.73 percentage point contribution to GDP. An almost bizarre revision was in health care expenditures. It's 3rd quarter GDP contribution is now –0.07 percentage points, whereas the 2nd revision Health care expenditures was +0.61 percentage points of Q3 GDP. What happens is the BEA has to do by proxy approximations of some expenditures due to raw data lag. Medical expenditures are from the quarterly services survey and are reported revenues from Hospitals, Medical facilities and was not available until this 3rd GDP revision. These medical expenditures should be actual collected gross revenues, not debt outstanding. It's not clear what happened but one must wonder if more and more people simply cannot pay their medical bills to have such a dramatic revision. That said, PCE is often revised as receipts and reports are collected and there is quite a bit of raw data lag and one of the reasons quarterly GDP is issued in a three revision series. Below is PCE with the breakdown of goods versus services.
Changes in private inventories subtracted –1.35 percentage points from Q3 2011 GDP. Last quarter changes in private inventories contributed a –0.28 percentage point change. The change in private inventories point contribution reduced Q3 GDP by 72.2%. Companies reduce inventories when they believe an economic slowdown will happen.
Below are real final sales of domestic product, or GDP - inventories change. This gives a better feel for real demand in the economy. This is also a downward revision from 3.6% to 3.2%. Q2 real demand was 1.6%. While this is a downward revision, it's still an improvement from Q2.
Below are net exports, or the trade deficit, in real chained dollars, for Q3 2011. The Q3 3rd revision gave a -0.07 percentage point contribution drag to Q3 GDP, mainly due to the increase in services imports.
The below graph shows real imports vs. exports. Exports increased, 4.7%, revised up from 4.3% in comparison to last quarter's 3.6% for Q2. Q3 imports increased 1.2%, revised significantly up from the 0.5% change reported in the advance report. Q2 was a 1.4% increase in imports. It is the trade deficit that matters for GDP, although volume of trade implies a slower global economy. These numbers are almost always revised from the advance report as Census trade data comes in from customs.
Below are the percentage changes of Q3 2011 GDP components in comparison to Q2, along with the 2nd GDP revision reported quarterly percent changes. Realize there is a difference between percentage change and percentage point change. Point change adds up to the total GDP percentage change and is reported above. The below is the individual quarterly percentage change, against themselves, of each component which makes up overall GDP.
• C = +1.7%, revised down +2.3%
• I = +1.3%, revised up from –0.9%%
• G = –0.01%, no change from 2nd revision report
• X = +4.7%, revised up from +4.3%
• M = +1.2% revised down from +0.5%
The BEA's comparisons in percentage change breakdown of 2nd quarter GDP components are below. Changes to private inventories is a component of I.
C: Real personal consumption expenditures increased 1.7 percent in the third quarter, compared with an increase of 0.7 percent in the second. Durable goods increased 5.7 percent, in contrast to a decrease of 5.3 percent. Nondurable goods decreased 0.5 percent, in contrast to an increase of 0.2 percent. Services increased 1.9 percent, the same increase as in the second.
I: Real nonresidential fixed investment increased 15.7 percent, compared with an increase of 10.3 percent. Nonresidential structures increased 14.4 per cent, compared with an increase of 22.6 percent. Equipment and software increased 16.2 percent, compared with an increase of 6.2 percent. Real residential fixed investment increased 1.3 percent, compared with an increase of 4.2 percent.
The change in real private inventories subtracted 1.35 percentage poi nts from the third-quarter change in real GDP, after subtracting 0.28 percentage point from the second-quarter change. Private businesses decreased inventories $2.0 billion in the third quarter, following increases of$39.1 billion in the second quarter and $49.1 billion in the first. X & M: Real exports of goods and services increased 4.7 percent in the third quarter, compared with an increase of 3.6 percent in the second. Real imports of goods and services increased 1.2 percent, compared with an increase of 1.4 percent. G: Real federal government consumption expenditures and gross investment increased 2.1 percent in the third quarter, compared with an increase of 1.9 percent in the second. National defense increased 5.0 percent, compared with an increase of 7.0 per cent. Nondefense decreased 3.8 percent, compared with a decrease of 7.6 percent. Real state and local government consumption expenditures and gross investment decreased 1.6 percent, compared with a decrease of 2.8 percent. Motor Vehicles was revised down, added +0.12 instead of +0.18 percentage points reported in the 2nd GDP revision, to Q3 real GDP while computer final sales added +0.22 percentage point changes, not revised. This is different from personal consumption, or C auto & parts. Motor vehicles, computers are bought as investment, as fleets, in bulk, by the government and so forth. Residential fixed investment was revised down, from +0.04 to +0.03 percentage points to Q3 GDP, after adding a paltry +0.09 percentage points in Q2. In other words, residential fixed investment is D.O.A.. Below is the raw totals on residential investment. If one could ever see the housing bubble and then it's collapse in terms of economic contributions, the below graph is it. Private, or not from the government, nonresidential fixed investment was revised up, from a 1.45 percentage point contribution to Q3 GDP to 1.49. Equipment and Software was another revision, this time up, from 1.08 to 1.12 percent point contribution. Equipment & software represents a 16.2% percentage change from Q2 to Q3. Since the GDP report is in real chained 2005 dollars, and the price index for what U.S. consumers pay was revised upward 0.1 percentage point to 2.0%. The core price index, or minus food and energy, increased 1.8%. In other words, slightly more inflation, less real value in comparison to the 2nd revision, but dramatically less inflation than the previous quarter. The Q2 price index was 2.7%. The price index for GDP was 2.6. There are a host of price indexes per GDP component category and are listed in table 4 of the GDP report. In current dollars, not adjusted for prices, GDP, or the U.S. output, is$15.1761 trillion, a downward revision of $4.8 billion and an increase of 1.09%, or$163.3 billion from Q2, revised down from 1.12% change between quarters. These percentages are not annualized although nominal GDP is. The annualized percentage change from Q2 was 4.4%. The Q1 to Q2 annualized percentage change for nominal GDP was 4.0%. Applying the price indexes, or chained, real 2005 dollars, real Q3 GDP was \$13.3316 trillion.
Here are the overview for the Q3 2011 GDP, 2nd revision report, unrevised.
Q2 2011 GDP remained the same at 1.3%.
* In Table 2, the BEA reports GDP contribution components with their equation sign. If durable goods for example, decreased over the quarter or year, it is reported as a negative number. Imports, from the GDP equation, are already a negative for that is not something produced domestically. A negative sign implies imports increased for the time period and a + sign means the change in imports decreased. Or, from the GDP equation: $X -(-M) = X + M$. Confusing but bottom line exports add to economic growth, imports subtract.
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Cornell RD 2....postponed : The B-School Application
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# Cornell RD 2....postponed
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Joined: 05 Mar 2006
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13 Dec 2006, 11:05
I talked to Cornell/Johnson Admissions this morning. I found out that they are about send a mass notice to state that the decision date is going to be postposned by upto 4 weeks in response to the extremely heavy application volume.
I haven't even received an interview invite yet.
Great!!
GMAT Club Legend
Affiliations: HHonors Diamond, BGS Honor Society
Joined: 05 Apr 2006
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13 Dec 2006, 11:17
agsfaltex wrote:
I talked to Cornell/Johnson Admissions this morning. I found out that they are about send a mass notice to state that the decision date is going to be postposned by upto 4 weeks in response to the extremely heavy application volume.
I haven't even received an interview invite yet.
Great!!
Woah, really? Thats got to be frustrating news!
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13 Dec 2006, 11:27
that suckkkkkkssssssssssssss
should i even apply to R3? Will they be done with all admits by R2.....
arrghhhhh
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13 Dec 2006, 11:57
Weird. It sounds like there is a significant spike in application volume this year. Schools reporting application incresaes as high as 15-50%, pushing deadlines, etc. I wonder why.
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13 Dec 2006, 15:05
I will tell you my theory - we are all applying to multiple schools, and probably more then in the past because everyone wants to get in.
I think a lot of schools are seeing the same applicants along with some increased volume generated by more interest in MBA programs in general.
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13 Dec 2006, 16:04
I totally agree with OasisNYK. The surprising thing is that GMAT volume is not up significantly from last year. Last year was one of the statistically easiest years to get in. Some top schools have accept rates of over %20. This is because there was a 3 year slide in app volume. The increase of %15-50 is a recovery to normal levels.
I believe part of the volume increase is because more people are filling out multiple apps. With all the new online resources, it is easier than ever to know how to fill out an app. Also, I think people are applying to more schools because of the hype (justified or not) that business school admission is going to be more competitive this year.
I agree with OasisNYK [#permalink] 13 Dec 2006, 16:04
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Change language to:
English - Français - 日本語 - Русский
See the recommended documentation of this function
Ajuda do Scilab >> CACSD > Linear System Representation > frep2tf
# frep2tf
transfer function realization from frequency response
### Syntax
```[h, err] = frep2tf(frq, repf, dg)
[h, err] = frep2tf(frq, repf, dg, dom, tols, weight)```
### Arguments
frq
vector of frequencies in Hz.
repf
vector of frequency response
dg
degree of linear system
dom
time domain (`'c'` or `'d'` or `dt`)
tols
a vector of size 3 giving the relative and absolute tolerance and the maximum number of iterations (default values are `rtol=1.e-2; atol=1.e-4, N=10`).
weight
vector of weights on frequencies
h
SISO transfer function
err
error (for example if `dom='c'` `sum(abs(h(2i*pi*frq) - rep)^2)/size(frq,*)`)
### Description
Frequency response to transfer function conversion. The order of `h` is a priori given in `dg` which must be provided. The following linear system is solved in the least square sense.
`weight(k)*(n( phi_k) - d(phi_k)*rep_k)=0, k=1,..,n`
where `phi_k= 2*%i*%pi*frq` when `dom='c'` and `phi_k=exp(2*%i*%pi*dom*frq` if not. If the `weight` vector is not given a default penalization is used (when `dom='c'`).
A stable and minimum phase system can be obtained by using function `factors`.
### Examples
```s=poly(0,'s');
h=syslin('c',(s-1)/(s^3+5*s+20))
frq=0:0.05:3;
repf=repfreq(h,frq);
clean(frep2tf(frq,repf,3))```
```Sys=ssrand(1,1,10);
frq=logspace(-3,2,200);
[frq,rep]=repfreq(Sys,frq); //Frequency response of Sys
[Sys2,err]=frep2tf(frq,rep,10);
Sys2=clean(Sys2) //Sys2 obtained from freq. resp of Sys
[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
clf();
bode(frq,[rep;rep2]) //Responses of Sys and Sys2
[gsort(spec(Sys('A'))), gsort(roots(Sys2('den')))] //poles```
```dom = 1/1000; // Sampling time
z = poly(0,'z');
h = syslin(dom,(z^2+0.5)/(z^3+0.1*z^2-0.5*z+0.08))
frq = (0:0.01:0.5)/dom;
repf = repfreq(h,frq);
[Sys2,err] = frep2tf(frq,repf,3,dom);
[frq,rep2] = repfreq(Sys2,frq); //Frequency response of Sys2
clf();
plot2d(frq, abs([repf;rep2])')```
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Publicité
Prochain SlideShare
Now remove the two lenses at +20-0 cm and 20-0 cm and replace them wit.docx
Chargement dans ... 3
1 sur 2
Publicité
### A compound lens system consists of two converging lenses one at z -20-.docx
1. A compound lens system consists of two converging lenses one at z -20.0 cm with focal length fi-+10.0 cm. and the other at z +20.0 cm with focal length f2 +8.00 cm. (Figure 1)An object 1.00 centimeter tall is placed at x 50.0cm What is the location of the final image produced by the compound lens system? Give the x coordinate of the image. Express your answer in centimeters, to three significant figures or as a fraction. View Available Hint(s -31.8 cm Previous Answers Correct Figure 1 of 1 Part How tall is the image? Express your answer in centimeters, to three significant figures or as a fraction View Available Hint(s) fi f2 cm Submit Solution here, for the first lens the focal length , f1 = 10 cm object distance , do1 = 30 cm let the image distance be di1 using the lens formula 1/f1 = 1/di1 + 1/do1 1/10 = 1/di1 + 1/30 di1 = 15 cm for the seccond lens the focal length , f2 = 8 cm object distance , do2 = 25 cm let the image distance be di2
2. using the lens formula 1/f2 = 1/di2 + 1/do2 1/8 = 1/di2 + 1/25 di2 = 11.8 cm B) the image height , hi = h0 * ( di1/do1) *(di2/do2) hi = 1 * ( 15/30) *(11.8/25) hi = 0.24
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## Friday, 30 October 2015
### My best math
WALT: Use more than one strategy to help us solve multiplication problems.
This is my timetable I well show you 3x6=18 9x10=90
## Tuesday, 27 October 2015
### Spending the day with my best dad Muna
One weekend me and my brother Misi went with my dad. His name is Muna.When we are with our dad we go to the movies or the mall. Sometimes we go to our cousin’s house to play. My dad is the best dad ever because he gives us some money. I like spending time with my dad because he loves us and when he leaves I feel sad.
This is me and my brother with my Dad.
We are 5 years younger.
## Friday, 23 October 2015
### Timetable
Walt: Use more than one strategy to help us solve multiplication problems.We are learning our timetable today.
### Timetable
Walt: Use more than one strategy to help us solve multiplication problems. We are learning our timetable.
## Thursday, 15 October 2015
### Times table
WALT:Use our knowledge of basic multiplication facts to help us solve word number problems. I know this because I been practicing at and at school it is cool doing times table. 5 x 6=30 2 x 4=6
## Wednesday, 14 October 2015
These holidays I went to Riverside Camp. When we got to Willow Park we put our bags away in our rooms and then we went to the Rima room. Mr Burt put us into groups. After that we played a game. It was fun but it was too hard and so after that game we played another game in the gym. It was funny. When the game finished we had some morning tea. It was so delicious. When it was dark we played a game called “Finding the Crunchy Bars”.It was fun and scary.
## Tuesday, 13 October 2015
### my math
WALT: This the timetable it is 3,4 and 6 it was easy
I will show you 2 x 6=12 1 x 5=5 that it.
## Monday, 12 October 2015
### Team 4 Inquiry PES Survivor
This term our inquiry is called "survivor". We are going to be learning about animals, creatures and living and how they adapt to survivor in their environment.
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# Is this the correct way to prove that this intersection is a subgroup of Z(G)
Suppose that $$H,C_G(H) \leq G$$ where $$G=HC_G(H)$$. I want to show that $$H\cap C_G(H) \leq Z(G).$$(H being a subgroup, $$C_G$$ the centraliser of H and Z the centre of the group.)
My attempt :
$$H,C_G(H) \leq G, \Rightarrow H \cap C_G(H) \leq G$$ and that $$|HC_G(H)|=\tfrac{|H||C_G(H)|}{|H\cap C_G(H)|}$$
However
$$|HC_G(H)|=|C_G(H)| \Rightarrow |H\cap C_G(H)|=|H|$$.
Next consider Z(G)
$$|Z(G)|=|G|-\sum|K(g)|$$
But looking at K(g) and G
$$K(g)=\{y \in G | y=x^{-1}gx , x \in G\}$$
$$G=\{hg|g=h^{-1}gh\}$$ which means that for all g, |K(g)|=0.
and so we are left with $$|Z|=|G|$$.
Now we know that $$|H|$$ divides $$|G|$$, which means that $$|H\cap C_G(H)|$$ divides $$|Z(G)|$$ and so by lagrange's theorem $$|H\cap C_G(H)|\leq |Z(G)|$$
• Is it given to you that $G$ is finite? – Anurag A Oct 23 '18 at 23:16
• @AnuragA No G is any group. – excalibirr Oct 23 '18 at 23:43
• In which case you cannot use the cardinality of different subgroups or Lagrange's theorem. – Anurag A Oct 23 '18 at 23:45
• damn, back to the drawing board – excalibirr Oct 24 '18 at 13:47
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{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.609375
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CC-MAIN-2019-35
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https://www.chenguanghe.com/analyze-user-website-visit-pattern/
| 1,674,771,619,000,000,000
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crawl-data/CC-MAIN-2023-06/segments/1674764494826.88/warc/CC-MAIN-20230126210844-20230127000844-00716.warc.gz
| 714,080,968
| 11,259
|
# Analyze User Website Visit Pattern
``````class Solution {
class Pair {
int c;
String s;
public Pair(String s, int c) {
this.s = s;
this.c = c;
}
}
class Triple {
int t;
String s;
String w;
public Triple(String s, int t, String w) {
this.s = s;
this.t = t;
this.w = w;
}
}
public List<String> mostVisitedPattern(String[] username, int[] timestamp, String[] website) {
List<Triple> t = new ArrayList<>();
for(int i = 0; i < n; i++) {
}
Collections.sort(t,(a, b) -> (a.t-b.t));
Map<String, List<String>> map = new HashMap<>();
for(Triple tt : t) {
map.putIfAbsent(tt.s, new ArrayList<>());
}
Map<String, Set<String>> countMap = new HashMap<>();
for(Map.Entry<String,List<String>> e : map.entrySet()) {
countMap.putIfAbsent(e.getKey(), new HashSet<>());
}
Map<String, Set<String>> countMapRev = new HashMap<>();
for(Map.Entry<String,Set<String>> e : countMap.entrySet()) {
for(String s : e.getValue()){
countMapRev.putIfAbsent(s, new HashSet<>());
}
}
List<String> res = new ArrayList<>();
PriorityQueue<Pair> pq = new PriorityQueue<>((a, b) -> (a.c == b.c ? a.s.compareTo(b.s) : b.c - a.c));
for(Map.Entry<String,Set<String>> e : countMapRev.entrySet()) {
}
String ss = pq.poll().s;
String[] strs = ss.split("-");
for(String s : strs)
return res;
}
private Set<String> getSeq(List<String> myArray) {
Set<String> res = new HashSet<>();
for(int i = 0; i < myArray.size() - 2; i++) {
for(int j = i + 1; j < myArray.size() - 1; j++) {
for(int k = j + 1; k < myArray.size(); k++) {
}
}
}
return res;
}
}
``````
| 442
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|
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| 2.640625
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CC-MAIN-2023-06
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latest
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en
| 0.315233
|
http://mathforum.org/library/drmath/view/56059.html
| 1,521,726,997,000,000,000
|
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|
crawl-data/CC-MAIN-2018-13/segments/1521257647885.78/warc/CC-MAIN-20180322131741-20180322151741-00284.warc.gz
| 192,966,023
| 3,280
|
Associated Topics || Dr. Math Home || Search Dr. Math
### When Casting Out Nines Fails
```
Date: 11/29/2001 at 21:05:19
From: Teresa Miller
Subject: Casting out 9's, division
My son is doing Abeka 6th grade math. I was intrigued with checking
math by casting out 9's. I introduced this technique to a friend.
Just to prove that casting out 9's worked, I intentionally used an
incorrect answer (quotient). I was shocked when the problem checked
out correctly. Here is the problem. Divisor 6, Dividend 5223, and
Quotient 875. Have I done something wrong? I know the correct answer
is 870 R. 3.
Really stumped,
Teresa Miller
```
```
Date: 11/29/2001 at 23:30:30
From: Doctor Peterson
Subject: Re: Casting out 9's, division
Hi, Theresa.
It's not at all surprising that casting out nines would fail; it puts
all numbers into one of 9 categories, so it will catch an error that
puts it into one of the 8 wrong categories, but not one that happens
to land it back in the "right" category. This means there is a 1 in 9
chance that a random error will look okay. When the method is taught,
it should always be pointed out that it can tell you if an answer is
wrong, but can't be trusted to tell you that it is right!
Claim: 875 * 6 + 0 = 5223
Check: 8 * 6 + 0 =? 3
48
3 =? 3
(There are different ways to arrange the work, of course. I calculated
the digit sums, then calculated the left side as 48 and found its
digit sum to be 3.)
The correct answer, checked, would be
Claim: 870 * 6 + 3 = 5223
Check: 6 * 6 + 3 =? 3
39
3 =? 3
You have added 5 to the quotient, which adds 5*6 (or 3) to the digit
sum; and you dropped the remainder of 3, which subtracted 3 from the
digit sum, so you came out even.
In case you are interested, here is my explanation of the method:
Casting Out Nines to Check Arithmetic
http://mathforum.org/library/drmath/view/55926.html
I checked, and I do explain the pitfalls of the method. Whew!
- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory
| 597
| 2,040
|
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| 3.921875
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CC-MAIN-2018-13
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en
| 0.911161
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https://homeschoolingcatolico.org/it/aggregator/sources/4?page=21
| 1,596,912,599,000,000,000
|
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|
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| 338,962,435
| 11,903
|
## Carrello
0 Prodotti Totale: MXN\$0.00
New exercises from Khan Academy 2020-08-07T05:32:39.000000
Aggiornato: 2 min 59 sec fa
### Periodic trends: metallic, nonmetallic, electropositive, & electronegative characters
Mar, 2020-05-12 11:42
Let's practice to identify the periodic trends of losing and gaining and electrons when we go from left to right and top to bottom of the periodic table.
### Physical and chemical changes
Mar, 2020-05-12 11:27
Let's practice to differentiate between a physical change and a chemical change by solving the given questions.
### Subtracting decimals (tenths)
Lun, 2020-05-11 23:49
Subtract small whole numbers and tenths like 1.6-0.3
### Subtract decimals (hundredths)
Lun, 2020-05-11 23:49
Subtract small whole numbers, tenths, and hundredths like 0.6-0.43 or 1.58-0.5
Lun, 2020-05-11 23:39
Add more challenging whole numbers, tenths, and hundredths like 5.7+4.51 or 47.75+11.98
Lun, 2020-05-11 23:38
Add larger numbers with tenths like 40.1+7.6
### Defining transformations
Lun, 2020-05-11 22:09
Refine definitions of rigid transformations. Given a description of the effect of a transformation, determine which rigid transformation it is.
### Identify parallel and perpendicular lines
Lun, 2020-05-11 22:07
Recognize parallel and perpendicular lines in geometric figures and pictures.
### Focus on causation: Human migration
Lun, 2020-05-11 21:30
Let's explore more perspectives on why populations moved.
### Convert units (metrics)
Lun, 2020-05-11 21:17
Convert between metric measures of distance, volume, and mass.
### Hundreds, tens, and ones
Lun, 2020-05-11 19:44
Practice thinking about place value of 3-digit numbers as hundreds, tens, and ones.
### Frequently confused words: assorted
Lun, 2020-05-11 17:33
Can you identify when to correctly use these words that often get confused with other words?
### Obscuring the truth: reading realistic fiction; The Open Window 8
Lun, 2020-05-11 16:42
### Mysteries of the Past: reading realistic fiction; A View from the Walnut Tree 7
Lun, 2020-05-11 16:23
### Mysteries of the Past: reading informational text; The Roanoke Voyages 7
Lun, 2020-05-11 15:09
### Mysteries of the Past: vocabulary; The Roanoke Voyages 7
Lun, 2020-05-11 15:08
7th grade applied vocabulary practice using an informational text about the lost colony of Roanoke
### Obscuring the truth: reading realistic fiction; One Big Mess 8
Lun, 2020-05-11 15:02
### Obscuring the truth: vocabulary; Why Do We Lie? 8
Lun, 2020-05-11 14:56
### Obscuring the truth: reading informational text; The Science of Lying 8
Lun, 2020-05-11 14:49
| 808
| 2,628
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.703125
| 4
|
CC-MAIN-2020-34
|
latest
|
en
| 0.73958
|
www.thesodguy.com
| 1,702,146,475,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100942.92/warc/CC-MAIN-20231209170619-20231209200619-00084.warc.gz
| 1,110,661,154
| 150,962
|
How To Measure
It is important to calculate the correct amount of square feet of sod needed for your lawn. We have provided some easy mathematics to help take some of the guess work out of measuring for your lawn.
Measuring A Circle
To calculate the area of a circle, first find the Radius. The Radius is a straight line from the center of a circle to the outside edge of the circle. Then multiply 3.14 times the radius times the radius again.
Area = 3.14 x r2
Area = 3.14 x 102
Area = 3.14 x 100
Area = 314 square feet
Measuring A Rectangle or A Square
To calculate the area of a rectangle or square, measure the length and width and then multiply together.
Area in square feet = Length in feet (L) x Width in feet (W)
Area = L x W
Let’s say your length is 20 feet and your width is 30 feet…
Area = 20 feet x 30 feet
Area = 600 square feet
Measuring A Triangle
To calculate the area of a triangle, measure the base and the height (both in feet). Then multiply the base and the height together. Divide the result by 2 to get the area.
Area = ( Base (B) x Height (H) ) ÷ 2
| 282
| 1,089
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.28125
| 4
|
CC-MAIN-2023-50
|
latest
|
en
| 0.885971
|
https://www.futurestarr.com/blog/author/30-60-90-triangle
| 1,660,625,205,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-33/segments/1659882572220.19/warc/CC-MAIN-20220816030218-20220816060218-00222.warc.gz
| 685,301,331
| 35,999
|
FutureStarr
30 60 90 Triangle
## What Is a 30-60-90 Triangle?
A right triangle is any triangle that has a 90-degree angle. A 30-60-90 triangle is a special type of right triangle that has a 30-degree angle and a 60-degree angle in addition to the right angle. This triangle has the angles labeled as shown in the diagram. (Source: study.com A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. The triangle is special because its side lengths are always in the ratio of 1: √3:2. (Source:www.storyofmathematics.com))
It is a triangle where the angles are always 30, 60 and 90. As one angle is 90, so this triangle is always a right triangle. As explained above that it is a special triangle so it has special values of lengths and angles. (Source: byjus.com)
## 30-60-90 Triangle Rules & Sides
study.com)Jeanne Rast has taught Mathematics in grades 7-12 and college for over 30 years. She has a Ph.D. in Math Education and a M.Ed. in Math both from Georgia State University, as well as a B.A. in Math from The University of the South. Dr. Rast is a certified teacher for the State of Georgia for Mathematics grades 7-12 (Source:
## What Is the 30 60 90 Triangle Rule?
The 30-60-90 triangle rule is for finding the the lengths of two sides when one side is given. The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle. The longer side is the square root of 3 times the shorter side, and the hypotenuse is twice the shorter side. (Source: study.com)
## How Do You Find the Side Lengths of a 30 60 90 Triangle?
To find the side lengths of a 30-60-90 one side must be given. If the shorter side is given, multiply it by 2 to get the hypotenuse, and multiply it by the square root of 3 to get the longer side. If the hypotenuse is given, divide it by 2 to get the shorter side and then multiply the shorter side by the square root of 3 to get the longer side. If the longer side is given, divide it by the square root of 3 to get the shorter side, and then multiply the shorter side by 2 to get the hypotenuse. (Source: study.com)
## 30-60-90 Triangl
There are different types of triangles such as obtuse, isosceles, acute, equilateral, and so on. But only a few types of triangles are considered special triangles. These triangles are special as their sides and angles are consistent and predictable. Their properties can be used to solve various geometry or trigonometry problems. A 30-60-90 triangle—pronounced "thirty sixty ninety"—is one such very special type of triangle indeed. (Source: www.cuemath.com)
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| 1,049
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|
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| 4.53125
| 5
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CC-MAIN-2022-33
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|
https://worldbuilding.stackexchange.com/questions/167873/how-big-of-a-wave-would-this-falling-cliff-create
| 1,642,328,488,000,000,000
|
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| 679,232,324
| 30,496
|
# How big of a wave would this falling cliff create?
I'm running a D&D campaign and, well, the players had blown up a cave filled with explosives under a 40-metr cliff. I told them the cliff cracked and fell into the ocean. 40 meters tall, 30 meters into the land, around 60 meters along the coastline from start to finish of a crack. How would it affect the marina in a city nearby? How tall would a wave be? The cliff, I'm assuming would just slide into the water quite fast.
• Argh. I cannot find the citation!!! I once read about a particular cliff (somewhere in the Caribbean) that has a near perfect parabola shape that may cleave off the side of its island, entering the water on a knife edge and widening. Computer models estimated a single wave a couple hundred feet tall resulting, heading toward a Mexico/USA. But I cannot find citation. Maybe your Google karma is better than mine. I do recall that shape mattered as much as mass in the wave created.
– SRM
Feb 8 '20 at 14:15
• Found it! Didn’t start in the Carribean, but it ends there... starts at Isle of Man: theguardian.com/uk/2004/aug/10/science.spain someone else can turn this into a proper answer.
– SRM
Feb 8 '20 at 14:21
• Looks like big, but not massive. Feb 8 '20 at 15:42
• this depends a lot on the sea floor in the area, how deep is the water it is falling into? where do you want the height measured right next to the impact, half a mile away?
– John
Feb 8 '20 at 15:57
• @SRM the article says it starts in the Canary Isles but the chunk of rock is the size of the Isle of Man. Good find though. Feb 8 '20 at 19:04
| 419
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| 2.53125
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https://www.fam-bundgaard.dk/SOMA/NEWS/N010919.HTM
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| 853,870,111
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SOMA News 19 Sep 2001 E-Mail.
# Coloring a SOMA cube.
On 14. Sep. 2001 Nick Dickens. Albuquerque, New Mexico, USA. (CO: Pat Bateman <horrorkid@excite.com>) asked me an interesting question about coloring of a SOMA cube.
Here is the question, and two answers.
Question:
Is it possible to form a cube,
Paint the outside of the cube,
Take it apart,
And then form a cube again, but have no paint visible?
NO.
There are 8 corners in the 3x3x3 cube.
Each piece can contribute, at most:
pieces #1, 4, 5, 6 & 7: 1 corner each
pieces #2 & 3: 2 corners each
Which gives us a maximum of 9 corners, which is more than the required 8.
But piece #3 has a strange property - it can either donate 2 corners, or no corners, but it is IMPOSSIBLE for it to donate just ONE corner.
If piece #3 donates NO corners, then the maximum number of corners left is only 7, not enough to form the 3x3x3 cube.
(This was explained in the newsletter, called "Winning Ways").
Therefore, piece #3 must ALWAYS donate 2 corners, which means it must ALWAYS have its spine along one of the edges of the 3x3x3 cube. Because the exposed spine is painted in one solution, then the painted spine will have to be exposed for all the other 239 solutions.
| 334
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http://arbtech.co.in/whatsappmessages/message/viewMessage/457/Puzzle-for-cricket-lovers
| 1,571,062,937,000,000,000
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| 16,328,017
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# Puzzle for cricket lovers
A question for all cricket lovers, maths genious, teachers and friends. .!!
How many runs a single player can score in One day match (50 overs/ 300 balls)
No 'no balls', no wides, no extras, no over throws...
So how much runs he can score max???
Choices :
A) 1800.
B) 1650.
C) 1653.
D) 1550.
E) 1555
F) 1506
### You may also like :
Q. How can you tell when an auto mechanic just had sex? A. One of his fingers is clean.
Q. What is the difference between a golf ball and a G-spot? A. Men will spend hours searching for a golf ball.
A man walks into his bedroom and sees his wife packing a suitcase. He says, What are you doing? She answers, I m moving to New York. I heard prostitutes there get paid Dollar100 for doing what I do for you for free! Later that night, while on her way out, the wife walks into the bedroom and sees her husband packing his suitcase. When she asks him where he s going, he replies, I m going to New York, too. I want to see you live on Dollar200 a year!
An Englishman, a Scotsman, and an Irishman are all to give speeches to the Deaf and Dumb Society. All are intent on making an impression on their audience. The Englishman goes first, and to the surprise of his colleagues, starts by rubbing first his chest, and then his groin. When he finishes, the Scotsman and Irishman ask him what he was doing. Well, he explained, by rubbing my chest I indicated breasts and thus ladies, and by rubbing my groin I indicated balls and thus gentlemen. So my speech started: Ladies and Gentlemen. On his way up to the podium the Scotsman thought to himself I ll one-up that English bastard! He started his speech by making an antler symbol with his fingers above his head before also rubbing his chest and his groin. When he finished, his colleagues asked what he was doing. Well, he explained, by imitating antlers and then rubbing my chest and groin I was starting my speech by saying, Dear Ladies and Gentlemen. On his way up to the podium the Irishman thought to himself, I ll go even further than those bastards! He started his speech by making an antler symbol above his head, rubbing his chest, and then his groin, and then masturbating furiously. When he finished, his colleagues asked him what he was doing. Well, he explained, by imitating antlers, rubbing my chest and then my groin, and then masturbating, I was starting my speech by saying, Dear Ladies and Gentlemen, it gives me great pleasure...
A recently deceased man stands at the pearly gates. St. Peter tells him that he cannot go to heaven right away because he cheated on his income taxes. The only way he might get into heaven would be to sleep with a stupid, ugly woman for the next five years and enjoy it. He decides that this is a small price to pay for an eternity in heaven. So off he goes with this woman, pretending to be happy. As he walks along, he sees his friend up ahead with an even uglier woman. When he asks what s going on, the friend replies, I cheated on my income taxes and scammed the government out of a lot of money. They both shake their heads in understanding and figure that they might as well hang out together to help pass the time. Now the two friends and their two ugly women are walking along minding their own business when they see someone who looks like their old friend. This man is with an absolutely gorgeous supermodel. Stunned, they approach the man and discover that it is indeed their friend. They ask him how come he s with this unbelievable goddess, while they re stuck with these god-awful women. He replies, I have no idea, but I m definitely not complaining. This has been absolutely the best time imaginable, and I have five years of the best sex any man could hope for to look forward to. There is only one thing that I can t seem to understand. Every time we finish having sex, she rolls over and murmurs to herself, Damn income taxes!
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# What date is 20 days added from Saturday December 16, 2023?
## Friday January 05, 2024
Adding 20 days from Saturday December 16, 2023 is Friday January 05, 2024 which is day number 005 of 2023. This page is designed to help you the steps to count 20, but understand how to convert and add time correctly.
• Days to add: 20
• Specific Date: Saturday December 16, 2023
• Days from Saturday December 16, 2023: Friday January 05, 2024
• Day of the year: 005
• Day of the week: Friday
• Month: January
• Year: 2023
## Calculating 20 days from Saturday December 16, 2023 by hand
Attempting to add 20 days from Saturday December 16, 2023 by hand can be quite difficult and time-consuming. A more convenient method is to use a calendar, whether it's a physical one or a digital application, to count the days from the given date. However, our days from specific date calculatoris the easiest and most efficient way to solve this problem.
If you want to modify the question on this page, you have two options: you can either change the URL in your browser's address bar or go to our days from specific date calculator to enter a new query. Keep in mind that doing these types of calculations in your head can be quite challenging, so our calculator was developed to assist you in this task and make it much simpler.
## Friday January 05, 2024 Stats
• Day of the week: Friday
• Month: January
• Day of the year: 005
## Counting 20 days forward from Saturday December 16, 2023
Counting forward from today, Friday January 05, 2024 is 20 from now using our current calendar. 20 days is equivalent to:
20 days is also 480 hours. Friday January 05, 2024 is 1% of the year completed.
## Within 20 days there are 480 hours, 28800 minutes, or 1728000 seconds
Friday Friday January 05, 2024 is the 005 day of the year. At that time, we will be 1% through 2024.
## In 20 days, the Average Person Spent...
• 4296.0 hours Sleeping
• 571.2 hours Eating and drinking
• 936.0 hours Household activities
• 278.4 hours Housework
• 307.2 hours Food preparation and cleanup
• 96.0 hours Lawn and garden care
• 1680.0 hours Working and work-related activities
• 1545.6 hours Working
• 2529.6 hours Leisure and sports
• 1372.8 hours Watching television
## Famous Sporting and Music Events on January 05
• 1911 British PM Neville Chamberlain (41) weds Anne de Vere Cole
• 1993 Brian Lara scores his maiden Test century with 277 for the West Indies v Australia in drawn 3rd Test at the Sydney Cricket Ground
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# Scaling laws
Curator and Contributors
1.00 - Benjamin Widom
Prof. Benjamin Widom accepted the invitation on 4 February 2009 (self-imposed deadline: 4 August 2009).
Scaling laws are the expression of physical principles in the mathematical language of homogeneous functions.
## Introduction
A function $$f (x, y, z,\ldots)$$ is said to be homogeneous of degree $$n$$ in the variables $$x,y,z,\ldots$$ if, identically for all $$\lambda\ ,$$
$\tag{1} f(\lambda x, \lambda y, \lambda z, \ldots) \equiv \lambda^{n}f (x, y, z, \ldots).$
For example, $$ax^2 + bxy + cy^2$$ is homogeneous of degree 2 in $$x$$ and $$y$$ and of the first degree in $$a, b,$$ and $$c\ .$$
By setting $$\lambda = 1/x$$ in (1) we have as an alternative expression of homogeneity$f (x, y, z, \ldots)$ is homogeneous of degree $$n$$ in $$x, y, z, \ldots$$ if
$\tag{2} f(x, y, z, \ldots) = x^nf(1, y/x, z/x, \ldots) \equiv x^n\phi(y/x, z/x, \ldots);$
i.e., the $$n^{th}$$ power of $$x$$ times some function $$\phi$$ of the ratios $$y/x, z/x, \ldots$$ alone.
If $$f (x, y, z, \ldots)$$ is homogeneous of degree $$n$$ in $$x, y, z, \ldots$$ it satisfies Euler's theorem :
$\tag{3} x\frac{\partial f}{\partial x}+y\frac{\partial f}{\partial y}+z\frac{\partial f}{\partial z}+\cdots \equiv nf.$
In thermodynamics, if the scale of a system is merely increased by a factor $$\lambda$$ with no change in its intensive properties, then all its extensive properties including its entropy $$S\ ,$$ energy $$E\ ,$$ volume $$V\ ,$$ and the masses $$m_1, m_2, \ldots$$ of each of its chemical constituents are increased by that factor, so the extensive function $$S(E, V, m_1, m_2, \ldots)$$ is homogeneous of degree 1 in its extensive arguments:
$\tag{4} S(\lambda E, \lambda V, \lambda {m_1}, \lambda {m_2}, \ldots ) = \lambda S(E, V, {m_1}, {m_2}, \ldots).$
With $$T$$ the temperature, $$p$$ the pressure, and $$\mu_i$$ the chemical potential of the species $$i\ ,$$ we have the thermodynamic relations $$\partial S/\partial E = 1/T\ ,$$ $$\partial S/\partial V = p/T\ ,$$ and $$\partial S/\partial m_i = - \mu_i/T\ ;$$ so from Euler's theorem,
$\tag{5} \frac{1}{T} (E + pV - \mu_1m_1 - \mu_2m_2 - \cdots) =S,$
an important identity. Any extensive function $$X(T, p, m_1, m_2, \ldots)\ ,$$ such as the volume V or the Gibbs free energy $$E+pV-TS\ ,$$ is homogeneous of the first degree in the $$m_i$$ at fixed $$p$$ and $$T\ ,$$ so
$\tag{6} X = m_1 \frac{\partial X}{\partial m_1} + m_2 \frac{\partial X}{\partial m_2} + \cdots ,$
an important class of relations.
## Scaling laws
The foregoing are scaling relations in classical thermodynamics. In more recent times, in statistical mechanics, the expression "scaling laws" has been taken to refer to the homogeneity of form of the thermodynamic and correlation functions near critical points, and to the resulting relations among the exponents that occur in those functions. There are many excellent references for critical phenomena and the associated scaling laws, among them the superb book by Domb [1] and the historic early review by Fisher [2].
Near the Curie point (critical point) of a ferromagnet, which occurs at $$T = T_c\ ,$$ the magnetic field $$H\ ,$$ magnetization $$M\ ,$$ and $$t = T/T_c-1\ ,$$ are related by
$\tag{7} H = M\mid M\mid ^{\delta-1} j(t/\mid M\mid ^{1/\beta})$
where $$j(x)$$ is the "scaling" function and $$\beta$$ and $$\delta$$ are two critical-point exponents [3-7]. Thus, from (2) and (7), as the critical point is approached $$(H\rightarrow 0$$ and $$t\rightarrow 0)\ ,$$ $$\mid H\mid$$ becomes a homogeneous function of $$t$$ and $$\mid M\mid ^{1/\beta}$$ of degree $$\beta \delta\ .$$ The scaling function $$j(x)$$ vanishes proportionally to $$x+b$$ as $$x$$ approaches $$-b\ ,$$ with $$b$$ a positive constant; it diverges proportionally to $$x^{\beta(\delta-1)}$$ as $$x\rightarrow \infty\ ;$$ and $$j(0) = c\ ,$$ another positive constant (Fig. 1). Although (7) is confined to the immediate neighborhood of the critical point $$(t, M, H$$ all near 0), the scaling variable $$x = t/\mid M\mid ^{1/\beta}$$ nevertheless traverses the infinite range $$-b < x < \infty\ .$$
Figure 1: Scaling function $$j(x)$$
When $$\mid H\mid = 0+$$ and $$t<0\ ,$$ so that $$M$$ is then the spontaneous magnetization, we have from (7), $$\mid M\mid = (-\frac{t}{b})^\beta\ ,$$ where $$\beta$$ is the conventional symbol for this critical-point exponent. When $$M\rightarrow 0$$ on the critical isotherm $$(t=0)\ ,$$ we have $$H \sim cM\mid M\mid ^{\delta-1}\ ,$$ where $$\delta$$ is the conventional symbol for this exponent. From the first of the two properties of $$j(x)$$ noted above, and Eq.(7), one may calculate the magnetic susceptibility $$(\partial M/\partial H)_T\ ,$$ which is then seen to diverge proportionally to $$\mid t\mid ^{-\beta(\delta-1)}\ ,$$ both at $$\mid H\mid = 0+$$ with $$t<0$$ and at $$H=0$$ with $$t>0$$ (although with different coefficients). The conventional symbol for the susceptibility exponent is $$\gamma\ ,$$ so we have [8]
$\tag{8} \gamma = \beta(\delta-1).$
Equations (7) and (8) are examples of scaling laws, Eq.(7) being a statement of homogeneity and the exponent relation (8) a consequence of that homogeneity.
A free energy $$F$$ may be obtained from (7) by integrating at fixed temperature, since $$M = -(\partial F/\partial H)_T\ ,$$ and the corresponding heat capacity $$C_H$$ then follows from $$C_H = -(\partial ^2 F/\partial T^2)_H\ .$$ One then finds from (7) that $$C_H$$ at $$H=0$$ diverges at the critical point proportionally to $$\mid t\mid ^{-\alpha}$$ (with different coefficients for $$t\rightarrow 0-$$ and $$t\rightarrow 0+)\ ,$$ with the critical-point exponent $$\alpha$$ related to $$\beta$$ and $$\gamma$$ by the scaling law [9]
$\tag{9} \alpha +2\beta +\gamma=2.$
When $$2\beta+\gamma=2$$ the resulting $$\alpha =0$$ means, generally, a logarithmic rather than power-law divergence together with a superimposed finite discontinuity occurring between $$t=0+$$ and $$t=0-$$ [4]. In the 2-dimensional Ising model the discontinuity is absent and only the logarithm remains, while in mean-field (van der Waals, Curie-Weiss, Bragg-Williams) approximation the logarithm is absent but the discontinuity is still present.
## Critical exponents
What were probably the historically earliest versions of critical-point exponent relations like (8) and (9) are due to Rice [10] and to Scott [11]. It was before Domb and Sykes [12] and Fisher [13] had noted that the exponent $$\gamma$$ was in reality greater than its mean-field value $$\gamma =1$$ but when it was already clear from Guggenheim's corresponding-states analysis [14] that $$\beta$$ had a value much closer to 1/3 than to its mean-field value of 1/2. Then, under the assumption $$\gamma =1$$ and $$\beta \simeq 1/3\ ,$$ Rice had concluded from the equivalent of (8) that $$\delta = 1+1/\beta \simeq 4$$ (the correct value is now known to be closer to 5) and Scott had concluded from the equivalent of (9) that $$\alpha =1-2\beta \simeq 1/3$$ (the correct value is now known to be closer to 1/10). The mean-field values are $$\delta =3$$ and (as noted above) $$\alpha =0\ .$$
The long-range spatial correlation functions in ferromagnets and fluids also exhibit a homogeneity of form near the critical point. At magnetic field $$H=0$$ (assumed for simplicity) the correlation function $$h(r,t)$$ as a function of the spatial separation $$r$$ (assumed very large) and temperature near the critical point (t assumed very small), is of the form [5,15]
$\tag{10} h(r,t)=r^{-(d-2+\eta)}G(r/\xi).$
Here $$d$$ is the dimensionality of space, $$\eta$$ is another critical-point exponent, and $$\xi$$ is the correlation length (exponential decay length of the correlations), which diverges as
$\tag{11} \xi\sim \mid t\mid ^{-\nu}$
as the critical point is approached, with $$\nu$$ still another critical-point exponent. Thus, $$h(r,t)$$ (with $$H=0)$$ is a homogeneous function of $$r$$ and $$\mid t\mid ^{-\nu}$$ of degree $$-(d-2+\eta)\ .$$ The scaling function $$G(x)$$ has the properties (to within constant factors of proportionality),
$\tag{12} G(x) \sim \left\{ \begin{array} {lc }x^{\frac{1}{2}(d-3)+\eta} e^{-x}, & x\rightarrow \infty \\ 1, & x\rightarrow 0 . \end{array} \right.$
Thus, as $$r\rightarrow \infty$$ in any fixed thermodynamic state (fixed t) near the critical point, $$h$$ decays with increasing $$r$$ proportionally to $$r^{-\frac{1}{2}(d-1)}e^{-r/\xi}\ ,$$ as in the Ornstein-Zernike theory. If, instead, the critical point is approached $$(\xi \rightarrow \infty)$$ with a fixed, large $$r\ ,$$ we have $$h(r)$$ decaying with $$r$$ only as an inverse power, $$r^{-(d-2+\eta)}\ ,$$ which corrects the $$r^{-(d-2)}$$ that appears in the Ornstein-Zernike theory in that limit. The scaling law (10) with scaling function $$G(x)$$ interpolates between these extremes.
In the language of fluids, with $$\rho$$ the number density and $$\chi$$ the isothermal compressibility, we have as an exact relation in the Ornstein-Zernike theory
$\tag{13} \rho kT \chi =1+\rho \int h(r) \rm{d}\tau$
with $$k$$ Boltzmann's constant and where the integral is over all space with $$\rm{d} \tau$$ the element of volume. The same relation holds in the ferromagnets with $$\chi$$ then the magnetic susceptibility and with the deviation of $$\rho$$ from the critical density $$\rho_c$$ then the magnetization $$M\ .$$ At the critical point $$\chi$$ is infinite and correspondingly the integral diverges because the decay length $$\xi$$ is then also infinite. The density $$\rho$$ is there just the finite positive constant $$\rho_c$$ and $$T$$ the finite $$T_c\ .$$ Then from the scaling law (10), because of the homogeneity of $$h(r,t)$$ and because the main contribution to the diverging integral comes from large $$r\ ,$$ where (10) holds, it follows that $$\chi$$ diverges proportionally to $$\xi^{2-\eta} \int G(x)x^{d-1}\rm{d}$$$$x\ .$$ But the integral is now finite because, by (12), $$G(x)$$ vanishes exponentially rapidly as $$x\rightarrow \infty\ .$$ Thus, from (11) and from the earlier $$\chi \sim \mid t\mid^{-\gamma}$$ we have the scaling law [15]
$\tag{14} (2-\eta)\nu = \gamma .$
The surface tension $$\sigma$$ in liquid-vapor equilibrium, or the analogous excess free energy per unit area of the interface between coexisting, oppositely magnetized domains, vanishes at the critical point (Curie point) proportionally to $$(-t)^\mu$$ with $$\mu$$ another critical-point exponent. The interfacial region has a thickness of the order of the correlation length $$\xi$$ so $$\sigma/\xi$$ is the free energy per unit volume associated with the interfacial region. That is in its magnitude and in its singular critical-point behavior the same free energy per unit volume as in the bulk phases, from which the heat capacity follows by two differentiations with respect to the temperature. Thus, $$\sigma/\xi$$ vanishes proportionally to $$(-t)^{2-\alpha}\ ;$$ so, together with (9),
$\tag{15} \mu + \nu = 2-\alpha= \gamma +2\beta,$
another scaling relation [16,17].
## Exponents and space dimension
The critical-point exponents depend on the dimensionality $$d\ .$$ The theory was found to be illuminated by treating $$d$$ as continuously variable and of any magnitude. There is a class of critical-point exponent relations, often referred to as hyperscaling, in which $$d$$ appears explicitly. The correlation length $$\xi$$ is the coherence length of density or magnetization fluctuations. What determines its magnitude is that the excess free energy associated with the spontaneous fluctuations in the volume $$\xi ^d$$ must be of order $$kT\ ,$$ which has the finite value $$kT_c$$ at the critical point. But the typical fluctuations that occur in such an elemental volume are just such as to produce the conjugate phase. The free energy $$kT$$ is then that for creating an interface of area $$\xi^{d-1}\ ,$$ which is $$\sigma \xi^{d-1}\ .$$ Thus, as the critical point is approached $$\sigma \xi^{d-1}$$ has a finite limit of order $$kT_c\ .$$ Then from the definitions of the exponents $$\mu$$ and $$\nu\ ,$$
$\tag{16} \mu = (d-1)\nu,$
a hyperscaling relation [16]. With (15) we then have also [16]
$\tag{17} d\nu = 2-\alpha = \gamma+2\beta,$
which, with (8) and (14), yields also [18]
$\tag{18} 2-\eta = \frac{\delta -1}{\delta +1} d.$
Unlike the scaling laws (8), (9), (14), and (15), which make no explicit reference to the dimensionality, the $$d$$-dependent exponent relations (16)-(18) hold only for $$d<4\ .$$ At $$d=4$$ the exponents assume the values they have in the mean-field theories but logarithmic factors are then appended to the simple power laws. Then for $$d>4\ ,$$ the terms in the thermodynamic functions and correlation-function parameters that have as their exponents those given by the mean-field theories are the leading terms. The terms with the original $$d$$-dependent exponents, which for $$d<4$$ were the leading terms, have been overtaken, and, while still present, are now sub-dominant.
This progression in critical-point properties from $$d<4$$ to $$d=4$$ to $$d>4$$ is seen clearly in the phase transition that occurs in the analytically soluble model of the ideal Bose gas. There is no phase transition or critical point in it for $$d \le 2\ .$$ When $$d>2$$ the chemical potential $$\mu$$ (not to be confused with the surface-tension exponent $$\mu$$) vanishes identically for all $$\rho \Lambda ^d \ge \zeta (d/2)\ ,$$ where $$\rho$$ is the density, $$\Lambda$$ is the thermal de Broglie wavelength $$h/\sqrt {2\pi mkT}$$ with $$h$$ Planck's constant and $$m$$ the mass of the atom, and $$\zeta (s)$$ is the Riemann zeta function. As $$\rho \Lambda^d \rightarrow \zeta(d/2)$$ from below, $$\mu$$ vanishes through a range of negative values. As $$\mu \rightarrow 0-\ ,$$ the difference $$\zeta(d/2)-\rho \Lambda^d$$ vanishes (to within positive proportionality factors) as
$\tag{19} \zeta(d/2)-\rho \Lambda^d \sim \left\{ \begin{array} {lc }(-\mu)^{d/2-1}, & 2<d<4 \\ \\ \mu \ln(-\mu/kT), & d=4 \\ \\ -\mu , & d>4 . \end{array}\right.$
When $$2<d<4$$ the mean-field $$-\mu$$ is still present but is dominated by $$(-\mu)^{d/2-1}\ ;$$ when $$d>4$$ the singular $$(-\mu)^{d/2-1}$$ is still present but is dominated by the mean-field $$-\mu\ .$$
This behavior is reflected again in the renormalization-group theory [19-21]. In the simplest cases there are two competing fixed points for the renormalization-group flows, one of them associated with $$d$$-dependent exponents that satisfy both the $$d$$-independent scaling relations and the hyperscaling relations, the other with the $$d$$-independent exponents of the mean-field theories [21]. The first determines the leading critical-point behavior when $$d<4\ .$$ At $$d=4$$ the two fixed points coincide and the exponents are now those of the mean-field theories but with logarithmic factors appended to the mean-field power laws. For $$d>4$$ the two fixed points separate again and the leading critical-point behavior now comes from the one whose exponents are those of the mean-field theories. The effects of both fixed points are present at all $$d\ ,$$ but the dominant critical-point behavior comes from only the one or the other, depending on $$d\ .$$
## Origin of homogeneity; block spins
A physical explanation for the homogeneity in (7) and (10) and for the exponent relations that are consequences of them is provided by the Kadanoff block-spin picture [5], which was itself one of the inspirations for the renormalization-group theory [19,20].
In a lattice spin model (Ising model), one considers blocks of spins, each of linear size $$L\ ,$$ thus containing $$L^d$$ spins, with $$L$$ much less than the diverging correlation length $$\xi$$ (Fig. 2).
Figure 2: Block spins
Each block interacts with its neighbors through their common boundary as though it were a single spin in a re-scaled model. Each block is of finite size so the spins in its interior contribute only analytic terms to the free energy of the system. The part of the free-energy density (free energy per spin) that carries the critical-point singularities and their exponents comes from the interactions between blocks. Let this free-energy density be $$f(t,H)\ ,$$ a function of temperature through $$t=T/T_c-1$$ and of the magnetic field $$H\ .$$ The correlation length is the same in the re-scaled picture as in the original, but measured as a number of lattice spacings it is smaller in the former by the factor $$L\ .$$ Thus, the re-scaled model is effectively further from its critical point than the original was from its; so with $$H$$ and $$t$$ both going to 0 as the critical point is approached, the effective $$H$$ and $$t$$ in the re-scaled model are $$L^xH$$ and $$L^yt$$ with positive exponents $$x$$ and $$y\ ,$$ so increasing with $$L\ .$$ From the point of view of the original model the contribution to the singular part of the free energy made by the spins in each block is $$L^df(t,H)\ ,$$ while that same quantity, from the point of the view of the re-scaled model, is $$f(L^yt, L^xH)\ .$$ Thus,
$\tag{20} f(L^yt, L^xH) \equiv L^df(t,H);$
i.e., by (1), $$f(t,H)$$ is a homogeneous function of $$t$$ and $$H^{y/x}$$ of degree $$d/y\ .$$
Therefore, by (2), $$f(t,H)=t^{d/y} \phi(H^{y/x}/t)=H^{d/x}\psi(t/H^{y/x})$$ where $$\phi$$ and $$\psi$$ are functions only of the ratio $$H^{y/x}/t\ .$$ At $$H=0$$ the first of these gives $$f(t,0)=\phi(0)t^{d/y}\ .$$ But two temperature derivatives of $$f(t,0)$$ gives the contribution to the heat capacity per spin, diverging as $$t^{-\alpha}\ ;$$ so $$d/y=2-\alpha\ .$$ Also, on the critical isotherm $$(t=0)\ ,$$ the second relation above gives $$f(0,H)=\psi(0)H^{d/x}\ .$$ But the magnetization per spin is $$-(\partial f/\partial H)_T\ ,$$ vanishing as $$H^{d/x-1}\ ,$$ so $$d/x-1=1/\delta\ .$$ The exponents $$d/x$$ and $$d/y$$ have thus been identified in terms of the thermodynamic exponents: the heat-capacity exponent $$\alpha$$ and the critical-isotherm exponent $$\delta\ .$$ In the meantime, again with $$-(\partial f/\partial H)_T$$ the magnetization per spin, the homogeneity of form of $$f(t,H)$$ in (20) is equivalent to that of $$H(t,M)$$ in (7), from which the scaling laws $$\gamma=\beta(\delta-1)$$ and $$\alpha + 2\beta + \gamma =2$$ are known to follow.
A related argument yields the scaling law (10) for the correlation function $$h(r,t)\ ,$$ with $$H=0$$ again for simplicity. In the re-scaled model, $$t$$ becomes $$L^yt\ ,$$ as before, while $$r$$ becomes $$r/L\ .$$ There may also be a factor, say $$L^p$$ with some exponent $$p\ ,$$ relating the magnitudes of the original and rescaled functions; thus,
$\tag{21} h(r,t) \equiv L^{p}h(r/L,L^yt);$
i.e., $$h(r,t)$$ is homogeneous of degree $$p$$ in $$r$$ and $$t^{-1/y}\ .$$ Then from the alternative form (2) of the property of homogeneity,
$\tag{22} h(r,t)\equiv r^p G(r/t^{-1/y})$
with a scaling function $$G\ .$$ Comparing this with (10), and recalling that the correlation length $$\xi$$ diverges at the critical point as $$t^{-\nu}$$ with exponent $$\nu\ ,$$ we identify $$p=-(d-2+\eta)$$ and $$1/y=\nu\ .$$ The scaling law $$(2-\eta)\nu=\gamma\ ,$$ which was a consequence of the homogeneity of form of $$h(r,t)\ ,$$ again holds, while from $$1/y=\nu$$ and the earlier $$d/y=2-\alpha$$ we now have the hyperscaling law (17), $$d\nu=2-\alpha\ .$$
The block-spin picture thus yields the critical-point scaling of the thermodynamic and correlation functions, and both the $$d$$-independent and $$d$$-dependent relations among the scaling exponents. The essence of this picture is confirmed in the renormalization-group theory [19,20].
## References
[1] C. Domb, The Critical Point (Taylor & Francis, 1996).
[2] M.E. Fisher, Repts. Prog. Phys. 30, part 2 (1967) 615.
[3] C. Domb and D.L. Hunter, Proc. Phys. Soc. 86 (1965) 1147.
[4] B. Widom, J. Chem. Phys. 43 (1965) 3898.
[5] L.P. Kadanoff, Physics 2 (1966) 263.
[6] A.Z. Patashinskii and V.L. Pokrovskii, Soviet Physics JETP 23 (1966) 292.
[7] R.B. Griffiths, Phys. Rev. 158 (1967) 176.
[8] B. Widom, J. Chem. Phys. 41 (1964) 1633.
[9] J.W. Essam and M.E. Fisher, J. Chem. Phys. 38 (1963) 802.
[10] O.K. Rice, J. Chem. Phys. 23 (1955) 169.
[11] R.L. Scott, J. Chem. Phys. 21 (1953) 209.
[12] C. Domb and M.F. Sykes, Proc. Roy. Soc. A 240 (1957) 214.
[13] M.E. Fisher, Physica 25 (1959) 521.
[14] E.A. Guggenheim, J. Chem. Phys. 13 (1945) 253.
[15] M.E. Fisher, J. Math. Phys. 5 (1964) 944.
[16] B. Widom, J. Chem. Phys. 43 (1965) 3892.
[17] P.G. Watson, J. Phys. C1 (1968) 268.
[18] G. Stell, Phys. Rev. Lett. 20 (1968) 533.
[19] K.G. Wilson, Phys. Rev. B 4 (1971) 3174.
[20] K.G. Wilson, Phys. Rev. B 4 (1971) 3184.
[21] K.G. Wilson and M.E. Fisher, Phys. Rev. Lett. 28 (1972) 240.
Internal references
• Eugene M. Izhikevich (2007) Equilibrium. Scholarpedia, 2(10):2014.
• Giovanni Gallavotti (2008) Fluctuations. Scholarpedia, 3(6):5893.
• Cesar A. Hidalgo R. and Albert-Laszlo Barabasi (2008) Scale-free networks. Scholarpedia, 3(1):1716.
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Reflection: Data Analysis Multiplying with Decimals - Section 6: Closure and Ticket to Go
Looking at students’ work on this ticket to go showed me the different stages my students were at in multiplying decimals. I grouped students in the following categories:
Novice: These students struggled with basic multiplication facts and working with decimals. Some of these students are only comfortable using the box method for multiplication. This method works best with smaller whole numbers. This student in particular was able to multiply the numbers but didn’t understand where the decimal point needed to go. It seems like this student made her estimate after she did the work and picked a round number that was near her answer, rather than using her number sense to make an estimate first. These students need extra instructional time to learn the traditional method of multiplication and how to use it with decimals. Unit 2.3 Student Work N.jpeg
Approaching Mastery: These were able to multiply using decimals, but only inconsistently. Most of these students were able to correctly find the product of problem one. The problem came with where to put the decimal point in problem 2. Most of these students incorrectly answered 0.35 instead of 0.035. Most of these students were able to make reasonable estimates. Unit 2.3 Student Work AM.jpeg
Proficient: These students were able to use the traditional algorithm to multiply decimals and they were able to make reasonable estimates.Unit 2.3 Student Work P.jpg
For this situation, I did not include an “advanced” category because the content did not require students to explain or analyze their work. Most of my students fell in the Approaching Mastery and Proficient categories. I will review the common mistakes in the next lesson, Multiplying with Decimals Day 2. For the novice students I will find time to work on the traditional algorithm with them.
Data Analysis: Ticket to Go Reflection
Multiplying with Decimals
Unit 2: The College Project - Working with Decimals
Lesson 4 of 16
Big Idea: How do you multiply decimals? Where does the decimal point go? Students work on answering these questions and developing an algorithm for multiplying decimals.
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18 teachers like this lesson
Standards:
Subject(s):
Math, Decimals, Number Sense and Operations, multiplication, 6th grade, master teacher project
60 minutes
Andrea Palmer
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How many is
Conversion between units of measurement
You can easily convert 2 inches into meters using each unit definition:
Inches
inch = 2.54 cm = 0.0254 m
Meters
1 m
With this information, you can calculate the quantity of meters 2 inches is equal to.
¿How many m are there in 2 in?
In 2 in there are 0.0508 m.
Which is the same to say that 2 inches is 0.0508 meters.
Two inches equals to zero meters. *Approximation
¿What is the inverse calculation between 1 meter and 2 inches?
Performing the inverse calculation of the relationship between units, we obtain that 1 meter is 19.685039 times 2 inches.
A meter is nineteen times two inches. *Approximation
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Question
# Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :
A
2101220
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B
20C10210
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C
2101210
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D
20C10220
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Solution
## The correct option is D 20C10220Total number of subsubsets of set X=210=1024 Number of subsets with zero element =10C0 Number of subsets with one element =10C1 Number of subsets with two elements =10C2 . . . . Number of subsets with 10 elements =10C10 A & B are taken from P(X) from 210 subsets so total ways =210×210 Number of ways such that A and B have equal number of elements=(10C0)2+(10C1)2+(10C2)2+........+(10C10)2 =20C10 Required probability =20C10220
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## A second example from tiling the Aztec diamond
Yesterday I learned about the Arctic Circle theorem and used it for a fun talk with the kids:
The Arctic Circle Theorem
This morning we had a fun little coincidence as one of the problems that my son was working on was the proof that $1 + 2 + 3 + \ldots + n = (n)(n+1) / 2$. The coincidence is that the number of different tilings of the nth Aztec Diamond is $2^{(n)(n+1)/2}$, so for a quick project this morning we looked at the sum and then tried to find the 8 different tilings of the level 2 Aztec Diamond:
Part 1 is a short discussion of the sum:
Part 2 is looking at the tilings of the Aztec Diamond – counting the number of tilings of the level 2 diamond is a pretty good challenge for kids.
So, a lucky second project with the Aztec Diamond. I definitely want to think more about how to share the ideas in the Arctic circle theorem with kids. I think the ideas here are something that kids will really love.
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# Find the derivative of $\frac{x^2+x-2}{x^2+5x+6}$
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## Final answer to the problem
$\frac{2x^2+5x-2}{\left(x+2\right)\left(x+3\right)^2}$
Got another answer? Verify it here!
## Step-by-step Solution
How should I solve this problem?
• Find the derivative
• Find the derivative using the definition
• Find the derivative using the product rule
• Find the derivative using the quotient rule
• Find the derivative using logarithmic differentiation
• Find the derivative
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
Can't find a method? Tell us so we can add it.
1
Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
$\frac{\frac{d}{dx}\left(x^2+x-2\right)\left(x^2+5x+6\right)-\left(x^2+x-2\right)\frac{d}{dx}\left(x^2+5x+6\right)}{\left(x^2+5x+6\right)^2}$
2
Simplify the product $-(x^2+x-2)$
$\frac{\frac{d}{dx}\left(x^2+x-2\right)\left(x^2+5x+6\right)+\left(-x^2-\left(x-2\right)\right)\frac{d}{dx}\left(x^2+5x+6\right)}{\left(x^2+5x+6\right)^2}$
3
Simplify the product $-(x-2)$
$\frac{\frac{d}{dx}\left(x^2+x-2\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\frac{d}{dx}\left(x^2+5x+6\right)}{\left(x^2+5x+6\right)^2}$
4
The derivative of a sum of two or more functions is the sum of the derivatives of each function
$\frac{\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-2\right)\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\frac{d}{dx}\left(x^2+5x+6\right)}{\left(x^2+5x+6\right)^2}$
5
The derivative of a sum of two or more functions is the sum of the derivatives of each function
$\frac{\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-2\right)\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(5x\right)+\frac{d}{dx}\left(6\right)\right)}{\left(x^2+5x+6\right)^2}$
6
The derivative of the constant function ($-2$) is equal to zero
$\frac{\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(x\right)\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(5x\right)+\frac{d}{dx}\left(6\right)\right)}{\left(x^2+5x+6\right)^2}$
7
The derivative of the constant function ($6$) is equal to zero
$\frac{\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(x\right)\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(5x\right)\right)}{\left(x^2+5x+6\right)^2}$
8
The derivative of the linear function is equal to $1$
$\frac{\left(\frac{d}{dx}\left(x^2\right)+1\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(5x\right)\right)}{\left(x^2+5x+6\right)^2}$
9
The derivative of the linear function times a constant, is equal to the constant
$\frac{\left(\frac{d}{dx}\left(x^2\right)+1\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(\frac{d}{dx}\left(x^2\right)+5\frac{d}{dx}\left(x\right)\right)}{\left(x^2+5x+6\right)^2}$
10
The derivative of the linear function is equal to $1$
$\frac{\left(\frac{d}{dx}\left(x^2\right)+1\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(\frac{d}{dx}\left(x^2\right)+5\right)}{\left(x^2+5x+6\right)^2}$
11
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$\frac{\left(2x+1\right)\left(x^2+5x+6\right)+\left(-x^2-x+2\right)\left(2x+5\right)}{\left(x^2+5x+6\right)^2}$
12
Simplify the derivative
$\frac{2x^2+5x-2}{\left(x+2\right)\left(x+3\right)^2}$
## Final answer to the problem
$\frac{2x^2+5x-2}{\left(x+2\right)\left(x+3\right)^2}$
## Explore different ways to solve this problem
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
SnapXam A2
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### Main Topic: Differential Calculus
The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.
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## Balls In Bins With Limited Capacity
```Given n indistinguishable balls and m bins, where each bin has a
capacity of c(i) (i = 1 to m) balls, in how many ways can the n balls
be distributed in the m bins? Note that n <= sum of c(i)'s; one
or more bins may have room for all n balls; we don't care which balls
are in which bins, nor do we distinguish between positions in the
bins; and bins need not be occupied.
problem, let's try something a little different. First, if N(k)
denotes the number of ways of packing k balls into m bins with
capacities c(i), i=1 to m, then we have
c
SUM N(k) = [c(1)+1][c(2)+1]...[c(m)+1] (1)
k=0
where c is the total capacity c(1) + c(2) + .. + c(m). For example,
if we have 5 bins with capacities 3,2,5,4,2 respectively, then c=16
and the values of N(k) for k = 0 to 16 are as shown below:
1 5 15 33 59 90 120 142 150 142 120 90 59 33 15 5 1
(Naturally we have N(k) = N(c-k), because the distribution of empty
spaces is symmetrical with the distribution of balls.) The total of
these values of N(k) is 1080, which can be computed directly as a
function of the individual bin capacities by equation (1) as
(3+1)(2+1)(5+1)(4+1)(2+1) = 1080
An interesting aspect of the values of N(k), for relatively small
perturbations from uniform capacities, is that they approach a
normal distribution with a mean of c/2. In fact, we can use this
feature to give an approximate formula for N(k). Letting A denote
the sum of the values of N(k) as given by (1), solve the equation
______
(c/2 + 1) / 2 pi
z exp(-(z^2)/2) = ----------------- (2)
A
for z, and set s = (c/2 + 1)/z. Then the individual values of N(k)
are given approximately by
A/s /-((k - c/2)/s)^2\
N(k) ~ ------------ exp( ---------------- ) (3)
(2 pi)^(1/2) \ 2 /
For example, to determine the number of ways of distributing 11
balls into 5 bins with the capacities 3,2,5,4,2, we have c=16 and
we compute A = 1080 from equation (1). Then equation (2) gives
z = 3.169, from which we compute s = 2.840. Inserting these values
into equation (3) gives
/-((k-8)/2.84)^2 \
N(k) ~ (151.7) exp( --------------- ) (4)
\ 2 /
For k=11 we get N(11) = 87, compared with the true value of 90.
For larger numbers of bins and greater total capacity, the probability
of roughly uniform capacities increases, assuming the capacities
are randomly chosen, so the true results approach more and more
closely a normal distribution and the approximation gets progressively
better.
This approach is reasonably valid if the bins all have roughly the
same capacity, but if one c(i) is much larger than the others, N(k)
will tend to look very flat around k = half the product of (c(i)+1).
Hence the normal approximation only applies to relatively small
perturbations around the condition of uniform capacities.
One approach, might be to observe that N(k) can be interpreted as
the number of lattice points contained in the intersection of an
m-dimensional block (one corner at the origin, other corners at
(c(1),0,..0), (0,c(2),0,...0), etc.) and the plane x+y+..+z = k.
This is how I originally looked at the problem, and I tried to see
how to estimate the area of that "plane" with its corners clipped
off by the limits at c(i) along the ith coordinate axis. I thought
about rotating this diagonal plane (and all the points of intersection
of the plane with the c(i)=constant truncating planes), and then
computing the enclosed "area".
But now I'm picturing it slightly differently, as a solid "brick"
with dimensions [c(1)+1], [c(2)+1], ...etc. The sum of all the N(k)
values equals the volume of this brick, and the individual values of
N(k) are the volumes swept out by a diagonal plane as it emanates out
from one corner of the brick. The values of N(k) start out small in
the corner, then get bigger as the plane sweeps through the middle of
the brick, and then get small again as the plane sweeps through the
diagonally opposite corner.
N(k) will change in a uniform way except when the plane passes
through a vertex of the brick. Also, by inclusion-exclusion you
can predict how the derivative of N(k) vs k will change at each
vertex. On this basis, I think we can formulate an exact solution.
Let N(k) denote the number of ways of distributing k identical items
into m containers with capacities c(1), c(2),.. c(m). Then
/m\
m \t/ / m+k-s(t,j)-1 \
N(k) = SUM (-1)^t SUM ( ) (1)
t=0 j=1 \ m-1 /
where s(t,j) is the jth sum of t "capacity-plus-1's".
For example, suppose we have m=5 containers with capacities 3, 6, 9,
12, and 15. The "capacity-plus-1s" are therefore 4, 7, 10, 13, and
16. Our formula for N(k) begins with t=0, and there is only one sum
of zero capacity-plus-1s, namely 0, so we have s(0,1) = 0. Thus the
outer SUM for t=0 contributes +C[5+k-1,4]. (Note that we define the
binomial coefficient C[i,j] to be zero for all i < j.)
With t=1 we will have 5 (=C[5,1]) negative terms, corresponding to
the five possible sums of exactly 1 c-plus-1s:
- C[k,4] - C[k-3,4] - C[k-6,4] - C[k-9,4] - C[k-12,4]
With t=2 we will have 10 (=C[5,2]) positive terms, corresponding to
the ten possible sums of exactly 2 c-plus-1s. For example, the
first of these ten terms is +C[k-7,4].
Continuing in this way the complete formula will have 32 (=2^m)
terms, giving the exact value of N(k) for any k. Of course, we won't
necessarily need all of these terms to evaluate N(k) for particular
values of k. In fact, we never need more than half of these terms,
because we only need to include terms with s[t,j] less than or equal
to k, and if k exceeds half of the total capacity c of all the
containers, we can just evaluate c-k instead.
To illustrate, suppose we want to evaluate N(31) for the above set
of five containers. By symmetry this is the same as N(14), so we
only need to use the terms
N(14) = C[18,4]-C[14,4]-C[11,4]-C[8,4]-C[5,4]+C[7,4]+C[4,4]
= 3060 - 1001 - 330 - 70 - 5 + 35 + 1 = 1690
By the way, in the special case where all the capacities c[i] are
equal to a single constant R, it's clear that the C[m,t] elements
of the inner summation in equation (1) for a given t are all equal
to C[m+k-s(t,j)-1,m-1] where each s(t,j) equals simply t(R+1).
Therefore, in this special case equation (1) reduces as one would
expect to the well known result
m /m\ / m+k-t(R+1)-1 \
N(k) = SUM (-1)^t ( )( )
t=0 \t/ \ m-1 /
```
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https://www.education.com/resources/second-grade/coloring/CCSS-Math-Content-2-NBT/
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# Search 2nd Grade Numbers and Operations, Base 10 Coloring Educational Resources
12 filtered results
12 filtered results
Coloring
Numbers and Operations, Base 10
Sort by
Dot to Dot Zoo: 10's
Worksheet
Dot to Dot Zoo: 10's
This elephant dot-to-dot has a mathematical twist. Instead of counting 1,2,3 kids will count by tens to connect the dots.
Math
Worksheet
Connect the Dots: Practice Skip Counting by Tens!
Worksheet
Connect the Dots: Practice Skip Counting by Tens!
Children skip count by tens to connect the dots and discover the hidden picture.
Math
Worksheet
Connect the Dots: Practice Skip Counting by Fours!
Worksheet
Connect the Dots: Practice Skip Counting by Fours!
Children skip count by fours to connect the dots and discover the hidden picture.
Math
Worksheet
Dot to Dot Zoo: 5's
Worksheet
Dot to Dot Zoo: 5's
A giraffe dot-to-dot might be just the thing for your zoo lover. Try this giraffe dot-to-dot with your child, and be challenged with an added twist.
Math
Worksheet
Skip Count by Two!
Worksheet
Skip Count by Two!
Count by multiples of two at the Dot-to-Dot Zoo to complete the coloring page picture!
Math
Worksheet
Dot to Dot Zoo: 2's
Worksheet
Dot to Dot Zoo: 2's
A zebra dot-to-dot worksheet is fun from the start, and this one has a special twist. Count by twos in this zebra dot-to-dot worksheet.
Math
Worksheet
Skip Count Dot-to-Dot
Worksheet
Skip Count Dot-to-Dot
Kids will skip count by fives in this hidden animal dot-to-dot. This connect the dots worksheet contains a hidden picture of a whiskered beaver.
Math
Worksheet
Skip Count by Three
Worksheet
Skip Count by Three
This coloring page dot-to-dot uses skip counting as an unexpected way to tie in multiplication learning and reviewing multiples of three!
Math
Worksheet
Skip Count at the Dot-to-Dot Zoo
Worksheet
Skip Count at the Dot-to-Dot Zoo
This hidden animal at the Dot-to-Dot Zoo is 'hopping' to meet you. Kids will skip count by fours to reveal a hidden kangaroo.
Math
Worksheet
Connect the Dots: Practice Skip Counting by Threes
Worksheet
Connect the Dots: Practice Skip Counting by Threes
Children skip count by threes to connect the dots and discover the hidden picture.
Math
Worksheet
Skip Count to Okapi
Worksheet
Skip Count to Okapi
Skip count by twos in this fun coloring and dot-to-dot exercise that features a hidden animal. Kids will connect the dots to reveal the exotic okapi.
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http://openstudy.com/updates/5055e83fe4b0a91cdf44a122
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crawl-data/CC-MAIN-2015-48/segments/1448398446997.59/warc/CC-MAIN-20151124205406-00352-ip-10-71-132-137.ec2.internal.warc.gz
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Mikael 3 years ago The rod is massless. At t = 0 rod is pointing up. It is of length R. rod is rotating without friction around the lower end which is hinged to rotation axis. The mass M is attached at the top end of the rod. The mass is pushed at t=0 with initial velocity . g is gravitational acceleration. All these parameters are given and known.
1. Mikael
2. Mikael
WHEN WILL THE MASS REACH THE LOWEST POINT ?
3. Mikael
@mukushla @UnkleRhaukus @experimentex @estudier
4. Mikael
5. Mikael
@sauravshakya
6. Mikael
@Hero @apoorvk @AccessDenied
7. UnkleRhaukus
find the angular velocity
8. Mikael
Well it is not constant and it is not explicit in energy - the linear v is there
9. Mikael
@ganeshie8 @ajprincess
10. Mikael
@ganeshie8 @ajprincess
11. Mikael
@ParthKohli @mathslover
12. Mikael
$0.5mv^2 + mgh = E_0 = constant$
13. Mikael
CAN ANYONE SOLVE IT AROUND HERE ?
14. Mikael
@Omniscience ?
15. Mikael
HINTS ?
16. Mikael
17. Mikael
At least some SIGNIFICAN part of the way forward ?
18. Mikael
19. apoorvk
Hmm I guess you will just have to find the general term for velocity at any instant, and integrate the term in 'dt' - since energy conservation and angular velocity fundae won't work here.
20. apoorvk
let me try this out...
21. Mikael
You ARE 20% forward
22. Mikael
Hi @ajprincess
23. Mikael
help
24. Mikael
Ok , the prize for the sover will be 25 minute-worth field integral from EM that I am ready to do in return !
25. Mikael
OK the beauty of this situation is that it is VERY common and simple setting. Buuut very unusual answer
26. Mikael
27. Mikael
28. Mikael
@demitris @Directrix can you help ?
29. Mikael
Hi @sauravshakya
30. Mikael
@demitris @Directrix can you help ?
31. sauravshakya
Hi @Mikael ..
32. Mikael
I AM VERY SORRY I STARTED WITHOUT YOU. Complete please
33. sauravshakya
Wait a minute.... Let me see what I can do.
34. Mikael
@Directrix ?
35. Mikael
36. Mikael
Hello @Callisto - try to help please
37. Mikael
Well imagine my sour expression when a nice timid student asks me this question in the middle of a nice sunny day ....
38. Algebraic!
Why no rotational energy term?
39. Mikael
Yea , you can use that. Although this is not the only way. Just do it please
40. sauravshakya
This requires physics too
41. mathslover
why not to use law of conservation of energy?
42. Mikael
Calculus and mechanics are essentially one united universal soul
43. Mikael
Good @mathslover USE it and do the soln. please
44. mathslover
potential energy + kinetic energy = constant. I cn help after 1 n half hours
45. Mikael
Actually I have already pointed that in a hint above. But go forward - when is the bottom reached ?
46. Mikael
@ganeshie8 @UnkleRhaukus help pls
47. Algebraic!
$\frac{ t ^{2} }{2 } + \frac{ V _{o}}{ R } t =\int\limits_{ }^{ }\int\limits_{ }^{ } \frac {-R }{ g \cos \theta }$ 0..pi
48. Mikael
A) What is the integration variable ? B) Why (suddenly ) double int ???? c) What is the reason you write this so categorically ?
49. Algebraic!
A) g, of course B) equation of motion C) integral is tough, not bothering
50. Algebraic!
theta is the angle the rod makes with the vertical 0...pi
51. Mikael
g CANNOT CHANGE - it is CONSTANT !
52. Algebraic!
it's theta, why would you ask?
53. Algebraic!
would it be g or R?
54. Mikael
Please Show the FULL argument. Double integral seems, on the face of it, out of place in this problem
55. Mikael
56. Algebraic!
argument from torque = -mgRcos(theta) I=mR^2 d^2/ dt^2 (theta) =- gRcos(theta)
57. Mikael
$E_0 = 2mgR +0.5 mv^2$
58. Mikael
Giving the solution soon in 3-4 minutes
59. Mikael
E = CONSTANT
60. Coolsector
h for you is like the y axis ?
61. Mikael
yes
62. Mikael
OK here goes the solution
I have concluded this problem may be above my pay-grade.
64. Mikael
$t(h) = \int\limits_{h=2R}^{h=0} \frac{dl}{v(h)} dh$
65. Mikael
Now $dl = \frac{dh}{\cos \theta}$
66. Mikael
Forgot to say - thta is the angle with the horizon of the rod.The relation dh to dl is a geometric fact that follows from$h = Sin \theta ====> dh = dl * Cos \theta$
67. Mikael
sorry h = R*Sin theta
68. Mikael
Thus gathering all the above observations until now we obtain the following integral
69. Mikael
$\int\limits_{h=2R}^{h=0} dh \frac{1}{\sqrt{1-\frac{h^2}{R^2}}*\sqrt{\frac{2E_0}{m} -2gh}}$
70. Mikael
Here the 1-st square root in the denominator is simply 1/Cos theta
71. Mikael
The second square root is the velocity as a function of h - of course derived from the law of conservation of energy stated above
72. Coolsector
can you please explain how h = rsintheta means dh = dl costheta
73. Mikael
Now by rescaling the distance by R and taking one convenient constant (from the denominator roots) out of the integral we simplify it all to
74. mathslover
I did this
75. Mikael
|dw:1347813111455:dw|
76. mathslover
$\large{t = \frac{-1+\sqrt{1+8\pi R}}{2v_0}}$
77. Coolsector
thanks
78. mathslover
did that make sense? @Coolsector and @Mikael
79. Mikael
@mathslover I would be amazed and thankful for COMPLETE explanation why do you claim the first equation - that the angle is a simple quadratic function of time. As you know the angular acceleration IS NOT CONSTANT HERE
80. Coolsector
i dont understand why alpha is what you said.. but maybe its just me
81. Coolsector
yes .. same problem here
82. Mikael
I think @mathslover is NOT correct in HIS FIRST STATEMENT on that page on which all is based upon
83. Mikael
So we proceed
84. Algebraic!
there's no g in your soln. @mathslover
85. mathslover
Oh I made it for horizontal plane... vertical plane hmn... well guys wait
86. Mikael
$\int\limits_{\xi_0}^{0} d \xi \frac{1}{\sqrt{(1-\xi^2)(A- \xi)}}$
87. mathslover
Mikael whts ur age? grade? so that I can understand the level of this
88. Mikael
HERE Xi is rescaled variable h, and A is some constant containing fractions of E_0 and g. Outside of the integral is of course a Multiplier (not written) which is physically crucial and mathematically trivial
89. mathslover
I think this is $$\large{\textbf{above}}$$ my level sorry.... I am in 9th grade and did my best.... sorry
90. Mikael
This is the level of a good Physical-Course on analytival mechanics in Cambridge/Berkeley/MIT 1-st or second year. Also Ms. @Algebraic! is probably generally pointed to a more Engineering diection of solution - using torques and angular accelerations. Aand Mr. @radar can I send you a message unrelated to math but related to this site ?
91. mathslover
Sorry.... above my level...
92. Algebraic!
Ms. I like that snark.
93. Mikael
I disagree with you @mathslover - you saw it is almost school level
94. mathslover
What do you mean mikael? well leave ti whatever do you mean........ continue your work..
95. mathslover
*it
96. Mikael
Well 1) This is all - please help me by some Tables / Wolframalpha to find what type of Integral this belongs to 2) I suspect it is elliptic Integral
97. Mikael
Aand please appreciate the effort by medals - you are welcome. The question itself was supplied by Mr. @henpen here http://openstudy.com/study#/updates/50549e72e4b0a91cdf445d5b
98. Mikael
Here is the answer as supplied by Wolframalph
99. Mikael
Sorry here in complete - as I thought elliptic integral
100. Mikael
Can see the soln @mukushla
101. mukushla
i just came here :)
102. Mikael
@mukushla The original challenge was for 2 sets of people 1) You, @sauravshakya, and other olympics-math types 2) Physicists So try solving without any reading the soln
103. Mikael
So I guesses right - about IMO participation ?
104. mukushla
sorry lost connection Mr.Mikael :) man im a chemical engineer :) what is the math part of question ?
105. Mikael
You need to find how long it takes for a spherical bead of polymer to slied without friction though a perfectly circular half circular tube to the sovent chamber if initially the small bead has v_0 velocity and starts from the top of the tube
106. Mikael
solvent chamber (i meant)
107. mukushla
out of my knowledge :)
108. Mikael
You should use the simple mechanical conservation of energy and definition of velocity. Some geometry too
109. Mikael
Well - see the solution and dissolve your sorrows...
110. sauravshakya
Actually this question is also out of my reach.
111. sauravshakya
Is this the question from a high school level?
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http://lbartman.com/worksheet/division-by-2-worksheets.php
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## lbartman.com - the pro math teacher
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# Division By 2 Worksheets
Public on 02 Nov, 2016 by Cyun Lee
### division maths worksheets for year 2 age 6 7
Name : __________________
Seat Num. : __________________
Date : __________________
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37 : 2 = ...
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Software Engineer Intern Interview Questions | Glassdoor
# Software Engineer Intern Interview Questions
1,050
Software engineer intern interview questions shared by candidates
## Top Interview Questions
Sort: RelevancePopular Date
Jul 5, 2012
Oct 18, 2011
How can one implement a queue with only a stack implementation?4 AnswersYou will need at least two stacks. public class Queue { private Stack inbox = new Stack(); private Stack outbox = new Stack(); public void queue(E item) { inbox.push(item); } public E dequeue() { if (outbox.isEmpty()) { while (!inbox.isEmpty()) { outbox.push(inbox.pop()); } } return outbox.pop(); } }you have double ended queue (Deque) and insertion and removal can be handled at both end either left or right. But if you want to implement Queue as stack, then restrict the operation at any one end either left. So Front and rear both become at the same end.Never mind my previous answer was wrong implementation. It is actually implementing stack using Queue.Show More Responses#include #include using namespace std; stack st1, st2; int pop( ) { if (!st1.empty()) { int t,t1; while(st1.size() != 1) { t = st1.top(); st1.pop(); st2.push(t); } t1 = st1.top(); st1.pop(); while(st2.size()) { t = st2.top(); st2.pop(); st1.push(t); } return t1; } } int main() { st1.push(2); st1.push(3); st1.push(4); st1.push(5); st1.push(6); cout<
Feb 10, 2013
### Software Engineer Intern at Amazon was asked...
Mar 20, 2012
Implement integer division4 Answerspublic class Solution { public void integerDivision(int num, int den){ int q=0,rem=0; while(num>=den){ num-=den; q++; } rem=num; System.out.println("Quotient "+q+" Remainder "+rem); } public static void main(String[] args) { Solution sol = new Solution(); sol.integerDivision(73, 9); } }public static int division(int a, int b) { if (a b) { int q = 1; int c = b; while ((b = b > 1; while ((a = a - b) >= c) { q++; } return q; } else { return 0; } }Minor correction public static int division(int a, int b) { if (a b) { int q = 1; int c = b; while ((b = b > 1; while ((a = a - b) >= c) { q++; } return q; } else { return 0; } }Show More ResponsesI hope this will be helpful int divFunc(int* num,int* den,int* rem) { int q = 1; int backupNum = *num; int backupDen = *den; while((backupDen = backupDen >=1; backupNum = backupNum - backupDen; *num = backupNum; *rem = backupNum; return q; } void divide(num,den) { int q=0,r=0; while(num>den) { q = q + divFunc(&num,&den,&r); } printf("Q = %d\t R = %d\n",q,r); }
Nov 6, 2012
Write a function to determine if a string is an integer.6 AnswersJava version: boolean checkInt(String s){ try{ Integer.parseInt(s) } catch(NumberFormatException e){ return False;} return True; } Java version without try/catch: public static boolean isInt(String s){ for (int i=0; i 0) return false; return true; }def is_digit(thing): if not isinstance(thing, basestring): return ValueError('Argument needs to be of instance basestring.') # Be nice and strip whitespace. thing = thing.strip() # If there is nothing there, bail. if thing == '': return False # If there is more than 1 decimal, bail. if thing.count('.') > 1: return False # Sort of a special case. If the number is a negative, just strip it out. if thing.startswith('-'): # Do another strip. We are explicitly allowing for space after the negative. thing = thing[1:].lstrip() # If there are characters left over after all valid characters were stripped, # then something is invalid. if re.sub(VALID_RE, '', thing) != '': return False return True
Nov 15, 2012
Given an unsorted array, extract the max and min value using the least number of comparison.4 Answersf(1)=1 f(2)=f(1)+1=2 f(3)=f(2)+f(1)+1=4 ...var min, max, arr = [3,4,2,7,1,9]; for(i in arr){ //n-iterations min = Math.min( arr[i], arr[i+1], min ); //2 comparisons max = Math.max( arr[i], arr[i+1], max ); //2 comparisons } //4n => nwell normal case n comparisons Compare in pair and you have n-1 comparisons...Show More ResponsesMinimum number of comparisons is 3n/2. The strategy is to go through the elements in pairs, and compare the smaller one to the minimum, and the bigger one to the maximum. This is 3 comparisons, done n/2 times in total, for 3n/2 running time. Working code in python: import random import sys r = [random.randint(1,100) for i in range(31)] print r mini = r[0] maxi = r[0] start = 0 if len(r) % 2 != 0: start = 1 for i in range(start,len(r)-1,2): n1 = r[i] n2 = r[i+1] # Exactly 3 comparisons each time if(n1 < n2): mini = min(n1,mini) maxi = max(n2,maxi) else: mini = min(n2,mini) maxi = max(n1,maxi) print mini print maxi
Dec 13, 2013
Given a string write a function which prints all the subsets of the string. Now make the function to return only unique solutions. For example if they give you "abc" you print out a ab abc ac b bc c Now for the unique solution constraint, if they give you "aba" the output should be: a ab aba b7 AnswersThere is a divide & conquer strategy with this problem. Divide string into two halves. Recursively print the string on left and then on right. Finally, for each string on left, combine it with every string on the right. (Note this will not give the unique solution.) To obtain the unique solution, a simple way is to use a set to keep track of every substrings we have constructed. If element is already in the set, we simply not add it. In the end, we print out every element in the set. Maybe there is a better way without using extra memory.What about counting the number of each character in a string? for "aba" we have a-2, b - 1. now recursive solution which takes charecter, for a we choose 0a, 1a, and 2a and push to the 'b' where take 0b or 1b. now we have "", "a","aa","ab","b". all subsets + empty one.@Allen: The interviewer specified that he wants a recursive solution and you are not allowed to use extra memory. Note: The interviewer gave me a big hint: "What happens if you sort the array and simply generate all the subsets?"Show More Responses@Marius: what do you mean by "sort the array"? There is no array in the questionSee this link and view discuss session for solution to unique subsets https://oj.leetcode.com/problems/subsets-ii/So this requires subsets to be printed and not substrings; ordering of characters doesn't matter. So sort the characters and generate unique subsets. import java.util.Arrays; import java.util.Scanner; public class UniqueSubsetGenerator { public static void main(String[] args) { final Scanner in = new Scanner(System.in); while (true) { System.out.println("Enter string : "); final String masterWord = in.nextLine(); char[] word = masterWord.toCharArray(); Arrays.sort(word); generateUniqueSubsets(word, 0, ""); } } private static void generateUniqueSubsets(char[] word, int start, String prefix) { //System.out.println("start " + start + " prefix " + prefix); if (start >= word.length) { System.out.println(prefix); return; } char ch = word[start]; int count = 1; for (int i=start+1; i= len(inpStr): return charLen = getLen(index, inpStr) for i in range(charLen + 1): posSet = currSet + inpStr[index] * i uniqueSubsetsHelper(subSets, posSet, index + charLen, inpStr) def getLen(index, inpStr): currChar = inpStr[index] currLen = 0 while index < len(inpStr): if inpStr[index] == currChar: currLen += 1 else: return currLen index += 1 return currLen
Mar 31, 2012
Given a number n, give me a function that returns the nth fibonacci number. Running time, space complexity, iterative vs. recursive.5 AnswersLet me give you a recursive & not-efficient solution to get n th fibonacci number. public int findNthFib(int n) { return (n < 2 ? n : (findNthFib(n-1)+findNthFib(n-2)); } This short method will recursively return fib number. However, running time is very awful! it's O(2^n) = exponential time. it will quickly become a non-usable method after n = 30~40. There is another quick and elegant linear time solution, but I want the next person to present that in here. (if you google it, you can find it easily)Closed form solution. GGint public(int n){ if(n == 0) return n; if(n == 1) return n; return (n-1)+(n-2); }Show More Responsespublic class fib { public static void main(String args[]){ int n=12; int counter=2; int[] arr = new int[n+1]; arr[0]=1; arr[1]=1; while(counter
### Software Engineer Intern at eBay was asked...
May 17, 2012
Assuming a preexisting list of 100 words, how would you efficiently see if a word received from input is an anagram of any of the 100 words?4 AnswersFirst Sort 100 words and keep the hash of sorted words.. Now when you recieve a word, SOrt it and check if Hash contains that key. O(nlogn) Where n is length of String.Hi I think you can take a look at the most efficient algorithm for this question in this link www.crackeasily.com/2012/01/find-whether-2-strings-are-anagrams.htmlTo say what MW said more clearly: If you sort words that are the same anagram they will always look the same. Example: "god" and "dog" both look like "dgo". So you sort the input word, then you iterate through the list of 100 words, and while looking at each word sort that word. compare if the input and that word are the same. If they are then you have found an anagram. if you made it to the end of the list and you haven't found an anagram then an anagram does not exist in the list.Show More ResponsesSorting takes O(nLogn) average time. This can be further improved by counting characters in the strings. So, for the given string calculate count of each character in an array [256]. For each word in the list, check if it contains the same count for its characters and return that word. Complexity O(n)
### Software Development Engineering Intern at Amazon was asked...
Jun 10, 2012
Can you think of an example of a scenario where you would want to use a tree with more degrees of branching than a binary tree?4 AnswersIf you need to represent a company's personal structure. For example, one president is trailed by more than just two vice presidents and it will span....Great example for this: modeling a dictionary of possible words. I.e. a->g->r works because aggregate but a->g->(g) wouldn't because the second g wouldn't exist in the tree (no words begin or are formed with the string "agg"). I've actually received this in an Amazon interview where I was asked to model the game Boggle.B-TreeShow More ResponsesDatabase indexes is a classic example
3140 of 1,050 Interview Questions
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# How to Trade the Gartley Harmonic Chart Pattern in Crypto Trading
Crypto Guide Today examines the relationship between the cryptocurrency market and the use of the Gartely Harmonic chart patterns in crypto trading. Specifically, the guide will provide an overview of how to trade using the Gartely harmonic chart pattern.
## Overview Gartely Harmonic Chart Pattern in Crypto Trading
The Gartley harmonic chart pattern is a technical analysis tool that is used by traders in the crypto market to identify potential reversal points in the price of a cryptocurrency. The pattern is based on Fibonacci ratios and is named after H.M. Gartley, who first described it in his 1935 book, “Profits in the Stock Market.”
As I mentioned above, what is the Gartley harmonic chart pattern in crypto trading, it is important for you to know, how to trade the Gartley harmonic chart pattern. The Gartley harmonic chart pattern is made up of five distinct points, labeled A, B, C, D, and E. Point A is the starting point of the pattern and is typically significantly low or high in the price of the cryptocurrency. Point B is the retracement of the move from point A, and point C is the extension of the move from point B. Point D is the retracement of the move from point C, and point E is the extension of the move from point D.
The key to identifying the Gartley pattern is that the move from point A to point B should be at a Fibonacci ratio of 0.618 or higher, and the move from point B to point C should be at a Fibonacci ratio of 1.272 or higher. The move from point C to point D should also be at a Fibonacci ratio of 0.618 or higher, and the move from point D to point E should be at a Fibonacci ratio of 1.272 or higher.
When the Gartley pattern is identified, traders can use it as a signal to enter a trade in the opposite direction of the pattern. For example, if the pattern is identified as a bullish Gartley pattern, traders would look to enter a short position.
It’s important to note that the Gartley pattern is not a foolproof indicator and should be used in conjunction with other technical analysis tools and fundamental analysis to make trading decisions. Also, the pattern is not present in every crypto chart, it’s very rare to see it.
The Gartley harmonic chart pattern is a useful tool for traders in the crypto market to identify potential reversal points in the price of a cryptocurrency. It is based on Fibonacci ratios and is named after H.M. Gartley. Traders should use it in conjunction with other technical analysis tools and fundamental analysis to make trading decisions.
Crypto Guide Today is a leading publication platform for the global crypto community, offering a wide range of coverage on blockchain technology and its applications. From reviews and analysis to guides and news on crypto assets, ecosystems, NFTs, metaverse, play-to-earn etc.
## How to Identify and Use the Gartely Harmonic Chart Pattern in Crypto Trading?
Identifying and using the Gartley harmonic chart pattern in crypto trading is a process that involves several steps:
• Look for a significantly low or high price of the cryptocurrency on the chart. This will be the starting point of the pattern, labeled as point A.
• Identify the retracement of the move from point A, labeled as point B. This move should be at a Fibonacci ratio of 0.618 or higher.
• Identify the extension of the move from point B, labeled as point C. This move should also be at a Fibonacci ratio of 1.272 or higher.
• Identify the retracement of the move from point C, labeled as point D. This move should be at a Fibonacci ratio of 0.618 or higher.
• Identify the extension of the move from point D, labeled as point E. This move should be at a Fibonacci ratio of 1.272 or higher.
Once the Gartley pattern is identified, traders can use it as a signal to enter a trade in the opposite direction of the pattern. For example, if the pattern is identified as a bullish Gartley pattern, traders would look to enter a short position.
When using the Gartley pattern, it’s important to keep in mind that it’s not a foolproof indicator and should be used in conjunction with other technical analysis tools and fundamental analysis to make trading decisions.
It’s also important to note that the Gartley pattern is not present in every crypto chart, it’s very rare to see it. So, it’s essential to be patient and not force the pattern in the chart, as it can lead to false signals and wrong trading decisions.
Identifying and using the Gartley harmonic chart pattern in crypto trading involves several steps, including identifying significant lows or highs, retracements, and extensions at specific Fibonacci ratios, and using the pattern as a signal to enter trades in the opposite direction. It’s important to use the Gartley pattern in conjunction with other technical analysis tools and fundamental analysis, and be aware of its rarity in crypto charts.
### What is a Bullish Gartley Harmonic Chart Pattern?
A Bullish Gartley Harmonic Chart Pattern is a specific type of Gartley pattern that is used to indicate a potential reversal in the price of a cryptocurrency from a bearish trend to a bullish trend. This pattern is formed when the price of a cryptocurrency makes a significant low, followed by a retracement, an extension, another retracement, and a final extension.
The key feature of a Bullish Gartley Harmonic Chart Pattern is that the retracement from the significant low to the extension (point B to point C) should be at a Fibonacci ratio of 0.618 or higher, and the extension from the retracement to the next retracement (point C to point D) should be at a Fibonacci ratio of 1.272 or higher. The retracement from the extension to the final extension (point D to point E) should also be at a Fibonacci ratio of 0.618 or higher.
When the Bullish Gartley Harmonic Chart Pattern is identified, it can be used as a signal to enter a long position in the cryptocurrency. Traders may also use it as a signal to exit a short position or to take profits on a long position.
It’s important to note that the Bullish Gartley Harmonic Chart Pattern is not a guarantee of a price reversal, and traders should use it in conjunction with other technical analysis tools and fundamental analysis to make trading decisions.
Bullish Gartley Harmonic Chart Pattern is a specific type of Gartley pattern that is used to indicate a potential reversal in the price of a cryptocurrency from a bearish trend to a bullish trend. It’s formed when the price of a cryptocurrency makes a significant low, followed by a retracement, an extension, another retracement, and a final extension. Traders can use it as a signal to enter a long position, exit a short position, or take profits in a long position. However, it’s important to use it in conjunction with other technical analysis tools and fundamental analysis to make trading decisions.
### What is a Bearish Gartely Harmonic Chart Pattern?
A Bearish Gartley Harmonic Chart Pattern is a specific type of Gartley pattern that is used to indicate a potential reversal in the price of a cryptocurrency from a bullish trend to a bearish trend. This pattern is formed when the price of a cryptocurrency makes a significant high, followed by a retracement, an extension, another retracement, and a final extension.
The key feature of a Bearish Gartley Harmonic Chart Pattern is that the retracement from the significant high to the extension (point B to point C) should be at a Fibonacci ratio of 0.618 or higher, and the extension from the retracement to the next retracement (point C to point D) should be at a Fibonacci ratio of 1.272 or higher. The retracement from the extension to the final extension (point D to point E) should also be at a Fibonacci ratio of 0.618 or higher.
When the Bearish Gartley Harmonic Chart Pattern is identified, it can be used as a signal to enter a short position in the cryptocurrency. Traders may also use it as a signal to exit a long position or to take profits on a short position.
It’s important to note that the Bearish Gartley Harmonic Chart Pattern is not a guarantee of a price reversal, and traders should use it in conjunction with other technical analysis tools and fundamental analysis to make trading decisions.
Bearish Gartley Harmonic Chart Pattern is a specific type of Gartley pattern that is used to indicate a potential reversal in the price of a cryptocurrency from a bullish trend to a bearish trend. It’s formed when the price of a cryptocurrency makes a significant high, followed by a retracement, an extension, another retracement, and a final extension. Traders can use it as a signal to enter a short position, exit a long position, or take profits in a short position. However, it’s important to use it in conjunction with other technical analysis tools and fundamental analysis to make trading decisions.
## The Gartley Harmonic Chart Pattern – Pros and Cons
The Gartley Harmonic Chart Pattern is a technical analysis tool that is used to identify potential price reversals in the cryptocurrency market. It is a popular pattern among traders and is widely used in both bullish and bearish market conditions.
Gartley Harmonic Chart Pattern is a widely used technical analysis tool that can be used to identify potential price reversals in the cryptocurrency market. It is considered to be highly accurate when used in conjunction with other technical analysis tools and fundamental analysis. However, it is not a guarantee of a price reversal. It requires experience and knowledge of technical analysis and the market to use it properly, and it has a risk of false signals.
## Final Words
I hope now that you’re well aware, of how to trade the Gartley Harmonic Chart Pattern in crypto trading. In conclusion, The Gartley Harmonic Chart Pattern is a popular technical analysis tool among traders in the cryptocurrency market. It is used to identify potential price reversals and can be applied to both bullish and bearish market conditions. However, it is important to note that the pattern is not a guarantee of a price reversal and should be used in conjunction with other technical analysis tools and fundamental analysis to make trading decisions. Additionally, it requires experience and knowledge of technical analysis to use it properly. Overall, while the Gartley Harmonic Chart Pattern can be a useful tool in crypto trading, it should be used with caution and proper understanding.
Crypto Guide Today provides the most up-to-date information to help the community understand and navigate this rapidly evolving field.
FAQs
### Which timeframe is best for harmonic patterns?
The preferred time frames for the Amazing Harmonic Pattern Trading Strategy are the 1-hour, 4-hour, or daily charts.
### What is ABCD harmonic pattern?
ABCD patterns are a type of harmonic pattern that involve two legs of equal length. They are easily recognizable in a price chart and offer high-probability trading opportunities. These patterns can signal both bullish and bearish reversals in the market.
### What is a butterfly pattern?
The butterfly pattern is a reversal indicator seen at the tops and bottoms of price movements. It signals the end of a trend and a potential entry point for traders, and it can be either bullish or bearish.
### How accurate is the Gartley pattern?
The Gartley pattern, also known as Gartley’s pattern, was first introduced in the book “Profits in the Stock Market” written by Gartley in 1935. It is found on page 222 of the book. This pattern has a close relationship with Fibonacci numbers and is known for its high profitability, with a reported success rate of over 70%.
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Submit a question to our community and get an answer from real people.
What resolution do human eyes see
Report as
Based on the above data for the resolution of the human eye, let’s try a “small” example first. Consider a view in front of you that is 90 degrees by 90 degrees, like looking through an open window at a scene. The number of pixels would be 90 degrees * 60 arc-minutes/degree * 1/0.3 * 90 * 60 * 1/0.3 = 324,000,000 pixels (324 megapixels).
At any one moment, you actually do not perceive that many pixels, but your eye moves around the scene to see all the detail you want. But the human eye really sees a larger field of view, close to 180 degrees. Let’s be conservative and use 120 degrees for the field of view.
Then we would see 120 * 120 * 60 * 60 / (0.3 * 0.3) = 576 megapixels.
The full angle of human vision would require even more megapixels. This kind of image detail requires A large format camera to record
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GC content track on GVIZ
1
0
Entering edit mode
@15877814
Last seen 7 days ago
Italy
Hi everyone, I'm trying to obtain a GC content track for the M. tuberculosis genome to plot on IGV. Below there is the code I have used to do this. However, when calculating the GC content, R blocks without giving an output. How can I solve the problem?
library(Biostrings)
library(Gviz)
# Calculate genome length
genome_length <- sum(width(genome_seq))
# GC content for a certain window size
window_size <- 10000
gc_content <- numeric(genome_length)
for (i in 1:(genome_length - window_size + 1)) {
window_seq <- subseq(genome_seq, start = i, end = i + window_size - 1)
gc_content[i] <- sum(unlist(strsplit(as.character(window_seq), "")) %in% c("G", "C")) / window_size * 100
}
Thank everyone for help
Gviz • 123 views
0
Entering edit mode
@james-w-macdonald-5106
Last seen 2 days ago
United States
This has nothing to do with Gviz. You shouldn't pick an unrelated package for questions because you are A.) directly asking that maintainer to answer an unrelated question and B.) not asking the relevant package's maintainer for help. But anyway.
> library(Biostrings)
## get windows
> starts <- seq(1, width(z), 1000)
> ends <- starts + 1000
## last one is too long, so fix
> ends[length(ends)] <- width(z)
## get the alphabet frequency for each 1000 bp window and rbind into a matrix
> zz <- do.call(rbind, lapply(seq(along = starts), function(x) alphabetFrequency(subseq(z, starts[x], ends[x]))))
## obvs
> zzz <- rowSums(zz[,2:3])/rowSums(zz)
[1] 0.5884116 0.5764236 0.6073926 0.5844156 0.6473526 0.6213786
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https://gimpppa.org/jeep-3-7-head-bolt-torque-specs/
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JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are watching: Jeep 3.7 head bolt torque specs
Hope this helps.Head layout red O = cylinder.Bolts 1 with 8 call for clean oil included to threads.* calls for sealant included to threads.Left financial institution shown, right financial institution is a mirror image.Head bolts; talk in succession 1,2,3,4,5,6,7,8, 9*,10*,11*,12*Torque making use of the adhering to steps:First step; speak bolts 1-8, to 20 ft. Lbs.Double examine all bolts 1-8 room still at 20 ft. Lbs.Torque bolts 9-12 come 10 ft. Lbs.Second step; revolve bolts 1-8, 90°.Third step; rotate bolts 1-8, 90° again. Torque bolts 9-12 to 19 ft. Lbs.-----11*----9*-----10**,,,|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯|7..|_______.| 5----12*,,,|___O__._|3..|______...| 1 ,,,|___O__._|2..|_______.| 4 ,,,|___O__._|6..|________| 8
Reactions:Hori, Scar0, Nitrogen and 1 other person
Hope this helps.Head layout red O
= cylinder.
See more: How Many Gallons Does A 2008 Honda Accord Hold ? 2008 Honda Accord
Bolts 1 v 8 call for clean oil added to threads.* needs sealant added to threads.Left financial institution shown, right bank is a winter image.Head bolts; speak in succession 1,2,3,4,5,6,7,8, 9*,10*,11*,12*Torque using the following steps:First step; speak bolts 1-8, to 20 ft. Lbs.Double check all bolts 1-8 room still at 20 ft. Lbs.Torque bolts 9-12 to 10 ft. Lbs.Second step; revolve bolts 1-8, 90°.Third step; turn bolts 1-8, 90° again. Speak bolts 9-12 come 19 ft. Lbs.-----11*----9*-----10**,,,|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯|7..|_______.| 5----12*,,,|___O__._|3..|______...| 1,,,|___O__._|2..|_______.| 4,,,|___O__._|6..|________| 8
Reactions:Scar0
Intake, speak in succession 1,2,3,4,5,6,7,8 come 105 in. Lbs.Right front come rear. 5,1,3,7Left front come rear. 6,2,4,8Exhaust; If the studs come out when removing, you have to replace the studs with new. You will require to add sealer top top the outlet threads the the brand-new studs.Start in ~ the center arm and working out. Torque to 18 ft. Lbs.Exhaust pipe to manifold 25 ft. Lbs.Both sides space the same.
In this insane world, it"s the sane male who shows up crazy!Mod links
RAM Air, CAI, Rack,FT Hood, JBA 2.5" Lift, Lighted cup-holders, Bumper Grill, Mudders, EuroTails, Winch Plate
Seeing an excellent info in this thread, ThanksHere"s mine story then the question.I to be told the after a leak down test that i had poor cylinder head gaskets. Traction the heads and also gaskets looked fine additionally noticed that cylinder 3 exhaust valve wasn"t moving and also sealing like it have to which is the very same cylinder that is giving an engine code. Not prepared to replace the left head I put the engine ago together with brand-new gaskets and new head bolts. Throughout the torque sequence (20lbs, examine 20lbs, 90deg, then another 90deg), specifically during the second sequence of 90deg turns, a pair of bolts (at about an 1/8 turn) every one of sudden got easier to turn; I would certainly say a palliation of about 40lbs of initiative to revolve the bolt. All other bolts maintained a constant level the torqueing effort to finish the last 90degs. Have actually you knowledgeable such a thing? Am i Screwed? did I just over big the bolt or possibly strip threads? I"ve pulled and also installed a couple of heads in my house garage mechanics carrier however I"ve never ever experienced this before. I since have started the engine and also it started appropriate up; operation the same as that did before and also still obtaining the cylinder 3 engine code. I have actually not run the engine since, trying to decision what to carry out next. Hoping to just replace head bolts and left cylinder head.Would evaluate any and also all comments and also feedback
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# [R] vectorizing a function
Robin Hankin r.hankin at auckland.ac.nz
Wed Oct 23 22:00:07 CEST 2002
```Hi Bill
> > besselI() does The Right Thing (tm), but it is internal ; what is the
> > best way to vectorize this type of function?
> >
> > [my clunky hypergeometric function deleted]
> [Bill's disclaimer]
> (NOTE: this is also vectorized wrt A, B and C as a kind of bonus.)
>
> hyper <- function(A, B, C, z, tol = sqrt(.Machine\$double.eps), maxit
> = 10000) {
> term <- z
> term[ ] <- 1
> partial.sum <- term
> n <- 0
> while(max(abs(term)) > tol && (n <- n+1) < maxit) {
> term <- term*A*B/C * z/n
> partial.sum <- partial.sum + term
> A <- A+1
> B <- B+1
> C <- C+1
> }
> if(n == maxit) warning("convergence may not have been achieved")
> partial.sum
> }
>
thank you very much for this: I guess the answer is to build
vectorization in, rather than to bolt it on afterwards!
The only advantage of my original function is that in mine, each
evaluation stops as soon as possible, whereas in Bill's improved
vectorized version, evaluation of each element continues until the
worst-case element finishes. I imagine that this isn't much of a
problem, unless one deliberatly finds some arguments to make it so.
(incidentally, I am particularly taken with "term[] <- 1",
considerably better than ,y term <- 1+term*0 )-:
Perhaps I should have rephrased my question. For a function which
absolutely cannot be written in a vectorized manner, eg pparz() below,
what is the best way to emulate true vectorization a la hyper() above?
[qparz() is a quantile function and pparz() inverts it to give the
CDF; try pparz(1:20,c(10,0.1, -0.1)) ]
qparz <- function(p , params) {
C <- params[1]
l1 <- params[2]
l2 <- params[3]
if(p <= 0) {return(0) }
if(p >= 1) {return(Inf)}
C*p^l1*(1-p)^l2
}
pparz <- function(x , params) {
f <- function(p,a){qparz(p=p,params=a[1:3])-a[4]}
options(warn = -1)
if(length(x)==1) {
return( uniroot(f,c(0,1),tol=1e-5,a=c(params,x))\$root)
} else {
return(sapply(x,pparz,params))
}
}
--
Robin Hankin, Lecturer,
School of Geography and Environmental Science
Tamaki Campus
Private Bag 92019 Auckland
New Zealand
r.hankin at auckland.ac.nz
tel 0064-9-373-7599 x6820; FAX 0064-9-373-7042
as of: Thu Oct 24 08:37:00 NZDT 2002
This (linux) system up continuously for: 420 days, 14 hours, 19 minutes
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
```
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# Tag Info
56
There are a bunch of teddy bears A, B, C, D and so on that are red on one side and blue on the other! (You choose how to color them) AND there are a bunch of 3 armed aliens with really long arms. Each alien grabs 3 teddy bear hands! (A teddy bear hand can be grabbed by more than one alien.) 3-SAT is the problem of whether you can color the teddy bears ...
39
Unfortunately, the original proof that Ramsey numbers exist (as in, are finite) was non-constructive, so mathematicians have been fighting an uphill battle from the beginning. Consider the diagonal Ramsey numbers $R(s, s)$. The smallest of these which remains unknown is $R(5, 5)$, so let's say we suspect $R(5, 5) = 43$—the current lower bound. We would ...
20
It doesn't work because it doesn't work. Say you have $W=10$ and there are three kinds of objects: Type $A$ has weight 9 and value 90. Type $B$ has weight 2 and value 19. Type $C$ has weight 1 and value 1. If you look at $v/w$, type $A$ wins, so you take one type $A$ object and fill up the remaining space with one type $C$, for total value $91$. But the ...
17
NP completeness means exactly that "all other NP problems could be reduced [in polynomial time] to the one", so yes, if a single NP-complete problem has a polynomial-time solution, then all NP problems do. See the formal definition. Note that it is not obvious that NP-complete problems exist in the first place! E.g. maybe for every NP problem A, I can find ...
15
It is currently unknown whether $P = NP$. All purported proofs have either been shown to be faulty, are under review, or are dismissed by the community at large without being considered. For more information on the last one, you might want to read Scott Aaronson's blog post detailing indicators why a purported proof is likely to be wrong and won't ...
13
If you could decide SAT problems in polynomial time, then you could also find a solution (for those instances that have them) in polynomial time. Namely, if Boolean expression $A$ is satisfiable and $x$ is a variable appearing in $A$, choose one of the expressions $A|_{x=T}$ and $A|_{x=F}$ (obtained by setting $x$ to "true" or "false" respectively) that is ...
12
The 9x9 board cannot be NP-complete, because there are finitely many instances of the problem.
10
Rather than strict NP-completeness, what I think what you're trying to ask is whether there is a transition similar to the one between 3-SAT and 2-SAT where the problem goes from being NP-hard to easy and in P. There is such a transition, but 9x9 Sudoku is on the wrong side of it. Solving a Sudoku puzzle is equivalent to deciding whether there is a valid ...
9
Actually, the classical NP-complete "vertex cover" problem is the decision problem: given natural number $k$ and graph $G$, is there a vertex cover of size $\le k$? If you could solve this problem in polynomial time, you could also find a cover of minimal size in polynomial time. The point is that given a vertex $v$, there is a vertex cover of size $k$ ...
8
there is some confusion in the question showing a lack of some basic understanding of the theory of NP completeness which is well documented in many places. particularly in this question: Is there any problem that been proven to be in NP? yes all NP complete problems are in NP. there are hundreds, maybe thousands of NP complete problems and minor ...
8
What would be if I be able to prove that one of the NP-Complete problems cannot be solved in polynomial time. I assume you mean "problems cannot be solved in polynomial time on a deterministic Turing machine". NP, after all, stands for "nondeterministic polynomial", and includes the decision problems that can be solved in polynomial time on a ...
8
A language $L$ is “NP-complete” if $L$ belongs to NP, and every language $X$ in NP can be polynomial-time reduced to $L$; that is the definition of “NP-complete”. How might we show that every problem $X$ in NP can be reduced to $L$? Well, $X$ is in NP, and the only thing we have to work with here is the definition of NP: There is a nondeterministic ...
7
Yes, at our current state of knowledge it is certainly conceivable that P=NP is independent of any given axiomatic foundation for mathematics (such as Peano Arithmetic or ZFC). It might even be "independent of the axioms, but not provably so". In contrast to some other enigmatic sentences, knowing that P=NP is independent of the axioms would not in itself ...
7
A language is in NP if a proposed solution can be verified in polynomial time. In this case a proposed solution is simply a listing of the vertices in the order they appear in the claimed cycle. This list is the so-called certificate. To check if this list is actually a solution to the Hamiltonian cycle problem, one counts the vertices to make sure they ...
6
THE SHORT VERSION 3-SAT is basically a bunch of questions separated into groups of threes. If at least one in each group is true, we say it is satisfiable. If not, we say it's unsatisfiable. THE LONG VERSION AN EXAMPLE For example, we can think of things in the kitchen. We can look at 4 things; an oven, a microwave, a toaster, and a refrigerator. Now ...
6
My understanding of your first paragraph. To prove a decision problem $C$ [is NP-complete], 2 things need to be shown: There is a [polynomial-time] verification for [$C$'s] solution. It requires a polynomial-time verification, for the proof of $C$'s solution, as $C$'s "solution" is simply a yes/no. The proof of the decision is essentially the ...
6
Assuming for now on you deal with the decision problem of the TSP, which is: Given as input a weighted undirected graph $G=(V,E, \omega)$ and at bound $C$, is there a Hamiltonian cycle in G whose weight is at most C? This is easily seen to be in NP (contrary to the optimization version you state in your question, which, if shown to be in NP, would yield ...
6
Must an algorithm that decides a problem in NP also be able to construct a solution for that problem which can then be verified in polynomial time? No, but a solution can be easily derived using the decision procedure for NP problems because all "natural" NP-complete problems seem to be downward self-reducible and all NP problems can be reduced to NP-...
6
Yes. By definition any NP problem can be reduced to an NP-complete problem in polynomial time. Since NP-complete problems are themselves NP problems, all NP-complete problems can be reduced to each other in polynomial time.
6
Yes, many problems known to be NP are thought to be not NP-Complete. These include: Any problem in P, other than $\varnothing$ and $\Sigma^*$. (If these problems are NP-Complete, then $\text{P} = \text{NP}$.) Any problem known to be in $\text{NP} \cap \text{coNP}$ but not known to be in P, for example, integer factorization (converted to a decision problem)....
6
First, the article is reducing 3SAT to Max2SAT (not Max2SAT to 3SAT). In 3SAT, each clause has 3 variables and has the form $c_i=(l_1 \cup l_2 \cup l_3)$. For each clause $c_i$, create the following 10 clauses: $(l_1), (l_2), (l_3), (d_i), (\lnot l_1 \cup \lnot l_2), (\lnot l_2 \cup \lnot l_3), (\lnot l_1 \cup \lnot l_3), (l_1 \cup \lnot d_i), (l_2 \cup \... 6 3-coloring a graph is reducible to 10-coloring by a padding argument. Given a graph$G$that you need to 3-color, create a new graph$H$by adding the complete graph$K_7$and making an edge from each of its vertices to all the vertices of$G$. The$K_7$part of$H$obviously cannot be colored with less than seven colors. None of those seven colors can be ... 5 This is a frequent source of confusion among people seeing NP for the first time. Let's see what the two definitions mean in the context of the Hamiltonian Circuit problem. HAMILTONIAN CIRCUIT: Given a description of a graph$G$(perhaps by an adjacency matrix), is there a simple circuit in$G$that contains all vertices of$G$? Definition 1 (verifying a ... 5 If you find a general algorithm that solves a single NP-complete problem in polynomial time, then you will have effectively proved that$P=NP$. Beware that solving one instance of a specific problem is not enough, you have to give an algorithm which solves any instances of the problem with any input data, and prove that the algorithm is polynomial in the ... 5 All of them. It's possible to verify if a proof is valid in polynomial time, and it's possible to check if the last step of a proof is the theorem under consideration in polynomial time, so just encode "valid proof of length N" as a satisfiability problem. N = 1 DO IF (there is a valid proof of length N that proves theorem T) THEN return TRUE IF (... 5 Yes. DNF and CNF formulas describe the solution space in different ways. DNF formulas are explicit in that they tell you exactly which assignments will satisfy the formula. CNF formulas are implicit in that they tell you what assignments won't satisfy the formula. Because DNF formulas are explicit, to determine satisfiability it suffices to go through ... 5 Every NP-complete problem is also a NP problem, by definition. Therefore, if NP=P, the same will be true for NP-complete problems. You can't say the same for NP-hard problems. These problems include all problems harder then NP problems, except for the NP-complete problems. In this case, we have that NP-hard$\cap $NP = NP-complete. So, even if NP=P, we ... 5 The comments point out that$\rm P=NP$"has to do with finite things". But formally speaking, it is a statement about the natural numbers. It is a first-order statement about the natural numbers. And in fact not a very complicated one. One can prove, quite easily once all the technical definitions had been understood, that the first-order theory of the ... 5 Yes, it comes up in OR (typically in references to problems being NP-complete or NP-hard). It is worth understanding, particularly in terms of understanding the limitations of what P versus NP versus not even NP (cannot be checked in polynomial time) means. The distinction is an asymptotic one (in terms of problem size). Too many papers use "it's NP-hard" ... 5 There is no polynomial-time procedure for deciding the satisfiability of 2-SAT + XOR-SAT unless P = NP. So, probably not. 2-SAT + XOR-SAT is easily proven NP-complete by direct polynomial reduction from 3-SAT. In a 3-SAT instance, each 3-CNF clause $$(x_1 \lor x_2 \lor x_3)$$ can be rewritten into the equisatisfiable 2-SAT + XOR-SAT expression$\$(x_1 \lor \...
Only top voted, non community-wiki answers of a minimum length are eligible
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Interesting script?
So post a link to it -
let others appraise it
You liked the script? Try it in the MetaTrader 5 terminal
# Unity - indicator for MetaTrader 5
Views:
2200
Rating:
Published:
2019.07.17 16:38
Unity is a cluster multi-currency indicator showing synchronous changes in the value of metals and major currencies in a generalized form. It was first published in the article "Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part II. Optimizing and forecasting".
In the essence its work is described by the following algorithm. Consider it on the minimalistic example with one currency pair (EURUSD) and gold (XAUUSD).
At every moment, the market state (that is current prices, or open prices of the bars) is expressed by obvious formulae:
EUR / USD = EURUSD
XAU / USD = XAUUSD
where variables EUR, USD, XAU are pure "values" of the assets, and EURUSD, XAUUSD are constants (exchange rates, or quotes).
To find the variables, we supplement the system with another equation, limiting the sum of the squares of the variables to unity:
EUR*EUR + USD*USD + XAU*XAU = 1
Hence the name of the indicator — Unity.
Simple substitution gives:
EURUSD*USD*EURUSD*USD + USD*USD + XAUUSD*USD*XAUUSD*USD = 1
Then USD can be found as:
USD = sqrt(1 / (1 + EURUSD*EURUSD + XAUUSD*XAUUSD))
and all other variables can be calculated.
In general:
x0 = sqrt(1 / (1 + sum(C(xi, x0)**2))), i = 1..n
xi = C(xi, x0) * x0, i = 1..n
where n — number of variables, C(xi,x0) — the quote of i-th pair including corresponding variables. Please note, that the number of variables is 1 more than instruments.
Since the coefficients C involved in the calculation are quotes that are usually very different, in the indicator they are additionally multiplied by contract's sizes: this gives more or less comparable values (at least, of one order). To see them in the indicator window (just for information) there is an AbsoluteValues input parameter that should be set to true. By default, it is, false, of course, and the indicator calculates the increments of variables:
yi = xi0 / xi1 - 1,
where xi0 and xi1 are values on the last and the previous bars respectively.
Here is the screenshot for the cluster of EURUSD,GBPUSD,USDCHF,USDJPY,AUDUSD,USDCAD,NZDUSD,XAUUSD:
Cluster multi-currency indicator Unity, XAUUSD
The lines of assets that make up work symbol of the current chart (in this case, XAU and USD) are shown thick, the rest are thin.
The main input parameters of the indicator:
• Instruments — the string with the names of work symbols separated by commas; it is necessary for all instruments to have one common currency - either base or quoting one;
• BarLimit — number of bars to calculate;
• Draw - drawing style;
• PriceType - price type used in calculations;
• SaveToFile — (option) a name of csv-file to which the indicator exports values for analysis in an external program, for example, in a neural network; the structure of the file is the following: the first column is the date, all subsequent ones are the values of the corresponding indicator buffers;
• ShiftLastBuffer - (option) flag for switching the mode in which the csv-file is formed; when the option is false, the data of the same bar are stored in the file on each line, the number of columns is equal to the number of instruments plus one due to the division of tickers into components, and plus one more — the first one — with dates, column names correspond to currencies and metals; when the option is true, an additional column called FORECAST is created, in which the values from the column with the last asset are saved with the shift to one bar forward; thus, in each row we see not only all the data for the current bar, but also next value of the last variable, which can be used by forecasting algorithms.
Recommended timeframes - D1 and higher.
PriceSpeed
This indicator shows average and peak speeds of price changes per minute.
RSI candles - lite ressource
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## Calculus and Vectors B
Unit code: MATH10131 Credit Rating: 15 Unit level: Level 1 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N
Co-Requisite
#### Aims
The course unit unit aims to provide an introduction to the basic elements of calculus.
#### Overview
This lecture course introduces the basic ideas of complex numbers relating them the standard transcendental functions of calculus. The basic ideas of the differential and integral calculus are revised and developed. Vectors in two and three dimensions are introduced and this leads on to the calculus of functions of more than one variable and the beginnings of vector calculus.
#### Learning outcomes
On successful completion of this module students will be able to:
• Represent complex numbers in the complex plane and use them to relate trigonometric and exponential functions.
• Sketch polynomial, rational, inverse and some standard functions of a single variable in Cartesian and polar coordinates.
• Evaluate and interpret limits and derivatives of algebraic functions, including functions expressed in implicit or parametric form.
• Select and deploy methods for evaluating integrals of functions of a single variable.
• Construct and manipulate Taylor series of scalar functions of one and two variables.
• Manipulate vectors using tools such as scalar and vector products, deploying these quantities to solve geometric problems.
• Construct, deploy and interpret derivatives of scalar functions of more than one variable.
• Construct, evaluate and interpret simple integrals of functions of two variables, using tools such as the Jacobian and Green's theorem. Construct and evaluate line integrals.
• Locate and classify extrema of functions of two variables.
#### Assessment methods
• Other - 25%
• Written exam - 75%
#### Assessment Further Information
Supervision attendance and participation; Weighting within unit 10%
Coursework; One in-class test, weighting within unit 15%
Two and a half hours end of semester examination; Weighting within unit 75%
#### Syllabus
• Numbers and Functions. Basic algebra of real and complex numbers; real line and complex plane; graphs and curve sketching; functions, domain and range, inverse functions; standard functions and inverse functions; basic algebra of real and complex numbers.
• Limits and Differentiation. Basic notion of limit and continuity; discontinuities, left and right limits; finding some limits; definition of derivative; derivatives of standard functions and their inverses; sums, products, quotients and the chain rule; implicit functions; logarithmic differentiation; higher derivatives (use in curve sketching).
• Infinite Series. Notation, basic notions of convergence, radius of convergence; infinite Taylor's series; expansions for standard functions.
• More on Complex Numbers. Euler's Theorem and De Moivre's Theorem; polar form of complex numbers (polar representation of the plane); roots of unity; complex forms of sin and cos, relationship to trigonometric identities.
• Integration. Definite and indefinite integrals; Fundamental Theorem of Calculus; techniques: linearity, integration by parts, partial fractions, substitution; lengths of curves, surfaces and volumes of revolution.
• Vectors in 2 and 3 Dimensions. Representation as directed line segments (magnitude, direction); choice of axes, components, Cartesian representation; basic properties, addition, subtraction, polar representation and relationship with complex numbers in 2 dimensions; scalar and vector product; representation of lines, planes, curves and surfaces.
• Functions of more than One Variable. Partial derivative, chain-rule, Taylor expansion; turning points (maxima, minima, saddle-points); grad, div and curl and some useful identities in vector calculus; integration in the plane, change of order of integration; Jacobians and change of variable; line integrals in the plane; path-dependence, path independence; Stokes' theorem and Green's theorem.
The course is based on the following text:
James Stewart, Calculus, Early Transcendentals, International Student Edition, Thomson (any recent edition).
#### Feedback methods
Feedback seminars will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.
#### Study hours
• Lectures - 33 hours
• Tutorials - 11 hours
• Independent study hours - 106 hours
#### Teaching staff
Sergei Fedotov - Unit coordinator
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# Chef and Equality Codechef Solution
Chef and Equality Codechef Solution: Chef has a box full of infinite number of identical coins. One day while playing, he made N piles each containing equal number of coins. Chef suddenly remembered an important task and left the room for sometime. While he was away, his newly hired assistant came across the piles and mixed them up while playing. When Chef returned home, he was angry to see that all of his piles didn’t contain equal number of coins as he very strongly believes in the policy of equality for all, may it be people or piles of coins.
In order to calm down the Chef, the assistant proposes to make all the piles equal. Chef agrees to give this task to him, but as a punishment gives him only two type of operations that he can perform.
• Pick some coins from any pile and put them back in Chef’s coin box.
• Pick some coins from the Chef’s coin box and put them on any one pile.
The assistant wants to do this task as fast as possible. So he wants to know the minimum number of operations needed to make all the piles equal.
### Input
• The first line of the input contains an integer T denoting the number of test cases.
• The first line of each test case contains a single integer N denoting the number of piles.
• The second line contains N space-separated integers A1A2, …, AN denoting the number of coins in each pile.
### Output
• For each test case, output a single line containing an integer corresponding to the minimum number of operations assistant needs to do.
### Constraints
• 1 ≤ T ≤ 10
• 1 ≤ N ≤ 105
• 1 ≤ Ai ≤ 105
• Subtask #1: 1 ≤ N ≤ 1000 (30 points)
• Subtask #2: original constraints (70 points)
```1
4
1 2 3 4
```
```3
```
### Explanation
• In test case 1, if you decide to convert all the piles to contain either of 1, 2, 3, or 4 coins you will have to change the other 3 piles. For any other choice you will have to alter more than 3 (i.e. 4) piles.
## Chef and Equality – CodeChef Solution in JAVA
```import java.util.*;
import java.lang.*;
import java.io.*;
/* Name of the class has to be "Main" only if the class is public. */
class Codechef
{
public static void main (String[] args) throws java.lang.Exception
{
Scanner s = new Scanner(System.in);
int T = s.nextInt();
while(T-->0){
int N = s.nextInt();
int[] arr = new int[N];
int maxCount = 0;
HashMap<Integer, Integer> set = new HashMap<>();
for(int i = 0; i< arr.length; i++){
arr[i] = s.nextInt();
if(set.containsKey(arr[i])){
set.put(arr[i], set.get(arr[i])+1);
}else{
set.put(arr[i], 1);
}
}
for(Map.Entry<Integer, Integer> entry: set.entrySet()){
maxCount = Math.max(maxCount, entry.getValue());
}
System.out.println(N-maxCount);
}
}
}
```
## Chef and Equality – CodeChef Solution in CPP
```#include <bits/stdc++.h>
using namespace std;
int main(){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int arr[n];
unordered_map<int,int>mp;
for(int i=0;i<n;i++){
cin>>arr[i];
mp[arr[i]]++;
}
int max_freq=INT_MIN;
for(auto i:mp){
if(max_freq<i.second){
max_freq=i.second;
}
}
int ans=n-max_freq;
cout<<ans<<endl;
}
return 0;
}
```
## Chef and Equality -CodeChef Solution in Python
```t=int(input())
for i in range(t):
n=int(input())
a=list(map(int,input().split()))
a.sort()
c=0;d=0;
for j in range(n-1):
if a[j]==a[j+1]:
c=c+1
if(c>d):
d=c
else:
c=0
print(n-d-1)```
Disclaimer: The above Problem(Chef and Equality ) is generated by CodeChef but the solution is provided by Chase2learn.This tutorial is only for Educational and Learning purpose.
Sharing Is Caring
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Related Articles
GATE | GATE-CS-2016 (Set 2) | Question 6
• Last Updated : 28 Jun, 2021
Among 150 faculty members in an institute, 55 are connected with each other through Facebook ® and 85 are connected through WhatsApp ® . 30 faculty members do not have Facebook ® or WhatsApp ® accounts. The number of faculty members connected only through Facebook ® accounts is ______________.
(A) 35
(B) 45
(C) 65
(D) 90
Explanation: Suppose
n(F) : number of faculty connected through facebook
n(W) : number of faculty connected through whatsapp
n(F ∪ W) : number of faculty connected through either facebook and whatsapp
n(F ∩ W) : number of faculty connected through both facebook and whatsapp
n(F ∪ W) = (total faculty – faculty not connected to anything) = (150-30) = 120
From number theory:
n(F ∪ W) = n(F) + n(W) – n(F ∩ W)
n(F) – n(F ∩ W) = n(F ∪ W) – n(W)
n(F) – N(F ∩ W) = (120-85) = 35
n(F)- n(F ∩ W) is the faculty that has only facebook account, Hence answer is 35.
This explanation has been contributed by Dharmesh Singh.
Quiz of this Question
Attention reader! Don’t stop learning now. Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.
Learn all GATE CS concepts with Free Live Classes on our youtube channel.
My Personal Notes arrow_drop_up
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http://spagades.com/my/one/framework/92009708c47a59505b-how-to-calculate-percentage-recovery-in-excel
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Calculate Portfolio Expected return. And also, 1 divided by this number of years is equal to the inverse of the fraction, or 12/14. 500% percentage of increase:= [Total]*500. Increases your productivity by 50%, and reduces hundreds of mouse clicks for you every day! ( new_value - old_value) / old_value Formula 2 A simplified Excel variance percentage formula that returns the same result. Suppose, you invest \$2,000 at 8% interest rate compounded monthly and you want to know the value of your investment after 5 years. The formulas that can be used are the following: NUMBER = * (1-PERCENTAGE%) subtract a percentage from a well-defined figure; = CELL * (1-PERCENTAGE%) to subtract a percentage from the value contained in a cell; =SUM (B:B)* (1-20%) to subtract a percentage from the total sum of a column (replacing a (B:B) the letter of the column to be added . So the CAGR formula is. However, I believe it produces misleading . First off, let's write down a list of components for your compound interest formula: PV = \$2,000. Example: Calculate the percentage change of the sales from the Monday to Sunday. Step 4: Hence the salary increment percentage is calculated. Step 1: Select the cells and right-click or use keyboard shortcut Ctrl+1 and select the Format Cells option. Then, enter the annual cash flow into another (e.g., A4). In the example shown, the formula in D6 is: = C6 / total. To calculate the percent of a total (i.e. You can view the resulting decimal fractions as percentages by clicking the Percent Style button (Home tab > Number group). It may be calculated in several different ways, depending on the data available. Note: the result is formatted with Percentage number format to show 36%, 18%, etc. 2. Select the cell that contains the result from step 2. Percentage of outstanding debtors. 3. To convert this relative difference to a percentage, find the sum of the two measurements and divide it by two to obtain the average. 900/-. This should be the cell in which you want to display the standard deviation value. Regards. In the example shown, the formula in D6 is: = C6 / total.
formula is given below and also excel sheet is attached for ready reference. Below in the picture you can see the example, how the above calculation can be represented as the Excel formula. The second chart (the Percentage Table Guide) asks for the convention - month or quarter - that you placed the Toyota in service. where total is the named range C15. The formula in the cell D2 calculates the percentage of deviation between the sales values for the current and last year: = (C2-B2)/B2. For this example, I'll use the settings for importing a Forex Tester file. Calculate your annual salary with the equation \$1,900 x 26 = \$49,400. 1. Decimal format is easier to calculate into a percentage. where total is the named range C15. To calculate the concentration factor for your system the calculation is: Example: if your feed flow is 100 GPM and your permeate flow is 75 GPM the recovery is (75/100) x 100 = 75%. The formula = (new_value-old_value)/old_value can help you quickly calculate the percentage change between two numbers. The picture illustrates two cases where in one case no solvent make-up volume is used and the other case where solvent is used to make-up the volume to a pre-determined volume mark. 1. Table 1. The first chart (the MACRS Depreciation Methods Table) tells you your Toyota is a non-farm 3-, 5-, 7- and 10-year property and that you use the GDS 200% method to calculate how much tax to deduct.
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https://socratic.org/questions/how-do-you-find-dy-dx-by-implicit-differentiation-of-y-sin-xy
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How do you find dy/dx by implicit differentiation of y=sin(xy)?
1 Answer
Apr 16, 2017
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y \cos \left(x y\right)}{1 - x \cos \left(x y\right)} ,$
,OR,
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{y}^{2} \sqrt{1 - {y}^{2}}}{y - \sqrt{1 - {y}^{2}} a r c \sin y} .$
Explanation:
$y = \sin \left(x y\right) .$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} , \text{ using the Chain Rule,}$
$= \frac{d}{\mathrm{dx}} \left(\sin \left(x y\right)\right) = \left\{\cos \left(x y\right)\right\} \left\{\frac{d}{\mathrm{dx}} \left(x y\right)\right\} , \text{ &, using the Product Rule,}$
$= \left\{x \cdot \frac{d}{\mathrm{dx}} \left(y\right) + y \cdot \frac{d}{\mathrm{dx}} \left(x\right)\right\} \cos \left(x y\right) ,$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = x \cos \left(x y\right) \frac{\mathrm{dy}}{\mathrm{dx}} + y \cos \left(x y\right) ,$
$\Rightarrow \left\{1 - x \cos \left(x y\right)\right\} \frac{\mathrm{dy}}{\mathrm{dx}} = y \cos \left(x y\right) .$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y \cos \left(x y\right)}{1 - x \cos \left(x y\right)} .$
Otherwise, $y = \sin \left(x y\right) \Rightarrow a r c \sin y = x y , \mathmr{and} , x = \frac{a r c \sin y}{y} .$
Hence, diff.ing both sides w.r.t. $y ,$ we have, by the Quotient Rule,
$\frac{\mathrm{dx}}{\mathrm{dy}} = \frac{y \cdot \frac{d}{\mathrm{dy}} \left(a r c \sin y\right) - \left(a r c \sin y\right) \cdot \frac{d}{\mathrm{dy}} \left(y\right)}{y} ^ 2 ,$
$= \frac{y \cdot \left(\frac{1}{\sqrt{1 - {y}^{2}}}\right) - \left(a r c \sin y\right) \cdot 1}{y} ^ 2 ,$
$= \frac{y - \sqrt{1 - {y}^{2}} a r c \sin y}{{y}^{2} \cdot \sqrt{1 - {y}^{2}}} ,$
Therefore, $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{y}^{2} \sqrt{1 - {y}^{2}}}{y - \sqrt{1 - {y}^{2}} a r c \sin y} .$
I leave it to the Questioner to show that both Answers tally with each other.
Enjoy Maths.!
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Physics
posted by on .
Some Carnot engine has an efficiency 0.700. The hot reservoir temperature is 900K. This means that the temperature of the cold reservoir is 270K. If the cold reservoir is dropped to 260K, the new efficiency is 0.701.
If the output of the power is kept constant by increasing the amount of time it takes to complete a cycle, what's the ratio of the wasted transfer of heat after the change to before the change?
• Physics - ,
In your first paragraph, the efficiency of a Carnot engine would be 0.711 with a 260 cold reservoir, not 0.701.
Your second paragraph does not make sense to me. Increasing the time it takes to make a cycle will not increase the power.
The ratio of wasted heat with 260 cold reservoir to that with 270 cold reservoir is (1-.711)/(1-0.700) = 289/300 = 96%
• Physics - ,
That didn't work. I think you're supposed to find work in each case but I'm not sure how to do that.
• Physics - ,
Oh wait never mind. Seems like there's some rounding issues going on with the online system. Thanks for the help drwls.
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collapse point 在 电力工业 分类中 的翻译结果: 查询用时：0.217秒
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collapse point 电压稳定临界点(2)崩溃点(8)
电压稳定临界点
A PRACTICAL DIRECT METHOD FOR VOLTAGE COLLAPSE POINT 电压稳定临界点的实用直接法 短句来源 In this paper,a direct method for static voltage collapse point in rectangle coordinate is presented. 本文提出了在直角坐标系下静态电压稳定临界点的一种直接计算方法。 短句来源
崩溃点
Predication for Voltage Collapse Point of Power System Based on Wide Area Measurement 基于广域测量的系统电压崩溃点预测 短句来源 After the voltage collapse point being found in AC/DC power systems, the relation between left eigen-vector W* and voltage collapse boundary surface is used to calculate the optimal control vector to increase load power margin. 在应用崩溃点法求得交直流联合系统电压崩溃点的基础上，利用左特征向量W*和电压崩溃边界曲面之间的关系计算出提高更直流联合系统负荷功率裕度的最优控制方向。 短句来源 Under the condition of suitable form ulation, the voltage collapse point and the left eigenvector ofthe dynam ic pow er system can be obtained by m eans of static pow er system m odel. The norm alvector to the bifurcation setis preferred to be used in optim um system controlnear bifurcation. 在适当建模的情况下用静态模型求得系统的鞍结分岔点及其左特征向量，按此方向控制系统的行为可以最快地远离电压崩溃点。 短句来源 These years, more and more power researchers have realized that voltage stability in power systems is a dynamic phenomenon, and voltage collapse point is predicted in advance. 近些年 ,越来越多的人认识到电力系统电压稳定问题是一个动态问题 ,而电压崩溃点是可以提前预知的。 短句来源 In recent years, more and more researchers have realized that voltage stability of power system is a dynamic phenomenon, and voltage collapse point can be predicted in advance. 近些年,越来越多的人认识到电力系统电压稳定问题是一个动态问题,而电压崩溃点是可以提前预知的。 短句来源 更多
“collapse point”译为未确定词的双语例句
Computation of Closest Voltage Collapse Point in Power System 电力系统最近电压崩溃临界点的确定 短句来源 A practical method of tracing static voltage collapse point 静态电压崩溃点的实用解法 短句来源 Power systems may keep the safety voltage level even near its limit, but that is very danger since maybe it is near the voltage collapse point. 本文主张为保证电压安全,电力系统在任何运行状态都应保持相应的电压安全裕度。 短句来源 The convergence of conventional continuation power flow calculation can't be guaranteed near collapse point because of the singularity of Jacobian matrix at collapse point. 由于潮流雅可比矩阵在临界点处奇异，临界点附近病态，连续潮流计算在临界点附近的收敛性无法得到有效保证。 短句来源 Wide area measurements technology is applied in the wider fields with the more applications of GPS (global position system) and PMU (Phasor measurement unit), so it is necessary that Wide area measurement technology is applied in the predicting of voltage collapse point in power systems. 随着GPS(全球定位系统 )和PMU(向量测量单元 )的进一步应用 ,广域测量技术应用范围越来越广 ,其用在电力系统电压崩溃点的预测也将成为必然。 短句来源 更多
我想查看译文中含有：的双语例句
collapse point
The synthesized networks formed a dense surface layer as the temperature increased past the gel collapse point. In DSC thermograms of swollen samples, the shape and onset temperature of the endothermic peak corresponded to the gel deswelling behavior and gel collapse point. In the interpenetrating polymer networks (IPN) system, the gel collapse point was not significantly changed by the amount of incorporated PTMEG. With increasing BMA content in the poly(NIPAAm-co-BMA) network, the gel collapse point was lowered and the gels deswelled in a more gradual manner with increasing temperature. Phys.79:1 (1995)], which excludes the existence of intermediate phases between the collapse point β=2 and the Kosterlitz-Thouless transition point βKT=4, is confirmed, however, a different analytic structure of this ansatz is suggested. 更多
The convergence of conventional continuation power flow calculation can't be guaranteed near collapse point because of the singularity of Jacobian matrix at collapse point.To overcome it,locally parameterized continuation power flow method is used for improvement.The improved method can effectively guarantee the convergence of continuation power flow calculation even near collapse point.Comparison with the CPFLOW program... The convergence of conventional continuation power flow calculation can't be guaranteed near collapse point because of the singularity of Jacobian matrix at collapse point.To overcome it,locally parameterized continuation power flow method is used for improvement.The improved method can effectively guarantee the convergence of continuation power flow calculation even near collapse point.Comparison with the CPFLOW program on IEEE-118 bus test system confirms its correctness and effectiveness. 由于潮流雅可比矩阵在临界点处奇异，临界点附近病态，连续潮流计算在临界点附近的收敛性无法得到有效保证。为克服该缺点，对局部参数连续法作了一定的改进，改进后的算法能够有效保证连续潮流计算在临界点及其附近的收敛性。与ＣＰＦＬＯＷ程序的比较结果证明了该方法的正确性和有效性。 After the voltage collapse point being found in AC/DC power systems, the relation between left eigen-vector W* and voltage collapse boundary surface is used to calculate the optimal control vector to increase load power margin. And then, some measures to increase the load power margin and avoid voltage collapse in AC/DC power systems are studied in this paper. 在应用崩溃点法求得交直流联合系统电压崩溃点的基础上，利用左特征向量Ｗ*和电压崩溃边界曲面之间的关系计算出提高更直流联合系统负荷功率裕度的最优控制方向。在此基础上，研究可提高交直流联合系统负荷功率裕度、防止电压崩溃发生的交流系统措施和直流系统措施。 Based on the load nearest to the voltage collapse point acquired from the m ethod ofthe nearest voltage collapse point, this paper defines the static voltage stability proxim ity of the system according to the load pow er proxim ity. An optim alvoltage stability controlm athem aticalm odelis setup to enhance the system 's static voltage stability proxim ity. In this m odelthe objective function is taken as the com prehensive objective function, and the constraint is considered to be the... Based on the load nearest to the voltage collapse point acquired from the m ethod ofthe nearest voltage collapse point, this paper defines the static voltage stability proxim ity of the system according to the load pow er proxim ity. An optim alvoltage stability controlm athem aticalm odelis setup to enhance the system 's static voltage stability proxim ity. In this m odelthe objective function is taken as the com prehensive objective function, and the constraint is considered to be the controlvariables, the outputvariables, the transm itted pow erofthe branch and the staticvoltagestability power proxim ity. The concepts of the security-econom y coordination factor and the synthetic controladjustm ent sequence coefficient are put forw ard in the m athem aticalm odel, w hich m akes the m odelm ore practicable. 在系统最近崩溃点的基础上，以系统的负荷功率裕度定义了系统的静态电压稳定裕度。目标函数考虑了系统的安全性和经济性，并以系统的控制变量、输出变量、支路传输功率和静态电压稳定功率裕度为约束条件，建立了提高系统静态电压稳定裕度的电压稳定控制数学模型。在控制模型中提出了安全经济协调因子和综合控制调节顺序加权系数的概念。使静态电压稳定控制模型更实用化。 << 更多相关文摘
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2008 CNKI－中国知网
2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社
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# Edexcel maths gcse formula sheet higher one account
## Chaconne piano sheet yiruma music
A formula is a group of mathematical symbols that expresses a relationship between one variable and other variables (e.g. A = π r ²).Formulae is the plural… A = πr²).Formulae is the plural of formula. Edexcel GCSE Maths past exam papers. Edexcel currently runs one syallbus GCSE (9-1) in Mathematics (1MA1), prior to 2017 Edexcel ran two syllabuses Mathematics A and Mathematics B. If you are not sure which exam tier (foundation or higher) you are sitting check with your teacher.
## 74ls373 datasheet
International GCSE Mathematics Formulae sheet – Higher Tier Arithmetic series Sum to n terms, S n = n 2 [2a + (n – 1)d] Area of trapezium = 1 2 (a + b)h b a h The quadratic equation The solutions of ax2 + bx + c = 0 where a v 0 are given by: x bb ac a = −± −2 4 2 Trigonometry AB C b a c In any triangle ABC Sine Rule a A b B c sin sin ... The formula sheets given to you in the GCSE Maths exams are below. Each exam board's formula sheet is very similar. AQA GCSE Maths formula sheet. Edexcel GCSE Maths formula sheet Surds 9-1 Maths. Surds 9-1 Maths consists of an extensive range of specimen and exam questions relating to surds, the majority of which come from the Higher Tier of Edexcel , AQA and OCR Examination Boards. These can be found in the table below.
## Sf16daz m1 4 datasheets
Edexcel GCSE Maths revision resources. Exam questions organised by topic, past papers and mark schemes for Edexcel GCSE Maths. Try it for yourself! Learn about and revise formulae and how to apply skills in substituting, creating and rearranging formulae with BBC Bitesize GCSE Maths Edexcel guide.
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https://mail.python.org/pipermail/tutor/2001-October/009136.html
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# [Tutor] logic ?
Danny Yoo dyoo@hkn.eecs.berkeley.edu
Thu, 4 Oct 2001 14:34:05 -0700 (PDT)
```On Thu, 4 Oct 2001, Jerry Lake wrote:
> for some reason, I can't get this to function
> properly, if someone can point me in the right
> direction, I'd appreciate it. the problem comes
> in at the if/else in the slope formula, it returns
> all slopes as 0.
>
> def slope(x1, y1, x2, y2):
> x = x1 - x2
> y = y1 - y2
> if (x or y == 0):
^^^^^^^^^^^^^
We as humans understand what you mean. However, Python's seeing this in a
different light:
if x or (y == 0):
That is, as long as x is a "true" value, the condition holds:
###
>>> 1 or 1 == 0
1
###
To fix this, you can write the logic like this:
###
if x == 0 or y == 0:
###
But I really like this way:
###
if 0 in (x, y):
###
which is neat since it reverses the "normal" role that we often see with
the 'in' operator. Usually, we have the variable to the left of 'in', but
we don't have to be constrained to this.
Hope this helps!
```
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http://prettymathpics.com/category/turtle/
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## Drawing Fractals with Lindenmayer Systems
Lindenmayer systems, or L-systems, provide a very powerful way to construct fractals. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. An L-system is a rewriting system and a …
## A Fake Circle made of Straight Lines
Inspired by this post on Reddit, I wrote this little script to do the same thing. The circle is an illusion created by 100 straight-line tangents to an invisible circle. The tangents are created by drawing a chord in a …
## Tweetable Python Code Golf
Code Golf is the amusement of writing as short as possible a program to perform a given task. So for example, if the task is to compute the average of a list of numbers (which could be changed at any …
## Random Walk
A colourful random walk. The basic idea is very simple: choose a random heading in the range 0:360 degrees. Step in that direction. Choose another random heading & step again. Do this 2,000 times. As a bonus, we go through …
## Turtle Star
A very simple Turtle program. Turtle can draw intricate shapes using programs that repeat simple moves.
Turtle graphics is a popular way for introducing programming to kids. It was part of the original Logo programming language developed by Wally Feurzig …
## Sierpinski Triangle, drawn by a Turtle
This is a classic fractal drawn with a recursion algorithm and Turtle graphics. The Sierpinski Triangle’s sides are bisected and the triangle they form is removed. The procedure is then applied to the 3 remaining triangles, and to them recursively …
## Square Spiral
This is a very simple introduction to Turtle graphics. The turtle starts in the middle of the window, moves forward a small distance, turns right, moves forward a slightly longer distance, right again, even further this time… until the distance …
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## Welcome to the Treehouse Community
The Treehouse Community is a meeting place for developers, designers, and programmers of all backgrounds and skill levels to get support. Collaborate here on code errors or bugs that you need feedback on, or asking for an extra set of eyes on your latest project. Join thousands of Treehouse students and alumni in the community today. (Note: Only Treehouse students can comment or ask questions, but non-students are welcome to browse our conversations.)
### Looking to learn something new?
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# JavaScript Recursive Binary Search
```const recursive_binary_search = (array, target) => {
if (array.length == 0) {
return false;
} else {
const midpoint = Math.floor(array.length / 2);
if (array[midpoint] == target) {
return true;
} else {
if (array[midpoint] < target) {
const newArray = array.filter((num) => num > array[midpoint]);
console.log(newArray);
return recursive_binary_search(newArray, target);
} else {
const newArray = array.filter((num) => num < array[midpoint]);
console.log(newArray);
return recursive_binary_search(newArray, target);
}
}
}
};
const numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
const result = recursive_binary_search(numbers, 10);
console.log(result);
```
I don't see Recursive Binary Search JavaScript version here, but only has plain Binary Search one. For some of you who learned only JS at this point and want to know how it works, you can copy and paste this code and run it. I added a couple of `console.log`s so that you can visualize how arrays are forming step by step. You can play with changing target numbers at the bottom. Happy Coding!
but .filter is linear runtime? i think the correct answer is below. function recursive_binary_search(list, target) { if (list.length === 0) { return false; } else { let midpoint = Math.floor(list.length / 2);
```if (list[midpoint] === target) {
return true;
} else {
if (list[midpoint] < target) {
return recursive_binary_search(list.slice(midpoint + 1), target);
} else if (list[midpoint] > target) {
return recursive_binary_search(list.slice(0, midpoint), target);
}
}
```
} }
Since the main Python code was rewritten to account for the cost of `array.slice()`, I built my `recursive_binary_search.js` like this:
```function recursive_binary_search( list, target, start = 0, end = false ) {
if ( ! end ) {
end = list.length - 1;
}
if ( start > end ) {
return false;
} else {
mid = Math.floor( ( ( start + end ) / 2 ) );
if ( target === list[mid] ) {
return mid;
} else if ( target < list[mid] ) {
return recursive_binary_search( list, target, start, mid - 1 );
} else {
return recursive_binary_search( list, target, mid + 1, end );
}
}
}
```
Gia Chan Yeah, I just wanted to code to look similar, but I never thought about that. Here: Medium, I could find some comparisons; however, nothing was mentioned regarding the time-complexity, but also Here: StackOverflow, someone claims that the `array.slice()` has linear runtime complexity, O(n). I just got into this algorithm course two days ago, so I need some more research on this . Thanks for your insight.
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https://curriculum.illustrativemathematics.org/k5/teachers/grade-1/unit-1/lesson-2/preparation.html
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# Lesson 2
Explore Expressions and Sums
### Lesson Purpose
The purpose of this lesson is to write addition expressions within 10 and find the sums.
### Lesson Narrative
This lesson builds on the previous lesson as students were asked to determine the sum of two dot cubes. It also builds on the work of kindergarten, where students wrote addition expressions to represent images and situations. In this lesson, students match expressions to dot images before they are asked to write addition expressions (MP2). Students also continue to build their math language related to the sums, addition expressions, and mathematical community (MP6).
Math Community
Tell students they will have an opportunity to revise their math community ideas at the end of this lesson, so as they work today they should think about actions that may be missing from the current list.
• Engagement
• MLR8
### Learning Goals
Teacher Facing
• Write addition expressions within 10 based on images and add in a way that makes sense to them.
### Student Facing
• Let’s write addition expressions and find the sum of two numbers.
### Required Materials
Materials to Gather
Materials to Copy
• Number Cards (0-10)
• Check It Off Stage 1 Recording Sheet Grade 1
### Required Preparation
Activity 2:
• Create a set of cards from the blackline master for each group of 2.
Building On
### Lesson Timeline
Warm-up 10 min Activity 1 15 min Activity 2 20 min Lesson Synthesis 10 min Cool-down 5 min
### Teacher Reflection Questions
How are you facilitating the creation of a productive Mathematical Community? Where can you point to evidence of this for students to see?
### Print Formatted Materials
For access, consult one of our IM Certified Partners.
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https://www.mtwallets.com/category/system-deep-dives/quadcopter/
| 1,726,820,307,000,000,000
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| 814,943,042
| 23,060
|
A Quadcopter study is a fun challenge. It’s a busy area of interest, so there are papers and materials to use as a guide and many hardware and software platform options to work with.
We visit optimal control, estimation, classical and state-space design techniques, applied math, and forays into underlying mechanics, electronics, software, etc.
Quad-Rotor Control Design Series
## Quad-Rotor Control Design Series
What is a “quad-rotor”? Well you probably know it’s a thing with four rotors. We buy it as a, “drone” and we fly it with a remote control or via a phone app acting like one. I’ll probably bounce between the terms quad-rotor and quadcopter throughout. I mean the same thing. It is incredible what …
QuadCopter DC Motor(BLDC) + Propeller Dynamics
## QuadCopter DC Motor(BLDC) + Propeller Dynamics
Ultimately we’ll buy Electronic Speed Controllers (ESCs) for our Quad motors. They take PWM in and produce drive voltages for brushless DC motors. Let’s jump in to understand the motor-propeller subsystem on a quadrotor. DC Motor Modelling You’ll find basic DC motor equations in any undergraduate dynamics textbook. I add the Bouabdallah model for the …
Quadrotor: 4 props to stabilize the platform
## Quadrotor: 4 props to stabilize the platform
In the last post we arrived at a mathematical model for the combination brushless DC motor (BLDC), gearbox, and propeller model. A small quadrotor motor will not have a gearbox. It will have the propeller mounted directly to the shaft of a small hobby motor. In larger craft a gearbox helps match the motor to …
Revisit the Motor-Propeller Model
## Revisit the Motor-Propeller Model
It’s been fun to mess with the motor-propeller differential equation and linearization in an post. However, when I got into looking-up some rough parameter estimates and performing dimensional analysis (seeing if the units worked-out right for me in the equations) I ran into some problems. I realized I was not only needing numbers, but I …
## Propeller Blade, “Lift”
In the last quadcopter post we clarified the load torque of the propeller applied through the gearbox to the motor shaft. We won’t even have a gearbox but the terms in the equation needed clarification. We haven’t yet covered the main point of the propeller: LIFT! A propeller blade is just a spinning wing at each …
Quadcoptor Platform Equations of Motion: Dynamic Model
## Quadcoptor Platform Equations of Motion: Dynamic Model
Here we’ll derive the equations of motion for copter attitude: it’s roll, pitch, and yaw or orientation in the sky relative to an observer on the ground. The X,Y,Z position of the craft relative to the same observer comprise the other degrees-of freedom. We’ll later see how thrust and attitude drive to the X,Y,Z position, …
Quadrotor Dynamic Model: Propeller Gyroscopic Effect.
## Quadrotor Dynamic Model: Propeller Gyroscopic Effect.
The equations below are from the last post, where we see we matched our Bouabdallah paper‘s equations for rotational motion. We know some propeller input is going to be a part of the applied torque. There is going to be a set of equations for linear motion too, but let’s clarify what is going on …
Finalizing Equations Of Motion: Thrust Inputs from Propellers
## Finalizing Equations Of Motion: Thrust Inputs from Propellers
This post explains how we determine propeller thrust and drag factors for our quadcopter project. The last couple of posts have been working out the sum of torque on our quadcopter. A few weeks ago, we covered the gyroscopic effect of the total airframe in the “equations of motion” post. Next, we looked at the …
Quadrotor: Simplifications for, “Classical” Controller Design
## Quadrotor: Simplifications for, “Classical” Controller Design
The last few posts covered each of three dynamic details separately: Gyroscopic effect of the rigid body (the entire quadcopter). Gyroscopic effect of the spinning propellers. Propeller thrust and drag effects. We’re going to use all of this information as we look at controlling the flight of a quadcopter, but first we’re going to make …
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17 Oct, 39 tweets, 9 min read
1/
Get a cup of coffee.
2/
We humans are simple creatures.
We like to boil down complex situations into a single number.
For example, the economy is complex. So we reduce it to one number -- GDP.
Valuing a company is complex. So we reduce it to one number -- a P/E ratio.
And so on.
3/
Averages are the same way.
Studying a population is complex. So we tend to look for one number that can represent the whole population.
This number -- more often than not -- ends up being the population's "average".
4/
In general, averages are pretty useful. In many cases, they represent the underlying population reasonably well.
But in one *important* case, they fail. This is when the population has significant outliers.
Outliers can skew averages so much that they become meaningless.
5/
In a nutshell, the problem is this:
When Warren Buffett walks into a McDonald's, the *average* diner there becomes a billionaire.
It's simple math: Buffett is worth ~\$80B. If he joins 9 diners who are each worth ~\$50K, the *average* net worth of the group is now ~\$8B.
Pic:
6/
But of course, this is absurd.
9 out of those 10 diners will probably never see anything like \$8B in their lifetimes.
What happened is that a single outlier -- Buffett -- skewed the group's average so much that the average itself became meaningless.
7/
In life, there are outliers everywhere.
A small part of the population often significantly skews the average of the whole.
The richest people skew the average net worth.
The biggest companies skew the average market cap.
Ultra luxury homes skew the average home price.
8/
One way to avoid this kind of skewing is to use the *median* instead of the average.
Unlike the average, the median doesn't sum up the population. Instead, it *sorts* the population and *picks the middle* of the pack.
9/
This way, the outliers -- who, by definition, are at the extreme ends of the pack, not in the middle -- don't have much of an impact.
So, even if Buffett walks into a McDonald's, he won't be able to single-handedly skew the median net worth of the diners:
10/
When analyzing businesses as potential investments, it's always a good idea to keep an eye out for outliers skewing averages.
Do a few large customers skew ARPU (Average Revenue Per User)?
Do a few highly profitable stores skew the average profit margin of the whole chain?
11/
Do a few luckily timed derivatives contracts mask losses from a large number of other trades?
12/
Whenever we think *average* numbers reported by a company are subject to outlier skewing, we should try and work out the *median* numbers.
If there are significant differences between the two, it's an indication that we should spend some effort understanding the outliers.
13/
Another observation: averages may be perfectly good for some applications, but not for others.
For example, here's a river that's 100 ft across. The water is 2 ft deep 90% of the way, but there's a 10 ft deep stretch in the middle.
The *average* water depth is 2.8 ft.
14/
Suppose we want to estimate the amount of water in this river.
For this task, using the *average* water depth works well. In fact, the average is exactly the right metric to use in this case.
15/
But suppose we didn't know swimming, and we want to figure out whether it's safe to walk across the river.
If we use the *average* depth for this, we will drown.
Here, we should of course decide based on the *worst case* depth (10 ft), not the *average* depth (2.8 ft).
16/
When making investment decisions, understanding the *worst case downside* is often far more important than understanding the *average case upside*.
Yet, most financial projections seem to be built around average case (and sometimes, better than average case) assumptions.
17/
For example, suppose we have 2 businesses: A and B.
A is in a rapidly changing industry, and its competitive advantages may or may not prove durable.
In other words, A's stock is a "big upside, big downside" type investment.
18/
Let's say there's a 10% chance that A's stock will go to 0 in the next 10 years, but a 90% chance that it will do very well (become a 5-bagger or 10-bagger).
Here are the possible outcomes and their respective probabilities:
19/
Therefore, the *average* return -- or expected return -- for stock A is ~12.04%.
Calculations:
20/
Business B, on the other hand, is in a stable industry -- where it enjoys a dominant position and predictable cash flows.
This is a "moderate upside, no downside" type investment.
Here's the distribution of outcomes for B's stock:
21/
The *average* return -- or expected return -- for stock B works out to 10.5% annualized:
22/
Suppose we could pick only one stock -- A or B -- to put our entire net worth into. Which one should we pick?
If we went solely on the basis of *averages*, the answer is obvious.
A (with its 12.04% expected return) clearly wins over B (with its 10.5%).
23/
If we went by this logic and picked A, we'd be following what's known as the "expectation maximization" strategy.
This simply means: from the available options, we pick the one that promises to deliver the greatest expected return on our investment.
24/
A lot of economic theory is based on expectation maximization.
When faced with two or more probabilistic choices, rational agents -- the theory goes -- would seek to maximize their expected return.
But if you gave *me* this exact choice, I'd pick B over A in a heartbeat.
25/
Why?
Because I don't believe in expectation maximization. I believe in *survival* -- first and foremost.
There's a 10% chance that stock A will go to 0. If we pick A, and this happens, our net worth is gone. Poof.
In my mind, this risk is simply not worth taking.
26/
As Charlie Munger is fond of saying: "All I want to know is where I'll die, so I'll never go there."
Going all in on stock A type situations is how investors die -- by taking excessive risk with a big portion of their capital.
As Buffett put it in his 2008 letter:
27/
One way to decide between A and B is to imagine repeating our choice many times in succession.
For example, what would happen if we bet our entire net worth on a "type A" bet again and again?
28/
We may get lucky a few times -- with a 5-bagger or 10-bagger. But sooner or later, we'd go to 0.
And once we go to 0, we stay there forever.
From Buffett's 2005 letter:
29/
This is the essence of the famous Kelly Criterion for position sizing.
Instead of treating bets as "one-off" events, we should imagine that we're going to bet repeatedly -- taking our winnings from each iteration and betting it all on the next iteration.
30/
Then the goal is simple: we try to maximize the long-term expected growth rate of our capital in this "repeated betting" scenario.
So, if there's even a tiny chance of a 100% loss, we shouldn't bet our entire net worth -- no matter how big the expected return is.
31/
So, if the choice is to bet our entire net worth on either A or B, Kelly would pick B over A every time.
But if we were allowed to split our net worth between A and B, then Kelly would put ~85% of it into A and the remaining ~15% into B.
For more:
32/
Another approach to get around the limitations of averages is to use "weighted averages".
Here, we assign a "utility" to each return outcome. Then we maximize "expected utility", rather than "expected return".
33/
A 100% loss has highly negative utility because of "loss aversion" -- our pain from a \$1 loss is more than our happiness from a \$1 gain.
And a 10-bagger has more utility than a 5-bagger, but not twice as much -- as utility diminishes with each incremental dollar.
34/
This way, "expectation maximization" becomes "expected utility maximization".
This is a whole new branch of economics -- and possibly a future thread topic.
35/
One final factoid on averages.
We often see headlines like: 90% of investors think they're better than average.
Or: 80% of people think they're better than average drivers.
As if these are mathematical impossibilities.
36/
But you know what?
It's definitely possible for 90% of investors to be better than average.
The remaining 10% just have to be really bad outliers.
Just as it's possible for 90% of McDonald's diners to be poorer than average. All it takes is 1 Buffett in the mix.
37/
To summarize:
When dealing with complex/uncertain situations, we tend to take decisions based solely on "average outcomes" and "average case scenarios".
But this can be a bad idea.
38/
Averages suffer from all kinds of problems.
Potential workarounds include: medians, worst case scenarios, Kelly-inspired strategies, and utility theory/weighted averages.
39/
If you're still with me, you're way above average -- a true outlier in the best possible way!
/End
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More from @10kdiver
10 Oct
1/
Get a cup of coffee.
2/
Imagine that you run an insurance company.
Every year, you write a policy that insures the city of San Francisco against an earthquake.
3/
Every year, on Jan 1'st, the city pays you an "insurance premium". You can invest this premium however you like.
If an earthquake hits, you need to pay the city \$1B on Dec 31'st.
If no earthquake hits, you get to keep the premium -- and any returns you made by investing it.
6 Oct
1/
I just listened to this wonderful episode of “Coffee With The Greats” — a conversation between @milesfisher, his dad, and Ajay Banga (the CEO of MasterCard, @Mastercard).
It’s packed with so many interesting nuggets — the threadaholic in me can’t resist summarizing them!
2/
Key things Ajay learned from his parents.
From his mom: Constantly educate yourself and keep improving yourself so you can help others more.
From his dad: Connect with everyone. Learn from everyone. Find the humanity in everyone.
3/
It’s super important to have “alone time” to think.
Ajay tries to set aside the first 45 mins of each day (8:00am to 8:45am) — to read, think, envision the future, etc.
And he tries to not have back to back meetings. Gaps between meetings help digest information better.
3 Oct
1/
Get a cup of coffee.
2/
Since this is a magical topic, we'll set this thread in the Harry Potter universe.
Imagine that you're Ollivander, the wand maker.
You source magical raw materials and make wands out of them. You sell these wands to witches and wizards out of a shop located in Diagon Alley.
3/
The wand business is highly seasonal.
95% of your sales happen in the two weeks before Hogwarts reopens each year.
Most witches and wizards buy a wand just before their first year at Hogwarts. And they use that wand their whole lives -- so there's not much repeat business.
26 Sep
1/
Get a cup of coffee.
2/
Imagine that you're Mack, the truck driver.
You work, of course, for Lightning McQueen -- the world famous race car.
Your job is to transport Mr. McQueen across the country, to wherever his next race happens to be.
3/
You work hard, and you take pride in your work.
After all, it is because of your efforts that Mr. McQueen always reaches his race venue safely, in time, well rested, and ready to win.
24 Sep
1/
Yesterday, I called out someone on Twitter.
On this blog, he was plagiarizing my threads — and also posts from top financial writers like @morganhousel and @dollarsanddata.
2/
After seeing my tweet, many of you came together and voiced your distaste for this kind of behavior.
Facing all this pressure, this person has since taken down the posts he plagiarized, and also apologized on his blog.
He also apologized to me via DM.
3/
This person clearly made a mistake.
But after getting caught, he’s tried to make amends and do the right thing.
Plus, being called out on Twitter by so many people can’t have been much fun for him.
So, I’m inclined to let this matter rest.
19 Sep
1/
Get a cup of coffee.
Geometric sequences are the basis for *so* many financial calculations -- from DCFs to mortgages.
And the math behind them is not very complicated. So I think it makes sense to master it.
2/
First things first. What is a geometric sequence?
In simple terms, it's just a list of numbers.
But not just any numbers.
No, these numbers have a very special property: they grow (or shrink) *exponentially*.
3/
Here's an example.
Suppose your 2020 salary is \$100K. And you get a 5% raise every year.
So, in 2021, your salary will be \$100K * 1.05 = \$105K.
And in 2022, your salary will be \$105K * 1.05 = \$110.25K.
And so on.
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Intern
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22 Nov 2010, 21:16
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BOOKMARKED
I just took the GMAT today. I've been a lurker here for a while. I've used a lot of different strategies that have been suggested here, and I thought I would add my 2 cents as to what I thought helped me the most during my studies. Hopefully my story can help others in some way in their preparation.
Materials Used:
Math:
Total GMAT math- This resource was pretty good. I would give it about a 7.5/10. It seemed like it was missing a few important formulas/concepts, but overall I thought it was a very good resource for getting an overall picture of what was to be expected in the math section.
Extreme Challenge- I thought this set was great. It definitely had about 35% probability/combinatorics questions, but it was still top notch. (By the way, I only got one question of this type on the GMAT, and it was really basic compared to some of the practice problems I had taken, so I'm not sure it's worth the time freaking out about probability/combinatorics.)
GMAT Club Tests- These tests were very difficult. I got pretty frustrated with how hard these tests were. I thought a lot of the questions weren't very realistic, but after I took and reviewed the first 15 tests, I knew that I was very prepared for the math section the GMAT. These tests are very recommended, but don't get dismayed if you don't do well at first. I averaged around 26 out of 37 on these tests.
Verbal:
Powerscore CR Bible- This book was awesome. It made critical reasoning go from my weakest area in verbal to my strongest. It goes through every question type and discusses all the possible wrong/right answers one could face. I can't speak highly enough about this book.
Manhattan SC- This book was pretty good. I view it as a great way to start off one's SC study. Everyone should supplement this with lots and lots of practice (via the OG, OG Verbal, or GMAT Prep SC Doc).
RC 99- This book was pretty good at enhancing my RC ability. I read about 10 of the difficult passages. It got me used to the most obscure, difficult to decipher types of passages. I'm not sure if I recommend this or not. I would maybe suggest reading all of the OG and OG Verbal passages instead. I did read the Economist, specifically the Science and Technology section, and I believe that helped my reading comprehension a decent amount, so I would definitely suggest doing that as well.
The OG Verbal Supplement- This supplement was pretty good. I thought the questions were rather on the easy side compared to the actual GMAT, so I'm not sure how much it helped overall. It was definitely good practice though.
Overall:
The OG- This was a very good resource. Both the math and verbal questions were probably a little easy compared to the actual GMAT, but this book contained good practice overall. I would definitely go through this book as part of my preparation.
Here's a summary of how I would rate the materials I used:
Total GMAT Math- 7.5/10
Extreme Challenge- 9/10
GMAT Club Tests- 9/10
Powerscore CR Bible- 10/10
MGMAT SC Guide- 8/10
RC 99- 7.5/10
OG- 8/10
OG Verbal-7.5/10
My practice tests:
MGMAT 1: 730- The math was brutal in this test.
MGMAT 2:730- Again, the math was brutal
GMAT Prep 1:770
Test Day Experience:
I didn't do anything special on test day. I just ate what I normally eat for breakfast and lunch and then drove to to the test center. When I was taking the test, I thought to myself "This isn't going very well. I've definitely missed a lot of questions." The message here is that even if you don't think you're doing well, don't get dismayed, because you might be doing better than you think!
Overall:
I do feel that the GMAT is very learnable. It doesn't really matter what one's natural math and English language abilities are, hard work and perseverance are what matter. With enough time and smart study methods, anyone can do well on this test.
Last edited by jauer112 on 23 Nov 2010, 05:49, edited 1 time in total.
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22 Nov 2010, 21:24
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22 Nov 2010, 22:54
awesamo!
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Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia
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23 Nov 2010, 08:47
Do you think it's necessary to go through the PowerScore CR bible? What were you scoring like before and after the book? I've been trying to improve on my CR with free resources from the net...not really inclined towards buying a whole book dedicated to CR and go through even more theory...is CR really that difficult?
_________________
1st Feb '11 -- Actual GMAT : 730 (Q48 V42) AWA 6.0
My Practice GMAT Scores
29th Jan '11 -- GMATPrep#2 : 700 (Q47 V38)
23rd Jan '11 -- MGMAT Practice Test #3 : 670 (Q45 V36)
19th Jan '11 -- GMATPrep#1 v.1 : 710 (Q49 V37)
15th Jan '11 -- GMATPrep#1 : 720 (Q47 V42)
11th Jan '11 -- MGMAT Practice Test #2 : 740 (Q47 V44)
6th Jan '11 -- Kaplan#2 : 620 (Q40 V35)
28th Dec '10 -- PowerPrep#1 : 670 (Q47 V35)
30th Oct '10 -- MGMAT Practice Test #1 : 660 (Q45 V35)
12th Sept '10 -- Kaplan Free Test : 610 (Q39 V37)
6th Dec '09 -- PR CAT #1 : 650 (Q44 V37)
25th Oct '09 -- GMATPrep#1 : 620 (Q44 V34)
If you feel like you're under control, you're just not going fast enough.
A goal without a plan is just a wish.
You can go higher, you can go deeper, there are no boundaries above or beneath you.
Senior Manager
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23 Nov 2010, 09:02
@jauer112 Congrats for your score. I think you pretty much used ALL the quality material available for GMAT. Kudos!
_________________
"Whether You Think You Can or Can't, You're Right"--Henry Ford
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My GMAT Journey
Senior Manager
Joined: 25 May 2010
Posts: 320
Location: United States
Concentration: Strategy, Finance
Schools: CBS '14 (A)
GMAT 1: 590 Q47 V25
GMAT 2: 560 Q47 V20
GMAT 3: 600 Q47 V25
GMAT 4: 680 Q49 V34
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23 Nov 2010, 09:05
@gmatdelhi - I'm not sure if CR Powerscore is a must have but definitely this is one of the best books available for tackling CR questions in GMAT. I've read this book and is definitely worth it. It's always recommended to prepare from at least two different books for the same topic to acquire all possible aspects.
_________________
"Whether You Think You Can or Can't, You're Right"--Henry Ford
680 Debrief
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My GMAT Journey
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23 Nov 2010, 09:26
gmatdelhi wrote:
Do you think it's necessary to go through the PowerScore CR bible? What were you scoring like before and after the book? I've been trying to improve on my CR with free resources from the net...not really inclined towards buying a whole book dedicated to CR and go through even more theory...is CR really that difficult?
For whatever reason I had difficult doing CR questions. I would say I went from around a 70-75% hit rate to an over 95% hit rate. I'll try to give an example of how it helped me.
-Assumption questions were especially tough for me. However, after reading the CR Bible, I felt like I knew all the potential types of correct answers. For example, one out of every 8 questions, I would wager, would have a correct answer that eliminates the possibility that the stated relationship in the stimulus is reversed. For whatever reason, such an answer never would have occurred to me prior to reading the book and I very likely would not have guessed that answer choice. After reading the book, if I ever saw such an answer choice, I would immediately know that it's the right answer. Also, I thought the Negation technique described in the book was a great way to double check that your answer choice is correct.
I would say I wasn't that inclined to go over the theory of CR either, but I really do feel strongly about this book. It isn't necessary to do well on the GMAT, but it will guaranteed help you if you do choose to go through it.
Manager
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23 Nov 2010, 10:07
Well done to you. This is a terrific score. Good luck with your apps.
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23 Nov 2010, 11:25
Excellent score..Congratulations.
Thanks for the debrief.
_________________
+1Kudos, if this helps
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24 Nov 2010, 04:10
Thanks a lot for your advice.I have ordered powerscore cr from Amazon;)
Posted from my mobile device
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24 Nov 2010, 06:43
Thank you, looks great!
Intern
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25 Nov 2010, 21:06
Congratulations for the massive score and best of luck for the app.. How did you find GMAT Verbal questions in comparison to OG tough,latter verbal questions in difficulty level.. Were CR questions lengthy ( more than 5-6 lines ) ?
Intern
Joined: 28 Aug 2010
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26 Nov 2010, 15:47
sv76 wrote:
Congratulations for the massive score and best of luck for the app.. How did you find GMAT Verbal questions in comparison to OG tough,latter verbal questions in difficulty level.. Were CR questions lengthy ( more than 5-6 lines ) ?
The last RC passage on the test was a lot harder than any of the passages in the OG. The RC passages in general were a little bit trickier than the OG. The SC and CR were about the same though.
Most of the CR questions weren't that lengthy. I didn't really notice that a lot of them were very long at least.
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26 Nov 2010, 17:05
Congratulations for such an excellent score..
Good Luck for ur applications..
_________________
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Varun
If you like my post, give me KUDOS!!
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26 Nov 2010, 21:25
I am taking the test on the 18th of december...just wondering if you got any one on one tutoring...and if so....I would like some help.
Thanks
Intern
Status: Preparing for GMAT; want to join MBA program in fall 2012
Joined: 18 Jul 2010
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Location: Sioux Falls, SD, USA
Schools: Tippie School of Management, University of Iowa, Iowa City
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27 Nov 2010, 01:02
Hi,
Could you please share your study timing? How much did you study each day and how many days did you prepare?
Thanks and Regards,
Abel
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Location: India
### Show Tags
27 Nov 2010, 01:10
great score bro, thanks for inspiring me about powwer cr, i will read it this weekens only.
_________________
When going gets tough, tough gets going.........
Intern
Joined: 28 Aug 2010
Posts: 5
### Show Tags
27 Nov 2010, 11:42
ebratemo wrote:
I am taking the test on the 18th of december...just wondering if you got any one on one tutoring...and if so....I would like some help.
Thanks
I didn't get any one on one tutoring. It was all self-study for me. I felt like the materials I used were good enough that I didn't need a tutor.
Intern
Joined: 28 Aug 2010
Posts: 5
### Show Tags
27 Nov 2010, 11:46
1
KUDOS
abelnazareth wrote:
Hi,
Could you please share your study timing? How much did you study each day and how many days did you prepare?
Thanks and Regards,
Abel
I studied haphazardly for 2-3 weeks and then I spent about 6 weeks of very focused studying. During the 6 weeks, I would study 3-4 hours on weekdays and then about 6 on weekends. I would also take one day a week off of studying to try not to get burned out.
Intern
Status: Preparing for GMAT; want to join MBA program in fall 2012
Joined: 18 Jul 2010
Posts: 17
Location: Sioux Falls, SD, USA
Schools: Tippie School of Management, University of Iowa, Iowa City
### Show Tags
27 Nov 2010, 13:46
jauer112 wrote:
abelnazareth wrote:
Hi,
Could you please share your study timing? How much did you study each day and how many days did you prepare?
Thanks and Regards,
Abel
I studied haphazardly for 2-3 weeks and then I spent about 6 weeks of very focused studying. During the 6 weeks, I would study 3-4 hours on weekdays and then about 6 on weekends. I would also take one day a week off of studying to try not to get burned out.
_________________
Regards,
Abel
Re: 770 (Q50, V46) [#permalink] 27 Nov 2010, 13:46
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# What are the Prime Numbers?
A prime number is any whole number that is greater than one, and only has a whole-number factor of the number one and then itself. Examples of these prime numbers are the numbers two, three, five, and seven.
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https://astarrevision.com/ib_biology/option-d-4-the-hardy-weinberg-principle/
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# Option D.4 – The Hardy-Weinberg Principle
Option D.4 – The Hardy-Weinberg Principle
D.4.1 – Explain how the Hardy-Weinberg equation is derived Evolution involves changes in allele frequency. The Hardy-Weinberg equation is often
Evolution involves changes in allele frequency. The Hardy-Weinberg equation is often used for doing calculations of allele frequency. The Hardy-Weinberg equation is a formula that gives proportions of the diploid
The Hardy-Weinberg equation is a formula that gives proportions of the diploid genotypes formed by random union of haploid gametes, or random mating between diploids.
If there are two alleles of a gene in a population, the frequency of the alleles is represented by p and q. The total frequency of the alleles is 1:
When there is random mating, the chance of inheriting two copies of the first allele is p x p. The chance of inheriting two copies of the second allele q x q. Thus, the expected frequency of the homozygous genotypes is p2 and q2, while the heterozygous genotype is 2pq. The sum of all the frequencies is 1.
D.4.2 – Calculate allele, genotype and phenotype frequencies for two alleles of a gene, using the Hardy-Weinberg equation
Allele Frequencies
The gene for tasting phenylthiocarbamide (PTC) has two alleles: ability to taste is dominant (T) and no tasting is the recessive (t).
In a survey of 3200 people, 922 could not taste PTC: a frequency of 0.288.
The genotype homozygous recessive (t t) is called q.
Thus, q2 = 0.288
q = 0.537
p = T allele, so p = (1 – q) = 0.463
Genotype Frequencies
Cystic fibrosis is caused by recessive alleles of a chloride channel gene. A screening of 27000 people who did not have cystic fibrosis tested for carriers of
A screening of 27000 people who did not have cystic fibrosis tested for carriers of the recessive gene. The frequency of the normal allele = p = 0.9776
The frequency of the normal allele = p = 0.9776
Frequency of the cystic fibrosis allele = q = 0.0224
When the tested people have children, the chance of the child having cystic fibrosis: q2 = (0.0224)2 = 0.000502
So, one child in 1900 would have cystic fibrosis. Meanwhile, the chance of a child being a carrier is:
2pq = 2(0.9776 x 0.0224) = 0.0438
So, one child in 23 would be a carrier.
Phenotype Frequencies
Pea plants have dwarf and tall varieties, in a ratio of three tall to one dwarf. The plants are then allowed to disperse seeds naturally.
Frequency of T (p) = 0.75
Frequency of t (q) = 0.25
Thus, the frequency of (t t) = q2 = 0.252 = 0.0625
The frequency of tall plants = 1 – q2 = 1 – 0.0625 = 0.0375
D.4.3 – State the assumptions made when the Hardy-Weinberg equation is used
• Large population with random mating
• Natural selection does not cause higher mortality of individuals with one allele or another – no allele-specific mortality
• No emigration or immigration
• No mutation
When the assumptions are correct, the population is in Hardy-Weinberg equilibrium.
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# JZ-C-41-Plus
1 //============================================================================
2 // Name : JZ-C-41-Plus.cpp
3 // Author : Laughing_Lz
4 // Version :
5 // Copyright : All Right Reserved
6 // Description : 和为s的连续正数序列：输入一个正数s，打印出所有和为s的连续正数序列（至少含有两个数）
7 //============================================================================
8
9 #include <iostream>
10 #include <stdio.h>
11 using namespace std;
12
13 void PrintContinuousSequence(int small, int big);
14
15 void FindContinuousSequence(int sum) {
16 if (sum < 3)
17 return;
18
19 int small = 1;
20 int big = 2;
21 int middle = (1 + sum) / 2;
22 int curSum = small + big; //这里curSum其实是从small到big之间所有数字的累加和
23
24 while (small < middle) {
25 if (curSum == sum)
26 PrintContinuousSequence(small, big);
27
28 while (curSum > sum && small < middle) {
29 curSum -= small; //每次更新curSum值
30 small++;
31
32 if (curSum == sum)
33 PrintContinuousSequence(small, big);
34 }
35 // while (curSum <= sum && small < middle) { //自己写的还是不如源码啊。。清晰却不简洁
36 // big++;
37 // curSum += big;
38 // if (curSum >= sum)
39 // break;
40 // }
41 big++;
42 curSum += big; //每次更新curSum值
43 }
44 }
45
46 void PrintContinuousSequence(int small, int big) {
47 for (int i = small; i <= big; ++i)
48 printf("%d ", i);
49
50 printf("\n");
51 }
52
53 // ====================测试代码====================
54 void Test(char* testName, int sum) {
55 if (testName != NULL)
56 printf("%s for %d begins: \n", testName, sum);
57
58 FindContinuousSequence(sum);
59 }
60
61 int main(int argc, char** argv) {
62 Test("test1", 1);
63 Test("test2", 3);
64 Test("test3", 4);
65 Test("test4", 9);
66 Test("test5", 15);
67 Test("test6", 100);
68
69 return 0;
70 }
—————————————————————————————————————行走在人猿的并行线——Laughing_Lz
posted @ 2016-06-24 19:50 回看欧洲 阅读(185) 评论(0编辑 收藏 举报
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# Crate sparse_interp[−][src]
Basic polynomial arithmetic, multi-point evaluation, and sparse interpolation.
This crate is very limited so far in its functionality and under active development. The current functionality isi mostly geared towards sparse interpolation with a known set of possible exponents. Expect frequent breaking changes as things get started.
The `Poly` type is used to represent dense polynomials along with traits for algorithm choices. The `ClassicalPoly` type alias specifies classical arithmetic algorithms via the `ClassicalTraits` trait.
```use sparse_interp::ClassicalPoly;
// f represents 4 + 3x^2 - x^3
let f = ClassicalPoly::<f32>::new(vec![4., 0., 3., -1.]);
// g prepresents 2x
let g = ClassicalPoly::<f32>::new(vec![0., 2.]);
// basic arithmetic is supported
let h = f + g;
assert_eq!(h, ClassicalPoly::new(vec![4., 2., 3., -1.]));```
# Evaluation
Single-point and multi-point evaluation work as follows.
```type CP = ClassicalPoly<f32>;
let h = CP::new(vec![4., 2., 3., -1.]);
assert_eq!(h.eval(&0.), Ok(4.));
assert_eq!(h.eval(&1.), Ok(8.));
assert_eq!(h.eval(&-1.), Ok(6.));
let eval_info = CP::mp_eval_prep([0., 1., -1.].iter().copied());
assert_eq!(h.mp_eval(&eval_info).unwrap(), [4.,8.,6.]);```
# Sparse interpolation
Sparse interpolation should work over any type supporting field operations of addition, subtration, multiplication, and division.
For a polynomial f with at most t terms, sparse interpolation requires eactly 2t evaluations at consecutive powers of some value θ, starting with θ0 = 1.
This value θ must have sufficiently high order in the underlying field; that is, all powers of θ up to the degree of the polynomial must be distinct.
Calling `Poly::sparse_interp()` returns on success a vector of (exponent, coefficient) pairs, sorted by exponent, corresponding to the nonzero terms of the evaluated polynomial.
```type CP = ClassicalPoly<f64>;
let f = CP::new(vec![0., -2.5, 0., 0., 0., 7.1]);
let t = 2;
let (eval_info, interp_info) = ClassicalPoly::sparse_interp_prep(
t, // upper bound on nonzero terms
0..8, // iteration over possible exponents
&f64::MAX, // upper bound on coefficient magnitude
);
let evals = f.mp_eval(&eval_info).unwrap();
let mut result = CP::sparse_interp(&evals, &interp_info).unwrap();
// round the coefficients to nearest 0.1
for (_,c) in result.iter_mut() {
*c = (*c * 10.).round() / 10.;
}
assert_eq!(result, [(1, -2.5), (5, 7.1)]);```
## Structs
ClassicalTraits PolyTraits implementation for classical (slow) algorithms. CloseToEq A struct to use for exact equality in the `CloseTo` trait. DefConv The default conversion from S to D, if it exists. EvalTrait A trait struct used for multi-point evaluation of polynomials. Poly Generic struct to hold a polynomial and traits for operations. RelativeParams A struct to use for approximate equality.
## Enums
Error Errors that arise in polynomial arithmetic or sparse interpolation.
## Traits
CloseTo A possibly-stateful comparison for exact or approximate types. EvalTypes Trait for evaluating polynomials over (possibly) a different domain. OneWay A trait for 1-way conversions between numeric types that may fail. PolyTraits Algorithms to enable polynomial arithmetic. TwoWay A trait for 2-way conversions that may fail.
## Functions
refpow Computes base^exp, where the base is a reference and not an owned value.
## Type Definitions
ClassicalPoly Univeriate polynomial representation using classical arithmetic algorithms. Result A specialized core::result::Result type for sparse interpolation.
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RE: Cases, Throw, and Catch
• To: mathgroup at smc.vnet.net
• Subject: [mg24197] RE: [mg24182] Cases, Throw, and Catch
• From: Wolf Hartmut <hwolf at debis.com>
• Date: Fri, 30 Jun 2000 01:57:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com
```> -----Original Message-----
> From: Mark Fisher [SMTP:me.fisher at atl.frb.org]
To: mathgroup at smc.vnet.net
> Sent: Thursday, June 29, 2000 4:51 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg24182] Cases, Throw, and Catch
>
> I just noticed that it is much faster to Throw and Catch from Cases than
> to have Cases return the first match on its own. Does anyone know why
> this is so and what, if anything, is to be learned?
>
> Here is the example:
>
> In[1]:=
> xtab = Table[x, {10^6}];
>
> In[2]:=
> Cases[xtab, x, Infinity, 1] // Timing
>
> Out[2]=
> {0.172 Second, {x}}
>
> In[3]:=
> Catch @ Cases[xtab, Throw[{x}], Infinity, 1] // Timing
>
> Out[3]=
> {0. Second, {x}}
>
> In[4]:=
> ytab = Append[xtab, y];
>
> In[5]:=
> Cases[ytab, y, Infinity, 1] // Timing
>
> Out[5]=
> {0.437 Second, {y}}
>
> In[6]:=
> Catch @ Cases[ytab, Throw[{y}], Infinity, 1] // Timing
>
> Out[6]=
> {0. Second, {y}}
[Wolf Hartmut]
Hello Mark,
your observation is an optical illusion, see
In[23]:= Attributes[Cases]
Out[23]= {Protected}
So in
In[6]:= Catch at Cases[ytab, Throw[{y}], Infinity, 1] // Timing
Out[6]= {0.01 Second, {y}}
Throw will execute immediately without Cases having worked at all! Compare
this with
In[21]:= Catch at Cases[ytab, y :> Throw[{y}], Infinity, 1] // Timing
Out[21]= {1.242 Second, {y}}
and on my machine I get
In[5]:= Cases[ytab, y, Infinity, 1] // Timing
Out[5]= {1.232 Second, {y}}
which is fairly consistent. Select however is much slower here
In[10]:= Select[ytab, y === # &, 1] // Timing
Out[10]= {32.307 Second, {y}}
which should not be astonishing for this application. Here two other
procedures to compare
In[16]:= Catch[If[y === #, Throw[{y}]] & /@ ytab] // Timing
Out[16]= {46.396 Second, {y}}
In[19]:= Do[If[y === ytab[[i]], Return[y]], {i, 1, Length[ytab]}] // Timing
Out[19]= {54.087 Second, y}
Kind regards, Hartmut
```
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# Implement Insertion Sort using Java
If you’re in a computer science background, widening your technical horizons is the best thing you should do. However, your programming skills matter the most and one must continuously keep sharpening these skills. And to become a better programmer in the future. Though there are multiple things to focus on, one specific area you must focus on is the world of data structures. Data structures in general are specific approaches to solve problems in such a way that computer resources get used minimum. In general, there are multiple data structures you can learn and implement as well. However, to keep things simple were going to start with some basic programs you must learn before moving on to complex algorithms. Therefore today we’re going to learn how to Implement Insertion Sort using Java.
## What is Insertion Sort?
• Comes in the list of simplest data structure, Insertion Sort is the way of arranging elements in ascending order. The array is either sorted or is unsorted.
## What’s The Approach?
• Consider `arr[n] `of size` n `we want to implement Insertion Sort on. So firstly we’ll iterate a loop from 1 to n.
• Next, we’ll compare the element at iterating index with its preceding element from the array. If the comparing element is smaller, we’ll again compare it with the before elements.
• Lastly, Move the greater elements one position up to make space for the swapped element.
## Java Program To Implement Insertion Sort
Input:
`12, 11, 13, 5, 6`
Output:
`5 6 11 12 13`
```// Java program for implementation of Insertion Sort
class TechDecodeTutorials {
/*Function to sort array using insertion sort*/
void sort(int arr[])
{
int n = arr.length;
for (int i = 1; i < n; ++i) {
int key = arr[i];
int j = i - 1;
/* Move elements of arr[0..i-1], that are
greater than key, to one position ahead
of their current position */
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
j = j - 1;
}
arr[j + 1] = key;
}
}
/* A utility function to print array of size n*/
static void printArray(int arr[])
{
int n = arr.length;
for (int i = 0; i < n; ++i)
System.out.print(arr[i] + " ");
System.out.println();
}
// Driver method
public static void main(String args[])
{
int arr[] = { 12, 11, 13, 5, 6 };
TechDecodeTutorials TDT = new TechDecodeTutorials();
TDT.sort(arr);
printArray(arr);
}
}
```
#### Ethix
I'm a coding geek interested in cyberspace who loves to write and read
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# Mencal
by INSTANT.CJ
\$1.99 in the App Store
Work on your mental math skills with this educational app.
Mencal is an app help you expand your ability to mentally solve math problems. All of us can do simple addition and subtraction of one or two digit numbers without a calculator.Now mencal is here to kick that ability into overdrive.
### App Details
Version
3.70
Rating
(48)
Size
9Mb
Genre
Education Reference
Last updated
January 1, 2018
Release date
April 26, 2013
### Mencal is \$1.99 but there are more add-ons
• \$0.99
Unlock all math games
### App Store Description
Mencal is an app help you expand your ability to mentally solve math problems. All of us can do simple addition and subtraction of one or two digit numbers without a calculator.Now mencal is here to kick that ability into overdrive.
Mencal provides you with lessons and simple tricks to allow you to: work with three digit numbers; fractions of different styles regardless if you are adding them or subtracting them; and finding sums with multiplication and division. Then it will test you on your grasp and knowledge of the methods you've learned.
• Example:
- Same ten's digit,1's sum to 10
38×32=1216
①:Multiply tens place digit by itself plus 1
(3+1)×3=12
②:Add two zeros to the end of step①
12<—00=1200
③:Multiply the two one's digits together
8×2=16
④:Add the results of step ②and③
1200+16=1216
• Quickly Square:
- Square numbers made up of 1's
- Square numbers made up of 3's
- Square numbers in the 90's
- Square numbers ten`s digit is 0
- Square a number ending in 25
- Square numbers made up of 6's
- Square numbers made up of 9's
- Square a number ending in 1
- Square a number ending in 5
- Square a number ending in 9
- Square numbers in the 10's
- Square numbers in the 40's
- Square numbers in the 50's
- Square numbers in the 500's
- Square numbers in the 600's
- Square numbers in the 700's
- Square numbers in the 800's
- Square numbers in the 900's
•Standard:
- Same ten's digit, 1's sum is 10
- Same ten's digit, 1's sum isn`t 10
- Same 1's digit, ten's digits sum is 10
- Same 1's digit, ten's digits sum isn`t 10
- two-digit number ab×cc (a+b=10)
- ab×ccc.....c (a+b=10)
- Multiply by 11
- 2-digit number if 1's digit is 1
- 2-digit number if tens place digit is 1
- 2-digit number ×2-digit number(universal)
- Multiply differing by 5
- Multiply differing by 6
- Multiply differing by 7
- Multiply differing by 8
- Multiply differing by 9
- Multiply differing by 10
- Multiply two numbers that in the 90‘s
- Two-digit number like ab+ba
- Three-digit number like abc+cba
- Two fractions like 1/a+1/b
- Two fractions like (a-1)/a + (b-1)/b
- Sum of first n odd numbers
- Sum of first n even numbers
- Two-digit number like ab-ba
- Three-digit number like abc-cba
- m-n if m+n=100,1000,10000...
- Two fractions like 1/a-1/b
- Two fractions like c/a-c/b
- Two fractions like (a-1)/a-(b-1)/b
- Divide any number by 5
- Divide any number by 25
- Divide any number by 125
- Divide any 3-figure number by 9
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# How does logistic regression predict?
Contents
Logistic regression is used to predict the class (or category) of individuals based on one or multiple predictor variables (x). … Logistic regression does not return directly the class of observations. It allows us to estimate the probability (p) of class membership. The probability will range between 0 and 1.
## What does a logistic regression tell you?
Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable. … The result is the impact of each variable on the odds ratio of the observed event of interest. The main advantage is to avoid confounding effects by analyzing the association of all variables together.
## What is predicted probability in logistic regression?
Logistic regression analysis predicts the odds of an outcome of a categorical variable based on one or more predictor variables. … It is used for predicting the probability of the occurrence of a specific event by fitting data to a logit Logistic Function curve.
## How does regression predict?
The Regression Approach for Predictions
Using regression to make predictions doesn’t necessarily involve predicting the future. Instead, you predict the mean of the dependent variable given specific values of the independent variable(s).
## How does logistic regression measure a relationship?
Logistic regression measures the relationship between the categorical dependent variable and one or more independent variables by estimating probabilities using a logistic function, which is the cumulative distribution function of logistic distribution.
## Why logistic regression is important?
It is used in statistical software to understand the relationship between the dependent variable and one or more independent variables by estimating probabilities using a logistic regression equation. This type of analysis can help you predict the likelihood of an event happening or a choice being made.
## How do you interpret beta logistic regression?
The logistic regression coefficient β associated with a predictor X is the expected change in log odds of having the outcome per unit change in X. So increasing the predictor by 1 unit (or going from 1 level to the next) multiplies the odds of having the outcome by eβ.
## How do you predict regression equations?
We can use the regression line to predict values of Y given values of X. For any given value of X, we go straight up to the line, and then move horizontally to the left to find the value of Y. The predicted value of Y is called the predicted value of Y, and is denoted Y’.
## What is correlation regression?
Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation.
## Does logistic regression check linear relationships?
Answer: First, logistic regression does not require a linear relationship betweenthe dependent and independent variables. … Finally, the dependent variable in logistic regression is not measured on an interval or ratio scale.
THIS IS INTERESTING: Frequent question: How banks use predictive analytics?
## How many predictors can be used in logistic regression?
There must be two or more independent variables, or predictors, for a logistic regression. The IVs, or predictors, can be continuous (interval/ratio) or categorical (ordinal/nominal).
## How does logistic regression handle the relationship of the dependent and independent variables?
Logistic regression does not require a linear relationship between the dependent and independent variables. However, it still needs independent variables to be linearly related to the log-odds of the outcome. Homoscedasticity (constant variance) is required in linear regression but not for logistic regression.
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https://au.mathworks.com/matlabcentral/answers/493903-block-diagonal-matrix-of-identity-times-scalar
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# Block diagonal matrix of identity times scalar.
1 view (last 30 days)
Mohammed Kagalwala on 29 Nov 2019
Edited: Philippe Lebel on 29 Nov 2019
Hi,
I currently have a vector a = [1 2]', I wish to create a block diagonal matrix. Each block is identity (3x3) times the corresponding scalar in the vector a.
i.e. with a = [1 2]' I want to produce b = [1 0 0 0 0 0; 0 1 0 0 0 0; 0 0 1 0 0 0; 0 0 0 2 0 0; 0 0 0 0 2 0; 0 0 0 0 0 2]. The catch is a can be a vector of N x 1, thus b is of size 3*N x 3*N
The answer also has to be for loop free. I've tried using blkdiag() and eye() but have dimension issues in my multiplication
Philippe Lebel on 29 Nov 2019
Edited: Philippe Lebel on 29 Nov 2019
here is my take.
a=[1,2];
c = round(a(1):1/(length(b(:,1))-1):a(2));
matrix = diag(c);
##### 3 CommentsShow 1 older commentHide 1 older comment
Mohammed Kagalwala on 29 Nov 2019
Philippe Lebel on 29 Nov 2019
Edited: Philippe Lebel on 29 Nov 2019
here it is:
clear
a=[1,2,3,4];
size_of_sub_matrices = 2;
a = arrayfun(@(x) ones(1,size_of_sub_matrices)*x, a, 'UniformOutput', false);
a = cell2mat(a);
matrix = diag(a)
matrix =
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 0 2 0 0 0 0
0 0 0 0 3 0 0 0
0 0 0 0 0 3 0 0
0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 4
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https://www.physicsforums.com/threads/op-amp-bandpass-audio-filter.650535/
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# Homework Help: Op-Amp Bandpass Audio Filter
1. Nov 8, 2012
### hutch3ka
I am attempting to build an Op-Amp circuit in which a sinusoidal input is used. Below is the description:
An active, op-amp bandpass filter circuit for audio frequency inputs. The
implemented filter circuit must provide a maximum gain of 14 dB inside the pass-band and less than 9 dB of gain below and above the critical frequencies of 1000 Hz and 5000 Hz.
Design and implement an LED indicator circuit that uses the output of the bandpass filter circuit as the input. Light a green LED when the frequency of a 1 V peak-to-peak amplitude sinusoidal signal is between 1000 Hz and 5000 Hz. Light a red LED when the frequency of the input signal is outside of this range.
Any help greatly appreciated!
2. Nov 8, 2012
### yungman
Get an Active Filter Cook Book and look up Sallen Key:
http://en.wikipedia.org/wiki/Sallen%E2%80%93Key_topology
What your requirement should be quite easy. As for the gain, put an op-amp gain stage before the filter to get the total gain you want.
Don't worry about all the math, all you have to do is follow the formulas to find the R and C to get the effect. I have the old Active-Filter Cookbook by SAMS, it is easy and it is good.
As for LED, did not give enough info. Is the input of the filter constant amplitude, only the frequency change? If so just use a peak detector and use a comparator to get the LED driving signal. If the input amplitude varies, then it would be difficult.
3. Nov 8, 2012
### dlgoff
Single supply LM124/LM224/LM324/LM2902 Low Power Quad Operational Amplifiers are good for audio.
And other tips can be found here: "www.ti.com/lit/ds/symlink/lm124-n.pdf" [Broken]
Last edited by a moderator: May 6, 2017
4. Nov 8, 2012
### Staff: Mentor
Welcome to the PF.
In the future, please be sure to show your attempt at solving your schoolwork question/project, or you post will likely be deleted. Thanks.
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https://brilliant.org/problems/coincidental-residue-powers/
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Coincidental residue powers?
If the last 2 digits of $$\underbrace{6\times6\times 6\times \cdots \times 6}_{\text{Number of 6's } =M}$$ is 76,
must the last 2 digits of $$\underbrace{4\times4\times 4\times \cdots \times 4}_{\text{Number of 4's } =M}$$ be 76 as well?
×
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https://www.canal-u.tv/chaines/inria/4-sequences-comparison/49-recursion-can-be-avoided-an-iterative-version
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Vidéo pédagogique
Notice
Lieu de réalisation
Grenoble
Sous-titrage
Sous-titre
Langue :
Anglais
Crédits
François Rechenmann (Intervention)
Conditions d'utilisation
Ces ressources de cours sont, sauf mention contraire, diffusées sous Licence Creative Commons. L’utilisateur doit mentionner le nom de l’auteur, il peut exploiter l’œuvre sauf dans un contexte commercial et il ne peut apporter de modifications à l’œuvre originale.
DOI : 10.60527/jw74-pq64
Citer cette ressource :
François Rechenmann. Inria. (2015, 5 février). 4.9. Recursion can be avoided: an iterative version , in 4. Sequences comparison. [Vidéo]. Canal-U. https://doi.org/10.60527/jw74-pq64. (Consultée le 19 juillet 2024)
4.9. Recursion can be avoided: an iterative version
Réalisation : 5 février 2015 - Mise en ligne : 9 mai 2017
• document 1 document 2 document 3
• niveau 1 niveau 2 niveau 3
Descriptif
We have written a recursive function to compute the optimal path that is an optimal alignment between two sequences. Here all the examples I gave were onDNA sequences, four letter alphabet. OK. The writing of this recursive function is very elegant but unfortunately we will see now that it isnot very efficient in execution time. Let's see why. Remember the computing schema weapply during the recursion, for example here, to compute the cost of this node, we saw that it was required to computerecursively the cost of that node, that node and that node. OK but to compute the cost of that node here, you need to compute the cost of that one, that oneand that one again that is this cost which was computed in order to compute the code of the ending node here has to be recomputed in the recursive function to compute the cost of that node. In a more general way, to computethe cost of a node like this one, you need to compute all of these nodes here but to compute the cost of that node, you need to compute all the costs of these nodes again and again and again. So the cost of one node in thiswriting of the function is computed many, many, many times. It's because we use this recursive function so it was nice but it was expensive in terms of execution time. So we can imagine a new version of the algorithm which is not recursive but iterative in two phases. Let's see how it works.
Intervention
Thème
Documentation
Dans la même collection
• Vidéo pédagogique
00:04:11
4.6. A path is optimal if all its sub-paths are optimal
Rechenmann
François
A sequence alignment between two sequences is a path in a grid. So that, an optimal sequence alignmentis an optimal path in the same grid. We'll see now that a property of this optimal path provides
• Vidéo pédagogique
00:04:54
4.1. How to predict gene/protein functions?
Rechenmann
François
Last week we have seen that annotating a genome means first locating the genes on the DNA sequences that is the genes, the region coding for proteins. But this is indeed the first step,the next very
• Vidéo pédagogique
00:09:26
4.10. How efficient is this algorithm?
Rechenmann
François
We have seen the principle of an iterative algorithm in two paths for aligning and comparing two sequences of characters, here DNA sequences. And we understoodwhy the iterative version is much more
• Vidéo pédagogique
00:04:22
4.4. Aligning sequences is an optimization problem
Rechenmann
François
We have seen a nice and a quitesimple solution for measuring the similarity between two sequences. It relied on the so-called hammingdistance that is counting the number of differencesbetween two
• Vidéo pédagogique
00:06:38
4.7. Alignment costs
Rechenmann
François
We have seen how we can compute the cost of the path ending on the last node of our grid if we know the cost of the sub-path ending on the three adjacent nodes. It is time now to see more deeply why
• Vidéo pédagogique
00:04:29
4.2. Why gene/protein sequences may be similar?
Rechenmann
François
Before measuring the similaritybetween the sequences, it's interesting to answer the question: why gene or protein sequences may be similar? It is indeed veryinteresting because the answer is related
• Vidéo pédagogique
00:03:50
4.5. A sequence alignment as a path
Rechenmann
François
Comparing two sequences and thenmeasuring their similarities is an optimization problem. Why? Because we have seen thatwe have to take into account substitution and deletion. During the alignment, the
• Vidéo pédagogique
00:07:41
4.8. A recursive algorithm
Rechenmann
François
We have seen how we can computethe optimal cost, the ending node of our grid if we know the optimal cost of the three adjacent nodes. This is this computation scheme we can see here using the notation
• Vidéo pédagogique
00:03:59
4.3. Measuring sequence similarity
Rechenmann
François
So we understand why gene orprotein sequences may be similar. It's because they evolve togetherwith the species and they evolve in time, there aremodifications in the sequence and that the sequence
Avec les mêmes intervenants et intervenantes
• Vidéo pédagogique
00:05:24
1.1. The cell, atom of the living world
Rechenmann
François
Welcome to this introduction to bioinformatics. We will speak of genomes and algorithms. More specifically, we will see how genetic information can be analysed by algorithms. In these five weeks to
• Vidéo pédagogique
00:09:07
1.9. Predicting the origin of DNA replication?
Rechenmann
François
We have seen a nice algorithm to draw, let's say, a DNA sequence. We will see that first, we have to correct a little bit this algorithm. And then we will see how such as imple algorithm can provide
• Vidéo pédagogique
00:08:21
2.8. DNA sequencing
Rechenmann
François
During the last session, I explained several times how it was important to increase the efficiency of sequences processing algorithm because sequences arevery long and there are large volumes of
• Vidéo pédagogique
00:04:45
3.5. Making the predictions more reliable
Rechenmann
François
We have got a bacterial gene predictor but the way this predictor works is rather crude and if we want to have more reliable results, we have to inject into this algorithmmore biological knowledge. We
• Vidéo pédagogique
00:04:11
4.6. A path is optimal if all its sub-paths are optimal
Rechenmann
François
A sequence alignment between two sequences is a path in a grid. So that, an optimal sequence alignmentis an optimal path in the same grid. We'll see now that a property of this optimal path provides
• Vidéo pédagogique
00:07:39
5.5. Differences are not always what they look like
Rechenmann
François
The algorithm we have presented works on an array of distance between sequences. These distances are evaluated on the basis of differences between the sequences. The problem is that behind the
• Vidéo pédagogique
00:05:48
1.4. What is an algorithm?
Rechenmann
François
We have seen that a genomic textcan be indeed a very long sequence of characters. And to interpret this sequence of characters, we will need to use computers. Using computers means writing program.
• Vidéo pédagogique
00:04:58
2.2. Genes: from Mendel to molecular biology
Rechenmann
François
The notion of gene emerged withthe works of Gregor Mendel. Mendel studied the inheritance on some traits like the shape of pea plant seeds,through generations. He stated the famous laws of inheritance
• Vidéo pédagogique
00:05:37
2.10. How to find genes?
Rechenmann
François
Getting the sequence of the genome is only the beginning, as I explained, once you have the sequence what you want to do is to locate the gene, to predict the function of the gene and maybe study the
• Vidéo pédagogique
00:06:09
3.8. Probabilistic methods
Rechenmann
François
Up to now, to predict our gene,we only rely on the process of searching certain strings or patterns. In order to further improve our gene predictor, the idea is to use, to rely onprobabilistic methods
• Vidéo pédagogique
00:03:59
4.3. Measuring sequence similarity
Rechenmann
François
So we understand why gene orprotein sequences may be similar. It's because they evolve togetherwith the species and they evolve in time, there aremodifications in the sequence and that the sequence
• Vidéo pédagogique
00:04:59
5.4. The UPGMA algorithm
Rechenmann
François
We know how to fill an array with the values of the distances between sequences, pairs of sequences which are available in the file. This array of distances will be the input of our algorithm for
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# Essay on My Lesson Plan: Mathematic Activity
Length: 559 words (1.6 double-spaced pages)
Rating: Good Essays
#### Essay Preview
For my lesson plan I decided to create a mathematic activity that every student in the classroom could complete (most require assistance). Since this is a special education classroom that contains students at a variety of academic levels, this required some flexibility when lesson planning. Though I wanted the activity to be fun, I also wanted it to be challenging for each student. I felt as though a Thanksgiving theme was appropriate and that it would add to the fun of the activity.
Each child was given a paper plate and a paper bag filled with a turkey cut out and a specific amount of feathers. Some children had feathers that displayed the numbers 2, 3 or 5 on them. (I explained to these children individually that these numbered feathers indicated that they would need to count by 2’s, 3’s, or 5’s in order to find their number.) We also utilized the classroom’s supply of glue sticks, scissors and crayons for the assembly of the turkey. Each child was also given a white board or an extra sheet of paper to help work out the problems. Finally they were all given a paper plate that c...
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## Essay on Eight Grade Mathematics Lesson Plan
- Objectives: * Eight Grade Mathematics State Curriculum Standards: o Standard 6.0 - Number Relationship and Computation- Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology. o Standard 7.0 Processes of Mathematics- Students demonstrate the processes of mathematics by making connections and applying reasoning to solve problems and to communicate their findings. * Maryland Technology Literacy Standards for Students: o Standard 3.0 – Technology for Learning and Collaboration: Use a variety of technologies for learning and collaboration o Standard 4.0 – Technol... [tags: Lesson Plan]
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- The detailed lesson plan and flow chart for follow on lessons, outline the teaching of measurement using the metre and the centimetre for year three students. The aim of the teaching sequence is that students are offered learning that will guide them through the construction of their own understanding of measurement and how to competently measure. Ensuring Engagement Key to any pedagogical practice is engaging the students in order to inspire learning (Peters & Le Cornu, 2006.). Regardless of the student’s age, if they are not engaged with their learning, construction of their understanding is not going to be as successful as if that engagement did occur (Jeanneret, et al, 2006.).... [tags: Education, Teacher, Teaching, Lesson plan]
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## The Lesson Plan Needs Improvement Essay
- What went well After doing the lesson, I felt that many things went well. According to the class evaluations and observation, the class really enjoyed the 4 different explore sound stations. The stations allowed for self-discovery, but were also structured enough for the teacher to have control. Classmates also liked the pictures that went along with the vocabulary terms. I think we did well with monitoring the students. We made sure the students were ready to continue to the next thing by having them give us “a thumbs up/ thumps down”.... [tags: Teacher, Learning, Education, Lesson plan]
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- A great Challenge Being a teacher is not easy as many people think the process of teaching a language class and prepare a lesson plan for 20 -30 students it is a new challenge to complete, but nevertheless it was an exciting and productive process. Something that I like is the fact that at the end of this process I learned how to prepare a lesson plan and I was able to help the rest of the group. At first I thought that the lesson went well but there were some aspects that could have been better, of the entire lesson plan one thing that I did not expect was the "Homework section", because this specific section did not coincide with the rest of the lesson plan.... [tags: Teacher, Education, Lesson plan]
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## Lesson Pl Reflection On Mathematics Essay
- Solano-Lesson Plan 2 Reflection When I was in high school, I struggled with geometry proofs. So, when my mentor told me which lesson she wanted me to teach, I got excited. I wanted to make sure that the students knew how to write a proof so that they would feel confident in geometry. I remembered how I wanted my high school teachers to break down every part of this lesson, so that I would understand it. Since they didn’t, I used to hate going to geometry because I would always feel like a failure.... [tags: Teacher, Education, Teaching, Lesson plan]
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875 words (2.5 pages)
## The Lesson Plan For Taking Minutes Essay
- From taking minutes we learnt that it was important to keep track of what we were doing each lesson as it is easy to lose track. The planning process can then be recounted and referred back to with ease. Being able to refer to the minutes was good as it was easy to check that everyone done what they had to. It also made the assignment easier to reflect on and assessed as it shows a timeline of the assignment process. Finally it also provides evidence that my capabilities were built upon gradually throughout the assignment.... [tags: Teacher, Lesson plan, Lesson, Teaching]
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1886 words (5.4 pages)
## Elementary School Math Lesson Plan Essay
- As teachers we plan our lessons and think to ourselves, "my students are going to love this lesson and will be able to understand what I am teaching", but sometimes that isn 't the case. You may plan a lesson in hopes that your students understand but it doesn 't go as planned. Every student learns differently and thinks differently and because of this we, as teachers must learn to differentiate our lessons. This may require us to change the way we deliver our lesson, change the activities for our lessons or even change the wording of our material so students understand.... [tags: Education, Learning, Teacher, Lesson plan]
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1877 words (5.4 pages)
## Innovation during a Crisis: Advancement of Aviation Technology during WWI Lesson Plan
- Innovation during a Crisis: Advancement of Aviation Technology during WWI Lesson Plan Context: This lesson is designed for students in the fifth to eight grade level. Many of these students will already have an extensive background in aviation and/or aviation history. The lesson plan occurs in an informal class setting at a Museum as one day during a five day summer camp session named Wright Flyer to Right Now. The summer camp spends each day exploring a different period in aerospace technology starting with the early days of flight and ending with current space exploration.... [tags: Lesson Plan]
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1137 words (3.2 pages)
## Lesson Plan Summary Essay
- Day One Objective 1 (Explaining & Understanding): Students will review the definitions of bias and point of view. Students will be taught how to determine bias and point of view (word choice). Summary of Lesson 1: Class will begin with students listening to the song “In the Living Years” and be asked to underline words that make them feel something. I will use this as my hook into our unit. Students will be given a brief overview of the unit and then we will move into the demonstration portion of class.... [tags: Lesson Plan]
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1471 words (4.2 pages)
## Weekly Lesson Plan Essay examples
- Monday (Day One) Objective: Students will recall conflict terms and prior knowledge of conflict and resolutions in various texts. Students will be introduced to unit- “Work out Turmoil”. Activities: 1) Warm-Up Activity-Diagnostic pre-test for prior knowledge of conflict and conflict resolution terms 2) Students will watch video of Daniel Beaty performing “Knock Knock”. 3) Inquiring questions presented for discussion: What is his drama. How does he work through his turmoil in his life. Can you relate to any issue he is facing.... [tags: Lesson Plan]
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# Category: Assignments
## Trigonometric Functions Class 11 Assignments
Class 11 Trigonometric Functions Assignments Trigonometric Functions Assignments Assignment 01 (CM23M110301) Answer key for Trigonometric Functions Assignment 01 (CM23M110301)
## Inverse Trigonometric Functions Class 12 Assignments
Class 12 Inverse Trigonometric Functions Assignments Inverse Trigonometric Functions Assignments Assignment 01 (CM23M120201) Solutions for class 12 Inverse Trigonometric
## Linear Inequalities Class 11 Assignments
Class 11 Linear Inequalities Assignments Linear Inequalities Assignments Assignment 01 (CM23M110501) Answer key for Linear Inequalities Assignment 01 (CM23M110501)
## Complex Numbers and Quadratic Equations Class 11 Assignments
Class 11 Complex Numbers and Quadratic Equations Assignments Complex Numbers and Quadratic Equations Assignments Assignment 01 (CM23M110401) Answer
## Relations and Functions Class 12 Assignments
Class 12 Relations and Functions Assignments Relations and Functions Assignments Assignment 01 (CM23M120101) Solutions for class 12 Relations
## Sets Class 11 Assignments
Class 11 Sets Assignments Sets Assignments Assignment 01 (CM23M110101) Solutions for class 11 Sets Assignment 01 (CM23M110101) Yet
## Relations and Functions Class 11 Assignments
Class 11 Relations and Functions Assignments Relations and Functions Assignments Assignment 01 (CM23M110201) Solutions for class 11 Relations
## Probability Class 10 Assignments
Class 10 Probability Assignments Probability Assignments Assignment 01 (CM23M101501) Solutions for class 10 Probability Assignment 01 (CM23M101501) Yet
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The circumference is the distance around a circle. But what do we do if we only want to find a fraction or a part of the distance around the circle? Calculate angle measures using both the circumference formula and the arc length theorem.
The circumference tells you the length of the perimeter of a circle. It takes about 3.14 diameters to Radians are an angle measure equivalent to an arc length of one radius of a circle. It is a relative Remember to check your calculator settings carefully to make sure it is set properly for either...
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Then the angle cuts off an arc of the circle, and the length of that arc is the radian measure of the angle. It is easy to convert between degree measurement and radian measurement. The circumference of the entire circle is 2π, so it follows that 360° equals 2π radians. Hence, 1° equals π/180 radians. and
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• The circumference formula is used to calculate the distance around a circle. The diameter is the longest chord that runs through the center of the circle.
• Let’s calculate the length of the arc (because obviously, the crust is the best part). To do that, we’ll use another part/whole relationship—the length of the arc from the slices, compared with the total circumference of the pizza. We were told that the radius of the circle is 12 inches.
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Circumference Calculation Explained. Understanding what a circumference of a circle is and how to calculate it is crucial as you move to higher level math. The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares.
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• Tap to take a pic of the problem. Online Math Calculators. Check out our full list of online math calculators.
• fraction, the ratio of a distance on the map to the same distance on the ground • Most maps fall between 1:1 million and 1:1000 • Digital and web maps are scale-less because maps can be enlarged and reduced and plotted at many scales other than that of the original data • But in fact, all maps when displayed have a scale
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Use the compound interest calculator to gain a picture of how the interest on your savings or investments might grow over a period of months and years. Using the compound interest formula, you can determine how your money might grow with regular deposits or withdrawals.
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The arc length of a circle can be found by first calculating what fraction of the circle is represented by the central angle. Then you find the circumference of the circle. Finally, you find the fraction of that circumference. For example, if a circle has a radius of 10.0 cm and a central angle of 60°, to calculate the arc length for that ...
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Jul 23, 2019 · Let AC be an chord of a circle with centre O, and let C be any point on the circumference anywhere. Let, angle AOC(on center) is the given . So angle should be on the circumference, angle ABC = angle AOC/2; An angle at the circumference of a circle is the half angle at the centre subtended by the same chord.
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Free Math Practice problems for Pre-Algebra, Algebra, Geometry, SAT, ACT. Homework Help, Test Prep and Common Core Assignments!
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# Content Tagged “Standard Deviation Rule”
## Normal Random Variables
Published: Feb 5th, 2014
Video (2:08) Transcript – Normal Random Variables This document linked from Normal Random Variables
## Summary (Unit 3B – Random Variables)
Published: Jan 20th, 2014
Random Variables Binomial Random Variables Continuous Random Variables We have almost reached the end our discussion of probability. We were introduced to the important concept of random variables, which are quantitative variables whose […]
## The Normal Shape
Published: Jul 23rd, 2013
View Lecture Slides with Transcript – The Normal Shape Video (5:34) This document is linked from The Normal Shape.
## Learn by Doing – Find Normal Scores
Published: Feb 9th, 2013
Recall the example from the last activity: According to the College Board website, the scores on the math part of the SAT (SAT-M) in a certain year had a mean […]
## Learn by Doing – Find Normal Probabilities
Published: Feb 9th, 2013
According to the College Board website, the scores on the math part of the SAT (SAT-M) in a certain year had a mean of 507 and standard deviation of […]
## Normal Applications
Published: Feb 9th, 2013
Working with Non-standard Normal Values – Finding Probabilities Finding Normal Scores – Backwards! Given probability, find the score. Normal Approximation for Binomial Rule of Thumb Continuity Correction CO-6: Apply basic concepts of probability, […]
## Learn by Doing – Normal Random Variables
Published: Feb 8th, 2013
The purpose of this interactive activity is to: Get a better feel for the behavior of normal random variables. Check the accuracy of the Standard Deviation Rule. Do some other […]
## Did I Get This – Using the Standard Deviation Rule
Published: Feb 8th, 2013
Length (in days) of human pregnancies is a normal random variable (X) with mean 266, standard deviation 16. For the questions below, it would be useful to sketch this normal distribution […]
## Learn by Doing – Using the Standard Deviation Rule
Published: Feb 8th, 2013
This document is linked from Normal Random Variables.
## Normal Random Variables
Published: Feb 8th, 2013
Observations of Normal Distributions The Standard Deviation Rule for Normal Random Variables CO-6: Apply basic concepts of probability, random variation, and commonly used statistical probability distributions. LO 6.2: Apply the standard deviation […]
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