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https://cracku.in/blog/odd-man-out-questions-for-mah-cet/
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# Odd Man Out Questions for MAH-CET
0
104
Question 1:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
a)Â 17
b)Â 13
c)Â 63
d)Â 71
e)Â 23
Solution:
Except 63, all are prime numbers, hence 63 is the odd one.
=> Ans – (C)
Question 2:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
a)Â Watermelon
b)Â Papaya
c)Â Jackfruit
d)Â Pineapple
e)Â Sweetlime
Solution:
Among the given options, only pineapple is grown underground, hence it is the odd one.
=> Ans – (D)
Question 3:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
a)Â Cuckoo
b)Â Crow
c)Â Bat
d)Â Parrot
e)Â Sparrow
Solution:
Except bat, all others are birds. Bat is a mammal, hence the odd one.
=> Ans – (C)
Question 4:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
a)Â Fruit
b)Â Flower
c)Â Leaf
d)Â Petal
e)Â Tree
Solution:
Fruit, flower, leaf and petal are all parts of tree, hence tree is the odd one out.
=> Ans – (E)
Question 5:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to the group?
a)Â Yellow
b)Â Blue
c)Â Pink
d)Â Green
e)Â Red
Solution:
Except for pink, remaining colours are rainbow colours, hence pink is the odd one out.
=> Ans – (C)
Question 6:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to the group?
a)Â 23
b)Â 29
c)Â 37
d)Â 39
e)Â 31
Solution:
Apart from 39, all are prime numbers. Thus, 39 is the odd one out.
=> Ans – (D)
Question 7:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to the group?
a)Â PS
b)Â FI
d)Â KN
e)Â GD
Solution:
(A) : P (+3 letters) = S
(B) : FÂ (+3 letters) =Â I
(C) : AÂ (+3 letters) =Â D
(D) : KÂ (+3 letters) =Â N
(E) : GÂ (-3 letters) =Â D
=> Ans –Â (E)
Question 8:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â Bat
b)Â Spider
c)Â Mosquito
d)Â Butterfly
e)Â Cockroach
Solution:
Spider, Mosquito, Butterfly and Cockroach are insects while bat is a bird, hence it is the odd one.
=> Ans – (A)
Question 9:Â Four of the following five are alike in a certain way and so form a group. Which is one that does not belong to that group ?
a)Â Orange
b)Â Apple
c)Â Guava
d)Â Papaya
e)Â Mango
Solution:
Apart from Mango, all have more than one seed, hence mango is the odd one.
=> Ans – (E)
Question 10:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â Table
b)Â Desk
c)Â Wardrobe
d)Â Computer
e)Â Chair
Solution:
Among the given options, only computer is an electrical appliance, hence it is the odd one.
=> Ans – (D)
Take Free MAH-CET mock tests here
Question 11:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â 21
b)Â 35
c)Â 42
d)Â 56
e)Â 49
Solution:
Among the given numbers, only 49 is a perfect square, hence it is the odd one.
=> Ans – (E)
Question 12:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â 50
b)Â 65
c)Â 170
d)Â 255
e)Â 290
Solution:
(A) : 50 = $7^2+1$
(B) : 65 =Â $8^2+1$
(C) : 170 =Â $13^2+1$
(D) : 255 =Â $16^2-1$
(E) : 290 =Â $17^2+1$
=> Ans – (D)
Question 13:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â Hill
b)Â Valley
c)Â Dam
d)Â River
e)Â Mountain
Solution:
River is a natural water habitat, hence it is the odd one.
=> Ans – (D)
Question 14:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â 24
b)Â 48
c)Â 32
d)Â 72
e)Â 64
Solution:
Among the given numbers, only 64 is a perfect square, hence it is the odd one.
=> Ans – (E)
Question 15:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
a)Â Garlic
b)Â Ginger
c)Â Carrot
e)Â Brinjal
Solution:
Garlic, ginger, carrot and radish grow below the surface, hence brinjal is the odd one.
=> Ans – (E)
Question 16:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
a)Â Leaf
b)Â Flower
c)Â Petal
d)Â Fruit
e)Â Tree
Solution:
Leaf, flower, petal and fruit are all parts of a tree, hence tree is the odd one.
=> Ans – (E)
Question 17:Â Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to the group?
a)Â 17
b)Â 31
c)Â 23
d)Â 13
e)Â 35
Solution:
Except for 35, all the given numbers are prime numbers.
=> Ans – (E)
Question 18:Â Four of the following five are alike in a certain way on the basis of their positions in English alphabet and so form a group. Which is the one that does not belong to that group ?
a)Â HJG
b)Â PQN
c)Â DEB
d)Â TUR
e)Â KLI
Solution:
(A) : HÂ (+2 letters) = J (-3 letters) =Â G
(B) : PÂ (+1 letter) = QÂ (-3 letters) = N
(C) : DÂ (+1 letter) = E (-3 letters) =Â B
(D) : TÂ (+1 letter) = U (-3 letters) =Â R
(E) : KÂ (+1 letter) = L (-3 letters) =Â I
=> Ans – (A)
Question 19:Â Four of the following five pairs are alike in a certain way and hence form a group. Which one does not belong to that group 7
a)Â DONE : NOED
b)Â WANT : NATW
c)Â WITH : TIHW
d)Â JUST : SUTJ
e)Â HAVE : AVEH
Solution:
The pattern followed is that the middle two letters are swapped and written at the beginning and the first and last letters are revered and written at the end.
Eg :- D(ON)EÂ : (NO) ED
Similar pattern is observed in the next three options, but HAVE should be changed to VAEH
=> Ans – (E)
Question 20:Â Four of the following five are alike in a certain way and so form a group, Which is the one that does not belong to that group ?
a)Â Clutch
b)Â Wheel
c)Â Break
d)Â Car
e)Â Gear
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https://www.physicsforums.com/threads/linear-transformation-matrix-problem.225803/
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# Linear transformation matrix problem
let A= $$\left( \begin{array}{Ccc} 9 & 0 \\ 2 & 6 \\ \end{array} \right)$$
and B= $$\left( \begin{array}{Ccc} 5 & 1 \\ 3 & 4 \\ \end{array} \right)$$
Find the matrix C of the linear transformation T(x)=B(A(x)).
3. The Attempt at a Solution
- Once again, I really don't know how to start a problem like this off. I tried finding just T(x)=Ax and then multiply that by B, but that didn't seem to work. Please help.
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https://jimmy-shen.medium.com/binary-tree-fb5c19cf338d?source=post_internal_links---------0-------------------------------
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# Binary Tree
545. Boundary of Binary Tree
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Solution: def boundaryOfBinaryTree(self, root: TreeNode) -> List[int]: if root is None:return [] if root.left is None and root.right is None:return [root.val] left, leaf, right = [root.val], [], [] def get_boundary(node, side='left'): if node is None:return if side =='left': if node.left or node.right:left.append(node.val) if node.left is None: get_boundary(node.right) else: get_boundary(node.left) else: if node.left or node.right:right.append(node.val) if node.right is None: get_boundary(node.left,'right') else: get_boundary(node.right,'right') def get_leaf(node): if node is None:return get_leaf(node.left) if node.left is None and node.right is None: leaf.append(node.val) get_leaf(node.right) get_boundary(root.left, 'left') get_leaf(root) get_boundary(root.right,'right') return left+leaf+right[::-1]`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Solution: def zigzagLevelOrder(self, root: TreeNode) -> List[List[int]]: res = [] if root is None:return [] def bfs(): current_level = [root] i = 0 while current_level: new_level = [] if i%2==0:res.append([node.val for node in current_level]) else:res.append([node.val for node in current_level[::-1]]) for node in current_level: if node.left: new_level.append(node.left) if node.right: new_level.append(node.right) i+=1 current_level = new_level bfs() return res`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Solution: def bstFromPreorder(self, preorder: List[int]) -> TreeNode: def helper(preorder): if not preorder:return None if len(preorder)==1: return TreeNode(preorder[0]) root_val = preorder[0] left = [val for val in preorder[1:] if val<root_val ] right = [val for val in preorder[1:] if val>root_val] left_node = helper(left) right_node = helper(right) root = TreeNode(root_val) root.left = left_node root.right = right_node return root return helper(preorder)`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Codec:def serialize(self, root: TreeNode) -> str: """Encodes a tree to a single string. """ if root is None:return "#"*100 nodes = [] def preorder(node): if node is None:return nodes.append(str(node.val)) preorder(node.left) preorder(node.right) preorder(root) #print(nodes) return ','.join(nodes)def deserialize(self, data: str) -> TreeNode: """Decodes your encoded data to tree. """ if data == "#"*100:return None nodes = data.split(',') vals = collections.deque() for node in nodes: vals.append(int(node)) def build(min_val, max_val): if vals and min_val < vals[0] < max_val: val = vals.popleft() node = TreeNode(val) node.left = build(min_val, val) node.right = build(val, max_val) return node return None`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Codec:def serialize(self, root: TreeNode) -> str: """Encodes a tree to a single string. """ if root is None:return "#"*100 nodes = [] def preorder(node): if node is None:return nodes.append(str(node.val)) preorder(node.left) preorder(node.right) preorder(root) #print(nodes) return ','.join(nodes)def deserialize(self, data: str) -> TreeNode: """Decodes your encoded data to tree. """ if data == "#"*100:return None nodes = data.split(',') def helper(preorder): if not preorder:return None if len(preorder)==1:return TreeNode(preorder[0]) root_val = preorder[0] rest = preorder[1:] #idx = bisect.bisect_left(rest, root_val) left = [val for val in rest if val<root_val] right = [val for val in rest if val>root_val] root = TreeNode(root_val) root.left = helper(left) root.right = helper(right) return root return helper(nodes)`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Solution: def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode': if p is q:return p if p is root or q is root:return root dummy = None parents = {} found = [False, False] parents_p = set() parents_q = set() def traverse(node, parent=dummy, level=0): if node is None:return else: if node == p: parents_p.add((level, p)) found[0] = True elif node == q: parents_q.add((level, q)) found[1] = True parents[node] = (level-1, parent) if found[0] and found[1]:return traverse(node.left, node, level+1) traverse(node.right, node, level+1) traverse(root) node = p while node is not None: parents_p.add(parents[node]) _, node = parents[ node] node = q while node is not None: parents_q.add(parents[node]) _, node = parents[node] _, lca_node = max(parents_p & parents_q) return lca_node`
`class Solution(object): def lowestCommonAncestor(self, root, p, q): if not root: return None if p == root or q == root: return root left = self.lowestCommonAncestor(root.left, p , q) right = self.lowestCommonAncestor(root.right, p , q) if left and right: return root if not left: return right if not right: return left`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass BSTIterator: def _inorder(self, node): if node is None:return self._inorder(node.left) self._stack.append(node.val) self._inorder(node.right) def __init__(self, root: TreeNode): self._stack = [] self._inorder(root) self._stack = self._stack[::-1] def next(self) -> int: """ @return the next smallest number """ if self._stack:return self._stack.pop() else:return -1 def hasNext(self) -> bool: """ @return whether we have a next smallest number """ return len(self._stack)>0# Your BSTIterator object will be instantiated and called as such:# obj = BSTIterator(root)# param_1 = obj.next()# param_2 = obj.hasNext()`
`class BSTIterator(object): def __init__(self, root): self.stack = [] self._extract(root) def _extract(self, root): while root: self.stack.append(root) root = root.left def hasNext(self): return len(self.stack) > 0 def next(self): node = self.stack.pop() if node.right: self._extract(node.right) return node.val`
`# Definition for a binary tree node.# class TreeNode:# def __init__(self, x):# self.val = x# self.left = None# self.right = Noneclass Solution: def levelOrder(self, root: TreeNode) -> List[List[int]]: res = [] if root is None:return [] def bfs(): current_level = [root] while current_level: this_res = [] new_level = [] for node in current_level: if node:this_res.append(node.val) if node.left:new_level.append(node.left) if node.right:new_level.append(node.right) res.append(this_res) current_level = new_level bfs() return res`
Data Scientist/MLE/SWE @takemobi
## More from Jimmy Shen
Data Scientist/MLE/SWE @takemobi
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# STAAR Released Test Math Formulas: Ace the STAAR Test!
The State of Texas Assessments of Academic Readiness (STAAR) math test can be a daunting challenge for many students. Navigating through various mathematical concepts and formulas can be overwhelming, but fear not! This guide is here to demystify the essential STAAR Test math formulas, turning them from intimidating equations into powerful tools to help you confidently ace the test.
Take STAAR Scholarship Test Now!
Memorization vs. Understanding: Before getting into the specifics of STAAR math formulas, let's address the elephant in the room: repeated memorization. Memorizing formulas might help you recall them temporarily, but true mastery comes from understanding the underlying principles. This guide will not just throw formulas at you; instead, we'll dissect each one, providing clear explanations, practice problems, and study tips to ensure a deeper comprehension.
## Foundation of STAAR Math Formulas
To build a solid foundation, let's categorize the formulas into key mathematical concepts. Whether it's geometry, algebra, or statistics, understanding the context in which these formulas operate is crucial. We'll explore how these concepts interconnect, creating a holistic view of the mathematical landscape.
• Geometry Formulas: Geometry often intimidates students, but breaking down the formulas and understanding the geometric relationships can make it more manageable. From the Pythagorean theorem to the area of different shapes, we'll explore not only the formulas themselves but also when and how to apply them in various situations.
Practice Problem: Calculate the hypotenuse of a right-angled triangle with legs measuring 3 cm and 4 cm.
Understanding the Pythagorean theorem is not just about plugging in numbers; it's about recognizing when to use it. In this example, we see how the theorem applies to a real-world scenario, preparing you for the diverse problems you might encounter on the STAAR test.
• Algebra Formulas: Algebra is the backbone of many mathematical concepts assessed on the STAAR test. From solving equations to manipulating expressions, these formulas are essential. We'll not only cover the formulas themselves but also provide strategies for efficiently solving problems, saving you valuable time during the test.
Practice Problem: Solve for x: 2x + 5 = 11.
Understanding algebraic formulas involves more than memorizing steps. It's about recognizing patterns and applying them to solve problems quickly. This practice problem demonstrates how to isolate the variable efficiently, a skill that will serve you well throughout the test.
• Statistics and Data Analysis Formulas: With an increasing emphasis on data interpretation, statistics plays a significant role in the STAAR test for Math. From mean and median to probability, we'll explore the formulas and how they relate to real-world scenarios. This section aims to enhance your ability to analyze and interpret data, a crucial skill for success.
Practice Problem: Calculate the mean of the following set of numbers: 10, 15, 20, 25, 30.
Solving statistical problems involves more than plugging numbers into a formula. It requires a keen understanding of the data and the ability to choose the appropriate formula. This practice problem helps you hone your skills in calculating the mean, setting you up for success on STAAR test day.
### Study Tips for Formula Mastery
Formula mastery goes beyond practicing problems. Incorporating effective study strategies will reinforce your understanding and boost your confidence. Utilize flashcards, create a formula cheat sheet, and engage in collaborative study sessions to enhance your retention and application of STAAR test math formulas.
Study Tip: Teach the formulas to someone else. Explaining concepts to others reinforces your understanding and identifies areas where you might need further review.
Teaching others is a powerful learning tool. When you can explain a formula to someone else, it indicates a thorough understanding of the material. Use this study tip to solidify your grasp of STAAR test math formulas.
Register STAAR Scholarship Test Now!
### Test Day Strategies
As the STAAR test day approaches, it's essential to have a game plan. From time management to staying calm under pressure, this section will provide valuable strategies to optimize your performance on the STAAR test for Mathematics.
Strategy: Review formulas strategically. Focus and practice formulas you find difficult and then move on to easier ones.
Prioritize your review to maximize your efforts. By tackling the more challenging formulas early in your study sessions, you give yourself ample time to seek additional help or clarification if needed.
Mastering STAAR-released test Math formulas are not just about surviving the test; it's about thriving in a mathematical landscape that can be both challenging and rewarding. By understanding the principles behind each formula, practicing problem-solving strategies, and implementing effective study techniques, you'll be well-equipped to tackle any mathematical challenge the STAAR test throws your way. So, embrace the formulas, connect the dots, and confidently step into the test canter, knowing that you have the tools to ace the STAAR test for Math!
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https://codegolf.meta.stackexchange.com/questions/2140/sandbox-for-proposed-challenges/19089
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# What is the Sandbox?
This "Sandbox" is a place where Code Golf users can get feedback on prospective challenges they wish to post to the main page. This is useful because writing a clear and fully specified challenge on the first try can be difficult. There is a much better chance of your challenge being well received if you post it in the Sandbox first.
See the Sandbox FAQ for more information on how to use the Sandbox.
## Get the Sandbox Viewer to view the sandbox more easily
To add an inline tag to a proposal use shortcut link syntax with a prefix: [tag:king-of-the-hill]
# Buildings made from cubes
Posted to main; thanks for input provided!
• this looks perfect for fastest-code. with fastest-algorithm it's difficult to do complexity analysis on the solutions. – ngn Jan 4 at 23:53
• @ngn thanks, I’ve amended the alternative suggestion – Nick Kennedy Jan 5 at 0:23
• it may be good to mention explicitly that all blocks must form a single connected component, otherwise 2 separate 1x1x2 pieces would technically satisfy rules 1-4 – ngn Jan 5 at 1:47
• Is this basically $a_n = \sum_{i=1}^n polyminoNumber(i)\cdot i^{n-i}$? – my pronoun is monicareinstate Feb 3 at 14:56
• @mypronounismonicareinstate no it's not, though it is related to the polyomino numbers. I've posted to main (sorry for not updating Sandbox post), so please see there for two implementations of code. – Nick Kennedy Feb 3 at 17:35
# Parse Iota
Iota is a simple programming language, considered the "sister" of the language Jot. More info can be found here Every Iota program consists of either an i, or a * followed by two Iota programs. In BNF, this is:
iota ::= i | *<iota><iota>
# Challenge
Your task is to, given any input, output a truthy or falsy value based on whether or not it is a valid Iota program.
• Your program may take input in any form agreed upon by the community here. It just has to be able to take input from the user in some form.
• The same rule goes for output. See the post above for valid output methods. Output may be any truthy or falsy value in your language, including integers, strings, arrays, or objects. If it can be converted to a Boolean, it is OK.
# Example I/O
Input: i
Output: 1
Input: hello
Output: 0
Input: *i*i*ii
Output: 1
Input: i*i
Output: 0
Input: ***
Output: 0
Input: *
Output: 0
Input: iiiiiiiii
Output: 0;
Input: i
Output: 1
Input: *ii
Output: 1
• Suggested test cases: *, ***, iiiiiiiiiii – 79037662 Feb 12 at 23:27
• Ok, I added those @79037662 – sugarfi Feb 13 at 0:37
• I don't get how i*i*i*ii is produced. If I understand the grammar right, this is equivalent to checking if parens are matched after removing the final i that must come at the end, using *i as (). – xnor Feb 13 at 7:12
• @xnor - sorry, my bad. i fixed that. – sugarfi Feb 13 at 12:02
• I think that despite the different presentation, this would be similar enough to checking paren matching to be a duplicate. – xnor Feb 14 at 11:22
# The uniquely solvable sudoku code-golfdecision-problem
Given a standard 9x9 sudoku board, output a Truthy value if that sudoku admits one and only one solution. Output a Falsy value if the sudoku has a number of solutions other than one. This means 0 solutions and two or more solutions.
# The input
The board can be given in any sensible format. Some come to mind, and I'll exemplify for a 4x4 sudoku.
• a 2D array with the state of the board, with any placeholder value for non-filled cells (including the digit 0, or no value at all if your language supports it): [[1,2,#,4],[#,4,1,2],[2,1,4,#],[4,#,2,1]]
• a string of the digits row by row or column by column, so "12#4#412214#4#21" or "1#24241##14242#1"
# The output
A Truthy value if the sudoku puzzle has a unique solution, Falsy otherwise.
# Test cases
### Falsy
• Hmm, I'm surprised this isn't a duplicate with the amount of Sudoku-related challenges we have. Closest related challenge I could find is perhaps this one. – Kevin Cruijssen Feb 18 at 16:21
• @KevinCruijssen Thanks for your search! I can link this one, but this is still a new challenge, right? :) – RGS Feb 18 at 17:44
## Square Deltas code-golfsequence
Given an strictly positive integer n, output all numbers in the sequence up to the index n. For the current test cases of the current challenge numbers are one-indexed. However, other formats are allowed as default.
## Base sequence
We start from this sequence:
1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, ...
The sequence is described as follows: 1, 2 (xN), 1 repeated arbitary times. There are 2 more 2's than the previous 2-set, and the 2-sequence starts at 1. i.e.:
1, 2, 1,
1, 2, 2, 2, 1,
1, 2, 2, 2, 2, 2, 1,
and so on ...
However, our point is not to output this sequence. For every item in this sequence, add the item by that item of that sequence.
## Adding the sequence
Here's an example of adding the sequence. Here, our sequence starts with 0:
The sequence
|
v
0 + 1 = 1
1 + 2 = 3
3 + 1 = 4
4 + 1 = 5
...
Our generated sequence is therefore
0, 1, 3, 4, ...
## Example test cases
Here is a sample program outputting the sequence up to the input.
3 -> [0, 1, 3]
10 -> [0, 1, 3, 4, 5, 7, 9, 11, 12, 13]
## Sandbox
• Can the challenge be clarified?
• Why is the task asking for infinite output after index n, rather than a standard sequence challenge? A "standard sequence challenge" usually allows several I/O formats in a single challenge, including "input n -> the number at index n", "input n -> first n numbers", "no input -> infinite output of the sequence". – Bubbler Mar 6 at 4:49
• No, you don't need to make it harder. And even if it is too easy, please don't try to fake up the difficulty by enforcing unnatural I/O requirements. – Bubbler Mar 6 at 4:56
• Are you sure that you want to override the default sequence IO? Do you actually have a good reason for doing so? – Jo King Mar 12 at 4:36
## Pendulum Encoding code-golfarray-manipulationsorting
Given an array as an input (which can be any acceptable/convenient format in your language), implement pendulum encoding.
## How do I do that?
The current iteration index starts at 0.
• If the iteration index is even, append the current item onto the output list.
• If the iteration index is odd, prepend the current item onto the output list.
## An example
The input is [a b c d e f g].
Note that the letters a-g are atoms, to prevent confusion from the iteration index.
N: the iteration index
N:0 Out: [a]
N:1 Out: [b a]
N:2 Out: [b a c]
N:3 Out: [d b a c]
N:4 Out: [d b a c e]
N:5 Out:[f d b a c e]
N:6 Out:[f d b a c e g]
The output should be [f d b a c e g].
# Another example
The input is [u d l n u e m p].
N:0 Out: [u]
N:1 Out: [d u]
N:2 Out: [d u l]
N:3 Out: [n d u l]
N:4 Out: [n d u l u]
N:5 Out: [e n d u l u]
N:6 Out: [e n d u l u m]
N:7 Out:[p e n d u l u m]
## Test cases
Here's a sample program doing this encoding.
Take note that the atoms in the list aren't always unique.
[a,b,c,d,e,f,g] -> [f,d,b,a,c,e,g]
[] -> []
[a] -> [a]
[a,b,c,d] -> [d,b,a,c]
[a,b] -> [b,a]
[a,b,d] -> [b,a,d]
[a,b,a,c,b,c] -> [c,c,b,a,a,b]
[a,a,b,b,c,c] -> [c,b,a,a,b,c]
[u,d,l,n,u,e,m,p] -> [p,e,n,d,u,l,u,m]
• I can't see any issues with this challenge apart from the usual "make sure that you specify that output and input can be taken in any reasonable and convenient format". – Lyxal Mar 18 at 0:00
• The "example" in the first paragraph is confusing. It seems to be example input, but it deson't have clear context. If feels very out of place. – Ad Hoc Garf Hunter Mar 20 at 15:16
• Are the "atoms" unique? If not, you should at least include a test case where they aren't. – FryAmTheEggman Mar 20 at 20:20
• Naming a generic array a, then redefining a as a generic atom and never referring to the original array is not very helpful in an explanation. – Jonathan Frech Mar 21 at 0:09
## Join by intersection code-golfstring
Given a list of strings, output these strings joined by their largest intersecting parts. Your output has to be optimal. Strings have to be joined in the order given.
## What is an intersection anyway?
Suppose you have two strings:
"abcbc" "bcbcd"
You extract all suffixes of the first string, as well as all prefixes of the second string:
["abcbc", "bcbc", "cbc", "bc", "c"]
["bcbcd", "bcbc", "bcb", "bc", "b"]
We trunctuate both of these lists to the length of the list of the smaller length (it's an identity in this current case).
Then, we find all items at the same index which are equal to the other item at the same index:
["bcbc", "bc"]
["bcbc", "bc"]
We return the longest string of the output. Therefore, the intersection is:
"bcbc"
## How to join two strings by the intersection
To join by the intersection you simply
1. Append the first string without the intersection to the output string
2. Append the intersection to the output string
3. Append the second string without the intersection to the output string
For example, in our example case:
"abcbc" "bcbcd"
(The intersection is "bcbc")
Step 1. Out:"a"
Step 2. Out:"abcbc"
Step 3. Out:"abcbcd"
## Reducing a join over a list
If you want to reduce a join over a list
["abc","bcd","rfh","hal"]
You connect them by their longest common substring:
abc
bcd
rfh
hal
=========
abcdrfhal
Therefore the expected output is abcdrfhal.
## Further walkdown
You cannot join two strings if their substring can be found in the middle. For example:
["aXc","bXd"]
If you try to match them by the middle substring:
aXc
bXd
You would realize that the other overlapping characters are not equal to each other. That is, a is not equal to b, and c is not equal to d. In that case you simply append the string in the join:
aXc
bXd
======
aXcbXd
Likewise, if either of these strings contain each other, but isn't equal to the other string, you should simply append the string. E.g.
["abcd","bc"]
would give
abcd
bc
======
abcdbc
Substrings can overlap past each other. E.g.
["abc","bcd","cde"]
would result in the following join:
abc
bcd
cde
=====
abcde
which would evidently make the output abcde.
Strings have to overlap as much as possible. That means, in this example:
["abcbc","bcbcd"]
This is not okay (even if they do overlap):
abcbc
bcbcd
========
abcbcbcd
Instead, this should be done:
abcbc
bcbcd
======
abcbcd
The join is consecutive based on the consecutive inputs. For example:
abcde
cde
abcde
==========
abcdeabcde
## Test cases
A program is worth a thousand words. Here 's a reference implementation that I use to check the test cases.
["abc","bcd","rfh","hal"] -> "abcdrfhal"
["mmm","qqq","rrr"] -> "mmmqqqrrr"
["abcbc","bcbcd"] -> "abcbcd"
["aXc","bXd"] -> "aXcbXd"
["abc","bcd","cde"] -> "abcde"
["abcd","bc"] -> "abcdbc"
["abcde", "cde", "abcde"] -> "abcdeabcde"
• How would you join aXc and bXd? They have the common substring X in the middle. – Bubbler Mar 25 at 2:24
• Can strings overlap past each other like abc,bcd,cde->abcde? – xnor Mar 25 at 2:25
• Do strings have to overlap as much as possible, or just overlap any amount? For example, for abcbc and bcbcd, is either of abcbcd or abcbcbcd OK? – xnor Mar 25 at 4:43
• Do strings have to be joined in the order given? I feel like the answer is surely "yes", but the text doesn't say outright. Really, I think all these Sandbox questions come from the fact that the task is never actually stated precisely, and doing that would probably head off any further question. – xnor Mar 25 at 4:49
• Along these lines, what happens if one string contains another? Do we do abcd,bc->abcd? – xnor Mar 25 at 4:51
• Suggested test case: abcde, cde, abcde. – Jonathan Frech Mar 25 at 4:52
• @JonathanFrech Well, what's the expected output? I thought it was abcde in this case. – user92069 Mar 25 at 6:00
• I was not completely sure what the output would be. abcdeabcde does seem reasonable. – Jonathan Frech Mar 25 at 7:40
• I still don't actually understand how the task works precisely. A reference implementation isn't a replacement for a specification. – xnor Mar 25 at 23:09
• @xnor I've added back the spec, can you understand it now? – user92069 Mar 26 at 6:24
• Not really, sorry. I still wouldn't know what abcd,bc would give. – xnor Mar 26 at 6:29
• @xnor Are there any more test cases you don't understand? – user92069 Mar 26 at 6:35
• This seems to be related to the shortest superstring problem for two strings, but you don't have to handle the case where one of the strings is a substring of another, and the joining order is fixed. Is that correct? Just informing that the specification spans four pages on my laptop, with default browser font size. – my pronoun is monicareinstate Mar 26 at 6:55
• – my pronoun is monicareinstate Mar 26 at 6:58
• @mypronounismonicareinstate Ah, it's a duplicate. Thank you for the mention. – user92069 Mar 26 at 6:58
## Sum in 2540 Sums code-golfpristine-programmingcode-shuffleboard
This is my attempt to pair with .
You need to write a program that sums all codepoints of the input string.
## Rules
• The input will always be in printable ASCII.
• The sum of the codepoints of your source must be exactly 2540.
• You are allowed to use your language's own code page to calculate your program's codepoints.
• Null bytes (which don't contribute to your codepoint sum) are banned.
• The program must not work with any consecutive substring removed.
• This is . Your score is the length of your source code, the shorter being better.
• You defined the "base score" only to reference that term exactly once. It seems to be move confusing than helpful. Wouldn't "The sum of the codepoints of your source must be exactly 2540" be clearer and shorter? – Ad Hoc Garf Hunter Apr 9 at 21:18
• Although I am neither suggesting nor recommending against, this could also work as code-bowling if you either outlaw null bytes or sum up the (codepoints+1). – Ad Hoc Garf Hunter Apr 9 at 21:22
• @AdHocGarfHunter The rules are a lot simpler if it were code-golf, and we haven't paired codepoint sum with code golf before. Also I need to fullfill a goal to pair code-bowling with code-golf. This analysis says that there are 11 tags not paired with code-golf, I'm going to make it 10. – user92069 Apr 9 at 21:24
• As far as I know, [pristine-programming] is the tag for programming with the substring removal restriction here. (I think this would work as a [code-bowling] as well as well) – my pronoun is monicareinstate Apr 10 at 0:12
• @mypronounismonicareinstate So which side are you for? Code golf or code bowling? – user92069 Apr 10 at 0:53
• Probably code-golf. – my pronoun is monicareinstate Apr 10 at 1:07
# Will this simplified befunge-93 program terminate? code-golfdecision-problem
The challenge today is to solve the halting problem for simplified befunge-93.
Simplified befunge-93 has exactly four instructions - > v < ^ @. The program is restricted to a 80x24 grid. Each of the commands modifies the instruction pointer (so that, for instance > makes the instruction pointer start executing commands to the right), except of the @ instruction, which terminates the program.
When the instruction pointer reaches the end, it wraps around (imagine the snake game).
You may read input in form of a string or a two-dimensional array using any reasonable device. The output may be either a truthy value if the program terminates, or a falsy value if the program doesn't terminate.
## Example data
Input:
>v
^<
Output: Doesn't terminate.
----------------------------------------
Input:
> v
@
^ <
Output: Doesn't terminate.
----------------------------------------
Input:
v@
[23 newlines]
>v
Output: Terminates.
----------------------------------------
Input:
v @
[23 newlines]
>v
Output: Doesn't terminate.
----------------------------------------
Input:
Output: Doesn't terminate.
• Possibly dupe? – HighlyRadioactive Apr 27 at 8:47
• is the instruction ptr initially at 0 0 and moving to the right? – ngn Apr 27 at 8:55
• yes, I maybe forgot to state that. But it's most probably a dupe right now, so I don't think I should push it forward anymore :P – Szewczyk Apr 27 at 8:56
• For the sake of completion: can I give my output as a list of strings? – Lyxal Apr 29 at 23:02
• @Lyxal Seeing as that's a generally accepted I/O method, yes. – sporeball Apr 30 at 0:09
# Complete a sequence using its distances code-golfsequenceinteger
Given $$\A = (a_1,\dots,a_k)\ k\ge2 \$$ a nonrepetitive sequence of positive integers.
Starting from $$\i=2\$$, while $$\a_i\in A:\$$
• If $$\d=|a_i-a_{i-1}|\$$ is not already in $$\A\$$, append $$\d\$$ to $$\A\$$
• Increase $$\i\$$
Output the completed sequence.
## Example
In: 16 20 13 3
16 20 13 3 4
--^
16 20 13 3 4 7
--^
16 20 13 3 4 7 10
--^
16 20 13 3 4 7 10 1
--^
16 20 13 3 4 7 10 1
--^
16 20 13 3 4 7 10 1
--^
16 20 13 3 4 7 10 1 9
--^
16 20 13 3 4 7 10 1 9 8
--^
Out: 16 20 13 3 4 7 10 1 9 8
This is
• You could define the self-distances completion for a sequence of positive integers instead of a k-permutation. I believe it would be clearer that way. Also, is the input guaranteed to be duplicate-free? – Zgarb Jun 1 at 20:15
• @Zgarb Yes, you're right, for the purpose of this challenge refer to a sequence would be totally ok, I've copied this def from the linked challenge where since it's fundamental to consider the max in the input sequence, this number in the context of k-permutation of n - containing n - will naturally be n... But that's not a problem, a k permutation is also a sequence of positive integer. And yes, I forgot to require the input to be duplicate-free – Domenico Modica Jun 1 at 20:44
• @Zgarb what do you think about the name? Does it make sense? It's a bit too bulky? – Domenico Modica Jun 1 at 20:53
• "append d to (the end of) A" could be clearer to programmers than "prolong A with d". Using "the end of" is optional. – Hiatsu Jun 2 at 3:05
• The name could be "Complete a sequence using its distances" if you want to go for maximum clarity. – Zgarb Jun 2 at 8:08
## _
• @mathjunkie then the codepoints given are incorrect. – Lyxal May 24 at 22:43
• @Lyxal Why are they incorrect? I wrote a program to generate the codepoints. – user92069 May 25 at 8:15
• Oh wait. I thought they were in binary. – Lyxal May 25 at 8:18
• As in, you were using the binary representation of each ordinal value. – Lyxal May 25 at 8:19
• @Lyxal No. I was using the decimal expansion of the ord codes. I am going to clarify that. – user92069 May 25 at 8:19
• I cam see that now. I just assumed those numbers were base 2,rather than base 10 – Lyxal May 25 at 8:20
• Seems pretty clear, but would benefit from test cases with odd-length strings. For example, 'rim' (false) and 'rum' (true) illustrate the 'first half longer' splitting rule. (Truthiness for these two words would be swapped if the rule were second half longer.) – Dingus May 29 at 7:24
# Bot Duels KOTH king-of-the-hilljavascript
Obligatory blurb adding story fluff. Or, maybe a self-referential paragraph about meta-self-referential blurbs? Or: <announcer voice> Will your bot survive... The Arena? </announcer voice>. Yes, I think a good non-self-referential (such as this) short paragraph full of short sentences without run-ons or many, many, many, many commas will suffice.
## Overview
This is a King-of-the-Hill challenge. Bot with the most wins wins. You may submit multiple bots as long as they differ in strategy. Bots will play against every other bot. The bot who is currently playing against every other bot goes first, and goes second when their opponent is playing against every other bot. Bots will face off in an arena with x boundaries of 10 and -10 and y boundaries of 10 and -10. Bots will either start at (-5, 0) or (5, 0). Your goal is to defeat the other bot by reducing it's HP to 0 or less. Bots start with 20+armor modifier HP and do not regenerate health. Your bot defeats the other bots using weapons, which have damage, range, and cooldown. Armor has speed.
## Submissions
Submissions should be a JS function that takes the following parameters:
• curr_x - the current x coordinate of your bot
• curr_y - the current y coordinate of your bot
• enemy_x - the current x coordinate of your opponent's bot
• enemy_y - the current y coordinate of your opponent's bot
• enemy_armor - the armor that your enemy is wearing
• storage - a storage object you can use to store data between function calls
The function should return an array with 3 items (in the following order):
• desired x - the x coordinate you want to move to
• desired y - the y coord you want to move to
• use weapon? - if true, and desired x and desired y are Infinity, then you use your weapon
Submissions should be structured as
Weapon: your weapon here
Armor: your armor here
function definition
block
Explanation underneath, if any.
## Armor
(currently designing new weapons and armor) The types of armor available are:
• Light - increases HP by 3, has a speed of 3
• Medium - increases HP by 5, has a speed of 2
• Heavy - increases HP by 7, has a speed of 1
## Weapons
The types of weapons are:
• Laser - High-range, high-damage, low ROF. 5 points of damage, 5 rounds to cool down, and a range of 6 units
• Rifle - General-purpose weapon. 5 damage, range of 4, 3 rounds to cool down.
• Sword - High-ROF, high-damage spiky thing. 5 points of damage, really low range of 1, and a rather quick 2 rounds to cool down.
## Turns
On your turn, you can either move or use weapon (or do nothing, if that's what you really want to do).
• If you move, you can move a distance (computed using the Euclidean Distance formula) less-than or equal-to (<=) your armor's speed.
• If you choose to use weapon, and if the enemy is in range of your weapon, then you deal damage equal to your weapon's damage and the weapon goes into cooldown. A weapon in cooldown can't be used. Weapons can be used after a number of turns equal to their cooldown property has passed after being used.
• To do nothing, simply return your current x and y coordinates, like so: return [curr_x, curr_y, false].
## Rules
• If you try to use a weapon during cooldown, nothing happens and your turn ends
• If you try to use a weapon and your opponent is out of range, nothing happens and your turn ends.
• If you try to move more than your armor's speed, nothing happens and your turn ends
• If you try to move out-of-bounds, same thing
• If you move into another bot's space, then the bot with the lowest HP loses and the bot with the highest HP wins, making this a viable strategy.
• All standard loopholes (accessing controller, duplicate bots, suicide bots, etc.) are, of course, disallowed.
## Examples
TowerDefense Weapon: Laser
Armor: Heavy
function(curr_x, curr_y, enemy_x, enemy_y, enemy_armor, storage) {
let actions = [Infinity, Infinity, true];
return actions;
}
Just sits and shoots, lol. A perfectly viable strategy (and a rather strong one, too, while weapons are still being reworked). Takes the highest-hp armor available because it doesn't need to move at all.
## DumbBot
Weapon: Rifle
Armor: Medium
function(curr_x, curr_y, enemy_x, enemy_y, enemy_armor, storage) {
let actions = [curr_x, curr_y, false];
// if storage is empty
if (!storage.data) {
// then write our starting loc
storage.data = curr_x.toString() + " " + curr_y.toString();
}
// if we're starting at x = -5
if (storage.data.includes("-5")) {
if (curr_x < 3) {
// move right
actions[0] += 2;
actions[1] = curr_y;
}
// otherwise we must be close enough
else {storage.data = "shoot";}
}
Assumes enemy doesn't move (such as TowerDefense). Moves to the enemy's starting location, then shoots. As such, takes the Medium armor and the Rifle. Kind of a generic all-purpose bot, like the weapons and armor it uses.
## Controller
The controller can be found here. Run all current submissions here.
Best of luck, and, may the odds be ever in your favor (even though this is a 1v1 and not a FFA)
## Sandbox
• Are the rules explained thoroughly? Is anything unclear?
• Is the game (armor, weapons, punishment for breaking rules, etc.) balanced well? Are there any strategies that dominate?
• Would this KOTH be fun?
• Would you participate in the competition?
• Any obvious bugs in the (horribly messy) controller code?
• Create a simple submission similar to something that you would actually submit and test it against the example bots. Is the code still working?
• An arena that contains the points (-5, 0) and (5, 0) would be larger than 10x10. Isn't the heavy armor creating more health that can be removed in a turn? – my pronoun is monicareinstate Jun 15 at 17:07
• Armor adds health at beginning of game. It’s a one-time buff. And yes, I messed up the field size. It’s 20x20 – nope Jun 15 at 21:32
• If armor is one-time, then the Light armor is strictly better than Medium because both last only for one shot, leading to various weirdness. – my pronoun is monicareinstate Jun 16 at 1:41
• a) How much health does each bot start with? b) Are you sure the arena is supposed to be 20x20? Not 21x21 or 19x19? As it is one of the bots will have to start closer to the edge (and which one it is isn't specified as far as I can tell). c) Is there a reason why some disallowed actions cause an immediate forfeit while others only make the offending bot skip a turn? d) The "Stuff Not Allowed" and "Other viable strategies" are confusing. Namely, under the first one you list a viable strategy, and under the second - something that's disallowed. – Alion Jun 16 at 12:02
• b.2) On further inspection, is this game grid-based or played on a continuous arena? As in, can you move in fractions? In the second case, (b) becomes irrelevant. – Alion Jun 16 at 12:40
• e) What's the mysterious "Distance formula"? Plain old euclidean distance? Taxicab? Chebyshev? f.1) How do you "include [what weapon and armor your bot is using] in your submission"? f.2) More generally, is there a specific submission format? Or will anything human-readable do? g) Are bots allowed to act randomly with the help of Math.random, for example? h) Is it really necessary to override this loophole? – Alion Jun 16 at 13:06
• i) Have you considered adding more weapon types or modifying the current set? Currently the choice is pretty one-dimensional, since you avoid varying the damage property. – Alion Jun 16 at 13:07
• As for whether this KotH is fun or not - it seems okay, but I think it lacks variety. Addressing (i) would probably help with that. I would definitely give this challenge a try regardless if it hit main (perhaps as a result of me being a JS KotH junkie). – Alion Jun 16 at 13:18
• Just an observation: the table is almost antisymmetric reading top-down vs bottom-up. That is, if you split the table in half based on the value of A, then the X value in any row in the top half of the table is mostly the opposite of the X value in the same row (reading upwards from the bottom) in the bottom half. Whether that simplifies the problem at all, I'm not sure. – Dingus Jun 15 at 0:23
• I think the [kolmogorov-complexity] tag should apply here, and the [number] tag doesn't seem very helpful. – my pronoun is monicareinstate Jun 16 at 5:58
# Polyglot: Convert Case
Your task is to write a program that performs case conversion from plain text, and other case formats, into one of the specified formats below. Inputs will be either plain lowercase text, or one of the detailed cases below. You must remove non-alphabetic characters, except (space), _ and -, split on these, or differences in case (e.g. bA), and either join on the desired chars or join on the empty string and capitalise the first char of each word (or not the first of doing camel case). Your program must be a polyglot in at least two different languages. For example, running your code in Python 2 transforms input to snake_case, running it in JavaScript transforms to kebab-case, Ruby transforms to PascalCase and 05AB1E transforms to camelCase.
The following case conversions must be completed:
### camelCase
this is a test thisIsATest
camelCaseTest camelCaseTest
PascalCaseTest pascalCaseTest
snake_case_test snakeCaseTest
kebab-case-test kebabCaseTest
Testing!!one!!!1!!! testingOne1
aBCDef aBCDef
ABCDef aBCDef
a_b_c_def aBCDef
a-b-c-def aBCDef
Try it online!
### PascalCase
this is a test ThisIsATest
camelCaseTest CamelCaseTest
PascalCaseTest PascalCaseTest
snake_case_test SnakeCaseTest
kebab-case-test KebabCaseTest
Testing!!one!!!1!!! TestingOne1
aBCDef ABCDef
ABCDef ABCDef
a_b_c_def ABCDef
a-b-c-def ABCDef
Try it online!
### snake_case
this is a test this_is_a_test
camelCaseTest camel_case_test
PascalCaseTest pascal_case_test
snake_case_test snake_case_test
kebab-case-test kebab_case_test
Testing!!one!!!1!!! testing_one_1
aBCDef a_b_c_def
ABCDef a_b_c_def
a_b_c_def a_b_c_def
a-b-c-def a_b_c_def
Try it online!
## UPPER_SNAKE_CASE
this is a test THIS_IS_A_TEST
camelCaseTest CAMEL_CASE_TEST
PascalCaseTest PASCAL_CASE_TEST
snake_case_test SNAKE_CASE_TEST
kebab-case-test KEBAB_CASE_TEST
Testing!!one!!!1!!! TESTING_ONE_1
aBCDef A_B_C_DEF
ABCDef A_B_C_DEF
a_b_c_def A_B_C_DEF
a-b-c-def A_B_C_DEF
Try it online!
### kebab-case
this is a test this-is-a-test
camelCaseTest camel-case-test
PascalCaseTest pascal-case-test
snake_case_test snake-case-test
kebab-case-test kebab-case-test
Testing!!one!!!1!!! testing-one-1
aBCDef a-b-c-def
ABCDef a-b-c-def
a_b_c_def a-b-c-def
a-b-c-def a-b-c-def
Try it online!
## Rules
• Your code should produce the same output as the linked examples.
• Entries with the most conversions win, with code length being a tie-breaker.
# Questions for sandbox
• Have I missed any other major naming schemes?
• in the example, at the start, you said python 2 and javascript, while below there are 4 conversions. Must you do all of them in a different language each? Also, do language versions (python 2 / python 3) count as different languages? – Command Master Jul 3 at 3:27
• @CommandMaster It was just a cut down example to explain the concept of a polyglot. I'm still unsure whether it makes sense to allow two or more languages or require all four. I feel like allowing two or more would enable more elegant solutions as snake Vs kebab is the same bar the delimiter and Pascal Vs camel is the same bar leading capitalisation. What're your thoughts? – Dom Hastings Jul 3 at 6:28
• Different language versions count as different languages (not sure of there's a relevant meta post. I'll try and look for it when I'm not on mobile.) – Dom Hastings Jul 3 at 6:29
• If the usual 'different command-line flags count as different languages' rule applies, then is there a risk that the snake vs kebab cases could be trivially solved using the command-line flag to specify the delimiter...? – Dominic van Essen Jul 6 at 11:23
• Yeah, I guess so. Something like Perl's -i flag could enable using \$^I to be either - or _. Although then doing the same would probably be tricky and potentially still at least a little ingenious. – Dom Hastings Jul 6 at 12:46
• "Have I missed any other major naming schemes?" Yes: Ada_Ninety_Five_Case, Title Case, and (jokingly) StRaNgEcAsE. What's wrong with UPPER_SNAKE_CASE? – fireflame241 Jul 9 at 5:55
• @fireflame241 I think that converting back from upper snake case might be slightly more tricky than just snake case, as checking for an underscore might not be enough to see if there's more transformation necessary, if for example there was already an underscore in normal text... I could state that isn't a problem though I guess? Adding more cases might make me lean towards mandating only a minimum of two transformations required as well and changing the scoring to number of transformations with code length as a tie-breaker... Thanks again, will think on this a bit. – Dom Hastings Jul 9 at 6:16
• If you restrict words to be composed only of letters, then you could avoid that issue, and a few others. For example, how would aB_Cd be handled? It could be snake case, where the _ separates the words, or camel case, where the _ is the start of the second word. I think right now there's too many test cases, too little explanation. – fireflame241 Jul 9 at 6:32
• @fireflame241 Yeah, I think you're right. Ok. I'll work on this. Thanks! – Dom Hastings Jul 9 at 6:45
• Re: flags as languages again. I was more thinking of a program 'checking' to see what flags had been used (even if they have no direct effect), and modifying its behaviour accordingly. For instance, perl -m foo + then checking whether foo is loaded. This would also be similar to language+library = different language. Worst cheat of all would be awk -v mode=1... – Dominic van Essen Jul 9 at 16:03
• Along the same lines, it would be important to specify that it isn't Ok to just run different versions of a language (which currently 'count' as different languages), and for the program to determine the version & modify its behaviour. – Dominic van Essen Jul 9 at 16:10
• I don't think it's possible to rule out different language versions for polyglot challenges, and using flags to classify as different languages might be questionable too. I guess if the answers aren't in the spirit of the task or are a little boring they'll be voted on accordingly. I'm open to more input on this though! Thank you for the feedback! – Dom Hastings Jul 9 at 21:13
• "polygot in at least two different languages" so we must write 4 programs, how can there be fewer than 4 languages? – qwr Jul 9 at 22:46
• @qwr I just amended the rules to allow 2 or more languages, you don't have to have all 5. I'm hoping this will allow some creative solutions. If I missed a reference to that I'm struggling to see it, but morning eyes... – Dom Hastings Jul 10 at 6:07
• For some reason I thought there were 4 programs. So to clarify, the minimum is two languages / two conversions? – qwr Jul 10 at 6:11
# Posted: Find the Block on the Extended Periodic Table Using the Diagonal Rule
• I would be more inclined to compete if all the elements were classified into the correct blocks. I know it's only a code-golf challenge, but somehow it seems annoying to deliberately give the wrong answer! I don't know whether there's a precedent for it, but is there any way to say, for instance "additional code to adjust the positions of elements (currently only 4: La, Ac, Lu & L4) that are exceptions to the diagonal rule will not be included in the byte-count"...? – Dominic van Essen Jul 10 at 6:22
• the real reason I made it require the wrong answer was because I do not quite know the behavior of the extended periodic table (are all group 3 elements in the d-block?) I will likely put the exceptions back, especially if I find the answer to that question @DominicvanEssen – golf69 Jul 10 at 6:33
• I think my guess about group 3 was correct. The best way to phrase the exceptions might be to say "all elements directly adjacent to an s-block element are in the d-block, and those directly adjacent to that block are also in that block" (phrasing tbd, as is that is way too ambiguous) @DominicvanEssen – golf69 Jul 10 at 6:56
• I like it if all the elements can be assigned in a rule-based way (rather than expermentally) to their correct positions. But, from the way you describe it, I get the impression that the 'diagonal rule' is more of a rule-of-thumb that breaks-down at tht 6th row... or have I misunderstood? – Dominic van Essen Jul 10 at 7:07
• A purely-cosmetic change could be to change the title to "Find the predicted block on the periodic table" and subtext as "as predicted by the Madelung_energy_ordering_rule". Then there'd be no exceptions (by definition), and nerds like me would be fooled into thinking that we're calculating 'correct' answers... – Dominic van Essen Jul 10 at 7:16
• The diagonal rule specifically breaks for the 3rd column (group 3). I like your idea of just changing the title, I will do that @DominicvanEssen – golf69 Jul 10 at 7:34
• I think it's still important to mention/highlight somewhere that the experimentally-measured periodic table deviates from that predicted by the diagonal rule at higher atomic numbers, and that this challenge is only to find the blocks predicted by the diagonal rule. Otherwise it could be confusing to understand what the intended output should be. – Dominic van Essen Jul 10 at 8:02
• Suggested testcase: 23:59 – fireflame241 Jul 13 at 17:11
• Can we take input base 60? – fireflame241 Jul 13 at 17:12
• 'in which you start both at exactly hh:mm:00' - should this rather say something like 'you start the timer when the clock shows exactly hh:mm:00'? – Dingus Jul 14 at 15:12
• @Third-party'Chef' Could you specify that handling unsolvable inputs is unnecessary? – fireflame241 Jul 14 at 15:57
• @fireflame241 Done. – user92069 Jul 15 at 13:24
• What's the upper limit of the output string Y? – user92069 Jul 25 at 5:24
• @Third-party'Chef' Y is a programming language not a string. – Ad Hoc Garf Hunter Jul 25 at 12:31
• Sorry, I meant X. – user92069 Jul 25 at 12:32
• @Third-party'Chef' I didn't put an upper limit, but its length is your score so longer means worse score. Is there some issue I am not seeing that means an upper limit is needed. – Ad Hoc Garf Hunter Jul 25 at 12:36
# 1+ Metagolf
So in order to make 1+ more popular (and ease the creation of golfed 1+ text-printing programs) here comes the metagolf challenge.
## The 1+ Language
1+ is a fun deque-based esolang where 1 is the only literal, and other numbers are constructed with operators. It is also "monotonic", that is, it only have the + and * operators and not - or /. The deque is often referred as a "stack" and one end of the deque is often referred to as the "top".
Here are the commands:
• 1 pushes 1.
• + and * pops two numbers and pushes their sum and product respectively.
• " duplicates the top number.
• / and \ rotates the stack upwards and downwards respectively. That is, / moves the top number to the bottom and \ does the exact reverse.
• ^ swaps the top two numbers.
• < is the only comparison operator (although it probably won't do much in kolmogorov-complexity challenges)
• . and , inputs an integer and a Unicode character respectively and push it onto the stack. You are not allowed to take input here.
• : and ; outputs an interger and a Unicode character respectively. In the original interpreter, the : command outputs with a trailing newline, but here we allow both with a trailing newline and without a trailing new line.
• # is a goto command that pops the top value n and sends program flow to immediately after the nth # in the current line of execution (where numbering starts from 0).
• Functions are defined with (name|code) and are called with (name). The name can be empty and the point where they are defined causes their execution too. They are separate lines of execution, so the numbering of #'s in them starts from 0.
Original interpreter
Slightly modified interpreter to remove integer output trailing newline
## Challenge
Your challenge is to write a program that inputs some text and outputs a 1+ program that outputs the text. The program can be in any language (lesser-known ones preferrably), but it must output valid programs for any text.
## Winning citeria
Your score for a particular test case is your output length divided by the input length. The total score is the sum of the scores of all test case.
The test cases are:
# Codington Crescent
Okay teams, it's now time to play the game called Codington Crescent. But first, I notice we have been swamped by a letter, which comes from a Mrs Trellis of North Wales. She writes "Dear Madam or Sir, Please make up your mind. Yours sincerely, Mrs Trellis". Okay, now on to the game
If you've ever listened to the radio program "I'm sorry, I haven't a clue", then you've probably heard of the game called "Mornington Crescent". For those who haven't, it's a game where players name random stations on the London Underground network. The first person to name "Mornington Crescent" wins the game.1
In the same sort of spirit as the classic radio game, I present to you Codington Crescent.
## The Challenge
The winner of this challenge is the first person to post a working program that prints the exact string Codington Crescent.
## The Rules
1. Each player has their own program that they will add/change characters. This is termed their running program.
2. Each answer (a turn) has to obey source restrictions defined by previous answers. These are called rules. Each varient lasts for 5 turns. Rules are in the style of either , or limiting of language names (but not both).
3. Running programs can change languages between turns.
4. Answerers (players) can either add or change (but not both) as many characters of their running program per turn as they like. Alternatively, they can choose to "pass", adding no new rules, and still counting as a turn.
5. At the end of each turn, the player declares a new rule that will span the next 5 turns. Rules must be objective, and a TIO verification program is highly recommended. Also, rules have to be able to be applied to every language (e.g. Programs must not error using Python 3.4.2 isn't a valid rule).
6. Play continues until a running program prints the target string.
## Starting Rules
As to kick off the game, the first 5 turns must follow these rules:
1. Turns may not print Codington Crescent.
2. Running programs must be irreducible.
## Example Rules
These are purely examples of what you could add as rules to the challenge. They do not apply unless someone decides to use them.
• Languages must have at least 3 characters in their name
• The first and last letter of the running program must be a space
• Running programs must have an even amount of bytes
• Languages must be in the practical category on TIO
• Running programs must not be more than 30 bytes
## Extra Answer Chaining Rules
• You cannot answer twice in a row. Someone else needs to answer before you have another go.
• Languages need to be on Try It Online in order to be valid answers.
## Feedback
Do you think the game will ever reach an end. Also, have I explained the rules clearly enough?
1 The original game of Mornington Crescent doesn't really have rules... It's more of an activity that looks like it's a complicated game.
Written with StackEdit.
• I think that it will never. Assumes that it's easy to see whether the program is "two step away from being complete", the next user is never going to move it "one step away from being complete", since they can't win in that case. – user202729 Jul 24 at 16:36
• I agree with @user202729 that it will never terminate in its current state. It would be more likely to terminate if: languages could be changed every answer; answers could not remove 3 characters (or weaken to maybe remove 1 character; presently it allows loops); maybe allow for more characters added per answer – fireflame241 Jul 24 at 19:24
• @user202729 I've updated the rules to potentially avoid such loops – Lyxal Jul 25 at 7:14
• @fireflame241 I've updated the rules to potentially avoid such loops – Lyxal Jul 25 at 7:14
• Bonus for the first answer in Mornington Crescent? :-) – Luis Mendo Jul 25 at 10:07
• @LuisMendo sure, imaginary brownie points it is – Lyxal Jul 25 at 10:29
• All hail Lyxal, +1 – HighlyRadioactive Jul 25 at 11:04
• I think it will not complete until an Unary answer is produced because you can simply replace all characters that are not as with a. A long string of as is seldom a useful program. (that is, extending user202729's comment: you don't have to see the "two step away from being complete" state, it's sufficient to find a large class of programs that are definitely not "one step from being complete") – my pronoun is monicareinstate Jul 25 at 11:41
• @mypronounismonicareinstate I've completely changed the rules of the challenge to make it model a more plausible game. – Lyxal Jul 28 at 4:35
# Road Sort Order
In Britain, road identifiers use a scheme of a letter, followed by a 1-4 digit number.
From Most-Important to Least-Important, the letters are:
M
A
B
C
D
U
The numbers also represent further assumptions around the importance of the road, such that a 1-digit number is more important than a 4-digit number.
Thus, the M898 is less important than the M8, but more important than the A8.
interesting but not relevant for the challenge - Roads are also sorted into nine Zones, of equal importance. The first number in each road identifier gives the Zone that the road starts in (e.g. A8 starts in Zone 8 - although there are exceptions where one Motorway spurs off of another, e.g. M48 is so named because it is a spur of the M4 even though it is officially in Zone 5).
## The challenge
Given a pair of road identifiers, identify and output which is the most important road. Where there is no difference in importance by the above rules (e.g "B4063" and "B1234") then either output is acceptable.
Usual I/O rules apply, this is so lowest bytes wins. There will be two inputs, and no invalid inputs (i.e. they will follow the rules, although they may not be actual real-life roads).
If you say so in your answer, you may instead output the least significant road (i.e. as long as I know which it is, you can do either).
You may take the input as a string, array of strings, or array of strings and integers as follows:
"M123M223"
["M123","M223"]
["M",123,"M",223]
#SANDBOX# If there are input formats that you think should/n't be allowed, let me know.
## Examples
• A11,M2 -> M2(Motorways come before A roads)
• M823,M89 -> M89 (two-digit roads are more important than 3-digit roads, even though 89 alphabetically comes after 823)
• A1262,A150 -> A150
• U6340,D6340 -> D6340
• M1,M2 -> Either
• B100,C99 -> B100
• I'd suggest simplifying sorting to just comparing two distinct values. Or even, mapping a value to a number so that the comparisons are right. – xnor Aug 4 at 19:56
• @xnor sorry I'm not sure what you mean. Do you mean only ever have two inputs? – simonalexander2005 Aug 5 at 7:25
• Yes, like have a possible input be like f("A11","M2") with it being a decision problem to tell if the first or second one is more important. Or, just have us write a function g producing a number so that, say, g("A11")>g("M2"). – xnor Aug 5 at 21:11
• @xnor how's that? I've made it return the most (or least) significant road of a pair – simonalexander2005 Aug 6 at 7:34
• Looks good! I'm a bit worried about the "any sensible format" since counting digits is important. Like, would a length-four array padded with nulls for missing digits count as acceptable? I think this would be you compare the number parts as a direct list comparison in some languages. – xnor Aug 7 at 3:15
# Count Syllables
The goal of this challenge is to write a program that can count the syllables in a word as accurately as possible.
## Input
On STDIN, your program will receive a number X followed by X lines, each containing a single word. Simple enough. (Should there be a limit on the size of X?) The words will come from this list.
4
challenge
to
count
syllables
## Output
Your output should be to STDOUT and have X lines. On each line should be the number of syllables counted in that word.
2
1
1
3
# Scoring
To score you program, it will receive a long secret list of words to test. All programs will receive the same list of words. For each word, the number of syllables that your program got wrong will be added to the score of the program. If it output a 4 or a 2 when the word had 3 syllables, then one point will be added. If it said a 15 instead of a 3, then 12 points will be added to the score. The lower the score, the better.
For example, if for the above input your program output 3 2 2 2 (which would be produced by a program that counts strings of vowels), then the program would receive a score of 2.
# Rules
Your program should not access any external files (such as the word list). Also, your program should be no more than 5,000 bytes long (is this a reasonable limit?).
The winner will be the person whose program has the lowest score, therefor the most accurate syllable counter. The deadline for submissions is [some time at least a month away].
# Suggestions
I am open to all constructive criticism. Is 5,000 bytes a reasonable limit for the program size? How long should the official scoring test be? How long should the deadline be?
• This has one major flaw: the output is subjective. How many syllables do these words have? Every; victory; hierarchy; desire; oil; hour; poem. The only real way I see to work around this is for you to produce a marked-up version of the word list. – Peter Taylor May 29 '12 at 20:40
• I was really worried about that, and I don't see a way around it. – PhiNotPi May 29 '12 at 20:42
• I personally would love to see more language processing challenges. I agree with @PeterTaylor on the difficulty of some words. Perhaps taking a specific text(s) and identifying explicitly in the challenge which words will have how many syllables? – Gaffi Jun 8 '12 at 3:34
• @PeterTaylor ...Or maybe you could filter ambiguous words out of the reference list? – user16991 Feb 8 '15 at 1:19
• What's the point of the first line of input? – msh210 Apr 27 '16 at 20:05
• If you provide a reference list, A hyphenated reference list, and hide a secret list which may or may not include members of the reference list, this would be a reasonable challenge – Rohan Jhunjhunwala Sep 17 '16 at 0:05
• Do you plan to post this? If not, I'd be happy to adopt it. (If you don't respond within two weeks, by community standards, I'm allowed to do so.) – MD XF Aug 18 '17 at 3:20
• The example of inaccurate program that would score 2 - did you mean to output 3 1 1 2 rather than 3 2 2 2? – Heimdall Nov 9 '17 at 18:31
• A reference list could be dynamic: potential contestants can ask for words of their choice to be added to the list. They won't know what's on the secret list but will try to make their programs as accurate as possible (according to your syllable count) so they should always be able to ask for specific words they are not sure about. Of course, you could make it in different language. In my language, Slovene, it's much clearer how many syllables words have. How about Solresol, haha! – Heimdall Nov 9 '17 at 18:38
• I am going to adopt this if you don''t respond – Christopher Dec 20 '17 at 16:48
## Play Simple 2-Dimensional Minecraft
Recently I found this video of "HansLemurson" showing a computer that was built in minecraft, which runs minecraft. He is playing minecraft on a computer that was built in minecraft that is running on his computer. To be specific, it is a two dimensional version with an 8x8 grid of cells. There is gravity, block placement, and even jumping. It is worth noting that the computer is single purpose. The same person has built programmable computers, but making them single purpose allows the computer to be much smaller.
## Details
The minecraft world is an 8x8 grid (one horizontal and one vertical dimension). The grid is comprised of either Xs (representing blocks) or empty spaces. The player is an X that is blinking on and off about once every second.
There are two modes in the game, controlled by a toggle switch. The first mode is movement. This is controlled by a WASD-like button arrangement. If the player chooses to move left/right/down, the computer checks to see if the space immediately in that direction is empty. If so, then the player moves into that space.
If the player chooses to move up, then the computer checks that the block underneath the player is solid. If so, then the player moves upward two units. Notice that this can propel the player into a solid block. If this happens, the player is obscured by the solid block, but can still move to an empty block next to him. When the player is inside on a solid block, the game continues as if the block isn't there, although the block is still there once the player leaves it.
After each move, the player falls down one unit if there is empty space there. This simulates gravity. This is also why moving up moves up two units, so that the gravity makes a net movement of up one unit. Gravity does not cause the player to fall all of the way to the ground, just one unit.
The second mode is block placement. In this mode, the same exact WASD buttons are used. Instead of moving the player, they toggle the state of the block in that direction. If the player presses "left" and there is a block there, then the block is destroyed. If there is not a block there, then a block is placed. Again after this move, the player is again subject to gravity. The blocks are not subject to falling.
Toggling the toggle switch does not count as a move, and does not invoke gravity.
The game board is a torus, so all actions (movement, block creation) can wrap around the board. The board does not scroll with the player. The player moves, and the blocks stay in the same place.
## The challenge
You challenge is to write the shortest program that simulates this game. Your program should display and update the map correctly (with Xs as blocks, and with the blinking player). It should accept input from a button that toggles the state and four buttons for movement and actions. This is code golf.
There are imaginary bonus points for adding more features (block types, game size, etc) to your game.
## Suggestions?
• With more complicated challenges I find that it helps to do a reference implementation so that you have a very concrete idea of how much work is involved. Aside from that, I like it. – dmckee --- ex-moderator kitten Jun 3 '12 at 20:11
• Is the blink rate selected to fit with the ANSI escape sequence? Either way I would explicitly allow that, because it's the obvious way to do it on compatible terminals. – Peter Taylor Jun 5 '12 at 7:14
• The blink rate wasn't selected to be anything specific. I think that I will broaden the restriction. Maybe any blink rate between 3 blinks per second to 1 blink every 2 seconds. – PhiNotPi Jun 5 '12 at 20:21
• @programmer5000 No, for two main reasons: First, challenges can go extended periods of time in the sandbox before they are posted and/or adopted. In the past I've posted challenges after not touching them for 4 years. Second, deleting this answer will not reduce lag, as deleted answers are still present, simply not visible. Users with sufficient rep will see all 4040 answers in the sandbox, and you will too once you earn the "view deleted answers" privilege. – PhiNotPi Apr 13 '17 at 18:15
## Bad Voice Recognition Calculator
Overview:
Let's say you've decided to operate your computer using voice recognition software, but unfortunately you did a horrible job researching the various products out there and chose a package that does not recognize numbers as numerals, only words. (i.e. "one" (spoken) == "one" (typed), not "1".) Rather than spend more money to get another option, you decide to make do. Now you want to use the computer's calculator, but this poses a problem, since your machine doesn't know how to add "one plus one".
Objective:
Implement a basic calculator that will read in a string of the written-out equation, perform the correct calculations, then return the result in its text form. Your code should be as short as possible; this is code golf.
Rules/Constraints:
• Input/output will be using your preferred method (STDIN, ARGV, etc.).
• Your calculator must be able to handle input and output within the billions (non-inclusive) -1,000,000,000 < i < 1,000,000,000, but you may expand to more if you wish.
• Decimal values and/or parts must be accepted (0 < i < 1) up to 3 places/digits.
• When calculating answers, proper rounding must be used, so "three point one four one five nine two six" must be returned as "three point one four two".
• Basic calculator functions required:
• "Add"/"Plus"/"Sum"/"And" (+)
• "Subtract"/"Minus"/"Remove" (-)
• "Multiply"/"Times" (*)
• "Divide"/"Divided"/"Divide by"/"Divided by" (/)
• "Raise"/"Exponent"/"Power"/"To the power of" (^)
• "<Base>Root"/"<Base>Radical" (√)
• "Point"/"Decimal" (.)
• "Pi" (π)
• All strings in the list above must be accounted for in your code, capitalization does not matter.
• Numbers may be presented as their full value ("one thousand") or by digit (one zero zero zero).
• Negative numbers may be assigned using "Minus" or "Negative".
• The string "Minus" bust be accounted for as an operator and identifier. (see example)
• "And" is only acceptable as an operator, not as part of a named number.
• "one hundred and one"
• "one hundred one"
• "a" or the absence of a number does not equate to any number; all numbers will be explicitly accounted for in the program input.
• "a hundred" does not equate to "one hundred" and is not a valid input.
• No more than 2 terms will be used.
• "one plus one minus one" will not be implemented.
• If an invalid input is supplied, your function/program should handle the error and exit gracefully with an error description.
Example I/O:
• "one add one" --> "two"
• "five thousand thirty four subtract ten thousand six hundred" --> "negative five thousand five hundred sixty six"
• Alternatively: "five zero three four subtract one zero six zero zero"
• "three root twenty seven" --> "three"
• "ten minus minus ten" --> "twenty"
• Alternatively: "ten subtract negative ten"
## Sandbox Questions:
1. Is this too basic/complicated? (I'm assuming some languages will handle this much more simply than the method I have in my head...)
2. Does the title fit?
3. Are there any constraints that should be added/lifted?
4. Are any more examples needed for clarification?
Thanks for your input, guys!
• Not everyone says numbers the same way. Does the parser have to treat the following as equivalent? "negative one hundred five", "minus one hundred five", "negative one hundred and five", "minus one hundred and five", "negative a hundred five", "negative a hundred and five", ...? – Peter Taylor Jun 15 '12 at 15:12
• @PeterTaylor I had had a similar thought re: operators. ("plus" versus "add", etc.) I think it would be more interesting to account for all, but given the wide variety of possible inputs, it may generally be better to limit the options to a specifically defined set (which I have yet to define). – Gaffi Jun 15 '12 at 15:18
• @PeterTaylor I've added some of these details. Please let me know if there's anything unclear about them. – Gaffi Jun 15 '12 at 16:10
• I don't spot any ambiguities in the parser. There is still an ambiguity relating to decimals, though. What precision should be used? Also, I notice now that there's no winning condition. Is this intended to be code-golf? (Ugh - tons of strings which will have to be hard-coded in most languages. I expect Perl has a suitable parser already in CPAN, though...) – Peter Taylor Jun 19 '12 at 9:03
• @PeterTaylor I don't know where I went... I've updated the spec. re: decimal places and objective. – Gaffi Jun 29 '12 at 13:24
• @PeterTaylor metacpan.org/pod/Lingua::EN::Words2Nums – msh210 Apr 27 '16 at 20:37
# Huffman Decoding
Write a programm which takes two strings as input and prints a text.
The first argument is a Huffman Tree, serialized in the following format:
• every ascii character except ~ is always a leaf, if ~ is the first characater it is also a leaf.
• <tree0><tree1>~ is a tree where <tree0> is the left subtree and <tree1> is the right subtree.
Example: ab~cde~~~ generates this tree:
┌─┴─┐
┌┴┐ ┌┴─┐
a b c ┌┴┐
d e
where a would have the key 00, b 01, c 10, d 110 and e the key 111.
The second argument is a text that has been compressed with with the Huffman code that is defined by the first parameter. This bit-string can contain any bit sequence (also null-bytes and non-printable characters) and is not byte aligned, therefore it has been encoded with a variation of the standard Base64 encoding:
• the characters used for the encoding are the standard base64 characters: ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/
• the bitstring is broken up into 6-bit chunks and mapped to this characters
• if the last chunk is smaller than 6 bits, a character with this prefix is used, and padding characters are added to the string:
• - : the last chunk was five bits long
• = : the last chunk was four bits long
• =- : the last chunk was three bits long
• == : the last chunk was two bits long
• ==- : the last chunk was one bit long
Example:
bits: 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1
chunks: |1 1 1 1 0 1|1 0 1 0 0 1|1 1 0 1 0 1|0 0 0 1 1 0|1[0 0 0 0 0]|
characters: 9 p 1 G g
base64: 9p1Gg==-
Your programm has to decode the text encoded in the second parameter and print it to stdout.
You have to provide your source code encoded in the way described above. The length of your encoded source code + the length of your serialized huffman tree will be the winning criterion.
TODO: example input
• It would be helpful to explicitly state the 64 characters used in the encoding. I presume they're A-Za-z0-9+/ but (especially if you're expecting people to implement that part explicitly) it's best to make the problem self-contained. – Peter Taylor Oct 8 '12 at 16:23
• Hello! This looks like a good but abandoned meta post, would you be willing to offer it for adoption? (If you want to, you can still post to main.) – programmer5000 Jun 9 '17 at 15:30
# Graphical Output -- Esoteric Artifacts -- The Glass Bead Game
## Draw the Cabalistic Tree of Life
Simply described, the Tree of Life is an undirected network of nodes representing the conduit between matter and higher forms of spiritual energy. It has an upper face arranged in a hexagon, and a lower fact built from equilateral triangles adjacent to the lower two edges of the upper face. Don't label the paths, paths may overlap however you wish, may be single (thick) lines, even. Code Golf. Bonus -100 for labels on the Sephiroth (nodes); Bonus -150 for Hebrew labels.
## Draw a Mandala for each Natural Number
Draw a circle with interesting visual patterns using the input N [ 1 .. \inf ) to determine the number of points around the circle to anchor figures whose shape is also modified by the input N. Actually, 12 seems like a good max: they're pretty much a blur after that no matter what.
//lotsoflines n = 1 ..12
(doesn't need to be this elaborate, This is >600 lines of showing-off.).
. . . need good images for these . . .
## Draw the Ptolemeic System of the Universe
All the stuff I could find is animated already. Maybe this one's done-to-death. :(
Update: Found good stuff on Alchemy. The "Keplar Platonic" model could be fun (3D and all). This one looks good, too. And this.
## Draw the Pythagorean Monochord
aka pre-classical nomogram. I misplaced my Pythagoras books, I know I've got a picture somewhere.
This is the one I was thinking of.
But I think this one's even cooler
## Draw the I-Ching Hexagrams in King Wen Sequence.
I suppose I need to implement this first to avoid copyright issues! :)
• The I-Ching one would have to be in standard order to be remotely interesting, and then becomes as much about kolmogorov-complexity as graphical-output – Peter Taylor Nov 22 '12 at 21:24
• For the others: images, please! – Peter Taylor Nov 22 '12 at 21:25
• I've emailed the owner of the Alchemy pages asking for permission to use his copyrighted images. Awaiting response. – luser droog Jan 28 '13 at 8:25
## DeCSS
It is known that the DVD Content Scrambling System can be deciphered with a rather short program (434 bytes of C, 472 bytes of Perl). Can you do better?
<< Test cases go here >>
I don't plan to include a more detailed spec, because it will just wind up duplicating some of the code. The test cases would be in the form of (key, link to data file, md5sum of the deciphered stream).
• And the winning criterion is who is the first to get post from the courts? – celtschk Oct 3 '15 at 20:18
• @celtschk, I think that would be unfair. Winning criteria shouldn't really depend on where people live... – Peter Taylor Oct 10 '15 at 20:56
• I think you should at least explain the general concept of the spec. – Rohan Jhunjhunwala Aug 2 '16 at 22:53
• This actually sounds interesting. @PeterTaylor Perhaps you could use (and link to) Charles Hannum's explanation of the algorithm and post this. (It would be fun to have it as a popularity contest for a program that looks like it's nothing DeCSS related, or a program that furthers the gallery's point about the text vs source code arbitrary distinction - but I don't know if popularity contests are popular any more!) – sundar - Reinstate Monica Jun 25 '18 at 8:25
## Code golfing problem: Surface classification
The task: Given a surface-word reply with the classification of what surface it is.
Example 1: Input: aba'b' ----> Output: 1T
Example 2: Input: aabcb'c' ----> Output: 3P
Bounds on the problem: Since there are only 26 letters, there will never be more than that many labels. Additionally output should be in the form S,nT,mP for n,m positive integers.
Background: In the study of algebraic topology students are often presented with diagrams such as the one below. The represent instructions for how to assemble a surface. The assembly is prescribed as: if there are two edges labeled with the letter x then glue them together so that the arrows point the same direction. To make our job easy, topologists have discovered an algorithmic way to classify surfaces using 'words' assembled from these 'plane gluing-diagrams'.
Choosing a corner arbitrarily (top right) and orientation (ccw) we read off the labels on the edges where an inverse appears wherever the arrow points against the orientation. In this case the 'word' that represents this plane model is given as abab.
A surface word is a string that contains the letters a,b,...,@ up to some letter @ and each letter is contained in it exactly twice. In the two occurrences of each letter: 0, 1, or 2 of them may be postfixed by a ' which I am considering using to represent 'inverse' (opposite orientation).
If in a surface word all letters appear twice: once without the ' and once with it (f.ex. ba'b'a) then we say that the surface the word represents is orientable. If a surface is orientable then it is necessarily the direct sum of n Tori for some non-negative integer n. If this condition doesn't hold (like in aab'b) then the surface represented is non-orientable: in this case it is the direct sum of m Projective Planes for some positive integer m.
Once you have found out if the reduced word is orientable or not, the final answer is given as follows. If orientable and number of unique letters in the reduced word is 1 then output should be S. Otherwise if the number of unique letters in an orientable word is n (it will be even) then the output should be sT where s = n/2. If the word is non-orientable then the output should be mP where m is the number of distinct letters in the reduced word.
The goal is to take as input some surface word, reduce it via reduction rules 1-6 and then classify it as a sphere, some number of connected tori, or some number of connected projective planes. Here are the 6 reduction rules where ~ represents 'reduces to':
Let M,A,B,C,D be surface words, x be a single letter, and juxtaposition represents concatenation:
1. Cycle Rule: If M = AB then M ~ BA
2. Flip Rule: M ~ M'
3. Sphere Rule: Axx'B ~ AB
4. Block Rule: ABC ~ ADC if B is a surface word and B ~ D by 1 or 2
5. Cylinder Rule: If M = AxBCx'D, then M ~ AxCBx'D
6. Möbius Rule: If M = AxBxC then M ~ AxxB'C ~ AB'xxC
I am looking for input on:
• should this be code-golf or programming-challenge?
• how would scoring work?
• ???
If I feel satisfied with the question in a few days I'll post it to the site.
• If, for each input, there is only one correct output, then it should probably be code-golf. The scoring criteria would then be source code length. – PhiNotPi Jun 8 '13 at 14:33
• Yes, this is the case. In general however there is not a unique series of applications of the reduction rules for any given instance. – Kaya Jun 8 '13 at 16:21
• I don't think the order of explanation is correct. You should explain reduction before talking about "the reduced word". And "reduce it via reduction rules" doesn't entirely make sense, because the rules are presented as equivalences rather than reductions, and most of them don't have a "natural" direction. – Peter Taylor Jun 10 '13 at 8:49
• It's also occurred to me that you haven't defined the notation M'. Does it just consist of toggling the orientation of each token, or does it also reverse the entire string? And do you have test cases which between them force implementation of all of the reduction rules? – Peter Taylor Jun 11 '13 at 8:32
• Good call on the string inverse, yes you have the right idea and I will make it clear. I have a lot of test cases from when I did a number of these computations by hand in a university course and (anecdotal experience) I am pretty sure that it is possible to force the use of all the reduction rules (except maybe 4 which is really just a meta-rule for convenience when doing proofs). Additionally you have alerted me to some concerns regarding the form of the proper output: it's definitely underspecified. I'll put some work into this today. – Kaya Jun 11 '13 at 14:04
Business Card Ray Tracer
I have no idea how to create a good code golf question!
See this description of a ray tracer with source code that fits on a business card. The author stopped when the code size was 1337 bytes.
Achieving identical output, optimise for minimum code size. Execution time is not relevant.
• I think what you have here is a straight ahead golf. All languages. You need only define the requirements. Do you want identical output or do you want "good output encompassing <list of features>"? – dmckee --- ex-moderator kitten Oct 6 '13 at 17:22
• For a minimum feature list I'd suggest something like (1) it is ray tracer (2) supports point-like lights and shadow + ambient light (3) supports mirrored (implies reflection) and matte surfaces (3) all objects are sphere and overlaps are allowed. With no requirement for (a) anti-aliasing; (2) finite sized light sources; (c) atmosphere effect or (d) depth of field; or (e) tiling and gradients. Notice however, that the example supports at least (b), (d) and (e). – dmckee --- ex-moderator kitten Oct 6 '13 at 17:29
• BTW--The one you linked can get a little bit more with #define Q return (R was already taken for the rand wrapper) and #define O operator. – dmckee --- ex-moderator kitten Oct 6 '13 at 17:33
• I suggest reading the Teapot question in the sandbox Mk IV and the comments - it's not the same question, but some of the same issues are relevant, and it might give you ideas for improvements to the spec. – Peter Taylor Oct 6 '13 at 22:48
• Yes. Read the teapot question for guidance. Ultimately I decided that one was too big, but we did get into some pertinent details. – luser droog Dec 1 '13 at 9:48
• This sandbox post has had little activity in a while and little positive reception from the community. Please improve / edit it or delete it to help us clean up the sandbox. – programmer5000 Jun 9 '17 at 15:32
# Count unique characters in text.
Given a string for input, output the unique non-whitespace characters in that string along with a count of their occurrences. The list should be sorted in ascending order of ASCII code.
Examples
Input:
Hello, World!
Output:
Character Count
! 1
, 1
H 1
W 1
d 1
e 1
l 3
o 2
r 1
Input:
The quick brown fox jumps over the lazy dog.
Output:
Character Count
. 1
T 1
a 1
b 1
c 1
d 1
e 3
f 1
g 1
h 2
i 1
j 1
k 1
l 1
m 1
n 1
o 4
p 1
q 1
r 1
s 1
t 1
u 1
v 1
w 1
x 1
y 1
z 1
The actual formatting (headers, spacing, etc) of the on-screen output is up to you. The only conditions are that it must be sorted in ascending order by ASCII code, and it must be easy to tell what represents a character from the string and what represents a count of a given character. (For example, given a string of 99999999, the output should be explicit so that it is not confused as saying I have 9 8s.)
Ultimate challenge (taken from here):
JKqdJg+oJgiowgyIJgkS+gyxJdeS+gyxJ4yoJdybJdioJdqIJ4kS+KwFJ4QS+gzYJg+ow4vIJ4yxvd+IJgy=+dv=JdQx+gzbJrzx24zYJgkxJ4qLJKQxJ4yxJKqx+KqdJKqdJg+oJgiowgyIJgkS+gyxJdeo24yxJm+xJdybJdioJdqIJKi=J4wF+dvS+gzYJg+ow4zYJ4yxvdy=J4i=+Kv=JdQo+KqxJrzdJKzYJgkxJ4qLJgkxJ4yxJKvSJ4qbJKqdJg+oJgiowgyIJgkdJgyxJdeo24yxJm+xJdybJd+oJd+S+dz=J4wF+dvS+g+SJg+ow4vIJ4yxJ4voJgy=+dv=+dzdJgqxJrzdJKzYJgkS+dweJKQxJ4yxJKvSJ4qbJKq=24yYJgiowgyIJgkdJgzdJryo24yxJm+d24zxJd+oJdqIJ4kS+KwFJ4QS+gzYJ4y=2gzYJ4yxJ4voJgy=+dv=+dzdJgqxJrzx24zYJgkS+dweJKQxJ4fK+dQSJ4qbJKq=24yYJgiowgyIJgkS+gzdJryS+gyxJ4yoJdybJd+oJd+S+dz=J4wF+dvS+gzYJ4y=2gvIJ4yxJ4voJgy=+dv=JdQo+KqxJrzx24zY+dzS+dweJKQxJ4yxJKqx+KqbJKq=24vbJdyowgyIJgkdJgzdJryS+gyxJm+d24zxJdioJd+S+dz=J4wF+dvS+gzYJg+ow4vIJ4yxJ4voJgy=+Kv=JdQx+gzbJrzx24zYJgkS+dweJgkxJ4yxJKvSJ4qdJKq=24yYJgiowgyIJgkdJgzdJryS+gyxJ4yoJdybJd+oJdqIJKi=J4wF+dvS+gzYJg+ow4vIJ4yxJ4v=J4i=+Kv=+dzdJgqxJrzx24zYJgkS+dweJgkxJ4fKJ4qx+KqdJKqdJg+SJdyowg+oJgkS+gyxJdeS+gyxJ4yoJdybJd+oJdqIJ4kS+KwFJ4QS+g+SJ4y=2gzYJ4yxJ4v=J4i=+Kv=JdQo+KqxJrzx24zY+dzS+dweJKQxJ4yxJKvSJ4qbJKqdJg+oJgiowg+oJgkS+gzdJryo24yxJ4yoJdybJdioJdqIJ4kS+KwFJ4QS+g+SJg+ow4vIJ4yxvd+IJgy=+dv=JdQo+KqxJrzdJKzY+dzxJ4qLJKQxJ4yxJKqx+KqdJKq=24vbJdyowg+oJgkS+gzdJryo24yxJ4yoJdybJdioJd+S+dz=J4wFJ4QS+gzYJg+ow4zYJ4yxvd+IJgy=+Kv=+dzdJgqxJrzdJKzYJgkxJ4qLJgkxJ4yxJKvSJ4qbJKq=24vbJdyowgyIJgkdJgyxJdeo24yxJm+xJdybJd+oJdqIJKi=J4wF+dvS+g+SJ4y=2gvIJ4yxvd+IJgy=+dv=+dzdJKzbJrzdJKzY+dzS+dweJgkxJ4yxJKvSJ4qbJKq=24yYJgiowg+oJgkS+gyxJdeo24yxJ4yoJKzxJd+oJdqIJKi=J4wF+dvS+gzYJg+ow4vIJ4yxJ4v=J4i=+dv=+dzdJgqxJrzx24zYJgkxJ4qLJKQxJ4fKJ4qx+KqdJKqdJg+oJgiowgyIJgkS+gzdJryS+gyxJm+d24zxJd+oJdqIJKi=J4wFJ4QS+gzYJ4y=2gzYJ4yxvdy=J4i=+Kv=+dzdJKzbJrzx24zY+dzxJ4qLJKQxJ4yxJKqx+KqdJKqdJg+SJdyowg+oJgkdJgzdJryo24yxJm+d24zxJd+5
• This isn't really an interesting problem. The shortest answer is almost certainly going to be fewer than 10 characters. – Peter Taylor Dec 11 '13 at 12:19
• @PeterTaylor While I mostly agree with your comment - already the header line may contain more than 10 characters. – Howard Dec 12 '13 at 6:15
• "The quick brown fox jumps over the lazy dog." contains "e" three times. – Howard Dec 12 '13 at 6:16
• @Howard Thanks. I must be blind - it took me about five times of reading your comment to find it. Also, do remember that the header is optional to a certain degree - you just need to make sure the output is unambiguous as to which items are characters from the string, and which are character counts. – Iszi Dec 12 '13 at 7:02
• My brain instantly went into bash mode. wc and uniq practically solve half of this, but not in any particularly short manner. – Rob Dec 17 '13 at 20:31
### PETSCII banner
In an other world... I was using a PET 2001 who used some particular PETSCII charset.
The screen green on black, with 40 columns and 25 lines, was only able to display characters from this charset. No way to draw dots or lines...
But in the chaset, there is some ▝ and ▚, which, ( by the use of reverse video in order to obtain 16 chars: ' ','▖','▗','▘','▝','▀','▄','▐','▌','▞','▚','▟','▛','▜','▙','█' ) make us able to draw graphics on a 80x50 dots plan.
Using an internal clock triggering IRQ, I've done a animated prompter like this:
The goal of this is to make a similar banner, with same charset, (but using UTF-8 characters: ' ','▖','▗','▘','▝','▀','▄','▐','▌','▞','▚','▟','▛','▜','▙','█'). Warn, this charset use inverted lower/upper cases.
• This imply the use of PETSCII charset, I will post them there as a json string, before getting this out of the sandbox if some interest...
• The tool have to change his position 20 time per second.
• The tool must accept as argument, the string to display.
• The tool must add date and time in the form - WDay MDay Mnth Year, HH:MM:SS -
• Scrolling have to be done bit per bit: I.E.: by half character!
• Shortest code...
• -3 if size of console is not limited to 40 columns
• -5 if cpu usage stay less than 90% (On my poor Core(TM)2 Duo CPU E8400 @ 3.00GHz, with 4G ram)
• -5+ if cpu usage stay less than 50%
• -5+ if cpu usage stay under 5%
C.U.
• as for the CPU bonuses - what is the target environment, what is the smoothing factor, and what processes count against this measure? – John Dvorak Dec 15 '13 at 6:19
• This sandbox post has had little activity in a while and little positive reception from the community. Please improve / edit it or delete it to help us clean up the sandbox. – programmer5000 Jun 9 '17 at 15:32
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S05 Screening & Diagnostic Tests (FILLED IN)
# 5 calculaung kappa c calculate expected agreement
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Unformatted text preview: alence of injury dropped to 2%? – Sn & Sp don’t change as they are not affected by prevalence (since they relate to the test) – What is the PPV and NPV? How did they change? – PPV = (9/44) = 20.5% NPV = (553/556) = 99.5% LOWER HIGHER PPV & Prevalence Prev é༎, PPVé༎ • Especially in low prevalence Prev é༎, NPVê༎ • Mainly only at high prevalence • ImplicaUons of this relaUonship: – All interpreta2ons of a test result should occur within the context of that disease prevalence – Screening programs should be targeted to groups with higher prevalence (or else many +ve tests will actually be disease - ve) Reliability (Repeatability) • Recall class ac.vity on Friday • Can the results be repeated? • Three types of varia2on can occur: 1. Intrasubject Varia2on • E.g. Change in an individual over 2me 2. Intraobserver Varia2on • E.g. Different interpreta2ons by same person; context 3. Interobserver Varia2on • E.g. Two people disagree on interpreta2on of a test Interobserver VariaUon • How can we measure this phenomenon? 1. Overall Percent Agreement – % of ra2ngs where observers agree – Generally, most evalua2ons are disease nega2ve, so ignore these observa2ons and evaluate percent agreement where one of the observers indicated a disease +ve result. a + b + c + d % Agreement = ____a____ x 100 a + b + c +ve Observer #2 % Agreement = ___a + d___ x 100 Observer #1 - ve +ve a b - ve c d Interobserver VariaUon 2. Kappa StaUsUc A staUsUc that measures agreement beyond what would be due to chance alone – Defini2on: _______________________________ • Can be used to measure agreement between mul2ple observers • Can also be used to measure agreement between two tests (recall use of mul2ple tests) – Steps t...
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## This document was uploaded on 01/14/2014.
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### adding chrono::months to a sys_days
Trying to add 1 month to today does not yield a sys_days!!!
``12`` ``````chrono::sys_days today = getToday(); auto next_month = today + chrono::months{ 1 };``````
next_month's type is time_point<system_clock, duration<int, ratio<54>>
Why?
Well with VS2022 next_month has type std::chrono::sys_days
What compiler are you using?
I am using VS2022... are you sure?
next_month's type is time_point<system_clock, duration<int, ratio<54>>
can't I cast to duration<days>?
Last edited on
Trying to add 1 month to today does not yield a sys_days!!! [...] next_month's type is time_point>
duration<int, ratio<54>> is the type used to represent the sum of n days and m months.
A duration is a count of ticks in units of p/q seconds. For std::chrono::days, the unit p/q is 86400 seconds. 86400 seconds = 1 day. For months it's 2629746 seconds = 1 month.
Those numbers come from the definition of days and months:
``12`` ``````using days = duration>; using months = duration>;``````
Using those numbers the relevant sum is:
n day + m month = n * 86400sec + m * 2629746sec
To evaluate it and store the result in a duration we need to choose just one unit p/q that is known at compile-time.
To do it, the compiler finds gcd(86400, 2629746) = 54 at compile time and factors each term:
54n * 1600sec + 54m * 48699sec = (1600n + 48699m) * 54sec
This says the duration that holds the sum should store (1600n + 48699m) "almost-minutes" where each "almost-minute" is 54 seconds long.
can't I cast to duration?
Since these durations are stored in time_points, use time_point_cast instead:
time_point_cast<days>(next_month);
Last edited on
Trying to add 1 month to today does not yield a sys_days!!!
Well my VS2022 intellisense shows the type of next_month as std::chrono::sys_days!
However typeid shows it as:
``` class std::chrono::time_point > > ```
so intellisense is again incorrect. AAhhh....
Topic archived. No new replies allowed.
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# CAT 2007 Solutions
Section I This section contains 25 questions 1. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal? (1) May 21 (2) April 11 (3) May 20 (4) April 10 (5) June 30 Solution: Note that the price of Darjeeling tea remains constant after the 100th day (n = 100). If the prices of the two varieties of tea become equal before n = 100, then 100 + 0.1n = 89 + 0.15n ∴ n = 220, which is not possible. (Since n is assumed to be less than 100) ∴ The prices of the two varieties will be equal after n = 100, i.e., when the price of Darjeeling tea = 100 + 0.1 × 100 = 110 ∴ 89 + 0.15n = 110 ∴ n = 140 2007 is not a leap year. Number of days till 30th April = 31 + 28 + 31 + 30 = 120 The prices of the two varieties will be equal on 20th May. Hence, option 3. 2. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10? (1) –119 (2) –159 (3) –110 (4) –180 (5) –105 Solution: Let f(x) = px2 + qx + k, where p, q and k are integers ∴ f(0) = k = 1 ∴ f(x) = px2 + qx + 1 f(x) = px2 + qx + k f’(x) = 2px + q
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CAT 2007 Solutions
When f’(x) = 0, x = −q/2p f(x) attains maximum at x = 1 ∴ q = −2p f(1) = p + q + 1 = 3 ∴1–p=3 ∴ p = −2 ∴q=4 ∴ f(x) = −2x2 + 4x + 1 ∴ f(10) = −200 + 40 + 1 = −159 Hence, option 2. 3. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees? (1) Between 0 and 90 (2) Between 0 and 30 (3) Between 0 and 60 (4) Between 0 and 75 (5) Between 0 and 45 Solution:
P and Q do not lie within the intersection of the two circles.
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CAT 2007 Solutions
So they lie on the circumferences or outside the circumferences. If they lie on the circumferences, then ΔAPQ forms an equilateral triangle. So, m ∠AQP = 60o From the diagram, if they lie outside the circumferences, m ∠AQ’P’ < 60o Also, m ∠AQP would be 0o if A, Q and P were collinear. But as P and Q cut each other in two distinct points, A, Q and P cannot be collinear. ∴ m ∠AQP > 0o ∴ m ∠AQP lies between 0o and 60o Hence, option 3. Directions for Questions 4 and 5: Let S be the set of all pairs (i, j) where 1 ≤ i < j ≤ n and n ≥ 4. Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies. 4. For general n, how many enemies will each member of S have? (1) n – 3 (2) (3) 2n – 7 (4) (5) Solution: Enemies of every pair are the pairs formed with all numbers other than the two in the member itself. ∴ If there are n elements then each member has
Hence, option 4.
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CAT 2007 Solutions
5. For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members? (1) (2) 2n – 6 (3) (4) n – 2 (5) Solution: Two members are friends if they have one element in common. ∴ All the members having one constituent as the common element are common friends. There are (n – 3) such friends. Also, one pair formed by the uncommon constituents of the two friends is a common friend. ∴ There are n – 3 + 1 = n – 2 common friends. Hence, option 4. Directions for Questions 6 and 7: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others. Option A: Invest in a public sector bank. It promises a return of +0.10% Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3% Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2% 6. The maximum guaranteed return to Shabnam is: (1) 0.25% (2) 0.10% (3) 0.20% (4) 0.15% (5) 0.30% Solution: Let Shabnam have Rs. 100 to invest. Let Rs. x, Rs. y and Rs. z be invested in option A, B and C respectively. ∴ x + y + z = 100 ... (I)
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CAT 2007 Solutions
If there is a rise in the stock market, returns = 0.001x + 0.05y – 0.025z If there is a fall in the stock market, returns = 0.001x – 0.03y + 0.02z Now, x, y and z should be such that regardless of whether the market rises or falls, they give the same return, which is the maximum guaranteed return. ∴ 0.001x + 0.05y – 0.025z = 0.001x – 0.03y + 0.02z ∴ y/z = 9/16 Now, consider different possible values of x, y and z. The returns are as follows: x 75 50 25 0 y 9 18 27 36 z 16 32 48 64 Returns = 0.001x + 0.05y – 0.025z 0.125 0.15 0.175 0.2
We see that as the values of y and z increase, the returns increase. ∴ The returns are maximum when x = 0%, y = 36% and z = 64% (Note that the values of y and x are multiples of 9 and 16.) The maximum returns are 0.2%. Hence, option 3. 7. What strategy will maximize the guaranteed return to Shabnam? (1) 100% in option A (2) 36% in option B and 64% in option C (3) 64% in option B and 36% in option C (4) 1/3 in each of the three options (5) 30% in option A, 32% in option B and 38% in option C Solution: As shown by the table formulated in the first question, maximum returns are guaranteed by investing 36% in option B and 64% in option C. Hence, option 2.
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CAT 2007 Solutions
Directions for Questions 8 and 9: Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day. Departure City B A Time 8:00 a.m. 4:00 p.m. City A B Arrival Time 3:00 p.m. 8: p.m.
Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour. 8. What is the time difference between A and B? (1) 1 hour and 30 minutes (2) 2 hours (3) 2 hours and 30 minutes (4) 1 hour (5) Cannot be determined Solution: Let the speed of the plane be x kmph. Then the speed from B to A is (x – 50) kmph and that from A to B is (x + 50) kmph. Note that the plane travels from B to A, halts for 1 hour and travels back to B, all in 12 hrs. ∴ 3000/(x – 50) + 1 + 3000/(x + 50) = 12 Now consider options for this question. We can easily see that x = 550 satisfies the above expression. Speed of plane = 550 kmph Now, the plane takes 3000/500 = 6 hrs to travel from B to A. It reaches A when the time at B is 8:00 am + 6 hrs = 2:00 p.m. => The time difference between A and B is 1 hour. Hence, option 4. 9. What is the plane’s cruising speed in km per hour? (1) 700 (2) 550 (3) 600
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CAT 2007 Solutions
(4) 500 (5) Cannot be determined Solution: As calculated in the first question, the cruising speed of the plane is 550 kmph. Hence, option 2. 10. Consider all four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? (1) 3 (2) 2 (3) 4 (4) 0 (5) 1 Solution: Let aabb (a ≠ 0, a and b being single digits) be a perfect square. aabb = 1100a + 11b = 11(100a + b) Also, as aabb is a perfect square, it is a multiple of 121. ∴ aabb = 121K, where K is also perfect square. For K = 4, aabb is a 3 digit number, while for K > 81, K is a 5 digit number. For 81 ≥ K ≥ 9, 121 × 9 = 1089 121 × 16 = 1936 121 × 25 = 3025 121 × 36 = 4356 121 × 49 = 5929 121 × 64 = 7744 121 × 81 = 9801 ∴ There is only one number 7744 of the form aabb, which is a perfect square. Hence, option 5. 11. In a tournament, there are n teams T1 , T2 ....., Tn with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & T1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together? (1) n(k – 1) (2) k(n – 1) (3) n(k – 2) (4) k(k – 2)
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CAT 2007 Solutions
(5) (n – 1)(k – 1) Solution: Each team has (k – 2) players to itself and shares 2 players with other two teams. n pairs of teams have 1 player in common and there are n teams. Total number of players = n(k – 2) + n = nk – 2n + n = nk – n = n(k – 1) Hence, option 1. Directions for Questions 12 and 13: Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit. 12. How many units should Mr. David produce daily? (1) 130 (2) 100 (3) 70 (4) 150 (5) Cannot be determined Solution: The cost function C(x) = 240 + bx + cx2 C(20) = 240 + 20b + 400c C(40) = 240 + 40b + 1600c C(60) = 240 + 60b + 3600c By conditions, 2/3 × C(20) = C(40) – C(20) ∴ C(40) = 5/3 × C(20) ∴ 240 + 40b + 1600c = 400 + 100b/3 + 2000c/3 ∴ 20b/3 + 2800c/3 = 160 ∴ 20b + 2800c = 480 ... (I)
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Also, ½ × C(40) = C(60) – C(40) ∴ 3/2 × C(40) = C(60) ∴ 360 + 60b + 2400c = 240 + 60b + 3600c ∴ c =1/10 ∴ b = 10 ... (from I) Profit for x units is 30x – C(x) P(x) = 30x – 240 – 10x – x2/10 = –240 + 20x – x2/10 The derivative of P(x) = P’(x) = 20 – x/5 For maximization of profit P’(x) = 0 and P’’(x) < 0 When P’(x) is zero, 20 – x/5 = 0 ∴ x = 100 P’’(x) = –0.2 Hence, option 2. 13. What is the maximum daily profit, in rupees, that Mr. David can realize from his business? (1) 620 (2) 920 (3) 840 (4) 760 (5) Cannot be determined Solution: Following from the first question, at x = 100 the profit is maximum. At that level of production P(x) = –240 + 20 (100) – (100)2/10 = –240 + 2000 – 1000 = 760 Hence, option 4.
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CAT 2007 Solutions
Directions for Questions 14 and 15: Let a1 = p and b1 = q, where p and q are positive quantities. Define: an = pbn – 1 ; bn = qbn − 1 (for even n > 1) and an = pan – 1 ; bn = qan − 1 (for odd n > 1) 14. (1) (2) (3) (4) (5) Solution: We have the following for different values of n n an bn 1 2 3 4 5 6 7 p pq p2q p2q2 p3q2 p3q3 p4q3 q q2 pq2 pq3 p2q3 p2q4 p3q4
∴ For even n (say, n = 4),
Now consider the given options, for n = 4 (1) gives pq²(p + q)² (2) gives pq²(p + q) (3) gives pq(p + q) (4) gives q²(p + q) (5) gives q²(p + q)² Hence, option 2.
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CAT 2007 Solutions
15. If p = 1/3 and q = 2/3, then what is the smallest odd n such that an + bn < 0.01? (1) 7 (2) 13 (3) 11 (4) 9 (5) 15 Solution: For odd n, an + bn = p(n + 1)/2 q(n – 1)/2 + q(n + 1)/2 p(n – 1)/2 = p(n – 1)/2 q(n – 1)/2 (p + q) Here, p = 1/3, q = 2/3 ∴ p+q=1 ∴ an + bn = p(n – 1)/2 q(n – 1)/2 = (2/9)(n – 1)/2 Now considering options starting from the lowest, For n = 7, an + bn = 8/729 = 1/91 > 1/100 For n = 9, an + bn = 16/6561 = 1/410 < 1/100 Hence, option 4. Directions for Questions 16 through 19: Each question is followed by two statements A and B. Answer each question using the following instructions. Mark (1) if the question can be answered by using statement A alone but not by using statement B alone. Mark (2) if the question can be answered by using statement B alone but not by using statement A alone. Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone. Mark (4) if the question cannot be answered on the basis of the two statements. 16. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI, of Section I is smaller than the average weight, WII, of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes WII and that of Section II becomes WI. What is the weight of Poonam? A. WII – WI = 1.0 B. Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.
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CAT 2007 Solutions
Solution: Let the weights of Deepak and Poonam be d and p respectively. (50WII + 50WI)/100 = 45 ∴ WII + WI = 90 ______ (i) 50WI + d – p = 50WII ∴ 50(WII – WI) = d – p ______ (ii) From Statement A, WII – WI = 1 ______ (iii) From (i), (ii) and (iii), WI and WII can be found. Also, d – p = 50 ______ (iv) However this information does not give us the value of p. Statement A is insufficient to answer the question. From Statement B, 49(WI + d) = 51(WII – d) ∴ 51WII – 49WI = 100d ______ (v) This alone cannot help us find the value of p. Statement B is insufficient to answer the question. Considering both statements together, we have values of WI and WII, which can be substituted in (v) to find d, which can be used to find p using (iv). Hence, option 3. 17. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z2 ? A. x + y + z = 89 B. Among x, y, z two are equal. Solution: Statement A: x + y + z = 89 x2 + y2 + z2 will be minimum when x = y = z = 89/3 But 89/3 is a non-integer. ∴ We consider integer values of x, y, z which are as close as possible to 89/3. We get two cases: 1. x, y, z = 30, 30, 29 x2 + y2 + z2 = 2641
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CAT 2007 Solutions
2. x, y, z = 31, 29, 29 x2 + y2 + z2 = 2643 Minimum possible value of x2 + y2 + z2 is 2641. Thus statement A is sufficient to get the answer. Though statement B states a fact related to the minimum value, it is not necessary to arrive at the minimum value. Hence, option 1. 18. Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square? A. The length of OM is twice that of OL. B. The length of OM is 4 cm. Solution: Let p be the side of square JKLM. From Statement A, OM = 2 × OL OM is maximum when it is the diagonal of the square and has length ( 2)p When OM is maximum, OM = ( 2)OL ∴ OM ≠2 × OL if O lies on JK. ∴ Rahim is unable to draw the square. Hence, option 1. 19. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC’s requirements? A. The inner diameter of the tank is at least 8 meters. B. The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc. Solution: Let the inner radius be r meter. Capacity of tank = (1 m3 = 1 kilolitre) From statement A, since r ≥ 4m ∴ Capacity of tank > 256 m3 Since the capacity needed is more than 256 m3 statement A is insufficient. From statement B,
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CAT 2007 Solutions
Volume of the material of tank = mass/density = 30000kg/(3 gm/cc) = 10,000,000 cm3 = 10 m3 Hence the inner volume of tank = Outer volume – Volume of material of tank Therefore, we can say that the tank capacity is adequate. Hence, option 2. 20. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos? (1) 17 (2) 16 (3) 18 (4) 15 (5) 19 Solution: The bill can be paid in 18 ways as shown in the given table. Hence, option 3. 50 Misos 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 2 10 Misos 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 0
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1 Miso 107 97 87 77 67 57 47 37 27 17 7 57 47 37 27 17 7 7
Total 107 107 107 107 107 107 107 107 107 107 107 107 107 107 107 107 107 107
CAT 2007 Solutions
21. How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60? (1) 6 (2) 4 (3) 7 (4) 5 (5) 3 Solution: 1/m + 4/n = 1/12 ∴ 1/m = 1/12 – 4/n ∴ m = 12n / (n – 48) As, m is a positive integer, n should be greater than 48 and moreover since n is a positive odd integer lesser than 60, n can take values 49, 51, 53, 55, 57 and 59. If n = 49, 51, 57 then m is a positive integer. If n = 53, 55, 59 then m is not an integer. ∴ 3 pairs of values of m and n satisfy the given equation. Hence, option 5. 22. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount? (1) Over Rupees 13 but less than Rupees 14 (2) Over Rupees 7 but less than Rupees 8 (3) Over Rupees 22 but less than Rupees 23 (4) Over Rupees 18 but less than Rupees 19 (5) Over Rupees 4 but less than Rupees 5 Solution: Let the amount on Shailaja’s cheque be Rs. x and paise y = (100x + y) paise (x and y are positive integers) The teller gives her (100y + x) paise. Now, 100y + x – 50 = 3(100x + y) ∴ 97y – 299x = 50 ∴ y = (50 + 299x)/97 = [50 + 8x + 291x]/97
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CAT 2007 Solutions
= [(50 + 8x)/97] + 3 Now as y is an integer, (50 + 8x) has to be a multiple of 97 with x, y ≤ 99 50 + 8x = 97k (k is an integer) ∴ x = 12k – 6 + [(k – 2)/8] ∴ k = 2, 10, 18… ∴ x = 18, 115, 212… ∴ x = 18 is the only possible value. This implies that y = 5 ∴ The amount on Shailaja’s cheque is over Rs. 18 but less than Rs. 19. Hence, option 4. 23. Consider the set S = {2, 3, 4, ...., 2n + 1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y? (1) 0 (2) 1 (3) n/2 (4) n + 1/2n (5) 2008 Solution: Y = (2 + 4 + 6 + 8 + … + 2n)/n X = (3 + 5 + 7 + 9 + … + (2n + 1))/n = ((2 + 1) + (4 + 1) + (6 + 1) + (8 + 1) + … + (2n + 1))/n = (2 + 4 + 6 + 8 + … + 2n)/n + (1 + 1 + 1 + 1 + … n times)/n =Y+1 ∴X–Y=1 Hence, option 2. Note: The information that 'n is a positive integer larger than 2007' does not affect the answer in any way. 24. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight member joint family is nearest to: (1) 23 years (2) 22 years (3) 21 years
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CAT 2007 Solutions
(4) 25 years (5) 24 years Solution: The sum of the ages of the members of the family ten years ago = 231 ∴ The sum of the ages of the members of the family seven years ago = 231 + (3 × 8) – 60 = 195 ∴ The sum of the ages of the members of the family four years ago = 195 + (3 × 8) – 60 = 159 ∴ The sum of the ages of the members of the family now = 159 + (4 × 8) = 191 ∴ Required average = 191/8 = 23.875 ≈ 24 Hence, option 5. 25. A function f(x) satisfies f (1) = 3600, and f(1) + f(2) + ... + f(n) = n² f(n), for all positive integers n >1. What is the value of f(9) ? (1) 80 (2) 240 (3) 200 (4) 100 (5) 120 Solution: f(1) + f(2) + f (3) + … + f(n −1) + f(n) = n2f(n) ... (i) Similarly, f(1) + f(2) + f (3) + … + f(n − 1) = (n − 1)2 f(n −1) ... (ii) Subtracting equation (ii) from (i), f(n) = n2 f(n) – (n – 1)2f(n − 1) ∴ (n2 – 1)f(n) = (n – 1)2f(n – 1)
Hence, option 1.
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Section II This section contains 25 questions Directions for Questions 26 to 29: Each question is followed by two statements, A and B. Answer each question using the following instructions: Mark (1) if the question can be answered by using the statement A alone but not by using the statement B alone. Mark (2) if the question can be answered by using the statement B alone but not by using the statement A alone. Mark (3) if the question can be answered by using either of the statements alone. Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone. Mark (5) if the question cannot be answered on the basis of the two statements. 26. In a football match, at half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match? A. In the second half Mahindra and Mahindra Club scored four goals. B. The opponent scored four goals in the match. Solution: From Statement A, the MM club scored 4 goals in the second half. The number of goals scored by the opponent is not known. So the winner cannot be determined. Statement A is insufficient. From Statement B, the opponent scored 4 goals in the match, but we do not know the number of goals that the MM club scored. Statement B is insufficient. Considering both the statements we have the following. First Half Second Half Final Score MM Club Opponent MM Club Opponent MM Club Opponent 0 3 4 1 4 4 1 4 4 0 5 4 Thus, MM club could have won the match or could have tied it. The question cannot be answered. Hence, option 5.
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27. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school? A. Sixty per cent of the top academic performers were not athletes. B. All the top academic performers were not necessarily athletes. Solution: From Statement A, 40% of the top academic performers were athletes. ∴ If there are x top academic performers, 10 = 0.4x ∴ x = 25 Statement A is sufficient. Statement B does not give any useful information. Hence, option 1. 28. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the median. Who among the five got the highest rank? A. Atul was the last rank holder. B. Bala was not among the top two rank holders. Solution: Chetan’s rank = 4 or 5 Now, Bala < Chetan and Dev < Ernesto. From Statement A, Case 1 Case 2 Case 3 1 Bala Dev Dev 2 Dev Ernesto Bala 3 Ernesto Bala Ernesto 4 Chetan Chetan Chetan 5 Atul Atul Atul The highest rank holder cannot be determined. Statement A is insufficient. Statement B is also insufficient. Considering both statements together (refer to the table), Case 2 holds. Dev got the highest rank. Hence, option 4.
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29. Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background? A. Twenty five per cent of the employees have engineering background. B. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background. Solution: Let there be 100x employees. So, 30x are male and 70x are female. ∴ 7x female employees have an engineering background. From statement A, 25x employees have an engineering background. ∴ 18x male employees have an engineering background. Required percentage = 18x × 100/ 30x Statement A is sufficient. From Statement B, Number of male employees having an engineering background = 1.2 × 7x Required percentage = 1.2 × 7x × 100/30x Statement B is also sufficient. Hence, option 3. DIRECTIONS for Questions 30 to 33: Answer the following questions based on the information given below: The proportion of male students and the proportion of vegetarian students in a school are given below. The school has a total of 800 students, 80% of whom are in the Secondary Section and rest equally divided between Class 11 and 12: Male (M) Vegetarian (V) Class 12 Class 11 Secondary Section Total 0.475 0.6 0.55 0.5 0.55 0.53
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30. What is the percentage of male students in the secondary section? (1) 40 (2) 45 (3) 50 (4) 55 (5) 60 Solution: From the table given in the question, Total students = 800 Students in Secondary = 0.8 × 800 = 640 Students in Class 11 = (800 – 640)/2 = 80 ∴ Students in Class 12 = 80 Males in Class 11 = 0.55 × 80 = 44 Males in Class 12 = 0.6 × 80 = 48 ∴ Males in Secondary = 0.475 × 800 – 44 – 48 = 288 Vegetarians in Class 11 = 0.5 × 80 = 40 Vegetarians in Secondary = 0.55 × 640 = 352
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Vegetarians in Class 12 = 800 × 0.53 – 40 – 352 = 32 Now, the percentage of male students in secondary section = 288 × 100/640 = 45% Hence, option 2. 31. In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians? (1) less than 8 (2) 10 (3) 12 (4) 14 (5) 16 Solution: Vegetarian Males in Class 12 = 0.25 × 48 = 12 ∴ Non-vegetarian Males in class 12 = 36 ∴ Vegetarian females in class 12 = Vegetarians in class 12 – Male vegetarians in class 12 = 32 – 12 = 20 (We derived the number of vegetarians in the class in the previous question) ∴ Required difference = 36 – 20 = 16 Hence, option 5. 32. What is the percentage of vegetarian students in Class 12? (1) 40 (2) 45 (3) 50 (4) 55 (5) 60
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Solution: In the first question we derived the number of vegetarians in class 12 as 32 and the total number of students in the class as 80. The percentage of vegetarians in class 12 = 32 × 100/80 = 40% Hence, option 1. 33. In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct? (1) Except vegetarian males, all other groups have same number of students. (2) Except non-vegetarian males, all other groups have same number of students. (3) Except vegetarian females, all other groups have same number of students. (4) Except non-vegetarian females, all other groups have same number of students (5) All of the above groups have the same number of students. Solution: (This question was not considered for evaluation as there was an error in the question) “50% of the students are vegetarian males” contradicts the data given initially. Interpreting it as “50% of the males are vegetarian”, we have the following: In secondary, Vegetarian males = 144 Non-vegetarian males = 144 Vegetarian females = 352 –144 = 208 Non-vegetarian females = 352 – 208 = 144 ∴ Except vegetarian females, all other groups have same number of students. Hence, option 3. Directions for Questions 34 to 37: Answer the following questions based on the information given below. The following table shows the break-up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product. The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures for the year 2007, answer the following questions.
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Volume of production Costs (Rs.) Material Labour Consumables Rent of building Rates and taxes Repair and maintenance expenses Operating cost of machines Selling and marketing expenses
Year 2002 1000 50,000 20,000 2,000 1,000 400 800 30,000 5,750
Year 2003 900 45,100 18,000 2,200 1,000 400 820 27,000 5,800
Year 2004 1100 55,200 22,100 1,800 1,100 400 780 33,500 5,800
Year 2005 1200 59,900 24,150 1,600 1,100 400 790 36,020 5,750
Year 2006 1200 60,000 24,000 1,400 1,200 400 800 36,000 5,800
34. What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007? (1) 104 (2) 107 (3) 110 (4) 115 (5) 116 Solution: Observing the values through the years, we can say that Material, Labour and Operating costs directly vary with the change in volume of production. The other costs are almost constant. If the production is x units, the variable cost for material, labour and operation is 50x, 20x and 30x respectively. ∴ Total variable cost = 100x
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Total fixed cost (using information for 2006) = 1400 + 1200 + 400 + 800 + 5800 = 9600 ∴ Total cost of producing x units = 100x + 9600 Now, x = 1400 Cost per unit = (1400 × 100 + 9600)/1400 = 106.85 Hence, option 2. 35. What is the minimum number of units that the company needs to produce and sell to avoid any loss? (1) 313 (2) 350 (3) 384 (4) 747 (5) 928 Solution: From the explanation given in the first question, to avoid any loss, 100x + 9600 ≤ 125x ∴ x ≥ 384 Hence, option 3. 36. If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units should the company produce to maximize its profit? (1) 1400 (2) 1600 (3) 1800 (4) 1900 (5) 2000 Solution: The new reduced price = 0.95 × 125 = 118.75
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Profit = 118.75x – 100x – 9600 = 18.75x – 9600 Profit will be maximum when 18.75x is maximum. As the maximum production capacity is 2000 units, profit is maximum when 2000 units are produced. Hence, option 5. 37. Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs. 5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that the company can earn? (1) 25,400 (2) 24,400 (3) 31,400 (4) 32,900 (5) 32,000 Solution: Profit for 1400 units = 1400 × 125 – (1400 × 100 + 9600) = 25400 Profit for (1400 + m) units = (1400 + m) × 120 – ((1400 + m) × 100 + 9600) = 18400 + 20m Maximum value of m = 300 Maximum profit for 1400 + 300 units = 24400 ∴ Maximum profit that the company can earn is 25400. Hence, option 1.
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Directions for Questions 38 to 41: Answer the following questions based on the information given below. The table below shows the comparative costs, in US Dollars, of major surgeries in USA and a select few Asian countries. Comparative Costs in USA and some Asian Countries Procedure (in US Dollars) USA India Thailand Singapore Malaysia Heart Bypass 130000 10000 11000 18500 9000 Heart Valve Replacement 160000 9000 10000 12500 9000 Angioplasty 57000 11000 13000 13000 11000 Hip Replacement 43000 9000 12000 12000 10000 Hysterectomy 20000 3000 4500 6000 3000 Knee Replacement 40000 8500 10000 13000 8000 Spinal Fusion 62000 5500 7000 9000 6000 The equivalent of one US Dollar in the local currencies is given below. 1 US Dollar Equivalent India 40.928 Rupees Malaysia 3.51 Ringits Thailand 32.89 Bahts Singapore 1.53 \$ Dollars A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below. Procedure Comparative Costs in USA and some Asian Countries (in US Dollars ‘000) USA India Thailand Singapore Malaysia 0 3 3 2 4 0 5 4 5 5 0 5 5 4 6 0 7 5 5 8 0 5 6 5 4 0 9 6 4 4 0 5 6 5 6
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Heart Bypass Heart Valve Replacement Angioplasty Hip Replacement Hysterectomy Knee Replacement Spinal Fusion
CAT 2007 Solutions
38. A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account? (1) India (2) Thailand (3) Malaysia (4) Singapore (5) USA Solution: As shown in the table, Malaysia will have the cheapest package. Hence, option 3. India Thailand Singapore Malaysia Angioplasty Hip Replacement Knee Replacement Total 16000 16000 17500 49500 18000 17000 16000 51000 17000 17000 17000 51000 17000 18000 12000 47000
USA 57000 43000 40000 140000
39. Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement? (1) India (2) Thailand (3) Malaysia (4) Singapore (5) India and Singapore Solution: Referring to the table formulated in the first question, India will be the most expensive for knee replacement. Hence, option 1. 40. Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her native country, taking into account the cost of poor quality? It costs 7500 Bahts for one-way travel between Thailand and India. (1) 23500
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(2) 40500 (3) 57500 (4) 67500 (5) 75000 Solution: Cost of Hysterectomy in Thailand = 4500 + 6000 = 10500 USD Cost of Hysterectomy in India = 3000 + 5000 = 8000 USD Travelling cost = 15000 Bahts = 15000/32.89 USD = 456 USD Required difference = 10500 – 8456 = 2044 USD = 2044 × 32.89 = 67227 Bahts Hence, option 4. 41. The rupee value increases to Rs. 35 for a US Dollar, and all other things, including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account? (1) 700 (2) 2500 (3) 4500 (4) 8000 (5) No difference
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Solution: Cost of spinal fusion in India = Rs. 5500 × 40.928 Cost with the increased value of Rupee = 5500 × 40.928/35 = 6431 USD Cost of Spinal Fusion in Singapore = 9000 USD Required difference = 9000 – 6431 = 2569 USD Hence, option 2. Directions for Questions 42 to 46: Answer the following questions based on the information given below. A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports. Sector No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Airport of Departure A A A A A A A B B B B C C C D D D D D Airport of Arrival B C D E F G H C H I J D F G E F G H J Distance between the Airports (km.) 560 790 850 1245 1345 1350 1950 1650 1750 2100 2300 460 410 910 540 625 640 950 1650 Price (Rs.) 670 1350 1250 1600 1700 2450 1850 2000 1900 2450 2275 450 430 1100 590 700 750 1250 2450
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20 21 22 23 24 25 26 27 28 29 30
E E E F F F G G H H I
F G H G I J I J I J J
1250 970 850 900 875 970 510 830 790 400 460
1700 1150 875 1050 950 1150 550 890 970 425 540
42. What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J? (1) 2275 (2) 2850 (3) 2890 (4) 2930 (5) 3340 Solution: Possible routes from A to J are as shown in the table below. Route ABJ ADJ AFJ AGJ AHJ ABHJ ABIJ ACDJ ACFJ ACGJ ADFJ ADGJ Distance 2860 2500 2315 2180 2350 2710 3120 2900 2170 2530 2445 2320 Price 2945 3700 2850 3340 2275 2995 3660 4250 2930 3340 3100 2890
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ADHJ AEFJ AEGJ AEHJ AFGJ AFIJ AGIJ AHIJ
2200 3465 3045 2495 3075 2680 2320 3200
2925 4450 3640 2900 3640 3190 3540 3360
The shortest distance is by the route A-C-F-J. The price is 1350 + 430 + 1150 = Rs. 2930 Hence, option 4. 43. The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight if it is priced 5% below the minimum price that they pay at present. What should the company charge approximately, in rupees, for this direct flight? (1) 1991 (2) 2161 (3) 2707 (4) 2745 (5) 2783 Solution: The current market price paid by the customers is Rs. 2275 (A-H-J). Therefore, the company should charge (2275 × 0.95) = Rs. 2161.25 Hence, option 2. 44. If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J? (1) 2275 (2) 2615 (3) 2850 (4) 2945 (5) 3190 Solution: If C, D and H are closed, the cheapest route will be A-F-J and it will cost Rs. 2850.
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Hence, option 3. 45. If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometer that the company incurs in flying from A to J? (1) 0.77 (2) 0.88 (3) 0.99 (4) 1.06 (5) 1.08 Solution: The minimum cost per km that the company incurs would correspond to the minimum price per km route. By observation from the table, minimum price per kilometre is for the route AHJ and is equal to 2275/2350 = 0.97 Minimum cost per kilometre = 0.97/1.1 = 0.88 Hence, option 2. 46. If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company? (1) 2170 (2) 2180 (3) 2315 (4) 2350 (5) 2390 Solution: Even if the margin for the prices changes the minimum cost per km would correspond to the same route namely A-H-J. ∴ From the table, the distance for the travel = 2350 km Hence, option 4. Directions for Questions 47 to 50: Answer the following questions based on the information given below. A health-drink company’s R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R, and S), which can be used in different proportions in the
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formulations. The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O: 150, P: 50, Q: 200, R: 500, S: 100. Composition Ingredient O P Q R S Carbohydrate % 50 80 10 5 45 Protein % 30 20 30 50 50 Fat % 10 0 50 40 0 Minerals % 10 0 10 5 5
47. For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients? (1) One (2) Two (3) Three (4) Four (5) None Solution: The diet should contain 10% minerals. P contains no minerals. ∴ P cannot be a part of any mixture. R and S both contain 5% minerals. ∴ Mix of R and S in any proportion cannot give 10% minerals. Consider O and R in the proportion x:y ∴ 10x + 5y = 10(x + y) ∴ 5y = 10y, which is not possible. Similarly, Q and S, O and S, and Q and R are not possible. Similarly a mix of three ingredients is not possible. ∴ The only possible mix is that of O and Q in equal proportion. Hence, option 1.
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48. Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? The diet has to be formed by mixing two ingredients. (1) P and Q (2) P and S (3) P and R (4) Q and S (5) R and S Solution: Consider the options. Option 1: P and Q have to be mixed in the proportion 4:1 to achieve 10% fat content. But this does not give 30% protein. Option 2: P and S do not contain fat. Option 3: P and R should be mixed in the proportion 3:1 to achieve 10% fat content. But 30% protein content is not achieved. Option 4: Q and S should be mixed in the proportion 1:4 to achieve 10% fat content and 46% protein content. The cost of this mix per unit would be 6/5. Option 5: R and S should be mixed in the proportion 1:3 to achieve 10% fat content and 50% protein content. The cost per unit of this mix would be 2. Therefore, lowest cost is for Q and S. Hence, option 4. 49. In what proportion should P, Q and S be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost? (1) 2 : 1 : 3 (2) 4 : 1 : 2 (3) 2 : 1 : 4 (4) 3 : 1: 2 (5) 4 : 1 : 1 Solution: P, Q and S contain 80%, 10% and 45% carbohydrates respectively. To achieve 60% carbohydrates, proportion of P should be maximum. Hence, options 1 and 3 are eliminated.
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CAT 2007 Solutions
Option 2: Carbohydrate content = (320 + 10 + 90)/700 = 420/700 = 60% Cost per unit = (200 + 200 + 200)/700 = 6/7 = 0.857 Option 4: Carbohydrate content = (240 + 10 + 90)/600 < 60% Option 5: Carbohydrate content = (320 + 10 + 45)/600 = 62.5% Cost per unit = (200 + 200 + 100)/600 = 5/6 = 0. 833 P, Q and S in the proportion 4 : 1 : 1 has the lowest cost per unit. Hence, option 5. 50. The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible? (1) O and P (2) R and S (3) P and S (4) Q and R (5) O and S Solution: A mixture of O and S in equal proportion satisfies the given constraints as can be seen from the table. Hence, option 5. Carbohydrate O&P R&S P&S Q&R O&S 65 25 62.5 7.5 47.5 Protein 25 50 35 40 40
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Fat 5 20 0 45 5
Minerals 5 5 2.5 7.5 7.5
CAT 2007 Solutions
Section III This section contains 25 questions Directions for Questions 51 to 53: In each question, there are four sentences. Each sentence has pairs of words/phrases that are italicized and highlighted. From the italicized and highlighted word(s)/phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one. 51. The cricket council that was[A]/were[B] elected last March is[A]/are[B] at sixes and sevens over new rules. The critics censored[A]/censured[B] the new movie because of its social inaccessibility. Amit’s explanation for missing the meeting was credulous[A]/credible[B]. She coughed discreetly[A]/discretely[B] to announce her presence. 1) 2) 3) 4) 5) BBAAA AAABA BBBBA AABBA BBBAA
Solution: The first sentence is the easiest to decide. Since the ‘cricket council’ is singular, singular verbs (was and is) are required. Hence the answer choice should begin with A. This eliminates option 1, 3, and 5. Comparing option 2 and 4, the difference is in the third choice – credulous vs. credible. Credulous means ready to believe easily and credible means: offering reasonable grounds for being believed. Hence Amit’s explanation is credible – B. Sequence AAB is option 4. Other confusable options: censor(v): to examine in order to delete anything that is objectionable. Censure(v): criticize. Discrete: distinct; discreet: modest, unnoticeable. Hence, the correct answer is option 4. 52. The further[A]/farther[B] he pushed himself, the more disillusioned he grew. For the crowds it was more of a historical[A]/historic[B] event; for their leader, it was just another day. The old man has a healthy distrust[A]/mistrust[B] for all new technology. This film is based on a real[A]/true [B] story.
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One suspects that the compliment[A]/complement[B] was backhanded. 1) BABAB 2) ABBBA 3) BAABA 4) BBAAB 5) ABABA Solution: Further is temporal and farther is spatial. The choice of A in the first sentence eliminates option 1, 3 and 5. Comparing 2 and 5 (ABBBA vs. ABABA), one can see that the third sentence is decisive. Distrust: misgiving, lack or absence of trust. Mistrust: a lack of confidence or uncertainty; to regard as untrustworthy. The tinge of ‘suspicion’ that colours mistrust eliminates mistrust. Hence distrust is the correct use in the context. Hence, the correct answer is option 5. 53. Regrettably[A]/Regretfully[B] I have to decline your invitation. I am drawn to the poetic, sensual[A]/sensuous[B] quality of her paintings. He was besides[A]/beside[B] himself with rage when I told him what I had done. After brushing against a stationary[A]/stationery[B] truck my car turned turtle. As the water began to rise over[A]/above[B] the danger mark, the signs of an imminent flood were clear. 1) BAABA 2) BBBAB 3) AAABA 4) BBAAB 5) BABAB
Solution: In this set, the last two sentences are the easiest to decide: stationary truck and to rise above are correct uses. The answer choice has to end with AB. Options 1 and 3 are eliminated. Beside oneself with rage is the correct idiom. Hence third sentence is B. Sensuous implies gratification of the senses for the sake of aesthetic pleasure- the sensuous delights of great music. Sensual tends to imply the gratification of the senses or the indulgence of the physical appetites as ends in themselves - a life devoted to sensual pleasures. Poetry is sensuous rather than sensual. Hence the second sentence is B.
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stories whole organizations are personified as actors. But these macro-level stories usually are not told from the perspective of the macro-level participants, because whole organizations cannot narrate their experiences in the first person. (1) More generally, data concerning the identities and relationships of the characters in the story are required, if one is to understand role structure and social networks in which that process is embedded. (2) Personification of a whole organization abstracts away from the particular actors and from traditional notions of level of analysis. (3) The personification of a whole organization is important because stories differ depending on who is enacting various events. (4) Every story is told from a particular point of view, with a particular narrative voice, which is not regarded as part of the deep structure. (5) The personification of a whole organization is a textual device we use to make macro-level theories more comprehensible. Solution: The paragraph briefly is about why stories are structured around focal characters. And why in stories of organizations, organizations have to be personified and focal characters as organizations cannot narrate their experiences. Option 5 concludes this chain of thoughts by saying that this kind of personification is a textual device resorted to bring coherence. Option 1 is incorrect as it continues the first part of the paragraph and is unrelated the second part. Option 2 is incorrect as it talks about abstracting away from the particular whereas the paragraph is talking about particularizing. Options 3 and 4 talk about different points of view, which is irrelevant to the paragraph. Hence, the correct answer is option 5. 58. Nevertheless, photographs still retain some of the magical allure that the earliest daguerreotypes inspired. As objects, our photographs have changed; they have become physically flimsier as they have become more technologically sophisticated. Daguerre produced pictures on copper plates; today many of our photographs never become tangible thins, but instead remain filed away on computers and cameras, part of the digital ether that envelops the modern world. At the same time, our patience for the creation of images has also eroded. Children today are used to being tracked from birth by digital cameras and video recorders and they expect to see the results of their poses and performances instantly. The space between life as it is being lived and life as it is being displayed shrinks to a mere second.
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(1) Yet, despite these technical developments, photographs still remain powerful because they are reminders of the people and things we care about. (2) Images, after all, are surrogates carried into battle by a soldier or by a traveller on holiday. (3) Photographs, be they digital or traditional, exist to remind us of the absent, the beloved, and the dead. (4) In the new era of the digital image, the images also have a greater potential for fostering falsehood and trickery, perpetuating fictions that seem so real we cannot tell the difference. (5) Anyway, human nature being what it is, little time has passed after photography’s inventions became means of living life through images. Solution: ‘Nevertheless ‘at the beginning of the paragraph, and “yet’ at the beginning of option 1 make the paragraph logically complete. Option 1 is the reason why the paragraph is written - to communicate that ‘photographs are still powerful’. The traveler in option 2, the beloved and the dead in option 3, falsehood and trickery in option 4, and the invention and means of living in option 5 do not help conclude the paragraph. Hence, the correct answer is option 1. 59. Mma Ramotswe had a detective agency in Africa, at the foot of Kgale Hill. These were its assets; a tiny white van, two desks, two chairs, a telephone, and an old typewriter. Then there was a teapot, in which Mma Ramotswe - the only private lady detective in Botswana - brewed red bush tea. And three mugs - one for herself, one for her secretary and one for the client. What else does a detective agency really need? Detective agencies rely on human intuition and intelligence, both of which Mma Ramotswe had in abundance. (1) But there was also the view, which again would appear on no inventory. (2) No inventory would ever include those, of course. (3) She had an intelligent secretary too. (4) She was a good detective and a good woman. (5) What she lacked in possessions was more than made up by a natural shrewdness.
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Solution: The paragraph mentions the tangible parts of the inventory that Mma Ramotswe had at the agency, and ‘human intuition and intelligence’. Option 2 concludes the paragraph by stating that ‘no inventory would ever be able to include those. Options 3, 4 and 5 are eliminated in comparison to options 1 and 2 which continue the idea of the inventory. Option 1, though continuing the idea of inventory is far inferior to option 2. The ‘those’ in option 2 scores over option 1. Hence, the correct answer is option 2. Directions for Questions 60 to 62: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question The difficulties historians face in establishing cause-and-effect relations in the history of human societies are broadly similar to the difficulties facing astronomers, climatologists, ecologists, evolutionary biologists, geologists, and palaeontologists. To varying degrees each of these fields is plagued by the impossibility of performing replicated, controlled experimental interventions, the complexity arising from enormous numbers of variables, the resulting uniqueness of each system, the consequent impossibility of formulating universal laws, and the difficulties of predicting emergent properties and future behaviour. Prediction in history, as in other historical sciences, is most feasible on large spatial scales and over long times, when the unique features of millions of small-scale brief events become averaged out. Just as I could predict the sex ratio of the next 1,000 newborns but not the sexes of my own two children, the historian can recognize factors that made inevitable the broad outcome of the collision between American and Eurasian societies after 13,000 years of separate developments, but not the outcome of the 1960 U.S. presidential election. The details of which candidate said what during a single televised debate in October 1960 could have given the electoral victory to Nixon instead of to Kennedy, but no details of who said what could have blocked the European conquest of Native Americans. How can students of human history profit from the experience of scientists in other historical sciences? A methodology that has proved useful involves the comparative method and so-called natural experiments. While neither astronomers studying galaxy formation nor human historians can manipulate their systems in controlled laboratory experiments, they both can take advantage of natural experiments, by comparing systems differing in the presence or absence (or in the strong or weak effect) of some putative causative factor. For example, epidemiologists, forbidden to feed large amounts of salt to people experimentally, have still been able to identify effects of high salt intake by comparing groups of humans who already differ greatly in their salt intake; and cultural
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anthropologists, unable to provide human groups experimentally with varying resource abundances for many centuries, still study long-term effects of resource abundance on human societies by comparing recent Polynesian populations living on islands differing naturally in resource abundance. The student of human history can draw on many more natural experiments than just comparisons among the five inhabited continents. Comparisons can also utilize large islands that have developed complex societies in a considerable degree of isolation (such as Japan, Madagascar, Native American Hispaniola, New Guinea, Hawaii, and many others), as well as societies on hundreds of smaller islands and regional societies within each of the continents. Natural experiments in any field, whether in ecology or human history, are inherently open to potential methodological criticisms. Those include confounding effects of natural variation in additional variables besides the one of interest, as well as problems in inferring chains of causation from observed correlations between variables. Such methodological problems have been discussed in great detail for some of the historical sciences. In particular, epidemiology, the science of drawing inferences about human diseases by comparing groups of people (often by retrospective historical studies), has for a long time successfully employed formalized procedures for dealing with problems similar to those facing historians of human societies. In short, I acknowledge that it is much more difficult to understand human history than to understand problems in fields of science where history is unimportant and where fewer individual variables operate. Nevertheless, successful methodologies for analyzing historical problems have been worked out in several fields. As a result, the histories of dinosaurs, nebulae, and glaciers are generally acknowledged to belong to fields of science rather than to the humanities. 60. Why do islands with considerable degree of isolation provide valuable insights into human history? (1) Isolated islands may evolve differently and this difference is of interest to us. (2) Isolated islands increase the number of observations available to historians. (3) Isolated islands, differing in their endowments and size may evolve differently and this difference can be attributed to their endowments and size. (4) Isolated islands, differing in their endowments and size, provide a good comparison to large islands such as Eurasia, Africa, Americas and Australia. (5) Isolated islands, in so far as they are inhabited, arouse curiosity about how human beings evolved there.
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Solution: The answer is supported by the paragraph beginning “The student of human history can draw on many more natural experiments than just comparisons among the five inhabited continents. Comparisons can also utilize large islands that have developed complex societies in a considerable degree of isolation ….. as well as societies on hundreds of smaller islands and regional societies within each of the continents.” Options 1 and 3 say the same thing. Option 1 is eliminated because the ‘difference’ mentioned in option 1 is explained in 3. Hence option 3 scores over option 1. Option 4 is eliminated because ‘the good comparison to large islands’ is inconsequential to the student of history. The student is more interested in knowing how endowments and size affect societies – as a natural experiment. Option 5 is eliminated because the paragraph says nothing about arousing ‘curiosity about how humans evolved’ as stated in the option. Hence, the correct answer is option 3. 61. According to the author, why is prediction difficult in history? (1) Historical explanations are usually broad so that no prediction is possible. (2) Historical out comes depend upon a large number of factors and hence prediction is difficult for each case. (3) Historical sciences, by their very nature, are not interested in a multitude of minor factors, which might be important in a specific historical outcome. (4) Historians are interested in evolution of human history and hence are only interested in log term predictions. (5) Historical sciences suffer from the inability to conduct controlled experiments and therefore have explanations based on a few long-term factors. Solution: This is directly stated in the passage. “Prediction in history, as in other historical sciences, is most feasible on large spatial scale and over long times, when the unique future of millions of small scale brief events become averaged out.” The answer option is merely the same thing expressed in different (even easier) words. Option 1 is eliminated because of “the complexity arising from enormous numbers of variables, the resulting uniqueness of each system, the consequent impossibility of formulating universal laws, and the difficulties of predicting emergent properties and future behaviour” - in other words the explanations are broad because prediction is not possible and not the other way round. In option 3 ‘not interested’ is first data inadequate (passage does not say not interested) and by implication incorrect, because history is interested “in a multitude of minor factors,” – in order that the average may be worked out over long periods of time.
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Option 4 is factually correct but does not answer the question – why prediction is difficult. Option 5 is also factually correct but does not explain why prediction is difficult –it merely explains the constraints that history faces and how then it operates. Hence, the correct answer is option 2. 62. According to the author, which of the following statements would be true? (1) Students of history are missing significant opportunities by not conducting any natural experiments. (2) Complex societies inhabiting large islands provide great opportunities for natural experiments. (3) Students of history are missing significant opportunities by not studying an adequate variety of natural experiments. (4) A unique problem faced by historians is their inability to establish cause and effect relationships. (5) Cultural anthropologists have overcome the problem of confounding variables through natural experiments. Solution: The answer is directly supported by “The student of human history can draw on many more natural experiments than …. the five inhabited continents. Comparisons can also utilize large islands ….. as well as societies on hundreds of smaller islands and regional societies within each of the continents”. The implication is expressed in option 3. Option 1 is false in “not conducting…” – this is not true in the context of the passage, nor is the author implying it. Option 2 is false – the passage nowhere says that large islands provide ‘great’ opportunities for natural experiments” – they are one of the opportunities among many. The problem faced by historians is not ‘unique’ as stated in option 4. The passage explicitly states that it is faced by several other studies mentioned in the first sentence itself. There is no data in the passage (even by implication) about cultural anthropologists. Hence option 5 too is eliminated. Hence, the correct answer is option 3. Directions for Questions 63 to 65: In each question, there are five sentences or parts of sentences that form a paragraph. Identify the sentence(s) or part(s) of sentence(s) that is/are correct in terms of grammar and usage. Then, choose the most appropriate option.
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63. A. When I returned to home, I began to read B. everything I could get my hand on about Israel. C. That same year Israel’s Jewish Agency sent D. a Shaliach a sort of recruiter to Minneapolis. E. I became one of his most active devotees. (1) C & E (2) C only (3) E only (4) B, C & E (5) C, D & E Solution: Statement A is incorrect because of the phrase, ‘returned to home’. The correct usage is ‘returned home’. Statement B is incorrect because the idiom is ‘get one’s hands on’ and not ‘hand on’. Statement C is correct. Statement D is incorrect because there should be a hyphen or a comma after a Shaliach. (a Shaliach – a sort of recruiter to Minneapolis.) “a sort of” though rather informal, is correct usage. Statement E is correct. Hence, the correct answer is option 1. 64. A. So once an economy is actually in recession, B. The authorities can, in principle, move the economy C. Out of slump - assuming hypothetically D. That they know how to - by a temporary stimuli. E. In the longer term, however, such policies have no affect on the overall behaviour of the economy. (1) A, B & E (2) B, C & E (3) C & D (4) E only (5) B only Solution: Statement A is incorrect – The use of the word, ‘so’ is redundant and inappropriate. (So and once, in the context are adverbs – one of them is enough). Statement B is correct.
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Statement C is incorrect because the use of ‘assuming hypothetically’ makes it redundant. One can either assume or hypothesize, but ‘assuming hypothetically’ is meaningless. Statement D is incorrect in the plural use of ‘stimuli’ instead of ‘stimulus’ with the article ‘a’. Statement E should have been ‘effect’ instead of ‘affect’. Hence, the correct answer is option 5. 65. A. It is sometimes told that democratic B. government originated in the city-states C. of ancient Greece. Democratic ideals have been handed to us from that time. D. In truth, however, this is an unhelpful assertion. E. The Greeks gave us the word, hence did not provide us with a model. (1) A, B & D (2) B, C & D (3) B & D (4) B only (5) D only Solution: Statement A is incorrect because the verb ‘told’ is incorrectly used. The verb ‘said’ should be used instead. There is no error in statement B. Statement C contains the incorrect idiom ‘handed to us’ instead of ‘handed down to us’. Statement D is correct. Statement E is incorrect because the word, ‘hence’ is used as a conjunction, whereas it is an adverb. The use of a proper conjunction (e.g. and / but) will improve the sentence. Hence the correct answer is option 3. Directions for Questions 66 to 68: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. Human Biology does nothing to structure human society. Age may enfeeble us all, but cultures vary considerably in the prestige and power they accord to the elderly. Giving birth is a necessary condition for being a mother, but it is not sufficient. We expect mothers to behave in maternal ways and to display appropriately maternal sentiments. We prescribe a clutch of norms or rules that govern the role of a mother. That the social role is
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independent of the biological base can be demonstrated by going back three sentences. Giving birth is certainly not sufficient to be a mother but, as adoption and fostering show, it is not even necessary! The fine detail of what is expected of a mother or a father or a dutiful son differs from culture to culture, but everywhere behaviour is coordinated by the reciprocal nature of roles. Husbands and wives, parents and children, employers and employees, waiters and customers, teachers and pupils, warlords and followers; each makes sense only in its relation to the other. The term ‘role’ is an appropriate one, because the metaphor of an actor in a play neatly expresses the rule-governed nature or scripted nature of much of social life and the sense that society is a joint production. Social life occurs only because people play their parts (and that is as true for war and conflicts as for peace and love) and those parts make sense only in the context of the overall show. The drama metaphor also reminds us of the artistic licence available to the players. We can play a part straight or, as the following from J.P. Sartre conveys, we can ham it up. Let us consider this waiter in the cafe. His movement is quick and forward, a little too precise, a little too rapid. He comes towards the patrons with a step a little too quick. He bends forward a little too eagerly; his voice, his eyes express an interest a little too solicitous for the order of the customer. Finally there he returns, trying to imitate in his walk the inflexible stiffness of some kind of automaton while carrying his tray with the recklessness of a tightrope-walker....All his behaviour seems to us a game....But what is he playing? We need not watch long before we can explain it: he is playing at being a waiter in a cafe. The American sociologist Erving Goffman built an influential body of social analysis on elaborations of the metaphor of social life as drama. Perhaps his most telling point was that it is only through acting out a part that we express character. It is not enough to be evil or virtuous; we have to be seen to be evil or virtuous. There is distinction between the roles we play and some underlying self. Here we might note that some roles are more absorbing than others. We would not be surprised by the waitress who plays the part in such a way as to signal to us that she is much more than her occupation. We would be surprised and offended by the father who played his part ‘tongue in cheek’. Some roles are broader and more far-reaching than others. Describing someone as a clergyman or faith healer would say far more about that person than describing someone as a bus driver.
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Solution: “There is distinction between the roles we play and some underlying self. Here we might note that some roles are more absorbing than others. We would not be surprised by the waitress who plays the part in such a way as to signal to us that she is much more than her occupation. We would be surprised and offended by the father who played his part ‘tongue in cheek’" (insincerely). The father’s self is denied by his identification with his biological relationship. If this does not happen, if a father behaves in a tongue in cheek manner, we are offended. If biological relations structured human society, it is enough to be a biological father to be accepted by society. His behavior (and with it, the reciprocal relationship) then becomes unimportant. All the other options support the fact that ‘reciprocal relationship’ structure human society. Hence, the correct answer is option 2. 68. It has been claimed in the passage that “some roles are more absorbing than others”. According to the passage, which of the following seem(s) appropriate reason(s) for such a claim? A. Some roles carry great expectations from the society preventing manifestation of the true self. B. Society ascribes so much importance to some roles that the conception of self may get aligned with the roles being performed. C. Some roles require development of skill and expertise leaving little time for manifestation of self. (1) A only (2) B only (3) C only (4) A & B (5) B & C Solution: The answer comes from the last paragraph where three examples are given, the father, the waitress, and the priest. The example of the priest makes statement A correct. (There is so much expectation from the society that the priest’s true self is not revealed at all). The father’s example makes statement B correct. (The father’s self gets aligned with his biological relationship and the self is denied). Statement C is incorrect in that the passage does not discuss the development of skill as a reason for the denial of the self. Hence, the correct answer is option 4.
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Directions for Questions 69 to 72: In each question, there are five sentences/paragraphs. The sentence/ paragraph labelled A is in its correct place. The four that follow are labelled B, C, D and E, and need to be arranged in the logical order to form a coherent paragraph/passage. From the given options, choose the most appropriate option. 69. A. In America, highly educated women, who are in stronger position in the labour market than less qualified ones, have higher rates of marriage than other groups. B. Some work supports the Becker thesis, and some appears to contradict it. C. And, as with crime, it is equally inconclusive. D. But regardless of the conclusion of any particular piece of work, it is hard to establish convincing connections between family changes and economic factors using conventional approaches. E. Indeed, just as with crime, an enormous academic literature exists on the validity of the pure economic approach to the evolution of family structures. (1) BCDE (2) DBEC (3) BDCE (4) ECBD (5) EBCD Solution: When the four statements are studied well, it is very easy to establish that EC and BD are mandatory pairs. Only statements E and C contain the idea of ‘crime’. Hence one cannot place any other statement along with statement E, but statement C. In the same way, statements B and D both have reference to written ‘piece of work’, making BD in that order mandatory. Once this is noticed, placing EC and BD in that order with the help of A (fixed) is easy. Hence, the correct answer is option 4. 70. A. Personal experience of mothering and motherhood are largely framed in relation to two discernible or “official” discourses: the “medical discourse and natural childbirth discourse”. Both of these tend to focus on the “optimistic stories” of birth and mothering and underpin stereotypes of the “godmother”. B. At the same time, the need for medical expert guidance is also a feature for contemporary reproduction and motherhood. But constructions of good mothering
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have not always been so conceived - and in different contexts may exist in parallel to other equally dominant discourses. C. Similarly, historical work has shown how what are now taken-for-granted aspects of reproduction and mothering practices result from contemporary “pseudoscientific directives” and “managed constructs”. These changes have led to a reframing of modern discourses that pattern pregnancy and motherhood leading to an acceptance of the need for greater expert management. D. The contrasting, overlapping and ambiguous strands within these frameworks focus to varying degrees on a woman’s biological tie to her child and predisposition to instinctively know and be able to care for her child. E. In addition, a third, “unofficial popular discourse” comprising “old wives” tales and based on maternal experiences of childbirth has also been noted. These discourses have also been acknowledged in work exploring the experiences of those who apparently do not “conform” to conventional stereotypes of the “good mother” (1) EDBC (2) BCED (3) DBCE (4) EDCB (5) BCDE Solution: The "two discernible" or "official discourses" makes it compulsory to place statement E after statement A, because statement E talks about "a third unofficial discourse". (In other words if not placed next to statement A, statement E cannot be placed anywhere else). AE is the first mandatory pair. 'These frameworks' in statement D is explained in statement E so that statement D unless placed next to statement E, will not make sense. (In other words ED too is mandatory.) The idea of motherhood from statement D (biological tie) is continued in statement B. Thus the links in EDB are most obvious. Statements C and B too are clearly linked because statement B ends with reference to 'dominant discourse' and statement C begins with 'historical work' making EDBC most logical sequence. Hence, the correct answer is option 1. 71. A. Indonesia has experienced dramatic shifts in its formal governance arrangements since the fall of President Soeharto and the close of his centralized, authoritarian "New Order" regime in 1997. B. The political system has taken its place in the nearly 10 years since Reformasi began. It has featured the active contest for political office among a proliferation of parties
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works do not differ from one another like a new horizon from a new horizon, but like a madonna from a madonna. The periods of art which are most vigorous in creative passion seem to occur when the established pattern of experience loosens its rigidity without as yet losing its force. Such a period was the Renaissance, and Shakespeare its poetic consummation. Then it was as though the discipline of the old order gave depth to the excitement of the breaking away, the depth of job and tragedy, of incomparable conquests and irredeemable losses. Adventurers of experience set out as though in lifeboats to rescue and bring back to the shore treasures of knowing and feeling which the old order had left floating on the high seas. The works of the early Renaissance and the poetry of Shakespeare vibrate with the compassion for live experience in danger of dying from exposure and neglect. In this compassion was the creative genius of the age. Yet, it was a genius of courage, not of desperate audacity. For, however elusively, it still knew of harbours and anchors, of homes to which to return, and of barns in which to store the harvest. The exploring spirit of art was in the depths of its consciousness still aware of a scheme of things into which to fit its exploits and creations. But the more this scheme of things loses its stability, the more boundless and uncharted appears the ocean of potential exploration. In the blank confusion of infinite potentialities flotsam of significance gets attached to jetsam of experience; for everything is sea, everything is at sea .... The sea is all about us; The sea is the land's edge also, the granite Into which it reaches, the beaches where it tosses Its hints of earlier and other creation ... - and Rilke tells a story in which, as in T.S. Eliot's poem, it is again the sea and the distance of 'other creation' that becomes the image of the poet's reality. A rowing boat sets out on a difficult passage. The oarsmen labour in exact rhythm. There is no sign yet of the destination. Suddenly a man, seemingly idle, breaks out into song. And if the labour of the oarsmen meaninglessly defeats the real resistance of the real waves, it is the idle single who magically conquers the despair of apparent aimlessness. While the people next to him try to come to grips with the element that is next to them, his voice seems to bind the boat to the farthest distance so that the farthest distance draws it towards itself. 'I don't know why and how,' is Rilke's conclusion, 'but suddenly I understood the situation of the poet, his place and function in this age. It does not matter if one denies him every place - except this one. There one must tolerate him.' 73. In the passage, the expression “like a madonna from a madonna” alludes to (1) The difference arising as a consequence of artistic license.
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(2) The difference between two artistic interpretations. (3) The difference between ‘life’ and ‘interpretation of life’. (4) The difference between ‘width’ and ‘depth’ of creative power. (5) The difference between the legendary character and the modern day singer. Solution: The lines, “… the art wield their creative power not so much in width as in depth. They do not create new experience, but deepen and purify the old. Their works do not differ from one another like a new horizon from a new horizon…” tell us that the works of art do not differ in their ‘width’ and ’depth’ (as mentioned in option 4) ‘life’ and its ‘interpretation’ (as mentioned in option 3), but are merely different interpretations of the ‘old’ experience as one painting of Madonna (Virgin Mary, the mother of Jesus) differs from another version. This eliminates options 3 and 4. The consequence of artistic license is not discussed in the passage so this eliminates option 1. Option 5 is ridiculous because the Madonna here does not refer to the modern day singer. Hence, the correct answer is option 2. 74. The sea and ‘other creation’ leads Rilke to (1) Define the place of the poet in his culture. (2) Reflect on the role of the oarsman and the singer. (3) Muse on artistic labour and its aimlesseness. (4) Understand the elements that one has to deal with. (5) Delve into natural experience and real waves. Solution: Rilke’s conclusion is repeated almost verbatim in option 1. “I don’t know why and how,’ is Rilke’s conclusion, ‘but suddenly I understood the situation of the poet, his place and function in this age.” These are the concluding words of Rilke from the passage after the example of the ‘sea’ and ‘the other creation’ mentioned in the question. Option 2 is mundane and quotes the example itself and not its purpose. Option 3 is abstract, and an ‘aimlessness’ cannot be attributed either to the oarsmen or the singer. Option 4 ‘understanding the elements’ is not the purpose of either the oarsmen or the singer. Option 5 is vague; the passage does not explain either natural experience or real waves. Hence, the correct answer is option 1.
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75. According to the passage, the term “adventurers of experience” refers to (1) Poets and artists who are driven by courage. (2) Poets and artists who create their own genre. (3) Poets and artists of the Renaissance. (4) Poets and artists who revitalize and enrich the past for us. (5) Poets and artists who delve in flotsam and jetsam in sea. Solution: “Adventurers of experience set out as though in lifeboats to rescue and bring back to the shore treasures of knowing and feeling which the old order had left floating on the high seas. The work of the early Renaissance and the poetry of Shakespeare vibrate with the compassion for live experience in danger of dying from exposure and neglect. In this compassion was the creative genius of the age.” Renaissance artists are cited as examples of ‘adventurers of experience’. These italicized words make option 4 right. As a result, option 3 is eliminated as being merely an example. Driven by courage (option1), create their own genre (option 2) are partial and not the intended meaning of the writer. This eliminates options 1 and 2. Option 5 is also related to the example in a literal way, whereas the writer is being symbolic in calling the artists adventurers. This eliminates option 5. Hence, the correct answer is option 4.
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# What do you mean by Celsius scale?
## What do you mean by Celsius scale?
Celsius, also called centigrade, scale based on 0° for the freezing point of water and 100° for the boiling point of water. Invented in 1742 by the Swedish astronomer Anders Celsius, it is sometimes called the centigrade scale because of the 100-degree interval between the defined points.
### What is Celsius scale short answer?
The Celsius scale, also known as the centigrade scale, is a temperature scale based on 0o for the freezing point of water and 100o for the boiling point of water.
#### What is an example of Celsius scale?
Examples. On the Celsius scale, water freezes at 0° and boils at 100°. Room temperature is about 20 °C. Absolute zero (the coldest possible temperature) is -273.15 °C.
What is the difference between the Fahrenheit and Celsius scales?
Celsius scale, or centigrade scale, is a temperature scale that is based on the freezing point of water at 0°C and the boiling point of water at 100°C. Fahrenheit scale is a temperature scale that is based on the freezing point of water at 32°F and the boiling point of water at 212°F.
What is meant by temperature scale?
Definition of temperature scale 1 : the scale of degrees on a thermometer. 2 : a system of reckoning temperature the centigrade temperature scale the Kelvin temperature scale the international temperature scale.
## What is Celsius used for?
Celsius is a scale (sometimes called Centigrade) that is used in many countries as a unit of measurement for temperature. The Celsius scale was created by a Swedish astronomer called Anders Celsius. On the scale, 0 degrees (°) Celsius is the melting point of pure water at sea level, at a normal pressure.
### What’s hotter Fahrenheit or Celsius?
In the Celsius scale there are 100 degrees between the freezing point and the boiling point of water compared to 180 degrees in the Fahrenheit scale. This means that 1 °C = 1.8 °F (check the section about temperature differences below).
#### How does the Celsius scale work?
The Celsius scale is based on a derived unit defined by assigning the temperatures of 0°C and 100°C to the freezing and boiling points of water, respectively, at 1 atm pressure. More precisely, the Celsius scale is defined by absolute zero and the triple point of pure water.
Is Celsius scale linear?
Fahrenheit and Celsius scales begin at different arbitrary points, so there cannot be a simple ratio between the two. Clearly, both values are linear, yet there is not a simple ratio between them.
What are some countries that use the Celsius scale?
Antigua and Barbuda
• Saint Kitts and Nevis
• British Virgin Islands
• Montserrat
• Belize
• Bermuda
• Turks and Caicos
• ## What does each degree on the Celsius scale represent?
The degree Celsius can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval, a difference between two temperatures or an uncertainty. The unit was known until 1948 as “centigrade” from the Latin centum translated as 100 and gradus translated as “steps”.
### Who devised the Celsius scale and in what year?
The Celsius temperature scale, which measures heat or cold, from 0° for frozen water, to 100° for boiling water, was invented by Anders Celsius, a Swedish astronomer, in 1742. He named the scale the centigrade scale, and people may occasionally still see temperatures listed with this term.
#### What is the difference between the Celsius and Kelvin scale?
The primary difference between the centigrade, or Celsius, scale and the absolute, or Kelvin, scale is in their respective starting points. The Celsius scale sets the freezing point of pure water at sea level as 0, while 0 degrees Kelvin is absolute zero, the coldest temperature theoretically possible.
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# What is an example of a ratio question?
## What is an example of a ratio question?
What is an example of a ratio question? A simple ratio question might be working out the ratio of boys and girls in a class. If there are 10 boys and 12 girls you could divide each number by a common denominator (in this case 2). So you get the answer that there’s a 5:6 ratio of boys to girls.
What is an example of ratios and rates?
A ratio is a comparison of two numbers. A ratio can be written using a colon, 3:5 , or as a fraction 35 . A rate , by contrast, is a comparison of two quantities which can have different units. For example 5 miles per 3 hours is a rate, as is 34 dollars per square foot.
### How do you find ratio and rate?
Use the formula r = d/t. Your rate is 24 miles divided by 2 hours, so: r = 24 miles ÷ 2 hours = 12 miles per hour.
What is a maths rate?
A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.
## What are 3 examples of rates?
Distance per unit time, quantity per cost, number of heartbeats per minute are three examples of rate.
What is the formula to calculate rate?
Step 1: To calculate your interest rate, you need to know the interest formula I/Pt = r to get your rate. Here, I = Interest amount paid in a specific time period (month, year etc.) You should remember this equation to calculate your basic interest rate.
### What is the ratio of 5 to 5?
Ratio of 5 to 5 (5:5) A ratio of 5 to 5 can be written as 5 to 5, 5:5, or 5/5. Furthermore, 5 and 5 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on. A ratio of 5 to 5 simply means that for every 5 of something, there are 5 of something else, with a total of 10.
What are some examples of rates?
## What is a rate example?
Is a ratio always a rate?
Both rates and ratios are a comparison of two numbers. A rate is simply a specific type of ratio. The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
### How do I calculate simple interest rate?
Simple Interest is calculated using the following formula: SI = P × R × T, where P = Principal, R = Rate of Interest, and T = Time period. Here, the rate is given in percentage (r%) is written as r/100. And the principal is the sum of money that remains constant for every year in the case of simple interest.
What is the ratio of 9 to 2?
Ratio of 9 to 2 (9:2) A ratio of 9 to 2 can be written as 9 to 2, 9:2, or 9/2. Furthermore, 9 and 2 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on. A ratio of 9 to 2 simply means that for every 9 of something, there are 2 of something else, with a total of 11.
Posted in Lifehacks
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# Making Good Sliders
In the most basic form, all you need is a bézier curve.
From Ephemeral,
always align slider endpoints to the smallest possible value - that is, if you drag them any further backwards, the slider will shorten. the point will center itself in the slider end and will make attaining passable curves much easier to accomplish.
Also, doing this makes reverse selection on sliders not fuck them up.
Which is a good thing.
## Arcs
Use essentially the same technique for any sliders symmetrical in one axis.
This is the easiest shape to make.
You basically place all of your points symmetrically in the grid first of all.
Select it and press `Ctrl` + `H` when you think you have it accurate to make sure the points are on symmetrical grids.
Then move the points around until the slider is the right length and falls just a little short of the final point.
It's important that whenever you move a point, you move the corresponding point exactly the same way to keep all the points symmetrical with each other.
Make sure you `Ctrl` + `H` often to check you haven't made a mistake.
To make the slider-end and endpoint line up hold shift to disable grid snap and move the top point down until the slider-end is right on the last point.
When you think it's perfect, select and `Ctrl` + `H` a few times and see if the endpoint moves around.
If it doesn't, congratulations, you have a beautiful slider.
Show it off to your friends.
If it does, move the top point around until it does.
If you want an arc at an angle, it's usually easiest to make it upright as above, then `Edit`, then `Rotate By...` to make it the angle you want.
## Waves
Use essentially the same technique for any sliders that are rotationally symmetrical.
Waves are made very similarly to arcs, only your points should be rotationally symmetrical with each other as opposed to horizontally flipped.
If you press `Ctrl` + `H` + `J` it rotates the slider by 180 Ddgrees so you can check the points correspond.
To line the slider-end and endpoint up choose two corresponding symmetrical points.
Disable grid snap and move them both in by a tiny bit at a time until the slider-end and last point are right on top of each other.
## Beat Blankets
Main page: Blanket Combos
Blankets are easiest to do if you eyeball the slider first of all to get it roughly correct, then scroll to a point on the timeline where the approach circle of the beat lines up with the closest edge of the slider's startpoint.
It may help to go into 1/8 snap to get it just right.
Then just tweak the points until the whole slider lines up with the approach circle as perfectly as you can.
Keep in mind that if you want a slider to blanket and be perfectly symmetrical, worry about symmetry first then adjust the points symmetrically to improve the blanket.
From Gonzvlo,
as a variation of beat blankets, sometimes I use a spinner to make nice circles.
## Circles
Courtesy of mm201.
The number of control points you want depends on the angle covered by your arc:
• 0 degrees: 2 points.
• 0 degrees - 20 degrees: 3 points.
• 20 degrees - 170 degrees: 4 points.
• 170 degrees - 200 degrees: 5 points.
• 200 degrees - 300 degrees: 6 points.
• 300 degrees - 350 degrees: 7 points.
None of this is really exact, just a general idea.
Similar to waves, the further the control point is from the start/end in order, the further away from the curve it goes.
Make sure the first and last control lines are pointed in the direction you want your loop to begin at.
The others, just adjust by eye until it's mostly round.
Using an approach circle as a guide can help with this.
Like with most shapes, keep one (two if the number of points is even) control point to take out of grid snap so you can line up the endpoint.
## Elbows
Use the same technique for any slider with straight bits and curved bits.
When you want a slider with a transition between a curved bit and a straight bit you use a red point where it switches.
The most important thing is to always put the red point and points on either side in a straight line.
Like exactly straight.
Get a ruler if you have to.
We don't want any sharp bends here kthx.
But yeah it's pretty straightforward apart from that.
## Hearts
Use same technique for any slider which is symmetrical, but the startpoint is on the centre line.
A nice shape to use sometimes.
Here is how you make one.
### How to make a heart shape
First, make a basic heart shape, slightly longer than you need, with both the start and end points in the same place at the bottom.
Try and copy these points roughly if you're having trouble.
Putting just a redpoint at the top is fine, but I prefer to use an elbow curve :P
Next, copy and paste this slider to the tick immediately after itself and horizontal flip like so.
Then grab the endpoint of the first slider and pull it back to the length you want your slider to be.
See how it's asymmetrical and ugly?
Well mess with the points on the tail half of the slider until it lines up perfectly with the slider behind.
If you managed all that, you're done!
Delete the slider behind and edit/scale by if you want to fill any gaps.
## Wiggles
There are a couple of ways to do this, depending on what kind of wiggle you're after.
### Type 1
Start and end pointing the same way.
The important thing here is that each arc that make up the wiggle is made up of four points, and as you get closer to the centre the taller the four points need to be.
Once you have the basic shape, it's just messing around and eyeballing until it looks even and the tail end of the slider lines up on the last point.
As with arcs, don't forget to be `Ctrl` + `H`ing all the time to make sure the points are symmetrical.
Other than that, it's mostly practice.
Once you've made a few nice looking wiggles you'll be able to knock them out in no time.
### Type 2
Start and end pointing different ways.
Similarly to type 1, each arc is made up of four points, but in my experience it helps if they're kinda twisted round, like in the image above.
These are rotationally symmetrical, like waves, so use `Ctrl` + `H` + `J` to check points.
### Type 3
Super Tight Wiggles.
Sometimes wiggles are just too tight to use the above method, so red-points are necessary.
Make sure that the points of each section between each pair of red-points are identical, apart from the end ones.
You can check this by duplicating the slider and moving them around, checking it lines up all the way along, or by simply counting grids.
Also, make sure that each redpoint and the two points either side make a perfect straight line, to avoid unwanted bumps.
The sections towards the end really need to be eyeballed, and should be what you adjust when you want to make the tail end land on the last point.
This just takes a lot of messing around, but hopefully you'll get there eventually.
## Loops
An easier said than done kind of slider.
The things to remember when forming loops is that the points go up a lot further than the loop does:
• The further each point is from the ends, the further away it needs to be from the slider.
The biggest issue I see with people's loops are the hole.
You're looking for an open, rounded teardrop shape like the above slider.
If the hole of the loop looks like any of these, your loop isn't as awesome as the above screenshot:
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# 差分约束系统的学习 poj1364（bellman和spfa）
1701人阅读 评论(2)
【概念】：对于一个序列。
【学习】：
B - A <= c (1)
C - B <= a (2)
C - A <= b (3)
我们想要知道C - A的最大值，通过(1) + (2)，可以得到 C - A <= a + c，所以这个问题其实就是求min{b, a+c}。将上面的三个不等式按照 三-1 数形结合 中提到的方式建图，如图三-2-1所示。
我们发现min{b, a+c}正好对应了A到C的最短路，而这三个不等式就是著名的三角不等式。将三个不等式推广到m个，变量推广到n个，就变成了n个点m条边的最短路问题了。
【例题】poj1364
Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 13843 Accepted: 4920
Description
Once, in one kingdom, there was a queen and that queen was expecting a baby. The queen prayed: If my child was a son and if only he was a sound king.'' After nine months her child was born, and indeed, she gave birth to a nice son.
Unfortunately, as it used to happen in royal families, the son was a little retarded. After many years of study he was able just to add integer numbers and to compare whether the result is greater or less than a given integer number. In addition, the numbers had to be written in a sequence and he was able to sum just continuous subsequences of the sequence.
The old king was very unhappy of his son. But he was ready to make everything to enable his son to govern the kingdom after his death. With regards to his son's skills he decided that every problem the king had to decide about had to be presented in a form of a finite sequence of integer numbers and the decision about it would be done by stating an integer constraint (i.e. an upper or lower limit) for the sum of that sequence. In this way there was at least some hope that his son would be able to make some decisions.
After the old king died, the young king began to reign. But very soon, a lot of people became very unsatisfied with his decisions and decided to dethrone him. They tried to do it by proving that his decisions were wrong.
Therefore some conspirators presented to the young king a set of problems that he had to decide about. The set of problems was in the form of subsequences Si = {aSi, aSi+1, ..., aSi+ni} of a sequence S = {a1, a2, ..., an}. The king thought a minute and then decided, i.e. he set for the sum aSi + aSi+1 + ... + aSi+ni of each subsequence Si an integer constraint ki (i.e. aSi + aSi+1 + ... + aSi+ni < ki or aSi + aSi+1 + ... + aSi+ni > ki resp.) and declared these constraints as his decisions.
After a while he realized that some of his decisions were wrong. He could not revoke the declared constraints but trying to save himself he decided to fake the sequence that he was given. He ordered to his advisors to find such a sequence S that would satisfy the constraints he set. Help the advisors of the king and write a program that decides whether such a sequence exists or not.
Input
The input consists of blocks of lines. Each block except the last corresponds to one set of problems and king's decisions about them. In the first line of the block there are integers n, and m where 0 < n <= 100 is length of the sequence S and 0 < m <= 100 is the number of subsequences Si. Next m lines contain particular decisions coded in the form of quadruples si, ni, oi, ki, where oi represents operator > (coded as gt) or operator < (coded as lt) respectively. The symbols si, ni and ki have the meaning described above. The last block consists of just one line containing 0.
Output
The output contains the lines corresponding to the blocks in the input. A line contains text successful conspiracy when such a sequence does not exist. Otherwise it contains text lamentable kingdom. There is no line in the output corresponding to the last null'' block of the input.
Sample Input
4 2
1 2 gt 0
2 2 lt 2
1 2
1 0 gt 0
1 0 lt 0
0
Sample Output
lamentable kingdom
successful conspiracy
【题意】：
【解析】：
bellman写法中可以省略超级源点，直接将dis数组清为0即可。
【代码】bellman和spfa（后者效率高）
#include<stdlib.h>
#include<stdio.h>
#include<string.h>
#include<queue>
using namespace std;
struct node{
int u,to,len,next;
}e[10101];
int n,m,cnt;
int dis[102];
int in[102];//记录入度
{
}
int bellman()
{
memset(dis,0,sizeof(dis));
//收缩操作
for(int i=0;i<=n;i++)
for(int j=0;j<cnt;j++)
if(dis[e[j].to]>dis[e[j].u]+e[j].len)
dis[e[j].to]=dis[e[j].u]+e[j].len;
for(int j=0;j<cnt;j++)
if(dis[e[j].to]>dis[e[j].u]+e[j].len)
return 0;
return 1;
}
int main()
{
while(scanf("%d",&n),n)
{
scanf("%d",&m);
memset(in,0,sizeof(in));
cnt=0;
while(m--)
{
int u,len,k; char s[9];
scanf("%d%d%s%d",&u,&len,s,&k);//sum(au~au+len)
if(s[0]=='g')//>要转<=
else
}
int ans=bellman();
if(ans)puts("lamentable kingdom");
else puts("successful conspiracy");
}
}
#include<stdlib.h>
#include<stdio.h>
#include<string.h>
#include<queue>
using namespace std;
struct node{
int u,to,len,next;
}e[10101];
int n,m,cnt;
int dis[102];
int in[102];//记录入度
{
}
int spfa(int s)
{
memset(dis,0x3f,sizeof(dis));
memset(in,0,sizeof(in));
queue<int>q;
q.push(s);
dis[s]=0;
while(!q.empty())
{
int u=q.front();q.pop();
{
int v=e[i].to;
if(dis[v]>dis[u]+e[i].len)
{
dis[v]=dis[u]+e[i].len;
q.push(v);
in[v]++;
if(in[v]>n+1)return 0;
}
}
}
return 1;
}
int main()
{
while(scanf("%d",&n),n)
{
scanf("%d",&m);
memset(in,0,sizeof(in));
cnt=0;
while(m--)
{
int u,len,k; char s[9];
scanf("%d%d%s%d",&u,&len,s,&k);//sum(au~au+len)
if(s[0]=='g')//>要转<=
else
}
//建超级源点
for(int i=0;i<=n;i++)//注意前面建的图实际上有n+1个点
int ans=spfa(n+2);
if(ans)puts("lamentable kingdom");
else puts("successful conspiracy");
}
}
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The Physics
Hypertextbook
Opus in profectus
# Forces in Two Dimensions
## Problems
### practice
1. A 4.5 kg Canada goose is about to take flight. It starts from rest on the ground, but after a single step it is completely airborne. After 2.0 s of horizontal flight the bird has reached a speed of 6.0 m/s (fast enough to stay aloft, but not so fast that we need to worry about air resistance… at first).
1. Draw a free body diagram of the goose in flight.
2. Determine the following quantities for the goose in flight…
1. its acceleration
2. its weight
3. the magnitude and direction of the net force acting on it
4. the magnitude of the upward lift provided by its wings
5. the magnitude of the forward thrust provided by its wings
3. Any object moving through the air will experience air resistance. We just decided to ignore it temporarily. If we now admit that air resistance was present to some extent, how will this change the computed values of…
1. the acceleration?
2. the weight?
3. the net force?
4. the lift?
5. the thrust?
• All the measurements given in the problem are still valid for part c of this problem. The mass is still 4.5 kg and the bird still accelerates from rest to 6.0 m/s in 2.0 s.
2. A laboratory cart (m1 = 500 g) is pulled horizontally across a level track by a lead weight (m2 = 25 g) suspended vertically off the end of a pulley as shown in the diagram below. (Assume the string and pulley contribute negligible mass to the system and that friction is kept low enough to be ignored.)
1. Draw a free body diagram for…
1. the cart
2. the weight
2. Determine…
1. the acceleration of the system
2. the tension in the string
3. A 100 kg wooden crate rests on a wooden ramp with an adjustable angle of inclination.
1. Draw a free body diagram of the crate.
2. If the angle of the ramp is set to 10°, determine…
1. the component of the crate's weight that is perpendicular to the ramp
2. the component of the crate's weight that is parallel to the ramp
3. the normal force between the crate and the ramp
4. the static friction force between the crate and the ramp
3. At what angle will the crate just begin to slip?
4. If the angle of the ramp is set to 30°, determine…
1. the component of the crate's weight that is perpendicular to the ramp
2. the component of the crate's weight that is parallel to the ramp
3. the normal force between the crate and the ramp
4. the kinetic friction force between the crate and the ramp
5. the net force on the crate
6. the acceleration of the crate
4. A pendulum can be used as an inexpensive accelerometer by a passenger in a car, airplane, roller coaster, or other vehicle. When the vehicle isn't accelerating, the pendulum will hang vertically. When the vehicle is accelerating, the pendulum will hang at an angle. Let m be the mass of the pendulum bob, be its length, a be the acceleration of the vehicle, and θ be the angle the pendulum deviates from the vertical.
1. Draw a free body diagram for the pendulum bob.
2. Derive an equation for acceleration of the vehicle in terms of the quantities given and known constants.
### disorganized
1. The T-38 Talon is a small (14 × 4 × 8 m), lightweight (4000 kg), twin-engine, high-altitude, supersonic jet used by various US Department of Defense groups and NASA for training purposes.
1. A T-38 requires 6670 N of thrust to fly at a constant horizontal velocity 300 m/s. Determine the following quantities for the T-38 at this moment…
1. the weight
2. the lift provided by the wings
3. the aerodynamic drag
2. The pilot has been instructed to accelerate horizontally at 0.10 g. Determine…
1. the new thrust of the engines (assuming the drag remains constant)
2. the time it takes to reach 360 m/s
2. A group of students in a physics class set up the experiment shown in the diagram below. A laboratory cart (m1 = 500 g) on a level track is connected by a horizontal string that runs over a pulley to a vertically suspended lead weight (m2 = 25 g). Friction on the cart is not negligible in this experiment. (Assume the string and pulley contribute negligible mass to the system, however.)
1. Draw a free body diagram for…
1. the lab cart
2. The students first use a cart with very sticky wheels and nothing moves. Determine…
1. the weight of the lead weight
2. the tension in the string connecting the weight to the cart
3. the friction force acting on the cart
3. The students find a small piece of debris lodged in one of the wheels and remove it. This reduces the fiction, but not to the point where it can be ignored. They perform the experiment and measure an acceleration of 0.40 m/s2. Determine…
1. the tension in the string
2. the new friction force acting on the cart
3. A laboratory cart (m1 = 500 g) rests on an inclined track (θ = 9°). It is connected to a lead weight (m2 = 100 g) suspended vertically off the end of a pulley as shown in the diagram below. (Assume the string and pulley contribute negligible mass to the system and that friction is kept low enough to be ignored.)
1. Draw a free body diagram for…
1. the laboratory cart
2. Determine…
1. the acceleration of the system (magnitude and direction)
2. the tension in the string
4. A kind of Atwood's machine is built from two cylinders of mass m1 and m2; a cylindrical pulley of mass m3 and radius r; a light, frictionless axle; and a piece of light, unstretchable string. The heavier mass m1 is held above the floor a height h and then relased from rest.
1. Draw a free body diagram showing all the forces acting on…
1. the heavier mass
2. the lighter mass
2. Determine…
1. the acceleration of the system
2. the tension in the string
3. the time it takes for the heavier mass to reach the floor
4. the speed of the system when the heavier mass hits the floor
5. A 61 kg skateboarder standing on a skateboard accelerates at a rate of 4.9 m/s2 down a 45° ramp.
1. Draw a free body diagram of the skateboarder.
2. Determine the…
1. normal force of the skateboard on the skateboarder's shoes
2. friction force between the skateboard and the skateboarder's shoes
3. What type of friction, static or kinetic, acts on the soles of the skateboarder's shoes? Explain your choice.
6. A 55 kg human cannonball is shot out the mouth of a 4.5 m cannon with a speed of 18 m/s at an angle of 60°. (Friction and air resistance are negligible in this problem.) Determine…
1. the acceleration of the human cannonball inside the cannon
2. the components of her weight that are parallel and perpendicular to the barrel of the cannon
3. the force on the feet of the human cannonball while she is inside the cannon
The human cannonball leaves the mouth of the cannon and soars toward a net that is at the same height as the mouth of the cannon. Determine…
1. the horizontal and vertical components of her initial velocity
2. the time she spends in the air
3. the distance from the mouth of the cannon to the center of a properly placed net
7. A slingshot is made of a single piece of rubber tubing, connected to two halves of a forked stick 5.0 cm apart, with a lightweight leather pocket attached to the middle of the rubber tubing. A Bart Simpson wannabe places a 28 g stone in the pocket and pulls back on the rubber tubing until the stone is 30 cm away from the center of the gap in the forked stick. This takes 11.6 N of force.
1. Draw a free body diagram of the stone before it is released.
2. Determine the tension in the rubber tubing before the stone is released.
3. Draw a free body diagram of the stone immediately after it is released.
4. Determine the acceleration of the stone immediately after it is released.
### statistical
1. incline-plane.txt
A group of physics students measured the acceleration of a laboratory cart on 120 cm long track that was inclined to several different heights. Transform the data so that a linear fit can be performed. Use the slope to determine the acceleration due to gravity.
2. wild-goose-chase.txt
American humans (Homo sapiens) aren't the only ones who love their lawns. Canada geese (Branta canadensis) love well trimmed grass as well. The humans love it as a pedestal for their suburban homes. The geese love it as a food source and a runway. College campuses in the US often have lots of grass. When they do, they often have lots of canada geese. They most certainly have lots of physics students and professors too. At the begining of the Twenty-first Century, the inevitable happened. A group of physics students and professors decided to chase a canada goose across a college campus in an attempt to learn something about the mechanics of flight. Their results are compiled in the accompanying text file.
1. The canada goose in this experiment basically flew horizontally. (These are big birds and they need a lot of space to get up to flight speed.)
1. Perform a quadratic fit on a position-time graph using the data in the text file.
2. Using your curve fit, calculate the horizontal accelertation of the bird.
2. A typical adult canada goose has a mass of about 4.7 kg. Determine the components of the force applied by the bird's wings in the…
1. horizontal and
2. vertical directions.
3. Given the values you calculated in part b, determine the…
1. magnitude and
2. direction (relative to the horizon) of the force applied by the bird's wings.
Source: The Physics of Bird Flight: An Experiment. Michael D. Mihail, Thomas F. George, Bernard J. Feldman. The Physics Teacher. Vol. 46, No. 155 (March 2008): 155–157.
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https://www.aqua-calc.com/one-to-one/surface-density/pound-per-square-nanometer/troy-ounce-per-square-yard/101
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# 101 pounds per square nanometer in troy ounces per square yard
## pounds/nanometer² to troy ounce/yard² unit converter
101 pounds per square nanometer [lb/nm²] = 1.23 × 10+21 troy ounces per square yard [oz t/yd²]
### pounds per square nanometer to troy ounces per square yard surface density conversion cards
• 101
through
125
pounds per square nanometer
• 101 lb/nm² to oz t/yd²
= 1.23 × 10+21 oz t/yd²
• 102 lb/nm² to oz t/yd²
= 1.24 × 10+21 oz t/yd²
• 103 lb/nm² to oz t/yd²
= 1.26 × 10+21 oz t/yd²
• 104 lb/nm² to oz t/yd²
= 1.27 × 10+21 oz t/yd²
• 105 lb/nm² to oz t/yd²
= 1.28 × 10+21 oz t/yd²
• 106 lb/nm² to oz t/yd²
= 1.29 × 10+21 oz t/yd²
• 107 lb/nm² to oz t/yd²
= 1.3 × 10+21 oz t/yd²
• 108 lb/nm² to oz t/yd²
= 1.32 × 10+21 oz t/yd²
• 109 lb/nm² to oz t/yd²
= 1.33 × 10+21 oz t/yd²
• 110 lb/nm² to oz t/yd²
= 1.34 × 10+21 oz t/yd²
• 111 lb/nm² to oz t/yd²
= 1.35 × 10+21 oz t/yd²
• 112 lb/nm² to oz t/yd²
= 1.37 × 10+21 oz t/yd²
• 113 lb/nm² to oz t/yd²
= 1.38 × 10+21 oz t/yd²
• 114 lb/nm² to oz t/yd²
= 1.39 × 10+21 oz t/yd²
• 115 lb/nm² to oz t/yd²
= 1.4 × 10+21 oz t/yd²
• 116 lb/nm² to oz t/yd²
= 1.41 × 10+21 oz t/yd²
• 117 lb/nm² to oz t/yd²
= 1.43 × 10+21 oz t/yd²
• 118 lb/nm² to oz t/yd²
= 1.44 × 10+21 oz t/yd²
• 119 lb/nm² to oz t/yd²
= 1.45 × 10+21 oz t/yd²
• 120 lb/nm² to oz t/yd²
= 1.46 × 10+21 oz t/yd²
• 121 lb/nm² to oz t/yd²
= 1.48 × 10+21 oz t/yd²
• 122 lb/nm² to oz t/yd²
= 1.49 × 10+21 oz t/yd²
• 123 lb/nm² to oz t/yd²
= 1.5 × 10+21 oz t/yd²
• 124 lb/nm² to oz t/yd²
= 1.51 × 10+21 oz t/yd²
• 125 lb/nm² to oz t/yd²
= 1.52 × 10+21 oz t/yd²
• 126
through
150
pounds per square nanometer
• 126 lb/nm² to oz t/yd²
= 1.54 × 10+21 oz t/yd²
• 127 lb/nm² to oz t/yd²
= 1.55 × 10+21 oz t/yd²
• 128 lb/nm² to oz t/yd²
= 1.56 × 10+21 oz t/yd²
• 129 lb/nm² to oz t/yd²
= 1.57 × 10+21 oz t/yd²
• 130 lb/nm² to oz t/yd²
= 1.59 × 10+21 oz t/yd²
• 131 lb/nm² to oz t/yd²
= 1.6 × 10+21 oz t/yd²
• 132 lb/nm² to oz t/yd²
= 1.61 × 10+21 oz t/yd²
• 133 lb/nm² to oz t/yd²
= 1.62 × 10+21 oz t/yd²
• 134 lb/nm² to oz t/yd²
= 1.63 × 10+21 oz t/yd²
• 135 lb/nm² to oz t/yd²
= 1.65 × 10+21 oz t/yd²
• 136 lb/nm² to oz t/yd²
= 1.66 × 10+21 oz t/yd²
• 137 lb/nm² to oz t/yd²
= 1.67 × 10+21 oz t/yd²
• 138 lb/nm² to oz t/yd²
= 1.68 × 10+21 oz t/yd²
• 139 lb/nm² to oz t/yd²
= 1.69 × 10+21 oz t/yd²
• 140 lb/nm² to oz t/yd²
= 1.71 × 10+21 oz t/yd²
• 141 lb/nm² to oz t/yd²
= 1.72 × 10+21 oz t/yd²
• 142 lb/nm² to oz t/yd²
= 1.73 × 10+21 oz t/yd²
• 143 lb/nm² to oz t/yd²
= 1.74 × 10+21 oz t/yd²
• 144 lb/nm² to oz t/yd²
= 1.76 × 10+21 oz t/yd²
• 145 lb/nm² to oz t/yd²
= 1.77 × 10+21 oz t/yd²
• 146 lb/nm² to oz t/yd²
= 1.78 × 10+21 oz t/yd²
• 147 lb/nm² to oz t/yd²
= 1.79 × 10+21 oz t/yd²
• 148 lb/nm² to oz t/yd²
= 1.8 × 10+21 oz t/yd²
• 149 lb/nm² to oz t/yd²
= 1.82 × 10+21 oz t/yd²
• 150 lb/nm² to oz t/yd²
= 1.83 × 10+21 oz t/yd²
• 151
through
175
pounds per square nanometer
• 151 lb/nm² to oz t/yd²
= 1.84 × 10+21 oz t/yd²
• 152 lb/nm² to oz t/yd²
= 1.85 × 10+21 oz t/yd²
• 153 lb/nm² to oz t/yd²
= 1.87 × 10+21 oz t/yd²
• 154 lb/nm² to oz t/yd²
= 1.88 × 10+21 oz t/yd²
• 155 lb/nm² to oz t/yd²
= 1.89 × 10+21 oz t/yd²
• 156 lb/nm² to oz t/yd²
= 1.9 × 10+21 oz t/yd²
• 157 lb/nm² to oz t/yd²
= 1.91 × 10+21 oz t/yd²
• 158 lb/nm² to oz t/yd²
= 1.93 × 10+21 oz t/yd²
• 159 lb/nm² to oz t/yd²
= 1.94 × 10+21 oz t/yd²
• 160 lb/nm² to oz t/yd²
= 1.95 × 10+21 oz t/yd²
• 161 lb/nm² to oz t/yd²
= 1.96 × 10+21 oz t/yd²
• 162 lb/nm² to oz t/yd²
= 1.98 × 10+21 oz t/yd²
• 163 lb/nm² to oz t/yd²
= 1.99 × 10+21 oz t/yd²
• 164 lb/nm² to oz t/yd²
= 2 × 10+21 oz t/yd²
• 165 lb/nm² to oz t/yd²
= 2.01 × 10+21 oz t/yd²
• 166 lb/nm² to oz t/yd²
= 2.02 × 10+21 oz t/yd²
• 167 lb/nm² to oz t/yd²
= 2.04 × 10+21 oz t/yd²
• 168 lb/nm² to oz t/yd²
= 2.05 × 10+21 oz t/yd²
• 169 lb/nm² to oz t/yd²
= 2.06 × 10+21 oz t/yd²
• 170 lb/nm² to oz t/yd²
= 2.07 × 10+21 oz t/yd²
• 171 lb/nm² to oz t/yd²
= 2.09 × 10+21 oz t/yd²
• 172 lb/nm² to oz t/yd²
= 2.1 × 10+21 oz t/yd²
• 173 lb/nm² to oz t/yd²
= 2.11 × 10+21 oz t/yd²
• 174 lb/nm² to oz t/yd²
= 2.12 × 10+21 oz t/yd²
• 175 lb/nm² to oz t/yd²
= 2.13 × 10+21 oz t/yd²
• 176
through
200
pounds per square nanometer
• 176 lb/nm² to oz t/yd²
= 2.15 × 10+21 oz t/yd²
• 177 lb/nm² to oz t/yd²
= 2.16 × 10+21 oz t/yd²
• 178 lb/nm² to oz t/yd²
= 2.17 × 10+21 oz t/yd²
• 179 lb/nm² to oz t/yd²
= 2.18 × 10+21 oz t/yd²
• 180 lb/nm² to oz t/yd²
= 2.19 × 10+21 oz t/yd²
• 181 lb/nm² to oz t/yd²
= 2.21 × 10+21 oz t/yd²
• 182 lb/nm² to oz t/yd²
= 2.22 × 10+21 oz t/yd²
• 183 lb/nm² to oz t/yd²
= 2.23 × 10+21 oz t/yd²
• 184 lb/nm² to oz t/yd²
= 2.24 × 10+21 oz t/yd²
• 185 lb/nm² to oz t/yd²
= 2.26 × 10+21 oz t/yd²
• 186 lb/nm² to oz t/yd²
= 2.27 × 10+21 oz t/yd²
• 187 lb/nm² to oz t/yd²
= 2.28 × 10+21 oz t/yd²
• 188 lb/nm² to oz t/yd²
= 2.29 × 10+21 oz t/yd²
• 189 lb/nm² to oz t/yd²
= 2.3 × 10+21 oz t/yd²
• 190 lb/nm² to oz t/yd²
= 2.32 × 10+21 oz t/yd²
• 191 lb/nm² to oz t/yd²
= 2.33 × 10+21 oz t/yd²
• 192 lb/nm² to oz t/yd²
= 2.34 × 10+21 oz t/yd²
• 193 lb/nm² to oz t/yd²
= 2.35 × 10+21 oz t/yd²
• 194 lb/nm² to oz t/yd²
= 2.37 × 10+21 oz t/yd²
• 195 lb/nm² to oz t/yd²
= 2.38 × 10+21 oz t/yd²
• 196 lb/nm² to oz t/yd²
= 2.39 × 10+21 oz t/yd²
• 197 lb/nm² to oz t/yd²
= 2.4 × 10+21 oz t/yd²
• 198 lb/nm² to oz t/yd²
= 2.41 × 10+21 oz t/yd²
• 199 lb/nm² to oz t/yd²
= 2.43 × 10+21 oz t/yd²
• 200 lb/nm² to oz t/yd²
= 2.44 × 10+21 oz t/yd²
#### Foods, Nutrients and Calories
BACON HICKORY SMOKED, UPC: 092825124146 contain(s) 500 calories per 100 grams (≈3.53 ounces) [ price ]
5029 foods that contain Histidine. List of these foods starting with the highest contents of Histidine and the lowest contents of Histidine
#### Gravels, Substances and Oils
CaribSea, Freshwater, African Cichlid Mix, White weighs 1 169.35 kg/m³ (73.00014 lb/ft³) with specific gravity of 1.16935 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Graphitic Carbon Nitride [g-C3N4] weighs 2 336 kg/m³ (145.83172 lb/ft³) [ weight to volume | volume to weight | price | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-438A, liquid (R438A) with temperature in the range of -40°C (-40°F) to 60°C (140°F)
#### Weights and Measurements
A centipoise (cP) is a non-SI (non-System International) measurement unit of dynamic viscosity in the centimeter gram second (CGS) system of units
Electric current is a motion of electrically charged particles within conductors or space.
long tn/dm³ to dwt/yd³ conversion table, long tn/dm³ to dwt/yd³ unit converter or convert between all units of density measurement.
#### Calculators
Body Mass Index calculator using person's weight and height
| 3,618
| 6,828
|
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| 2.671875
| 3
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CC-MAIN-2024-30
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latest
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| 0.065139
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https://golf.com/instruction/mudball-a-new-study-reveals-how-mud-can-curve-your-shot/
| 1,659,963,527,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-33/segments/1659882570827.41/warc/CC-MAIN-20220808122331-20220808152331-00037.warc.gz
| 283,837,601
| 24,891
|
x
Join INSIDEGOLF and get \$100 of value for \$20!
# Mudball! A New Study Reveals How Mud Can Curve Your Shot
May 28, 2016
You piped your drive down the fairway, but your ball picked up a clump of mud along the way—a common occurrence in soft conditions. Barring a local rule that lets you lift and clean the ball, you’ll have to play it as it lies and deal with the dirt.
Deciding how a muddy ball will affect your shot’s trajectory has always been a guessing game. Traditionally, it’s been assumed that as the ball flies, the mud creates air resistance—or drag—that sends the shot in the direction of the ball’s soiled side. So mud on the ball’s left quadrant, for example, would tug the ball to the left. But there’s never been compelling data to confirm or refute this assumption—until now.
With the help of the Keiser University golf staff in West Palm Beach, Fla., GOLF used TrackMan to analyze 400 “muddy” 6-iron shots hit by 10 single-digit-handicappers. We used weighted lead tape to simulate a 1.9-gram chunk of dirt (a bit less than the width of your thumb) clinging to various locations near the ball’s equator. We compared these 400 swings with some mud-free base swings, then tallied the results.
Contrary to conventional wisdom, every single “muddy” ball curved in the opposite direction of the sphere’s dirty side (results, right). It’s clearly time to rethink our assumptions about mud’s effect on ball flight.
Here are some more takeaways to keep in mind, based on our research:
• If the clump of mud or dirt is smaller than the width of your thumb, it will tend to make the ball fade when it’s on the left side of the ball and draw when it’s on the right side.
• If the hunk of mud is wider than your thumb, the volume is likely large enough to curve the shot in the direction of the ball’s muddy side, in keeping with the old rule of thumb.
• Club up! Our testers lost an average of 5.3 yards on mud-ball shots.
• The farther the mud is from the clubface/ball contact point, the more it will curve.
Use this cheat sheet to take perfect aim—and take your opponents to the cleaners!
THIS MUD’S FOR YOU
How dirt impacts the shape of your shots
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CC-MAIN-2022-33
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https://education.ti.com/en/timathnspired/us/detail?id=61040A1F75E743A6A2A3A9908BC21FFA&t=E51B8F52AF8A4099A8204BE3B9ED5BD6
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crawl-data/CC-MAIN-2024-30/segments/1720763517648.65/warc/CC-MAIN-20240721060614-20240721090614-00132.warc.gz
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|
Education Technology
• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software
TI-Nspire™
TI-Nspire™ CAS
3.2
# Geometry: Transformations: Rotations
by Texas Instruments
#### Objectives
• Students will identify a rotation as an isometry, also called a congruence transformation.
• Students will identify which properties (side length, angle measure, perimeter, area, and orientation) of a figure are preserved in a rotation and which are not.
• Students will describe the relationship between the sign of the angle and the direction of rotation.
• Students will identify coordinates of an image that is rotated about the origin through angles of ±90°, ±180°, ±270°, and ±360°.
• Students will generalize the relationship between the coordinates of a pre-image and its image in a rotation about the origin in the coordinate plane.
#### Vocabulary
• pre-image
• image
• transformation
• rotation
• clockwise / counterclockwise direction
• congruent figures
• congruence transformation
• isometry
• positive and negative angles
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https://gmatclub.com/forum/math-152107.html
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It is currently 25 Nov 2017, 02:49
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# Math
Author Message
TAGS:
### Hide Tags
Intern
Joined: 23 May 2012
Posts: 3
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### Show Tags
03 May 2013, 07:02
11+11=4
22+22=16
33+33=?
Need Explanation.
Kudos [?]: [0], given: 0
Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 87
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Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
### Show Tags
03 May 2013, 09:42
wahedhossain wrote:
11+11=4
22+22=16
33+33=?
Need Explanation.
Look Wahed .. this is Not a GMAT type Question However this is a logical reasoning Question with a very simple logic behind this. Look Carefully !!
11 + 11 = 4 So, Here, they used the logic as follows :::::::
1+1 =2 & 1+1 = 2 again & then Multiply the result i.e.; 2 * 2 = 4.
Similarly, for 22+22=16 ..... 2+2 = 4 & 2+2 = 4 & now multiply 4 * 4 = 16.
Now for 33+33 ...
we have 3+3 = 6 & then 3+3 = 6 & now multiply the result as ::: 6*6 = 36.
Hence, 33+33 = 36.... Let me know if you have any question .....
_________________
If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.
Kudos [?]: 90 [0], given: 11
Re: Math [#permalink] 03 May 2013, 09:42
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# Math
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https://datascience.stackexchange.com/questions/85064/where-is-the-rotated-angle-actually-located-in-fitellipse-method/85082
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# Where is the rotated angle actually located in fitEllipse method?
Main task: I fit the ellipse using the fitEllipse() method and then I'd like to count the rotation angle between the horizontal axis and the major axis of the generated ellipse. I'm going to do this using the 3rd returned argument from the fitEllipse() method - $$\theta$$ (rotation angle).
Main issue: I can't find exact information about which axes this angle is located between.
Other: If I'm right the length of minor axis and the length of major axis in ellipse it's the same lengths as two sides in a rotated rectangle.
Sources:
1. From documentation here (section nb. 9) it seems that this angle is between horizontal axis and the first side how it's written in CvBox2D section. So, it means that the angle can be between the horizontal axis and minor or major axis. But:
2. In this article (section 3) the first example is good but in the 2nd example the angle should be between horizontal axis and height instead of width (referring to my aforementioned first point).
3. In this article it shows that the angle is between vertical axis and one side of rectangle.
So, where is the rotated angle located in fitEllipse() method?
Any hints how it works are welcome.
I've implemented the following simple code:
import cv2
import numpy as np
nr_im = 9876
font = cv2.FONT_HERSHEY_SIMPLEX
fontScale = 1
colorText = (0, 0, 255)
thickness = 2
img = cv2.imread('testing/' + str(nr_im) + '.jpg')
original = img.copy()
blured_img = cv2.GaussianBlur(img,(17,17),5)
image = cv2.cvtColor(img, cv2.COLOR_BGR2HSV)
lower = np.array([0, 0, 140], dtype="uint8")
upper = np.array([0, 0, 255], dtype="uint8")
# Morphological Closing: Get rid of the noise inside the object
# Find contours
cnts, _ = cv2.findContours(mask, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)
print(len(cnts))
cntsElps = []
for num_cnt, cnt in enumerate(cnts):
genElipse = cv2.fitEllipse(cnt)
cntsElps.append(genElipse)
cv2.ellipse(original,genElipse,(0,255,0),2)
cv2.putText(original, str(num_cnt+1), (int(genElipse[0][0]),int(genElipse[0][1])), font, fontScale, colorText, thickness, cv2.LINE_AA)
print("Ellipse nb: " + str(num_cnt+1) + " has angle: " + str(genElipse[2]) + "\n")
cv2.imwrite('testing/' + str(nr_im) + '_' + 'trash2' + '.png', original)
And I used this image as example:
I've got the following image result:
And the rotation angle for each ellipse was:
1. Ellipse nb: 1 has angle: 55.63788986206055
2. Ellipse nb: 2 has angle: 108.58539581298828
3. Ellipse nb: 3 has angle: 170.23861694335938
4. Ellipse nb: 4 has angle: 73.59089660644531
So, my conclusion is that an angle between horizontal axis and major side of rectangle(=major ellipse axis) is the rotation angle in fitEllipse() method.
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# Introduction to Adaptive Boosting Classifier
I am just finishing writing my master’s thesis, whose subject is recognizing epileptic states based on the EEG signal using the ensemble classifiers. One of the ensemble classifiers that I used in my research was Adaptive Boosting Classifier. I decided to write an article about it. This will be a brief theoretical introduction to Adaptive Boosting Classifier and an example of its implementation in Python using the Scikit-learn library.
Theoretical introduction
Adaptive Boosting Classifier is an ensemble classifier developed by Yoav Freund and Robert Schapire. This algorithm works by creating a prediction model in the form of a set of weak models. It requires specifying a set of weak learners before actually starting it. The weight of each model is determined based on whether it correctly predicted the sample or not. In a situation where the learner has predicted wrong, his weight is slightly reduced. The whole process is carried out until convergence[1].
The algorithm can be presented in the following steps:
1. Assignment of all samples w^{(i)} the initial value of \frac{1}{m}
2. Learn the first predictor and calculate the weighted error rate r_1 for it (where \widehat{y}_j^{(i)} is the j-th forecast for the i-th case):
3. Calculation of the predictor weight \alpha_j, where $\eta$ is the learning factor:
4. Updating weights – strengthening of incorrectly classified samples:
5. Normalization of all weights of examples.
6. Learning a new predictor using updated weights and repeating the whole process until the intended number of predictors is achieved or satisfactory results are obtained.
7. Algorithm forecasting by checking the predictions of all predictors and their weights using the w^{(i)} factor, and then selecting the predicted class by majority vote:
Example in Python
If you want to use this algorithm in Python, you can do that with the sklearn library. Just import the following method:
from sklearn.ensemble import AdaBoostClassifier
Let me leave part of the implementation responsible for preparing the training and test set. I will proceed to use the classifier:
abc = AdaBoostClassifier()
abc.fit(x_train, y_train.ravel())
predictions = abc.predict(x_test)
The library allows you to set certain parameters for the classifier, such as the depth of individual estimators or tolerance for premature stopping of the process. All information can be found in the documentation.
Summary
I wanted to introduce you to Adaptive Boosting Classifier. The subject of ensemble classifiers is very extensive and interesting. The classifier which I presented today is one of the pillars. I really recommend that you delve deeper into this. I also encourage you to read my latest article about Cohen’s kappa coefficient.
Sources
1. Aurelien Geron, Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, O’Reilly Media, Inc, USA, 2019
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Problem with objects copying each other in memory
andrew cooke andrew at acooke.org
Fri Feb 13 00:04:23 CET 2009
```the official answer to that question is here -
http://docs.python.org/reference/datamodel.html?highlight=containers - at
i think it's a hard question and really in a sense (imho) the real reason
is just that this tends to be the best compromise for the kind of language
that python is.
andrew
Cameron Pulsford wrote:
> Thanks, that did it! Why is that the case though? Or rather, why do
> the assignments to temp.x and temp.y not effect the self.x and self.y?
> How come I only run into the problem with the list?
>
>
> On Feb 12, 2009, at 5:15 PM, andrew cooke wrote:
>
>>
>> you're setting the new knight's "sl" to the value self.sl and then
>> values to it. that's the same list - so you are adding values to the
>> self.sl list when you add them to the knight's sl.
>>
>> this is easier to understand just by seeing the fix, which is to use:
>>
>> temp = Knight(self.x, self.y, self.g, self.h, self.gp, list(self.sl))
>>
>> which will make a new copy of the list, so you are only adding to
>> the sl
>> in the (new) knight.
>>
>> andrew
>>
>>
>>
>> dlocpuwons wrote:
>>> Using Python 2.6.1...
>>>
>>> I am (attempting) to make an A* search for a chess problem, but I am
>>> running into a really annoying shared memory issue in my successor
>>> function. Here it is stripped down to the important parts that relate
>>> to my problem.
>>>
>>> def successors(self):
>>> result = []
>>> moves = [[2, 1], [2, -1], [-2, 1], [-2, -1], [1, 2], [1, -2], [-1,
>>> 2], [-1, -2]] #possible moves for a knight
>>>
>>> for i in moves:
>>> temp = Knight(self.x, self.y, self.g, self.h, self.gp, self.sl)
>>> temp.x += i[0]
>>> temp.y += i[1]
>>> temp.sl.append([temp.x, temp.y]) #Adds the new current state to
>>> the
>>> visited states list
>>> result.append(temp)
>>> return result
>>>
>>> The method creates a temporary Knight object, increments it to the
>>> new
>>> position and then adds this new position to its list of visited
>>> states. Then it returns a list of these 8 new objects. The problem
>>> seems to be with the "result.sl.append()" line. As the method chugs
>>> along and creates the new objects the "temp.sl" lines seems to stay
>>> in
>>> memory, so when the method is done all the new objects have all the
>>> new states that were made over the course of the method instead of
>>> just their own created in the loop. For example when I try to get
>>> successors for a piece that is initially at (2,2) with no previously
>>> visited states, the method prints this out for the sl (state list)
>>> value
>>>
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>> [[2, 2], [4, 3], [4, 1], [0, 3], [0, 1], [3, 4], [3, 0], [1, 4], [1,
>>> 0]]
>>>
>>> but what it should print out is
>>>
>>> [[2, 2], [4, 3]]
>>> [[2, 2], [4, 1]]
>>> [[2, 2], [0, 3]]
>>> [[2, 2], [0, 1]]
>>> [[2, 2], [3, 4]]
>>> [[2, 2], [3, 0]]
>>> [[2, 2], [1, 4]]
>>> [[2, 2], [1, 0]]
>>>
>>> It sort of seems like python is trying to be too smart and is trying
>>> to keep things in memory. Is there anyway to work around this?
>>> --
>>> http://mail.python.org/mailman/listinfo/python-list
>>>
>>>
>>
>>
>
>
```
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# ChenSort
ChenSort is an improved bucket sort, which is a general-purpose sorting algorithm.
The time complexity is O(n) at best and O(nlogn) at worst, the space complexity is O(n), and it is stable.
Randomly generate [1000,10000000] random numbers in the range [-2^63,2^63-1], average speed is 3 times faster than Quicksort, fastest is 20 times. Traditional counting sorts and bucket sorts cannot handle such a large range of values because the performance is worse than Quicksort.
Android APK demo, 6.05 MB
Windows exe demo, 5.8 MB
The demos are all built on Flutter.
Currently writing an academic paper and expecting to be recognized by the academic community.
Dart code:
```/// The essence of Chen Sort is an improved bucket sort
void chenSort(List<int> list) {
if (list.length < 2) {
return;
}
int maxValue = list[0];
int minValue = maxValue;
for (final element in list.skip(1)) {
if (element > maxValue) {
maxValue = element;
}
if (element < minValue) {
minValue = element;
}
}
/// All elements are the same and do not need to be sorted.
if (maxValue == minValue) {
return;
}
/// Limit the maximum size of the bucket to ensure the performance of long list
/// sorting, which can be adjusted according to the actual situation.
///
/// The essential difference between this and bucket sorting is that the size of
/// the bucket is only related to the length of the list, not the range of element values.
int bucketSize = min(list.length, 50000);
int maxBucketIndex = bucketSize - 1;
List<List<int>?> buckets = List.filled(bucketSize, null);
int slot;
/// Calculate the bucket in which the element is located based on the value of the element
/// and the maximum and minimum values.
/// Overflow detection
BigInt range = BigInt.from(maxValue) - BigInt.from(minValue);
if (BigInt.from(range.toInt()) == range) {
int range = maxValue - minValue;
double factor = maxBucketIndex / range;
for (final element in list) {
// slot = (((element - minValue) / range) * maxBucketIndex).toInt();
slot = ((element - minValue) * factor).toInt();
if (buckets[slot] == null) {
buckets[slot] = [];
}
}
} else {
/// Overflowed(positive minus negative)
int positiveRange = maxValue;
int negativeRange = -1 - minValue;
int positiveStartBucketIndex = maxBucketIndex ~/ 2 + 1;
int positiveBucketLength = maxBucketIndex - positiveStartBucketIndex;
int negativeBucketLength = positiveStartBucketIndex - 1;
for (final element in list) {
if (element < 0) {
slot = (((element - minValue) / negativeRange) * negativeBucketLength)
.toInt();
} else {
slot = positiveStartBucketIndex +
((element / positiveRange) * positiveBucketLength).toInt();
}
if (buckets[slot] == null) {
buckets[slot] = [];
}
}
}
int compare(int left, int right) {
return left - right;
}
int index = 0;
for (final bucket in buckets) {
if (bucket != null) {
if (bucket.length > 1) {
if (bucket.length >= 1000) {
chenSort(bucket);
} else {
/// The sort method here represents the fastest comparison-type algorithm (Quick sort, Tim sort, etc.)
bucket.sort(compare);
}
for (final element in bucket) {
list[index++] = element;
}
} else {
list[index++] = bucket[0];
}
}
}
}```
```static void chenSort(Integer[] list) {
int length = list.length;
if (length < 2) {
return;
}
Integer maxValue = Integer.MIN_VALUE;
Integer minValue = Integer.MAX_VALUE;
for (Integer element : list) {
if (element > maxValue) {
maxValue = element;
}
if (element < minValue) {
minValue = element;
}
}
/// All elements are the same and do not need to be sorted.
if (maxValue.equals(minValue)) {
return;
}
/// Limit the maximum size of the bucket to ensure the performance of long list
/// sorting, which can be adjusted according to the actual situation.
///
/// The essential difference between this and bucket sorting is that the size of
/// the bucket is only related to the length of the list, not the range of element values.
int bucketSize = Math.min(length, 50000);
int maxBucketIndex = bucketSize - 1;
ArrayList<Integer>[] buckets = new ArrayList[bucketSize];
int slot;
/// Calculate the bucket in which the element is located based on the value of the element
/// and the maximum and minimum values.
/// Overflow detection
BigInteger bigRange = BigInteger.valueOf(maxValue).subtract(BigInteger.valueOf(minValue));
if (BigInteger.valueOf(bigRange.intValue()).equals(bigRange)) {
double factor = maxBucketIndex * 1.0 / (maxValue - minValue);
for (Integer element : list) {
slot = (int) ((element - minValue) * factor);
if (buckets[slot] == null) {
buckets[slot] = new ArrayList<>();
}
}
} else {
/// Overflowed(positive minus negative)
double positiveRange = maxValue;
double negativeRange = -1 - minValue;
int positiveStartBucketIndex = maxBucketIndex / 2 + 1;
int positiveBucketLength = maxBucketIndex - positiveStartBucketIndex;
int negativeBucketLength = positiveStartBucketIndex - 1;
Integer zero = 0;
for (Integer element : list) {
if (element < zero) {
slot = (int) (((element - minValue) / negativeRange) * negativeBucketLength);
} else {
slot = (int) (positiveStartBucketIndex + ((element / positiveRange) * positiveBucketLength));
}
if (buckets[slot] == null) {
buckets[slot] = new ArrayList<>();
}
}
}
Comparator<Integer> comparator = Comparator.comparingInt(left -> left);
CountDownLatch countDownLatch = new CountDownLatch(buckets.length);
for (ArrayList<Integer> bucket : buckets) {
if (bucket != null) {
if (bucket.size() > 1) {
executor.execute(() -> {
bucket.sort(comparator);
countDownLatch.countDown();
});
} else {
countDownLatch.countDown();
}
} else {
countDownLatch.countDown();
}
}
try {
countDownLatch.await();
} catch (InterruptedException ignored) {
}
int index = 0;
for (ArrayList<Integer> bucket : buckets) {
if (bucket != null) {
if (bucket.size() > 1) {
for (Integer element : bucket) {
list[index++] = element;
}
} else {
list[index++] = bucket.get(0);
}
}
}
}```
Performance(10 million random numbers sorted):
```Random random = new Random();
Integer[] arr = new Integer[10000000];
long maxValue = Integer.MAX_VALUE;
long minValue = Integer.MIN_VALUE;
long range = maxValue - minValue + 1;
for (int i = 0; i < arr.length; i++) {
arr[i] = (int) (minValue + random.nextLong(range));
}
Integer[] copy = new Integer[arr.length];
System.arraycopy(arr, 0, copy, 0, arr.length);
long start = System.currentTimeMillis();
chenSort(arr);
long chenSortTimeUsage = System.currentTimeMillis() - start;
start = System.currentTimeMillis();
Arrays.sort(copy);
long quickSortTimeUsage = System.currentTimeMillis() - start;```
```chen sort: 3384 ms, quick sort: 9366 ms, 63.869314541960286%(2.767730496453901x) faster
chen sort: 3450 ms, quick sort: 7223 ms, 52.2359130555171%(2.093623188405797x) faster
chen sort: 1693 ms, quick sort: 5000 ms, 66.14%(2.9533372711163617x) faster
chen sort: 2306 ms, quick sort: 6267 ms, 63.204084889101644%(2.717692974848222x) faster
chen sort: 2922 ms, quick sort: 10145 ms, 71.19763430261213%(3.471937029431896x) faster
chen sort: 3285 ms, quick sort: 9211 ms, 64.33611985669309%(2.803957382039574x) faster
chen sort: 2661 ms, quick sort: 9236 ms, 71.18882633174535%(3.4708756106726795x) faster
chen sort: 2538 ms, quick sort: 6422 ms, 60.47960137028963%(2.530338849487786x) faster
chen sort: 1749 ms, quick sort: 4928 ms, 64.50892857142857%(2.8176100628930816x) faster
chen sort: 1775 ms, quick sort: 5254 ms, 66.21621621621621%(2.96x) faster
chen sort: 1626 ms, quick sort: 5155 ms, 68.45780795344326%(3.1703567035670357x) faster
chen sort: 2375 ms, quick sort: 4877 ms, 51.302029936436334%(2.0534736842105263x) faster
chen sort: 1923 ms, quick sort: 5250 ms, 63.37142857142857%(2.730109204368175x) faster
chen sort: 3028 ms, quick sort: 9237 ms, 67.21879398072967%(3.0505284015852046x) faster
chen sort: 2692 ms, quick sort: 9030 ms, 70.18826135105205%(3.3543833580980684x) faster```
Blog
XiSort The slowest sorting algorithm I’ve developed with the most efficient code execution in the world.
# Support me
If it helps you a lot, consider sponsoring me a cup of milk tea, or giving a star. Your support is the driving force for me to continue to maintain.
Paypal
Thanks to the following netizens for their sponsorship.
1. 小小鸟 2022.06.08
2. 孟焱 2022.06.08
View Github
| 2,209
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| 2.859375
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# WW Hand Held Calculator
Discussion in 'Weight Watchers' started by Wendi, 9 October 2010 Social URL.
1. ### WendiFull Member
Posts:
82
2
Start Weight:
20st8lb
Current Weight:
18st8lb
Goal Weight:
9st7lb
Lost(%):
2st0lb(9.72%)
Diet:
WW
Hello, joined WW this morning so fingers crossed it works!
I did WW years ago and bought the WW calculator to help work out points and log them daily.
Does anyone have one and still use it? I can't remember how to use it (bar working out points for 100g of foods) and would love to be able to use it again. I think I threw away the instructions years ago. I think I recall you could work out portions on it as well (i.e. if the portion/packet size was more or less than 100g)
Some of the functions it had were you could record water drunk; how much weight you had lost amongst others.
3. ### missybctnomnomnom
Posts:
1,563
27
Start Weight:
19st13lb
Current Weight:
19st13lb
Goal Weight:
10st0lb
Lost(%):
0st0lb(0%)
Diet:
Weight Watchers
I had a calculator from last year and the only thing it tracked was the amount of points you'd used during that day, up until the end of the week. So instance if you were out, you could calculate the amount of points and then "bank" it in your calculator memory so you would be able to put it down on a tracker, if that makes sense.
If I'm honest, a new plan for Weight Watchers is happening in November and I was about to buy a new points calculator but decided not to, because they will become obslete when this new plan is in place because the points values of foods will change.
I think there is a thread somewhere in this batch of topics that talks about the new plan, so may be worth having a look over that xxx
4. ### WendiFull Member
Posts:
82
2
Start Weight:
20st8lb
Current Weight:
18st8lb
Goal Weight:
9st7lb
Lost(%):
2st0lb(9.72%)
Diet:
WW
Thanks. After I posted my question, I read the post about the new plan so will keep an eye on it!!
The calculator I have is from 2003 but the part that calculates points is still ok - I will have to try and remember how the rest of it works
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# Roof
Calculate roof materials, squares of shingles, bundles of ridge, roof estimate, figure roof materials, roof calculator.
• ## Roof pitch determined 2 ways
How to determine or calculate roof pitch or roof slope Roof pitch calculator is determined by the number of inches it rises vertically for every 12 inches it extends horizontally. (Also referred to as roof slope or roof slant.) So…
• ## Pros and cons of popular roofing materials
Popular Roofing Materials What most homeowners desire is a roof that’s not too expensive, requires no maintenance, and lasts forever. But most roofs are replaced – or at least repaired – every ten years. By carefully choosing your home’s roofing…
• ## Angle finder tool for roof pitch or for finding angles of anything
Roof Pitch finder This tool will find your roof pitch Most angle finders only work on the top side of a roof. This handy little tool is the easiest way to accurately find your roof pitch. Simply set it on your…
• ## Tips on measuring residential roof plans
Tips on measuring residential roof plans After measuring thousands of roof plans, over a period of 20 years ranging from apartments, tract houses custom homes here are some good tips. To accurately measure a roof plan, one of first things…
• ## How to measure a roof and determine squares of materials
How to measure a roof? Start by looking around and decide how to section the roof. (See plan below). The red dotted lines divide the sections. Count how many sections you have. Write this number down. Start with the largest…
• ## 12/12 Roof Pitch
12/12 Roof Pitch Information 12/12 Roof Pitch 45° Degrees Question: What is a 12/12 roof pitch? Answer: 12/12 roof pitch equivalents roof rises 12″ in a length of 12″. 12/12 roof pitch angle = 45.00 degrees. 12/12 roof pitch to…
• ## 10/12 Roof Pitch
10/12 Roof Pitch Information 10/12 Roof Pitch 40° Degrees Question: What is a 10/12 roof pitch? Answer: 10/12 roof pitch equivalents roof rises 10″ in a length of 12″. 10/12 roof pitch angle = 39.81 degrees. 10/12 roof pitch to…
• ## 9/12 Roof Pitch
9/12 Roof Pitch Information 9/12 Roof Pitch 37° Degrees Question: What is a 9/12 roof pitch? Answer: 9/12 roof pitch equivalents roof rises 9″ in a length of 12″. 9/12 roof pitch angle = 36.87 degrees. 9/12 roof pitch to…
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# 1 milligram per liter [mg/l] in micrograms per cubic meter
## milligrams/liter to microgram/meter³ unit converter of density
1 milligram per liter [mg/l] = 1 000 000 micrograms per cubic meter [µg/m³]
### milligrams per liter to micrograms per cubic meter density conversion cards
• 1
through
25
milligrams per liter
• 1 mg/l to µg/m³ = 1 000 000 µg/m³
• 2 mg/l to µg/m³ = 2 000 000 µg/m³
• 3 mg/l to µg/m³ = 3 000 000 µg/m³
• 4 mg/l to µg/m³ = 4 000 000 µg/m³
• 5 mg/l to µg/m³ = 5 000 000 µg/m³
• 6 mg/l to µg/m³ = 6 000 000 µg/m³
• 7 mg/l to µg/m³ = 7 000 000 µg/m³
• 8 mg/l to µg/m³ = 8 000 000 µg/m³
• 9 mg/l to µg/m³ = 9 000 000 µg/m³
• 10 mg/l to µg/m³ = 10 000 000 µg/m³
• 11 mg/l to µg/m³ = 11 000 000 µg/m³
• 12 mg/l to µg/m³ = 12 000 000 µg/m³
• 13 mg/l to µg/m³ = 13 000 000 µg/m³
• 14 mg/l to µg/m³ = 14 000 000 µg/m³
• 15 mg/l to µg/m³ = 15 000 000 µg/m³
• 16 mg/l to µg/m³ = 16 000 000 µg/m³
• 17 mg/l to µg/m³ = 17 000 000 µg/m³
• 18 mg/l to µg/m³ = 18 000 000 µg/m³
• 19 mg/l to µg/m³ = 19 000 000 µg/m³
• 20 mg/l to µg/m³ = 20 000 000 µg/m³
• 21 mg/l to µg/m³ = 21 000 000 µg/m³
• 22 mg/l to µg/m³ = 22 000 000 µg/m³
• 23 mg/l to µg/m³ = 23 000 000 µg/m³
• 24 mg/l to µg/m³ = 24 000 000 µg/m³
• 25 mg/l to µg/m³ = 25 000 000 µg/m³
• 26
through
50
milligrams per liter
• 26 mg/l to µg/m³ = 26 000 000 µg/m³
• 27 mg/l to µg/m³ = 27 000 000 µg/m³
• 28 mg/l to µg/m³ = 28 000 000 µg/m³
• 29 mg/l to µg/m³ = 29 000 000 µg/m³
• 30 mg/l to µg/m³ = 30 000 000 µg/m³
• 31 mg/l to µg/m³ = 31 000 000 µg/m³
• 32 mg/l to µg/m³ = 32 000 000 µg/m³
• 33 mg/l to µg/m³ = 33 000 000 µg/m³
• 34 mg/l to µg/m³ = 34 000 000 µg/m³
• 35 mg/l to µg/m³ = 35 000 000 µg/m³
• 36 mg/l to µg/m³ = 36 000 000 µg/m³
• 37 mg/l to µg/m³ = 37 000 000 µg/m³
• 38 mg/l to µg/m³ = 38 000 000 µg/m³
• 39 mg/l to µg/m³ = 39 000 000 µg/m³
• 40 mg/l to µg/m³ = 40 000 000 µg/m³
• 41 mg/l to µg/m³ = 41 000 000 µg/m³
• 42 mg/l to µg/m³ = 42 000 000 µg/m³
• 43 mg/l to µg/m³ = 43 000 000 µg/m³
• 44 mg/l to µg/m³ = 44 000 000 µg/m³
• 45 mg/l to µg/m³ = 45 000 000 µg/m³
• 46 mg/l to µg/m³ = 46 000 000 µg/m³
• 47 mg/l to µg/m³ = 47 000 000 µg/m³
• 48 mg/l to µg/m³ = 48 000 000 µg/m³
• 49 mg/l to µg/m³ = 49 000 000 µg/m³
• 50 mg/l to µg/m³ = 50 000 000 µg/m³
• 51
through
75
milligrams per liter
• 51 mg/l to µg/m³ = 51 000 000 µg/m³
• 52 mg/l to µg/m³ = 52 000 000 µg/m³
• 53 mg/l to µg/m³ = 53 000 000 µg/m³
• 54 mg/l to µg/m³ = 54 000 000 µg/m³
• 55 mg/l to µg/m³ = 55 000 000 µg/m³
• 56 mg/l to µg/m³ = 56 000 000 µg/m³
• 57 mg/l to µg/m³ = 57 000 000 µg/m³
• 58 mg/l to µg/m³ = 58 000 000 µg/m³
• 59 mg/l to µg/m³ = 59 000 000 µg/m³
• 60 mg/l to µg/m³ = 60 000 000 µg/m³
• 61 mg/l to µg/m³ = 61 000 000 µg/m³
• 62 mg/l to µg/m³ = 62 000 000 µg/m³
• 63 mg/l to µg/m³ = 63 000 000 µg/m³
• 64 mg/l to µg/m³ = 64 000 000 µg/m³
• 65 mg/l to µg/m³ = 65 000 000 µg/m³
• 66 mg/l to µg/m³ = 66 000 000 µg/m³
• 67 mg/l to µg/m³ = 67 000 000 µg/m³
• 68 mg/l to µg/m³ = 68 000 000 µg/m³
• 69 mg/l to µg/m³ = 69 000 000 µg/m³
• 70 mg/l to µg/m³ = 70 000 000 µg/m³
• 71 mg/l to µg/m³ = 71 000 000 µg/m³
• 72 mg/l to µg/m³ = 72 000 000 µg/m³
• 73 mg/l to µg/m³ = 73 000 000 µg/m³
• 74 mg/l to µg/m³ = 74 000 000 µg/m³
• 75 mg/l to µg/m³ = 75 000 000 µg/m³
• 76
through
100
milligrams per liter
• 76 mg/l to µg/m³ = 76 000 000 µg/m³
• 77 mg/l to µg/m³ = 77 000 000 µg/m³
• 78 mg/l to µg/m³ = 78 000 000 µg/m³
• 79 mg/l to µg/m³ = 79 000 000 µg/m³
• 80 mg/l to µg/m³ = 80 000 000 µg/m³
• 81 mg/l to µg/m³ = 81 000 000 µg/m³
• 82 mg/l to µg/m³ = 82 000 000 µg/m³
• 83 mg/l to µg/m³ = 83 000 000 µg/m³
• 84 mg/l to µg/m³ = 84 000 000 µg/m³
• 85 mg/l to µg/m³ = 85 000 000 µg/m³
• 86 mg/l to µg/m³ = 86 000 000 µg/m³
• 87 mg/l to µg/m³ = 87 000 000 µg/m³
• 88 mg/l to µg/m³ = 88 000 000 µg/m³
• 89 mg/l to µg/m³ = 89 000 000 µg/m³
• 90 mg/l to µg/m³ = 90 000 000 µg/m³
• 91 mg/l to µg/m³ = 91 000 000 µg/m³
• 92 mg/l to µg/m³ = 92 000 000 µg/m³
• 93 mg/l to µg/m³ = 93 000 000 µg/m³
• 94 mg/l to µg/m³ = 94 000 000 µg/m³
• 95 mg/l to µg/m³ = 95 000 000 µg/m³
• 96 mg/l to µg/m³ = 96 000 000 µg/m³
• 97 mg/l to µg/m³ = 97 000 000 µg/m³
• 98 mg/l to µg/m³ = 98 000 000 µg/m³
• 99 mg/l to µg/m³ = 99 000 000 µg/m³
• 100 mg/l to µg/m³ = 100 000 000 µg/m³
#### Foods, Nutrients and Calories
Chicken and noodles with vegetable, dessert (frozen meal) contain(s) 136 calories per 100 grams or ≈3.527 ounces [ price ]
#### Gravels, Substances and Oils
Substrate, Clay/Laterite weighs 1 019 kg/m³ (63.61409 lb/ft³) with specific gravity of 1.019 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Thallium [Tl] weighs 11 850 kg/m³ (739.77133 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ]
Volume to weightweight to volume and cost conversions for Lesquerella oil with temperature in the range of 23.9°C (75.02°F) to 110°C (230°F)
#### Weights and Measurements
kilometer per gallon (km/gallon, US) is a measure of fuel consumption or fuel economy
Amount of substance is a quantity proportional to the number of entities N in a sample.
kg/tsp to gr/US qt conversion table, kg/tsp to gr/US qt unit converter or convert between all units of density measurement.
#### Calculators
Calculate the volume and area of the surface of a quarter cylinder
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http://mathhelpforum.com/math-topics/51111-another-annuity.html
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1. You wish to purchased a house for $120,000 in 12 years. You can invest your money at 4.5%/a compounded semiannually for the first 5 years and then you can get 6%/a compounded semiannually for the next 7 years. How much do you need to invest now? (Hint: start with the last 7 years) 2. ## another annuity Originally Posted by euclid2 1. You wish to purchased a house for$120,000 in 12 years. You can invest your money at 4.5%/a compounded semiannually for the first 5 years and then you can get 6%/a compounded semiannually for the next 7 years. How much do you need to invest now? (Hint: start with the last 7 years)
For the last seven years,
interest, $\displaystyle i = \frac{6}{2}\%=3\%=0.03$
number of interest periods, $\displaystyle n = 7 \times 2 = 14$
The value of investment at the end of first five years
$\displaystyle = \frac {120 000}{(1.03)^{14}}$
$\displaystyle = \$79 334.14$For the first five years, interest,$\displaystyle i = \frac{4.5}{2}\%=2.25\%=0.0225$number of interest periods,$\displaystyle n = 5 \times 2 = 10$The present value of investment is$\displaystyle = \frac {\$79 334.14}{(1.0225)^{10}}$
$\displaystyle = \$63 507.78\$
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https://www.coursehero.com/file/207368/Homework-2-Solutions/
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Homework 2 Solutions
# Homework 2 Solutions - 1.4 Problem 9(a xL(x Jerry(b xyL(x...
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§ 1.4 Problem 1 ( a ): “For every number x , there is a bigger number y .” ( b ): “For any two numbers x and y , if x and y are nonnegative then so is their product.” ( c ): “For any two numbers x and y , there is another number z that is equal to their product.” § 1.4 Problem 9 ( a ): xL ( x, Jerry) ( b ): x yL ( x,y ) ( c ): x yL ( y,x ) ( d ): ¬∃ x yL ( x,y ) ( e ): x ¬ L (Lydia ,x ) ( f ): x y ¬ L ( y,x ) ( g ): x y ( x = y ) ( zL ( z,y )) ( h ): x y ( ( x negationslash = y ) ∧ ∀ z ( x = z x = y ) L (Lynn ,z ) ) ( i ): xL ( x,x ) ( j ): x y ( x negationslash = y ) → ¬ L ( x,y ) The book gives the inequivalent solution x y ( L ( x,y ) x = y ) . This says that everyone loves them- selves and nobody else, whereas my solution allows for the possibility that people might not love themselves. It is unclear from the English which is intended. § 1.4 Problem 12 ( e ): ( x ( x negationslash = Joseph) C (Sanjay ,x ) ) ( f ): x ¬ I ( x ) ( g ): ¬∀ xI ( x ) ( h ): x y ( ( x = y ) I ( y ) ) ( i ): x y ( ( x negationslash = y ) I ( y ) ) ( j ): x ( I ( x ) → ∃ y ( ( y negationslash = x ) C ( x,y ) )) ( k ): x ( I ( x ) ∧ ∀ y ( ( y negationslash = x ) → ¬ C ( x,y ) )) ( l ): x y ( ( x negationslash = y ) ∧ ¬ C ( x,y ) ) ( m ): x yC ( x,y ) ( n ): x y z ( ( x negationslash = y ) ∧ ¬ C ( x,z ) ∧ ¬ ( y,z ) ) ( o ): x y bracketleftbig ( x negationslash = y ) ∧ ∀ z ( C ( x,z ) C ( y,z ) )bracketrightbig Some of these are open to interpretation, due to the vagueness of the English language. For instance, take part ( n ), for which the solutions manual gives x y ( x negationslash = y ∧ ∀ z ¬ ( C ( x,z ) C ( y,z ) )) My solution says, “There are two people x and y and a person z with whom x and y have not chatted,” so that x and y have not chatted with the same person. The solutions manual’s solution says, “There are two
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https://cracku.in/103-which-of-the-following-port-has-registered-the-thi-x-iift-2017
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### IIFT 2017 Question Paper Question 103
Instructions
India has 13 major ports, out of which 6 ports are located in Eastern Coast and 6 ports are in Western Coast of India. 13th port is at Port Blair, located in Andaman & Nicobar Island, which has negligible cargo traffic: Table below provides the traffic data bandied by 12 major ports (thousand tonnes) of India for the period 2011-12 to 2015-16. Based on the table, answer the questions:
Question 103
# Which of the following port has registered the third highest growth in traffic (000) from year2011-12 to 2015-16?
Solution
Ports with growth in traffic are Kolkata, Paradip, Kamarajar, Chidambaranar, Kochin, New Mangalore, Mumbai and Kandla.
From year 2011-12 to year 2015-16,
Growth for Kolkata = 7000Â Â
Growth for Kamarajar = 17000
Growth for Chidambaranar = 9000
Growth for Kochin = 2000
Growth for New Mangalore = 3000
Growth for Mumbai = 5000
Growth for Kandla = 17500
Since all values are approximate, port with third highest growth is either Kandla or Kamarajar whichever is lower.
Actual Growth for Kamarajar = 17250
Actual Growth for Kandla = 17550Â
Hence Kamarajar is the port with 3rd highest growth rate.
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http://www.moomoomathblog.com/2018/09/prime-factorization-of-72-and-24.html
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# Prime Factorization of 72 and 24
What are the prime factors of 72?
What are the prime factors of 24?
Prime factorization is the process of finding which prime numbers multiply together to make the original number.
The prime numbers multiplied together to equal 72 equals 2 x 2 x 2 x 3 x 3.
2^3 x 3^2
Prime factorization of 24 equals 2 x 2 x 2 x 3.
2^3 x 3
MooMooMath and Science upload a new Math and Science video every day.
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https://www.convertunits.com/from/poiseuille/to/poundal+hour/square+foot
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## ››Convert Poiseuille [France] to poundal hour/square foot
poiseuille poundal hour/square foot
How many poiseuille in 1 poundal hour/square foot? The answer is 0.00041337887.
We assume you are converting between Poiseuille [France] and poundal hour/square foot.
You can view more details on each measurement unit:
poiseuille or poundal hour/square foot
The SI derived unit for dynamic viscosity is the pascal second.
1 pascal second is equal to 1 poiseuille, or 2419.0883293091 poundal hour/square foot.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between poiseuille and poundal hour/square foot.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of poiseuille to poundal hour/square foot
1 poiseuille to poundal hour/square foot = 2419.08833 poundal hour/square foot
2 poiseuille to poundal hour/square foot = 4838.17666 poundal hour/square foot
3 poiseuille to poundal hour/square foot = 7257.26499 poundal hour/square foot
4 poiseuille to poundal hour/square foot = 9676.35332 poundal hour/square foot
5 poiseuille to poundal hour/square foot = 12095.44165 poundal hour/square foot
6 poiseuille to poundal hour/square foot = 14514.52998 poundal hour/square foot
7 poiseuille to poundal hour/square foot = 16933.61831 poundal hour/square foot
8 poiseuille to poundal hour/square foot = 19352.70663 poundal hour/square foot
9 poiseuille to poundal hour/square foot = 21771.79496 poundal hour/square foot
10 poiseuille to poundal hour/square foot = 24190.88329 poundal hour/square foot
## ››Want other units?
You can do the reverse unit conversion from poundal hour/square foot to poiseuille, or enter any two units below:
## Enter two units to convert
From: To:
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!
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https://www.gktoday.in/aptitude/a-library-has-an-average-number-of-510-visitor-on-sunday-and-240-on-other-days-the-average-number-of-visitors-per-day-in-a-month-of-30-days-beginning-with-sunday-is/
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A library has an average number of 510 visitor on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with Sunday is :
[A]285
[B]290
[C]295
[D]300
285
That month will have 5 sundays.
∴ Required average =
$= \frac{5 \times 510 + 25 \times 240}{30}$
$= \frac{2550+6000}{30}$
$= \frac{8550}{30} = 285$
Hence option [A] is correct answer.
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https://www.enotes.com/homework-help/what-value-acute-angle-346824
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# what is the value of acute angle
sciencesolve | Certified Educator
You should remember that the value of an acute angle needs to be found in interval `(0^o,90^o)` expressed in degrees or `(0^o,pi/2)` expressed in radians.
Notice that the interval does not include the value of `90^o` , since an angle that measures `90^o` is no more an acute angle, but a right angle.
If the angle is larger than 90^o but smaller than `180^o` , then, the angle is obtuse. Notice that the angle that measures exactly `180^o` is a straight angle.
You also should remember that you may identify different types of triangles, based on angles classification such that:
1. acute triangle with all three angles less than `90^o`
2. right triangle with an angle of `90^o`
3. obtuse triangle with an angle larger than `90^o` but smaller than `180^o` .
rdhlnryn | Student
An angle that measures anything between 0 degrees and 90 degrees is called an acute angle
So angles that measure less than 90 degrees, (for example they could be 89.9degrees, 15 degrees, 0.15 degrees, 30 degrees) are all acute angles.
If you find that an angle measures 90degrees, it's a Right angle.
Those measuring more than 90degrees are called obtuse angles.
If an angle measures 180 degrees , it is called a straight angle.
Those measuring between 180 and 360 degrees are called reflex angles.
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http://mathhelpforum.com/discrete-math/206687-i-tried-working-question-i-reached-certain-point-i-really-need-help.html
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Thread: i tried working this question and i reached to a certain point. i really need help
1. i tried working this question and i reached to a certain point. i really need help
Let a,b is an element of Z. prove that for all x is an element of Z we have gdc(a,b)= gcd(a,b-xa)
2. Re: i tried working this question and i reached to a certain point. i really need hel
i meant gcd**
3. Re: i tried working this question and i reached to a certain point. i really need hel
The pairs (a, b) and (a, b - xa) have not only the same greatest common divisor, but the same set of common divisors.
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https://www.esaral.com/q/one-half-of-a-convex-lens-is-covered-with-a-black-paper
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# One-half of a convex lens is covered with a black paper.
Question.
One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.
solution:
The convex lens will form complete image of an object, even if its one half is covered with black paper. Only the brightness of the image will reduce, in this case it will be half of the brightness of original image. It can be understood by the following two cases:
(a) Let the upper half of the lens be covered and an object be placed between optical centre and the focus $\mathrm{F}_{1}$. The light rays from the object falling on the lower half of the lens form a virtual, erect and magnified image [see fig.(a)]
(b) Let the lower half of the lens be covered and an object be placed between optical centre and the focus $\mathrm{F}_{1}$. The light rays from the object falling on the upper half of the lens form a virtual, erect and magnified image [see fig.(b)]
Leave a comment
Click here to get exam-ready with eSaral
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http://mizar.uwb.edu.pl/version/current/html/catalan1.html
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:: Catalan Numbers
:: by Dorota Cz\c{e}stochowska and Adam Grabowski
::
:: Copyright (c) 2004-2018 Association of Mizar Users
theorem Th1: :: CATALAN1:1
for n being Nat st n > 1 holds
n -' 1 <= (2 * n) -' 3
proof end;
theorem Th2: :: CATALAN1:2
for n being Nat st n >= 1 holds
n -' 1 <= (2 * n) -' 2
proof end;
theorem Th3: :: CATALAN1:3
for n being Nat st n > 1 holds
n < (2 * n) -' 1
proof end;
theorem Th4: :: CATALAN1:4
for n being Nat st n > 1 holds
(n -' 2) + 1 = n -' 1
proof end;
theorem :: CATALAN1:5
for n being Nat st n > 1 holds
(((4 * n) * n) - (2 * n)) / (n + 1) > 1
proof end;
theorem Th6: :: CATALAN1:6
for n being Nat st n > 1 holds
((((2 * n) -' 2) !) * n) * (n + 1) < (2 * n) !
proof end;
theorem Th7: :: CATALAN1:7
for n being Nat holds 2 * (2 - (3 / (n + 1))) < 4
proof end;
definition
let n be Nat;
func Catalan n -> Real equals :: CATALAN1:def 1
(((2 * n) -' 2) choose (n -' 1)) / n;
coherence
(((2 * n) -' 2) choose (n -' 1)) / n is Real
;
end;
:: deftheorem defines Catalan CATALAN1:def 1 :
for n being Nat holds Catalan n = (((2 * n) -' 2) choose (n -' 1)) / n;
theorem Th8: :: CATALAN1:8
for n being Nat st n > 1 holds
Catalan n = (((2 * n) -' 2) !) / (((n -' 1) !) * (n !))
proof end;
theorem Th9: :: CATALAN1:9
for n being Nat st n > 1 holds
Catalan n = (4 * (((2 * n) -' 3) choose (n -' 1))) - (((2 * n) -' 1) choose (n -' 1))
proof end;
theorem :: CATALAN1:10
theorem Th11: :: CATALAN1:11
Catalan 1 = 1
proof end;
theorem Th12: :: CATALAN1:12
Catalan 2 = 1
proof end;
theorem Th13: :: CATALAN1:13
for n being Nat holds Catalan n is Integer
proof end;
theorem Th14: :: CATALAN1:14
for k being Nat holds Catalan (k + 1) = ((2 * k) !) / ((k !) * ((k + 1) !))
proof end;
theorem Th15: :: CATALAN1:15
for n being Nat st n > 1 holds
Catalan n < Catalan (n + 1)
proof end;
theorem Th16: :: CATALAN1:16
for n being Nat holds Catalan n <= Catalan (n + 1)
proof end;
theorem :: CATALAN1:17
for n being Nat holds Catalan n >= 0 ;
theorem Th18: :: CATALAN1:18
for n being Nat holds Catalan n is Element of NAT
proof end;
theorem Th19: :: CATALAN1:19
for n being Nat st n > 0 holds
Catalan (n + 1) = (2 * (2 - (3 / (n + 1)))) * ()
proof end;
registration
let n be Nat;
coherence by Th18;
end;
theorem Th20: :: CATALAN1:20
for n being Nat st n > 0 holds
Catalan n > 0
proof end;
registration
let n be non zero Nat;
cluster Catalan n -> non zero ;
coherence
not Catalan n is zero
by Th20;
end;
theorem :: CATALAN1:21
for n being Nat st n > 0 holds
Catalan (n + 1) < 4 * ()
proof end;
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https://pondscienceinstitute.on-rev.com/svpwiki/tiki-index.php?page=WaveFunction&fullscreen=y
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wavefunction
WaveFunction WaveFunction Sympsionics Symbol
A wave function or wavefunction is a probability amplitude? in quantum mechanics describing the quantum state of a particle or system of particles. Typically, it is a function of space or momentum or rotation and possibly of time that returns the probability amplitude? of a position or momentum for a subatomic particle. Mathematically, it is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time.
The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.
The common application is as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and where | ψ | 2 is equal to the chance of finding the subject at a certain time and position. For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.
A simple wave function is that for a particle in a box. Another simple example is a free particle (or a particle in a large box), whose wave function is a sinusoid where, in the spirit of the uncertainty principle?, the momentum is known but the position is not known.
The modern usage of the term wave function refers to a complex vector or function, i.e. an element in a complex Hilbert space?. Typically, a wave function is either:
a complex vector with finitely many components,
a complex vector with infinitely many components,
a complex function of one or more real variables (a continuously indexed complex vector).
In all cases, the wave function provides a complete description of the associated physical system. An element of a vector space can be expressed in different bases; and so the same applies to wave functions. The components of a wave function describing the same physical state take different complex values depending on the basis being used; however the wave function itself is not dependent on the basis chosen. In this respect they are like spatial vectors in ordinary space because choosing a new set of cartesian axes by rotation of the coordinate frame does not alter the vector itself, only the representation of the vector with respect to the coordinate frame. A basis in quantum mechanics is analogous to the coordinate frame in that choosing a new basis does not alter the wavefunction, only its representation, which is expressed as the values of the components above. (underline added)
Because the probabilities that the system is in each possible state should add up to 1, the norm of the wave function must be 1. wikipedia - wavefunction
12.11 - Eighteen Attributes or Dimensions
Angular Momentum coupling
Born Oppenheimer approximation
Function
magnetic moment
Quantum coupling
Renner-Teller Effect
Rotational-vibrational coupling
rovibronic coupling
Russell WaveFunction
Russell Wavefunction Equation
spin-orbit coupling
spintronics
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# Curriculum Catalog
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## Transcription
1 Curriculum Catalog 2017 Glynlyon, Inc.
2 Table of Contents ALGEBRA II FUNDAMENTALS COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND PROBLEMS... 1 UNIT 3: LINEAR EQUATIONS AND INEQUALITIES... 2 UNIT 4: POLYNOMIALS... 2 UNIT 5: ALGEBRAIC FRACTIONS... 2 UNIT 6: SEMESTER REVIEW AND EXAM... 2 UNIT 7: REAL NUMBERS... 3 UNIT 8: QUADRATIC RELATIONS AND SYSTEMS... 3 UNIT 9: EXPONENTIAL FUNCTIONS... 3 UNIT 10: COUNTING PRINCIPLES... 4 UNIT 11: REVIEW... 4 UNIT 12: SEMESTER REVIEW AND EXAM... 4 UNIT 13: FINAL EXAM Glynlyon, Inc. i
3 Course Overview Algebra II is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic techniques and methods in order to develop student understanding of advanced number theory, concepts involving linear, quadratic and polynomial functions, and precalculus theories. This course also integrates geometric concepts and skills throughout the units, as well as introducing students to basic trigonometric identities and problem solving. By the end of the course, students will be expected to do the following: Understand set notation and the structure of mathematical systems. Know how to use functional notation and operations on functions. Simplify and solve algebraic fractions. Perform operations on polynomials, including factoring, long division, and synthetic division. Solve algebraic word problems involving mixtures, money, integers, and work. Evaluate and solve radical expressions and equations. Solve systems of equations with graphing, substitution, and matrices. Graph and solve quadratic equations, including conic sections. Graph and solve exponential and logarithmic equations. Calculate permutations, combinations, and complex probabilities. Unit 1: Set, Structure, and Function 1. Course Overview 13. Algebraic Expressions: Exponents Part 2 2. Properties of Sets 14. Algebraic Expressions: Multiplication and Division 3. Operations of Sets Part 1 4. Quiz 1: Set Theory 15. Algebraic Expressions: Multiplication and Division 5. Structure: Axioms Part 2 6. Structure: Applications 16. Exponents of Exponential Expressions 7. Relations and Functions: Definitions 17. Algebraic Expressions: Combining Terms 8. Relations and Functions: Graphs 18. Quiz 3: Algebraic Expressions 9. Relations and Functions: Function Notation 19. Special Project* 10. Relations and Functions: Inverses 20. Test 11. Quiz 2: Relations and Functions 21. Alternate Test* 12. Algebraic Expressions: Exponents Part Glossary and Credits Unit 2: Numbers, Sentences, and Problems 1. Number Order and Absolute Value 11. Compound Sentences 2. Sums and Products 12. Quiz 2: Equalities and Inequalities 3. Quiz 1: Numbers 13. Number Problems 4. Solving Equations 14. Motion Problems 5. Multiplication Property 15. Miscellaneous Problems 6. Multi-step Equations 16. Quiz 3: Problems 7. Equations with Parentheses 17. Special Project* 8. Literal Expressions 18. Test 9. Solving Inequalities 19. Alternate Test* 10. Graphing Solution Sets for Inequalities 20. Glossary and Credits 2017 Glynlyon, Inc. 1
4 Unit 3: Linear Equations and Inequalities 1. Line Graphs 12. Solutions by Addition 2. Line Graphs by Two Points 13. Solutions by Substitution 3. Slope of Lines Part Application of Systems of Equations 4. Slope of Lines Part Quiz 2: Solutions for Systems 5. Equations: Point Slope Part Solving Inequalities 6. Equations: Point Slope Part Solving Two-order Inequalities 7. Equations: Point Slope Part Quiz 3: Solving Inequalities 8. Equations: Slope-Intercept 19. Special Project* 9. General Equation of a Line 20. Test 10. Quiz 1: Lines 21. Alternate Test* 11. Solutions for Systems of Equations 22. Glossary and Credits Unit 4: Polynomials 1. Products and Factoring 12. Quiz 2: Polynomials 2. Multiplying Polynomials by Polynomials 13. Direct Variation 3. Using Special Products Part Inverse Variation 4. Using Special Products Part Joint and Combined Variation 5. Factoring Trinomials 16. Quiz 3: Working Variations 6. Factoring Special Products Part Project: Creating an Algorithm 7. Factoring Special Products Part Special Project* 8. Quiz 1: Special Products 19. Test 9. Addition and Subtraction Operations 20. Alternate Test* 10. Division with Polynomials 21. Glossary and Credits 11. Synthetic Division Unit 5: Algebraic Fractions 1. Multiplying and Dividing with Fractions 12. Proportions 2. Reducing Rational Expressions 13. Quiz 3: Fractional Equations 3. Multiplying Algebraic Fractions 14. Applications of Fractions 4. Dividing Algebraic Fractions 15. Mixture Problems 5. Quiz 1: Algebraic Fractions 16. Work Problems 6. Adding and Subtracting Algebraic Fractions 17. Quiz 4: Problems with Fractions 7. Addition and Subtraction 18. Special Project* 8. Mixed Expressions and Complex Fractions 19. Test 9. Quiz 2: Addition and Subtraction of Fractions 20. Alternate Test* 10. Equations with Fractions 21. Glossary and Credits 11. Fractional Equations Unit 6: Semester Review and Exam A II F 1. Review 3. Alternate Exam - Form A* 2. Exam 4. Alternate Exam - Form B* 2017 Glynlyon, Inc. 2
5 Unit 7: Real Numbers 1. Real Numbers 11. Word Problems Involving Quadratic Equations 2. Law of Radicals 12. Sum and Product of Roots 3. Conjugates 13. The Discriminant 4. Radical Equations 14. Imaginary Numbers 5. Quiz 1: Real Numbers 15. Quiz 3: Quadratic Formula 6. Quadratic Equations 16. Special Project* 7. Factoring Quadratic Equations 17. Test 8. Completing the Square 18. Alternate Test* 9. Quiz 2: Quadratic Solutions 19. Glossary and Credits 10. Quadratic Formula Unit 8: Quadratic Relations and Systems 1. Distance Formula 12. Systems of Equations 2. Circle 13. Solutions of Inequalities 3. Ellipse 14. Applications of Conic Sections: Part 1 4. Ellipse Continued 15. Applications of Conic Sections: Part 2 5. Quiz 1: Conics and the Coordinate Plane 16. Applications of Conic Sections: Part 3 6. Conic Sections: Parabola 17. Constant of Proportionality 7. Conic Sections: Parabola Continued 18. Quiz 3: Applications of Conics 8. Conic Sections: Hyperbola 19. Special Project* 9. Conic Sections: Hyperbola Continued 20. Test 10. Identifying Conic Sections 21. Alternate Test* 11. Quiz 2: Conics 22. Glossary and Credits Unit 9: Exponential Functions 1. Exponential Functions 13. Graphs of Logarithmic Functions 2. Fractional Exponents 14. Solving Logarithmic Equations 3. Exponential Equations 15. Logarithmic Applications 4. Graphing Exponential Functions 16. Quiz 2: Logarithmic Functions 5. Exponential Applications 17. Matrices 6. Quiz 1: Exponential Functions 18. System Solutions with Matrices 7. Logarithmic Functions 19. Addition and Multiplication of Matrices 8. Evaluation of Logarithms 20. Quiz 3: Matrices 9. Evaluating Exponential Functions, Common 21. Special Project* Logarithms, and Natural Logarithms 22. Test 10. General Properties of Logarithms 23. Alternate Test* 11. Scientific Notation 24. Glossary and Credits 12. Calculation of Common Logarithms 2017 Glynlyon, Inc. 3
6 Unit 10: Counting Principles 1. Progressions: Sequences 11. Quiz 3: Combinations 2. Progressions: Series 12. Probability: Concepts 3. Quiz 1: Sequences and Series 13. Probability: Equally Likely Outcomes 4. Permutations: Factorials 14. Probability: Multiplication Principle 5. Permutation Formula 15. Conditional Probability 6. Permutations: Applications 16. Quiz 4: Probability 7. Quiz 2: Permutations 17. Special Project* 8. Combination Formula 18. Test 9. Combinations: Applications 19. Alternate Test* 10. Combinations: Binomial Coefficients 20. Glossary and Credits Unit 11: Review 1. Integers 14. Real Numbers Continued 2. Integers Continued 15. Quiz 2: Review 3. Open Sentences 16. Quadratic Relations and Systems 4. Open Sentences Continued 17. Quadratics Continued 5. Graphs 18. Exponential Functions 6. Graphs Continued 19. Exponential Functions Continued 7. Quiz 1: Review 20. Counting Principles 8. Polynomials 21. Counting Principles Continued 9. Polynomials Continued 22. Quiz 3: Review 10. Algebraic Fractions Part Special Project* 11. Algebraic Fractions Part Test 12. Algebraic Fractions Part Alternate Test* 13. Real Numbers 26. Glossary and Credits Unit 12: Semester Review and Exam A II F 1. Review 3. Alternate Exam - Form A* 2. Exam 4. Alternate Exam - Form B* Unit 13: Final Exam A II F 1. Exam 3. Alternate Exam - Form B* 2. Alternate Exam - Form A* (*) Indicates alternative assignment 2017 Glynlyon, Inc. 4
### This image cannot currently be displayed. Course Catalog. Algebra II Glynlyon, Inc.
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JOIN
Match Editorial
Room 1 Review Archive Rookie Review Discuss this match Problem Set Want to write a feature? Lessons Learned
SRM 93
May 30, 2002
Lessons Learned the Hard Way
SRM 93 was a Thursday night contest. As a landmark, it was the night before the 2002 Soccer World Cup kicked off. There were 653 coders for the match, with 392 coders and 42 rooms in Div-II.
The problem slate appeared relatively simple, but each of the problems tripped up at least 40% of submissions. One thing that springs out is that the problem slate was not as diverse as usual: the 250 and 500 both required rounding calculations, and the 500 and 1050 both required looping on r objects selected from a pool of n objects.
250 (Median):
This problem was to return the middle value(s) of an array of ints. In the case of even length, return the mean of the two middle-most values. All rounding should be upward.
This problem appears to have been approached as a speed-typing test. Unfortunately, the result was a car-wreck. Of the submitted solutions, less than 50% passed systest. This was consistent in all three groupings (greens, greys and rookies.)
The solution to this problem is extremely simple: Sort the array, then either return the mid value if length is odd, or take the two inner values and combine them. The following should work.
```Arrays.sort(input);
if (input.length % 2 ==1) {
return input[input.length/2];
} else {
int sum = input[input.length/2] + input[input.length -1];
int av = sum/2;
if (2*av < sum) return av+1;
return av;
}
```
Problems:
1. Failing to sort the array. Such a solution would not have passed two of the examples.
2. Failing to deal with negative numbers correctly. Problem is that -(2n + 1)/2 = -n so any solution that relied on adding 1 failed. This problem appears to have been the main cause of failure.
3. Incorrect calculation of the mean (by using the input[n/2] and input[n/2+1] instead of input[n/2-1].
4. Having two variables with similar names, and working with one in one loop branch, and another in a second.
5. Not rounding at all.
What I find fascinating about this problem was that only 25% of problems which failed were actually successfully challenged. Since most solutions required less than 15 lines of code....
500 (Hiring):
Given an array containing the exam results and salary requirements of prospective employees, along with a salary cap, calculate the best 3 candidates whose total salaries do not exceed the cap. Because the average is taken of three values, rounding is to the nearest integer.
This problem is best tackled as an exhaustive search, using fixed loops. Notable was the fact that the pass rate varied from 58% among the greens to 47% in the grey rooms.
Problems:
1. Not making any attempt to generate the possible solutions.
2. Not checking that you aren't using the same entry/employee more than once
3. Not rounding correctly.
4. Concentrating on rounding the average, then actually returning the sum.
5. Looping over the possible solutions correctly, but then returning then first one found.
1050 (Big2):
This was a simulation problem based on the card game poker. Given 13 cards, count the number of poker hands which can be made with these cards, which contain a straight or better.
The solution requires the generation of the hands, and then their analysis. For hand generation, fixed loops is the easiest way to go. The key to the problem, of course is the hand evaluator.
The number of submissions for this problem was tiny: only 15% of the Div-II coders submitted. As with most simulation problems, the complexity of the solution was the main problem.
Problems:
1. Failing to deal with the fact that (for straights), and Ace is both high and low.
2. Typos in lookup tables.
3. Not looping over possible hands correctly.
By slowjoe
TopCoder Member
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+0
0
140
1
The equation y = -16t^2 + 80t describes the height (in feet) of a projectile launched from the ground at 80 feet per second. At what t will the projectile reach 86 feet in height for the first time? Express your answer as a decimal rounded to the nearest tenth.
Jul 24, 2022
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In going over possible 3x3x3 cuboids (of which there are, ahem, a lot), there's one which I find particularly interesting and would like to present as a challenge for mechanism designers.
First, the doctrinaire description: Make a 3x3x3 cuboid which can't move on the U and D axes and only allows greater than deep cuts on the F, B, R and L axes. To make things more interesting, the mechanism should also allow slice moves, in fact as long as you're moving, say R and L, you should be able to rotate both of them completely independently without an internal mechanism ever getting stuck.
A possibly more intuitive way of understanding the puzzle is to think of it as a regular shallow cut 3x3x3 cuboid, with four axes which can turn and the curious property that whenever you rotate a face then the four axes which aren't opposite that one flip which ones can rotate and which ones can't. The slicing property still applies, so as long as you're moving just R and L they should rotate completely independently without any internal mechanism catching. Thinking about the puzzle this way makes the way the slicing property works out seem much more magical.
Epicyclic gearing may be helpful in designing this one, although I honestly am not sure how to do it even using that, so I present it as a mechanism design challenge for all you inventors out there.
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Paolo Lava paoloplava at gmail.com
Mon Nov 19 14:40:52 CET 2012
```There was an error(a(38)=35 was not correct). The first terms should be:
1,2,3,4,5,8,6,10,7,12,9,11,18,16,13,22,15,14,
17,23,19,20,34,21,24,25,26,33,27,40,32,42,29,
28,30,46,31,*37*,35,39,36,38,41,42,52,44,45,47,62,48,53,....
Paolo
2012/11/19 Paolo Lava <paoloplava at gmail.com>
> Dear Seqfans,
>
>
>
> I am thinking to a sort of headache sequence (permutation of natural
> numbers) like the following:
>
>
>
> “Starting from a(1)=1, for any n the sum of the next a(n) numbers is a
> prime. No repetition of numbers is allowed. At any step the minimum integer
> not yet used and not leading to a contradiction should be choosen.”
>
>
>
> The squence starts with 1, 2, 3, 4, 5, 8, 6, 10, 7, 12…
>
>
>
> a(1)=1 -> Next term is 2, prime.
>
> a(2)=2 -> the sum of the next two terms 3+4=7, prime.
>
> a(3)=3 -> 4+5+8=17, prime.
>
> a(4)=4 -> 5+8+6+10=29, prime.
>
> a(5)=5 -> 8+6+10+7+12=43, prime.
>
> a(6)=8 but I have also a(7)=6 that must be covered before a(6). Therefore
> the sequence became:
>
>
>
> 1, 2, 3, 4, 5, 8, 6, 10, 7, 12, 9, 11, 18,… with 10+7+12+9+11+18=67, prime.
>
> Then coming back to a(6)=8 : 1, 2, 3, 4, 5, 8, 6, 10, 7, 12, 9, 11, 18,
> 16… with 6+10+7+12+9+11+18+16=89.
>
>
>
> I calculated:
>
> 1,2,3,4,5,8,6,10,7,12,9,11,18,16,13,22,14,15,17,23,19,20,34,21,24,25,26,33,27,40,
> x…
>
>
>
> The problem is that the next term “x”, that is a(31), must satisfy at the
> same time a(13)=18 and a(17)=14 but
>
>
>
> 16+13+22+14*+*15+17+23+19+20+34+21+23+24+25+26+27+30=369, that is odd,
> and 15+17+23+19+20+34+21+23+24+25+26+27+30=304, that is even and therefore
> no integer “x” can satisfy the system 369+x=p1 and 304+x=p2, with p1 and p2
> both prime.
>
>
>
> To avoid the incongruence I changed a(17)=14 (because it came after the
> choice of a(13)=18) with the minimum available integer greater than 14,
> that is 15.
>
> Of course this problem will arise again in the contruction process (two or
> more terms to be satisfied at the same point).
>
>
>
> I calculated 42 terms that should be OK:
>
>
> 1,2,3,4,5,8,6,10,7,12,9,11,18,16,13,22,15,14,17,23,19,20,34,21,24,25,26,33,27,40,32,42,29,28,30,46,31,35,36,48,37,49
>
>
>
> The sequence I found was:
>
> 1,2,3,4,5,8,6,10,7,12,9,11,18,16,13,22,15,14,17,23,19,20,34,21,24,25,26,33,27,40,32,42,29,28,30,46,31,35,36,48,37,49,39,38,44,41,43,45,63,47,54,50,56,51,52,57,62,53,55,58,65,96,69,59,
> 64, 60, 61, 70, 65, 67, 66, 68, 85, 71, 73, 72, 74, 79, 75, 76, 77, x…
>
>
>
> Again, the choice of x depends on a(36)=46 and a(43)=39 but
>
> 31+35+36+48+37+49+39+38+44+41+43+45+63+47+54+50+56+51+52+57+62+53+55+58+65+96+69+59+64+60+61+70+65+67+66+68+85+71+73+72+74+79+75+76+77=2636
> (even) and
> 38+44+41+43+45+63+47+54+50+56+51+52+57+62+53+55+58+65+96+69+59+64+60+61+70+65+67+66+68+85+71+73+72+74+79+75+76+77=2361
> (odd).
>
>
>
> Therefore a(43)=39 must be changed into a(43)=45. And so on.
>
>
>
> Is anybody willing to check/extend the numbers in this sequence? Thank in
>
>
>
> Paolo
>
>
> P.S. Variant for masochists: “Starting from a(1)=1, for any n the sum of
> the next a(n) digits is a prime. No repetition of numbers is allowed. At
> any step the minimum integer not yet used and not leading to a
> contradiction should be choosen.”. 1,2,3,4,5,8,6,40,10,7,14,...
>
>
>
```
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# Boundary conditions with dielectrics question
Hi all,
I'm doing what should be a pretty simple problem, but some theory is giving me trouble.
Basically, in this problem I have a conducting sphere, surrounded by a thick insulating layer, and then vacuum outside that. I'm attempting to solve for the potential in the insulating layer by using a Legendre Polynomial expansion. To find the coefficients of the expansion in the different regions, I have to match boundary conditions (BC's) at the interfaces.
Now, I just did a different problem in Jackson, a dielectric sphere in a uniform E field. Here, he uses the same method, and the BC's he applies at the dielectric/vacuum interface are that $E_{parallel}$ and $D_{normal}$ must be continuous at the boundary, which he writes as (a is the radius of the dielectric sphere and epsilon is its dielectric constant):
$E_{parallel}$:
$(-1/a)\frac{\partial \phi_{in}}{\partial \theta} |_{r =a}= (-1/a)\frac{\partial \phi_{out}}{\partial \theta}|_{r =a}$
$D_{normal}$:
$-\epsilon\frac{\partial \phi_{in}}{\partial r}|_{r =a} = -\epsilon_0\frac{\partial \phi_{out}}{\partial r}|_{r =a}$
And then he proceeds to solve it like that. So I tried applying that to this problem, but it gave me garbage answers (the potential of the conducting sphere is constant, so $E_{parallel}$ & $D_{normal}$ are zero for it, which then made all the coefficients of the Legendre expansion for the insulator potential 0...which clearly isn't right).
Luckily, I found a solution to this problem (It's actually problem 4.24 in Griffiths), but I still don't understand it. In this problem, the BC's they used were that the potential has to be continuous on the conductor/insulator interface, but nothing about either D or E. They said the same thing about the insulator/vacuum interface, but that one also seems to have the $D_{normal}$ condition.
My question is, why is the continuous potential the only BC on the first interface, while they use both on the second interface? Further, why isn't there the E_parallel BC at all?
If it helps, the solution I found to this problem is here, on page 2: www.physics.utah.edu/~wu/phycs4420/notes/solutions06.pdf
Thanks!
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OpenTS Tutorial
MyMoveManager
The MyMoveManager Object
The move manager is responsible for determining which moves are valid for each iteration. If we had defined our move to be "Move from position X to position Y," we would have the same set of moves at each iteration, but we don't, so we have to determine how far each customer can move forward and back at each iteration.
As before the complete source is available, but we've duplicated it here:
import org.coinor.opents.*;
public class MyMoveManager implements MoveManager
{
public Move[] getAllMoves( Solution solution )
{
int[] tour = ((MySolution)solution).tour;
Move[] buffer = new Move[ tour.length*tour.length ];
int nextBufferPos = 0;
// Generate moves that move each customer
// forward and back up to five spaces.
for( int i = 1; i < tour.length; i++ )
for( int j = -5; j <= 5; j++ )
if( (i+j >= 1) && (i+j < tour.length) && (j != 0) )
buffer[nextBufferPos++] = new MySwapMove( tour[i], j );
// Trim buffer
Move[] moves = new Move[ nextBufferPos];
System.arraycopy( buffer, 0, moves, 0, nextBufferPos );
return moves;
} // end getAllMoves
} // end class MyMoveManager
The move manager generates a number of moves being careful not to generate any that are logically impossible such as moving a customer from position three to a spot five places earlier. That would be a negative position which we cannot allow.
We expect that some moves will turn out to be duplicates of each other: If Customer A is followed by Customer B, then an A+1 move would be the same as a B-1 move. Since the hash code for the move is based on the customer only, we might find that A+1 is on the tabu list but B-1 is not.
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https://www.doorsteptutor.com/Exams/BITSAT/Physics/Questions/Topic-Current-Electricity-11/Part-1.html
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# Current Electricity [BITSAT (Birla Institute of Technology & Science Admission Test) Physics]: Questions 1 - 6 of 27
Access detailed explanations (illustrated with images and videos) to 382 questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. Unlimited Access, Unlimited Time, on Unlimited Devices!
View Sample Explanation or View Features.
Rs. 250.00 -OR-
## Question 1
Current Electricity
### Question
MCQ▾
If current flowing in a conductor changes by , then power will change by –
### Choices
Choice (4)Response
a.
b.
c.
d.
## Question 2
Current Electricity
### Question
MCQ▾
When the key K is pressed at time , then which of the following statement about the current in the resistor of the given circuit is true?
### Choices
Choice (4)Response
a.
oscillates between and
b.
At and with time it goes to
c.
at all
d.
and at all .
## Question 3
Current Electricity
### Question
MCQ▾
When current flows in a conductor, then the ratio of the intensity of electric field at any point within the conductor and the current density at a point is called –
### Choices
Choice (4)Response
a.
Inductance
b.
Specific resistance
c.
Resistance
d.
Conductance
## Question 4
### Question
MCQ▾
If a wire of resistance is covered with ice and a voltage of is applied across the wire then rate of melting of ice will be –
### Choices
Choice (4)Response
a.
b.
c.
d.
None of the above
## Question 5
Current Electricity
### Question
MCQ▾
electric heater operates on a line, then the rate at which it develops heat in watts will be –
### Choices
Choice (4)Response
a.
670
b.
1310
c.
810
d.
1210
## Question 6
Current Electricity
### Question
MCQ▾
Two identical batteries, each of emf and internal resistance by passing a current through it. The maximum power that can be developed across using these batteries is –
### Choices
Choice (4)Response
a.
b.
c.
d.
Developed by:
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# Gain of a transistor
1. May 23, 2010
### Danish_Khatri
I am studying the design of an amplifier in common emitter configuration. I am studying from microelectronic circuits by sedra and smith. the author has described two terms for gain of a amplifier. one is the represented by Av and is called the voltage gain of that amplifier and the other is Gv called the overall gain of amplifier. I m not able to understand the difference between the two. can anybody help me out with this confusion?
2. May 23, 2010
### sophiecentaur
Voltage gain just says what it says. It is the ratio of the volts out over the volts in.
'Overall gain' will be referring to the gain in actual Power, that is achieved. After all, a transformer can give you a voltage gain of 100, but the power transferred can't be greater than unity.
It's a matter of input impedance and output impedance. For instance, if you want to feed 100V into 50Ω you need 200W. To feed 100V into 1kΩ you only need 10W.
3. May 23, 2010
### Danish_Khatri
Dear I was not able to grasp on your answer. would you please explain it in terms of transistor itself
4. May 23, 2010
### waht
Depending on the edition that you have, in the fifth edition Sedra/Smith on page 463 the quantities G_v and A_v are clearly defined.
G_v is the ratio of v_out to the open voltage of the source generator (it's not the input voltage of the amplifier).
A_v is the ratio of v_out to the input voltage of the amplifier.
Last edited: May 23, 2010
5. May 23, 2010
### sophiecentaur
A fair enough question but you need to realise that a transistor never operates in isolation. It is part of an amplifying circuit and it has no inherent Voltage Gain without being in a circuit - you actually state your question in the context of a common emitter circuit so you appreciate what I have just said.
6. May 25, 2010
### Danish_Khatri
Thanks for your help dear. I understood this concept when I repeated the paragraph.
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Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!
#### Online Quiz (WorksheetABCD)
Questions Per Quiz = 2 4 6 8 10
### MEAP Preparation - Grade 7 Mathematics2.56 Addition of Binomials - I
#### Horizontal Method
In this method, the expressions to be added are summed first. Then like terms in the expressions are written together using Associative Law for addition.
Example: Add the expressions (3a2+2b), (7a-4b) and (a2-6a).
Solution:
Summing the expressions, we have,
(3a2+2b)+(7a-4b)+(a2-6a)
Writing the like-terms together using Associative Law,
(3a2+a2)+(2b-4b)+(7a-6a)
=(3a2+a2)+[2b+(-4)b]+[7a+(-6)a]
=(3+1)a2+[2+(-4)]b+[7+(-6)]a
=4a2-2b+a.
Directions: Add the binomials given below. Also write at least 10 examples of your own.
Q 1: Add (3x+4y) and (x-2y).4x+2y2a+6b3x2+2y2 Q 2: Add (5a+4b) and (-3a+2b).2a+6b14ab8a+6b4x+2y Q 3: Add (2m+n) and (3n-m).3m+4n2m-2nm+4n4m+4n Q 4: Add (-3c-4d) and (8c-6d).-9c+4d11c-10d5c-10d11c+2d Q 5: Add (8p-9q) and (5q+6p).13p-3q15p+15q14p+14q14p-4q Q 6: Add (a2+b2) and (a2-b2).5a2a23a26a Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!
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# I need help with this transfer function.
Discussion in 'Homework Help' started by dimatizer, Dec 1, 2012.
1. ### dimatizer Thread Starter New Member
Dec 1, 2012
3
0
Vout is across Vc2
Last edited: Dec 1, 2012
2. ### WBahn Moderator
Mar 31, 2012
18,093
4,918
#1) What help do you need?
#2) What efforts have you made to work the problem?
3. ### dimatizer Thread Starter New Member
Dec 1, 2012
3
0
G(s)= (3RCS+(RCS)^2+1)/[(SC)^2)(RSC+2)^2]
I achieved this answer by doing VC2=I2/CS=(Inot/cs)(1/SRC+2) and
Vin=(Inot)(Z) were Z is the equivalent impedance and my Transfer function is Vc2/Vin
I need help figuring out what I'm doing wrong because I don't believe I'm getting the right answer
4. ### WBahn Moderator
Mar 31, 2012
18,093
4,918
Without commenting (yet) one whether you are right or wrong, why is it that you believe you aren't getting the right answer? What have you done to check you answer?
5. ### dimatizer Thread Starter New Member
Dec 1, 2012
3
0
i found the transfer function of just the left circuit to be 1/(1+RCS) . i believe the right answer should be [(1/(1+RCS))(1/(1+RCS))]
6. ### blah2222 Well-Known Member
May 3, 2010
565
33
Also, it would help if you used LaTeX formatting to read these equations easier.
http://en.wikibooks.org/wiki/LaTeX/Mathematics
$
G(s)\ =\ \frac{3RCS+(RCS)^{2}+1}{(SC)^{2}(RSC+2)^{2}}
$
Is a lot easier to read than:
G(s)= (3RCS+(RCS)^2+1)/[(SC)^2)(RSC+2)^2]
Now, I have not verified if this is indeed correct but for the sake of making it easier to read. Click "quote" to see the formatting.
7. ### ramancini8 Member
Jul 18, 2012
447
119
Look to the left of the dotted line and calculate the Thevenin equivalent circuit. Replace the stuff to the left with the TEC, and use the voltage divider rule to calculate the voltage across C2.
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# Pi R Squared
[Another guest blog entry by Dr. Gene Chase.]
You’ve heard the old joke.
Teacher: Pi R Squared.
Student: No, teacher, pie are round. Cornbread are square.
The purpose of this Pi Day note two days early is to explain why $\pi$ is indeed a square.
The customary definition of $\pi$ is the ratio of a circle’s circumference to its diameter. But mathematicians are accustomed to defining things in two different ways, and then showing that the two ways are in fact equivalent. Here’s a first example appropriate for my story.
How do we define the function $\exp(z) = e^z$ for complex numbers z? First we define $a^b$ for integers $a > 0$ and b. Then we extend it to rationals, and finally, by requiring that the resulting function be continuous, to reals. As it happens, the resulting function is infinitely differentiable. In fact, if we choose a to be e, the $\lim_{n\to\infty} (1 + \frac{1}{n})^n \,$ not only is $e^x$ infinitely differentiable, but it is its own derivative. Can we extend the definition of $\exp(z) \,$ to complex numbers z? Yes, in an infinite number of ways, but if we want the reasonable assumption that it too is infinitely differentiable, then there is only one way to extend $\exp(z)$.
That’s amazing!
The resulting function $\exp(z)$ obeys all the expected laws of exponents. And we can prove that the function when restricted to reals has an inverse for the entire real number line. So define a new function $\ln(x)$ which is the inverse of $\exp(x)$. Then we can prove that $\ln(x)$ obeys all of the laws of logarithms.
Or we could proceed in the reverse order instead. Define $\ln(x) = \int_1^x \frac{1}{t} dt$. It has an inverse, which we can call $\exp(x)$, and then we can define $a^b$ as $\exp ( b \ln (a))$. We can prove that $\exp(1)$ is the above-mentioned limit, and when this new definition of $a^b\,$ is restricted to the appropriate rationals or reals or integers, we have the same function of two variables a and b as above. $\ln(x)$ can also be extended to the complex domain, except the result is no longer a function, or rather it is a function from complex numbers to sets of complex numbers. All the numbers in a given set differ by some integer multiple of
[1] $2 \pi i$.
With either definition of $\exp(z)$, Euler’s famous formula can be proven:
[2] $\exp(\pi i) + 1 = 0$.
But where’s the circle that gives rise to the $\pi$ in [1] and [2]? The answer is easy to see if we establish another formula to which Euler’s name is also attached:
[3] $\exp(i z) = \sin (z) + i \cos(z)$.
Thus complex numbers unify two of the most frequent natural phenomena: exponential growth and periodic motion. In the complex plane, the exponential is a circular function.
That’s amazing!
Here’s a second example appropriate for my story. Define the function on integers $\text{factorial (n)} = n!$ in the usual way. Now ask whether there is a way to extend it to (some of) the complex plane, so that we can take the factorial of a complex number. There is, and as with $\exp(z)$, there is only one way if we require that the resulting function be infinitely differentiable. The resulting function is (almost) called Gamma, written $\Gamma$. I say almost, because the function that we want has the following property:
[4] $\Gamma (z - 1) = z!$
Obviously, we’d like to stay away from negative values on the real line, where the meaning of (–5)! is not at all clear. In fact, if we stay in the half-plane where complex numbers have a positive real part, we can define $\Gamma$ by an integral which agrees with the factorial function for positive integer values of z:
[5] $\Gamma (z) = \int_0^\infty \exp(-t) t^{z - 1} dt$.
If we evaluate $\Gamma (\frac{1}{2})$ we discover that the result is $\sqrt{\pi}$.
In other words,
[6] $\pi = \Gamma(\frac{1}{2})^2$.
Pi are indeed square.
That’s amazing!
I suspect that the $\pi$ arises because there is an exponential function in the definition of $\Gamma$, but in other problems involving $\pi$ it’s harder to find where the $\pi$ comes from. Euler’s Basel problem is a good case in point. There are many good proofs that
$1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}$
One proof uses trigonometric series, so you shouldn’t be surprised that $\pi$ shows up there too.
$\pi$ comes up in probability in Buffon’s needle problem because the needle is free to land with any angle from north.
Can you think of a place where $\pi$ occurs, but you cannot find the circle?
George Lakoff and Rafael Núñez have written a controversial book that bolsters the argument that you won’t find any such examples: Where Mathematics Comes From. But Platonist that I am, I maintain that there might be such places.
# Rationalization Rant
Every high school math student has been taught how to rationalize the denominator. We tell students not to give an answer like
$\frac{1}{\sqrt{2}}$
because it isn’t fully “simplified.” Rather, they should report it as
$\frac{\sqrt{2}}{2}.$
This is fair, even though the second answer isn’t much simpler than the first. What does it really mean to simplify an expression? It’s a pretty nebulous instruction.
We also don’t consider
$\frac{12}{1+\sqrt{5}}$
to be rationalized because of the square root in the denominator, so we multiply by the conjugate to obtain
$2-2\sqrt{5}.$
In this particular example, multiplying by the conjugate was really fruitful and the resulting expression does indeed seem much more desirable than the original expression.
But here’s where it gets a little ridiculous. Our Algebra 2 book also calls for students to rationalize the denominator when (1) a higher root is present and (2) roots containing variables are present. Let me show you an example of each situation, and explain why this is going a little too far.
## Rationalizing higher roots
First, when a higher root is present like
$\sqrt[5]{\frac{15}{2}},$
the book would have students multiply the top and bottom of the fraction inside the radical by $2^4$ so as to make a perfect fifth root in the denominator. The final answer would be
$\frac{\sqrt[5]{240}}{2}.$
Simpler? You decide.
This becomes especially problematic when we encounter sums involving higher roots. It’s certainly possible, using various tricks, to rationalize the denominator in expressions like this:
$\frac{1}{2-\sqrt[3]{5}}.$
But is that really desirable? The result here is
$\frac{1}{2-\sqrt[3]{5}}\cdot\frac{4+2\sqrt[3]{5}+\sqrt[3]{25}}{4+2\sqrt[3]{5}+\sqrt[3]{25}}=\frac{4+2\sqrt[3]{5}+\sqrt[3]{25}}{3},$
which is, arguably, more complex than the original expression. Can anyone think of a good reason to do this, except just for fun?
## Rationalizing variable expressions
Now, let’s think about variable expressions. Here is a problem, directly from our Algebra 2 book (note the directions as well):
Write the expression in simplest form. Assume all variables are positive.
$\sqrt[3]{\frac{x}{y^7}}$
The method that leads to the “correct” solution is to multiply the fraction under the radical by $\frac{y^2}{y^2}$, and to finally write
$\frac{\sqrt[3]{xy^2}}{y^3}.$
This is problematic for two reasons. (1) This isn’t really simpler than the original expression and (2) this expression isn’t even guaranteed to have a denominator that’s rational! (Suppose $y=\sqrt{2}$ or even $y=\pi$.) Once again I ask, can anyone think of a good reason to do this, except just for fun??
## So how far do we take this?
Is it reasonable to ask someone to rationalize this denominator?
$\frac{1}{2\sqrt{2}-\sqrt{2}\sqrt[3]{5}+2\sqrt{5}-5^{5/6}}$
You can rationalize the denominator, but I’ll leave that as an exercise for the reader. So how far do we take this? I had to craft the above expression very carefully so that it works out well, but in general, most expressions have denominators that can’t be rationalized (and I do mean “most expressions” in the technical, mathematical way–there are are an uncountable number of denominators of the unrationalizable type). All that being said, I think this would make a great t-shirt:
And I rest my case.
# Leap Day Birthday Math
## Happy leap day!!!
Here are some leap-day birthday thoughts I discussed with my colleagues and students today:
### What’s the probability of a leap year birthday?
The probability that someone is born on a leap day is $\frac{1}{365\cdot 4+1}=\frac{1}{1461}\approx 0.000684$. Oh wait, that’s not completely true. Leap years don’t really occur every four years. Years divisible by 100 are not leap years, unless also divisible by 400. So, the actual probability is
$\frac{100-4+1}{365\cdot 400+100-4+1}= \frac{97}{146097}\approx 0.000639$.
### What’s the probability of having triplets on a leap day?
One of our RM students is a triplet, born today. What are the chances of that occurring? Well, the statistics on triplets are pretty hard to get right. But let’s say the occurrence of a triplet birth is 1 in 8000. (That’s my informal estimate based on this site and this site.) I think we can say that the probability of being a triplet is 3 times that (right?). Then, the probability of being a triplet born on a leap day is
$\left(\frac{100-4+1}{365\cdot 400+100-4+1}\right)\left(\frac{3}{8000}\right)= \frac{291}{1168776000}\approx\frac{1}{4016412} \approx 0.249 \times 10^{-7}$.
The current US population is 311,591,917, so that means there are roughly 77 triplets in the US with leap day birthdays. Happy birthday to all of you!
Bonus thought question: Iif you have quadruplets born on a leap day, you get to celebrate 4 birthdays every four years, so doesn’t that average out to one birthday a year?
### Half-birthday for those born on August 29
One of my other colleagues has a birthday on August 29th. So today is her half birthday! But it only comes around every four years (roughly). Hooray!
But then that got us thinking about half birthdays: Some people, like those born on August 30th or 31st NEVER have a half birthday. How sad!! This happens to anyone born on August 30th, August 31st, March 31st, October 31st, May 31st, or December 31st. That’s a lot of people without half birthdays.
But wait. When is your actual half birthday? Shouldn’t it be 182.5 days before/after your birthday? That’s not necessarily the same date in the month. For instance, my birthday is May 15. So my half birthday should be November 15, right? Wrong. My half birthday is (May 15 + 182.5 days), which is November 13th or November 14th, depending on if you round up or down. Even accounting for a leap year, it’s still not quite right.
Who else is miscalculating their half birthday? Unless your birthday is in June, April, October, or December, you’re half-birthday isn’t what you think it is. To calculate your half birthday, use this amazing half birthday calculator I just discovered!
# Square One
I was raised on this show, and it’s so fun that you can find clips of it on youtube, including these three gems. At the end of every episode of Square One there was a mathematical music video. I just showed my Precalculus class this first video, but I spared them the other two. If you’ve never seen Square One, these will give you a little bit of a feel for the show, or if you know and loved the show, these will help you take a walk down memory lane.
# Inverse functions and the horizontal line test
I have a small problem with the following language in our Algebra 2 textbook. Do you see my problem?
Horizontal Line Test
If no horizontal line intersects the graph of a function f more than once, then the inverse of f is itself a function.
Here’s the issue: The horizontal line test guarantees that a function is one-to-one. But it does not guarantee that the function is onto. Both are required for a function to be invertible (that is, the function must be bijective).
Example. Consider $f:\mathbb{R}\to\mathbb{R}$ defined $f(x)=e^x$. This function passes the horizontal line test. Therefore it must have an inverse, right?
Wrong. The mapping given is not invertible, since there are elements of the codomain that are not in the range of $f$. Instead, consider the function $f:\mathbb{R}\to (0,\infty)$ defined $f(x)=e^x$. This function is both one-to-one and onto (bijective). Therefore it is invertible, with inverse $f^{-1}:(0,\infty)\to\mathbb{R}$ defined $f(x)=\ln{x}$.
This might seem like splitting hairs, but I think it’s appropriate to have these conversations with high school students. It’s a matter of precise language, and correct mathematical thinking. I’ve harped on this before, and I’ll harp on it again.
Love this.
# Why are infinite series so hard to grasp?
I’ve posted on infinite series a few times before. But I was inspired to touch on the topic again because I saw this post, yesterday, over at the Math Less Traveled. Actually, the post isn’t really about infinite series as much as it is about p-adic numbers and zero divisors. I’m excited to read more from Brent on this subject. But I digress.
The point I want to make with this post is that students struggle with wrapping their minds around convergent infinite series, and yet they live with them all the time. Students have inconsistently held beliefs about infinite sums.
The simplest convergent series is a geometric series $\sum_{n=1}^\infty a_n=a_1r^{n-1}$ which converges to $\frac{a_1}{1-r}$. The easy proof of this fact goes like this: we look at the sum formula for a finite geometric series, $s_n=\frac{a_1(1-r^n)}{1-r}$ and we notice that
$\lim_{n\to\infty}\frac{a_1(1-r^n)}{1-r}=\frac{a_1}{1-r}$
for $|r|<1$.
But this proof isn’t very satisfying for the student encountering infinite series for the first time ever. Evaluating the limit feels like ‘magic.’ The idea of adding up an infinite amount of things and getting a finite value is unsettling. I admit, it sounds like quite a lot to swallow. That being said, however, students have no problem declaring the infinite series
$0.3 + 0.03 + 0.003 + 0.0003 + \cdots$
to be $1/3$. It’s not “close to” $1/3$, it’s not “approaching” $1/3$, it IS EQUAL TO $1/3$. And my Precalculus students already accept this as fact. So without even thinking about it, they’ve been living with convergent infinite series all along. Hah!
Once they finally shake their denial, they can more easily accept the convergence of other infinite series like $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$. At first when students encounter a series like this, they think, “surely we can’t say the sum is EQUAL to $\frac{\pi^2}{6}$. It must be close to $\frac{\pi^2}{6}$ or approach it, but equal to?” But the same students make no such distinction with $0.3+0.03+0.003+\cdots = \frac{1}{3}$.
So there it is. An inconsistently held belief about infinite sums. To the student: You cannot have it both ways. Either you must agree with, or deny, both of the following equations:
$0.3+0.03+0.003+\cdots = \sum_{n=1}^\infty 0.3(0.1)^{n-1}=\frac{1}{3}$
$1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\cdots = \sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$
But to believe one equation is true and the other is only ‘kind of’ true is inconsistent. I rest my case. 🙂
# The Arc Cotangent Controversy
I love this discussion at squareCircleZ. All my readers should check it out. Which is the graph of arccot(x)?
from squarecircleZ
from squarecircleZ
I especially like this controversy because some big players have weighed in on each side. Mathcad and Maple prefer the first interpretation, Mathematica and Matlab prefer the second.
For a more thorough treatment, check out the original post here. Three cheers for great math blogging! 🙂
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# Find out whose turn it is to buy the croissants
A team has decided that every morning someone should bring croissants for everybody. It shouldn't be the same person every time, so there should be a system to determine whose turn it is next. The purpose of this question is to determine an algorithm for deciding whose turn it will be to bring croissants tomorrow.
Constraints, assumptions and objectives:
• Whose turn it is to bring croissants will be determined the previous afternoon.
• On any given day, some people are absent. The algorithm must pick someone who will be present on that day. Assume that all absences are known a day in advance, so the croissant buyer can be determined on the previous afternoon.
• Overall, most people are present on most days.
• In the interest of fairness, everyone should buy croissants as many times as the others. (Basically, assume that every team member has the same amount of money to spend on croissants.)
• It would be nice to have some element of randomness, or at least perceived randomness, in order to alleviate the boredom of a roster. This is not a hard constraint: it is more of an aesthetic judgement. However, the same person should not be picked twice in a row.
• The person who brings the croissants should know in advance. So if person P is to bring croissants on day D, then this fact should be determined on some previous day where person P is present. For example, if the croissant bringer is always determined the day before, then it should be one of the persons who are present the day before.
• The number of team members is small enough that storage and computing resources are effectively unlimited. For example the algorithm can rely on a complete history of who brought croissants when in the past. Up to a few minutes of computation on a fast PC every day would be ok.
This is a model of a real world problem, so you are free to challenge or refine the assumptions if you think that they model the scenario better.
Origin: Find out who's going to buy the croissants by Florian Margaine. My reformulation here has slightly different requirements.
• What exactly was the question? Can we assume that people are absent more or less the same amount? What is wrong with taking the person who has done this the least number of times, or simply a random person? – Pål GD Jul 24 '13 at 22:15
• @PålGD Assuming that people are absent by about the same amount would be a simplification. Do it if you want, but if your algorithm works for part-timers, that's better. Taking the person who has done this the least number of times is one solution (though mind the requirement that they know one day in advance, it does make the solution not completely trivial). A random person can also work, but randomness introduces a deviation from fairness which you might want to bound. – Gilles 'SO- stop being evil' Jul 24 '13 at 22:20
• What? No salivating picture? You want us to slave away at our desk doing maths instead of slipping out to the bakery? – Caleb Jul 25 '13 at 7:13
• @Gilles - FYI, running an experiment on P.SE with your version of this question. Now that both sites are a bit older, I'm curious to see how each community's answers shape up. – user9347 Jul 25 '13 at 18:54
There are two categories of solutions to this sort of problem that I'm aware of: biased lotteries and filtered/generated random sequences.
First, let's dispense with easy but wrong solutions that keep no state. Any lottery-style solution that maintains no state will have the number of wins in a binomial distribution, which fails the "as many times" criterion. You can select a random sequence that picks all people equally (just going around the list does that; permutations provide randomness), but once people start going on vacation your sequence now has holes. Unless you keep track, you will again find yourself with binomial distributions instead of maintenance of equal effort.
Let's also commit to having actual randomness. You might want this so that, for instance, a person cannot schedule their vacation on the basis of a deterministic algorithm so that they are never present when it is their turn to buy croissants (until they use up all their vacation days, I suppose).
So, on to the two types of solutions.
1. To construct a biased lottery, first note that we can pick from pretty much any continuous distribution (with finite deviation) to generate numbers for our lottery. The loser can then be the person with the lowest number. Then the simplest bias is to keep track of whether each individual has bought more or less than their share. You can measure the bias in units of croissants. You can tune the degree of randomness by changing the width and shape of the distribution--this will also determine how far away any individual can get from "the same number of times". Gaussians are easy; they allow for reasonable surprise without having tails that are too long ("unfair"). So the basic shape of the solution is (in Scala code)
case class Employee(var bias: Double) {
def eat { bias -= 1 }
def buy(n: Int) { bias += n }
def roll = bias + stdev * Random.nextGaussian
}
You can keep track of who bought last and give them a hefty bias bonus (e.g. 10*stdev) to keep people from buying twice in a row save in the edge case where vacation structure allowed everyone to have bought "last" time. (i.e. you buy, then go on vacation.) Same thing for not being present on the day they're selected. (If someone is absent every other day they eventually will come up as they burn through their bias bonus; I consider this a feature rather than a bug.)
So, you collect your list of present employees for the day, have them all roll for the lottery, pick the lowest, and update. You can choose whether to have the buying bonus be equal to the number of employees (good when the cost is negligible but the trip to get croissants is burdensome), the number of employees present (good if the trip is easy but the cost is burdensome), or something in between (to acknowledge both burdens). It's probably better to only have the "eat" penalty for people who are present, but you can do it either way if you feel that merely being on vacation doesn't give you a right pitch in less.
2. To construct a filtered random sequence, first you need to generate a random sequence. Shuffling a list of the employees is as good a way as any to start. Just go through the list, in order, from day to day. If someone can't buy because they're absent or can't be told or bought before, skip them. Now you have a problem: you're accumulating people who have been skipped. That's okay, though. When you get to the end of your sequence, append the list of skipped employees to the full list before shuffling. Now the probability of coming up is proportional to the number of times you've been skipped, which maintains the "same number of times" property.
If you use a standard shuffle, it's also particularly easy to quantify the randomness when there are no vacations. If you picked people completely at random, the knowledge of who was to bring next would contain $\log_2(N)$ bits of information if there were $N$ employees. Instead, however, only $N!$ instead of $N^N$ possible sequences are allowed, so the information is reduced by $\log_2\left[\left( {N!} \over {N^N} \right)^{1/N}\right] \approx -{1 \over {\log(2)}} + {\log_2{\sqrt{2 \pi / N}} \over N } \approx -1.4$ bits (for large $N$; for $N=10$ it's $~1.14$).
Personally I favor the biased lottery solution as the control over the randomness is better. With filtered sequences, you can come up with more complex ways to generate sequences. For example, rather than taking a random permutation, perform local swaps out to a certain distance, or allow swapping of people out of the pool entirely (but they go onto the skipped-list)—but these things require more algorithmic effort. With the lottery, you just adjust the standard deviation.
Let $\{P_1,...,P_n\}$ be the set of croissant's byers. Let ${v_i}^k-1$ be the amount spent by $P_i$ on croissant up to the day $k$ (it can be the number of times he buy croissant if they always spend the same money whatever the number of peoples present, which don't look clever enough for our croissants lover); the $-1$ is for initialisation and to avoid division by $0$.
For some parameter $l$, let $v^k=\sum_{i=1}^n ({v_i}^k)^l$.
At day $k$, they choose the next day's croissant's buyer by firing a random variable that outcome $i$ with probability $1-\frac{(v_i^k)^l}{v^k}$. If the chosen one is not here (today or the day after) they toss the coin again until they find a suited one (he does exists, because they are mostly here every day...).
And they lived happily until they find out that $P_1$, that coward, was there, only one day over two, and so, never buys any croissant!
After some reflection (and may be a bit of torture on $P_1$ so that he refund the croissant he eat without paying) they modifies a their algorithm.
They compute the average price of croissant they pay every day and call it $v$.
On the first day they compute a planning of buyers for the days to come. To do so they do as before with the random variable, and updating the $v_i^k$ by the price they should have paid on day $k$, i.e. adding $v$ each time they are planned to go to the baker. Because they are clever and they don't want to pay too much they also remember how much they really paid at day $k$ so that when they will update the planning no one is penalised.
They plan, until every $P_i$ has a date in the future where he should buy croissant.
If $P_i$ was planned to buy croissant on day $k+1$ but announces that he can't on day $k$ (or if he hasn't be warmed) he give his place to someone present that has no obligation the following day e.g. $P_j$ and he take the next turn of $P_j$.
The day when the first of the $P_i$ is not planned to buy croissant in the future, they prolong their planning (with the random variable computed with the $v_i^k$ updated to the real amount they have paid and the amount planned) until everyone is back on the line.
And when this goes forever, they live happy, sharing equally the price of croissant.
But $P_1$ is not happy. Indeed, he think that the chosen $l$ is too small and so the probability of paying twice in a row too big. Whatever ... The others let him choose $l$ as large as he wants. Because he is grumpy but not stupid, he chose $l=k$ that way as time pass even if the ratio between big payers and small players tend to not be seen the big $l$ tend to emphasize it.
Still $P_1$ is not so happy, he is there only half of the days (so half of the croissant) and has to pay as much as $P_2$ that is here every days. Unfair!
But because they are tired of grumpy $P_1$, they chase in away. But in the corner of their head they are still thinking of changing the $v_i^k$ in the difference between what they paid and what they eat (normalized to get positive values) but they are too lazy and too full of croissants.
Ps: Sorry for the bad English but I'm not native speaker and it's late ... please feel free to correct mistakes (and may be add so spices to the story ...)
Every iteration you have
• A list of people who are present and available to buy
If you pick a person at random among the people in the list and excluded the previous buyer, you achieve your objectives:
1. The algorithm is "maximally" random as we use the minimum amount of information from the previous iteration and choose randomly.
2. On average people pay for (N/(N-1)) croissants every time they participate in an extraction making the algorithm as fair as possible.
3. I would suggest to eliminate the no-repeat rule to make this maximally random.
Other algorithms I've seen proposed are less random or less fair:
1. "Deck shuffle" algorithms are not really random in the sense that the probability to have to pay is not constant (1/N in the first pick, 1/(N-1) in the second... 1 at the Nth pick -- if one hasn't been picked yet). Furthermore, if you are picked first, you have exactly zero chances to be picked for the next N times. The system is easily broken by coming in rarely until picked and then constantly.
2. "Compensative" algorithms that try to actively make everyone get the same number of croissants instead of relying on the properties of random numbers fail to be random or fair (or both).
• With $N$ people and $m$ employees present on average per day, the deviation in number of times will be approximately $\sqrt{N / m}$. Since solutions exist that never deviate more than $1$, this is a strange definition of "fair" (especially since it was specified to be "as many times"). – Rex Kerr Jul 25 '13 at 2:05
• $N$ purchases, of course, not people. – Rex Kerr Jul 25 '13 at 13:05
• @RexKerr why would you buy more croissants than employees? – Sklivvz Jul 25 '13 at 13:25
• I'm confused. Where did I suggest one would? – Rex Kerr Jul 25 '13 at 17:06
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• # question_answer One day, Ravi left home and cycled 10 km southwards, turned right and cycled 5 km and turned right and cycled 10 km and turned left and cycled 10 km. How many kilometers will he have to cycle to reach his home straight? A) 10km B) 15km C) 20km D) 25km
Here, Ravi starts from home at A, moves 10 km southwards up to B, turns right and moves 10 km up to C, turns right again and moves 10 km up to D and finally turns left and moves 10 km up to E. Thus, his distance from initial position A = AE $=AD+DE$ $=BC+DE=\left( 5+10 \right)km=15km.$
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Mathbox for Alexander van der Vekens < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > Mathboxes > setsnidel Structured version Visualization version GIF version
Theorem setsnidel 43834
Description: The injected slot is an element of the structure with replacement. (Contributed by AV, 10-Nov-2021.)
Hypotheses
Ref Expression
setsidel.s (𝜑𝑆𝑉)
setsidel.b (𝜑𝐵𝑊)
setsidel.r 𝑅 = (𝑆 sSet ⟨𝐴, 𝐵⟩)
setsnidel.c (𝜑𝐶𝑋)
setsnidel.d (𝜑𝐷𝑌)
setsnidel.s (𝜑 → ⟨𝐶, 𝐷⟩ ∈ 𝑆)
setsnidel.n (𝜑𝐴𝐶)
Assertion
Ref Expression
setsnidel (𝜑 → ⟨𝐶, 𝐷⟩ ∈ 𝑅)
Proof of Theorem setsnidel
StepHypRef Expression
1 setsnidel.c . . . . . 6 (𝜑𝐶𝑋)
21elexd 3489 . . . . 5 (𝜑𝐶 ∈ V)
3 setsnidel.n . . . . . 6 (𝜑𝐴𝐶)
43necomd 3066 . . . . 5 (𝜑𝐶𝐴)
5 eldifsn 4693 . . . . 5 (𝐶 ∈ (V ∖ {𝐴}) ↔ (𝐶 ∈ V ∧ 𝐶𝐴))
62, 4, 5sylanbrc 586 . . . 4 (𝜑𝐶 ∈ (V ∖ {𝐴}))
7 setsnidel.s . . . 4 (𝜑 → ⟨𝐶, 𝐷⟩ ∈ 𝑆)
8 setsnidel.d . . . . 5 (𝜑𝐷𝑌)
9 opelres 5837 . . . . 5 (𝐷𝑌 → (⟨𝐶, 𝐷⟩ ∈ (𝑆 ↾ (V ∖ {𝐴})) ↔ (𝐶 ∈ (V ∖ {𝐴}) ∧ ⟨𝐶, 𝐷⟩ ∈ 𝑆)))
108, 9syl 17 . . . 4 (𝜑 → (⟨𝐶, 𝐷⟩ ∈ (𝑆 ↾ (V ∖ {𝐴})) ↔ (𝐶 ∈ (V ∖ {𝐴}) ∧ ⟨𝐶, 𝐷⟩ ∈ 𝑆)))
116, 7, 10mpbir2and 712 . . 3 (𝜑 → ⟨𝐶, 𝐷⟩ ∈ (𝑆 ↾ (V ∖ {𝐴})))
12 elun1 4127 . . 3 (⟨𝐶, 𝐷⟩ ∈ (𝑆 ↾ (V ∖ {𝐴})) → ⟨𝐶, 𝐷⟩ ∈ ((𝑆 ↾ (V ∖ {𝐴})) ∪ {⟨𝐴, 𝐵⟩}))
1311, 12syl 17 . 2 (𝜑 → ⟨𝐶, 𝐷⟩ ∈ ((𝑆 ↾ (V ∖ {𝐴})) ∪ {⟨𝐴, 𝐵⟩}))
14 setsidel.r . . 3 𝑅 = (𝑆 sSet ⟨𝐴, 𝐵⟩)
15 setsidel.s . . . 4 (𝜑𝑆𝑉)
16 setsidel.b . . . 4 (𝜑𝐵𝑊)
17 setsval 16504 . . . 4 ((𝑆𝑉𝐵𝑊) → (𝑆 sSet ⟨𝐴, 𝐵⟩) = ((𝑆 ↾ (V ∖ {𝐴})) ∪ {⟨𝐴, 𝐵⟩}))
1815, 16, 17syl2anc 587 . . 3 (𝜑 → (𝑆 sSet ⟨𝐴, 𝐵⟩) = ((𝑆 ↾ (V ∖ {𝐴})) ∪ {⟨𝐴, 𝐵⟩}))
1914, 18syl5eq 2869 . 2 (𝜑𝑅 = ((𝑆 ↾ (V ∖ {𝐴})) ∪ {⟨𝐴, 𝐵⟩}))
2013, 19eleqtrrd 2917 1 (𝜑 → ⟨𝐶, 𝐷⟩ ∈ 𝑅)
Colors of variables: wff setvar class Syntax hints: → wi 4 ↔ wb 209 ∧ wa 399 = wceq 1538 ∈ wcel 2114 ≠ wne 3011 Vcvv 3469 ∖ cdif 3905 ∪ cun 3906 {csn 4539 ⟨cop 4545 ↾ cres 5534 (class class class)co 7140 sSet csts 16472 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2178 ax-ext 2794 ax-sep 5179 ax-nul 5186 ax-pr 5307 ax-un 7446 This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2622 df-eu 2653 df-clab 2801 df-cleq 2815 df-clel 2894 df-nfc 2962 df-ne 3012 df-ral 3135 df-rex 3136 df-rab 3139 df-v 3471 df-sbc 3748 df-dif 3911 df-un 3913 df-in 3915 df-ss 3925 df-nul 4266 df-if 4440 df-sn 4540 df-pr 4542 df-op 4546 df-uni 4814 df-br 5043 df-opab 5105 df-id 5437 df-xp 5538 df-rel 5539 df-cnv 5540 df-co 5541 df-dm 5542 df-res 5544 df-iota 6293 df-fun 6336 df-fv 6342 df-ov 7143 df-oprab 7144 df-mpo 7145 df-sets 16481 This theorem is referenced by: (None)
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Worksheet Basic Practice with Springs
1. A vertical helical spring 20 cm long extends to a length of 25 cm when it supports a load of 50 N. Determine its spring constant.
2. A vertical helical spring is 50 cm long when a load of 80 N is hung from it and 52 cm when the load is changed to 82 N. Find its spring constant.
3a. Two identical helical springs are attached to one another, end-to-end, making one long vertical spring. If k = 250 N/m is the elasticity constant for each spring separately, what is the constant for this combination?
3b. How large a load, in newtons, is required to stretch the system 10 cm?
4. Two identical helical springs are attached side-by-side, making a parallel vertical combination. If k = 250 N/m is the elasticity constant for each spring separately, how large a load, in kilograms, will extend the system 10 cm?
5. A certain spring that obeys Hooke's Law stretches 30 cm when a load of 0.35 N is added to it. How much energy is stored in the spring when it is compressed 5.0 cm?
Refer to the following information for the next two questions.
A 400-g mass is attached to the end of a spring (k = 80 N/m). The spring is then stretched (along a horizontal surface) 3.5 cm from its equilibrium position and released.
6a. Find the speed of the mass as it passes through the equilibrium position.
6b. Find the mass' acceleration just as it was released.
Refer to the following information for the next two questions.
A spring system consists of a stationary spring and a 60-gram mass attached to one end that slides along a horizontal, frictionless surface. When a horizontal force of 0.80 N is applied to the mass, it stretches the spring 4.0 cm.
7a. What is the acceleration of the mass when the system is initially released?
7b. What is the speed of the mass as it passes through its equilibrium position?
Refer to the following information for the next four questions.
A spring system consists of a stationary spring and a 100-gram mass attached to one end that slides along a horizontal, frictionless surface. When a horizontal force of 8.0 N applied to the mass, it stretches the spring 10.0 cm.
8a. How much total energy is initially stored in the spring?
8b. What is the speed of the mass as it passes through a point 5.0 cm from its equilibrium position?
8c. What is its speed at the exact instant when it passes through its equilibrium position?
8d. Why aren't these speeds in a ratio of 1:2?
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### slight issue with a greatest common divisor calculator
Hello everyone. Someone gave me the following program that calculates the greatest common divisor of two positive whole numbers (posted below). I understand why the program works if I enter two numbers that aren't equal. So if I enter 10 and 15, I understand why it outputs 5. However, the program works even if I enter two numbers that are equal, and I can't figure out why. If I input 10 and 10, for example, then in the g_c_d function neither the if nor the else if block are entered. So the computer shouldn't know what value of "low" is, since low hasn't been given a value. So when I entered 10 and 10, I was expecting to get nonsense output or something. However, it correctly outputs 10. Can somebody explain why? Thanks!
#include <iostream>
/*Determines greatest common divisor*/
using namespace std;
int g_c_d(int x, int y); //function g_c_d with 2 integers
int main(){
int input1;
int input2;
cout<<"Enter a whole number"<<endl;
cin>>input1;
cout<<"Enter another whole number"<<endl;
cin>>input2;
cout<<"The greatest common divisor is"<<endl;
cout<<g_c_d(input1, input2); //outputs function determined below
return 0;
}
int g_c_d(int x, int y){
int low;
int high;
if (x>y){
low=y;
high=x;
}
else if (y>x){
low=x;
high=y;
}
while (y%low!=0 || x%low!=0){
low--;
}
return low;
}
if i enter the following code and run it i get an error of low being used without being intitialized which you should be getting and you were correct in your assumption that that would happen. as to why you are not getting the error i do not know maybe you have >= or <= sign in there instead of the > or < which would then output the correct answer
If it gives the correct answer you are lucky. Both high and low are uninitialised and may contain any random value.
If `low` is larger than both x and y, it will be decremented repeatedly until it is equal to x or y. That gives the answer you want.
If `low` is smaller than both x and y, then the wrong answer is returned.
And if `low` happens to be zero, you get a divide by zero error and the program will crash.
Last edited on
If it gives the correct answer you are unlucky
@ tag and Chervil: I copied an pasted this program, so it looks exactly like that in my compiler. So I don't know why it's not giving me an error. Like I say, I have input 20 and 20, and it outputs 20. I've put in 15 and 15, and it outputs 15. So I'm still not sure why it behaves properly.
what compiler are you using?
Xcode
strangelove1221 wrote:
So I don't know why it's not giving me an error.
Statistically, if the value of low is chosen at random, and both x and y are quite small, the probability that it will give the right answer but for the wrong reason is very high.
I originally said it was luck that gave you the right answer.
ne555 pointed out that it was in fact bad luck if it gives the right answer. Why? because it means the bug goes undetected, but is still there, waiting to bite you.
Some compilers will issue a warning when a variable might be used without being initialised, if so, pay attention to that warning. In any case, it's good practice to give all variables an initial value.
Last edited on
I understand now, thanks. So if I haven't assigned a value to low but I start to use it as if it has a value, then the compiler will assign it a random value?
Not exactly. The compiler allocates a particular memory location to hold the contents of the variable. If it is not initialised, whatever value is already in that memory (from some previous use) will be interpreted as its value. It's not a good idea to use this method to generate random numbers.
Topic archived. No new replies allowed.
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## Introduction
Reading an ECG is like juggling fire while riding a unicycle: performing the fundamentals systematically, the same way, every time, will prevent you from getting burned. Presented here is the authors' approach to reading an ECG. It is less important to follow 1 particular approach; rather, choose 1 validated approach that works for you and apply it the same way, every time, to every tracing.
## Step 1: Rate
Recall that each "little box" on the time axis of a tracing is 0.04 seconds in duration, with each "big box" comprising 5 little boxes and equal to 0.2 seconds. Thus, calculate the rate as 300 divided by the number of big boxes between complexes (300/1 = rate of 300; 300/2 = rate of 150; etc). Alternatively (more accurate and more difficult math), calculate the rate as 1500 divided by the number of little boxes between complexes (1500/5 = rate of 300; 1500/17 = rate of 88; etc).
The above methods are accurate only if the rhythm is regular. A second approach to calculate rate is to recall that the rhythm strip is 10 seconds in duration. Count the number of complexes present in the rhythm strip and multiply by 6, yielding the rate. This method is accurate whether the rhythm is regular or irregular.
Using your choice of these methods, calculate the atrial rate (P waves) and the ventricular rate (QRS complexes).
## Step 2: Rhythm analysis
First, search for atrial activity. Are there P waves? The best place to find P waves is in the inferior leads (II, III, and aVF) and V1.
Second, are the P waves sinus P waves or nonsinus P waves? Sinus P waves should be upright in the inferior leads and biphasic in lead V1. If the atrial activity is not a sinus P wave, what is it? Atrial flutter? Atrial tachycardia? Is there no organized atrial activity suggesting atrial fibrillation?
Finally, what is the relationship between the atrial activity and the ventricular activity? Does the atrial activity precede the ventricular activity with a constant interval? Does the atrial activity follow the ventricular activity, suggesting retrograde conduction? Are the atrial and ventricular depolarizations independent of each other? Is A-V block present?
## Step 3: Axis
Consider first if the axis is normal or not. Recall that lead I is located at 0 degrees, lead II at +60 degrees, and lead aVF at +90 degrees:
If the QRS complex is more positive than negative in leads I, II, and aVF, the axis is normal, defined as axis between +100 and -30 degrees.
If the QRS complex is positive in aVF but predominantly negative in lead I, a rightward axis is present.
If the QRS complex ...
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https://www.techyv.com/questions/learn-about-pmt-function-in-excel-2007-in-detail/
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## Learn About Pmt Function In Excel 2007 In Detail.
Asked By 0 points N/A Posted on -
Hello,
I am currently using Microsoft Excel 2007 on my Windows 10 PC. I just wish to know about the pmt function in excel 2007. If someone has some information on the same, please share your views.
SHARE
Answered By 50 points N/A #299295
## Learn About Pmt Function In Excel 2007 In Detail.
The function PMT has a syntax as follows:
• PMT(rate, np, pv)
• Here,Rate is the rate of interest.
• Np is the total number of installments/payments for the loan.
• Pv is the present value; which can be the principal amount.
For Example, Consider the image given below:
The payment in cell C6 will depend on the formula as:
=-PMT(C2/12,C3,C4)
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0
# Percent increase in 12000 to 14000?
Wiki User
2010-01-16 14:12:25
The increase is from the original, so take (2000 divided by 12000) x 100 = the % increase = 16 and 2/3 %
Wiki User
2010-01-16 14:12:25
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jasdumas/Notes from xgboost: GBM.md
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Notes on xgboost: Extreme Gradient Boosting Machine
default
Background
• Computation in C++
• tree-based models
• easy to use, install, R/python interface
• Automatic parallel computation on a single Machine
• Tunable parameters
• requires a spare matrix (dgcMatrix) which is more memory efficient
• need to provide input features, target, objective, number of iterations
• can score or predict model based on new data
• cross validation measures a model's predictive power
Supervised Machine Learning
• to train a model we need to optimize a loss function.
• Root Mean Square Error (RMSE) is typically used for regression
${RMSD}({\hat {\theta }})={\sqrt {{MSE}({\hat {\theta }})}}={\sqrt { {E} (({\hat {\theta }}-\theta )^{2})}}$
• Logloss is for binary/logistic classification
$$log loss = -\frac{1}{N}\sum_{i=1}^N\sum_{j=1}^My_{ij}\log(p_{ij})$$
$$log loss = -\frac{1}{N}\sum_{i=1}^N {(y_i\log(p_i) + (1 - y_i)\log(1 - p_i))}$$
• mLogloss is for multi classification for multinomial logistic analysis
$$F = -\frac{1}{N}\sum_{i}^{N}\sum_{j}^{M}y_{ij} \cdot Ln(p_{ij}))=\sum_{j}^{M} \left (-\frac{1}{N}\sum_{i}^{N}y_{ij} \cdot Ln(p_{ij})) \right ) = \sum_{j}^{M}F_i$$
• Regularization is another important part of the model. A good regularization term controls the complexity of the model which prevents over-fitting.
• The training objective is: objective = loss function + regularization
obj = ${L} + \Omega$
where the loss function controls the predictive power and regularization controls simplicity (or rather complexity)
• in xgboost: gradient decent is used to optimize the objective which is a first order optimization algorithm to take steps to find the local minimum point or peak. The performance can be improved by considering both the first and second order.
Tree Building algorithm
• how can we define a tree that improves the prediction along the gradient/
• decision tree (binary splits), each data point flows to one of the leaves following the direction on each node
• internal node: each internal node splits the flow of the data points by one the features (variables)
• the condition on the edge of specifies what data can flow through
• leaves: data points reach a leaf and assigned by weight, which is the prediction
• how to find a good structure?
• how to choose features to split?
• when to split?
• how to assign a prediction score?
• In each split we want to greedily find the best point that can optimize the objective by:
1. sorting the number
2. scan the best splitting point
3. choose the best feature
• Calculate gain (gini index or entropy)
Nice note! Thx.
Jason2Brownlee commented May 25, 2024
Excellent notes on the algorithm!
I note that even knowing the algorithm internals does not help to configure the algorithm in practice. We still end up using a grid search to configure xgboost in practice.
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## NVIDIA Interview Question
• 0
Country: India
Comment hidden because of low score. Click to expand.
0
of 0 vote
Sorting would do it in O(nlogn + n) which is O(nlogn)
Comment hidden because of low score. Click to expand.
1
of 1 vote
Subarray. Not sub-sequence.
Comment hidden because of low score. Click to expand.
0
BTW whats the difference between subarray and subsequence
Comment hidden because of low score. Click to expand.
0
According to the example given, it's neither. If you look at the example it seems the poster meant "subset"
Comment hidden because of low score. Click to expand.
0
So Manan is right.
Comment hidden because of low score. Click to expand.
0
of 0 vote
O(n) time with hashtable.
``````def get_consecutive_sequence(list):
# key = element in list;
# value[0] = the number of elements in the left side of the key
# value[1] = the number of elements in the right side of the key
d = {}
for x in list:
if x not in d:
d[x] = [0,0]
if x - 1 in d:
d[x][0] = d[x-1][0] + 1
if x + 1 in d:
d[x][1] = d[x+1][1] + 1
# get the element who has maximum of value[0] + value[1]
max_x = max(d, key=lambda x : d[x][0] + d[x][1])
# construct the result
result = [i for i in range(max_x - d[max_x][0], max_x)] \
+ [i for i in range(max_x, max_x + d[max_x][1] + 1)]
return result``````
Comment hidden because of low score. Click to expand.
0
I've seen this code many a times for this problem, but it doesn't return a subarray with consecutive numbers, it returns a permutation of the original array with consecutive numbers. Take for example the array
[1,7,12,3,9,18,4,25,-6,2]
there is no continuously increasing subarray here but your program will return [1,2,3,4] not the right answer.
Comment hidden because of low score. Click to expand.
0
of 0 vote
Use hashtable to achieve O(n) complexity. Please let me know if there is any mistake.
``````public static int[] find(int[] array)
{
// Contains the number of elements of each subarray
ArrayList<Integer> list = new ArrayList<Integer>();
// Key: the element in the int array, e.g. array[i].
// Value: the index of the element in "list" that saves
// the number of elements of the subarray that array[i] belongs in.
Hashtable<Integer, Integer> table = new Hashtable<Integer, Integer>();
int seqIndex = 0; // The number of subarrays so far.
for(int i = 0; i < array.length; ++i)
{
if(table.containsKey(array[i]-1))
{
table.put(array[i], table.get(array[i]-1)); // array[i] and array[i-1] belong to the same subarray
list.set(table.get(array[i]-1),list.get(table.get(array[i]-1))+1); // Increase the number of elements of the subarray by 1
}
else if(table.containsKey(array[i]+1))
{
table.put(array[i], table.get(array[i]+1));
list.set(table.get(array[i]+1),list.get(table.get(array[i]+1))+1);
}
else if(table.containsKey(array[i]))
{
list.set(table.get(array[i]),list.get(table.get(array[i]))+1);
}
else
{
table.put(array[i], seqIndex++); // array[i] does not belong to any subarray.
list.add(1); // The new array contains only array[i], so it has only 1 element.
}
}
// Find the subarray that contains maximum number of elements.
int max = 0;
for(int i = 0; i < list.size(); ++i)
{
if(max < list.get(i))
{
max = list.get(i);
}
}
int[] result = new int[max];
int resultIndex = 0;
for(int i = 0; i < array.length; ++i)
{
if(list.get(table.get(array[i])) == max)
{
result[resultIndex++] = array[i];
}
}
return result;
}``````
Comment hidden because of low score. Click to expand.
0
can you explain what you're trying to do here, reading an explanation is 100 times easy and better than reading raw code.
Comment hidden because of low score. Click to expand.
0
actully it is like first we have to sort the array .. then apply some logic to get the longest consequitive sequence of integers from the array
Comment hidden because of low score. Click to expand.
0
So we can use ArrayList list to store the number of elements in each subarray (here by subarray I mean the subarray that contains consecutive numbers).
Also, we can use Hashtable table to store each element in array. The KEY is array[i], while VALUE is the index of subarray it belongs in.
Then, we traverse the array. For example: {4,5,34,33,32,11,10,31}
1. Put <4, 0> in table, and let list[0] = 1; (4 belongs to the 0-th subarray, so the 0-th subarray has 1 element)
2. Put<5, 0> in the table, and let list[0] = 2; (we know 5 belongs to the 0-th subarray because we check if array[i]-1 or array[i]+1 has been put into the table)
3. Put<34, 1> in the table, and let list[1] = 1; (this is because neither 33 nor 35 has been put int the table, so we think 34 belongs to a new subarray).
4. We keep this procedure until the last element in array.
5. Then list.size represents the number of subarray, while list[m] represents the number of elements in the m-th subarray.
===============
I just found this method cannot correctly deal with the array {4, 5, 8, 7, 6}. The above method will build two subarrays: {4, 5}, {8, 7, 6}. I think can be revised as follows:
For array[i] (say array[4] = 6), we check array[i]-1 AND array[i]+1. If both are in the table but with different subarray index (say {4, 5} is the 0-th subarray, {8, 7} is the 1st subarray), we merge them by changing the subarray index of {8, 7} to 0, and put<6, 0> into the table. Of course list[0] += list[1] and list.remove(1) should be done.
Comment hidden because of low score. Click to expand.
0
of 0 vote
#include<stdio.h>
#include<conio.h>
int arr[] = {5,2,7,9,3,6,8,1};
int max=0, max_in,count;
int longest(int);
int main()
{
int i;
for(i=0;i<8;i++)
{
count = 1;
longest(arr[i]);}
for(i=0;i<max;i++)
{
printf("%d\t",max_in);
max_in++;
}
getch();
return 0;
}
int longest(int in)
{
int i,in_1=in;
for(i=0;i<8;i++)
{
if(arr[i]==in+1)
{
longest(in+1);
count=count+1;
break;
}
}
if(count>max)
{
max=count;
max_in = in_1;
}
return 0;
}
Comment hidden because of low score. Click to expand.
0
of 0 vote
Using arraylist or hash table would use another O(n) space.
Comment hidden because of low score. Click to expand.
0
of 0 vote
According to the input length and range, choose a proper sort algorithm.
Then find out longest ascending "subset" as below.
(If there are 2+ longest subset, the first will be displayed)
main()
{
int list[]={1,2,3,6,7,9,10,11,12,14,15,16,17,45,46,48};
int i,j,start,longest;
longest = 1;
start =0;
int length = sizeof(list)/sizeof(int);
for (i = 0 ;i<length ;i=j+1 ){
j= i ;
while( (list[j+1]-list[j]) == 1) j++;
if( (j-i+1) > longest ) {
longest = j-i+1;
start = i;
}
}
printf("Longest length is %d.\n ",longest);
for(i = start;i<longest+start ;i++ ) printf("%d, ",list[i]);
}
Comment hidden because of low score. Click to expand.
0
of 0 vote
#include<stdio.h>
#include<conio.h>
void goFun(int arr[],int n)
{
int i,arr1[10][10],print=0,count=0,max=0,k2=0,k=0,j,z=1,flag=1,k1=0;
printf("array is : ");
for(i=0;i<n;i++)
printf("%d\t",arr[i]);
for(i=0;i<10;i++)
for(j=0;j<10;j++)
arr1[i][j]=0;
for(i=0;i<n;i++)
{
//i=0;
//flag=1;
z=1;
k1=0;
for(j=i;j<n;j++)
{
if((arr[i] == arr[j+1]+z) || (arr[i] == arr[j+1]-z) )
{
if(k1==0)
{
arr1[k2][k]=arr[i];
k++;
}
arr1[k2][k]=arr[j+1];
//flag=1;
z++;
k++;
k1=1;
count++;
}
//else
// continue;
}
if(count > max)
{
max = count;
print = k2;
}
count = 0;
k2++;
}
printf("\nLongest consecutive nos are : ");
for(i=0;i<k2;i++)
{
if(i == print)
{
//printf("\n");
for(j=0;j<k;j++)
printf("%d\t",arr1[i][j]);
}
}
}
int main()
{
int arr[10];
int i,n;
printf("how many elements you want to insert ?? ");
scanf("%d",&n);
printf("\nEnter elements : ");
for(i=0;i<n;i++)
scanf("%d",&arr[i]);
goFun(arr,n);
getch();
return 0;
}
Comment hidden because of low score. Click to expand.
0
of 0 vote
I think sorting and find consecutive numbers would be the best way.
``````public class JE15 {
public static void main(String[] args) {
// Find the longest consecutive numbers from input array
int[] input = {4, 5, 13, 33, 32, 10, 11, 34, 12, 31, 14};
int[] res = findLongestConsecNum(input);
System.out.println(Arrays.toString(res));
}
static int[] findLongestConsecNum(int[] input) {
// sorting and find the longest consecutive num : O(nlogn) + O(n)
// scan all numbers if a number belongs to certain consecutive chain : 1+2+3+...+n-1 = O(n^2)
Arrays.sort(input);
int[] temp = new int[input.length];
int[] res = new int[input.length];
temp[0] = input[0];
int count=1, maxcount = -1;
for(int i=1; i<input.length; i++) {
if(input[i]-input[i-1] != 1) {
if(count > maxcount) {
maxcount = count;
for(int j=0; j<temp.length; j++) {
res[j] = temp[j];
}
}
count = 0;
}
temp[count++] = input[i];
}
return Arrays.copyOf(res, maxcount);
}
}``````
Comment hidden because of low score. Click to expand.
0
of 0 vote
``````package nvidia;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
// import org.junit.Assert;
public class LongestConsecutiveSubarray {
static void findAndPrintMaxConsecSubArray(int[] a) {
int n = a.length;
int maxL = 1, maximizerStart = 0;
Set<Integer> s = new HashSet<Integer>();
for(int i = 0; i < n; i++){
for(int j = i+1; j < n; j++){
if(j-i < maxL) {
continue;
}
// find min and max, check if distinct
s.clear();
int min = a[i], max = a[i];
for(int k = i; k < j; k++){
if(s.contains(a[k])) {
break;
} else {
if(a[k] < min){
min = a[k];
} else if (a[k] > max) {
max = a[k];
}
}
}
int m = j-i;
if((s.size() == m) && (max-min == m-1)) {
maxL = m;
maximizerStart = i;
}
}
}
System.out.println("max length " + maxL);
for(int i = maximizerStart; i < maximizerStart + maxL; i++){
System.out.print(a[i] + "\t");
}
System.out.println();
}
static void findAndPrintMaxConsecSubSeq(int[] a) {
Arrays.sort(a);
int n = a.length;
// 4 , 5 , 10, 11, 31, 32, 33, 34
int maxL = 1, currL = 1, maximizerStart = 0;
for(int i = 0; i < n; i++){
if(i+1 < n && (a[i+1] == a[i] + 1)) {
currL = currL + 1;
if(currL > maxL){
maxL = currL;
maximizerStart = i - currL+2;
}
} else {
currL = 1;
}
}
System.out.println("max length " + maxL);
for(int i = maximizerStart; i < maximizerStart + maxL; i++){
System.out.print(a[i] + "\t");
}
System.out.println();
}
public static int getNOnes(int n)
{
int result = 0;
while(n>0)
{
n = n&(n-1);
result++;
}
return result;
}
public static void main(String[] args){
int[] testcase1 = {4, 5, 34, 33, 32, 11, 10, 31};
int[] testcase2 = {4, 5, 34, 32, 11, 33, 10, 31};
findAndPrintMaxConsecSubSeq(testcase1);
findAndPrintMaxConsecSubSeq(testcase2);
int[] testcase3 = { 4 , 5 , 33, 34, 32, 31, 11, 10};
findAndPrintMaxConsecSubArray(testcase3);
}
}``````
Comment hidden because of low score. Click to expand.
0
of 0 vote
test
Comment hidden because of low score. Click to expand.
0
of 0 vote
``````package nvidia;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
// import org.junit.Assert;
public class LongestConsecutiveSubarray {
static void findAndPrintMaxConsecSubArray(int[] a) {
int n = a.length;
int maxL = 1, maximizerStart = 0;
Set<Integer> s = new HashSet<Integer>();
for(int i = 0; i < n; i++){
for(int j = i+1; j < n; j++){
if(j-i < maxL) {
continue;
}
// find min and max, check if distinct
s.clear();
int min = a[i], max = a[i];
for(int k = i; k < j; k++){
if(s.contains(a[k])) {
break;
} else {
if(a[k] < min){
min = a[k];
} else if (a[k] > max) {
max = a[k];
}
}
}
int m = j-i;
if((s.size() == m) && (max-min == m-1)) {
maxL = m;
maximizerStart = i;
}
}
}
System.out.println("max length " + maxL);
for(int i = maximizerStart; i < maximizerStart + maxL; i++){
System.out.print(a[i] + "\t");
}
System.out.println();
}
static void findAndPrintMaxConsecSubSeq(int[] a) {
Arrays.sort(a);
int n = a.length;
// 4 , 5 , 10, 11, 31, 32, 33, 34
int maxL = 1, currL = 1, maximizerStart = 0;
for(int i = 0; i < n; i++){
if(i+1 < n && (a[i+1] == a[i] + 1)) {
currL = currL + 1;
if(currL > maxL){
maxL = currL;
maximizerStart = i - currL+2;
}
} else {
currL = 1;
}
}
System.out.println("max length " + maxL);
for(int i = maximizerStart; i < maximizerStart + maxL; i++){
System.out.print(a[i] + "\t");
}
System.out.println();
}
public static int getNOnes(int n)
{
int result = 0;
while(n>0)
{
n = n&(n-1);
result++;
}
return result;
}
public static void main(String[] args){
int[] testcase1 = {4, 5, 34, 33, 32, 11, 10, 31};
int[] testcase2 = {4, 5, 34, 32, 11, 33, 10, 31};
findAndPrintMaxConsecSubSeq(testcase1);
findAndPrintMaxConsecSubSeq(testcase2);
int[] testcase3 = { 4 , 5 , 33, 34, 32, 31, 11, 10};
findAndPrintMaxConsecSubArray(testcase3);
}
}``````
Comment hidden because of low score. Click to expand.
-1
of 1 vote
``````sort the numbers then find the ranges then choose the maximum range
here is the pseudo code
main()
{
int N;
scanf("%d",&N);
int arr[N];
int arrsort[N];
int i;
for(i=0;i<N;++i)
{
scanf("%d",&arr[i]);
arrsort[i]=arr[i];
}
qsort(arrsort, N, sizeof(int), sort);
int range[N][2];
int l,h,c,d,count=0;
l=arrsort[0];c=l;h=l;
for(i=0;i<N;++i)
{
d=arrsort[i];
if(d==c+1||d==c) { h=d;c=d;}
else
{
range[count][0]=l;range[count][1]=h;count++;
l=d;c=d;h=d;
}
}
range[count][0]=l;range[count][1]=h;count++;
printf(" %d ",count) ;
for(i=0;i<count;++i)
{
printf("\nl %d h %d ",range[i][0],range[i][1]);
}
form these range values have a mximum range having maximum value of range[i][1]-range[i][0] + 1``````
Comment hidden because of low score. Click to expand.
-1
of 1 vote
void main()
{
int temp=0,count=0,arr[100],i,j,size,arry[100];
printf("size of array : ");
scanf("%d",&size);
for(i=0;i<size;i++)
{
fflush(stdin);
scanf("%d",&arr[i]);
}
for(i=0;i<size;i++)
{
if(arr[i]==(arr[i-1]+1))
{
temp++;
}
else
temp=0;
if(temp>=count)
{
count=temp;
if((i-count)>0)
count++;
for(j=0;j<count;j++)
{
arry[j]=arr[i+j-count+1];
}
}
}
printf("\n\n");
for(j=0;j<count;j++)
printf("%d " , arry[j]);
}
Name:
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| 3.359375
| 3
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CC-MAIN-2021-04
|
latest
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en
| 0.842288
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https://uva.onlinejudge.org/board/viewtopic.php?f=9&t=37104&p=373966
| 1,563,782,896,000,000,000
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text/html
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crawl-data/CC-MAIN-2019-30/segments/1563195527828.69/warc/CC-MAIN-20190722072309-20190722094309-00368.warc.gz
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## 10041 - Vito's Family
All about problems in Volume 100. If there is a thread about your problem, please use it. If not, create one with its number in the subject.
Moderator: Board moderators
raj
Learning poster
Posts: 78
Joined: Fri Feb 15, 2013 5:39 pm
### Re: 10041 - Vito's Family
1
10 30 25 15 1 1 1 23 23 90 10
for this WHY THE OUTPUT BECOMES 163 INSTEAD OF 211??????????????
PLEASE ANYONE TELL ME?????
lbv
Experienced poster
Posts: 128
Joined: Tue Nov 29, 2011 8:40 am
### Re: 10041 - Vito's Family
raj wrote:1
10 30 25 15 1 1 1 23 23 90 10
for this WHY THE OUTPUT BECOMES 163 INSTEAD OF 211??????????????
PLEASE ANYONE TELL ME?????
Take your time to carefully read the problem statement, and then the previous messages from this forum thread. You should come to realize that Vito should locate his house in a street that is the median of all the numbers given in the input.
For the set of integers { 30 25 15 1 1 1 23 23 90 10 }, the median will be 19 (although any integer between 15 and 23 will work equally well). If you add all the distances from each street to the median, your result will be 163. If you try any other number outside the range [ 15 : 23 ] for Vito's house, you'll notice that the result will be a bigger number, so 163 is the optimal answer.
P.S. As you may know, writing something in ALL CAPS is usually interpreted as "shouting". I'd suggest you try to avoid that in a forum like this one.
raj
Learning poster
Posts: 78
Joined: Fri Feb 15, 2013 5:39 pm
### Re: 10041 - Vito's Family
:@ lbv i am extremely sorry for mistakes
i didnt know how to get medians but now i know it
but one thing i can not understand why sometimes MEDIAN doesnt work???
can you please explain...
lbv
Experienced poster
Posts: 128
Joined: Tue Nov 29, 2011 8:40 am
### Re: 10041 - Vito's Family
raj wrote:i am extremely sorry for mistakes
It's okay, we all make mistakes; the important thing is to learn from them .
raj wrote: but one thing i can not understand why sometimes MEDIAN doesnt work???
can you please explain...
I'm not sure what you mean by "median doesn't work". Are you referring to this problem? Do you have an example in mind? If you do, please share it, but carefully check it again. Using the median should always give you the right answer for this problem, so if it doesn't for some reason, it might be a subtle bug in your code.
raj
Learning poster
Posts: 78
Joined: Fri Feb 15, 2013 5:39 pm
### Re: 10041 - Vito's Family
sorry sir...
median works all the time....
i saw a previous post the i think median doesnt work...........
now its accepted... thanks
mmoonn
New poster
Posts: 1
Joined: Sun Jul 07, 2013 6:02 am
### Re: 10041 - Vito's Family
i want to know what is wrong with my code plz,it gives WA
Code: Select all
``````import java.util.Arrays;
import java.util.Scanner;
public class Main{
public static int[] streets;
private static int getDis(int mid) {
int dis = 0;
for (int i = 0; i < streets.length; i++) {
dis += Math.abs(mid - streets[i]);
}
return dis;
}
public static void main(String[] args) {
// get median
Scanner sc = new Scanner(System.in);
int tests = sc.nextInt();
int[][] input = new int[tests][];
sc.nextLine();
for (int i = 0; i < tests; i++) {
String[] sp = sc.nextLine().trim().split(" ");
input[i] = new int[sp.length - 1];
for (int j = 1; j < sp.length; j++) {
input[i][j - 1] = Integer.parseInt(sp[j]);
}
}
// evaluate
for (int i = 0; i < input.length; i++) {
int mid = 0;
streets = input[i];
for (int j = 0; j < input[i].length; j++) {
mid += input[i][j];
}
mid = mid / input[i].length;
int temp = mid;
Arrays.sort(streets);
int min = getDis(mid);
int j = 0;
while (j < streets.length) {
mid += 1;
int x = getDis(mid);
if (x < min)
min = x;
else
break;
j++;
}
j = 0;
mid = temp;
while (j < streets.length) {
mid -= 1;
int x = getDis(mid);
if (x < min)
min = x;
else
break;
j++;
}
System.out.println(min);
}
}
}
``````
brianfry713
Guru
Posts: 5947
Joined: Thu Sep 01, 2011 9:09 am
Location: San Jose, CA, USA
### Re: 10041 - Vito's Family
Input:
Code: Select all
``````1
6 1 1 1 1 1000 1000``````
Output should be 1998
Check input and AC output for thousands of problems on uDebug!
Orni Noor
New poster
Posts: 1
Joined: Mon Dec 30, 2013 1:02 am
Location: Dhaka, Bangladesh
### 10041 - Vito's Family
I cannot understand why I am getting RUNTIME ERROR in my code. Can anyone please help???
Code: Select all
``````#include<stdio.h>
#include<stdlib.h>
int compare(const void* p1, const void* p2)
{
if (*(long*)p1 < *(long*)p2)
{
return (-1);
}
if(*(long*)p1==*(long*)p2)
{
return (0);
}
if(*(long*)p1> *(long*)p2)
{
return (1);
}
}
int main()
{
long n;
int s,r,i,j,k;
while((scanf("%ld",&n))==1)
{
scanf("%d",&s);
long a[500],d[500];
for(i=0;i<s;i++)
{
scanf("%ld",&a[i]);
}
qsort(a,s,sizeof(long),compare);
long median,sum=0;
if(s%2!=0)
{
i=(s+1)/2;
median=a[i-1];
}
else if(s%2==0)
{
i=s/2;
j=(s/2)+1;
median=(a[i-1]+a[j-1])/2;
}
for(k=0;k<s;k++)
{
d[k]=median-a[k];
if(d[k]<0)
{
d[k]=-d[k];
}
sum=sum+d[k];
}
printf("%ld\n",sum);
}
return 0;
}``````
Last edited by brianfry713 on Tue Nov 18, 2014 9:45 pm, edited 1 time in total.
Reason: Added code blocks
uDebug
A great helper
Posts: 475
Joined: Tue Jul 24, 2012 4:23 pm
### Re: 10041 - Vito's Family
Here's some input / output I culled from this thread and that I found useful when testing / debugging.
Input:
Code: Select all
``````9
2 2 4
3 2 4 6
6 11 2 1 6 5 11
6 7 8 2 3 6 1
6 1 1 1 1 1000 1000
4 1 2 4 5
10 30 25 15 1 1 1 23 23 90 10
5 1 1 1 2 3
16 5 49 12 23 29 100 44 47 69 41 23 12 11 6 2 62
``````
AC Output:
Code: Select all
``````2
4
20
15
1998
6
163
3
347``````
Check input and AC output for over 7,500 problems on uDebug!
Find us on Facebook. Follow us on Twitter.
uDebug
A great helper
Posts: 475
Joined: Tue Jul 24, 2012 4:23 pm
### Re: 10041 - Vito's Family
Orni Noor wrote:I cannot understand why I am getting RUNTIME ERROR in my code. Can anyone please help???
First thing, if you want people to read your code, use the code tags. It improves readability.
Next, your code is going off bounds since you aren't reading in the input correctly.
Since we know how many cases are going to be there, this line
Code: Select all
``while((scanf("%ld",&n))==1)``
needs to be changed to something like
Code: Select all
``````/* Read in the number of cases */
scanf("%ld",&n);
/* Process each case */
for(x = 0; x < n; x++)
{...
``````
I've made the changes to your program here.
http://pastebin.com/hmcJrDcp
It compiles and runs just fine.
Check input and AC output for over 7,500 problems on uDebug!
Find us on Facebook. Follow us on Twitter.
sejan
New poster
Posts: 6
Joined: Sun Nov 16, 2014 8:32 pm
### Re: 10041 - Vito's Family
why WA?
Code: Select all
``````ACCEPTED THANK YOU
``````
Last edited by sejan on Wed Nov 19, 2014 3:43 pm, edited 1 time in total.
brianfry713
Guru
Posts: 5947
Joined: Thu Sep 01, 2011 9:09 am
Location: San Jose, CA, USA
### Re: 10041 - Vito's Family
Make the initial value of temp bigger.
#include <limits.h>
int temp = INT_MAX;
Check input and AC output for thousands of problems on uDebug!
mpmohi
New poster
Posts: 13
Joined: Wed Feb 26, 2014 10:15 pm
### Re: 10041 - Vito's Family
lbv wrote:
raj wrote:1
10 30 25 15 1 1 1 23 23 90 10
for this WHY THE OUTPUT BECOMES 163 INSTEAD OF 211??????????????
PLEASE ANYONE TELL ME?????
Take your time to carefully read the problem statement, and then the previous messages from this forum thread. You should come to realize that Vito should locate his house in a street that is the median of all the numbers given in the input.
For the set of integers { 30 25 15 1 1 1 23 23 90 10 }, the median will be 19 (although any integer between 15 and 23 will work equally well). If you add all the distances from each street to the median, your result will be 163. If you try any other number outside the range [ 15 : 23 ] for Vito's house, you'll notice that the result will be a bigger number, so 163 is the optimal answer.
P.S. As you may know, writing something in ALL CAPS is usually interpreted as "shouting". I'd suggest you try to avoid that in a forum like this one.
though it is very late but how the Medin here can be 19 ?
brianfry713
Guru
Posts: 5947
Joined: Thu Sep 01, 2011 9:09 am
Location: San Jose, CA, USA
### Re: 10041 - Vito's Family
For the set of integers { 1 1 1 10 15 23 23 25 30 90 }, the median will be 19 = (15 + 23) / 2
Check input and AC output for thousands of problems on uDebug!
mpmohi
New poster
Posts: 13
Joined: Wed Feb 26, 2014 10:15 pm
### Re: 10041 - Vito's Family
Thanks brainfry713
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http://wizzluck.com/water-with-a-static-pressure-of-1-96kn-m2-flows/
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Question
# Water with a static pressure of 1.96kN/M2 flows through an 800 mm diameter pipe. A pitot tube pressure gage in
this pipe reads a pressure of 5.88 kN/M2. How do you determine the volume flow rate (Q) of the water? (Q = 1.40 M^3/sec, V=2.79 M/sec)
Q) Water with a static pressure of 1.96kN/M2 flows through an 800 mm
diameter pipe. A pitot tube pressure gage in this pipe reads a pressure of
5.88 kN/M2. How do you determine the volume flow rate…
Engineering Technology
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https://math.answers.com/basic-math/What_is_30_percent_off_of_756
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0
What is 30 percent off of 756?
Updated: 4/28/2022
Wiki User
11y ago
30 percent off of 756 = 529.20
30% off of 756
= 30% discount applied to 756
= 756 - (30% * 756)
= 756 - (0.30 * 756)
= 756 - 226.8
= 529.20
Wiki User
11y ago
Earn +20 pts
Q: What is 30 percent off of 756?
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Still have questions?
Related questions
What is 30 percent of 756?
30% of 756 is 226.8
What is 30 percent of 2520?
30% of 2520 = 2520*30/100 = 756
What is 34 percent of 756?
34% of 756= 34% * 756= 0.34 * 756= 257.04
What is 37 percent of 756?
37% of 756 = 279.72
What is 25 percent of 756?
25% of 756 is 189.
What is 128 percent of 756?
It is: 1.28*756 = 967.68
What is 756 percent of 840?
756 is 90% of 840
What is 756 percent of 662?
To find 756 percent of a number, multiply the number by 7.56. In this instance, 7.56 x 662 = 5004.72. Therefore, 756 percent of 662 is equal to 5004.72.
What is 30 percent off 30 dollars?
30 percent off of \$30 would be \$9 off.
What percent increase is 596 to 756?
The increase from 596 to 756 is: 26.85%
It is 75600%.
What is 30 percent off of 5.68?
30 percent off of 5.68 is 1.70.
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http://pytorch.org/docs/2.3/generated/torch.fft.irfft.html
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Shortcuts
# torch.fft.irfft¶
torch.fft.irfft(input, n=None, dim=-1, norm=None, *, out=None)
Computes the inverse of rfft().
input is interpreted as a one-sided Hermitian signal in the Fourier domain, as produced by rfft(). By the Hermitian property, the output will be real-valued.
Note
Some input frequencies must be real-valued to satisfy the Hermitian property. In these cases the imaginary component will be ignored. For example, any imaginary component in the zero-frequency term cannot be represented in a real output and so will always be ignored.
Note
The correct interpretation of the Hermitian input depends on the length of the original data, as given by n. This is because each input shape could correspond to either an odd or even length signal. By default, the signal is assumed to be even length and odd signals will not round-trip properly. So, it is recommended to always pass the signal length n.
Note
Supports torch.half and torch.chalf on CUDA with GPU Architecture SM53 or greater. However it only supports powers of 2 signal length in every transformed dimension. With default arguments, size of the transformed dimension should be (2^n + 1) as argument n defaults to even output size = 2 * (transformed_dim_size - 1)
Parameters
• input (Tensor) – the input tensor representing a half-Hermitian signal
• n (int, optional) – Output signal length. This determines the length of the output signal. If given, the input will either be zero-padded or trimmed to this length before computing the real IFFT. Defaults to even output: n=2*(input.size(dim) - 1).
• dim (int, optional) – The dimension along which to take the one dimensional real IFFT.
• norm (str, optional) –
Normalization mode. For the backward transform (irfft()), these correspond to:
• "forward" - no normalization
• "backward" - normalize by 1/n
• "ortho" - normalize by 1/sqrt(n) (making the real IFFT orthonormal)
Calling the forward transform (rfft()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make irfft() the exact inverse.
Default is "backward" (normalize by 1/n).
Keyword Arguments
out (Tensor, optional) – the output tensor.
Example
>>> t = torch.linspace(0, 1, 5)
>>> t
tensor([0.0000, 0.2500, 0.5000, 0.7500, 1.0000])
>>> T = torch.fft.rfft(t)
>>> T
tensor([ 2.5000+0.0000j, -0.6250+0.8602j, -0.6250+0.2031j])
Without specifying the output length to irfft(), the output will not round-trip properly because the input is odd-length:
>>> torch.fft.irfft(T)
tensor([0.1562, 0.3511, 0.7812, 1.2114])
So, it is recommended to always pass the signal length n:
>>> roundtrip = torch.fft.irfft(T, t.numel())
>>> torch.testing.assert_close(roundtrip, t, check_stride=False)
## Docs
Access comprehensive developer documentation for PyTorch
View Docs
## Tutorials
Get in-depth tutorials for beginners and advanced developers
View Tutorials
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# Solve my problem
In addition, there are also many books that can help you how to Solve my problem. Our website can help me with math work.
## Solving my problem
Do you need help with your math homework? Are you struggling to understand concepts how to Solve my problem? A simultaneous equations solver is a mathematical tool that can be used to solve a system of two or more linear equations with two or more unknowns. The tool can be used to find the values of the unknowns that satisfy all of the equations in the system.
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With the internet, students have easy access to homework cheat websites. These websites provide answers to homework questions, making it easy for students to find the answers they need without putting in any effort. While this may seem like a quick and easy way to get homework done, it can actually lead to problems. First, if students are relying on these websites for answers, they are not learning the material. This can lead to problems when the student is tested on the material. Additionally, if a teacher
To solve inverse functions, you must first understand what a function is. A function is a set of ordered pairs, where each element in the set corresponds to a unique output. An inverse function is a function that "undoes" another function. In other words, it is a function that reverse the output of another function. To find an inverse function, you must first determine what the function is doing. For example, if the function is addition, then the inverse function is subt
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Polina Ramirez
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https://www.nagwa.com/en/videos/180136480814/
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Video: Finding the Integration of a Function Involving Logarithmic Functions by Using Integration by Substitution
Determine β« β(4/(9π₯(ln 9π₯)β·) dπ₯) by using the substitution method.
03:58
Video Transcript
Determine the indefinite integral of negative four over nine π₯ multiplied by the natural logarithm of nine π₯ to the seventh power with respect to π₯ by using the substitution method.
Now, this looks like a very complicated integral to evaluate. We have a reciprocal, and in the denominator we have the product of an algebraic function and a natural logarithm function, which is raised to the seventh power. But fortunately, weβre given a clue. Weβre told that we should answer this question using the substitution method. In the substitution method, weβre looking to change the variable, so that the integral becomes more straightforward to perform. What weβre looking for when we use the substitution method is for the integrand to be in the form π prime of π₯ multiplied by π of π of π₯. Thatβs a function of a function multiplied by the derivative of the other function or at least some multiple of this.
Now, we noticed that the derivative with respect to π₯ of the natural logarithm of nine π₯ is one over π₯. And if we rewrite our integral slightly as negative four-ninths times the integral of one over π₯ multiplied by one over the natural logarithm of nine π₯ to the seventh power with respect to π₯, then we see that we do indeed have some function of the natural logarithm of nine π₯ multiplied by the derivative of the natural logarithm of nine π₯. Letβs see what happens then if we make this substitution will introduce a new variable π’ to equal the natural logarithm of nine π₯.
Weβve already said that the derivative with respect to π₯ of the natural logarithm of nine π₯ is one over π₯. So we have dπ’ by dπ₯ equals one over π₯. Remember that dπ’ by dπ₯ is not a fraction. But it is equivalent to say that dπ’ is equal to one over π₯ dπ₯. So looking at the second form that we wrote our integral in, we can replace one over π₯ dπ₯ with dπ’ and we can replace the natural logarithm of nine π₯ with π’. This gives us negative four-ninths of the integral of one over π’ to the seventh power with respect to π’ and weβve, therefore, changed our integral fully from an integral in terms of π₯ to an integral in terms of π’.
Itβs also an integral that we can perform without any great difficulty. If we will call that one over π’ to the seventh power can be expressed as π’ to the power of negative seven and integrate powers of π’ not equal to negative one, we increase the power by one and then divide by the new power. So we have negative four-ninths multiplied by one over negative six π’ to the power of negative six. And we also need to include a constant of integration π, as this is an indefinite integral. We can perform some simplification at our answer that negative in the numerator will cancel with the negative in the denominator. And the four in the numerator can be divided by two to give two. And the six in the denominator can be divided by two to give three.
We, therefore, have to over 27π’ to the six power plus our constant of integration π. But we arenβt finished yet. This answer is in terms of π’ and the original integral was in terms of π₯. As this is an indefinite integral, we must make sure we reverse our substitution. So we need to swap π’ for its definition in terms of π₯. Thatβs the natural logarithms of nine π₯. And so we have a final answer. By using the substitution method, we found that the indefinite integral of negative four over nine π₯ multiplied by the natural logarithm of nine π₯ to the seventh power with respect to π₯ is equal to two over 27 multiplied by the natural logarithm of nine π₯ to the sixth power plus a constant of integration π.
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# Physics
posted by .
The wind blows a 0.50 kg Styrofoam box, initially at rest, across level ground and then up an incline where it comes to a rest. The box slides 6.0 m on level ground before sliding up the 20.0
Ovincline. If the effective coefficient of friction between the ground and the box is 0.60, and the wind exerts a constant, horizontally-directed force of 5.0 N, how far up the incline will the box be blown by this wind before it
comes to a stop?
• Physics -
Horizontal motion
m •a=F-μ•m•g.
a= (F-μ•m•g )/m=
=F/m - μ•g =5/0.5 – 0.6•9.8 = 4.12 m/s²
s1=at²/2 => t=sqrt(2•s/a) =1.7 s.
v=at=4.12•1.7 = 7.03 m/s.
The law of conservation of energy for incline:
mv²/2 +W(F) = W(fr) +ΔPE.
mv²/2 +F•x•cosθ = μ•m•g•cosθ•x+m•g•x•sinθ.
x= mv²/2{μ•m•g•cosθ-F•cosθ - m•g•sinθ} = 0.5 m.
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https://ai.stackexchange.com/questions/24400/how-to-design-my-neural-network-for-game-ai
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# How to design my Neural Network for Game AI
For my school project, I have to develop an agent to play my game.
The base I have is a 'GameManager' which call 2 AIs, each taking a random move to do.
To make my AI perform, I decided to make a deep RL algorithm.
Here is how I've designed my solution.
1st : the board is a 8x8 board. making 112 possible lines to draw. 2nd : on each decision, my Agent has to choose 1 line in the remaining one. 3rd : each decision the Agent take is one among 112 possible.
I read some codes on the internet, the most relevant for me was a 'CartPole' example, which is a cart we have to slide to prevent a mass to fall.
I made an architecture which is this one: a game is simulated: the board is clean, making all 112 possibilities available. Our Agent is interroged by the gameManager to make a move passing him the actual state of the game (the state shape is a 112*1 vector of Boolean values, 1 means a line can be drawn, 0 means there is already a line on this position) (the action shape is a vector of 112*1 Boolean values, All values are set to 'False' except the line we want to draw) So, our Agent return his move decision.
Each time our agent perform a move, i store the initial state, the action we take, the reward we get performing the action, the state we reach and a boolean to know if the game is done or not.
The rewards I choose are: +1 if our action make us close a box, -1 if our action make other close a box, +10 if our action make us win the game, -10 if our action make us loose the game
The point is it's my 1st Deep learning project and I'm not sure about the mecanism i'm doing. when i launch a simulation, the Neural Network is running, but the move he does seems not to be better and better.
I give you the code I've wrote:
Here is the gameManager code:
while True:
gameIsEnd = False
rewardFCB = 0
doneFCB = False
if GRAPHIC_MODE:
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
sys.exit()
disp_board()
if playerTurns=="1":
stateFCB = possibilitiesToBoolList(possible_moves[0])
boolArrayPossibleMoves = possibilitiesToBoolList(possible_moves[0])
theAction = players[playerTurns].play(boxes, possible_moves[0], boolArrayPossibleMoves, False)
#print(possible_moves[0])
#print(theAction)
if playerTurns =="1":
actionFCB = theAction
if playerTurns=="1":
is_box = move(True, theAction)
elif playerTurns=="2":
is_box = move(False, theAction)
if is_box:
if playerTurns =="1":
#rewardFCB = 1
rewardFCB = 1
pass
else:
rewardFCB = -1
if check_complete():
gameIsEnd = True
rewardFCB += 10 if score[0]>score[1] else -10 #does loosing is a reward null or negativ ?
queueOfLastGame.pop(0)
#Scotch pour affichage winrate
isWin = 1 if score[0]>score[1] else -1
queueOfLastGame.append(isWin)
if queueOfLastGame.count(-1)+queueOfLastGame.count(1) > 0:
print(queueOfLastGame.count(1)/(queueOfLastGame.count(-1)+queueOfLastGame.count(1)) * 100 , " % Winrate")
doneFCB = True
#si c'est notre IA vient de faire un carré
#on connait directement l'état qui succede
nextStateFCB = possibilitiesToBoolList(possible_moves[0])
if playerTurns=="2":
nextStateFCB = possibilitiesToBoolList(possible_moves[0])
if nextStateFCB is not None:
bufferSARS.append([stateFCB, actionFCB, rewardFCB, nextStateFCB, doneFCB])
#ai_player_1.remember(stateFCB, actionFCB, rewardFCB, nextStateFCB, doneFCB)
rewardFCB = 0
nextStateFCB = None
if gameIsEnd:
flushBufferSARS()
reset()
continue
#switch user to play if game is not end
playerTurns="1" if playerTurns == "2" else "2"
And here's my code about the Agent:
class Agent:
def __init__(self, name, possibleActions, stateSize, actionSize, isHuman=False, alpha=0.001, alphaDecay=0.01, batchSize=2048, learningRate=0.1, epsilon= 0.9, gamma = 0.996, hasToTrain=True):
self._memory = deque(maxlen=100000)
self._actualEpisode=1
self._episodes=7000
self._name=name
self._possibleAction=possibleActions
self._isHuman=isHuman
self._epsilon=epsilon
self._epsilonDecay = 0.99
self._epsilonMin = 0.05
self._gamma=gamma
self._stateSize=stateSize
self._actionSize=actionSize
self._alpha=alpha
self._hasToTrain=hasToTrain
self._batchSize=batchSize
self._totalIllegalMove = 0
self._totalLegalMove = 0
self._path = "./modelWeightSave/"
self._model = self._buildModel()
def save_model(self):
self._model.save(self._path)
def getName(self):
return self._name
def _buildModel(self):
model = Sequential()
#if os.path.isfile(self._path):
return model
def act(self, UNUSED_state, stateAsBool):
playableIndexes = []
for i in range(len(stateAsBool[0])):
if stateAsBool[0][i] == 1:
playableIndexes.append(i)
indexForRand = playableIndexes[random.randint(0, len(playableIndexes) - 1)]
if np.random.random() <= self._epsilon:
action= [0]*self._actionSize
action[indexForRand]=1
else:
arrayState = np.array(stateAsBool)
action = self._model.predict(arrayState)
#Set index of max esperence to 1, we play this line.
tmp=[0]*self._actionSize
tmp[np.argmax(action)] = 1
action = tmp
isLegalMove = True
if sum(action) != 1:
isLegalMove = False
for i in range(len(action)):
if action[i] == 1:
if stateAsBool[0][i] == 0:
isLegalMove = False
break
if isLegalMove:
pass
#print("Legal move")
else:
#print("Illegal move")
#AI try to play on an already draw line, we choose a random line in remainings
self._totalIllegalMove+=1
action = [0] * self._actionSize
action[indexForRand] = 1
#print("My AI took action : ",action)
return action
def remember(self, state, action, reward, nextState, done):
self._memory.append((state.copy(), action, reward, nextState, done))
self._actualEpisode+=1
if self._actualEpisode > self._episodes:
self._actualEpisode = 0
self.replay(self._batchSize)
def replay(self, batchSize):
x_batch, y_batch = [], []
minibatch = random.sample(self._memory, min(len(self._memory), self._batchSize))
for state, action, reward, next_state, done in minibatch:
actionIndex = np.argmax(action)
y_target = self._model.predict(state)
y_target[0][actionIndex] = reward if done else reward + self._gamma * np.max(self._model.predict(next_state)[0])
x_batch.append(state[0])
y_batch.append(y_target[0])
self._model.fit(np.array(x_batch), np.array(y_batch),epochs=10, batch_size=len(x_batch), verbose=1)
if self._epsilon > self._epsilonMin:
self._epsilon *= self._epsilonDecay
self.save_model()
def play(self, board, state, statesAsBool, player):
actionTaken= self.act(state, statesAsBool)
return actionTaken
def callBackOnPreviousMove(self, state, action, reward, nextState, done):
self.remember(state, action, reward, nextState, done)
Example of output i have during fit method:
Epoch 1/10
1/1 [==============================] - 0s 0s/step - loss: 109.9612 - accuracy: 0.8867
Epoch 2/10
1/1 [==============================] - 0s 998us/step - loss: 109.9467 - accuracy: 0.8867
Epoch 3/10
1/1 [==============================] - 0s 0s/step - loss: 109.9456 - accuracy: 0.8867
Epoch 4/10
1/1 [==============================] - 0s 0s/step - loss: 109.9332 - accuracy: 0.8867
Epoch 5/10
1/1 [==============================] - 0s 998us/step - loss: 109.9339 - accuracy: 0.8867
Epoch 6/10
1/1 [==============================] - 0s 0s/step - loss: 109.9337 - accuracy: 0.8867
Epoch 7/10
1/1 [==============================] - 0s 997us/step - loss: 109.9305 - accuracy: 0.8867
Epoch 8/10
1/1 [==============================] - 0s 0s/step - loss: 109.9314 - accuracy: 0.8867
Epoch 9/10
1/1 [==============================] - 0s 0s/step - loss: 109.9306 - accuracy: 0.8867
Epoch 10/10
1/1 [==============================] - 0s 0s/step - loss: 109.9301 - accuracy: 0.8867
My questions are:
1. Is my architecture good (inputs = [0,0,1,1,0,0,1,0.....,1,0] (112x1 shape) to represent the state, and
output = [0,0,0,0,0,0,0,0,0,1,0,0,0...0,0,0,0] (112x1 shape with only one '1') ) to represent an action ?
2. How to nicely choose the architecture of the Neural Network model (self._model) (I have only the basics of Neural Network, so I don't really know all activation fonction, how to design the hiden layers, choose a loss...)
3. To train my NN, is it good to call the 'fit' function with (state, action) as parameter to make it learn?
4. Is there something really important I forget in my design to make it work?
• Please, ask one question per post. If you have multiple questions, ask each of them in their separate post. – nbro Nov 4 '20 at 18:14
• they are highly linked :/ post 4 time the same description with only a different question should be a waste of time I think here, but i'll try to make differents posts for the next time, thanks – Benjamin Darras Nov 4 '20 at 18:18
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Roman Numerals
# Roman Numerals: DCXXXVII = 637
## Convert Roman Numerals
Arabic numerals:
Roman numerals:
Arabicnumerals 0 1 M C X I 2 MM CC XX II 3 MMM CCC XXX III 4 CD XL IV 5 D L V 6 DC LX VI 7 DCC LXX VII 8 DCCC LXXX VIII 9 CM XC IX
The converter lets you go from arabic to roman numerals and vice versa. Simply type in the number you would like to convert in the field you would like to convert from, and the number in the other format will appear in the other field. Due to the limitations of the roman number system you can only convert numbers from 1 to 3999.
To easily convert between roman and arabic numerals you can use the table above. The key is to handle one arabic digit at a time, and translate it to the right roman number, where zeroes become empty. Go ahead and use the converter and observe how the table shows the solution in realtime!
## Current date and time in Roman Numerals
2024-08-15 17:35:56 MMXXIV-VIII-XV XVII:XXXV:LVI
Here is the current date and time written in roman numerals. Since the roman number system doesn't have a zero, the hour, minute, and second component of the timestamps sometimes become empty.
## The year 637
Here you can read more about what happened in the year 637.
## The number 637
The number 637 is divisble by 7, 13, 49 and 91 and can be prime factorized into 72×13.
637 as a binary number: 1001111101
637 as an octal number: 1175
637 as a hexadecimal number: 27D
## Numbers close to DCXXXVII
Below are the numbers DCXXXIV through DCXL, which are close to DCXXXVII. The right column shows how each roman numeral adds up to the total.
634 = DCXXXIV = 500 + 100 + 10 + 10 + 10 + 5 − 1 635 = DCXXXV = 500 + 100 + 10 + 10 + 10 + 5 636 = DCXXXVI = 500 + 100 + 10 + 10 + 10 + 5 + 1 637 = DCXXXVII = 500 + 100 + 10 + 10 + 10 + 5 + 1 + 1 638 = DCXXXVIII = 500 + 100 + 10 + 10 + 10 + 5 + 1 + 1 + 1 639 = DCXXXIX = 500 + 100 + 10 + 10 + 10 + 10 − 1 640 = DCXL = 500 + 100 + 50 − 10
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# Postulate
statement that is taken to be true
A postulate (also sometimes called an axiom) is a statement everyone agrees to be correct. This is useful for creating proofs in mathematics and science. Along with definitions, postulates are often the basic truth of a much larger theory or law.[1] For this reason a postulate is a hypothesis advanced as an essential part to a train of reasoning.[2]
Postulates themselves cannot be proven, but since they are usually self-evident, their acceptance is not a problem. Here is a good example of a postulate (given by Euclid in his studies about geometry).
Two points determine (make) a line.
Using this postulate and four others like it, Euclid brought a new understanding of geometry to the world, and many people think they are some of the most influential works in geometry (even in modern time).
Sometimes, postulates are not obviously correct, but are required for their consequences. One example is Albert Einstein's postulate that the universe is homogenous. This type of postulate was necessary to make possible some major scientific achievements, but can also be problematic since it is not self-evident.
As a rule of thumb, postulates tend to have the following characteristics:
1. Obvious and easy to understand
2. Does not contain many words that are difficult to explain
3. Few in quantity
4. Work together without making any strange result (that is, they are consistent)
5. True when used alone (which means that they can be used independently)
Postulates are sometimes proved to be wrong after they have been known for a long time, but this is usually because something new has been discovered, and the original creator could not have known any better.
## References
1. "The Definitive Glossary of Higher Mathematical Jargon: Axiom". Math Vault. 2019-08-01. Retrieved 2020-10-08.
2. "Definition of POSTULATE". www.merriam-webster.com. Retrieved 2020-10-08.
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Still kind of reeling from "Representing Monads" and the concomitant leveling-up of my understanding of delimited continuations. Deep, fascinating stuff. I poked around in Paul Blain Levy's old stuff expecting to find him telling me what the focusing story of them is, but I didn't yet find anything that I see as really satisfying. I mean clearly I kind of have a satisfying sense of what it means for the CPS monad itself to arise from the self-adjointness of negation, but I'm still kind of lost when it comes to how delimited continuations are connected to representation types like (τ → σ1) → σ2 when the two answer types are different, and what those types really "mean" vis-a-vis category theory or focusing or whatever.
In other news, I still think that bunched logic has a straightforwardly sound semantics in the category of directed graphs, and I have a burning curiosity as to whether it is complete, but, to paraphrase xkcd, all my normal approaches are useless here in the land of semantics.
Particularly because my first guess at a completeness theorem is obviously false! Recall from previous doodle and semi-formal exposition that I posit the tensor product of two graphs G1 and G2 is the graph that has
(1) a set of vertices equal to V1 x V2, the cartesian product of the vertices of G1 and the vertices of G2
(2) a set of edges isomorphic to the union of V1 x E2 and E1 x V2. For every element (v1, e : v2 → v2') in V1 x E2, you map it to an edge (v1, v2) → (v1, v2') in G1 ⊗ G2. For every element (e : v1 → v1', v2) in E1 x V2, you map it to an edge (v1, v2) → (v1', v2) in G1 ⊗ G2.
Okay, so, in bunched logic, you can't generally prove A ⊢ A ⊗ A. So it should semantically fail, too, right? Except there is always a function from ⟦A⟧ (the interpretation of A) to ⟦A ⊗ A⟧. Either ⟦A⟧ is the empty graph, in which case you get a trivial map out of ⟦A⟧, or else it isn't empty, in which case you can pick an arbitrary vertex v in ⟦A⟧, and find a trivial way of mapping ⟦A⟧ to the subgraph of ⟦A ⊗ A⟧ that looks like, you know, "v ⊗ A".
Except this prescription is blatantly non-constructive. So is there some kind of completeness theorem that says for every constructive graph homomorphism ⟦Γ⟧ → ⟦A⟧ there's a proof of Γ ⊢ A back in BI? How would you even get started proving such a thing? Mumble parametricity mumble relation mumble? I haven't a clue what a syntactic model would look like for this kind of setup. I started trying to formalize a little of this in Agda and got bogged down in dependent type index tarpits.
Tags:
• #### (no subject)
A paper on describing circuits in an agda DSL: http://www.staff.science.uu.nl/~swier004/publications/2015-types-draft.pdf
• #### (no subject)
Going more carefully now through this little tutorial on fpga programming with the iCEstick. It's in spanish, which makes it slightly more…
• #### (no subject)
Some further progress cleaning up the https://xkcd.com/1360/ -esque augean stables that is my hard drive. Tomato chicken I made a couple days ago…
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# Physics
posted by .
A bead of mass m slides without friction on a vertical hoop of radius R . The bead moves under the combined action of gravity and a spring, with spring constant k , attached to the bottom of the hoop. Assume that the equilibrium (relaxed) length of the spring is R. The bead is released from rest at θ = 0 with a non-zero but negligible speed to the right.
What is the magnitude of the force the hoop exerts on the bead when θ = 90∘ ? Express your answer in terms of m, R, k, and g.
• Physics -
sqrt(( (2*sqrt(2)-2)*k*R^2)/m+2*g*R)
(2*(sqrt(2)-1)*k*R)+(2*m*g)-((sqrt(2)-1)*(k*R)*(1/sqrt(2)))
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# sol.ex05[1] - Data structures Spring 2008 Solution 5 Heap...
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Unformatted text preview: Data structures, Spring 2008 Solution 5: Heap, AVL Tree Instructions • Exercises in this course should be submited to the course box in Ross -2. • Cooperation between students is permitted according to the course guidelines. We remind that: 1. Exercises are for you, benefit from them! 2. Each student must submit his own exercises. 3. Is is not permitted to share any written material. 4. Cheating is a serious university offense which may lead to severe consequences. It will be treated accordingly by course staff. • Write your name, ID, and CS login at the top of the first page (3pt). • Give correctness and complexity proofs for every algorithm you write. • Prove everything. If you suppose anything - write so explicitly. • For every problem find the most efficient algorithm. A non-efficient algorithm will be considered as an incomplete answer. • In this exercise there are 100 regular points! and 3 bonus. Binary Search Tree 1. (a) (5 pt) Suppose that we have numbers between 1 and 1000 in a binary search tree (BST) and want to search for the number 363. Which of the following sequences could not be the sequence of nodes examined? i. 2, 252, 401, 398, 330, 344, 397, 363. ii. 924, 220, 911, 244, 898, 258, 362, 363. iii. 925, 202, 911, 240, 912, 245, 363. iv. 2, 399, 387, 219, 266, 382, 381, 278, 363. v. 935, 278, 347, 621, 299, 392, 358, 363. solution: ( iii ) , ( v ) are sequences that can not be the series of nodes examined. Suppose in our BST if y is a node in the left subtree of x and z is a node in the right subtree of x, then key [ y ] < key [ x ] ≤ key [ z ]. In ( iii ), 912 appears in the subtree rooted 5: Heap, AVL Tree-1 at the left son of 911, which is not legal. Similarly 299 is smaller than 347 but is in the right subtree. (b) (9 pt) It is possible to convert any binary search tree with n nodes to any other BST with n nodes using rotations. The number of rotations required for this in the worst case is: i. Θ(log n ) ii. Θ( n ) iii. Θ( n log n ) iv. Θ( n 2 ) Prove your answer. The correct answer is Θ( n ). The algorithm to convert a tree to a left-linked list is the flowing. Consider the path from the root of the tree to the minimal node. While there is a node on this path with a right child perform a left rotation on that node....
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# An Architect's Look at Critical Reasoning. By Veritas Prep.
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An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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An Architect's Look at Critical Reasoning -- Drawing a Blueprint for Nearly All S/W Questions
a Video Lecture by Veritas PrepA part of the 1,000,000 posts celebration
Much like an x-ray allows doctors to see past the surface to the skeleton of a human, sound Critical Reasoning strategy can take you past the skin-deep subject matter that so often makes these questions difficult, and attack each question surgically by focusing on the way that all questions are structured. Join Brian Galvin, Veritas Prep’s Director of Academic Programs, as he teaches you how to solve even the most complex Critical Reasoning questions.
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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14 Nov 2012, 11:14
Is it possible to post the direct link to video (youtube etc) like it is done for Kaplan's breaking 700 video?
Not able to access this video as it asks for fb login.
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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14 Nov 2012, 11:21
This was a really good video! crisp and to the point very informative.
@vips000 all videos will be made available on gmatclub but after a few hours.
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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15 Nov 2012, 09:42
Veritas Prep video is now available in the first post: an-architect-s-look-at-critical-reasoning-by-veritas-prep-142434.html#p1143539
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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15 Nov 2012, 15:04
Best questions & answers from comments
Ace Richards wrote:
does having a solid base of sentence correction and critical reasoning helps in solving RC questions?
Veritas Prep wrote:
Definitely, Ace - this link stays updated with the next few seminars: http://www.veritasprep.com/free-gmat-webinar/. Tonight's is specific to verbal so some of it is like what you just saw, and we'll hit some Sentence Correction too. The next one will be quant-based, and we alternate from there so that we can dive a little deeper than just general coverage with the time we have.
Sonya Shah wrote:
BG, are there any cr follow up videos....
Veritas Prep wrote:
Hey Sonya - we have all of our classroom lessons filmed as full videos for our students, or available for individual lesson sale on iTunes. For free videos, we have a YouTube channel (https://www.youtube.com/user/veritaspre ... sults_main) and some free resources at www.veritasprep.com.
Sonya Shah wrote:
out of the five examples you gave, only 2 questions i could ans. correctly...working cr from ogs is sufficient?
Veritas Prep wrote:
Hey Sonya - well, I intentionally chose pretty tough examples since I've always believed you learn a lot more from your mistakes than from your triumphs. So that's sort of by design. A good combination of the OG, the official practice tests, and thorough analysis of not just "what was the right answer?" but "what was the trap I fell for in the wrong answer?" and "how can I better approach these in the future?" should be a really good study strategy. Those are great tools, but remember that it's more about what you learn from them than just the fact that you did them!
For more check: http://www.facebook.com/photo.php?fbid= ... nt_count=1
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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15 Nov 2012, 20:01
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Great video Brian!
Now I have a link to direct people to when they get stuck in strengthen/weaken questions!
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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18 Jul 2013, 00:11
Bumped for review.
From GMAT Club's 10 Years & 1,000,000 Posts Milestone Celebration: 15 GMAT and MBA lectures jointly designed with our partners
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink]
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29 Mar 2017, 14:35
thanks for a highly informative video and other free resources as cited by you on this page... heart felt thanks again.. GOD BLESS...
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Re: An Architect's Look at Critical Reasoning. By Veritas Prep. [#permalink] 29 Mar 2017, 14:35
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# An Architect's Look at Critical Reasoning. By Veritas Prep.
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Home / Expert Answers / Accounting / use-the-present-value-tables-in-appendix-a-and-appendix-b-to-compute-the-npv-of-each-of-the-followin-pa503
# (Solved): Use the present value tables in Appendix A and Appendix B to compute the NPV of each of the followin ...
Use the present value tables in Appendix A and Appendix B to compute the NPV of each of the following cash inflows: Required: a.
`\$21,350`
received at the end of 15 years. The discount rate is 8 percent. b.
`\$7,180`
received at the end of four years and
`\$14,200`
received at the end of eight years. The discount rate is 10 percent. c.
`\$2,080`
received annually at the end of each of the next seven years. The discount rate is 8 percent. d.
`\$64,750`
received annually at the end of each of the next three years and
`\$77,750`
received at the end of the fourth year. The discount rate is 3 percent. Note: For all requirements, round discount factor(s) to 3 decimal places, all other intermediate calculations and final answers to the nearest whole dollar amount. \table[[,Amount],[a. Net present value,],[b. Net present value,],[c. Net present value,],[d. Net present value,]]
We have an Answer from Expert
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# Calculation based on last known value in time
Hi all,
at the moment I’m trying to get our stocklevel values and we would like to compare these over the last months. However, at the beginning of this year, only stock level was registred in our database, not the product price at that moment.
So, I would like to calculate the stock level value for the first months against the first known value. So in this case, the value on 1-4-2020 needs to be used to calculate stock level values for Jan, Feb and March.
and then it should not change when I change date filters on my page, so when I’m looking at only Nov and Dec, it should not change to € 6,- per product.
Does somebody know how to fix this?
Kind regards, Marieke
This code is embarassingly verbose, but it works. I’ll work on slimming it down/optimizing it, but here it is for now:
``````Adj Price =
VAR SelPrice = SELECTEDVALUE( Data[Price] )
VAR vTable =
FILTER( ALL(Data), Data[Price] <> BLANK() )
VAR FirstPriceDate =
CALCULATE(
MINX( vTable, [Date] ),
REMOVEFILTERS( Data[Date] )
)
VAR FirstPrice =
CALCULATE(
MINX( vTable, [Price] ),
FILTER( vTable, [Date] = FirstPriceDate )
)
VAR Result =
IF( SelPrice = BLANK(), FirstPrice, SelPrice )
RETURN
Result
``````
Hope this is helpful. Full solution file provided below.
A bit less verbose:
``````Adj Price2 =
VAR SelPrice =
SELECTEDVALUE ( Data[Price] )
VAR vTable =
TOPN ( 1, FILTER ( ALL ( Data ), Data[Price] <> BLANK () ), Data[Date], ASC )
VAR Alt1 =
CALCULATE ( MAXX ( vTable, Data[Price] ), REMOVEFILTERS ( Data[Date] ) )
VAR Result =
IF ( SelPrice = BLANK (), Alt1, SelPrice )
RETURN
Result
``````
• Brian
2 Likes
Hi @marieke, did the response provided by @BrianJ help you solve your query? If not, how far did you get and what kind of help you need further? If yes, kindly mark the thread as solved. Thanks!
Hi @BrianJ
Many thanks for looking into this. I have just tried to translate your code into my original model, but it is not working properly. Most likely I’m doing something wrong, but I can’t figure out what.
I have now attached a dummy copy of the original report I’m working on, hopefull this will help in making my issue more clear.
for each day, I want to calculate the value of the stock. This is based on the Stockmovement History table. It should be QTY * Costs. But as you can see, the Costs column is not always filled in, as we only start doing this from 15-04-2020. So we want the period from 01-01-2020 te be calculated by the costs on 15-04-2020.
If the date filter is based on complete period from the database, the measure for “pricedate” and “costs on pricedate” seem to be okay. but if i change this date filter to only this month, it is changing the pricedate and costs to the first date in the selected period. But it should always be the values for 15-04 as that was the first day the cost field was filled in the database.
The measure 'Inkoopwaarde voorraad" was made by me, but this is based on the current product value and they may change over time, so this is not correct. The measure “Inkoopwaarde voorraad obv cost” should look at the cost field from Stockmovement history and this is working correctly from 15-04 onwards, but this needs to be filled for the period befor 15-04.
I hope you will be able to have another look at this and help me out with it
Thanks!
Sure - I’ll be glad to take a look at this and hopefully have a solution back to you later today.
• Brian
1 Like
I’ve been working on this for a while, and I think I see the problem. In the example you first provided, there was only one price per date, however in the new post there are thousands of prices (actually, costs in the revised post ) per date.
Thus, two things will help me rewrite the measure to get you what you need:
1. the data set is too big to easily work with for testing purposes. In power query, can you please filter it to keep only one of every 750 records? This will still allow for a rigorous construct with 5+ costs per date (I would do this, but don’t have access to the base data)
2. given the multiple costs per date, what is the decision rule I should use for which cost to select associated with the first nonblank date?
Once I have this, I think it will be relatively straightforward to revise the work I did tonight and get you a working solution.
Thanks!
• Brian
Hi @BrianJ ,
I’m sorry I wasnt clear enough about having multiple products in the database, which is causing multiple prices per date.
In the database, for every day and for every product, the actual prize (costs) for that day and product is stored. This is because the products costs may vary over time.
Indeed this will give a large dataset. For each product, I want to have the first known costs. for most products this will be the costs on 15-04-20 as from that date, costs were added to the database. I think this will answer your question 2.
and for the first question, I have now only loaded the information for only 2 of the products, so the dataset is much smaller now.
Please let me know if this is okay for now, thanks a lot for all of your help!
This took some playing around with, but I think this measure gets you what you need. Thanks for paring down the dataset – that made it a lot easier to work with.
``````Adj Cost2 =
VAR SelCost =
SELECTEDVALUE ( 'Stockmovement history'[Cost] )
VAR vTable =
CALCULATETABLE(
TOPN (
1,
FILTER (
ALLSELECTED( 'Stockmovement history' ),
'Stockmovement history'[Cost] <> BLANK ()
),
'Stockmovement history'[Date],
ASC
),
VALUES( 'Producten Uitgebreid'[product_id] )
)
VAR RetrieveVal =
CALCULATE (
MAXX ( vTable, 'Stockmovement history'[Cost] ),
REMOVEFILTERS ( 'Stockmovement history'[Date] ),
FILTER(
vTable,
[product_id] = SELECTEDVALUE( 'Producten Uitgebreid'[product_id] )
)
)
VAR Result =
CALCULATE(
IF ( SelCost = BLANK (), RetrieveVal, SelCost ),
ALLEXCEPT( 'Producten Uitgebreid', 'Producten Uitgebreid'[product_id] )
)
RETURN
Result
``````
I hope this is helpful. Full solution file attached below.
3 Likes
Hi @marieke, did the response provided by @BrianJ help you solve your query? If not, how far did you get and what kind of help you need further? If yes, kindly mark the thread as solved. Thanks!
Hi @BrianJ,
many thanks, I will check it asap and let you know if it really works in my model, but as far as I can see now, it looks great!
Many thanks,
Marieke
1 Like
Hi @Marieke, did the response provided by @BrianJ help you solve your query? If not, how far did you get and what kind of help you need further? If yes, kindly mark the thread as solved. Thanks!*
Hi @Marieke, we’ve noticed that no response has been received from you since the 24th of December. We just want to check if you still need further help with this post? In case there won’t be any activity on it in the next few days, we’ll be tagging this post as Solved. If you have a follow question or concern related to this topic, please remove the Solution tag first by clicking the three dots beside Reply and then untick the checkbox. Thanks!
A response on this post has been tagged as “Solution”. If you have a follow question or concern related to this topic, please remove the Solution tag first by clicking the three dots beside Reply and then untick the check box. Thanks!
Hi All and @BrianJ,
sorry for my late response to this topic. I finally had the time to look into this today and this is exactly what I need to get this sorted.
So many thanks for your help!
Kind regards,
Marieke
2 Likes
Hi @BrianJ ,
Not sure whether I should start a new topic, or reply to my previous issues, as I have another issue with my Stock Value calculation unfortunatelly.
I hope you will be able to help me once again with this.
I have used your calculation to calculate the total stock value (Adj Cost 2 * Stock Level). On each individually row this is working perfect, but the total value for all products, is giving an incorrect result.
As you can see on Pagina 1 in this report, total stock value for product 3793 is € 24.800 and for 4723 is is €74.795, which should be a total of € 99.595, but the calculation is returning a value of € 113.269.
I want to have the total stock values for all products at any given moment in time, mostly this will be at the beginning of a month.
Is there a way to fix this?
Kind regards, Marieke
eDNA Forum - DUMMY - Issues with Total.pbix (521.2 KB)
On a thread that has been previously marked “solved”, always best to start a new thread if you’ve got a significant new issue like this one - that way it will get maximum attention and the fastest response.
@Greg has put together an awesome compilation of resources on fixing iincorrect totals in the DAX Patterns section of the forum:
Have you been through this yet and tried the techniques he outlines?
• Brian
Hi Brian,
many thanks, I will have a good look at that topic and do my best to fix this all by myself.
In case I can’ft figure it out, I will open a new thread for it…
Thanks!
1 Like
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https://www.pharmacy-tech-study.com/math-equations-on-pharmacy-tech-exam.html
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## Math equations on Pharmacy Tech Exam
by Arlene Bishop
(Chesterfield, Michigan)
How do I know when to use what formula for math equations? That's what goofed me up the last 2 times I took the test.
## Comments for Math equations on Pharmacy Tech Exam
Jun 18, 2010 Math Moves by: Keith In Pharmacy Tech math, I recommend that you first write down your factors in a very organized way before you even determine which method you will use to solve the problem. I say this because most of them are situational word type problems and there are usually 2-3 ways to solve them.After that, you really just have to pick which way you will need to go. The best way to do this is by practicing alot of Math problems. Repetition will train you to remember "Math Moves" I know that sounds terribly trite, but it's really the only way.Additionally, you'll find that basic Math (addition, sub., Mult. Div) and proportions math covers the majority of the problems you encounter.I believe that the only real secret to doing the math better is to 1)not ever rush a math problem and 2)stay very organized.If anyone else has ideas to remember the best methods to tackle Math Problems please add a comment using the link below
Nov 14, 2010 Make sure the units are right by: Anonymous Organization is key to this, and neatness helps. Check what units they are giving you and what units they are asking you for. Do any necessary conversions to get to the proper units asked for and make sure everything else cancels out. Always write down your units. Another thing is to make sure that the information given in the problem is necessary to solve it. Many times they give superfluous information in an attempt to confuse you. Don't get confused; eliminate extra info and use only what you need to solve the problem.
Nov 20, 2010 Dimensional Analysis Method for math formula by: Darcetha I am also studying for the PTCB exam and math has always been my weakness. After doing some internet research, I found this article that explains math formulas, it is called Medication Math A self-Learning Module for 1st Semester Associate Degree Nursing Students. It is very informative and easy to understand.The formula that works for me is the Dimensional Analysis Method. This method is actually the preferred way to solve medication math problems. It is a method of factor analysis or units conversion that is widely used in physics and chemistry. Hope this helps.
privacy
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https://history-computer.com/technology/visicalc-of-dan-bricklin-and-bob-frankston-guide/
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Home
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VisiCalc of Dan Bricklin and Bob Frankston Guide: History, Origin, and More
# VisiCalc of Dan Bricklin and Bob Frankston Guide: History, Origin, and More
### Key Points and Facts about VisiCalc:
• VisiCalc (short for “visible calculator”) was the first spreadsheet computer program for personal computers, launched by VisiCorp in 1979 for the Apple II.
• VisiCalc is famously known as “The killer app” for the Apple II.
• It sold over 700,000 copies in six years and up to one million copies during its existence.
• In formulas, VisiCalc uses the A1 notation.
• VisiCalc of Dan Bricklin and Bob Frankston uses Apple II, Apple SOS, CP/M, Atari 8-bit family, Commodore PET, TRSDOS, Sony SMC-70, DOS, HP series 80 operating system.
## What is VisiCalc: Explained
VisiCalc was the first spreadsheet program released in 1979 for the Apple II computer. It was easy to use and allowed for data sorting and storing in tabular rows and columns. VisiCalc was created to address and replace the manual spreadsheet management method. Changing a single value meant modifying the entire spreadsheet because changes made to one cell were automatically applied to all connected cells with VisiCalc. This program was one of the most critical factors in making personal computers more appealing to everyday customers and companies instead of hobbyists and techies.
For many users, the application best demonstrated the value of personal computers for small businesses, reducing a 20-hour-per-week bookkeeping task to a few minutes of data entry in certain circumstances. A simple spreadsheet with columns for employee names and addresses, Social Security numbers, hourly pay, hours worked, tax deductions, and net income, for example, might hold payroll data. For each employee, a formula might be applied to cells in the last column to compute compensation as a function of cells in the three preceding columns. The spreadsheet would display the net pay and the formula upon request. All net pay cells could be recalculated if tax withholding rates were modified.
### Quick Facts
Creator (person)
Dan Bricklin, Bob Frankston
Release Date
17/10/1979
Original Price
under \$100
Units sold
1000000
Operating System
Apple II, Apple SOS, CP/M, Atari 8-bit family, Commodore PET, TRSDOS, Sony SMC-70, DOS, HP series 80
Developed By (company)
It’s widely regarded as the first “killer app,” a piece of software so crucial that you’d buy a computer only to use it. Steve Jobs eventually recognized that VisiCalc “powered the Apple II to the success it achieved,” according to Mr. Bricklin’s website. As a result, many accountants and business owners divided their professional experience into two periods within a few years: before and after the computerized spreadsheet was introduced.
## VisiCalc: Release History
In the spring of 1978, a Harvard Business School student, Dan Bricklin, came up with the idea for an interactive visible calculator, the program (called VisiCalc), which will be called later the First Killer App of the Computer Era. Bricklin certainly was not the inventor of the electronic spreadsheet. First known ideas for such a program were from 1961, when professor Richard Mattessich pioneered the development of computerized spreadsheets for use in business accounting. Then in 1969 Rene Pardo and Remy Landau co-invented “LANPAR” LANguage for Programming Arrays at Random, an electronic spreadsheet type application, which was used for budgeting at Bell Canada, AT&T, Bell operating companies, and General Motors. Mattessich, Pardo and Landau’s work and that of other developers of spreadsheets on mainframe computers probably had no influence on Bricklin however. Thus, a history of the modern era of microcomputer-based electronic spreadsheets should begin with the VisiCalc.
Daniel Singer Bricklin was born on 16 July, 1951, in Philadelphia, USA, where he attended Akiba Hebrew Academy during his high school years. Then he received a B.S. in electrical engineering/computer science from the MIT (Massachusetts Institute of Technology), before to go for a MBA from Harvard University in 1977.
Once sitting in his room, as he remembered …I would daydream. “Imagine if my calculator had a ball in its back, like a mouse…” (I had seen a mouse previously, I think in a demonstration at a conference by Doug Engelbart, and maybe the Alto). And “…imagine if I had a heads-up display, like in a fighter plane, where I could see the virtual image hanging in the air in front of me. I could just move my mouse/keyboard calculator around on the table, punch in a few numbers, circle them to get a sum, do some calculations, and answer ‘10% will be fine!'” (10% was always the answer in those days when we couldn’t do very complicated calculations…)
Later in the summer of 1978, between first and second year of the MBA program, while riding a bike along a path on Martha’s Vineyard, he decided that he wanted to pursue this idea and create a real product to sell after I graduated.
So in the spring of 1978 Bricklin tried prototyping the product’s display screen in Basic on a video terminal connected to the Business School’s timesharing system. His hope for using a mouse was replaced in the first personal computer prototype in the early fall of 1978 by the game paddle of the Apple ][. (This was a dial one could turn to move game objects back and forth). One could move the cursor left or right, and then push the “fire” button, and then turning the paddle would move the cursor up and down. The R-C circuit or whatever in the Apple ][ was too sluggish and my pointing too imprecise to accurately position the cursor that way, so I switched to the two arrow keys of the Apple ][ keyboard (it only had 2) and used the space bar instead of the button to switch from horizontal movement to vertical
The first PC prototype of VisiCalc was created over a weekend on an Apple ][ (using Apple Integer Basic), borrowed for the purpose from a friend, Dan Fylstra, later his publisher. It did not scroll, yet, but it had the columns and rows and some arithmetic.
Then Bricklin decided to recruit a more experienced programmer, to do a real, assembler version of the program (first for the MOS Technology 6502 microprocessor used in the Apple ][). Thus he called his MIT colleague Bob Frankston, to build production code (faster speed, better arithmetic, scrolling, etc.). Frankston not only managed to code the program in assembler (using an assembler, which ran on a minicomputer equipped with the Multics operating system), but also expanded the program and packed the code into a mere 20k of machine memory, making it both powerful and practical enough to be run on a microcomputer. Actually the size of the program was the biggest problem for Frankston, because Apple II had a limited memory, 16 KB of RAM on the low-end Apple II. No matter how hard Frankston tried however, he could not fit VisiCalc in the 16, that’s why VisiCalc would only be available for the much more expensive 32 KB Apple II.
Bricklin and Frankston formed Software Arts Corporation in January, 1979. In May 1979, the firm Personal Software of Dan Fylstra (later renamed VisiCorp) began marketing VisiCalc with a teaser ad in Byte Magazine (see the nearby image). Initially Bricklin conceived several names for the program, between them Calcu-ledger and Calcu-paper, but the name “VisiCalc” is an abbreviated form of the phrase “visible calculator” was chosen by Dan Fylstra.
VisiCalc was one of the key products that helped bring the microcomputer from the hobbyist’s desk into the office. Before the release of this groundbreaking software, microcomputers were thought of as toys; VisiCalc changed that.
VisiCalc went on sale in November of 1979 and became immediately a big hit. It retailed for US\$100 and sold so well that many dealers started bundling the Apple II with VisiCalc. The success of VisiCalc was one of the main reasons Apple to be turned into a successful company, selling tens of thousands of the pricey 32 KB Apple IIs to businesses that wanted them only for the spreadsheet.
## VisiCalc: End of Development
VisiCalc’s price had climbed from \$100 to \$250 by 1982. Several competitors entered the market, including SuperCalc and Multiplan, each of which offered new capabilities and rectified flaws in VisiCalc, but they could not challenge the software’s market domination.
Lotus 1-2-3, written by former Personal Software-VisiCorp employee Mitch Kapor, who had also written VisiTrend and VisiPlot, was released in 1983 and marked a more significant shift. Unlike VisiCalc for the PC, 1-2-3 was designed to take full advantage of the PC’s more excellent memory, screen, and performance. However, it was created to be as similar to VisiCalc as possible, including the menu layout so that VisiCalc users could transfer to 1-2-3. However, due to the striking features of Lotus, sales of VisiCalc practically evaporated.
By 1984, sales of VisiCalc had “rapidly declined,” according to InfoWorld, and it was “the first successful software product to have gone through a complete life cycle, from conception in 1978 to introduction in 1979 to peak success in 1982 to decline in 1983 to a probable death according to industry insiders in 1984.” According to the magazine, the business was hesitant to improve the program, only delivering an Advanced Version of VisiCalc for the Apple II in 1983 and announcing one for the IBM PC in 1984. Its sales plummeted so swiftly that it was forced to declare bankruptcy by 1985.
Lotus Development purchased the company in 1985 and promptly discontinued the sale of VisiCalc and the remainder of the company’s products.
## Up Next…
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• How to Convert Excel to Google Sheets in 5 Easy Steps. Excel not your thing? It’s easy to swap it to Google Sheets.
• How to Delete Duplicates in Excel Permanently. Tired of multiples? Here you go!
## Frequently Asked Questions
When did VisiCalc Come out?
VisiCalc was released on October 17, 1979. It became a sensation almost immediately Dan Bricklin, and Bob Frankston released VisiCalc, a deceptively simple spreadsheet program, in 1979, which ignited the personal computer revolution. VisiCalc’s first computer spreadsheet was massive—until Lotus 1-2-3 came along, which, due to its striking features, got the users’ attention to the point that VisiCalc discontinued.
What was the original price of VisiCalc?
After a presentation at the fourth West Coast Computer Faire and an official debut on June 4 at the National Computer Conference, the Personal Software firm began offering VisiCalc for under \$100 in mid-1979.
What happened to VisiCalc?
VisiCalc has now been discontinued. VisiCalc sales nearly vanished when Lotus 1-2-3 was released in 1983, taking full use of the PC’s enhanced memory and screen. The company’s sales decreased so quickly that it went bankrupt. In 1985, Lotus Development bought the company and immediately stopped selling VisiCalc and the rest of the company’s products.
What was VisiCalc?
VisiCalc was the first spreadsheet computer program for personal computers, launched by VisiCorp in 1979 for the Apple II. It is widely credited with transforming the microcomputer from a pastime for computer enthusiasts to a serious business tool, motivating IBM to release the IBM PC two years later. VisiCalc is famously known as “The killer app” for the Apple II. It sold over 700,000 copies in six years and up to one million copies during its existence.
Who invented VisiCalc?
Dan Bricklin and Bob Frankston, a Harvard MBA student and his former MIT classmate, invented VisiCalc. Dan Bricklin and Bob Frankston were eager to see their calculators come to life in 1979. They wanted to amend their final answers and modify numbers in their computations. That’s what they did when they created VisiCalc, the first computer spreadsheet.
Why was VisiCalc so important?
VisiCalc was the software that made the capabilities of the personal computer access to the average person. Before its inception, only persons who had put forth the effort to master a programming language could program computers, even personal computers.
#### Heather, Author for History-Computer
Heather is a secondary education teacher who is well-versed in the technological world. In her spare time, she enjoys listening to history podcasts, gaming, and posting on social media.
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17.2: Equilibrium statistical mechanical phenomena concerning Axiom 1 ( Measurement)
In this section we shall study the probabilistic aspects of equilibrium statistical mechanics. For completeness, note that
(F) the argument (e.g., Ergodic theorem) in the previous section is not related to "probability"
since Axiom 1 (measurement; $\S$2.7) does not appear in Section 17.1. Also, Recall the linguistic interpretation ($\S$3.1) : there is no probability without measurement .
Note that the (17.12) implies that the equilibrium statistical mechanical system at almost all time $t$ can be regarded as:
(G) a box including about $10^{24}$ particles such as the number of the particles whose states belong to $\Xi$ $({}\in {\cal B}_{{\mathbb R}^6 }{})$ is given by $\rho_{{}_E} ({}\Xi{}) \times 10^{24}$.
Thus, it is natural to assume as follows.
(H) if we, at random, choose a particle from $10^{24}$ particles in the box at time $t$, then the probability that the state $(q_1, q_2, q_3,$ $p_1, p_2, p_3)$ $(\in {\mathbb R}^6)$ of the particle belongs to $\Xi$ $({}\in {\cal B}_{{\mathbb R}^6 }{})$ is given by $\rho_{{}_E} ({}\Xi{})$.
In what follows, we shall represent this (H) in terms of measurements. Define the observable ${\mathsf O}_0=({\mathbb R}^6 , {\cal B}_{{\mathbb R}^6}, F_0)$ in $L^\infty( {\Omega}_{{}_E} )$ such that
\begin{align} & [F_0( \Xi ) ]( q,p) = [ D_{K_N}^{({}q, p{}) }](\Xi) \Big(\equiv \frac{\sharp[\{ k \;|\;{\pi}_k ({}q,p{})\in \Xi \} ]}{\sharp [{}K_N] } \Big) \nonumber \\ & \quad \qquad ( \forall \Xi \in {\cal B}_{{\mathbb R}^6}, \forall (q,p{}) \in {{\Omega}}_{{}_E} ({}\subset {\mathbb R}^{6 N}{}) ). \tag{17.15} \end{align}
Thus, we have the measurement ${\mathsf M}_{L^\infty ( {\Omega}_{{}E} )}( {\mathsf O}_0:= ({\mathbb R}^6 , {\cal B}_{{\mathbb R}^6}, F_0), S_{[ \delta_{\psi_t ( q_{{}_0} , p_{{}_0})}]} )$. Then we say, by Axiom 1 (measurement; $\S$2.7), that
(I) the probability that the measured value obtained by the measurement ${\mathsf M}_{L^\infty ( {\Omega}_{{}E} )}( {\mathsf O}_0:= ({\mathbb R}^6 , {\cal B}_{{\mathbb R}^6}, F_0), S_{[ \delta_{\psi_t ( q_{{}_0} , p_{{}_0} )}]} )$ belongs to $\Xi ( \in {\cal B}_{{\mathbb R}^6})$ is given by $\rho_{{}_E} ( \Xi )$. That is because Theorem 17.4 says that $[ F_0( \Xi ) ]( \psi_t ( q_{{}_0} , p_{{}_0}) )$ $\approx \rho_{{}_E} ( \Xi )$ $\text{(almost every time$t$)}$.
Also, let $\Psi^{{}_E}_t: L^\infty (\Omega_{_E}) \to L^\infty (\Omega_{_E})$ be a deterministic Markov operator determined by the continuous map $\psi^{{}_E}_t: \Omega_{{}_E} \to \Omega_{{}_E}$ (cf. Section 17.1.2). Then, it clearly holds $\Psi^{{}_E}_t{\mathsf{O}_0}={\mathsf{O}_0}$. And, we must take a ${\mathsf{M}}_{L^\infty ( \Omega_{{}_E} )}( {\mathsf{O}_0}, S_{[{(q(t_k),p(t_k))}]} )$ for each time $t_1,t_2,\ldots,t_k, \ldots, t_n$. However, the linguistic interpretation ($\S$3.1) : ( there is no probability without measurement) says that it suffices to take the simultaneous measurement ${\mathsf{M}}_{C( \Omega_{{}_E} )}({\Large \times}_{k=1}^n {\mathsf{O}_0} ,$ $S_{[\delta_{(q(0),p(0))}]} )$.
Remark 17.6 [The principle of equal a priori probabilities ]. The (H) (or equivalently, (I)) says "choose a particle from $N$ particles in box"$\!$, and not "choose a state from the state space $\Omega_{{}_E}$". Thus, the principle of equal (a priori) probability is not related to our method. If we try to describe Ruele's method in terms of measurement theory, we must use mixed measurement theory (cf. Chapter 9). However, this trial will end in failure.
17.3 Conclusions
Our concern in this chapter may be regarded as the problem: {\lq\lq}What is the classical mechanical world view?" Concretely speaking, we are concerned with the problem: $$\mbox{ "our method" vs. "Ruele's method ( which has been authorized for a long time )" }$$ And, we assert the superiority of our method to Ruele's method in Remarks 17.2, 17.5 17.6.
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This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (April 2018) (Learn how and when to remove this template message)
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.[1]
Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients.
Instead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the L1 norm of the parameter vector. The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.
## Pros and cons
The advantages of the LARS method are:
1. It is computationally just as fast as forward selection.
2. It produces a full piecewise linear solution path, which is useful in cross-validation or similar attempts to tune the model.
3. If two variables are almost equally correlated with the response, then their coefficients should increase at approximately the same rate. The algorithm thus behaves as intuition would suggest, and also is more stable.
4. It is easily modified to produce efficient algorithms for other methods producing similar results, like the lasso and forward stagewise regression.
5. It is effective in contexts where p ≫ n (i.e., when the number of predictors p is significantly greater than the number of points n)[2]
The disadvantages of the LARS method include:
1. With any amount of noise in the dependent variable and with high dimensional multicollinear independent variables, there is no reason to believe that the selected variables will have a high probability of being the actual underlying causal variables. This problem is not unique to LARS, as it is a general problem with variable selection approaches that seek to find underlying deterministic components. Yet, because LARS is based upon an iterative refitting of the residuals, it appears to be especially sensitive to the effects of noise. This problem is discussed in detail by Weisberg in the discussion section of the Efron et al. (2004) Annals of Statistics article.[3] Weisberg provides an empirical example based upon re-analysis of data originally used to validate LARS that the variable selection appears to have problems with highly correlated variables.
2. Since almost all high dimensional data in the real world will just by chance exhibit some degree of collinearity across at least some variables, the problem that LARS has with correlated variables may limit its application to high dimensional data.
## Algorithm
The basic steps of the Least-angle regression algorithm are:
• Start with all coefficients ${\displaystyle \beta }$ equal to zero.
• Find the predictor ${\displaystyle x_{j))$ most correlated with ${\displaystyle y}$.
• Increase the coefficient ${\displaystyle \beta _{j))$ in the direction of the sign of its correlation with ${\displaystyle y}$. Take residuals ${\displaystyle r=y-{\hat {y))}$ along the way. Stop when some other predictor ${\displaystyle x_{k))$ has as much correlation with ${\displaystyle r}$ as ${\displaystyle x_{j))$ has.
• Increase (${\displaystyle \beta _{j))$, ${\displaystyle \beta _{k))$) in their joint least squares direction, until some other predictor ${\displaystyle x_{m))$ has as much correlation with the residual ${\displaystyle r}$.
• Increase (${\displaystyle \beta _{j))$, ${\displaystyle \beta _{k))$, ${\displaystyle \beta _{m))$) in their joint least squares direction, until some other predictor ${\displaystyle x_{n))$ has as much correlation with the residual ${\displaystyle r}$.
• Continue until: all predictors are in the model.[4]
## Software implementation
Least-angle regression is implemented in R via the lars package, in Python with the scikit-learn package, and in SAS via the GLMSELECT procedure.
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CCD.DDN43: There are four steps to calculating the derivative of a function $f$ based primarily on analysis of the difference quotient used in the definition .
Alternative $\Delta x = x-a$:
$f '(a) = \lim_{x \to a} \frac{f(x)-f(a)}{x-a}$
Step I: Evaluate $f (x)$ and $f (a)$.
Step II: Subtract: Find (and simplify when possible) the difference: $\Delta y = f (x) - f (a)$.
Step III: Divide by $\Delta x = x - a$ to find $\frac{f(x)-f(a)}{x-a}$ and then simplify algebraically (when possible) to eliminate $\Delta x = x - a$ from the denominator.
Step IV: Think! Finally, analyze the simplified expression to see what happens when $x\to a$, remembering that $x \ne a$.
If the last expression, $\frac{\Delta y}{\Delta x}=\frac{f(x)-f(a)}{x-a}$ approaches a single number,$L$, then $L=f '(a)$.
Alternative $\Delta x= h$. The four steps can use $x=a+h$ and $\Delta x = h$.
$\ f'(a) = \lim_{h \to 0}\frac {f(a+h) - f(a)}{h}$
Step I: Evaluate: $f (a+h)$ and $f (a)$.
Step II: Subtract: Find (and simplify when possible) the difference: $\Delta y = f (a+h) - f (a)$.
Step III: Divide by $\Delta x = h$ to find $\frac{f(a+h)-f(a)}{h}$ and then simplify algebraically (when possible) to eliminate $\Delta x = h$ from the denominator.
Step IV: Think! Finally, analyze the simplified expression to see what happens when $h\to 0$, remembering that $h \ne 0$.
If the last expression, $\frac{f(a+h)-f(a)}{h}$ approaches a single number,$L$, then $L=f '(a)$.
Alternative $\Delta x$:
$\ f'(a) = \lim_{\Delta x \to 0}\frac {f(a+\Delta x) - f(a)}{\Delta x}$
Step I. Evaluate: $f(a+\Delta x)$ and $f(a)$
Step II. Subtract: Find (and simplify when possible) the difference: $\Delta y =f(a+\Delta x) - f(a)$
Step III. Divide: $\frac {\Delta y}{\Delta x} =\frac {f(a+\Delta x) - f(a)}{\Delta x}$ and simplify if possible.
Step IV. Think! As $\Delta x \to 0$, does $\frac {f(a+\Delta x) - f(a)}{\Delta x} \to L$ ? If so, then $L =f'(a)$.
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# How to Find Limits at Infinity
Understanding limits at infinity is a fundamental concept in calculus, which involves analyzing the behavior of a function as the independent variable approaches either positive or negative infinity. Here's a step-by-step guide to help you grasp the concept:
## Step-by-step Guide to Find Limits at Infinity
Here is a step-by-step guide to finding limits at infinity:
### Step 1: Understand the Concept of a Limit
Before diving into limits at infinity, you need to understand what a limit is. A limit describes the value that a function approaches as the input (or independent variable) approaches a certain number. For limits at infinity, that certain number is either positive or negative infinity.
### Step 2: Recognize the Notation
• When we write $$lim_{x→∞}f(x)=L$$, we mean that as $$x$$ becomes very large (approaches infinity), the function $$f(x)$$ gets closer and closer to some value $$L$$.
• Similarly, $$lim_{x→−∞}f(x)=M$$ means that as $$x$$ becomes very negative (approaches negative infinity), $$f(x)$$ approaches the value $$M$$.
### Step 3: Analyzing Polynomial Functions
Let’s start with polynomial functions such as $$f(x)=x^2$$.
• As $$x$$ increases to large positive numbers, $$x^2$$ becomes very large. So, $$lim_{x→∞}x^2=∞$$.
• As $$x$$ decreases to large negative numbers, $$x^2$$ is still very large (since squaring a negative number gives a positive result). So, $$lim_{x→−∞}x^2=∞$$.
### Step 4: Rational Functions
For rational functions like $$f(x)=\frac{1}{x}$$, you have to consider the degree of the polynomial in the numerator and denominator.
• For $$f(x)=\frac{1}{x}$$, as $$x$$ approaches infinity, $$\frac{1}{x}$$ gets smaller and smaller, approaching zero. So, $$lim_{x→∞}\frac{1}{x}=0$$.
• The same logic applies when $$x$$ approaches negative infinity. The function still approaches zero.
### Step 5: Functions with Horizontal Asymptotes
A horizontal asymptote is a horizontal line that the graph of the function approaches as $$x$$ goes to infinity or negative infinity.
• If $$lim_{x→∞}f(x)=L$$ and $$lim_{x→−∞}f(x)=L$$, then the line $$y=L$$ is a horizontal asymptote to $$f(x)$$.
### Step 6: Dealing with More Complex Functions
For more complex functions, such as those with exponents or roots, you may need to use algebraic techniques to find the limit at infinity.
• Consider $$f(x)=\sqrt{x^2+x}−x$$. As �x goes to infinity, $$x^2$$ grows much faster than $$x$$, so you can consider $$x^2$$ as the dominant term. By factoring out $$x^2$$ inside the square root, you can simplify the expression to find the limit.
### Step 7: Use L’Hôpital’s Rule
If you find an indeterminate form like $$\frac{∞}{∞}$$ or $$\frac{0}{0}$$, you may use L’Hôpital’s Rule.
• This rule states that if $$lim_{x→c} \frac{f(x)}{g(x)}$$ yields an indeterminate form, then under certain conditions, $$lim_{x→c} \frac{f(x)}{g(x)}$$$$=lim_{x→c} \frac{f′(x)}{g′(x)}$$, where $$f′(x)$$ and $$g′(x)$$ are the derivatives of $$f(x)$$ and $$g(x)$$, respectively.
### Step 8: Infinite Limits and Infinite Asymptotes
Understand the difference between a horizontal asymptote and other kinds of asymptotes. For example:
• If $$lim_{x→a}f(x)=∞$$, this means that as $$x$$ approaches $$a$$, $$f(x)$$ increases without bound. This is often the case with vertical asymptotes, where the function does not approach a finite value but instead goes off to infinity.
### Step 9: Practice with Graphs
Use graphing to visualize limits at infinity.
• Look at the graph of a function as $$x$$ increases or decreases without bound.
• Notice how the function behaves: does it level off (horizontal asymptote), go off to infinity (infinite limit), or oscillate without approaching any value?
### Step 10: Abstract Functions and General Rules
Learn some general rules that often apply to limits at infinity.
• For instance, if a function $$f(x)$$ is dominated by a term with the highest degree in $$x$$, the behavior of that term often determines the limit at infinity.
• In the case of exponential functions, recognize that as $$x$$ approaches infinity, $$e^x$$ approaches infinity, and $$e^{−x}$$ approaches zero.
### Step 11: Review and Practice
Finally, practice is crucial.
• Work through multiple examples of different types of functions.
• Solve exercises from textbooks or online resources.
• Use limit calculators to check your work, but ensure you understand the steps.
Through this process, you’ll develop intuition for limits at infinity and be able to tackle a wide range of problems involving this concept.
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# Math Worksheets For 5Th Grade Volume
These volume worksheets for grade 5 is. 5th grade volume base and volume worksheet irregular volume shapes worksheet volume and word problems worksheet volume calculations introduction #1 worksheet volume cubed #1 worksheet calculating volume worksheet volume cubed #3 worksheet measurement & data review worksheet volume calculations introduction #3 worksheet smallest or biggest? Free capacity worksheets and free capacity distance learning.
Source: theeducationmonitor.com
Grade 5 math worksheets on volume & surface area of rectangular prisms. Get your first month free, then \$12.99/mo.
### These Volume Worksheets For Grade 5 Is.
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### Below, You Will Find A Wide Range Of Our Printable Worksheets In Chapter Surface Area And Volume Of Section Measurement.these Worksheets Are Appropriate For Fifth Grade Math.we Have Crafted Many Worksheets Covering Various Aspects Of This Topic, Surface Area, Estimate Volume, Volume Of Cubes And Rectangular Prisms, Perimeter, Area And Volume, And Many More.
Practice quiz 1 level up on the above skills and collect up to 400 mastery points start quiz decompose figures to find volume learn volume in unit cubes by decomposing shape volume through decomposition decompose figures to find volume practice practice If you are looking for 5th grade volume worksheets with answers 5th grade volume printable you've visit to the. We manage to pay for 5th grade math volume worksheets and numerous books collections from fictions to scientific research in any way.
Pin on 5th grade math worksheets source: (a) square meter (b) square feet (c) centimeter (d) cubic centimeter area of a square can be measured in ______. Find the unknown edges height length or width given the source:
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### (A) Square Meter (B) Feet (C) Centimeter (D) Cubic Centimeter ____ Is The Measure Of The Amount Of Space Inside Of A Solid Figure.
5th grade math volume worksheets google search julias math board source: 20 best 5th grade worksheets images on best worksheets collection Free irregular volume shapes printable math worksheets for 5th grade students.
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# y+<1
Register Blogs Members List Search Today's Posts Mark Forums Read
July 30, 2002, 17:31 y+<1 #1 Valerio Guest Posts: n/a Hi, some time ago I posted a message asking if somebody knows where the rule of thumb of having one cell below a y+1 for two-equation TMs comes from. I haven't had any reply and I am surprised nobody knows. So I am asking the same question again to see if this time somebody who knows the answer (I don't!) will reply. Thanks again. Valerio
July 31, 2002, 05:54 Re: y+<1 #2 Pauline Guest Posts: n/a Hi, I don't know about the rule that y+ has to be below 1. The rules I know are that for the High Reynolds k-e model with the wall function y+ should be around 30 for the near wall cell. The reason for this is that the near wall cell is supposed to be in the log layer (usually in the region of 30 < y+ < 300 - 500) for the wall function to work. The other y+ rule is for the Low Reynolds k-e model. Here the equations for k and e are solved through the boundary layer. The eddy dissipation at the near wall cell is determined with an algebraic function. For this one the y+ value at the near wall cell should be around 1. Again this is necessary for the near wall function to be applicable. I hope that helps a bit.
August 1, 2002, 16:44 Re: y+<1 #3 Steve Guest Posts: n/a It is just a guideline rather than a strict relationship, and it may vary for different flows. It definitely varies between different turbulence models. I'd say it was formulated based on grid convergence studies.
August 5, 2002, 06:30 Re: y+<1 #4 hasan Guest Posts: n/a hi how are you
August 8, 2002, 08:08 Re: y+<1 #5 Holidays Guest Posts: n/a If You are using models that integratyes to the walls (Low Re k-Eps, k_Omega, Menter etc.) you then want small y+ values of the order of 1 or below. In models with wall functions, this is not the case because yuou approximate the flow profile at the walls!
August 26, 2002, 22:28 Re: y+<1 #6 soupy Guest Posts: n/a The y+ of one value comes from an understanding of the velocity sub-layer in a viscous flow. The sub-layer corresponds to the region of the flow where the velocity is linear. Hence, having a y+ of roughly one puts your first cell in the linear sub-layer and your solution will be accurate.
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, 03.07.2019 18:00 leeplott4747
# The chu family can hike 3 miles per hour. how long will it take them to hike 15 miles
### Another question on Mathematics
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Ana drinks chocolate milk out of glasses that each holdof a liter. she has of a liter of chocolate milk in her refrigerator. 10 how many glasses of chocolate milk can she pour?
Mathematics, 21.06.2019 22:30
We have 339 ounces of jam to be divided up equally for 12 people how muny ounces will each person get
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JavaTM 2 Platform
Std. Ed. v1.4.2
## java.awt Interface Shape
All Known Implementing Classes:
Area, CubicCurve2D, GeneralPath, Line2D, Polygon, QuadCurve2D, Rectangle, RectangularShape
public interface Shape
The `Shape` interface provides definitions for objects that represent some form of geometric shape. The `Shape` is described by a `PathIterator` object, which can express the outline of the `Shape` as well as a rule for determining how the outline divides the 2D plane into interior and exterior points. Each `Shape` object provides callbacks to get the bounding box of the geometry, determine whether points or rectangles lie partly or entirely within the interior of the `Shape`, and retrieve a `PathIterator` object that describes the trajectory path of the `Shape` outline.
Definition of insideness: A point is considered to lie inside a `Shape` if and only if:
• it lies completely inside the`Shape` boundary or
• it lies exactly on the `Shape` boundary and the space immediately adjacent to the point in the increasing `X` direction is entirely inside the boundary or
• it lies exactly on a horizontal boundary segment and the space immediately adjacent to the point in the increasing `Y` direction is inside the boundary.
The `contains` and `intersects` methods consider the interior of a `Shape` to be the area it encloses as if it were filled. This means that these methods consider unclosed shapes to be implicitly closed for the purpose of determining if a shape contains or intersects a rectangle or if a shape contains a point.
`PathIterator`, `AffineTransform`, `FlatteningPathIterator`, `GeneralPath`
Method Summary ` boolean` ```contains(double x, double y)``` Tests if the specified coordinates are inside the boundary of the `Shape`. ` boolean` ```contains(double x, double y, double w, double h)``` Tests if the interior of the `Shape` entirely contains the specified rectangular area. ` boolean` `contains(Point2D p)` Tests if a specified `Point2D` is inside the boundary of the `Shape`. ` boolean` `contains(Rectangle2D r)` Tests if the interior of the `Shape` entirely contains the specified `Rectangle2D`. ` Rectangle` `getBounds()` Returns an integer `Rectangle` that completely encloses the `Shape`. ` Rectangle2D` `getBounds2D()` Returns a high precision and more accurate bounding box of the `Shape` than the `getBounds` method. ` PathIterator` `getPathIterator(AffineTransform at)` Returns an iterator object that iterates along the `Shape` boundary and provides access to the geometry of the `Shape` outline. ` PathIterator` ```getPathIterator(AffineTransform at, double flatness)``` Returns an iterator object that iterates along the `Shape` boundary and provides access to a flattened view of the `Shape` outline geometry. ` boolean` ```intersects(double x, double y, double w, double h)``` Tests if the interior of the `Shape` intersects the interior of a specified rectangular area. ` boolean` `intersects(Rectangle2D r)` Tests if the interior of the `Shape` intersects the interior of a specified `Rectangle2D`.
Method Detail
### getBounds
`public Rectangle getBounds()`
Returns an integer `Rectangle` that completely encloses the `Shape`. Note that there is no guarantee that the returned `Rectangle` is the smallest bounding box that encloses the `Shape`, only that the `Shape` lies entirely within the indicated `Rectangle`. The returned `Rectangle` might also fail to completely enclose the `Shape` if the `Shape` overflows the limited range of the integer data type. The `getBounds2D` method generally returns a tighter bounding box due to its greater flexibility in representation.
Returns:
an integer `Rectangle` that completely encloses the `Shape`.
`getBounds2D()`
### getBounds2D
`public Rectangle2D getBounds2D()`
Returns a high precision and more accurate bounding box of the `Shape` than the `getBounds` method. Note that there is no guarantee that the returned `Rectangle2D` is the smallest bounding box that encloses the `Shape`, only that the `Shape` lies entirely within the indicated `Rectangle2D`. The bounding box returned by this method is usually tighter than that returned by the `getBounds` method and never fails due to overflow problems since the return value can be an instance of the `Rectangle2D` that uses double precision values to store the dimensions.
Returns:
an instance of `Rectangle2D` that is a high-precision bounding box of the `Shape`.
`getBounds()`
### contains
```public boolean contains(double x,
double y)```
Tests if the specified coordinates are inside the boundary of the `Shape`.
Parameters:
`x` - the specified x coordinate
`y` - the specified y coordinate
Returns:
`true` if the specified coordinates are inside the `Shape` boundary; `false` otherwise.
### contains
`public boolean contains(Point2D p)`
Tests if a specified `Point2D` is inside the boundary of the `Shape`.
Parameters:
`p` - a specified `Point2D`
Returns:
`true` if the specified `Point2D` is inside the boundary of the `Shape`; `false` otherwise.
### intersects
```public boolean intersects(double x,
double y,
double w,
double h)```
Tests if the interior of the `Shape` intersects the interior of a specified rectangular area. The rectangular area is considered to intersect the `Shape` if any point is contained in both the interior of the `Shape` and the specified rectangular area.
This method might conservatively return `true` when:
• there is a high probability that the rectangular area and the `Shape` intersect, but
• the calculations to accurately determine this intersection are prohibitively expensive.
This means that this method might return `true` even though the rectangular area does not intersect the `Shape`. The `Area` class can be used to perform more accurate computations of geometric intersection for any `Shape` object if a more precise answer is required.
Parameters:
`x` - the x coordinate of the specified rectangular area
`y` - the y coordinate of the specified rectangular area
`w` - the width of the specified rectangular area
`h` - the height of the specified rectangular area
Returns:
`true` if the interior of the `Shape` and the interior of the rectangular area intersect, or are both highly likely to intersect and intersection calculations would be too expensive to perform; `false` otherwise.
`Area`
### intersects
`public boolean intersects(Rectangle2D r)`
Tests if the interior of the `Shape` intersects the interior of a specified `Rectangle2D`. This method might conservatively return `true` when:
• there is a high probability that the `Rectangle2D` and the `Shape` intersect, but
• the calculations to accurately determine this intersection are prohibitively expensive.
This means that this method might return `true` even though the `Rectangle2D` does not intersect the `Shape`.
Parameters:
`r` - the specified `Rectangle2D`
Returns:
`true` if the interior of the `Shape` and the interior of the specified `Rectangle2D` intersect, or are both highly likely to intersect and intersection calculations would be too expensive to perform; `false` otherwise.
`intersects(double, double, double, double)`
### contains
```public boolean contains(double x,
double y,
double w,
double h)```
Tests if the interior of the `Shape` entirely contains the specified rectangular area. All coordinates that lie inside the rectangular area must lie within the `Shape` for the entire rectanglar area to be considered contained within the `Shape`.
This method might conservatively return `false` when:
• the `intersect` method returns `true` and
• the calculations to determine whether or not the `Shape` entirely contains the rectangular area are prohibitively expensive.
This means that this method might return `false` even though the `Shape` contains the rectangular area. The `Area` class can be used to perform more accurate computations of geometric intersection for any `Shape` object if a more precise answer is required.
Parameters:
`x` - the x coordinate of the specified rectangular area
`y` - the y coordinate of the specified rectangular area
`w` - the width of the specified rectangular area
`h` - the height of the specified rectangular area
Returns:
`true` if the interior of the `Shape` entirely contains the specified rectangular area; `false` otherwise or, if the `Shape` contains the rectangular area and the `intersects` method returns `true` and the containment calculations would be too expensive to perform.
`Area`, `intersects(double, double, double, double)`
### contains
`public boolean contains(Rectangle2D r)`
Tests if the interior of the `Shape` entirely contains the specified `Rectangle2D`. This method might conservatively return `false` when:
• the `intersect` method returns `true` and
• the calculations to determine whether or not the `Shape` entirely contains the `Rectangle2D` are prohibitively expensive.
This means that this method might return `false` even though the `Shape` contains the `Rectangle2D`. The `Area` class can be used to perform more accurate computations of geometric intersection for any `Shape` object if a more precise answer is required.
Parameters:
`r` - The specified `Rectangle2D`
Returns:
`true` if the interior of the `Shape` entirely contains the `Rectangle2D`; `false` otherwise or, if the `Shape` contains the `Rectangle2D` and the `intersects` method returns `true` and the containment calculations would be too expensive to perform.
`contains(double, double, double, double)`
### getPathIterator
`public PathIterator getPathIterator(AffineTransform at)`
Returns an iterator object that iterates along the `Shape` boundary and provides access to the geometry of the `Shape` outline. If an optional `AffineTransform` is specified, the coordinates returned in the iteration are transformed accordingly.
Each call to this method returns a fresh `PathIterator` object that traverses the geometry of the `Shape` object independently from any other `PathIterator` objects in use at the same time.
It is recommended, but not guaranteed, that objects implementing the `Shape` interface isolate iterations that are in process from any changes that might occur to the original object's geometry during such iterations.
Before using a particular implementation of the `Shape` interface in more than one thread simultaneously, refer to its documentation to verify that it guarantees that iterations are isolated from modifications.
Parameters:
`at` - an optional `AffineTransform` to be applied to the coordinates as they are returned in the iteration, or `null` if untransformed coordinates are desired
Returns:
a new `PathIterator` object, which independently traverses the geometry of the `Shape`.
### getPathIterator
```public PathIterator getPathIterator(AffineTransform at,
double flatness)```
Returns an iterator object that iterates along the `Shape` boundary and provides access to a flattened view of the `Shape` outline geometry.
Only SEG_MOVETO, SEG_LINETO, and SEG_CLOSE point types are returned by the iterator.
If an optional `AffineTransform` is specified, the coordinates returned in the iteration are transformed accordingly.
The amount of subdivision of the curved segments is controlled by the `flatness` parameter, which specifies the maximum distance that any point on the unflattened transformed curve can deviate from the returned flattened path segments. Note that a limit on the accuracy of the flattened path might be silently imposed, causing very small flattening parameters to be treated as larger values. This limit, if there is one, is defined by the particular implementation that is used.
Each call to this method returns a fresh `PathIterator` object that traverses the `Shape` object geometry independently from any other `PathIterator` objects in use at the same time.
It is recommended, but not guaranteed, that objects implementing the `Shape` interface isolate iterations that are in process from any changes that might occur to the original object's geometry during such iterations.
Before using a particular implementation of this interface in more than one thread simultaneously, refer to its documentation to verify that it guarantees that iterations are isolated from modifications.
Parameters:
`at` - an optional `AffineTransform` to be applied to the coordinates as they are returned in the iteration, or `null` if untransformed coordinates are desired
`flatness` - the maximum distance that the line segments used to approximate the curved segments are allowed to deviate from any point on the original curve
Returns:
a new `PathIterator` that independently traverses the `Shape` geometry.
JavaTM 2 Platform
Std. Ed. v1.4.2
Submit a bug or feature
For further API reference and developer documentation, see Java 2 SDK SE Developer Documentation. That documentation contains more detailed, developer-targeted descriptions, with conceptual overviews, definitions of terms, workarounds, and working code examples.
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## 14943
14,943 (fourteen thousand nine hundred forty-three) is an odd five-digits composite number following 14942 and preceding 14944. In scientific notation, it is written as 1.4943 × 104. The sum of its digits is 21. It has a total of 3 prime factors and 8 positive divisors. There are 9,344 positive integers (up to 14943) that are relatively prime to 14943.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 21
• Digital Root 3
## Name
Short name 14 thousand 943 fourteen thousand nine hundred forty-three
## Notation
Scientific notation 1.4943 × 104 14.943 × 103
## Prime Factorization of 14943
Prime Factorization 3 × 17 × 293
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 14943 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 14,943 is 3 × 17 × 293. Since it has a total of 3 prime factors, 14,943 is a composite number.
## Divisors of 14943
1, 3, 17, 51, 293, 879, 4981, 14943
8 divisors
Even divisors 0 8 4 4
Total Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 21168 Sum of all the positive divisors of n s(n) 6225 Sum of the proper positive divisors of n A(n) 2646 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 122.242 Returns the nth root of the product of n divisors H(n) 5.64739 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 14,943 can be divided by 8 positive divisors (out of which 0 are even, and 8 are odd). The sum of these divisors (counting 14,943) is 21,168, the average is 2,646.
## Other Arithmetic Functions (n = 14943)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 9344 Total number of positive integers not greater than n that are coprime to n λ(n) 1168 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1751 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 9,344 positive integers (less than 14,943) that are coprime with 14,943. And there are approximately 1,751 prime numbers less than or equal to 14,943.
## Divisibility of 14943
m n mod m 2 3 4 5 6 7 8 9 1 0 3 3 3 5 7 3
The number 14,943 is divisible by 3.
## Classification of 14943
• Arithmetic
• Deficient
• Polite
• Square Free
### Other numbers
• LucasCarmichael
• Sphenic
## Base conversion (14943)
Base System Value
2 Binary 11101001011111
3 Ternary 202111110
4 Quaternary 3221133
5 Quinary 434233
6 Senary 153103
8 Octal 35137
10 Decimal 14943
12 Duodecimal 8793
20 Vigesimal 1h73
36 Base36 bj3
## Basic calculations (n = 14943)
### Multiplication
n×i
n×2 29886 44829 59772 74715
### Division
ni
n⁄2 7471.5 4981 3735.75 2988.6
### Exponentiation
ni
n2 223293249 3336671019807 49859875048976001 745056112856848382943
### Nth Root
i√n
2√n 122.242 24.6308 11.0563 6.83735
## 14943 as geometric shapes
### Circle
Diameter 29886 93889.6 7.01496e+08
### Sphere
Volume 1.39766e+13 2.80599e+09 93889.6
### Square
Length = n
Perimeter 59772 2.23293e+08 21132.6
### Cube
Length = n
Surface area 1.33976e+09 3.33667e+12 25882
### Equilateral Triangle
Length = n
Perimeter 44829 9.66888e+07 12941
### Triangular Pyramid
Length = n
Surface area 3.86755e+08 3.9323e+11 12200.9
## Cryptographic Hash Functions
md5 3ee99048971f0284e4c36e56c2502977 f05b17bc60860fc0168edec53b0c7b678b1208d6 0add68ae3f397f1a7788703a53a2060fa12d0b846316dc7677266becef2208db bf66af8df2cea915c6589aa0eac719b70b4c8439a31301ca077ae9e7ab5797c0556c196030155a4d2c37f970d3753ebf9ebb590cb45e7f20d4ca80133cf11cee b1e8329be6e881bc7f3a9e323319183c20120899
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https://discuss.ardupilot.org/t/what-concepts-does-rover-code-use-to-steer-between-2-waypoints-and-stay-on-track/35624
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# What concepts does Rover code use to steer between 2 waypoints and stay on track
My main question relates to driving an autonomous differential drive rover between 2 waypoints and staying on the track between the two waypoints
I have built an autonomous grass mowing machine for my garden. We wrote the code from the ground up. I have used pixhawk in the past but could not get it to work for our needs. Its written in C++ Arduino code. Coding is not my speciality.
It is set up to mow lanes that are 17 inches apart due to the blade size. All the software does is drives our chassis up a lane to a waypoint and then makes a 180 degree turn and drives down the next lane to the next waypoint which is located 17 inches over to one side of the first waypoint.
It uses a pair Ublox C94 M8P RTK gps with a reliable AHRS compass (with very little distortion due to magnetic or ferrous material). The vehicle follows waypoints by calculating the difference between the target heading (maths and the gps) and the actual heading (compass) and it uses the difference to send a value in a drive command to the motor controller that alters the speeds to the 2 driving wheels. this variable is called turnSpeed. the chassis is differentially driven.
After many months of work the mower drives well. The heading errors are generally below 5 degrees. However if the mower for some reasons gets off the straight line track between the 2 waypoints the code does not do a good job of getting the mower back on the straight line track quickly as it is aiming at a distant waypoint. In short, it is good at heading to a distant point but not good at getting on the straight line track between the 2 way points and then heading to the point
In order to solve this we started calculating a cross track distance error. And we use a set point of 0 cross track error and a PID to try to get the vehicle back on the straight tract between the two waypoints.
The problem now is that we have 2 inputs to the motor command variable turnSpeed. One from the heading error and the other from the PID. So this is getting real confusing.
Normally I would use the heading error variable if the heading error is greater than 2 degrees. To get the PID tuned I eased off the heading error so that the heading error only works if the heading error is more than ±20 degrees. I set Ki and Kd to zero and increased Kp until the mower went in to a stable oscillation.
I then timed the period of the oscillation for 1 complete wavelength it was 6 seconds.
I then used the following
New Kp= Kp*0.60
New Ki = Period/2
New Kd = Period/8
this gave Kp=5
ki= 3
Kd= 0.7
before this I did many other runs and got poor control response. After running this the mower is still in an oscilation.
I would really appreciate some help here.
1 what are the general mathematical concepts that need to be employed to drive a differential drive robot along a straight path between 2 waypointsand minimize the cross track error.
2 Can we expect our method to work when with have 2 inputs to the same variable, heading error and the PID
3 Do you have a rule of thumb method to tune the PID
Any help on this will be appreciated
regards
Max
PS Max, you don;t have to be sorry to be new on the site. Welcome welcome, thirst for knowledge and understanding is what we do here!
I have built an autonomous grass mowing machine for my garden. We write the code from the ground up. Its basically C++ Arduino code. Coding is not my speciality.
It is set up to mow lanes that are 17 inches apart due to the blade size. All the software does is drives our chassis up a lane to a waypoint and then makes a 180 degree turn and drives down the next lane to the next waypoint which is located 17 inches over to one side of the first waypoint.
It uses a pair Ublox C94 M8P RTK gps with a reliable AHRS compass (with very little distortion due to magnetic or ferrous material). The vehicle follows waypoints by calculating the difference between the target heading (maths and the gps) and the actual heading (compass) and it uses the difference to send a value in a drive command to the motor controller that alters the speeds to the 2 driving wheels. this variable is called turnSpeed. the chassis is differentially driven.
After many months of work the mower drives well. The heading errors are generally below 5 degrees. However if the mower for some reason gets off the straight line track between the 2 waypoints the code does not do a good job of getting the mower back on the straight line track quickly as it is aiming at a distant waypoint. In short, it is good at heading to a distant point but not good at getting on the straight line track between the 2 way points and then heading to the point
In order to solve this we started calculating a cross track distance error. And we use a set point of 0 cross track error and use a PID to try to get the vehicle back on the straight tract between the two waypoints.
The problem now is that we have 2 inputs to the motor command variable turnSpeed. One from the heading error and the other from the PID. So this is getting real confusing.
Normally I would use the heading error variable if the heading error is greater than 2 degrees. To get the PID tuned I eased off the heading error so that the heading error only works if the heading error is more than ±20 degrees. I set Ki and Kd to zero and increased Kp until the mower went in to a stable oscillation.
I then timed the period of the oscillation for 1 complete wavelength it was 6 seconds.
I then used the following
New Kp= Kp*0.60
New Ki = Period/2
New Kd = Period/8
this gave Kp=5
ki= 3
Kd= 0.7
before this I did many other runs and got poor control response. After running this the mower is still in an oscilation.
I would really appreciate some help here.
1 what are the general concepts that need to be employed to drive a robot along a straight path between 2 waypoints. Especially to get back on. This is my main question. You seems to have cracked this very well
track if it gets off track
2 Can we expect our method to work when with have 2 inputs to the same variable, heading error and the PID
3 Do you have a rule of thumb method to tune the PID
Any help on this will be appreciated
regards
Max
PS Max, you don;t have to be sorry to be new on the site. Welcome welcome, thirst for knowledge and understanding is what we do here!
2 Likes
In a shorter request which modules of the Ardupilot Rover2 code concentrate specifically on steering in auto mode.
Would really appreciate a short conceptual pointer to the correct mathematics to differential drive steering between and on a track between 2 waypoints
Hi Max,
I’ve written a wiki page here on Rover’s L1 navigation controller and it includes a link to the original paper that it was based upon. The L1 controller was originally written for Plane and it’s been inherited by Rover. Leonard Hall and I are thinking of rewriting it in a few months but what we have for now is what’s described on that wiki page.
ArduPilot (Rover and Copter anyway) have layered controllers. So at the top is the navigation controller (i.e. L1) and this outputs a lateral acceleration which is then converted into a desired turn rate and passed into a turn rate controller (a PID controller).
1 Like
I hope this is the correct area (newbe). My question is for trolling motor application (vectored thrust). What I cant find is a setting for what I call “return to original calculated heading”. In other words you have a heading from way point “1” to “2”. Now it seams to vector to next way point from current location. I would like for it to return to the calculated heading if it becomes off coarse (wind, current, way point overshoot) then resume to way point.
I hope this makes sense.
I don’t quite understand unfortunately. The way the navigation works is that the vehicle will try to get back on the line between the waypoints. It may not point directly at the next waypoint especially if there is a current pushing it off the line.
If Auto is interrupted (by switching the vehicle to another mode and then back to Auto) it will probably pick up from where it is currently. It won’t go back to the line between waypoints.
Hope this gets close to an answer…
I found my answer in your previous post on L1 calculations “http://ardupilot.org/dev/docs/rover-L1.html”. Sorry I didn’t read first. Working much better now. Very good write up by the way. I found that Rover defaulted to 6 seconds on navl1-period. This was to long.
I like your video of your boat in loiter mode in a strong current, this was what made me pursue my project with my trolling motor. It is winter hear in Wisconsin so I am not on the water. I am doing testing with an RC truck I converted with Pixhawk.
New Questions:
I am using a 320A ESC for the main drive motor and a rear wiper motor from a mini van for the steering. I am using a arduino to convert the RC PWM signal from Pixhawk, so I can incorporate a ten turn pot for steering position feedback. This all works using a regular RC transmitter and receiver and bench testing with Pixhawk. Has any progress been made on multiple types of motor drives in Rover (RC-PWM and DC motor drive PWM at same time)? Do you know if its possible to close a position loop with analog input on a Pixhawk, so I can eliminate the arduino in my steering control?
This is my trolling motor sketch. I hope you can read it ok.
1 Like
Nice use of the wiper motor.
It should be possible to use RC-PWM output for servo control on one channel with DC motor PWM on another channel. The issue may be the “output bank” restrictions on Pixhawks (and some other flight controllers). In particular on a Pixhawk1 or Cube, I think the first four outputs must use the same type of output. but 5 and 6 can be different from the first four. This isn’t documented but it’s on my list to add. Also on my list is a page describing how to setup the brushed motor output for both Copters and Rovers.
Re adding a PID controller into AP to support closed loop steering control - I haven’t heard of this before so perhaps opening an issue on the issues list would be good. I don’t think it’s something that I will personally be able to look at any time soon but perhaps another developer will. If a few users show up asking for this then it’s more likely I could prioritise it and do it myself. Sorry, it’s just there are so many requests I can’t do them all … of course another developer might do it though.
I have started an issue for my problem #10172. https://github.com/ArduPilot/ardupilot/issues/10172
I hope it conforms to the policies for posting issues. I also am changing from a DC PWM drive to a ESC. Haven’t re-coded my Arduino yet but this should work satisfactory. I found an issue already proposed for supporting the DC drive I was using (2 PWM input, fwd/rev) that seams to not be moving forward so another ESC for steering may be a better solution. Thank You very much for your input on this mater
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https://topic.alibabacloud.com/a/in-depth-analysis-font-colorredoffont-longest-public-font-colorredsubstringsfont_8_8_32414994.html
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In-depth analysis of longest public substrings
Source: Internet
Author: User
Question: If all the characters of string 1 appear in the second string in the order of the strings, then string 1 is called a substring of string 2. Note that the character of a substring (string 1) must appear in string 2 consecutively. Compile a function, enter two strings, calculate their longest public substrings, and print the longest public substrings.
For example, if two strings BDCABA and ABCBDAB are input, and both BCBA and BDAB are their longest common substrings, the output length is 4 and any substring is printed.
Analysis:Longest Common Subsequence (LCS) is a very classic dynamic programming question. Therefore, some companies that pay attention to algorithms, such as MicroStrategy, regard it as an interview question.
It will take a long time to fully introduce dynamic planning. Therefore, I do not intend to fully discuss the concepts related to dynamic planning here. I will only focus on the content directly related to LCS. If you are not familiar with dynamic planning, refer to the relevant algorithm book for example, algorithm discussion.
Consider how to break down the longest common subsequence into sub-problems, set A = "a0, a1 ,..., Am-1 ", B =" b0, b1 ,..., Bn-1 ", and Z =" z0, z1 ,..., Zk-1 "is their longest common subsequence. It is not hard to prove that it has the following features:
(1) If am-1 = bn-1, then zk-1 = am-1 = bn-1, and "z0, z1 ,..., Zk-2 "is" a0, a1 ,..., Am-2 "and" b0, b1 ,..., A Longest Common subsequence of bn-2;
(2) If am-1! = Bn-1, if zk-1! = Am-1, contains "z0, z1 ,..., Zk-1 "is" a0, a1 ,..., Am-2 "and" b0, b1 ,..., A Longest Common subsequence of bn-1;
(3) If am-1! = Bn-1, if zk-1! = Bn-1, contains "z0, z1 ,..., Zk-1 "is" a0, a1 ,..., Am-1 "and" b0, b1 ,..., A Longest Common subsequence of bn-2.
In this way, when looking for A and B Public sub-sequence, if there is am-1 = bn-1, then further solve A sub-problem, find "a0, a1 ,..., Am-2 "and" b0, b1 ,..., A Longest Common subsequence of bm-2; If am-1! = Bn-1, it is to solve two sub-problems, find out "a0, a1 ,..., Am-2 "and" b0, b1 ,..., Bn-1 "of a Longest Common subsequence and finding out" a0, a1 ,..., Am-1 "and" b0, b1 ,..., The longest common subsequence of bn-2, and the elders of the two are used as the longest common subsequence of A and B.
Solution:
Introduce a two-dimensional array c [] [], and use c [I] [j] to record the LCS length of X [I] AND Y [j, B [I] [j] records c [I] [j] based on the value of a subproblem to determine the search direction when the longest common string is output.
So before c [I, j] is calculated, c [I-1] [J-1], c [I-1] [j] and c [I] [J-1] have been calculated. In this case, we can determine whether X [I] = Y [j] Or X [I]. = Y [j] to calculate c [I] [j].
The recursive expression of the problem is as follows:
Process of backtracking output Longest Common subsequence:
Algorithm analysis:
Since each call moves at least one step up or to the left (or to the left at the same time), I = 0 or j = 0 will occur when you call (m + n) at most, return starts at this time. The return time is the opposite to the recursive call time. Because the number of steps is the same, the algorithm time complexity is merge (m + n ).
The complete implementation code is as follows:Copy codeThe Code is as follows :/**
Returns the length of the longest common substring of two strings.
** Author: liuzhiwei
** Data: 2011-08-15
**/
# Include "stdio. h"
# Include "string. h"
# Include "stdlib. h"
Int LCSLength (char * str1, char * str2, int ** B)
{
Int I, j, length1, leng2, len;
Length1 = strlen (str1 );
Lengh2 = strlen (str2 );
// Apply for a dynamic two-dimensional array using the double pointer Method
Int ** c = new int * [length1 + 1]; // a total of length1 + 1 rows
For (I = 0; I <length1 + 1; I ++)
C [I] = new int [lengty2 + 1]; // a total of lengty2 + 1 columns
For (I = 0; I <length1 + 1; I ++)
C [I] [0] = 0; // all columns are initialized to 0.
For (j = 0; j <length1 + 1; j ++)
C [0] [j] = 0; // All The 0th rows are initialized to 0
For (I = 1; I <length1 + 1; I ++)
{
For (j = 1; j <length1 + 1; j ++)
{
If (str1 [I-1] = str2 [J-1]) // Since 0 rows 0 columns of c [] [] are not used, the line I element of c [] [] corresponds to the I-1 element of str1
{
C [I] [j] = c [I-1] [J-1] + 1;
B [I] [j] = 0; // The search direction when the public substring is output
}
Else if (c [I-1] [j]> c [I] [J-1])
{
C [I] [j] = c [I-1] [j];
B [I] [j] = 1;
}
Else
{
C [I] [j] = c [I] [J-1];
B [I] [j] =-1;
}
}
}
/*
For (I = 0; I <length1 + 1; I ++)
{
For (j = 0; j <length1 + 1; j ++)
Printf ("% d", c [I] [j]);
Printf ("\ n ");
}
*/
Len = c [length1] [length1];
For (I = 0; I <length1 + 1; I ++) // release the dynamically applied two-dimensional array
Delete [] c [I];
Delete [] c;
Return len;
}
Void PrintLCS (int ** B, char * str1, int I, int j)
{
If (I = 0 | j = 0)
Return;
If (B [I] [j] = 0)
{
PrintLCS (B, str1, I-1, J-1); // recursion starts from the back, so first recursion to the front of the substring, and then output the substring from the back
Printf ("% c", str1 [I-1]); // the line I element of c [] [] corresponds to the I-1 element of str1
}
Else if (B [I] [j] = 1)
PrintLCS (B, str1. I-1, j );
Else
PrintLCS (B, str1, I, J-1 );
}
Int main (void)
{
Char str1 [1, 100], str2 [100];
Int I, length1, leng2, len;
Printf ("Enter the first string :");
Gets (str1 );
Printf ("enter the second string :");
Gets (str2 );
Length1 = strlen (str1 );
Lengh2 = strlen (str2 );
// Apply for a dynamic two-dimensional array using the double pointer Method
Int ** B = new int * [length1 + 1];
For (I = 0; I <length1 + 1; I ++)
B [I] = new int [length1 + 1];
Len = LCSLength (str1, str2, B );
Printf ("The Longest Common substring is % d \ n", len );
Printf ("the longest public substring is :");
PrintLCS (B, str1, length1, leng22 );
Printf ("\ n ");
For (I = 0; I <length1 + 1; I ++) // release the dynamically applied two-dimensional array
Delete [] B [I];
Delete [] B;
System ("pause ");
Return 0;
}
The program is as follows:
The second method is:
Copy codeThe Code is as follows :/**
Returns the length of the longest common substring of two strings.
** Author: liuzhiwei
** Data: 2011-08-15
**/
# Include "stdio. h"
# Include "string. h"
# Include "stdlib. h"
Int LCSLength (char * str1, char * str2) // obtain the maximum length of the two strings and output the common substrings
{
Int I, j, length1, leng22;
Length1 = strlen (str1 );
Lengh2 = strlen (str2 );
// Apply for a dynamic two-dimensional array using the double pointer Method
Int ** c = new int * [length1 + 1]; // a total of length1 + 1 rows
For (I = 0; I <length1 + 1; I ++)
C [I] = new int [lengty2 + 1]; // a total of lengty2 + 1 columns
For (I = 0; I <length1 + 1; I ++)
C [I] [0] = 0; // all columns are initialized to 0.
For (j = 0; j <length1 + 1; j ++)
C [0] [j] = 0; // All The 0th rows are initialized to 0
For (I = 1; I <length1 + 1; I ++)
{
For (j = 1; j <length1 + 1; j ++)
{
If (str1 [I-1] = str2 [J-1]) // Since 0 rows 0 columns of c [] [] are not used, the line I element of c [] [] corresponds to the I-1 element of str1
C [I] [j] = c [I-1] [J-1] + 1;
Else if (c [I-1] [j]> c [I] [J-1])
C [I] [j] = c [I-1] [j];
Else
C [I] [j] = c [I] [J-1];
}
}
// Output public substrings
Char s [100];
Int len, k;
Len = k = c [length1] [length1];
S [k --] = '\ 0 ';
I = length1, j = leng2;
While (I> 0 & j> 0)
{
If (str1 [I-1] = str2 [J-1])
{
S [k --] = str1 [I-1];
I --;
J --;
}
Else if (c [I-1] [j] <c [I] [J-1])
J --;
Else
I --;
}
Printf ("the longest public substring is :");
Puts (s );
For (I = 0; I <length1 + 1; I ++) // release the dynamically applied two-dimensional array
Delete [] c [I];
Delete [] c;
Return len;
}
Int main (void)
{
Char str1 [1, 100], str2 [100];
Int length1, leng2, len;
Printf ("Enter the first string :");
Gets (str1 );
Printf ("enter the second string :");
Gets (str2 );
Length1 = strlen (str1 );
Lengh2 = strlen (str2 );
Len = LCSLength (str1, str2 );
Printf ("The Longest Common substring is % d \ n", len );
System ("pause ");
Return 0;
}
Problem expansion: Set A, B, and C to three strings with the length of n, which are taken from the alphabet of the same constant. Design a time Algorithm for Finding the longest common substring O (n ^ 3) of the three strings.
Idea: this is the same idea as finding the public substrings of two strings. However, here we need to dynamically apply for a three-dimensional array. When the tail characters of the three strings are different, there are more situations to consider.Copy codeThe Code is as follows :/**
Find the maximum length of the three strings.
** Author: liuzhiwei
** Data: 2011-08-15
**/
# Include "stdio. h"
# Include "string. h"
# Include "stdlib. h"
Int max1 (int m, int n)
{
If (m> n)
Return m;
Else
Return n;
}
Int max2 (int x, int y, int z, int k, int m, int n)
{
Int max =-1;
If (x> max)
Max = x;
If (y> max)
Max = y;
If (z> max)
Max = z;
If (k> max)
Max = k;
If (m> max)
Max = m;
If (n> max)
Max = n;
Return max;
}
Int LCSLength (char * str1, char * str2, char * str3) // obtain the maximum length of common substrings of the three strings and output the common substrings
{
Int I, j, k, length1, leng2, length3, len;
Length1 = strlen (str1 );
Lengh2 = strlen (str2 );
Length3 = strlen (str3 );
// Apply for a dynamic 3D Array
Int *** c = new int *** [length1 + 1]; // a total of length1 + 1 rows
For (I = 0; I <length1 + 1; I ++)
{
C [I] = new int * [lengty2 + 1]; // a total of lengty2 + 1 columns
For (j = 0; j <length1 + 1; j ++)
C [I] [j] = new int [length3 + 1];
}
For (I = 0; I <length1 + 1; I ++)
{
For (j = 0; j <length1 + 1; j ++)
C [I] [j] [0] = 0;
}
For (I = 0; I <length1 + 1; I ++)
{
For (j = 0; j <length3 + 1; j ++)
C [0] [I] [j] = 0;
}
For (I = 0; I <length1 + 1; I ++)
{
For (j = 0; j <length3 + 1; j ++)
C [I] [0] [j] = 0;
}
For (I = 1; I <length1 + 1; I ++)
{
For (j = 1; j <length1 + 1; j ++)
{
For (k = 1; k <length3 + 1; k ++)
{
If (str1 [I-1] = str2 [J-1] & str2 [J-1] = str3 [k-1])
C [I] [j] [k] = c [I-1] [J-1] [k-1] + 1;
Else if (str1 [I-1] = str2 [J-1] & str1 [I-1]! = Str3 [k-1])
C [I] [j] [k] = max1 (c [I] [j] [k-1], c [I-1] [J-1] [k]);
Else if (str1 [I-1] = str3 [k-1] & str1 [I-1]! = Str2 [J-1])
C [I] [j] [k] = max1 (c [I] [J-1] [k], c [I-1] [j] [k-1]);
Else if (str2 [J-1] = str3 [k-1] & str1 [I-1]! = Str2 [J-1])
C [I] [j] [k] = max1 (c [I-1] [j] [k], c [I] [J-1] [k-1]);
Else
{
C [I] [j] [k] = max2 (c [I-1] [j] [k], c [I] [J-1] [k], c [I] [j] [k-1], c [I-1] [J-1] [k], c [I-1] [j] [k-1], c [I] [J-1] [k-1]);
}
}
}
}
Len = c [length1] [lengh2] [length3];
For (I = 1; I <length1 + 1; I ++) // release the 3D array of the Dynamic Application
{
For (j = 1; j <length1 + 1; j ++)
Delete [] c [I] [j];
Delete [] c [I];
}
Delete [] c;
Return len;
}
Int main (void)
{
Char str1 [100], str2 [100], str3 [100];
Int len;
Printf ("Enter the first string :");
Gets (str1 );
Printf ("enter the second string :");
Gets (str2 );
Printf ("enter the third string :");
Gets (str3 );
Len = LCSLength (str1, str2, str3 );
Printf ("The Longest Common substring is % d \ n", len );
System ("pause ");
Return 0;
}
The program is as follows:
Related Keywords:
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https://www.numbersaplenty.com/14
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Cookie Consent by FreePrivacyPolicy.com
Search a number
14 = 27
BaseRepresentation
bin1110
3112
432
524
622
720
oct16
915
1014
1113
1212
1311
1410
15e
hexe
• 14 can be written using four 4's:
See also 113.
14 has 4 divisors (see below), whose sum is σ = 24. Its totient is φ = 6.
The previous prime is 13. The next prime is 17. The reversal of 14 is 41.
Added to its reverse (41) it gives a triangular number (55 = T10).
14 = 12 + 22 + 32.
14 is nontrivially palindromic in base 6 and base 13.
14 is an esthetic number in base 4, base 12 and base 14, because in such bases its adjacent digits differ by 1.
It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length.
It is the 4-th Catalan number.
14 is a repfigit number.
It is a fibodiv number, since the Fibonacci-like sequence with seeds 1 and 4 contains 14 itself.
It is a magnanimous number.
It is an alternating number because its digits alternate between odd and even.
It is a Curzon number.
14 is a nontrivial repdigit in base 6 and base 13.
It is a plaindrome in base 3, base 5, base 6, base 8, base 9, base 10, base 11, base 12 and base 13.
It is a nialpdrome in base 2, base 4, base 6, base 7, base 13 and base 14.
It is a zygodrome in base 6 and base 13.
It is a congruent number.
It is a panconsummate number.
It is a pernicious number, because its binary representation contains a prime number (3) of ones.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 2 + ... + 5.
It is an arithmetic number, because the mean of its divisors is an integer number (6).
14 is a deficient number, since it is larger than the sum of its proper divisors (10).
14 is an equidigital number, since it uses as much as digits as its factorization.
14 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 9.
The product of its digits is 4, while the sum is 5.
The square root of 14 is about 3.7416573868. The cubic root of 14 is about 2.4101422642.
Adding to 14 its reverse (41), we get a palindrome (55).
Subtracting 14 from its reverse (41), we obtain a cube (27 = 33).
The spelling of 14 in words is "fourteen", and thus it is an aban number and an iban number.
Divisors: 1 2 7 14
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https://www.northernarchitecture.us/naval-architecture/ship-form-calculations.html
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## Ship form calculations
It has been seen that the three dimensional hull form can be represented by a series of curves which are the intersections of the hull with three sets of mutually orthogonal planes. The naval architect is interested in the areas and volumes enclosed by the curves and surfaces so represented. To find the centroids of the areas and volumes it is necessary to obtain their first moments about chosen axes. For some calculations the moments of inertia of the areas are needed. This is obtained from the second moment of the area, again about chosen axes. These properties could be calculated mathematically, by integration, if the form could be expressed in mathematical terms. This is not easy to do precisely and approximate methods of integration are usually adopted, even when computers are employed. These methods rely upon representing the actual hull curves by ones which are defined by simple mathematical equations. In the simplest case a series of straight lines are used.
## How To Have A Perfect Boating Experience
Lets start by identifying what exactly certain boats are. Sometimes the terminology can get lost on beginners, so well look at some of the most common boats and what theyre called. These boats are exactly what the name implies. They are meant to be used for fishing. Most fishing boats are powered by outboard motors, and many also have a trolling motor mounted on the bow. Bass boats can be made of aluminium or fibreglass.
Get My Free Ebook
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http://excelmathmike.blogspot.com/2012/10/teaching-students-to-count-objects-up.html
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## Monday, October 29, 2012
### Teaching Students to Count Objects Up to 20
Try these fun counting games with whichever numbers you are teaching. Start with 0 or 1 and continue through 20 or higher. Hold up 10 pencils, paper clips, pieces of colored paper, crayons, drinking straws, or other objects in your classroom. Ask the students how many you are holding. Check by having the class count the items aloud as a child takes them from you and places them on a table. Draw the number 10 on the board.
Count the objects again as a student points to them from left to right on the table. Choose a new volunteer to point to the objects from right to left as the class counts the objects once more.
Copy this number chart and bring 20 beans, paper clips bottle caps, or other counters for each student. For younger students, just copy the first two to four rows of the chart. Click here to download a PDF file of this chart:
Excel Math Number Chart Download a PDF file here
Give each student 10 counters. Let each student place a counter on the chart as you count aloud numbers 1 through 10.
With Excel Math, students develop a strong foundation in math beginning in Kindergarten. Used in classrooms for over 30 years, Excel Math curriculum carefully presents math in a spiraling fashion. Students learn and review different concepts throughout the year while developing a solid foundation of math skills. Using strategically placed spaced repetition, Excel Math gives educators a proven approach to teach math concepts to students from Kindergarten through sixth grade for long-term retention. Read more here.
To help your students visualize counting, duplicate the number line below on the board. Have a student point to each number as the class says it aloud. Then have the student circle the numbers as they are counted.
If you have time, enlarge the number line so it can span across the floor of your classroom or hallway (with the numbers spaced about 5 inches apart).
Read more . . .
When your students are ready to begin counting by twos, read our previous blog post and download a frog counting game.
How do you help your students learn to count numbers? Leave a comment below.
New to Excel Math? Visit our website to learn more: www.excelmath.com.
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http://de.metamath.org/mpeuni/eelT12.html
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Mathbox for Alan Sare < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > Mathboxes > eelT12 Structured version Visualization version GIF version
Theorem eelT12 37955
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eelT12.1 (⊤ → 𝜑)
eelT12.2 (𝜓𝜒)
eelT12.3 (𝜃𝜏)
eelT12.4 ((𝜑𝜒𝜏) → 𝜂)
Assertion
Ref Expression
eelT12 ((𝜓𝜃) → 𝜂)
Proof of Theorem eelT12
StepHypRef Expression
1 3anass 1035 . . 3 ((⊤ ∧ 𝜓𝜃) ↔ (⊤ ∧ (𝜓𝜃)))
2 truan 1492 . . 3 ((⊤ ∧ (𝜓𝜃)) ↔ (𝜓𝜃))
31, 2bitri 263 . 2 ((⊤ ∧ 𝜓𝜃) ↔ (𝜓𝜃))
4 eelT12.3 . . 3 (𝜃𝜏)
5 eelT12.2 . . . 4 (𝜓𝜒)
6 eelT12.1 . . . . 5 (⊤ → 𝜑)
7 eelT12.4 . . . . 5 ((𝜑𝜒𝜏) → 𝜂)
86, 7syl3an1 1351 . . . 4 ((⊤ ∧ 𝜒𝜏) → 𝜂)
95, 8syl3an2 1352 . . 3 ((⊤ ∧ 𝜓𝜏) → 𝜂)
104, 9syl3an3 1353 . 2 ((⊤ ∧ 𝜓𝜃) → 𝜂)
113, 10sylbir 224 1 ((𝜓𝜃) → 𝜂)
Colors of variables: wff setvar class Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 ⊤wtru 1476 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 This theorem depends on definitions: df-bi 196 df-an 385 df-3an 1033 df-tru 1478 This theorem is referenced by: (None)
Copyright terms: Public domain W3C validator
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https://www.programmingassignmenthelper.com/game-of-life-in-cusp-assembly-homework-sample/
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# Game of Life in CUSP Assembly Homework Sample
The game of life was designed by John Conway, and is an example of a cellular automata. It consists of 3 basic rules, if a cell has less than 2 neighbors it dies of loneliness, and if it has more than 3 it dies of overcrowding, and if a cell has 3 neighbors it becomes alive. Although it sounds very simple, it can lead to very complex behavior. 3 cells in a straight line is called a blinker, and alternates between horizontal and vertical. You can assume cells outside the grid are always 0 (dead). For more assembly language programming assignments contact us for a quote.
Solution:
hw6.csp
.EQU KEYB_VECTOR,\$FF8 ; keyboard interrupt vector
.EQU @,\$000 ; main program start address
main:
LDS# \$E00 ; initialize stack to \$E00
LDA# keyboardISR
STA KEYB_VECTOR ; save isr routine address in vector
CLR generation ; start in generation 0
LDA# array1 ; save ptr to array 1 in variable
STA arr1ptr
LDA# array2 ; save ptr to array 2 in variable
STA arr2ptr
PSH# startlen ; length of string
PSH# startmsg ; string to print
JSR \$E05 ; prints starting message
ADS# 2 ; restore stack pointer
JSR \$E06 ; prints newline separation
JSR \$E06 ; prints newline separation
; Print grid
PSH arr1ptr ; address of array of current grid
PSH rows ; number of rows
PSH columns ; number of columns
PSH generation
JSR printGrid ; print grid
ADS# 4 ; restore stack pointer
start:
PSH# prmlen ; length of string
PSH# prompt ; string to print
JSR \$E05 ; prints prompt
ADS# 2 ; restore stack pointer
STA ngen ; save input in ngen
JSR \$E06 ; prints newline separation
CMA# 0
JEQ exit
generate:
PSH arr1ptr ; address of array of current grid
PSH rows ; number of rows
PSH columns ; number of columns
PSH arr2ptr ; address of array of new grid
JSR nextGen ; calculate next grid
ADS# 4 ; restore stack pointer
INC generation
; Print grid
PSH arr2ptr ; address of array of current grid
PSH rows ; number of rows
PSH columns ; number of columns
PSH generation
JSR printGrid ; print grid
ADS# 4 ; restore stack pointer
; swap pointers
LDA arr1ptr
LDX arr2ptr
STA arr2ptr
STX arr1ptr
CLR endwait ; clear keyboard wait flag
LDA# \$80 ; enable keyboard interrupts
OUTB \$0
SIE ; enable interrupts
LDA count ; set count for initializing timer
OUTW \$31
LDA# \$50 ; disable timer interrupt, clear ready bit, load and start timer
OUTB \$030
waitTimer:
INB \$030 ; read status register
AND# \$80 ; see if count is complete
JNE countdone ; if so, exit loop
LDA endwait ; see if keyboard was pressed
CMA# 1
JNE waitTimer ; if not, keep waiting
countdone:
CIE ; disable interrupts
DEC ngen ; decrement number of generations to print
JNE generate ; repeat if not zero
JMP start ; start over
exit:
PSH# endlen ; length of string
PSH# endmsg ; string to print
JSR \$E05 ; prints end of program
ADS# 2 ; restore stack pointer
HLT ; terminate program
; printGrid subroutine
.EQU grid,5
.EQU nr,4
.EQU nc,3
.EQU gen,2
printGrid:
PSHF ; push FP on stack
TSF ; load stack pointer in FP
PSH# genlen ; length of string
PSH# genmsg ; string to print
JSR \$E05 ; prints generation
ADS# 2 ; restore stack pointer
LDA ! gen
JSR \$E00 ; prints the generation number
LDX# 0 ; start at position 0 in array
CLR Y ; initialize row index to zero
forY:
CLR X ; initialize column index to zero
forX:
LDA& ! grid ; load value from array
CMA# 0 ; see if the cell was dead
JEQ cell0
cell1:
LDA# ‘*’ ; char to print
JSR \$E08 ; prints a star
cell0:
LDA# ‘.’ ; char to print
JSR \$E08 ; prints a dot
LDA# ‘ ‘ ; char to print
JSR \$E08 ; prints a space
ADX# 1 ; increment array position
INC X ; increment column index
LDA X ; load index in ACC
CMA ! nc ; compare with number of columns
JLT forX ; if I < nColumns, continue loop
JSR \$E06 ; print carriage return
INC Y ; increment row index
LDA Y ; load index in ACC
CMA ! nr ; compare with number of rows
JLT forY ; if I < nRows, continue loop
JSR \$E06 ; print carriage return
POPF ; restore FP from stack
; Keyboard Interrupt Service Routine
keyboardISR:
PSHA ; save A in stack
INC endwait ; set endwait to 1 to terminate wait
LDA# \$40 ; disable keyboard interrupt and flush buffer
OUTB \$0
POPA ; recover A
IRTN
; Variables used in main
Y: .word 0 ; row index
X: .word 0 ; column index
PTR: .word 0
generation: .word 0
ngen: .word 0
count: .word 1000000
startmsg: .char ‘Here is the starting grid:’,startlen
genmsg: .char ‘Generation: ‘,genlen
prompt: .char ‘How many new generations would you like to print (enter 0 to end)?’,prmlen
endmsg: .char ‘End of program.’,endlen
endwait: .word 0
arr1ptr: .word 0
arr2ptr: .word 0
array1: .word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 1
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 1
.word 0
.word 0
.word 0
.word 0
.word 1
.word 1
.word 1
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
.word 0
array2: .blkw 42,0
rows: .word 6
columns: .word 7
; NextGen subroutine
.EQU @,\$400 ; subroutine start address
.EQU curGrid,5
.EQU nRows,4
.EQU nColumns,3
.EQU nextGrid,2
nextGen:
PSHF ; push FP on stack
TSF ; load stack pointer in FP
CLR I ; initialize row index to zero
forRow:
CLR J ; initialize column index to zero
forCol:
LDA I ; load current row
MUL ! nColumns ; multiply row by ncolumns
STA pos ; save position in pos
LDA I
CMA# 0 ; see if row == 0
JEQ midleft ; if so, test middle neighbors
uptop:
LDA J
CMA# 0 ; see if col == 0
JEQ upmiddle ; if so, test up middle neighbor
LDX pos ; get position
SBX ! nColumns ; subtract ncolumns to get position in previous row
SBX# 1 ; subtract 1 to get position at top left
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
upmiddle:
LDX pos ; get position
SBX ! nColumns ; subtract ncolumns to get position in previous row
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
upright:
LDA J
CMA ! nColumns ; see if col >= n columns
JGE midleft ; if so, test midleft neighbor
LDX pos ; get position
SBX ! nColumns ; subtract ncolumns to get position in previous row
ADX# 1 ; get position at top right
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
midleft:
LDA J
CMA# 0 ; see if col == 0
JEQ midright ; if so, test middle right neighbor
LDX pos ; get position
SBX# 1 ; get position at left
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
midright:
LDA J
CMA ! nColumns ; see if col >= n columns
JGE down ; if so, test down neightbors
LDX pos ; get position
ADX# 1 ; get position at right
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
down:
LDA I
CMA ! nRows ; see if row + 1 >= n rows
JGE updatecell ; if so, update cell
dnleft:
LDA J
CMA# 0 ; see if col == 0
JEQ dnmiddle ; if so, test down middle neighbor
LDX pos ; get position
ADX ! nColumns ; add ncolumns to get position in next row
SBX# 1 ; subtract 1 to get position at down left
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
dnmiddle:
LDX pos ; get position
ADX ! nColumns ; add ncolumns to get position in next row
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
dnright:
LDA J
CMA ! nColumns ; see if col >= n columns
JGE updatecell ; if so, update cell
LDX pos ; get position
ADX ! nColumns ; add ncolumns to get position in next row
ADX# 1 ; get position at down right
LDA& ! curGrid ; load value from array
STA neighbors ; update number of neighbors
updatecell:
LDX pos ; get position
LDA& ! curGrid ; load value from array
STA& ! nextGrid ; copy cell to next grid
CMA# 0 ; see if the cell was dead
alive:
LDA neighbors ; load number of neighbors of current cell
CMA# 1 ; see if there are 1 or less neighbors
JGT testoc ; if there are more than 1, test overcrowding
LDA# 0 ; else, clear A to kill cell
STA& ! nextGrid ; set cell as dead in next grid
JMP next ; continue the loop
testoc:
CMA# 4 ; see if there are 4 or more neighbors
JLT next ; if there are less than 4, go to next cell
LDA# 0 ; else, clear A to kill cell
STA& ! nextGrid ; set cell as dead in next grid
JMP next ; continue the loop
LDA neighbors ; load number of neighbors of current cell
CMA# 3 ; see if there are exactly 3 neighbors
JNE next ; if there are not 3 neighbors, go to next cell
LDA# 1 ; else, set A to make cell alive
STA& ! nextGrid ; set cell as alive in next grid
next:
INC J ; increment column index
LDA J ; load index in ACC
CMA ! nColumns ; compare with number of columns
JLT forCol ; if I < nColumns, continue loop
INC I ; increment row index
LDA I ; load index in ACC
CMA ! nRows ; compare with number of rows
JLT forRow ; if I < nRows, continue loop
POPF ; restore FP from stack
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https://docshare.tips/sbi-po-paper_575a127db6d87fab218b4719.html
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# SBI-PO-paper
of 24
SBI PO
## Content
SBI P.O.
Solved Paper
REASONING ABILITY
1. In a certain code language ‘how many goals
scored’ is written as ‘5 3 9 7’; ‘many more
matches’ is written as ‘9 8 2’ and ‘he scored five’
is written as ‘1 6 3’. How is ‘goals’ written in
that code language ?
(1) 5 (2) 7 (3) 5 or 7
(5) None of these
2. In a certain code TEMPORAL is written as
OLDSMBSP. How is CONSIDER written in that
code?
(1) RMNBSFEJ (2) BNMRSFEJ
(3) RMNBJEFS (4) TOPDQDCH
(5) None of these
3. How many meaningful English words can be
made with the letters DLEI using each letter only
once in each word ?
(1) None (2) One (3) Two
(4) Three (5) More than three
4. Among A, B, C, D and E each having different
weight, D is heavier than only A and C is lighter
than B and E. Who among them is the heaviest ?
(1) B (2) E (3) C
(5) None of these
5. Each odd digit in the number 5263187 is
substituted by the next higher digit and each even
digit is substituted by the previous lower digit
and the digits so obtained are rearranged in
ascending order, which of the following will be
the
,
third digit from the left end after the
rearrangement ?
(1) 2 (2) 4 (3) 5
(4) 6 (5) None of these
6. Pratap corrrectly remembers that his mother’s
birthday is before twenty third April but after
Nineteenth April, whert as his sister correctly
remembers that their mother’s birthday is not on
or after twenty second April. On which day in
April is definitely their mother’s birthday ?
(1) Twentieth (2) Twenty-first
(3) Twentieth or twenty-first
(4) Cannot be determined
(5) None of these
7. Ashok started walking towards South. After
walking 50 meters he took a right turn and
walked 30 meters. He then took a right turn and
walked 100 meters. He again took a right turn
and walked 30 meters and stopped. How far and
in which direction was he from the starting point?
(1) 50 meters South (2) 150 meters North
(3) 180 meters East (4) 50 meters North
(5) None of these
8. If’–‘ means ‘+’; ‘–’means
×
;
×
means ‘÷’and
+’means ‘–’; then 15 – 8 × 6 + 12 + 4 = ?
(1) 20 (2) 28 (3)
4
8
7
(4) 2 3 (5) None of these
9. Town D is towards East of town F. Town B is
towards North of town D. Town H is towards
South of town B. Towards which direction is
town H from town F ?
(1) East (2) South-East
(5) None of these
Held on:
18-04-10
10. How many such pairs of letters are there in the
word SEARCHES each of which has as many
letters between them in the word as in the English
alphabet ?
(1) None (2) One (3) Two
(4) Three (5) More than three
Direction: In each of the questions below are given
four statements followed by four conclusions
numbered I, II, III 8s IV. You have to take the given
statements to be true even if they seem to be at given
conclusions logically follows from the given
statements disregarding commonly known facts.
11. Statements: All cups are bottles. Some bottles
are jugs. No jug is plate. Some plates are tables.
Conclusions:
I. Some tables are bottles.
II. Some plates are cups.
III. No table is bottle.
IV. Some jugs are cups.
(1) Only I follows (2) Only II follows
(3) Only III follows (4) Only IV follows
(5) Only either I or III follows
12. Statements: Some chairs are handles. All
handles are pots. All pots are mats. Some mats
are buses.
Conclusions:
I. Some buses are handles.
II. Some mats are chairs.
III. No bus is handle.
IV. Some mats are handles.
(1) Only I, II and IV follow
(2) Only II, III and IV follow
(3) Only either I or III and II follow
(4) Only either I or III and IV follow
(5) Only either I or III and II and IV follow
13. Statements: All birds are horses. All horses are
tigers. Some tigers are lions. Some lions are
monkeys.
Conclusions:
I. Some tigers are horses.
II. Some monkeys are birds.
III. Some tigers are birds.
IV. Some monkeys are horses.
(1) Only I and III follow
(2) Only I, II and III follow
(3) Only II, III and IV follow
(4) All I, II, III and IV follow
(5) None of these
14. Statements: Some benches are walls. All walls
are houses. Some houses are jungles. All jungles
Conclusions:
II. Some jungles are walls.
III. Some houses are benches.
(1) Only land II follow
(2) Only I and III follow
(3) Only III and IV follow
(4) Only II, III and IV follow
(5) None of these
15. Statements: Some sticks are lamps. Some
flowers are lamps. Some lamps are dresses. All
dresses are shirts.
Conclusions:
I. Some shirts are sticks.
II. Some shirts are flowers.
III. Some flowers are sticks.
IV. Some dresses are sticks.
(1) None follows (2) Only I follows
(3) Only II follows (4) Only III follows
(5) Only IV follows
Direction: Study the following information
carefully and answer the questions given below:
A, B, C, D, E, F, G and H are eight employees
of an organization working in three departments viz.
Personnel, Administration and Marketing with not
more than three of them in any department. Each of
them has a different choice of sports from football,
hockey and table tennis not necessarily in the same
order.
D works in Administration and does not like
either football or cricket. F works in Personnel with
only A who likes table tennis. Eand H do not work in
the same department as D. C likes hockey and does
not work in marketing. G does not work in
administration and does not like either cricket or
likes football. The one who likes volleyball works in
personnel. None of those who work in administration
likes either badminton or lawn tennis. H does not like
cricket.
16. Which of the following groups of employees
(1) EGH (2) AF (3) BCD
17. In which department does E work ?
(1) Personnel (2) Marketing
(5) None of these
18. Which of the following combinations of
employee-department-favourite sport is correct?
(1) E – Administration – Cricket
(2) F – Personnel – Lawn Tennis
(3) H – Marketing – Lawn Tennis
(4) B – Administration – Table Tennis
(5) None of these
19. What is E’s favourite sport ?
(5) None of these
20. What is G’s favourite sport ?
(5) None of these
Direction: In the following questions, the symbols
# and S are used with the following meaning as
illustrated below.
P \$ Q’ means ‘P is not smaller than Q’.
P @ Q’ means ‘P is neither smaller than nor equal to ‘Q
‘P # Q’ means ‘P is neither greater than nor equal to Q’.
P δ Q’ means ‘P is neither greater than nor smaller than
Q’.
‘P Q’ means ‘P is not greater than Q’.
Now in each of the following questions
assuming the given statements to be true, find which
of the four conclusions I, II, III and IV given below
accordingly.
21. Statements: H @ T, T # F, F δ E, E VV
Conclusions: I. V \$ F II. E @ T
III. H @ V IV. T # V
(1) Only I, II and III are true
(2) Only I, II and IV are true
(3) Only II, III and IV are true
(4) Only I, III and IV are true
(5) All I, II, III and IV are true
22. Statements: D#R, R K, K@F, F\$J
Conclusions: I. J # R II. J # K
III. R # F IV. K @ D
(1) Only I, II and III are true
(2) Only II, III and IV are true
(3) Only I, III and IV are true
(4) All I, II, III and IV are true
(5) None of these
23. Statements: N δ B, B \$ W, W # H, H M
Conclusions : I. M @ W II. H @ N
III. W S N IV. W# N
(1) Only I is true (2) Only III is true
(3) Only IV is true
(4) Only either III or IV is true
(5) Only either III or IV and I are true
24. Statements: R D, D \$ J, J # M, M @ K
Conclusions: I. K # J II. D @ M
III. R # M
IV. D @ K
(1) None is true (2) Only I is true
(3) Only II is true (4) Only III is true
(5) Only IV is true
25. Statements: M \$ K, K @ N, N R, R # WW
Conclusions: I. W @ K II. M \$ R
III. K @ W
IV. M @ N
(1) Only I and II are true
(2) Only I, II and III are true
(3) Only III and IV are true
(4) Only II, III and IV are true
(5) None of these
Direction: Study the following information
carefully and answer the questions given below
Following are the conditions for selecting Senior
Manager-Credit in a bank. The candidate must—
(i) be a graduate in any discipline with atleast 60
percent marks.
(ii) have post qualification work experience of at
least ten years in the Advances Section of a bank.
(iii) be at least 30 years and not more than 40 years
as on 1.4.2010. (iv) have secured at least 40
percent marks in the group discussion. (v) have
secured at least 50 percent marks in interview.
In the case of a candidate who satisfies all the
conditions EXCEPT—
(A) at (i) above but has secured at least 50 percent
marks in graduation and at least 60 percent marks
in post graduation in any discipline the case is
to be referred to the General Manager Advances.
(B) at (ii) above but has total post qualification work
experience of at least seven years out of which
at least three years as Manager-Credit in a bank,
the case is to be referred to Executive
Director.
In each question below details of one candidate
is given. You have to take one of the following
courses of action based on the information
provided and the conditions and sub-conditions
given above and mark the number of that course
anything other than the information provided in
each question. All these cases are given to you
as on 01.04.2010.
(1) if the case is to be referred to Executive
Director.
(2) if the case is to be referred to General
(3) if the data are inadequate to take a decision.
(4) if the candidate is not to be selected.
(5) if the candidate is to be selected.
26. Shobha Gupta has secured 50 percent marks in
the Interview and 40 percent marks in the Group
Discussion. She has been working for the past
eight years out of which four years as Manager-
Credit in a bank after completing her B. A. degree
with 60 percent marks. She was born on 12th
September 1978.
27. Rohan Maskare was born on 8th March 1974. He
has been working in a bank for the past twelve years
after completing his B.Com. degree with 70 percent
marks. He has secured 50 percent marks in both
the Group Discussion and the Interview.
28. Prakash Gokhale was born on 4th August 1977.
He has secured 65 percent marks in. post
He has been working for the past ten years in
the Advances Department of a bank after
completing his post graduation. He has secured
45 percent marks in the Group Discussion and
50 percent marks in the Interview.
29. Sudha Mehrotra has been working in the
Advances department of a bank for the past
twelve years after completing her B.Com. degree
with 60 percent marks. She has secured 50
percent marks in the Group Discussion and 40
percent marks in the Interview. She was born on
15th February 1972.
30. Amit Narayan was born on 28th May 1974. He
has been working in the Advances department of a
bank for the past eleven years after completing his
B.Sc. degree with 65 percent marks. He has secured
55 percent marks in the Group discussion and 50
percent marks in the interview.
Direcion: In each question below is given a
statement followed by three courses of action
numbered (A), (B) and (C). A course of action is a
step or administrative decision to be taken for.
improvement, follow-up or further action in regard
to the problem, policy, etc. On the basis of the
information given in the statement, you have to
assume everything in the statement to be true, then
decide which of the suggested courses of action
logically follow(s) for pursuing.
31. Statement : A heavy unseasonal downpour
during tho last two days has paralysed the,
normal life in the state in which five persons were
killed but this has provided a huge relief to the
problem of acute water crisis in the state.
Courses of action:
(A) The state government should set up a
committee to review the alarming situation.
(B) The state government should immediately
remove all the restrictions, on use of potable
water in all the major cities in the state.
(C) The state government should send relief
supplies to all the affected areas in the state.
(1) None (2) Only (A)
(3) Only (B) and (C) (4) Only (C)
(5) All (A), (B), (C)
32. Statement: A large private bank has decided to
retrench one-third of its employees in view of
the huge losses incurred by it during the past
three quarters.
Courses of action:
(A) The Govt. should issue a notification to
general public to immediately: stop all
transactions with the bank.
(B) The Govt. should direct the bank to refrain
from retrenching its employees.
(C) The Govt. should ask the central bank of the
country to initiate an enquiry into the bank’s
activities and submit its report.
(1) None (2) Only (A)
(3) Only (B) (4) Only (C)
(5) Only (A) and (C)
33. Statement: Many political activists have
decided to stage demonstrations and block traffic
movement in the city during peak hours to protest
against the steep rise in prices of essential
commodities.
Courses of action:
(A) The Govt. should immediately ban all forms
of agitations in the country.
(B) The police authority of the city should deploy
additional forces all over the city to help
traffic movement in the city.
(C) The state administration should carry out
preventive arrests of the known criminals
staying in the city.
(1) Only (A) (2) Only (B)
(3) Only (C) (4) Only (A) and (B)
(5) None of these
34. Statement: The school dropout rate in many
districts in the state has increased sharply during
the last few years as the parents of these children
make them work in the fields owned by others
to earn enough for them to get at least one meal
a day.
Courses of action:
(A) The Govt. should put up a mechanism to
provide foodgrains to the poor people in these
districts through public distribution system
to encourage the parents to send their wards
to school.
(B) The Govt. should close down some of these
schools in the district and deploy the teachers
of these schools to nearby schools and also
ask remaining students to join these schools.
(C) Govt. should issue arrest warrants for all the
parents who force their children to work in
(1) Only (A) (2) Only (B)
(3) Only (C) (4) Only (A) and (B)
(5) None of these
35. Statement: One aspirant was killed due to
stampede while participating in a recruitment
drive of police constables.
Courses of action:
(A) The officials incharge of the recruitment
process should immediately be suspended.
(B) A team of officials should be asked to find
out the circumstances which led to the death
of the aspirant and submit its report within a
week.
(C) The Govt. should ask the home department
to stagger the number of aspirants over more
number of days to avoid such incidents in
future.
(1) Only (A) (2) Only (B)
(3) Only (C) (4) Only (B) and (C)
(5) None of these
36. Effect: Majority of the employees of the ailing
organization opted for voluntary retirement
scheme and left the organization with all their
retirement benefits within a fortnight of
launching the scheme.
Which of the following can be a probable cause
of the above effect ?
(1) The company has been making huge losses
for the past five years and is unable to pay
salaryto its employees in time.
(2) The management of the company made huge
personal gains through unlawful activities.
(3) One of the competitors of the company went
bankrupt last year.
(4) The company owns large tracts of land in the
state which will fetch huge sum to its owners.
(5) None of these
37. Statement: Most of the companies in IT and
ITES sectors in India have started hiring from
engineering college campuses this year and are
likely to recruit much more than yearly
recruitment of the earlier years.
Which of the following substantiates the facts
stated in the above statement ?
(1) IT and ITES are the only sectors in India
which are hiring from engineering college
campuses.
(2) Govt. has stepped up recruitment activities
after a gap of five years.
(3) The IT and ITES companies have now
decided to vi sit the engineering college
campuses for tier II cities in India as well.
(4) Availability of qualified engineers will
substantially in crease in the near future.
(5) None of these
38. Cause: The Govt. has recently increased its taxes
or, petrol and diesel by about 10 percent. Which
of the following can be a possible effect of the
above cause ?
(1) The petroleum companies will reduce the
prices of petrol and diesel by about 10
percent.
(3) The petroleum companies will increase the
prices of petrol and diesel by about 5 percent.
(4) The petrol pumps will stop selling petrol and
diesel till the taxes are rolled back by the govt.
(5) None of these
39. Statement : The Govt. has decided to instruct
the banks to open new branches in such a way
that there is one branch of any of the banks in
every village of population 1000 and above or a
cluster of villages with population less than 1000
to provide banking services to all the citizens.
Which of the following will weaken the step
taken by the Govt. ?
(1) The private sector banks in India have
stepped up their branch expansion activities
in rural India.
(2) Many Govt. owned banks have surplus
manpower in its urban branches.
(3) All the banks including those in private sector
(4) Large number of branches of many Govt.
owned banks in the rural areas are making
huge losses every year due to lack of adequate
(5) None of these
Direction: Study the following information
carefully and answer the questions given below.
The centre reportedly wants to continue
providing subsidy to consumers for cooking gas and
kerosene for five more years. This is not good news
from the point of view of reining in the fiscal deficit.
Mounting subventions for subsidies means diversion
of savings by the government from investment to
consumption, raising the cost of capital in the process.
The government must cut expenditure on subsidies
to create more fiscal space for investments in both
physical and social infrastructure. It should outline a
plan for comprehensive reform in major subsidies
including petroleum, food and fertilizers and set goal
posts.
40. Which of the following is a conclusion which
can be drawn from the facts stated in the above
paragraph ?
(1) Subsidy provided by the government under
various heads to the citizen increases the cost
of capital.
(2) Govt. is unable to withdraw subsidies
provided to various items.
(3) Govt. subsidy on kerosene is purely a
political decision.
(4) Govt. does not have enough resources to
continue providing subsidy on petroleum
products.
(5) None of these
41. Which of the following is an inference which
can be made from the facts stated in the above
paragraph ?
(1) India’s fiscal deficit is negligible in
(omparison to other emerging economies in
the world.
(2) Subsidy on food and fertilizers are essential
for growth of Indian economy.
(3) Reform in financial sector will weaken
India’s position in the international arena.
(4) Gradual withdrawal of subsidy is essential
for effectively managing fiscal deficit in
India.
(5) None of these
42. Which of the following is an assumption which
is implicit in the facts stated in the above
paragraph ?
(1) People in India may not be able to pay more
for petroleum products.
(2) Many people in India are rich enough to buy
petroleum products at market cost.
(3) Govt. may not be able to create more
infrastructural facilities if the present level
of subsidy continues for a longer time.
(4) Govt. of India has sought assistance from
international financial organizations for its
infrastructural projects
(5) None of these
Direcion: Study the following information carefully
and answer the questions given below.
Poverty measurement is an unsettled issue, both
conceptually and methodologically. Since poverty is
a process as well as an outcome; many come out of it
while others may be falling into it. The net effect of
these two parallel processes is a proportion commonly
identified as the ‘head count ratio’, but these ratios
hide the fundamental dynamism that characterizes
poverty in practice. The most recent poverty
reestimates by an expert group has also missed the
crucial dynamism. In a study conducted on 13,000
households which represented the crucial dynamism.
In a study conducted on 13,000 households which
represented the entire country in 1993-94 and again
on 2004-05, it was found that in the ten-year period
18.2% rural population moved out of poverty whereas
another 22.1 % fell into it over this period. This net
increase of about four percentage points was seen to
have a considerable variation across states and
regions.
43. Which of the following is a conclusion which
can be drawn from the facts stated in the above
paragraph ?
(1) Accurate estimates of number of people
living below poverty line in India is possible
(2) Many expert groups in India are not
interested to measure poverty objectively.
(3) Process of poverty measurement needs to
take into account various factors to tackle its
dynamic nature.
(4) People living below poverty line remain in
that position for a very long time.
(5) None of these
44. Which of the following is an assumption which
is implicit in the facts stated in the above
paragraph ?
(1) It may not be possible to have an accurate
poverty measurement in India.
(2) Level of poverty in India is static over the
years.
(3) Researchers avoid making conclusions on
poverty measurement data in India.
(4) Govt. of India has a mechanism to measure
level of poverty effectively and accurately.
(5) None of these
45. Which of the following is an inference which
can be made from the facts stated in the above
paragraph ?
(1) Poverty measurement tools in India are
outdated.
(2) Increase in number of persons falling into
poverty varies considerably across the
country over a period of time.
(3) Govt. of India has stopped measuring poverty
related studies.
(4) People living in rural areas are more
susceptible to fall into poverty over the time.
(5) None of these
Direction: In each of the questions given below
which one of the five answer figures on the right
should come after the problem figures on the left,
if the sequence were continued ?
46. Problem Figure
1 2 3 4 5
47. Problem Figure
1 2 3 4 5
48. Problem Figure
A O T
A
T
T
A
T
A
Z
T A
1 2 3 4 5
49. Problem Figure
A
A
A
A
A K K
K
K K
O OO O OO O
A A
A
A
A K
K K K K O
OO O OO O O
1 2 3 4 5
50. Problem Figure
DD
D
DD Z
Z
Z Z Z
O O
O
O O
D
D
DDD
Z Z Z
Z
Z
O O O
O
O
1 2 3 4 5
DATA ANALYSIS AND INTERPRETATION
Direction: Study the following table carefully to answer the questions that follow
Number (n) of candidates (in lakhs) appearing for an entrance examination From six different states
and the percentage (p) of candidates clearing the same over the years
STATE A B C D E F
YEAR N P N P N P N P N P N P
2004 1.23 42 1.04 51 1.11 32 1.32 24 1.23 36 1.33 31
2005 1.05 43 1.12 62 1.07 47 1.15 49 1.18 55 1.24 24
2006 2.04 38 1.48 32 1.08 28 1.96 35 1.42 49 1.58 26
2007 1.98 41 2.07 43 1.19 30 1.88 46 1.36 47 1.79 29
2008 1.66 53 1.81 50 1.56 42 1.83 60 1.73 57 1.86 34
2009 1.57 39 1.73 36 1.64 52 2.01 56 1.69 55 1.95 37
51. What is the respective ratio of total number of
candidates clearing the entrance exam from State
B in the year 2004 to those clearing the entrance
exam from State C in the same year
(1) 221: 148 (2) 218: 143
(3) 148: 221 (4) 143: 218
(5) None of these
52. In which year did the highest number of candidates
clear the entrance exam from State D ?
(1) 2008 (2) 2006
(3) 2009 (4) 2007
(5) None of these
53. What is the number of candidates not clearing
the entrance exam from State A in the year 2007?
(1) 186820 (2)
.
11682
(3) 1868200 (4) 1.16820
(5) None of these
54. What is the total numberof candidates clearing
the entrance exam from States E and F together
in the year 2006 ?
(1) 16160 (2) 110660
(3) 1.1066 (4) 1106600
(5) None of these
55. What is the average number of candidates
appearing for the entrance exam from State D in
the years 2007, 2008 and 2009 together ?
(1)
2
1.907
3
(2)
1
18666
3
(3)
1
1.866
3
(4)
2
190666
3
(5) None of these
Direction: Study the given information carefully
and answer the questions that follow
An urn contains 6 red, 4 blue, 2 green and 3
yellow marbles.
56. If four marbles are picked at random, what is
the probability that at least one is blue ?
(1)
4
15
(2)
69
91
(3)
11
15
(4)
22
91
(5) None of these
57. If two marbles are picked at random, what is the
probability that both are red ?
(1)
1
6
(2)
1
3
(3)
2
15
(4)
2
5
(5) None of these
58. If three marbles are picked at random, what is
the probability that two are blue and one is
yellow?
(1)
3
91
(2)
1
5
(3)
18
455
(4)
7
15
(5) None of these
59. If four marbles are picked at random, what is
the probability that one is green, two are blue
and one is red ?
(1)
24
455
(2)
13
35
(3)
11
15
(4)
7
91
(5) None of these
60. If two marbles are picked at random, what is the
probability that either both are green or both are
yellow ?
(1)
5
91
(2)
1
35
(3)
1
3
(4)
4
105
(5) None of these
Direction: Study the given pie-charts carefully to
Breakup of number of employees working
in different departments of an organisation,
the, number of males and the number of
employees who recently got promoted in
each department break-up of employees
working in different departments total
number of employees = 3,600 Employees
working in different departments:
Accounts
20%
Production
35%
Marketing
18%
HR
12%
IT
15%
Break-up of number of males in each
department
Total number of males in the organisation
= 2,040
Break-up of number of males working in
each department
A
c
c
t
s
.
5
%
M
a
r
k
e
t
i
n
g
1
5
%
HR 10%
IT 20%
Production
50%
Break-up of number of employees who
recently got promoted in each department
Total number of employees who got
promoted = 1,200
Number of employees who recently got
promoted from each department
A
c
c
o
u
n
t
8
%
Marketing
22%
H
R
1
1
%
IT 26%
Production
33%
61. If half of the number of employees who got
promoted from the IT department were males,
what was the approximate percentage of males
who got promoted from the IT department ?
(1) 61 (2) 29 (3) 54
(4) 42 (5) 38
62. What is the total number of females working in
the Production and Marketing departments
together ?
(1) 468 (2) 812 (3) 582
(4) 972 (5) None of these
63. How many females work in the Accounts
department ?
(1) 618 (2) 592 (3) 566
(4) 624 (5) None of these
64. The total number of employees who got
promoted from all the departments together was
what percent of the total number of employees
working in all the departments together ?
(Rounded off to the nearest integer)
(1) 56 (2) 21 (3) 45
(4) 33 (5) 51
65. The number of employees who got promoted
from the HR department was what percent of
the total number of employees working in that
department ? (rounded off to two digits after
decimal)
(1) 36.18 (2) 30.56 (3) 47.22
(4) 28.16 (5) None of these
Direction: Study the graph carefully to answer the
questions that follow
Percent rise in profit of two companies over the years
40
35
30
25
20
15
10
5
0
P
r
o
f
i
t
P
e
r
c
e
n
t
2004 2005 2006 2007 2008 2009
Company L Company M
66. If the profit earned by Company L in the year
2005 was Rs. 1.84 lakhs, what was the profit
earned by the company in the year 2006 ?
(1) Rs. 2.12 lakhs (2) Rs. 2.3 lakhs
(3) Rs. 2.04 lakhs
(4) Cannot be determined
(5) None of these
67. If the profit earned by Company M in the year
2008 was Rs. 3.63 lakhs, what was he amount
of profit earned by it in the year 2006 ?
(1) Rs. 2.16 lakhs (2) Rs.1.98 lakhs
(3) Rs. 2.42 lakhs
(4) Cannot be determined
(5) None of these
68. What is the average percent rise in profit of
Company L over all the years together ?
(1)
1
15
3
(2)
1
25
3
(3)
5
18
6
(4)
5
21
6
(5) None of these
69. Which of the following statements is TRUE with
respect to the above graph ?
(1) Company M made the highest profit in the
year 2009
(2) Company L made least profit in the year 2005
(3) The respective ratio between the profits
earned by Company L and M In the year 2006
was 6:5
(4) Company L made the highest profit in the
year 2008
(5) All are true
70. What is the percentage increase in percent rise
in profit of Company M in the year 2009 from
the previour year ?
(1) 25 (2) 15 (3) 50
(4) 75 (5) None of these
Direction: Study th a information carefully to
A school consisting of a total of 1560 students
has boys and girls in the ratio of 7:5 respectively. All
the students are enrolled in different types of hobby
classes, viz: Singing, Dancing and Painting. One-fifth
of the boys are enrolled in only Dancing classes.
Twenty percent of the girls are enrolled in only
Painting classes. Ten percent of the boys are enrolled
in only Singing classes. Twenty four percent of the
girls are enrolled in both Singing and Dancing classes
together. The number of girls enrolled in only Singing
classes is two hundred percent of the boys enrolled
in the same. One-thirteenth of the boys are enrolled
in all the three classes together. The respective ratio
of boys enrolled in Dancing and Painting classes
together to the girls enrolled in the same is 2 :1
respectively. Ten percent of the girls are enrolled in
only Dancing classes whereas eight percent of the girls
are enrolled in both Dancing and Painting classes
together. The remaining girls are enrolled in all the
three classes together. The number of boys enrolled
in Singing and Dancing classes together is fifty
percent of the number of girls enrolled in the same.
The remaining boys are enrolled in only Painting
classes.
71. What is the total number of boys who are
enrolled in Dancing ?
(1) 318 (2) 364
(3) 292 (4) 434
(5) None of these
72. Total number of girls enrolled in Singing is
approximately what percent of the total number
of students in the school ?
(1) 37 (2) 19
(3) 32 (4) 14
(5) 26
73. What is the total number of students enrolled in
all the three classes together ?
(1) 135 (2) 164
(3) 187 (4) 142
(5) None of these
74. Number of girls enrolled in only Dancing classes
is what percent of the boys enrolled in the same?
(rounded off to two digits after decimal)
(1) 38.67 (2) 35.71
(3) 41.83 (4) 28.62
(5) None of these
75. What is the respective ratio of the number of
girls enrolled in only Painting classes to the
number of boys enrolled in the same ?
(1) 77 : 26 (2) 21 : 73
(3) 26 : 77 (4) 73 : 21
(5) None of these
76. What is the respective ratio between the profit
earned by shopkeeper U in the months
February-2010 and March - 2010 together to that
earned by shopkeeper Q in the same months ?
(1) 637: 512 (2) 621 : 508
(3) 512: 637 (4) 508: 621
(5) None of these
77. What is the percent increase in profit of
shopkeeper S in the month of December - 2009
over the previous month ? (rounded off to two
digits after decimal)
(1) 3.15 (2) 2.67
(3) 2.18 (4) 3.33
(5) None of these
78. Which shopkeeper’s profit kept increasing
continuously over the given months ?
(1) R (2) Q (3) T
(4) U (5) None of these
79. What is the difference in profit earned by
shopkeeper T in January - 2010 from the
previous month ?
(1) Rs. 640/- (2) Rs. 420/-
(3) Rs. 380/- (4) Rs. 760/-
(5) None of these
80. What was the average profit earned by
shopkeeper R in the months of October – 2009
and November – 2009 together ?
(1) 5405 (2) 5040 (3) 4825
(4) 4950 (5) None of these
Direction: Study the given graph carefully to answer
the questions that follow
Number of days taken by three carpenters to
finish making one piece each of four different
items of furniture
16
14
12
10
8
6
4
2
0
Chair Table Bed Cupboard
Company X Company Y Company Z
81. If Carpenter X and Carpenter Y were to make a
chair together how many days would they take?
(1) 1 day (2) 4 days (3) 3 days
(4) 2 days (5) None of these
82. If Carpenters X, Y and Z were to make a table
together how many days would they take ?
(1) 4 days (2) 3 days (3) 1 day
(4) 2 days (5) None of these
83. What is the total number of days that Carpenter
Z will take to make one piece each of all the
four items together ?
(1) 32 days (2) 24 days
(3)
1
1
59
days (4)
1
1
32
days
(5) None of these
Direction: Study the table carefully to answer the questions that follow.
Profit (in rs. ‘000) made by six different shopkeepers over the months
Month October November December January February March
Shopkeeper 2009 2009 2009 2010 2010 2010
P 5.25 6.04 5.84 6.10 5.95 6.02
Q 4.84 4.28 4.97 4.88 5.04 5.12
R 4.99 5.82 5.48 5.45 5.68 5.36
S 5.06 5.11 5.28 5.38 5.44 5.59
T 5.28 4.96 5.31 5.69 4.93 5.72
U 5.94 6.23 5.87 6.07 6.19 6.23
84. The radius of a circular field is equal to the side
of a square field whose perimeter is 784 feet.
What is the area of the circular field ?
(1) 107914 Sq.ft (2) 120736 Sq.ft.
(3) 107362 Sq.ft. (4) 127306 Sq.ft.
(5) None of these
85. In how many different ways can the letters of
the word ‘STRESS’ be arranged
(1) 360 (2) 240
(3) 720
(4) 120
(5) None of these
86. Total number of people staying in locality J forms
approximately what percent of the total number
of people staying in locality F ?
(1) 81 (2) 72 (3) 78
(4) 93 (5) 87
87. What is the total number of children staying in
localities H and I together ?
(1) 1287 (2) 1278 (3) 1827
(4) 1728 (5) None of these
88. The number of women staying in which locality
is the highest ?
(1) H (2) J (3) F
(4) G (5) None of these
89. What is the total number of men and children
staying in locality I together
(1) 4115 (2) 4551 (3) 4515
(4) 4155 (5) None of these
90. What is the respective ratio of number of men
staying in locality F to the number of men staying
in locality H ?
(1) 517: 416 (2) 403: 522
(3) 416: 517 (4) 522: 403
(5) None of these
91. The compound interest earned by Suresh on a
certain amount at the end of two years at the rate
of 8 p.c.p.a was Rs. 1,414.4. What was the total
Direction: Study the given table carefully to answer the questions that follow
Number of people staying in five different localities and the percentage breakup of men, women and
children in them
LOCALITY TOTAL NO. PERCENTAGE
OF PEOPLE MEN WOMEN CHILDREN
F 5640 55 35 10
G 4850 34 44 22
H 5200 48 39 13
I 6020 65 25 10
J 4900 42 41 17
amount that Suresh got back at the end of two
years in the form of principal plus interest
earned?
(1) Rs. 9,414.4 (2) Rs. 9,914.4
(3) Rs. 9,014.4 (4) Rs. 8,914.4
(5) None of these
92. The respective ratio of the present ages of a
mother and daughter is 7 : 1. Four years ago the
respective ratio of their ages was 19:1. What will
be the mother’s age four years from now ?
(1) 42 years (2) 38 years
(3) 46 years (4) 36 years
(5) None of these
93. Three friends J, K and Ljog around a circular
stadium and complete one round in 12, 18 and
20 seconds respectively. In how many minutes
will all the three meet again at the starting point
(1) 5 (2) 8 (3) 12
(4) 3 (5) None of these
94. 4 men can complete a piece of work in 2 days. 4
women can complete the same piece of work in
4 days whereas 5 children can complete the same
piece of work in 4 days. If, 2 men, 4 women
anW 10 children work together, in how many
days can the work be completed ?
(1) 1 day (2) 3 days (3) 2 days
(4) 4 days (5) None of these
95. The speed of a boat when travelling downstream
is 32 Kms. / Hr. , whereas when travelling
upstream it is 28 kms/hr. What is the speed of
the boat in still water ?
(1) 27 Kms./Hr. (2) 29 Kms./ Hr.
(3) 31 Kms./ Hr.
(4) Cannot be determined
(5) None of these
Direction: Study the following tables carefully and
Number of Candidates appeared in a
CompetitiveExamination from five centres over
the years
NUMBER
Center Mumbai Delhi Kolkata Hydera Chennai
2001 35145 65139 45192 51124 37346
2002 17264 58248 52314 50248 48932
2003 24800 63309 56469 52368 51406
2004 28316 70316 71253 54196 52315
2005 36503 69294 69632 58350 55492
2006 29129 59216 64178 48230 57365
2007 32438 61345 563041 49178 58492
Approximate-Percentages of candidatesqualified
to appeared in the
-
Competitiveexamination from
five centres over the years
PERCENTAGE
12 24 18 17 9
10 28 12 21 12
15 21 23 25 10
11 27 19 24 8
13 23 16 23 13
14 20 21 19 11
16 19 24 20 14
96. In which of the following years was the
difference in number of candidates appeared
from Mumbai over the previous year the
minimum ?
(1) 2004 (2) 2006 (3) 2007
(4) 2002 (5) None of these
97. In which of the following years was the number
of candidates qualified from Chennai, the
maximum among the given years ?
(1) 2007 (2) 2006 (3) 2005
(4) 2003 (5) None of these
98. Approximately what was the total number of
candidates qualified from Delhi in 2002 and
2006 together ?
(1) 27250 (2) 25230 (3) 30150
(4) 28150 (5) 26250
99. Approximately how many candidates appearing
from Kolkata in 2004 qualified in the
competitive examination ?
(1) 13230 (2) 13540 (3) 15130
(4) 15400 (5) 19240
100.Approximately what was the difference between
the number of candidates qualified from
Hyderabad in 2001 and 2002 ?
(1) 1680 (2) 2440 (3) 1450
(4) 2060 (5) 1860
GENERAL AWARENESS /
MARKETING / COMPUTERS
101. What is the full form of ‘NBFC’ as used in the
Fir ancial Sector ?
(1) New Banking Finance Company
(2) National Banking & Finance Corporation
(3) New Business Finance & Credit
(5) None of these
102.100% concession has been given for travelling
in the Indian Railways for patients of ...
(1) AIDS (2) Cancer (3) Swine Flu
(4) T. B. (5) None of these
Right (SDR) in newspapers. As per its definition,
SDR is a monetary unit of the reserve assets of
which of the following organizations / agencies?
(1) World Bank
(2) International Monetary Fund (IMF)
(3) Asian Development Bank
(4) Reserve Bank of India
(5) None of these
104.Which of the following is/are the highlights of
the Union Budget 2010-11 ?
(A) Number of new steps taken to simplify the
Foreign Direct Investment (FDI) regime.
(B) Rs. 16,500 crore provided to ensure that the
Public Sector Banks are able to attain a
minimum 8% capital (Tier I) by March 2011.
(C) More than Rs. 1,74,000 crore provided for
the development of the infrastructure in the
country.
(1) Only A (2) Only B
(3) Only C (4) All A, B & C
(5) None of these
105.In how many Routes special tourist trains called
‘Bharat Tirth’ is to start?
(1) 19 (2) 16 (3) 17
(4) 18 (5) None of these
106.As per the newspaper reports, the Govt. of India
made an auction of the Third Generation
Spectrum (3G) recently. Which of the following
ministries was actively involved in the process a
(1) Ministry of Heavy Industries
(2) Ministry of Science & Technology
(3) Ministry of Commerce
(4) Ministry of Foreign Affairs
(5) None of these
107.As per the recent announcement, the Govt. of
India will provide an amount of Rs.48,000 crore
to develop Rural Infrastructure in the country.
This planned development is being undertaken
under which of the following schemes ?
(1) Bharat Nirman
(2) Indira Aawas Yojana
(3) Backward Region Grant Fund
(4) Drought Mitigation Fund
(5) None of these
108.Ladies special trains to be renamed with the
Name of ...
(1) Bharat Bhoomi Specials
(2) Sonia Gandhi Specials
(3) Matri Bhoomi Specials
(4) Rajiv Gandhi Specials
(5) None of these
109.How much funds has been allocated to the
Unique Identification Authority of India?
(1) Rs 1,500 Crore (2) Rs 1,900 Crore
(3) Rs 1,600 Crore (4) Rs 1,800 Crore
(5) None of these
110. What is the rate of Income Tax for incomesz
above Rs 1.6 lakh upto Rs 5 lakh?
(1) 10% (2) 12% (3) 15%
(4) 20% (5) None of these
111. Recently, India took part in “Nuclear New Build
2010 Conference” organized in -
(1) New Delhi (2) London
(3) Paris (4) Hong Kong
(5) None of these
112. What is the reduction in Service Charges on e-
tickets?
(1) Sleeper Class Rs. 20 & AC Class Rs. 10
(2) Sleeper Class Rs. 10 & AC Class Rs. 20
(3) Sleeper Class Rs. 30 & AC Class Rs. 20
(4) Sleeper Class Rs. 20 & AC Class Rs. 30
(5) None of these
113. As we know, with the launch of Nano by Tatas,
India has become favourite Small Car
Destination of the world. Other than India, which
of the following countries is also a popular
destination of small cars ?
(1) Britain (2) France
(3) Germany (4) Thailand
(5) None of these
114. Imports from China in the Year of 2008-09 in
Rs...
(1) 100,000 Crore (2) 140,000 Crore
(3) 147,605 Crore (4) 151,000 Crore
(5) None of these
115. How many new teams have been added in IPL
2010?
(1) 2 (2) 1 (3) 4
(4) 7 (5) None of these
116.Which countries have recently faced Tsunami
Waves?
(1) Japan & Chile (2) Sallie & Korea
(3) China & Thailand (4) Japan & China
(5) None of these
117. North Korea and USA decided to resume their
peace talks after a gap of several months. Both
the countries have a dispute over which of the
following issues ?
(1) Bailout package offered by USA
(2) Membership of ASEAN to North Korea
(3) Nuclear programme of North Korea
(4) Soaring relations of China with North Korea
(5) None of these
118. Who amongst the following was the Chairperson
of the 13th Finance Commission which
submitted its report to the President of India
recently ?
(1) Mr. M. V. Kamath (2) Dr. C. Rangarajan
(3) Dr. D. Subbarao (4) Dr. Rakesh Mohan
(5) Dr. Vijay Kelkar
119.As per the news published in various
newspapers, the RBI is considering the grant of
licence to some new companies, particularly
NBFCs to act as full-fledged banks. Which of
the following will be considered NBFC ?
(1) NABARD
(2) Life Insurance Corporation of India
(3) Reliance Capital
(4) SEBI
(5) None of these
120.Who has scored the highest individual ODI
Score?
(1) Saeed Anwar (Pak)
(2) Charls Coventry (Zim)
(3) Sachin Tendulkar (IND)
(5) Ricky Pointing (Aus)
(5) None of these
121. What is an ‘intranet’
(1) Internal internet used to transfer information
internally
(2) Internal internet used to transfer information
to the outside company
(3) Internal network designed to serve the
internal informational needs of a single
organization
(4) Internal network designed to transfer the
information between two organizations
(5) None of these
122.Which of the following groups of cricket teams
was declared joint winner of the Col. C K Naidu
Trophy for 2009 ?
(2) Maharashtra & Kerala
(3) Punjab & Delhi
(4) West Bengal & Maharashtra
(5) None of these
123. Kaiane Aldorino who was crowned Miss World
2009 is from which of the following countries?
(1) Germany (2) Russia
(3) Austria (4) Belgium
(5) Gibraltar
124. Which of the following teams won the Davis Cup
Tennis Finals 2009 ?
(1) Germany (2) Spain
(3) Russia (4) France
(5) None of these
125. Who amongst the following is the recipient of
the “CNN-IBN Indian of the Year” Award for
2009?
(1) Ratan Tata (2) A.R.Rahman
(3) Manmohan Singh (4) Sachin Tendulkar
(5) None of these
126. The deficit reduction plan of which of the
following countries was reviewed recently in the
meeting of the Finance Ministers of the European
Union ?
(1) Germany (2) Romania
(3) Brazil (4) Hungary
(5) Greece
127. The database administrator’s function in an
organization is —
(1) To be responsible for the more technical
aspects of managing the information
contained in organizational databases
(2) To be responsible for the executive level
aspects of decisions regarding the
information management
(3) To show the relationship among entity classes
in a data warehouse
(4) To define which data mining tools must be
used to extract data
(5) None of these
128.Every device on the Internet has a unique______
identifies it in the same way that a street address
identifies the location of a house.
(1) DH (2) DA (3) IP
(4) IA (5) None of these
129. To send another station a message, the main thing
a user has to know is
(1) how the network works
(3) whether the network is packet-switched or
circuit-switched
(4) whether this is a voice or data network
(5) None of these
130. In a client/ server model, a client orogram -
(2) provides information and files
(3) serves software files to other computers
(4) distributes data files to other computers
(5) None of these
131. Control in design of an information system is
used to —
(1) inspect the system and check that it is buiit
as per specifications
(2) ensure that the system processes data as it
was designed to and that the results are
reliable
(3) ensure privacy of data processed by it
(4) protect data from accidental or intentional
loss
(5) None of these
132. Each of the following is a true statement
except—
(1) on-line systems continually update the master
file
(2) in on-line processing, the user enters
transactions into a device that is directly
connected to the computer system
(3) batch processing is still used today in older
systems or in some systems with massive
volumes of transactions
(4) information in batch systems will always be
up-to-date”
(5) None of these
133.A set of interrelated components that collect,
process, store, and distribute information to
support decision making and control in an
organization best defines -
(1) communications technology
(2) a network
(3) an information system
(4) hardware
(5) None of these
134.Ais a computer connected to two networks.
(3) gateway (4) bridge way
(5) None of these
135. When you save a presentation,
(1) all slides in a presentation are saved in the
same file
(2) two files are created; one for graphics and
one for content
(3) a file is created for each slide
(4) a file is created for each animation or graphic
(5) None of these
136.In a customer database, a customer’s surname
would be keyed into a —
(1) row (2) text field
(3) record (4) computed field
(5) None of these
137. Who is the new Prime Minister of Hungry ?
(1) Victor Orban (2) Gorden Bajnai
(3) Jeno Fock (4) Ference Gyurcsany
(5) None of these
138. Storing same data in many places is called
(1) iteration (2) concurrency
(3) redundancy (4) enumeration
(5) None of these
139.Which of the following is the first step in the
‘transaction processing cycle’, which captures
business data through various modes such as
optical scanning or at an electronic commerce
website ?
(1) Document and report generation
(2) Database maintenance
(3) Transaction processing
(4) Data Entry
(5) None of these
140.CRM (Customer Relationship Management)
is—
(1) Apre-sales activity
(2) A tool for lead generation
(3) An ongoing daily activity
(4) The task of a DSA
(5) All of the above
141. Who is the new prime minister of Denmark ?
(1) Anders Fogh Rasmussen
(2) Lars Looke Rasmussen
(3) Poul Nyrup Rasmussen
(4) Poul Hartling
(5) None of these
142. Who is the Author of the book “My China Diary”
(1) Kanwal Sibal (2) Salman Haider
(3) J.N. Dixit (4) Natwar Singh
(5) None of these
143.One of the following is not involved in the
Growth Strategies of a Company -
(1) Horizontal integration
(2) Vertical integration
(3) Diversification
(4) Intensification (5) None of these
144.A successful “Blue Ocean Strategy” requires -
(1) Effective communication
(2) Innovative skills
(3) Motivation
(4) All of the above (5) None of these
145.Programs from the same developer , sold
bundled together , that provide better integration
and share common features , toolbars and menus
are known as ....
(1) software suites
(2) integrated software packages
(3) software processing packages
(4) personal information managers
(5) none of these
146.A data warehouse is which of the following ?
(1) Can be updated by the end users
(2) Contains numerous naming conventions and
formats
(3) Organized around important subject areas
(4) Contains only current data
(5) None of these
147.__________ servers store and manages files for
network users.
(1) Authentication (2) Main
(3) Web (4) File
(5) None of these
148.One of the following is not included in the 7 P’s
of Marketing. Find the same
(1) Product (2) Price
(3) Production (4) Promotion
(5) None of these
149. The target group for SME loans is -
(1) All Businessmen (2) All Professionals
(3) All SSIs (4) All of the above
(5) None of these
150. Home Loans can be best canvassed among -
(1) Builders (2) Flat owners
(3) Land developers (4) Agriculturists
(5) Individuals wanting to buy a flat or house
ENGLISH LANGUAGE
Direction: Read the following passage carefully and
answer the questions given below it. Certain words/
them while answering some of the questions.
economic progress with steel mills and cement
factories. While urban centers thrive and city dwellers
get rich, hundreds of millions of farmers remain mired
in poverty. However, fears of food shortages, a
rethinking of antipoverty priorities and the crushing
recession in 2008 are causing a dramatic shift in world
economic policy in favour of greater support for
agriculture.
The last time when the world’s farmers felt such
love was in the 1970s. At that time, as food prices
spiked, there was real concern that the world was
facing a crisis in which the planet was simply unable
to produce enough grain and meat for an expanding
population. Governments across the developing world
and international aid organisations plowed investment
into agriculture in the early 1970s, while technological
breakthroughs, like high-yield strains of important
food crops, boosted production. The result was the
Green Revolution and food production exploded.
But the Green Revolution became a victim of
its own success. Food prices plunged by some 60%
by the late 1980s from their peak in the mid- 1970s.
Policymakers and aid workers turned their attention
to the poor’s other pressing needs, such as health care
and education. Farming got starved of resources and
investment. By 2004, aid directed at agriculture sank
to 3.5% and “Agriculture lost its glitter.” Also, as
consumers in high-growth giants such as China and
India became wealthier, they began eating more meat,
so grain once used for human consumption got
diverted to beef up livestock. By early 2008, panicked
buying by importing countries and restrictions slapped
on grain exports by some big producers helped drive
prices upto heights not seen for three decades. Making
matters worse, land and resources got reallocated to
produce cash crops such as biofuels and the result was
that voluminous reserves of grain evaporated. Protests
broke out across the emerging world and fierce food
riots toppled governments.
This spurred global leaders into action. This
made them aware that food security is one of the
fundamental issues in the world that has to be dealt
with in order to maintain administrative and political
stability. This also spurred the U.S. which traditionally
provisioned food aid from American grain surpluses
to help needy nations, to move towards investing in
farm sectors around the globe to boost productivity.
This move helped countries become more productive
for themselves and be in a better position to feed their
own people.
Africa, which missed out on the first Green
Revolution due to poor policy and limited resources,
also witnessed a ‘change’. Swayed by the success of
East Asia, the primary poverty-fighting method
favoured by many policymakers in Africa was to get
farmers off their farms and into modern jobs in
factories and urban centers. But that strategy proved
to be highly insufficient. Income levels in the
countryside badly trailed those in cities while the FAO
estimated that the number of poor going hungry in
2009 reached an all time high at more than one billion.
In India on the other hand, with only 40% of its
farmland irrigated, entire economic boom currently
underway is held hostage by the unpredictable
monsoon. With much of India’s farming areas
suffering from drought this year, the government will
have a tough time meeting its economic growth
targets. In a report, Goldman Sachs predicted that if
this year too receives weak rains, it could cause
agriculture to contract by 2% this fiscal year, making
the government’s 7% GDP-growth target look “a bit
rich”. Another green revolution is the need of the hour
and to make it a reality, the global community still
has much backbreaking farm work to do.
151. What is the author’s main objective in writing
the passage
(1) Criticising developed countries for not
bolstering economic growth in poor nations
(2) Analysing the disadvantages of the Green
Revolution
(3) Persuading experts that a strong economy
depends on industrialization and not
agriculture
(4) Making a case for the international society
to engineer a second Green Revolution
(5) Rationalising the faulty agriculture policies
of emerging countries
152.Which of the following is an adverse impact of
the Green Revolution ?
(1) Unchecked crop yields resulted in large tracts
of land becoming barren
(2) Withdrawal of fiscal impetus from agriculture
to other sectors
(3) Farmers began soliciting government
subsidies for their produce
(4) Farmers rioted as food prices fell so low that
they could not make ends meet
(5) None of these
153.What is the author trying to convey through the
phrase “making the government’s 7% GDP
growth target look “a bit rich” ?
(1) India is unlikely to achieve the targeted
growth rate
(2) Allocation of funds to agriculture has raised
India’s chances of having a high GDP
(3) Agricultural growth has artificially inflated
India’s GDP and such growth is not real
(4) India is likely to rave one of the highest GDP
growth rates
(5) A large portion of India’s GDP is contributed
by agriculture
154.Which of the following factors was/were
responsible for the neglect of the farming sector
after the green revolution ?
(A) Steel and cement sectors generated more
revenue for the government as compared to
agriculture.
(B) Large scale protests against favouring
agriculture at the cost of other important
sectors such as education and healthcare.
(C) Attention of policy makers and aid
organizations was diverted from agriculture
to other sectors.
(1) None (2) Only (C)
(3) Only (B) & (C) (4) Only (A) 8s (B)
(5) All (A), (B) & (C)
155.What prompted leaders throughout the world to
take action to boost the agriculture sector in
2008?
(1) Coercive tactics by the U.S. which restricted
food aid to poor nations
(2) The realization of the link between food
security and political stability
(3) Awareness that performance in agriculture is
necessary in order to achieve the targeted
GDP
(4) Reports that high-growth countries like China
and India were boosting their agriculture
sectors to capture the international markets
(5) Their desire to influence developing nations
to slow down their industrial development.
156.What motivated the U.S. to focus on investing
in agriculture across the globe ?
(1) To make developing countries become more
reliant on U.S. aid
(2) To ensure grain surpluses so that the U.S. had
no need to import food
(3) To make those countries more self sufficient
to whom it previously provided food
(4) To establish itself in the market before the
high-growth giants such as India and China
could establish themselves
(5) None of these
157. What impact did the economic recession of 2008
have on agriculture ?
(1) Governments equated economic stability
with industrial development and shifted away
from agriculture
(2) Lack of implementation of several innovative
agriculture programmes owing to shortage of
funds
(3) It prompted increased investment and interest
in agriculture
(4) The GDP as targeted by India was never
achieved because of losses in agriculture
(5) None of these
158. What encouraged African policymakers to focus
on urban jobs ?
(1) Misapprehension that it would alleviate
poverty as it did in other countries
(2) Rural development outstripped urban
development in many parts of Africa
(3) Breaking out of protests in the country and
the fear that the government would topple
(4) Blind imitation of western models of
development
(5) None of these
159.Which of the following had contributed to
exorbitant food prices in 2008 ?
(A) Hoarding of food stocks by local wholesalers
which inadvertently created a food shortage.
(B) Export of foodgrains was reduced by large
producers.
(C) Diverting resources from cultivation of
foodgrains to that of more profitable crops.
(1) None (2) Only (C)
(3) Only (B) (4) All (A), (B) & (C)
(5) Only (B) & (C)
160.Which of the following is true about the state of
agriculture in India at present ?
(A) Of all the sectors, agriculture needs the
highest allocation of funds.
(B) Contribution of agriculture to India’s GDP
this year would depend greatly upon the
monsoon rains.
(C) As India is one of the high-growth countries,
it has s jrplus food reserves to export to other
nations.
(1) Only (A) and (C) (2) Only (C)
(3) Only (B) (4) Only (B) and (C)
(5) None of these
Direction: Choose the word/group of words which
is most similar it meaning to the word printed in
bold as used in the passage.
161. STARVED
(3) Hungry (4) Fasting
(5) Emaciated
162. SLAPPED
(1) Beaten (2) Imposed
(3) Withdrawn (4) Avoided
163. PLOWED
(1) Cultivated (2) Bulldozed
(3) Recovered (4) Instilled
(5) Withdrew
Direction: Choose the word/phrase which is most
opposite in meaning to the word printed in bold as
used in the passage.
164. PRESSING
(1) Unpopular (2) Undemanding
(3) Unobtrusive (4) Unsuitable
(5) Unimportant
165. EVAPORATED
(1) Absorbed (2) Accelerated
(3) Grew (4) Plunged
(5) Mismanaged
Direction: Which of the phrases (1), (2),(3) and (4)
given below each statement should be placed in the
blank space provided so as to make a meaningful
and grammatically correct sentence ? If none of
the sentences is appropriate, mark (5) i.e. ‘None of
166.Refuting the rationale behind frequent agitations
for formation of separate States, a recent report
(1) proved that such agitations result in loss of
governmental property
(2) indicated that the formation of small states
does not necessarily improve the economy
(3) suggested that only large scale agitations have
been effective in bringing out desired change
in the past
(4) recommended dividing large States into
smaller ones to improve governance
(5) None of these
167. Overlooking the fact that water scarcity
intensifies during summer,
(1) the government issued guidelines to all
builders to limit their consumption to
acceptable limits
(2) provision for rainwater harvesting has been
made to aid irrigation in drought prone areas
(3) the water table did not improve even after
receiving normal monsoon in the current year
(4) many residential areas continue to use
swimming pools, wasting large quantities of
water
(5) None of these
168.He has lost most of his life’s earning in the stock
market but
(1) He still seems to be leading his life
luxuriously and extravagantly
(2) he could not save enough to repay his
enormous debts
(3) stock market is not a safe option to invest
money unless done with caution
(4) experts have been suggesting to avoid
investments in stock market because of its
unpredictable nature
(5) None of these
169.Achieving equality for women is not only a
laudable goal,
(1) political reforms are also neglected
preventing women from entering legislatures
and positions of power
(2) the problem is also deep rooted in the society
and supported by it
(3) their empowerment is purposefully hampered
by people with vested interests in all sections
of the society
(4) it is also equally difficult to achieve and
maintain for a long term
(5) None of these
170. _______or else they would not keep electing him
year after year.
(1) The party leader gave a strong message to
the mayor for improving his political style
(2) Owing to numerous scandals against the
mayor, he was told to resign from the post
immed iately
(3) The mayor threatened the residents against
filing a complaint against him
(4) The residents must really be impressed with
the political style of their mayor
(5) None of these
Direction: Each question below has two blanks,
each blank indicating that something has been
omitted. Choose the set of words for each blank that
best fits the meaning of the sentence as a whole.
171. Drawing attention to the pitfalls of______solely
on Uranium as a fuel for nuclear reactors, Indian
scientists warned that Uranium will not last for
long and thus research on Thorium as its____
must be revived.
(1) using, substitute
(2) believing, replacement
(3) depending, reserve
(4) reckoning, option
(5) relying, alternative
172. In an effort to provide ______ for higher
education to all, most of the universities have
infrastructure, thus churning out ______
(1) chances, fresh
(2) platform, capable
(3) opportunities, unemployable
(4) prospects, eligible
(5) policy, incompetent
173.The move to allow dumping of mercury _____
an outcry from residents of the area who _____
that high levels of mercury will affect their health
and destroy ecologically sensitive forest area.
(1) resulted, insist
(2) provoked, fear
(3) incited, determined
(4) activated, accept
(5) angered, believe
174. _______ has been taken against some wholesale
drug dealers for dealing in surgical items without
a valid license and maintaining a stock of _____
drugs.
(1) Note, overwhelming
(2) Step, impressive
(3) Execution, outdated
(4) Action, expired
(5) Lawsuit, invalid
175. Even as the _____ else where in the world are
struggling to come out of recession, Indian
consumers are splurging on consumer goods and
to _____ this growth, companies are investing
heavily in various sectors.
(1) economies, meet
(2) countries, inhibit
(3) governments, measure
(4) nations, inflict
(5) companies, counter
Direction:Rearrange the following sentences (A),
(B), (C), (D), (E) and (F) to make a meaningful
paragraph and then answer the questions which
follow
(A) While these disadvantages of bio fuels are
serious, they are the only alternate energy source
of the future and the sooner we find solutions to
these problems the faster we will be able to solve
the problems wo are now facing with gasoline.
(B) This fuel can also help to stimulate jobs locally
since they are also much safer to handle thaw”
gasoline and can thus have the potential to
turnaround a global economy.
(C) These include dependence on fossil fuels for the
machinery required to produce biofuel which
ends up polluting as much as the burning of fossil
fuels on roads and exorbitant cost of biofuels
which makes it very difficult for the common
man to switch to this option.
(D) This turnaround can potentially help to bring
world peace and end the need to depend on
foreign countries for energy requirements.
(E) Biofuels are made from plant sources and since
these sources are available in abundance and can
be reproduced on a massive scale they form an
energy source that is potentially unlimited.
(F) However everything is not as green with the
biofuels as it seems as there are numerous
176. Which of the following sentence should be the
FIFTH after rearrangement ?
(1) A (2) B (3) C
(4) E (5) F
177. Which of the following sentence should be the
THIRD after rearrangement ?
(1) A (2) B (3) C
(4) D (5) E
178. Which of the following sentence should be the
FIRST after rearrangement ?
(1) A (2) B (3) C
(4) D (5) E
179. Which of the following sentence should be the
SIXTH (LAST) after rearrangement ?
(1) A (2) C (3) D
(4) E (5) F
180. Which of the following sentence should be the
SECOND after rearrangement ?
(1) A (2) B (3) D
(4) E (5) F
Direction: Which of the phrases (1), (2), (3) and
(4) given below each statement should replace the
phrase printed in bold in the sentence to make it
grammatically correct ? If the sentence is correct
as it is given and ‘No correction is required’, mark
181. Soon after the Tsunami had killed thousands of
people along the coasts of southern India,
parliament psssas a bill that proposed to set up
an institutional mechanism to respond promptly
to natural disasters.
(1) passed a bill that proposed
(2) passes a bill with purpose
(3) pass a bill proposing
(4) passed a bill which propose
(5) No correction required
182. Denial of wages forced scientists and teachers
at the agriculture universities throughout the
country to go on strike, crippling crucial
research that could help the state of agriculture
in the country.
(1) from going on strike
(2) which went on strike
(3) on going for a strike
(4) for going to strike
(5) No correction required
183. In an attempt to boost their profits many edible
oil producing companies have been engaging
themselves in propaganda against commonly
used oils and. promoting exotic and expensive
varieties of oils as more healthier options.
(1) as most healthiest options
(2) as less healthy option
(3) as a healthier option
(4) as much healthiest option
(5) No correction required
184. Thanks to numerous government initiatives, rural
masses which was earlier unaware of the
luxuries of urban ways of living are now
connected to the same lifestyle.
(1) who was earlier unaware
(2) which were earlier aware
(3) who were earlier conversant
(4) who were earlier unaware
(5) No correction required
185. Over the last few months, while most industries
are busy in restructuring operations, cutting costs
and firing, the Indian pharmaceutical and
healthcare industry was adding manpower and
giving salary hikes.
(1) as many industries are
(2) while most industries were
(3) while many industries is
(4) where many industries were
(5) No correction required
Direction: In the following passage there are blanks,
each of which ]’as been numbered. These numbers
are printed below the passage and against each, five
words/phrases are suggested, one of which fits the
blank appropriately. Find out the appropriate word/
phrase in each case.
There is a considerable amount of research about
the factors that make a company innovate. So is it
possible to create an environment (186 ) to
innovation? This is a particularly pertinent (187) for
India today. Massive problems in health, education
etc. (188) be solved using a conventional approach
but (189) creative and innovative solutions that can
ensure radical change and (190). There are several
factors in India’s (191). Few countries have the rich
diversity that India or its large, young population
(192). While these (193) innovation policy
interventions certain additional steps are also required.
These include (194) investment in research and
development by (195) the government and the private
sector, easy transfer of technology from the academic
world etc. To fulfill its promise of beng prosperous
and to be at the forefront, India must be innovative.
186. (1) stimuli (2) conducive
(3) incentive (4) facilitated
(5) impetus
187. (1) objective (2) controversy
(3) doubt (4) question
(5) inference
188. (1) cannot (2) possibly
(3) should (4) never
(5) must
189. (1) necessary (2) apply
(3) need (4) consider
(5) requires
(3) increase (4) chaos
(5) growth
191. (1) challenges (2) praises
(3) favour (4) leverage
(5) esteem
192. (1) blessed (2) enjoys
(3) endows (4) prevails
(5) occurs
193. (1) aid . (2) jeopardise
(3) promotes (4) endure
(5) cater
194. (1) acute (2) utilising
(3) restricting (4) inspiring
(5) increased
195. (1) both (2) besides
(3) combining (4) participating
(5) a ;o
Direction: In each of the following questions four
words are given of which two words are most nearly
the same or opposite in meaning. Find the two words
which are most nearly the same or opposite in
meaning and indicate the number of the correct
letter combination, by darkening the appropriate
196.(A) consent (B) nascent
(C) emerging (D) insecure
(1) A–C (2) B–D
(3) B–C (4) A–D
(5) A–B
197.(A) elated (B) eccentric
(C) explicit (D) abnormal
(1) A–B (2) B–D
(3) A–C (4) A–D
(5) D–C
198.(A) abundance (B) incomparable
(C) projection (D) plethora
(1) A–C (2) A–B
(3) C–D (4) B–D
(5) A–D
199.(A) purposefully (B) inaccurately
(1) A–C (2) A–B
(3) B–C (4) B–D
(5) A–D
200.(A) germane (B) generate
(C) reliable (D) irrelevant
(1) B–D (2) B–C
(3) A–B (4) C–D
(5) A–D
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# Pls sir I have problem ????????
Dear student,
By given information ,we draw our figure ,As :
Now
In $∆$ APO and $∆$ BPO
OA = OB ( As these are the radius of the circle )
$\angle$ APO = $\angle$ BPO ( As we draw to perpendiculars on side AB from centre O to P )
OP = OP ( Common side )
So,
$∆$ APO $\cong$ $∆$ BPO ( By SAS rule )
Hence
AP = BP ( by CPCT ) ( Hence proved )
Regards
• 0
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MullOverThings
Useful tips for everyday
What is 5V power supply?
What is 5V power supply?
5V power supplies (or 5VDC power supplies) are one of the most common power supplies in use today. In general, a 5VDC output is obtained from a 50VAC or 240VAC input using a combination of transformers, diodes and transistors.
Why we use 5V power supply?
It was designed to use 5 volts because that provided the best combination of noise immunity, power consumption and speed with the existing technology. Naturally, connecting circuits such as sensors and other devices tried to use the same voltage to avoid the need for extra power supplies.
Can 5V power 12V?
So now you know you can get 12V DC from 5V DC but as you increased the voltage, the output current must reduce to respect conservation principle. So in reality you can extract very limited amount of power from your converter.
Are all USB 5V?
All USB ports are 5 volts DC. The transformer (or computer) will take care of converting the 120/220 AC current to the necessary 5 volts DC.
How do I convert 220V to 5V?
In order to use the 220V AC supply as 5V DC supply, voltage step down transformer and a rectifier circuit are used, which is shown in Fig. 3. In this circuitry, a step-down transformer is used to convert 220V AC to 9V AC. This 9V AC is then transformed into 9V DC by a full bridge rectifier circuit.
How do I get 5V supply?
Step by step method to design 5V DC power supply
1. Step 1: The selection of regulator IC.
2. Step 2: The selection of transformer.
3. Step 3: The selection of diodes for the bridge.
4. Step 4: The Selection of smoothing capacitor and calculations.
5. Step 5: Making the power supply safe.
What happens if I plug 12V into 5V?
The device will very likely burn out. In addition, depending on what the device is and the capacity of the 12V supply, connecting a 12V supply to a device rated 5V max could lead to a hazard – fire, explosion, etc.
How does a stabilized power supply unit work?
The circuit of stabilized power supply unit utilized voltage regulated IC for regulated output and few other active as well as passive components for audio-visual indication of short-circuit. The input AC of 230V is stepped down using 9V-0-9V stepped down transformer and is further rectified using bridge rectifier build using diode D 1 to D 2.
What should the secondary voltage be for a 5V DC power supply?
This means we should select the transformer with a secondary voltage value equal to 9V or at least 10% more than 9V. From these points, for the 5V DC power supply design, we can select a transformer of current rating 1A and a secondary voltage of 9V.
Can a 5V DC power supply be made without a rectifier?
A rectifier circuit is the combination of diodes arranged in such a manner that converts AC into DC voltage. Without the rectifier circuit, it is not possible to have the required output 5V DC voltage. This circuit comes in nice integrated packages or you can make it using four diodes as well. You will see how we design it in later sections.
Which is the best filter for a 5V power supply?
The best filter in our case is the capacitor. You may have heard, a capacitor is a charge storing device. But actually, it can be best used as a filter. It is the most inexpensive filter for our basic 5V power supply design. A regulator is the linear integrated circuit use to provide a regulated constant output voltage.
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Basic Audio is a free introductory textbook to the basics of audio physics and electronics. See the editorial for more information....
# The Grounded-Grid Amplifier
Author: N.H. Crowhurst
Let us first take the grounded- or common-grid circuit. If the input voltage is applied between cathode and grid, it is the same as placing an opposite voltage between grid and cathode. (Making the grid 5 volts negative to the cathode is the same as making the cathode 5 volts positive to the grid.) No current flows in the grid, circuit because it is negative with respect to the cathode and repels all electron flow. Current does flow in the cathode circuit, and it is the same current that flows in the plate circuit.
With the same resistance in the plate circuit as before and a supply of 250 volts, with a fluctuation between +5 an<* +10 volts at the cathode, the current will fluctuate, as in the grounded-cathode arrangement, between 5 milliamperes and 2.5 milliamperes, respectively, while the plate-to-cathode voltage fluctuates between (150 - 5) or 145 volts and (200 - 10) or 190 volts. Thus the input fluctuates between +5 volts at 5 milliamperes and +10 volts at 2.5 milliamperes, the current in each case opposing the input voltage. This means the change in input current corresponding to a 5-volt change in input voltage is 2.5 milliamperes, which represents an a-c resistance for the input circuit of 5/.0025 or 2000 ohms.
In the grounded-cathode arrangement, there is no current in the input circuit, hence the a-c input resistance is 5/0 or infinity. (Anything divided by zero is infinity.) Here, however, we have what in tube circuits is a low input resistance - in this example, 2000 ohms.
Grounded-grid amplifier
Last Update: 2010-11-03
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# You have a construction that costs \$800,000. It has a 1/3 ch
You have a construction that costs \$800,000. It has a 1/3 chance of paying off \$3,000,000 and a 2/… Show more You have a construction that costs \$800,000. It has a 1/3 chance of paying off \$3,000,000 and a 2/3 chance of paying off \$0. What is the expected profit from the new construction? • Show less
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# Should the notation “$\log x$” mean the decimal logarithm? [duplicate]
I'm confused how do i can justifying to my students the difference between the two Notation “$\log x$” and “$\ln x$” however i checked the definition here in wikipedia. Really many people understand that the notation “$\log x$” must be the decimal logarithm (base $10$). But what I think is $\log x$ can be written as $\log_{e}x$ which is $\ln x$. The difference occurs only when I put the base $a$ as $\log_{a}x$ different from $e$.
My question here is:
Should the notation “$\log x$” mean the decimal logarithm and how can I give the correct notation with the correct definition to my students?
Thank you for any help
## marked as duplicate by leonbloy, Community♦Dec 25 '16 at 22:47
• yeah, it used to be $lg$, but the mathematical society was sued by a certain electronics manufacturer. – Jorge Fernández Hidalgo Dec 25 '16 at 22:05
• It depends what part of mathematics you are working in and at what level. Most of the time "$\log x$" will mean base $e$ in higher mathematics whereas at lower levels the notation $\ln$ is often used. – ÍgjøgnumMeg Dec 25 '16 at 22:06
• @Jorge: In some areas of mathematics $\lg x$ is commonly used for $\log_2x$. – Brian M. Scott Dec 25 '16 at 22:08
• I think if i said log x it must be to inform my student that i meant for example base 2 or 10 or e – zeraoulia rafik Dec 25 '16 at 22:10
• @Jahambo99 In my (European) country, almost everybody in Mathematics uses now ln(x) either in secondary school or University. – Jean Marie Dec 25 '16 at 22:14
It honestly doesn't matter as long as you are clear. For example, wolfram uses $\log(x)$ even when it means the natural log but clarifies this in a footnote. I personally prefer $\ln(x)$ (when teaching highscool) because it requires no further clarification.
At the end of the day it doesn't really matter; definitions and notation are two separate things. Just pick one and be consistent. Don't penalize your students for choosing certain accepted notations over others as long as they are clear about their intent i.e. $\log_e(x)$ is as valid as $\ln(x)$ which is as valid as $\log(x)$ where $\log(x)$ is the natural logarithm.
Being too picky about these things can cause students to associate Mathematics with some suffocating and obscure set of rules and rituals that really have nothing to do with Mathematical thinking.
• @gowrath, really all students in my country belive that log x must be meant logarithm decimal without any precdent definition or indication , that is the problem !!! – zeraoulia rafik Dec 25 '16 at 22:14
• @user51189 There are very few cases I can think of where it wouldn't be clear from the context which one they mean. I teach a lot of international students so I see huge varieties in notation. If the majority of your students have a regional preference, then let them stick with the convention that $\log(x)$ is the base 10 logarithm and $\log_e(x)$ or $\ln(x)$ is the natural log. It is true in early years that the base 10 logarithm seems more important and so $\log(x)$ is preferred by students. It really depends what you think is best for your students in terms of learning and understanding. – gowrath Dec 25 '16 at 22:31
In pure mathematics there is one and only one logarithm $\log$ defined to be the inverse function of $\exp$. Personally I do not like the notation $\ln$ since for example in real, complex or functional analysis you will never encounter any other logarithm than the natural one. The most clear notation I've encountered in the Book Analysis I by Vladimir A. Zorich: He uses $\log$ to denote the natural one and $\log_a$ for $a>0$ is the inverse function of the exponential mapping $a^x := \exp(x\log a)$. See, even here we use just the most fundamental transcendental functions.
But this is my way of how I would define it. There are several possibilities and most of the time definitions are a matter of taste. The most important part is to be consistent.
• Thanks and this is what i think , i hate using ln x and I use the notation log to mean base e with log_a(x) for a different from 0 to define any base – zeraoulia rafik Dec 25 '16 at 22:22
• Maybe it would be helpfull if you add what "my students" are, i.e. there are other almost standard conventions in computer science. – TheGeekGreek Dec 25 '16 at 22:26
• students high school level , the inconvinient which i found when students use the notation "ln" is : calculation of limit for example , as student mixed between lim and ln , lim ln(x) it's not gud as lim log(x) , the latter let students forget ln because they are seen it as limit " – zeraoulia rafik Dec 25 '16 at 22:28
Calculators denote the the logarithm in base 10 as "Log" and the natural logarithm by "Ln". Teachers then need to refer to the logarithms in the way these are indicated by the calculators as students are first exposed to simple pre-calculus problems involving exponentials and logarithms where they need to use their calculators, like powers of two and then trying to find for which power of two the outcome is some given number etc. etc.
When students are exposed to calculus, they will have gotten used to "Ln" for natural logarithm, so the teachers will not switch to the official notation. Only at University will students have to get used to "log" for the natural logarithm because that's the way it's used in the scientific literature.
• Infact. When I had 17 years, "Log" was $\log_{10}(x)$. – user401938 Dec 25 '16 at 22:40
• I think that is mostly the problem as students nowadays not really understand what they are doing. I mean, I see it quite often that a student just types the question one to one in a calculator, i.e. solving an equation, but does not even understand what the purpose is. – TheGeekGreek Dec 25 '16 at 22:44
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# Categorical Reparameterization with Gumbel-Softmax (@ ICLR 2017)
### Eric Jang, Shixiang Gu, Ben Poole
The idea is based on the Gumbel-Max trick. Let's say we have a vector of integers: $v = [1, 2, 3]$. Say we want a way to draw a vector $v'$ of 3 integers, such that the probability of each index being the maximum of that vector is proportional to the value. A little more precisely, I want $p(\arg\max_i v'_i = 1) = \frac{1}{6}$, $p(\arg\max_i v'_i = 2) = \frac{2}{6}$, $p(\arg\max_i v'_i = 3) = \frac{3}{6}$. One natural idea one might have is to draw a vector of uniform samples in the range $[0, v_i]$. That's almost right, but it's a bit biased: the probability of the last element being the maximum is not exactly $\frac{1}{2}$ in this example, but actually a bit higher. The Gumbel-Max trick is a way to fix that: if you add a random noise drawn from the Gumbel distribution to each uniform sample, then the resulting distribution has exactly the property we want.
On top of this, Gumbel-Softmax simply uses a Softmax layer as a continuous relaxation of the $\max$ operation. In the forward pass, you use softmax, and then discretize the output. In the backward pass, you just pretend the gradient for the discrete output is exactly the gradient to the continuous softmax prediction, and follow on normally. In practice, the softmax predictions of the model will tend to be almost one-hot, so this makes sense and works well. Apparently, it also has a lower variance than REINFORCE. The paper has an experiment demonstrating that. It also seems important to anneal the Softmax temperature during training, i.e. to take the predictions as "less one-hot" in the beginning, and increasingly make them more "one-hot".
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