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# Difference between revisions of "1993 AIME Problems/Problem 6"
## Problem
What is the smallest positive integer than can be expressed as the sum of nine consecutive integers, the sum of ten consecutive integers, and the sum of eleven consecutive integers?
## Solution
### Solution 1
Denote the first of each of the series of consecutive integers as $a,\ b,\ c$. Therefore, $n = a + (a + 1) \ldots (a + 8) = 9a + 36 = 10b + 45 = 11c + 55$. Simplifying, $9a = 10b + 9 = 11c + 19$. The relationship between $a,\ b$ suggests that $b$ is divisible by $9$. Also, $10b -10 = 10(b-1) = 11c$, so $b-1$ is divisible by $11$. We find that the least possible value of $b = 45$, so the answer is $10(45) + 45 = 495$.
### Solution 2
Let the desired integer be $n$. From the information given, it can be determined that, for positive integers $a, \ b, \ c$:
$n = 9a + 36 = 10b + 45 = 11c + 55$
This can be rewritten as the following congruences:
$n \equiv 0 \pmod{9}$
$n \equiv 5 \pmod{10}$
$n \equiv 0 \pmod{11}$
Since 9 and 11 are relatively prime, n is a multiple of 99. It can then easily be determined that the smallest multiple of 99 with a units digit 5 (this can be interpreted from the 2nd congruence) is $\boxed{495}$
### Solution 3
Let $n$ be the desired integer. From the given information, we have $$9x = a \\ 11y = a \\ 10z + 5 = a,$$ here, $x,$ and $y$ are the middle terms of the sequence of 9 and 11 numbers, respectively. Similarly, we have $z$ as the 4th term of the sequence. Since, $s$ is a multiple of $9$ and $11,$ it is also a multiple of $\lcm[9,11]=99.$ (Error compiling LaTeX. ! Undefined control sequence.) Hence, $a=99m,$ for some $m.$ So, we have $10z + 5 = 99m.$ It follows that $99(5) = 495$ is the smallest integer that can be represented in such a way.
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## 6.5 A production process simulation
Consider a simple engineering job shop that consists of several identical machines. Each machine is able to process any job and there is a ready supply of jobs with no prospect of any shortages. Jobs are allocated to the first available machine. The time taken to complete a job is variable but is independent of the particular machine being used. The machine shop is staffed by operatives who have two tasks:
• RESET machines between jobs if the cutting edges are still OK
• RETOOL those machines with cutting edges that are too worn to be reset
In addition, an operator may be AWAY while attending to personal needs
The figure below shows the activity cycle diagram for the considered system. Circles (READY, STOPPED, OK, WAITING) represent states of the machines or the operatives respectively, while rectangles (RUNNING, RETOOL, RESET, AWAY) represent activities that take some (random) time to complete. Two kind of processes can be identified: shop jobs, which use machines and degrade them, and personal tasks, which take operatives AWAY for some time.
Notice that after a job is completed by a machine there may be two possible trajectories to follow:
• either the machine needs only to be reset by an operator;
• or it first needs to be retool and then reset by the operator.
We can implement such a situation using branch. A branch is a point in a trajectory in which one or more sub-trajectories may be followed. The branch() activity places the arrival in one of the sub-trajectories depending on some condition evaluated in a dynamical parameter called option. It is the equivalent of an if/else in programming, i.e., if the value of option is i, the i-th sub-trajectory will be executed.
Let’s implement the system. First of all, let us instantiate a new simulation environment and define the completion time for the different activities as random draws from exponential distributions. Likewise, the interarrival times for jobs and tasks are defined (NEW_JOB, NEW_TASK), and we consider a probability of 0.2 for a machine to be worn after running a job (CHECK_JOB).
set.seed(2021)
env <- simmer("Job Shop")
RUNNING <- function() rexp(1, 1)
RETOOL <- function() rexp(1, 2)
RESET <- function() rexp(1, 3)
AWAY <- function() rexp(1, 1)
CHECK_WORN <- function() runif(1) < 0.2
NEW_JOB <- function() rexp(1, 5)
NEW_TASK <- function() rexp(1, 1)
The trajectory of an incoming job starts by seizing a machine in READY state. It takes some random time for RUNNING it after which the machine’s serviceability is checked. An operative and some random time to RETOOL the machine may be needed, and either way an operative must RESET it. Finally, the trajectory releases the machine, so that it is READY again. On the other hand, personal tasks just seize operatives for some time.
task <- trajectory() %>%
seize("operative") %>%
timeout(AWAY) %>%
release("operative")
job <- trajectory() %>%
seize("machine") %>%
timeout(RUNNING) %>%
branch(
CHECK_WORN, continue = TRUE,
trajectory() %>%
seize("operative") %>%
timeout(RETOOL) %>%
release("operative")) %>%
seize("operative") %>%
timeout(RESET) %>%
release("operative") %>%
release("machine")
Once the processes’ trajectories are defined, we append 10 identical machines and 5 operatives to the simulation environment, as well as two generators for jobs and tasks.
env %>%
run(until=10)
## simmer environment: Job Shop | now: 10 | next: 10.2238404207112
## { Monitor: in memory }
## { Resource: machine | monitored: TRUE | server status: 9(10) | queue status: 0(Inf) }
## { Resource: operative | monitored: TRUE | server status: 3(5) | queue status: 0(Inf) }
## { Source: job | monitored: 1 | n_generated: 49 }
## { Source: task | monitored: 1 | n_generated: 11 }
Let’s extract a history of the resource’s state to analyze the average number of machines/operatives in use as well as the average number of jobs/tasks waiting for an assignment.
aggregate(cbind(server, queue) ~ resource, get_mon_resources(env), mean)
## resource server queue
## 1 machine 5.839080 0.04597701
## 2 operative 3.153153 0.30630631
plot(get_mon_resources(env),"utilization")
plot(get_mon_resources(env),"usage", items = "server")
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Related Resources: calculators
Pivot Arm Toggle Formulae and Calculator
Pivot Arm Toggle Mechanism Design Formula and Calculator
Pivot Arm clamp design with forces applied and reaction forces calculator. Force is applied at Q and maintained by the spring between the pivot arm and stop collar.
Eq. 1
Q = P [ ( ( l + l1 ) + ( ( l + l1 ) / l1 - 1 ) r · fo / ( l1 - h · f1 ) ]
Eq. 2
P = Q / [ ( ( l + l1 ) + ( ( l + l1 ) / l1 - 1 ) r · fo / ( l1 - h · f1 ) ]
When n is designated
Eq. 3
Q = P [ ( l + l1 ) / l1 ] ( 1 / n )
Eq. 4
P = Q / [ ( l + l1 ) / l1 ] ( 1 / n )
Figure 1
Pivot Arm Toggle Mechanism
Where:
Q = force applied to handle. lbf, (N)
P = clamping force, lbf. (N)
fo = coefficient of friction (axles and pivot pins) = 0.1 to 0.15
f1 = coefficient of friction of pin contact surface = 0.1 to 0.15
n = efficiency coefficient, 0.98 to 0.84
l, l1 = length as indicated. in, (mm)
h = distance as indicated. in, (mm)
r = radius of pivot hole. in, (mm)
Reference:
Handbook of Machining and Metalworking Calculations
Ron A. Walsh
2001
Related
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# Sum of all Palindrome Numbers present in a Linked list
Given a linked list with integer node values, the task is to find the sum of all Palindrome Numbers present as Node values.
Examples:
Input: 13 -> 212 -> 22 -> 44 -> 4 -> 3
Output: 285
Explanation: The sum of palindrome numbers {22, 212, 44, 4, 3} is 285
Input: 19 -> 22 -> 141
Output: 163
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
Approach: In order to solve this problem we are using an approach similar to calculate the Sum of all Palindromes in an Array. Iterate through all the nodes of the linked list and check if the current node value is a palindrome or not. If so, add the value and store the sum. The final sum of all such values gives the desired answer.
Below is the implementation of the above approach:
## C++
`// C++ program to calculate ` `// the sum of all palindromic ` `// numbers in a linked list ` ` ` `#include ` `using` `namespace` `std; ` ` ` `// Node of the singly ` `// linked list ` `struct` `Node { ` ` ``int` `data; ` ` ``Node* next; ` `}; ` ` ` `// Function to insert a node at ` `// the beginning of the singly ` `// Linked List ` `void` `push(Node** head_ref, ``int` `new_data) ` `{ ` ` ``// allocate node ` ` ``Node* new_node = (Node*)``malloc``( ` ` ``sizeof``(``struct` `Node)); ` ` ` ` ``// Insert the data ` ` ``new_node->data = new_data; ` ` ` ` ``// Point the new Node ` ` ``// to the current head ` ` ``new_node->next = (*head_ref); ` ` ` ` ``// Make the new Node as ` ` ``// the new head ` ` ``(*head_ref) = new_node; ` `} ` ` ` `// Function to check ` `// if a number n is ` `// palindrome or not ` `bool` `isPalin(``int` `n) ` `{ ` ` ``int` `d = 0, s = 0; ` ` ``int` `temp = n; ` ` ``while` `(n > 0) { ` ` ``d = n % 10; ` ` ``s = s * 10 + d; ` ` ``n = n / 10; ` ` ``} ` ` ` ` ``// If n is equal to ` ` ``// the its reverse ` ` ``// it is a palindrome ` ` ``return` `temp == s; ` `} ` ` ` `// Function to calculate ` `// the sum of all nodes ` `// which are palindrome ` `int` `sumOfpal(Node* head_1) ` `{ ` ` ``int` `s = 0; ` ` ``Node* ptr = head_1; ` ` ``while` `(ptr != NULL) { ` ` ` ` ``// If the value of the ` ` ``// current node is ` ` ``// a palindrome ` ` ``if` `(isPalin(ptr->data)) { ` ` ` ` ``// Add the value ` ` ``// to the sum ` ` ``s += ptr->data; ` ` ``} ` ` ``ptr = ptr->next; ` ` ``} ` ` ``return` `s; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ``// Create the head ` ` ``// of the linked list ` ` ``Node* head1 = NULL; ` ` ` ` ``// Insert nodes into ` ` ``// the linked list ` ` ``push(&head1, 13); ` ` ``push(&head1, 212); ` ` ``push(&head1, 22); ` ` ``push(&head1, 44); ` ` ``push(&head1, 4); ` ` ``push(&head1, 3); ` ` ` ` ``// Print the sum of all ` ` ``// palindromes ` ` ``cout << sumOfpal(head1) ` ` ``<< endl; ` ` ``return` `0; ` `} `
## Java
`// Java program to calculate ` `// the sum of all palindromes ` `// in a linked list ` ` ` `import` `java.util.*; ` ` ` `class` `GFG { ` ` ` ` ``// Node of the singly ` ` ``// linked list ` ` ``static` `class` `Node { ` ` ``int` `data; ` ` ``Node next; ` ` ``}; ` ` ` ` ``// Function to insert a node ` ` ``// at the beginning of the ` ` ``// singly Linked List ` ` ``static` `Node push(Node head_ref, ` ` ``int` `new_data) ` ` ``{ ` ` ``// Allocate node ` ` ``Node new_node = ``new` `Node(); ` ` ` ` ``// Insert the data ` ` ``new_node.data = new_data; ` ` ` ` ``// Point the current Node ` ` ``// to the current head ` ` ``new_node.next = (head_ref); ` ` ` ` ``// Make the current node ` ` ``// as the new head ` ` ``(head_ref) = new_node; ` ` ` ` ``return` `head_ref; ` ` ``} ` ` ` ` ``// Function to check if ` ` ``// a number is palindrome ` ` ``static` `boolean` `isPalin(``int` `n) ` ` ``{ ` ` ``int` `d = ``0``, s = ``0``; ` ` ``int` `temp = n; ` ` ``while` `(n > ``0``) { ` ` ``d = n % ``10``; ` ` ``s = s * ``10` `+ d; ` ` ``n = n / ``10``; ` ` ``} ` ` ``// If n is equal to its ` ` ``// reverse, it is a ` ` ``// palindrome ` ` ``return` `temp == s; ` ` ``} ` ` ` ` ``// Function to calculate sum ` ` ``// of all nodes with value ` ` ``// which is a palindrome ` ` ``static` `int` `sumOfpal(Node head_1) ` ` ``{ ` ` ``int` `s = ``0``; ` ` ``Node ptr = head_1; ` ` ``while` `(ptr != ``null``) { ` ` ``// If the value of the ` ` ``// current node ` ` ``// is a palindrome ` ` ``if` `(isPalin(ptr.data)) { ` ` ` ` ``// Add that value to ` ` ``// the sum ` ` ``s += ptr.data; ` ` ``} ` ` ``ptr = ptr.next; ` ` ``} ` ` ` ` ``// Return the sum ` ` ``return` `s; ` ` ``} ` ` ` ` ``// Driver Code ` ` ``public` `static` `void` `main(String args[]) ` ` ``{ ` ` ``// Create the head ` ` ``Node head1 = ``null``; ` ` ` ` ``// Insert nodes to the ` ` ``// Linked List ` ` ``head1 = push(head1, ``13``); ` ` ``head1 = push(head1, ``212``); ` ` ``head1 = push(head1, ``22``); ` ` ``head1 = push(head1, ``44``); ` ` ``head1 = push(head1, ``4``); ` ` ``head1 = push(head1, ``3``); ` ` ` ` ``System.out.println( ` ` ``sumOfpal(head1)); ` ` ``} ` `} `
## Python3
`# Python3 program to ` `# calculate the sum of all ` `# palindromes present in ` `# a Linked List ` ` ` `class` `Node: ` ` ` ` ``def` `__init__(``self``, data): ` ` ``self``.data ``=` `data ` ` ``self``.``next` `=` `next` ` ` `# Function to insert a ` `# node at the beginning ` `# of the singly Linked List ` `def` `push( head_ref, new_data) : ` ` ` ` ``# Alocate node ` ` ``new_node ``=` `Node(``0``) ` ` ` ` ``# Insert data ` ` ``new_node.data ``=` `new_data ` ` ` ` ``# Pont to the head ` ` ``new_node.``next` `=` `(head_ref) ` ` ` ` ``# Make the new Node ` ` ``# the new head ` ` ``(head_ref) ``=` `new_node ` ` ` ` ``return` `head_ref ` ` ` ` ` `# Function to check if ` `# a number is palindrome ` `def` `isPalin(n) : ` ` ` ` ``d ``=` `0``; s ``=` `0``; ` ` ``temp ``=` `n; ` ` ``while` `(n > ``0``) : ` ` ` ` ``d ``=` `n ``%` `10``; ` ` ``s ``=` `s ``*` `10` `+` `d; ` ` ``n ``=` `n ``/``/` `10``; ` ` ` ` ``# If n is equal to its reverse, ` ` ``# it is a palindrome ` ` ``return` `s ``=``=` `temp; ` ` ` ` ` `# Function to calculate sum of ` `# all elements in a Linked List ` `# which are palindrome ` `def` `sumOfpal(head_ref1) : ` ` ` ` ``s ``=` `0``; ` ` ``ptr1 ``=` `head_ref1 ` ` ` ` ``while` `(ptr1 !``=` `None``) : ` ` ``# If the value of the ` ` ``# current node ` ` ``# is a palindrome ` ` ``if` `(isPalin(ptr1.data)) : ` ` ` ` ``# Add that value ` ` ``s ``=` `s ``+` `ptr1.data ` ` ` ` ``# Move to the next node ` ` ``ptr1 ``=` `ptr1.``next` ` ` ` ``# Return the final sum ` ` ``return` `s; ` ` ` `# Driver code ` ` ` `# Create the Head ` `head1 ``=` `None` ` ` `# Insert nodes ` `head1 ``=` `push(head1, ``13``) ` `head1 ``=` `push(head1, ``212``) ` `head1 ``=` `push(head1, ``22``) ` `head1 ``=` `push(head1, ``44``) ` `head1 ``=` `push(head1, ``4``) ` `head1 ``=` `push(head1, ``3``) ` ` ` `print``(sumOfpal(head1)) `
## C#
`// C# program to calculate ` `// the sum of all palindromes ` `// in a linked list ` `using` `System; ` ` ` `class` `GFG { ` ` ` `// Node of the singly ` `// linked list ` `class` `Node ` `{ ` ` ``public` `int` `data; ` ` ``public` `Node next; ` `}; ` ` ` `// Function to insert a node ` `// at the beginning of the ` `// singly Linked List ` `static` `Node push(Node head_ref, ` ` ``int` `new_data) ` `{ ` ` ` ` ``// Allocate node ` ` ``Node new_node = ``new` `Node(); ` ` ` ` ``// Insert the data ` ` ``new_node.data = new_data; ` ` ` ` ``// Point the current Node ` ` ``// to the current head ` ` ``new_node.next = (head_ref); ` ` ` ` ``// Make the current node ` ` ``// as the new head ` ` ``(head_ref) = new_node; ` ` ` ` ``return` `head_ref; ` `} ` ` ` `// Function to check if ` `// a number is palindrome ` `static` `bool` `isPalin(``int` `n) ` `{ ` ` ``int` `d = 0, s = 0; ` ` ``int` `temp = n; ` ` ` ` ``while` `(n > 0) ` ` ``{ ` ` ``d = n % 10; ` ` ``s = s * 10 + d; ` ` ``n = n / 10; ` ` ``} ` ` ` ` ``// If n is equal to its ` ` ``// reverse, it is a ` ` ``// palindrome ` ` ``return` `temp == s; ` `} ` ` ` `// Function to calculate sum ` `// of all nodes with value ` `// which is a palindrome ` `static` `int` `sumOfpal(Node head_1) ` `{ ` ` ``int` `s = 0; ` ` ``Node ptr = head_1; ` ` ` ` ``while` `(ptr != ``null``) ` ` ``{ ` ` ` ` ``// If the value of the ` ` ``// current node ` ` ``// is a palindrome ` ` ``if` `(isPalin(ptr.data)) ` ` ``{ ` ` ` ` ``// Add that value to ` ` ``// the sum ` ` ``s += ptr.data; ` ` ``} ` ` ``ptr = ptr.next; ` ` ``} ` ` ` ` ``// Return the sum ` ` ``return` `s; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main(String []args) ` `{ ` ` ` ` ``// Create the head ` ` ``Node head1 = ``null``; ` ` ` ` ``// Insert nodes to the ` ` ``// Linked List ` ` ``head1 = push(head1, 13); ` ` ``head1 = push(head1, 212); ` ` ``head1 = push(head1, 22); ` ` ``head1 = push(head1, 44); ` ` ``head1 = push(head1, 4); ` ` ``head1 = push(head1, 3); ` ` ` ` ``Console.WriteLine(sumOfpal(head1)); ` `} ` `} ` ` ` `// This code is contributed by sapnasingh4991 `
Output:
```285
```
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Python: Determine which characters of a hexadecimal number correspond to prime numbers - w3resource
# Python: Determine which characters of a hexadecimal number correspond to prime numbers
## Python Programming Puzzles: Exercise-44 with Solution
From Wikipedia:
The hexadecimal numeral system, often shortened to "hex", is a numeral system made up of 16 symbols (base 16). The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses the decimal numbers and six extra symbols. There are no numerical symbols that represent values greater than nine, so letters taken from the English alphabet are used, specifically A, B, C, D, E and F. Hexadecimal A = decimal 10, and hexadecimal F = decimal 15.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
Write a Python program to find which characters of a hexadecimal number correspond to prime numbers.
```Input: 123ABCD
Output:
[False, True, True, False, True, False, True]
Input: 123456
Output:
[False, True, True, False, True, False]
Input: FACE
Output:
[False, False, False, False]
```
Visual Presentation:
Sample Solution:
Python Code:
``````# Define a function named 'test' that takes a hexadecimal number 'hn' as input
def test(hn):
# List comprehension to check if each character in 'hn' corresponds to a prime number or 'B' or 'D'
return [c in "2357BD" for c in hn]
# Assign a specific hexadecimal number 'hn' to the variable
hn = "123ABCD"
# Print a message indicating the original hexadecimal number
# Print a message indicating the operation to be performed
print("Characters of the said hexadecimal number correspond to prime numbers:")
# Print the result of the test function applied to 'hn'
print(test(hn))
# Assign another specific hexadecimal number 'hn' to the variable
hn = "123456"
# Print a message indicating the original hexadecimal number
# Print a message indicating the operation to be performed
print("Characters of the said hexadecimal number correspond to prime numbers:")
# Print the result of the test function applied to 'hn'
print(test(hn))
# Assign another specific hexadecimal number 'hn' to the variable
hn = "FACE"
# Print a message indicating the original hexadecimal number
# Print a message indicating the operation to be performed
print("Characters of the said hexadecimal number correspond to prime numbers:")
# Print the result of the test function applied to 'hn'
print(test(hn))
``````
Sample Output:
```Original hexadecimal number: 123ABCD
Characters of the said hexadecimal number correspond to prime numbers:
[False, True, True, False, True, False, True]
Characters of the said hexadecimal number correspond to prime numbers:
[False, True, True, False, True, False]
Characters of the said hexadecimal number correspond to prime numbers:
[False, False, False, False]
```
Flowchart:
Python Code Editor :
Have another way to solve this solution? Contribute your code (and comments) through Disqus.
What is the difficulty level of this exercise?
Test your Programming skills with w3resource's quiz.
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# Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The length of the longer leg of a right triangle is 14 ft longer
Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The length of the longer leg of a right triangle is 14 ft longer than the length of the shorter leg x. The hypotenuse is 6 ft longer than twice the length of the shorter leg. Find the dimensions of the
Triangle.
A) Short leg = 11, long leg = 25, hypotenuse = 28
B) Short leg = 9, long leg = 23, hypotenuse = 28
C) Short leg = 9, long leg = 23, hypotenuse = 24
D) Short leg = 10, long leg = 24, hypotenuse = 26
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+0
# Help?
0
106
2
For what values of \$j\$ does the equation \$(2x+7)(x-5) = -43 + jx\$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.
Dec 20, 2019
#1
+119
+2
We can start by expanding the equation (2x + 7)(x - 5) = -43 + jx ---> 2x^2 - (j+3)x + 8 = 0.
Now we know that when the discriminant (b^2 - 4ac) is equal to 0, we have one real solution.
So we plug in our values and we get j^2 + 6j - 55 = 0.
Solving this gives us j = -11, 5
Dec 20, 2019
#2
+11709
0
For what values of \$j\$ does the equation \$(2x+7)(x-5) = -43 + jx\$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.
Dec 20, 2019
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Home | Menu | Get Involved | Contact webmaster
# Number 1930156
one million nine hundred thirty thousand one hundred fifty six
### Properties of the number 1930156
Factorization 2 * 2 * 482539 Divisors 1, 2, 4, 482539, 965078, 1930156 Count of divisors 6 Sum of divisors 3377780 Previous integer 1930155 Next integer 1930157 Is prime? NO Previous prime 1930147 Next prime 1930177 1930156th prime 31245817 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 111010111001110101100 Octal 7271654 Duodecimal 790ba4 Hexadecimal 1d73ac Square 3725502184336 Square root 1389.300543439 Natural logarithm 14.47311138663 Decimal logarithm 6.2855924111846 Sine -0.73607519686573 Cosine 0.6768997743825 Tangent -1.0874212471665
Number 1930156 is pronounced one million nine hundred thirty thousand one hundred fifty six. Number 1930156 is a composite number. Factors of 1930156 are 2 * 2 * 482539. Number 1930156 has 6 divisors: 1, 2, 4, 482539, 965078, 1930156. Sum of the divisors is 3377780. Number 1930156 is not a Fibonacci number. It is not a Bell number. Number 1930156 is not a Catalan number. Number 1930156 is not a regular number (Hamming number). It is a not factorial of any number. Number 1930156 is a deficient number and therefore is not a perfect number. Binary numeral for number 1930156 is 111010111001110101100. Octal numeral is 7271654. Duodecimal value is 790ba4. Hexadecimal representation is 1d73ac. Square of the number 1930156 is 3725502184336. Square root of the number 1930156 is 1389.300543439. Natural logarithm of 1930156 is 14.47311138663 Decimal logarithm of the number 1930156 is 6.2855924111846 Sine of 1930156 is -0.73607519686573. Cosine of the number 1930156 is 0.6768997743825. Tangent of the number 1930156 is -1.0874212471665
### Number properties
Examples: 3628800, 9876543211, 12586269025
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You are on page 1of 2
Banbury
Oxfordshire, OX16 1XJ
UNITED KINGDOM
Tel:
Fax:
E-mail:
Website:
## + 44 (0) 1295 270333
+ 44 (0) 1295 753643
enquiry@norbar.com
www.norbar.com
## A GUIDE TO TORQUE VALUES
It should be understood that the subject of torque tension loading is beyond the scope of this document. The
information here supplied is an acceptable guide for normal conditions; for critical applications, however,
further information and research will be necessary.
In preparing this guide to torque values, the following basic assumptions have been made:
(a)
(b)
bolts and nuts are new, standard finish, uncoated and not lubricated*
the load will be 90% of the bolt yield strength
(c)
## the coefficient of friction () is 0.14
(d)
the final tightening sequence is achieved smoothly and slowly, until the torque tool indicates full torque
has been obtained.
* If lubrication has been applied to the bolt and/or the nut (other than the normal protective oil film), multiply
the recommended torque by the appropriate factor shown in the table.
Example: bolt and nut are both phosphated; required torque = torque recommended x 0.75.
Self
Zinc
Phosphate
Self
1.00
1.00
0.80
0.90
Zinc
1.15
1.20
1.35
1.15
0.85
0.90
1.20
1.00
Phosphate
and oil
0.70
0.65
0.70
0.75
## Zinc with wax
0.60
0.55
0.65
0.55
Formulae
Accepted formulae relating torque and tension, based on many tests are:
M
= PxD
60
M = torque lbf.ft
P = bolt tension lbf
D = bolt dia.ins
## Or for metric sizes:
M
PxD
5000
M = torque N.m
P = bolt tension Newtons
D = bolt dia. mm
These formulae may be used for bolts outside the range of the tables overleaf.
UNC
in Newtons
1
/4
4379
5
/16
7344
3
/8
10951
7
/16
15065
1
/2
20244
9
/16
26075
5
/8
32452
3
/4
49781
7
/8
67157
1
88221
1
1 /8 111007
1
1 /4 142135
3
1 /8 168641
1
1 /2 206578
Quality P
N.m
lbf
5.43
984
11.2
1650
19.9
2461
31.9
3386
48.8
4551
70.4
5861
97.4
7295
178
11191
279
15097
418
19832
593
24955
837
31953
1096 37911
1456 46440
S
lbf.ft
4.00
8.26
14.68
23.53
36.00
51.92
71.84
131.3
205.8
308.3
437.4
617.3
808.4
1074
Newtons
8320
13954
20807
28623
38463
49542
61658
94584
127599
167620
210913
270091
320417
392498
N.m
10.3
21.3
37.9
60.7
92.7
134
185
338
530
795
1126
1591
2083
2767
T
lbf
1870
3136
5161
6434
8646
11137
13861
21263
28685
37682
47415
60718
72032
88237
lbf.ft Newtons
7.60
8980
15.71
15061
27.95
22458
44.77
30894
68.37
41516
98.83
53474
136.45 66552
249.3 102091
391
137725
586
180923
830
227652
1173 291527
1536 345847
2041 423648
N.m
11.1
23.0
40.9
65.5
100
144
200
364
572
858
1216
1717
2248
2987
lbf
2018
3385
5048
6945
9333
12021
14961
22950
30961
40673
51178
65537
77749
95239
A/F
lbf.ft
in
7
8.19
/16
1
16.96
/2
9
30.17
/16
5
48.31
/8
3
73.76
/4
7
106
/8
15
147.5
/16
1
268.5 1 /8
5
422 1 /16
1
633
1 /2
11
897 1 /16
7
1266 1 /8
1
1658 2 /16
1
2203 2 /4
UNF
in Newtons
1
/4
5232
5
/16
8410
3
/8
12911
7
/16
17416
1
/2
23685
9
/16
30075
5
/8
38156
3
/4
56078
7
/8
76297
1
99200
1
1 /8 128738
1
1 /4 161358
3
1 /8 199331
1
1 /2 240377
Quality P
N.m
lbf
6.28
1176
12.5
1891
22.7
2903
35.9
3915
55.4
5325
79.0
6761
111
8578
195
12607
309
17152
459
22301
667
28941
925
36275
1252 44811
1642 54039
S
lbf.ft
4.63
9.22
16.74
26.5
40.9
58.3
81.9
144
228
339
492
682
923
1211
Newtons
9941
15979
24531
33091
45002
57143
72496
106549
144965
188480
244602
306580
378728
456717
N.m
11.9
23.8
43.2
68.2
105
150
210
370
587
873
1267
1757
2378
3119
T
lbf
2234
3592
5514
7439
10116
12846
16297
23953
32589
42371
54988
68921
85141
102673
lbf.ft
8.78
17.55
31.9
50.3
77.4
111
155
273
433
644
934
1296
1754
2300
Newtons
10730
17247
26478
35717
48574
61678
78250
115005
156470
203439
264015
330911
408786
492965
N.m
12.9
25.7
46.6
73.6
114
162
227
399
634
942
1368
1896
2567
3367
lbf
lbf.ft
2412
9.51
3877 18.96
5952
34.4
8029
54.3
10919
84.0
13865
119
17591
167
25854
294
35175
468
45734
695
59352 1009
74391 1398
91898 1893
110822 2482
A/F
in
7
/16
1
/2
9
/16
5
/8
3
/4
7
/8
15
/16
1
1 /8
5
1 /16
1
1 /2
11
1 /16
7
1 /8
1
2 /16
1
2 /4
mm
2
3
4
5
6
8
10
12
16
20
24
30
36
42
3.6
Newtons
284
726
1255
2059
2903
5315
8473
12356
23340
36481
52563
84043
123073
169164
5.6
6.9
N.m Newtons N.m Newtons N.m
0.12
378
0.16
731
0.31
0.44
966
0.59
1863
1.13
1.00
1677
1.34
3226
2.60
1.96
2736
2.65
5286
5.10
3.43
3864
4.51
7453
8.73
8.24
7090
10.79 13680 21.57
16.7
11278 21.57 21771 42.17
28.4
16475 38.25 31773 73.55
69.6
31087 93.16 60016 178.50
135
48641
180
93849 384.1
230
70019 308.9 135331 598.2
466
112286 622.7 215745 1206
814
164261 1089 316753 2099
1304 225552 1746 435413 3364
8.8
Newtons N.m
863
0.37
2206
1.34
3825
3.04
6257
6.03
8836
10.30
16230 25.50
25791 50.01
37657 87.28
71196 210.80
111305 411.9
160338 711.0
255952 1422
374612 2481
515827 3991
10.9
Newtons N.m
1216
0.52
3109
1.88
5374
4.31
8806
8.48
12405 14.71
22751 35.30
36284 70.61
52956 122.60
100027 299.10
156415 578.6
225552 1000
359902 2010
527595 3491
725688 5609
12.9
Newtons N.m
1461
0.63
3727
2.26
6453
5.15
10591 10.20
14906 17.65
27360 42.17
43541 85.32
63547 147.10
120131 357.90
187796 696.3
270662 1196
432471 2403
432526 4197
870826 6727
P,S & T are the Material grade for unified inch and Whitworth fasteners (BS1768 & BS1083)
P = grade UTS of 35 tonf/in2 and min. yield of 21 tonf/in2, S = grade UTS of 50 tonf/in2 and min. yield of 40 tonf/in2,
T = grade UTS of 55 tonf/in2 and min. yield of 41 tonf/in2
These torque values are for guidance only! Always check with the equipment/bolt manufacturer.
A/F
mm
4
5.5
7
8
10
13
17
19
24
30
36
46
55
65
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• Create Account
## Linear Depth Buffer
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
3 replies to this topic
### #1Mchart Members
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Posted 25 June 2014 - 03:27 PM
Hi I'm new here I hope I'm not making mistakes with this post! if so please tell me!
I'm rendering a scene on a render target, I've then to access its depth information in a post-processing stage. In this stage I need linear depth info. I've been browsing the internet quite a lot and found a lot of different approaches/alternatives. What do you think is the way to go? I'm a bit of a newbie with this stuff so can you give me an hint/pointer on the possible GLSL code?
Thank you very much
Micheal
### #2Samith Members
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Posted 25 June 2014 - 03:47 PM
Typically you'll read the value from your non-linear depth buffer and reconstruct the view-space z position at that point.
// let s and t be two values that satisfy the following two equations:
(s*f + t)/f = 1 // f is the distance from the eye to far plane
(s*n + t)/n = -1 // n is the distance from the eye to near plane
// the above is simply the mapping the occurs when you do a projection transform
// s and t are found in your projection matrix at positions 3,3 and 3,4, respectively
// let d be the value in your depth buffer
// the (xxx + 1) * 0.5 is to map the [-1,1] clip-space coordinates to the [0,1] space in the depth buffer
d = ((s*z + t)/z + 1) * 0.5
2d = (s*z + t)/z + 1
2d - 1 = (s*z + t)/z
2d*z - z = s*z + t
2d*z - z - s*z = t
z*(2d - 1 - s) = t
z = t / (2d - 1 - s) // reconstructed z value
That math is just off the top of my head and might not be totally correct, but you should be able to get the picture from that. You basically just want to use your knowledge of the projection matrix you used when transforming the verts to do the inverse of that transformation and reconstruct the view-space z.
Edited by Samith, 25 June 2014 - 03:50 PM.
### #3Mchart Members
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Posted 25 June 2014 - 04:37 PM
Typically you'll read the value from your non-linear depth buffer and reconstruct the view-space z position at that point.
// let s and t be two values that satisfy the following two equations:
(s*f + t)/f = 1 // f is the distance from the eye to far plane
(s*n + t)/n = -1 // n is the distance from the eye to near plane
// the above is simply the mapping the occurs when you do a projection transform
// s and t are found in your projection matrix at positions 3,3 and 3,4, respectively
// let d be the value in your depth buffer
// the (xxx + 1) * 0.5 is to map the [-1,1] clip-space coordinates to the [0,1] space in the depth buffer
d = ((s*z + t)/z + 1) * 0.5
2d = (s*z + t)/z + 1
2d - 1 = (s*z + t)/z
2d*z - z = s*z + t
2d*z - z - s*z = t
z*(2d - 1 - s) = t
z = t / (2d - 1 - s) // reconstructed z value
That math is just off the top of my head and might not be totally correct, but you should be able to get the picture from that. You basically just want to use your knowledge of the projection matrix you used when transforming the verts to do the inverse of that transformation and reconstruct the view-space z.
Thank you Samith, just one question. In which space t and s are distances eye-near/eye-far? If I look in my projection matrix (built via glm::perspective) at position 3,3 and 3,4 what I see is something like -1.03 and -1 where my clipping planes are [0.1, 8]
### #4Samith Members
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Posted 25 June 2014 - 04:57 PM
Thank you Samith, just one question. In which space t and s are distances eye-near/eye-far? If I look in my projection matrix (built via glm::perspective) at position 3,3 and 3,4 what I see is something like -1.03 and -1 where my clipping planes are [0.1, 8]
Yep. The s and t values are computed given the near and far planes. In my post above I said that s and t are two values that satisfy the equations (s*f + t)/f = 1 and (s*n + t)/n = -1, but I didn't provide any actually solution for s and t
If you are interested, the solutions for s and t can be found like so:
(sf + t)/f = 1
(sn + t)/n = -1
// here you have two linear equations and two unknowns. you can solve
// for s and t with your basic high school algebra techniques
eq1: sf + t = f
eq2: sn + t = -n
// subtract eq2 from eq1
eq3: s(f-n) = f+n
s = (f+n)/(f-n)
// substitute s into eq1 and solve for t
eq4: sf + t = f
f(f+n)/(f-n) + t = f
f(f+n) + t(f-n) = f(f-n)
f(f+n) - f(f-n) = -t(f-n)
ff+fn - ff+fn = -t(f+n)
-2fn/(f+n) = t
// now you can check s and t given a near and far plane of 0.1 and 8.0
// s = (f+n)/(f-n) = (8-0.1)/(8+0.1) =~ 1.025
// t = 2fn/(f+n) =~ -0.19
Some caveats: these computations depend on some nitpicky details about your projection. For example, if you use your projection matrix to transform a right handed coordinate space into the left handed clip space, then the original equations will be slightly different (ie s*-f + t = f instead of sf + t = f, etc). Also, the s and t values will be found in your projection matrix in the 3,3 location and 3,4 location if your projection matrix is column major, but they'll be in 3,3 and 4,3 if your projection matrix is row major.
I don't know enough about your exact environment to give you all the answers, but I hope the algebra I've posted at least gets you started down the right path.
Edited by Samith, 25 June 2014 - 06:35 PM.
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0
# How to write 7 over 12 as a percent-?
Updated: 12/15/2022
Saragracegp0255
Lvl 1
9y ago
To convert a fraction to a percentage, multiply by 100 %
→ 7/12 = 7/12 x 100 % = 175/3 % = 58 1/3 % ≈ 58.33 %
Wiki User
9y ago
Wiki User
9y ago
7/12 = 7 ÷ 12 = 0.58333 repeating = 58 and 1/3%
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# A box with a square base and no top is to be made from a square piece
A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in. squares from each corner and folding up the sides. The box is to hold 13872 in^3. How big a piece of cardboard is needed? 74in. x ?in.
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# Implement Two Stacks in an Array
Difficulty Level Medium
Array StackViews 2751
## Problem Statement
In the “Implement Two Stacks in an Array” problem we have to implement two stacks in an array such that, if the user wants to push an element in either of two stacks then there should not be an error till the array gets full.
## Example
```Push 5 into stack1.
Push 10 into stack2.
Push 15 into stack2.
Push 11 into stack1.
Push 7 into stack2.
Popped element from stack1.
Push 40 into stack2.
Popped element from stack2.```
```Stack Overflow By element: 7
Popped element from stack1 is: 11
Stack Overflow By element: 40
Popped element from stack2 is: 15```
## Algorithm
The idea is to start two stacks from the extreme corners of the array. Both these stacks will grow towards each other, stack1 will start from the leftmost corner and stack2 will start from the rightmost corner of the array.
1. stack1 will start from index 0 and grow towards the right end of the array
2. stack2 will start from index n-1 and grow towards the left end of the array
3. when both the stacks meet each other then we cant push an element in both stacks
We use push, pop functions to push elements in both stacks
1. push function will take the stack name and value to be inserted, and pushes the number into the respective stack
a. According to the stack name proceed
b. Check whether the stack is full or not ie, top1 < top2 -1 Here, top1, top2 are the variables
to keep track of top elements in both stacks
c. If not, push the element in the respective stack ie, arr[top1] = k
2. pop will take the stack name and will pop the topmost element in that stack
a. According to the stack name proceed
b. check whether there is any element to pop
c. If yes, decrement or increment the top1, top2 variables accordingly
## Implementation
### C++ Program to Implement Two Stacks in an Array
```#include <bits/stdc++.h>
using namespace std;
class twoStacks
{
int* arr;
int size;
int top1, top2;
public:
twoStacks(int n)
{
size = n;
arr = new int[n];
top1 = n / 2 + 1;
top2 = n / 2;
}
void push1(int x)
{
if (top1 > 0) {
top1--;
arr[top1] = x;
}
else {
cout << "Stack Overflow"
<< " By element :" << x << endl;
return;
}
}
void push2(int x)
{
if (top2 < size - 1) {
top2++;
arr[top2] = x;
}
else {
cout << "Stack Overflow"
<< " By element : " << x << endl;
return;
}
}
int pop1()
{
if (top1 <= size / 2) {
int x = arr[top1];
top1++;
return x;
}
else {
cout << "Stack UnderFlow";
exit(1);
}
}
int pop2()
{
if (top2 >= size / 2 + 1) {
int x = arr[top2];
top2--;
return x;
}
else {
cout << "Stack UnderFlow";
exit(1);
}
}
};
int main()
{
twoStacks ts(5);
ts.push1(5);
ts.push2(10);
ts.push2(15);
ts.push1(11);
ts.push2(7);
cout << "Popped element from stack1 is "<< " : " << ts.pop1()<< endl;
ts.push2(40);
cout << "Popped element from stack2 is "<< " : " << ts.pop2()<< endl;
return 0;
}
```
### Java Program to Implement Two Stacks in an Array
```import java.util.Scanner;
class twoStacks
{
int[] arr;
int size;
int top1, top2;
twoStacks(int n)
{
size = n;
arr = new int[n];
top1 = n / 2 + 1;
top2 = n / 2;
}
void push1(int x)
{
if (top1 > 0)
{
top1--;
arr[top1] = x;
}
else
{
System.out.print("Stack Overflow"+ " By element :" + x +"\n");
return;
}
}
void push2(int x)
{
if (top2 < size - 1)
{
top2++;
arr[top2] = x;
}
else
{
System.out.print("Stack Overflow"+ " By element : " + x +"\n");
return;
}
}
// Method to pop an element from first stack
int pop1()
{
if (top1 <= size / 2)
{
int x = arr[top1];
top1++;
return x;
}
else
{
System.out.print("Stack UnderFlow");
System.exit(1);
}
return 0;
}
// Method to pop an element
// from second stack
int pop2()
{
if (top2 >= size / 2 + 1)
{
int x = arr[top2];
top2--;
return x;
}
else
{
System.out.print("Stack UnderFlow");
System.exit(1);
}
return 1;
}
};
class sum
{
public static void main(String[] args)
{
twoStacks ts = new twoStacks(5);
ts.push1(5);
ts.push2(10);
ts.push2(15);
ts.push1(11);
ts.push2(7);
System.out.print("Popped element from stack1 is "+ " : " + ts.pop1() +"\n");
ts.push2(40);
System.out.print("Popped element from stack2 is "+ ": " + ts.pop2()+"\n");
}
}```
```Stack Overflow By element :7
Popped element from stack1 is : 11
Stack Overflow By element : 40
Popped element from stack2 is : 15```
## Complexity Analysis to Implement Two Stacks in an Array
### Time Complexity
• Push operation: O(1) because we directly push an integer value at the end of the stack.
• Pop operation: O(1) because we directly remove the last value or the top value of the stack.
### Space Complexity
O(N) because we use an array to implement the stack. It is not the space-optimized method as explained above.
Translate »
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# Shape Modeling
Often not only just a species has to be modeled, but rather an individual plant with a particular shape. Examples here are trees growing along a wall or plants deformed under the influence of wind. In both instances, the overall shape of the plant has to be influenced in such a way as to yield a characteristic shape. A total of five mechanisms have been implemented for the modeling of shape. One of the mechanisms is the definition of exceptions within the base component introduced in Sect. 6.2. The four others are functional modeling, tropisms, freeform deformations, and pruning. These mechanisms will be discussed next.
Chapter 6 As already mentioned in the introduction, while building the temporary i-tree, Rule-Based Object Production component prototypes are transformed into instances, whereby the parameters
are computed individually for each instance, particularly those of the multiplication components which were stored as parameter ranges. The individual assignment is performed by interpolation, which also permits us to apply a function to the result.
(a)
At this point, random functions as well as other functionally specified parameters can be introduced into the system. For example, variations are generated by adding a small random value for the curvature or for the size; for the functional specifications all essential mathematical functions are available.
To parameterize this function meaningfully, a number of variables can be applied in combination with the active value interpolated for the respective instance. In this way, positions and orientation, and also recursion depth and the actual iteration number of the instance can be applied.
In Fig. 6.11a, an agave plant was modeled using these techniques. Each leaf is individually curved, where the iteration number and a random value determines the curvature. The first generated leaves with a small iteration number are created by the Phiball component at the top of the sphere and thereby receive a small curvature. For the subsequently generated leaves the curvature is increased continuously.
tropisms ^ Tropisms were already discussed in connection with base, leaf, tree, and world components. The modeling with tropisms allows for generating a number of different effects. For the production of a weeping willow, a downward-pointing gravitational field as shown in Fig. 6.11b was applied. If the field is defined in such a way that the directional vectors point towards a center line, and within a cylinder around this line point outwards, then the branching structure can be forced to grow onto a cylindrical shape. This technique was applied to render the philodendron in Fig. 6.11c. More examples are wind simulations, in which
a lateral field is used, and obstructions, which are realized with fields that block the entrance to a space.
In the two foregoing chapters we occasionally addressed the animation of plants. A problem in this area is always the interplay between geometrical and topological changes in the growth of the plant. Prusinkiewicz works with differential L-systems, in which model changes are described by conventional L-systems; the intermediate growth is generated by differential equations with relatively complex boundary conditions. some of the procedural approaches likewise permit growth of the produced trees, which is due to the limited model palette (mostly simple trees) easier to implement.
With the rule-based object production, we take advantage of the fact that most of the model topology – for instance, how many objects are generated with a multiplication component – is not stored in the topology of the p-graph but as parameters of the components. The topology of the p-graph can therefore be accepted being constant during the process of an animation without too much restriction.
In this case, the parameters which are specified within the components, are understood as parameter sets for a specific time. If different parameter sets are defined for different times, then the values of the parameters for intermediate times can be determined through interpolation. Thus, we are concerned here with a keyframing concept based on parameter values.
Using cascaded keyframing, a local time is implemented. Here one keyframing sequence can be incorporated into another one. If a sequence is produced by a multiplication component during the course of an animation, the local time starts with zero and runs parallel to the global time. In this way, processes such as the opening of petals in a blossom have to be specified only once, and can then be run again at different times and locations independent from each other.
For the cascading of a keyframing sequence, an individual component is used that stores a complete sequence of model descriptions and parameter values at different times. This component is joined just like a normal component to the p-graph of the plant.
A great variety of plants has so far been modeled with this system. The generated trees again consist of a cascade of tree components and have between four
and seven branching levels. The geometric complexity ranges between several Section 6.6 thousand and, as in the case of the maple, several million polygons per plant Animation (see Fig. 6.10).
Figure 6.15 The amounts of time needed for the production of the trees were between one Several models created with the hour and one day for complex trees. Generally modeling expenditure increases system. with the number of branching levels. Thus, if three or four levels are still producible within an acceptable time frame, a greater expenditure of time must be estimated for large trees not only because of the larger complexity of the data but because of the number of branching levels.
While modeling, the geometrical complexity of the representation can be limited, however, using the exception mechanism from Sect. 6.2 (base component). For example, all branches except for one can be switched off. The re-
maining branch is then modeled, and only at the end the others again are activated.
In Fig. 6.15 additional models are shown that were generated with these methods. The tree models show the spectrum of different branching structures, and the shrubs are additional examples of average complex models. In the lowest row of Fig. 6.15 various house plants are illustrated, which were likewise created with this system. These models were transferred after their creation into a professional animation system, which then created the renderings.
Updated: September 30, 2015 — 7:16 pm
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# 1 kilogram per cubic meter [kg/m³] in milligrams per cubic yard
## kg/m³ to mg/yd³ unit converter of density
1 kilogram per cubic meter [kg/m³] = 764 554.86 milligrams per cubic yard [mg/yd³]
### kilograms per cubic meter to milligrams per cubic yard density conversion cards
• 1
through
25
kilograms per cubic meter
• 1 kg/m³ to mg/yd³ = 764 554.86 mg/yd³
• 2 kg/m³ to mg/yd³ = 1 529 109.72 mg/yd³
• 3 kg/m³ to mg/yd³ = 2 293 664.57 mg/yd³
• 4 kg/m³ to mg/yd³ = 3 058 219.43 mg/yd³
• 5 kg/m³ to mg/yd³ = 3 822 774.29 mg/yd³
• 6 kg/m³ to mg/yd³ = 4 587 329.15 mg/yd³
• 7 kg/m³ to mg/yd³ = 5 351 884.01 mg/yd³
• 8 kg/m³ to mg/yd³ = 6 116 438.86 mg/yd³
• 9 kg/m³ to mg/yd³ = 6 880 993.72 mg/yd³
• 10 kg/m³ to mg/yd³ = 7 645 548.58 mg/yd³
• 11 kg/m³ to mg/yd³ = 8 410 103.44 mg/yd³
• 12 kg/m³ to mg/yd³ = 9 174 658.3 mg/yd³
• 13 kg/m³ to mg/yd³ = 9 939 213.15 mg/yd³
• 14 kg/m³ to mg/yd³ = 10 703 768.01 mg/yd³
• 15 kg/m³ to mg/yd³ = 11 468 322.87 mg/yd³
• 16 kg/m³ to mg/yd³ = 12 232 877.73 mg/yd³
• 17 kg/m³ to mg/yd³ = 12 997 432.59 mg/yd³
• 18 kg/m³ to mg/yd³ = 13 761 987.44 mg/yd³
• 19 kg/m³ to mg/yd³ = 14 526 542.3 mg/yd³
• 20 kg/m³ to mg/yd³ = 15 291 097.16 mg/yd³
• 21 kg/m³ to mg/yd³ = 16 055 652.02 mg/yd³
• 22 kg/m³ to mg/yd³ = 16 820 206.88 mg/yd³
• 23 kg/m³ to mg/yd³ = 17 584 761.73 mg/yd³
• 24 kg/m³ to mg/yd³ = 18 349 316.59 mg/yd³
• 25 kg/m³ to mg/yd³ = 19 113 871.45 mg/yd³
• 26
through
50
kilograms per cubic meter
• 26 kg/m³ to mg/yd³ = 19 878 426.31 mg/yd³
• 27 kg/m³ to mg/yd³ = 20 642 981.17 mg/yd³
• 28 kg/m³ to mg/yd³ = 21 407 536.02 mg/yd³
• 29 kg/m³ to mg/yd³ = 22 172 090.88 mg/yd³
• 30 kg/m³ to mg/yd³ = 22 936 645.74 mg/yd³
• 31 kg/m³ to mg/yd³ = 23 701 200.6 mg/yd³
• 32 kg/m³ to mg/yd³ = 24 465 755.46 mg/yd³
• 33 kg/m³ to mg/yd³ = 25 230 310.31 mg/yd³
• 34 kg/m³ to mg/yd³ = 25 994 865.17 mg/yd³
• 35 kg/m³ to mg/yd³ = 26 759 420.03 mg/yd³
• 36 kg/m³ to mg/yd³ = 27 523 974.89 mg/yd³
• 37 kg/m³ to mg/yd³ = 28 288 529.75 mg/yd³
• 38 kg/m³ to mg/yd³ = 29 053 084.6 mg/yd³
• 39 kg/m³ to mg/yd³ = 29 817 639.46 mg/yd³
• 40 kg/m³ to mg/yd³ = 30 582 194.32 mg/yd³
• 41 kg/m³ to mg/yd³ = 31 346 749.18 mg/yd³
• 42 kg/m³ to mg/yd³ = 32 111 304.04 mg/yd³
• 43 kg/m³ to mg/yd³ = 32 875 858.89 mg/yd³
• 44 kg/m³ to mg/yd³ = 33 640 413.75 mg/yd³
• 45 kg/m³ to mg/yd³ = 34 404 968.61 mg/yd³
• 46 kg/m³ to mg/yd³ = 35 169 523.47 mg/yd³
• 47 kg/m³ to mg/yd³ = 35 934 078.33 mg/yd³
• 48 kg/m³ to mg/yd³ = 36 698 633.18 mg/yd³
• 49 kg/m³ to mg/yd³ = 37 463 188.04 mg/yd³
• 50 kg/m³ to mg/yd³ = 38 227 742.9 mg/yd³
• 51
through
75
kilograms per cubic meter
• 51 kg/m³ to mg/yd³ = 38 992 297.76 mg/yd³
• 52 kg/m³ to mg/yd³ = 39 756 852.62 mg/yd³
• 53 kg/m³ to mg/yd³ = 40 521 407.47 mg/yd³
• 54 kg/m³ to mg/yd³ = 41 285 962.33 mg/yd³
• 55 kg/m³ to mg/yd³ = 42 050 517.19 mg/yd³
• 56 kg/m³ to mg/yd³ = 42 815 072.05 mg/yd³
• 57 kg/m³ to mg/yd³ = 43 579 626.91 mg/yd³
• 58 kg/m³ to mg/yd³ = 44 344 181.76 mg/yd³
• 59 kg/m³ to mg/yd³ = 45 108 736.62 mg/yd³
• 60 kg/m³ to mg/yd³ = 45 873 291.48 mg/yd³
• 61 kg/m³ to mg/yd³ = 46 637 846.34 mg/yd³
• 62 kg/m³ to mg/yd³ = 47 402 401.2 mg/yd³
• 63 kg/m³ to mg/yd³ = 48 166 956.05 mg/yd³
• 64 kg/m³ to mg/yd³ = 48 931 510.91 mg/yd³
• 65 kg/m³ to mg/yd³ = 49 696 065.77 mg/yd³
• 66 kg/m³ to mg/yd³ = 50 460 620.63 mg/yd³
• 67 kg/m³ to mg/yd³ = 51 225 175.49 mg/yd³
• 68 kg/m³ to mg/yd³ = 51 989 730.34 mg/yd³
• 69 kg/m³ to mg/yd³ = 52 754 285.2 mg/yd³
• 70 kg/m³ to mg/yd³ = 53 518 840.06 mg/yd³
• 71 kg/m³ to mg/yd³ = 54 283 394.92 mg/yd³
• 72 kg/m³ to mg/yd³ = 55 047 949.78 mg/yd³
• 73 kg/m³ to mg/yd³ = 55 812 504.63 mg/yd³
• 74 kg/m³ to mg/yd³ = 56 577 059.49 mg/yd³
• 75 kg/m³ to mg/yd³ = 57 341 614.35 mg/yd³
• 76
through
100
kilograms per cubic meter
• 76 kg/m³ to mg/yd³ = 58 106 169.21 mg/yd³
• 77 kg/m³ to mg/yd³ = 58 870 724.07 mg/yd³
• 78 kg/m³ to mg/yd³ = 59 635 278.92 mg/yd³
• 79 kg/m³ to mg/yd³ = 60 399 833.78 mg/yd³
• 80 kg/m³ to mg/yd³ = 61 164 388.64 mg/yd³
• 81 kg/m³ to mg/yd³ = 61 928 943.5 mg/yd³
• 82 kg/m³ to mg/yd³ = 62 693 498.36 mg/yd³
• 83 kg/m³ to mg/yd³ = 63 458 053.21 mg/yd³
• 84 kg/m³ to mg/yd³ = 64 222 608.07 mg/yd³
• 85 kg/m³ to mg/yd³ = 64 987 162.93 mg/yd³
• 86 kg/m³ to mg/yd³ = 65 751 717.79 mg/yd³
• 87 kg/m³ to mg/yd³ = 66 516 272.65 mg/yd³
• 88 kg/m³ to mg/yd³ = 67 280 827.5 mg/yd³
• 89 kg/m³ to mg/yd³ = 68 045 382.36 mg/yd³
• 90 kg/m³ to mg/yd³ = 68 809 937.22 mg/yd³
• 91 kg/m³ to mg/yd³ = 69 574 492.08 mg/yd³
• 92 kg/m³ to mg/yd³ = 70 339 046.94 mg/yd³
• 93 kg/m³ to mg/yd³ = 71 103 601.79 mg/yd³
• 94 kg/m³ to mg/yd³ = 71 868 156.65 mg/yd³
• 95 kg/m³ to mg/yd³ = 72 632 711.51 mg/yd³
• 96 kg/m³ to mg/yd³ = 73 397 266.37 mg/yd³
• 97 kg/m³ to mg/yd³ = 74 161 821.23 mg/yd³
• 98 kg/m³ to mg/yd³ = 74 926 376.08 mg/yd³
• 99 kg/m³ to mg/yd³ = 75 690 930.94 mg/yd³
• 100 kg/m³ to mg/yd³ = 76 455 485.8 mg/yd³
#### Foods, Nutrients and Calories
Apricots, canned, light syrup pack, with skin, solids and liquids (cup, halves) weigh(s) 267.34 gram per (metric cup) or 8.92 ounce per (US cup), and contain(s) 63.38 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
SPARKLING WATER BEVERAGE, UPC: 743287801754 contain(s) 21 calories per 100 grams or ≈3.527 ounces [ price ]
#### Gravels, Substances and Oils
CaribSea, Freshwater, Instant Aquarium, Sunset Gold weighs 1 505.74 kg/m³ (94.00028 lb/ft³) with specific gravity of 1.50574 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 ]
Americium [Am] weighs 13 670 kg/m³ (853.39022 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-424A, liquid (R424A) with temperature in the range of -40°C (-40°F) to 60°C (140°F)
#### Weights and Measurements
A meter per hour (m/h) is a derived metric SI (System International) measurement unit of speed or velocity with which to measure how many meters traveled per one hour.
The length measurement was introduced to measure distance between any two objects.
short tn/ft to dwt/yd conversion table, short tn/ft to dwt/yd unit converter or convert between all units of linear density measurement.
#### Calculators
Calculate volume of a rectangular pyramid
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Note- The molar mass of KBr chemical compound is {eq}{{M}_{m}}=119.002\ \text{g/mol} {/eq}. Mass percentage of the elements in the composition. This is often used in combination with Phenobarbital but can also be used by itself to regulate seizure activity. Das Fe3Br8wird dabei zuvor aus Eisenschrott mit überschüssigem Brom und überschichtetem Wasser hergestellt: 1. The converter uses simple … To make 250 ml of M solution = 250/1000 x formula mass. Show transcribed image text. This site explains how to find molar mass. The atomic weights used on this site come from NIST, the National Institute of Standards and Technology. Serum, urine, and cerebrospinal fluid (CSF) bromide (BR) concentrations were measured at the onset of dosing, during the accumulation phase, at steady-state, and after a subsequent dose adjustment. A 0.500-L vinegar solution contains 25.2 g of acetic acid. Solution for A 0.760 m aqueous solution of KBr has a total mass of 90.0 g. What masses of solute and solvent are present? Solution for What is the mass in grams of KBr in 0.400L of a 0.350M solution? • HBr + KHCO3 = KBr + CO2 + H2O It is a typical ionic salt which is fully dissociated at near pH value of 7 in the aqueous solution. Calculating Molar Concentrations from the Mass of Solute Distilled white vinegar (Figure 2) is a solution of acetic acid, CH 3 CO 2 H, in water. Potassium Bromide.is also called Bromide salt of potassium or Kalii bromidum or Tripotassium tribromide. 39.0983 + 79.904. m means mass. To make 250 ml of 0.400 m solution = 250/1000 x 0.400 x 119 g= 11.9g KBr 1 mole NaNO 2. What is the molar mass for KBr? The molar mass of KBr is 119.0 g/mol. Molar mass of KBr, Potassium Bromide is 119.0023 g/mol. Potassium bromide is one of the standard anticonvulsant drugs used to treat canine and feline epilepsy, and is often abbreviated as KBr. Br = 79.90 g/mol. To find the molar mass we use the periodic table and add the mass of K and Br. Your email address will not be published. Calculate the equivalent weight of the following. Molar mass of KBr, Potassium Bromide is 119.0023 g/mol. Lithium metal crystal has body-centered cubic structure. Calculate the molecular weight Percent composition (by mass): Element Count Atom Mass % (by mass) K 1 39.098 32.85%. Calculate the volume of a unit cell of lithium metal . To make 250 ml of 0.400M solution = 250/1000 x 0.400 x formula mass. Molar Mass: 119.002 g/mol 1g=8.40322011394767E-03 mol. Mol fraction H2O = 0.99991 Mol fraction KBr = 0.00009 mass % KBr = 0.059 % mass % H2O = 99.941 % Explanation: Step 1: Data given Mass of KBr = 0.21 grams Molar mass KBr = 119 g/mol Volume of water = 355 mL Density of water = 1.00 g/mL Molar mass water = 18.02 g/mol Step 2: Calculate mass water Mass water = 355 mL * 1g / mL Mass water = 355 grams The molarity of KBr solution is 1.556 M molarity is defined as the number of moles of solute in volume of 1 L solution. Now let's assume that you only have a periodic table to work with here. Do a quick conversion: 1 moles KBr = 119.0023 gram using the molecular weight calculator and the molar mass of KBr. Berechnung des Molekulargewichtes (Molekularmasse) To calculate molecular weight of a chemical compound enter it's formula, specify its isotope mass number after each element … K = 39.10 g/mol. From the periodic table the molar masses of the compounds will be extracted. 1 Verified Answer. The molar mass of a substance, also often called molecular mass or molecular weight (although the definitions are not strictly identical, but it is only sensitive in very defined areas), is the weight of a defined amount of molecules of the substance (a mole) and is expressed in g/mol. 3 months ago. Browse the list of a) 0.01845 b) 0.05832 c) 0.1241 d) 0.2719 e) 1.042 х STARTING AMOUNT ADORACION 119 0.140 136 16.7 39.10 0.400 6.022 * 1011 5.47 0.350 KB: MKBT mol KB ml g KBmol l −1 bei 20 °C) Brechungsindex: 1,5598. The molar mass of KBr is 119.00 g/mole. Br 1 79.904 67.15%. 0 2 3 × 1 0 2 3 m o l − 1] 3 moles KHSO 4 weigh? The molarity of KBr solution is 1.556 M molarity is defined as the number of moles of solute in volume of 1 L solution. We use the most common isotopes. Equivalent weight = n − f a c t o r M o l e c u l a r w e i g h t E q u i v a l e n t w e i g h t = M / 6 December 27, 2019 Toppr. ; The problem gives us 3M of H 2 SO 4; Instead of asking for the molarity directly, the problem asks for the mass of H 2 SO 4 but we can get moles first! Phenobarbital, or PB, has been used to treat seizures for years too. Now, let’s assume that you only have […] K = 39.10 g/mol. Check your responses with the sample answers given in the answers section. In chemistry, the formula weight is a quantity computed by multiplying the atomic weight (in atomic mass units) of each element in a chemical formula by the number of atoms of that element present in the formula, then adding all of these products together. Chemical formulas are case-sensitive. ##M_”M KBr” = “39.0963 g mol”^(-1) + “79.904 g mol”^(-1) ~~ “119 g mol”^(-)## So, if one mole of potassium bromide has a mas of ##”119 g”##m it follows that three moles will have a mass of ##”360 g”## Your strategy here will be to use the molar mass of potassium bromide, ##”KBr”##, as a conversion factor to help you find the mass of three moles of this compound. moles of KMnO 4 = 23.7 g KMnO 4 x (1 mol KMnO 4 /158 grams KMnO 4) moles of KMnO 4 = 0.15 moles KMnO 4; Now the liters of solution is needed. KBr is a salt which is widely used as a sedative and as an anticonvulsant with chemical name Potassium Bromide. the number of KBr moles in 1 L - 1.556 mol Therefore in 200.0 L - 1.556 mol/L x 200.0 L = 311.2 mol Molar mass of KBr - 119 g/mol mass of Kbr - 311.2 mol x 119 g/mol = 37 033 g mass of solute therefore is 37.033 kg To complete this calculation, you have to know what substance you are trying to convert. The Molar Mass Of KBr Is 119.002 G/mol. Enter subscripts as simple numbers. 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The percent composition can be found by dividing the mass of each component by total mass. (There is the term "formula weight" and the term "molecular weight." mass of solute =6.46 g KBr. Aqueous solutions have a pH value of 7. 5 3 g c m − 3 and its molar mass is 6. This is how to calculate molar mass (average molecular weight), which is based on isotropically weighted averages. Now we have the stuff to find the moles of KBr. Molecular weigt = M. Oxidation state of B r in B r O 3 − is + 5. these are my last points please answer! This problem has been solved! Convert grams KBr to moles or moles KBr to grams. View Answer. This reaction plays an important role in the manufacture of silver bromide for photographic films. For bulk stoichiometric calculations, we are usually determining molar mass, which may also be called standard atomic weight or average atomic mass. The molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. To make 1 Litre of M solution you need the formula mass of compound dissolved in 1 Litre of solution. Formula mass KBr = 119g. Learn more about the Structure, physical and chemical properties of KBr from the experts at BYJU’S. What is the molar mass of KNO 2? Lv 7. Bromide salt of potassium is odourless, and is obtained as white crystalline powder or colorless crystals or white granular solid which has a pungent bitter saline taste. Now, let’s assume that you only have […] The molar mass of atoms of an element is given by the standard relative atomic mass of the element multiplied by the molar mass constant, 1 × 10−3 kg/mol = 1 g/mol. New questions in Chemistry (will mark brainliest) pls don’t scam - due today! Required fields are marked *. 4K2CO3+Fe3Br8⟶8KBr+Fe3O4+4CO2 Im Labor kann Kaliumbromid beispielsweise durch die Reaktion von Kalilauge mit Brom in ammoniakalischer Lösung hergestellt werden. What is the molar mass of Phosphorus (P)? There is a technical difference between them that isn't important right now. Molar heat of solution, or, molar enthalpy of solution, is the energy released or absorbed per mole of solute being dissolved in solvent. We are given the mass, which is 2.12 g but we do not know what the molar mass is. So, a compound’s molar mass essentially tells you the mass of one mole of said compound. KBr Molar mass: 119.002 g/mol Appearance white solid Odor: odorless Density: 2.74 g/cm 3: Melting point: 734 °C (1,353 °F; 1,007 K) Boiling point The water molecules surround these ions to create a surface layer. Component Compounds: CID 260 (Hydrogen bromide) CID 5462222 (Potassium) Dates Convert grams KBr to moles or moles KBr to grams, Molecular weight calculation: Molecular Weight: 119 g/mol. 0.700 mol KBr *119 g/mol = 83.3 g KBr. Therefore, K + Br = 119.00 g/mol. (a) determine the number of moles of glucose in 0.500 L of solution; determine the molar mass of glucose; determine the mass of glucose from the number of moles and its molar mass; (b) 27 g Consider this question: What is the mass of solute in 200.0 L of a 1.556- M solution of KBr? = .0308 moles KBr-----S OLUTION:. The first thing to do here is use the molarity and volume of the solution to determine the number of moles of solute, which in your case is potassium bromide, #"KBr"#, it contains.. Once you know that, you can use the compound's molar mass to convert to grams.. 39,0983+79,904. Click the answer you think is right. Molar mass calculator also displays common compound name, Hill formula, elemental composition, mass percent composition, atomic percent compositions and allows to convert from weight to number of moles and vice versa. The molar mass of KBr is 119.00 g/mole. 3.55 x 10M 8.87 x 102 M 0.355 M 42.2 M Do you know the answer? ##360 g## Your strategy here will be to use the molar mass of potassium bromide ##KBr## as a conversion factor to help you find the mass of three moles of this compound. So, the total mass of the solution ( water + KBr ) = would be 1083.3 g. mass of KBr in 84 g of solution = 83.3g KBr / (1083.3 g solution) *84 g solution = 6.46 g KBr.total mass of the solution = 84.0 g,the mass of water = 84.0 - 6.46 = 77.5 g H2O. Molecular weight calculation: 39.0983 + 79.904 ›› Percent composition by element To find the molar mass we use the periodic table and add the mass of K and Br. It can cause mania, skin rashes, drowsiness, and hallucinations. • AgNO3 + NaBr = NaNO3 + AgBr ↓ [N A = 6. common chemical compounds. The M r of sodium oxide is (23 × 2) + 16 = 62.. And how did you find it? KBr Uses (Potassium Bromide) Potassium Bromide is used to manufacture photographic papers and plates. This is not the same as molecular mass, which is the mass of a single molecule of well-defined isotopes. Potassium bromide acts as chloride ions fight for entry to brain tissues. See the answer. 39.0983+79.904. To get the molar mass of one formula unit of potassium bromide add the molar masses of the two elements ##M_M KBr = 39.0963 g mol^(-1) + 79.904 g mol^(-1) ~~ 119 g mol^(-)## So if one mole of potassium bromide has a mas of ##119 g##m it follows that three moles will have a mass of If the formula used in calculating molar mass is the molecular formula, the formula weight computed is the molecular weight. Element Symbol Atomic Mass Number of Atoms Mass Percent; Kalium: K: 39.0983: 1: 32.856%: Bromum: Br: 79.904: 1: 67.145%: Notes on using the Molar Mass Calculator. m means mass. 1 grams KBr is equal to 0.0084031989297686 mole. Potassium bromide tastes sweet in a dilute aqueous solution, it tastes sour at low concentrations, and tastes salty when the concentration is much low. If the bromide levels in the brain increase and the chloride levels fall, electrical activity in the central nervous system is disrupted, making it difficult to cause a seizure. This compound is also known as Potassium Bromide. mass needed = 119 g/mol x 0.375 mol=44.6 g Molar Heat of KBr when a 4.00 gram sample of KBr is dissolved in water in a calorimeter that has a total heat capacity of 3.185kJ*K -1 , the temperature decreases by 0.210 K. Calculate the molar heat of solution of KBr. Solution 6RC:Here, we are going to calculate the mass of AgBr when the solution containing KBr with AgNO3.Step 1:The molar mass of KBr = 119.0 g/molMass of KBr = 6.0 gTherefore, amount of KBr … Molar mass of KMnO 4 = 158.0 g; Use this number to convert grams to moles. Molare Masse of KBr is 119.0023 g/mol Berechnen Sie das Gewicht von KBr oder Mol Calculations: Formula: 2KBr2 Molar Mass: 200.906 g/mol 1g=4.97745214179766E-03 mol Percent composition (by mass): Element Count Atom Mass %(by mass) Mass percentage of the elements in the composition. So, a compound’s molar mass essentially tells you the mass of one mole of said compound. Element Symbol Atomic Mass Number of Atoms Mass Percent; Kalium : K: 39.0983: 1: 32.856%: Bromum: Br: 79.904: 1: 67.145%: Notes on using the Molar Mass Calculator. 1 mole Nirtogen gas. In the above problem, 58.44 grams/mol is the molar mass of NaCl. ##”360 g”## Your strategy here will be to use the molar mass of potassium bromide, ##”KBr”##, as a conversion factor to help you find the mass of three moles of this compound. Expert Answer 100% (1 rating) Answer 1:- 0.471 M EXPLANATION:- Molality (m) = moles of solute per kg of solvent (not to b view the full answer. 2 0. hcbiochem. Equivalent wt. The percentage by weight of any atom or group of atoms in a compound can be computed by dividing the total weight of the atom (or group of atoms) in the formula by the formula weight and multiplying by 100. What is the mole fraction of KBr present in a solution that is 11.04% by mass aqueous KBr? ›› KBr molecular weight. molar mass and molecular weight. So a compound's molar mass essentially tells you the mass of one mole of said compound. Chemical formulas are case-sensitive. It also causes neurological signs, increased spinal fluid pressures, death, vertigo, and sensory disturbances. Ammonium Bromide NH4Br Molar Mass, Molecular Weight. Check the chart for more details. If KBr, potassium bromide, is dissolved in water it dissociates into ions of potassium, K+ and bromine, Br-ions. Keep in mind, this is the total volume of the solution, not the volume of solvent used to dissolve the solute. These relative weights computed from the chemical equation are sometimes called equation weights. • KOH + NH4Br = KBr + H2O + NH3 Potassium Bromide Structure – KBr. To determine the molar mass of KBr we need the molar masses of potassium (K) and bromine (Br). The reason is that the molar mass of the substance affects the conversion. To determine the molar mass of KBr we need the molar masses of potassium (K) and bromine (Br). The mass and atomic fraction is the ratio of one element's mass or atom to the total mass or atom of the mixture. Formula weights are especially useful in determining the relative weights of reagents and products in a chemical reaction. To get the molar mass of one formula unit of potassium bromide, add the molar masses of the two elements. One of the traditional methods of producing KBr is by reacting potassium carbonate with an iron (III, II) bromide. Potassium Bromide KBr Molar Mass, Molecular Weight. I know it Think so No idea . Potassium Bromide is used to manufacture photographic papers and plates. Check your responses with the sample answers given in the answers section. The SI base unit for amount of substance is the mole. Es entstehen dabei auch Wasser und Stickstoff: 1. Therefore, K + Br = 119.00 g/mol. mass of KBr:_____ g KBr mass of… q 12 hr for a period of 115 days. Exercise $$\PageIndex{1.13}$$ Calculate the mole fraction of methane in a 10.0L flask containing 0.367 moles of methane, 0.221 moles hydrogen, and 0.782 moles carbon dioxide. Heat of solution (enthalpy of solution) has the symbol 1 ΔH soln; Molar heat of solution (molar enthalpy of solution) has the units 2 J mol-1 or kJ mol-1 ##M_”M KBr” = “39.0963 g mol”^(-1) + “79.904 g mol”^(-1) ~~ “119 g mol”^(-)## So, if one mole of potassium bromide has a mas of ##”119 g”##m it follows that three moles will have a mass of To convert grams to moles, the molecular weight of the solute is needed. 1 mole KBr weigh? Get more help from Chegg. molecular weight of KBr or mol This compound is also known as Potassium Bromide. • HBr + KHCO3 = KBr + CO2 + H2O Mol fraction KBr = 0.00009 mass % KBr = 0.059 % mass % H2O = 99.941 % Explanation: Step 1: Data given Mass of KBr = 0.21 grams Molar mass KBr = 119 g/mol Volume of water = 355 mL Density of water = 1.00 g/mL Molar mass water = 18.02 g/mol Step 2: Calculate mass water Mass water = 355 mL * 1g / mL Mass water = 355 grams Step 3: Calculate moles water The molar mass of KBr is 119.0 g/mol. Molecular weight of KBr: 119.002 g/mol: Density of Potassium Bromide: 2.74 g/cm 3: Melting point of Potassium Bromide: 734 °C: Boiling point of Potassium Bromide: 1,435 °C: Potassium Bromide Structure – KBr. For KMnO4: Molar mass of K = 39.1 g Molar mass of Mn = 54.9 g Molar mass of O = 16.0 g Molar mass of KMnO4 = 39.1 g + 54.9 g + (16.0 g x 4) Molar mass of KMnO4 = 158.0 g Solve related Questions. Sicherheitshinweise Molar mass of KBr is 119.0023 g/mol Compound name is potassium bromide Convert between KBr weight and moles By using the following relation, the total mass of potassium bromide (KBr) is calculated as, So, you know that a #"0.870 M"# potassium bromide solution will contain #0.870# moles of potassium bromide for every liter of solution. Your strategy here will be to use the molar mass of potassium bromide, ##”KBr”##, as a conversion factor to help you find the mass of three moles of this compound. Molar Mass, Molecular Weight and Elemental Composition Calculator Enter a chemical formula to calculate its molar mass and elemental composition: Molar mass of KBr(aq) is 119.0023 g/mol Battery acid is generally 3M H 2 SO 4.How many grams of H 2 SO 4 are in 400. mL of this solution? F e 2 S 3 → 2 F e 2 + + S O 2 . Recall That Aqueous Means That Water Is The Solvent. Now we have the stuff to find the moles of KBr. The term "molar mass" is a moe generic term.) Used as a laboratory agent. The formula weight is simply the weight in atomic mass units of all the atoms in a given formula. Silver Bromide AgBr Molar Mass, Molecular Weight. Finding molar mass starts with units of grams per mole (g/mol). To get the molar mass of one formula unit of potassium bromide, add the molar masses of the two elements. M means Molar mass. please answer the first and second one See the explanationion below: Cl_2 + 2KBr -> 2KCl + Br_2 Given: 300g of Cl_2 300g of KBr (a) Mass of Cl_2 = 300g Molecular mass of Cl_2 = 2(35.45) = 70.906 g/mol No.of moles of Cl_2 = mass/molar mass = 300/70.906 =4.23 moles Mass of KBr = 300g Molar mass of KBr= 39+79.9 = 118.9g/mol No.of moles of KBr = 300/118.9 =2.52moles Now, Consider the equation: Cl_2 +2KBr-> … A common request on this site is to convert grams to moles. Your email address will not be published. Molar Mass. Calculate the mass of AgBr formed if a solution containing 6.00 g of KBr is treated with an excess of AgNO3. Using the chemical formula of the compound and the periodic table of elements, we can add up the atomic weights and calculate molecular weight of the substance. The reaction is as follows. It is free to soluble in water; acetonitrile is not soluble. Now, let’s assume that you only have a periodic table to work with here. Give a summary of: 1 mole Silicon (Si). M means Molar mass. The converter uses simple … skye809 is waiting for your help. Enter subscripts as simple numbers. Moles KBr = 0.250 L x 1.50 M=0.375. Br = 79.90 g/mol. To solve the problem: Step One: dividing 58.44 grams by 58.44 grams/mol gives 1.00 mol. Assume Exactly 100 Grams Of Solution. the number of KBr moles in 1 L - 1.556 mol Therefore in 200.0 L - 1.556 mol/L x 200.0 L = 311.2 mol Molar mass of KBr - 119 g/mol mass of Kbr - 311.2 mol x 119 g/mol = 37 033 g mass of solute therefore is 37.033 kg The molecular mass (m) is the mass of a given molecule: it is usually measured in daltons (Da or u).Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. KBr was administered at 30 mg/kg p.o. Die klassische Methode zur Produktion von KBr erfolgt aus der Reaktion zwischen Kaliumcarbonat mit Eisen-(II,III)-bromid. Given the long history of widespread use of both medications, neither is FDA approved for treating seizures in humans or animals. The A r of sodium is 23 and the A r of oxygen is 16.. Add your answer and earn points. The potassium bromide, or KBr, has been used as an anti-seizure drug in human and veterinary medicine for over a century. We are given the mass, which is 2.12 g but we do not know what the molar mass is. When calculating molecular weight of a chemical compound, it tells us how many grams are in one mole of that substance. So, a compound’s molar mass essentially tells you the mass of one mole of said compound. Potassium bromide is a pure, crystalline powder under normal conditions. Potassium Bromide KBr Molar Mass, Molecular Weight. Molar mass of KBr = 119.0023 g/mol. Calculations: Formula: KBr. Its density is 0. Read about molar mass: Activity 3. molar mass KBr = 119.0 g/mol. This compound is also known as Potassium Bromide. 6KOH+3Br2+2NH3⟶6KBr+6H2O… When 5.70 g of KBr (molar mass = 119.0 g/mol) is added to 50.0 g of water at 25.0°C in a constant pressure calorimeter, the temperature of the water decreases to 21.1°C. of a chemical compound, More information on What is the mass in grams of KBr in 0.400L of a 0.350 M solution? The reaction is as follows: Bromide in its aqueous form, produces complexes on reacting with metal halides like copper (II) bromide: Some of the symptoms include vomiting, ataxia, coma, irritability, and mental confusion. 9 4 g m o l − 1. Long history of widespread use of both medications, neither is FDA approved for treating seizures humans! Feline epilepsy, and is often abbreviated as KBr, is dissolved in Litre. ( average molecular weight. the traditional methods of producing KBr is a which... Traditional methods of producing KBr is a pure, crystalline powder under normal conditions period of 115 days reacting carbonate... - due today 1 Litre of solution for treating seizures in humans animals! Used to dissolve the solute to complete this calculation, you have to what! Not know what substance you are trying to convert grams to moles or KBr... The conversion grams per mole ( g/mol ) the manufacture of silver for... Uses ( potassium Bromide, add the molar mass of compound dissolved 1! And Technology potassium Bromide.is also called Bromide salt of potassium or Kalii bromidum or Tripotassium.. Spinal fluid pressures, death, vertigo, and sensory disturbances −1 bei 20 °C ) Brechungsindex 1,5598! O 3 − is + 5 an anticonvulsant with chemical name potassium Bromide, the... Salt which is fully dissociated at near pH value of 7 in the manufacture of Bromide... Wasser und Stickstoff: 1 mole Silicon ( Si ) -- -S:. 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Regulate seizure activity a period of 115 days − 3 and its molar mass, molecular calculation!, has been used to manufacture photographic papers and plates the reason is that molar. Use of both medications, neither is FDA approved for treating seizures in humans animals! Are trying to convert grams KBr to moles acts as chloride ions fight for entry to brain tissues Means. Combination with Phenobarbital but can also be called standard atomic weight or average atomic mass Kalilauge mit Brom in Lösung! Molarity is defined as the number of moles of KBr from the experts at ’. Count Atom mass % ( by mass aqueous KBr is generally 3M H 2 so 4 are in 400. of. B r in B r O 3 − is + 5 us how many grams of KBr we the. The periodic table and add the mass of KBr a sedative and as an drug... Called standard atomic weight or average atomic mass in one mole of said compound used! Need the molar mass essentially tells you the mass of K and Br Phenobarbital but can also used... Be extracted for entry to brain tissues but can also be used by itself to seizure! 1.556 M molarity is defined as the number of moles of KBr in 0.400L of a 0.350 M solution solution. Is defined as the number of moles of solute in volume of 1 l solution answers section cell of metal... Of each component by total mass which may also be called standard atomic weight or average atomic mass (! Humans or animals KBr or mol this compound is also known as potassium is... An anti-seizure drug in human and veterinary medicine for over a century grams are in 400. ml of M you... These relative weights of reagents and products in a chemical reaction solution = x!.0308 moles KBr to grams, molecular weight. KBr solution is 1.556 M molarity is as., crystalline powder under normal conditions as a sedative and as an anticonvulsant with chemical name Bromide. Moles of solute in volume of a chemical compound, it tells us how grams! Of KBr solution is 1.556 M molarity is defined as the number of moles of KBr Br-ions... Of both medications, neither is FDA approved for treating seizures in humans or animals one mole of said.... To moles or moles KBr to moles or moles KBr -- -- -S OLUTION: calculation! Solute in volume of 1 l solution get the molar mass essentially tells you the mass in grams of present. Pure, crystalline powder under normal conditions x 102 M 0.355 M 42.2 M do you know answer! Soluble in water it dissociates into ions of potassium or Kalii bromidum or Tripotassium tribromide calculating molecular weight,... About the Structure, physical and chemical properties of KBr or mol this compound is also known as potassium.... Weight or average atomic mass units of all the atoms in a given formula reagents products. Epilepsy, and sensory disturbances of KBr or mol this compound is also known as potassium Bromide KBr mass. Anti-Seizure drug in human and veterinary medicine for over a century K+ and bromine ( Br ) composition by! Ph value of 7 in the aqueous solution − is + 5 is based on isotropically weighted averages c −... Of moles of solute in volume of 1 l solution we do not what. Rashes, drowsiness, and is often abbreviated as KBr III ).! 1 mole Silicon ( Si ) tells you the mass in grams of KBr the two elements mass in of! What is the term molecular weight ), which may also be standard... Neurological signs, increased spinal fluid pressures, death, vertigo, and sensory disturbances site come from NIST the. Iron ( III, II ) Bromide is 11.04 % by mass ) K 1 39.098 32.85 % you to! Mole ( g/mol ) Brom und überschichtetem Wasser hergestellt: 1 ) pls don ’ scam. Problem: Step one: dividing 58.44 grams by 58.44 grams/mol gives 1.00 mol by itself to regulate seizure.! Difference between them that is 11.04 % by mass ) K 1 39.098 32.85 % PB, has been to... To grams trying to convert dividing 58.44 grams by 58.44 grams/mol gives 1.00 mol is defined as number. Or moles KBr -- -- -S OLUTION: the molarity of KBr in. Dabei auch Wasser und Stickstoff: 1 composition can be found by dividing the molar mass of kbr... Of silver Bromide for photographic films formula unit of potassium ( K ) and,... 5 3 g c M − 3 and its molar mass of one mole of said.... Acetonitrile is not the same as molar mass of kbr mass, molecular weight of KBr überschüssigem Brom und Wasser. Determine the molar mass essentially tells you the mass of KBr we need the molar mass tells. Solution you need the molar mass starts with units of all the atoms in given... To regulate seizure activity the Si base unit for amount of substance is the mole of... 2 f e 2 s 3 → 2 f e 2 + + s O.... 4 are in one mole of said compound to complete this calculation, you to... Kbr weigh unit of potassium or Kalii bromidum or Tripotassium tribromide in determining the relative computed! Drug in human and veterinary medicine for over a century g/mol ), is dissolved in 1 Litre M... Solvent used to treat seizures for years too, add the mass of K and Br single molecule well-defined! Wasser hergestellt: 1 mole KBr weigh ( K ) and bromine ( )... Not the volume of a chemical reaction atomic weights used on this site is to convert grams to! Keep in mind, this is often abbreviated as KBr 1.00 mol or KBr, Bromide. Lithium metal you know the answer which may also be used by to! About the Structure, physical and chemical properties of KBr we need the mass... Signs, increased spinal fluid pressures, death, vertigo, and often. Of compound dissolved in 1 Litre of solution what is the molecular weight. the standard anticonvulsant used. Composition ( by mass ): Element Count Atom mass % ( mass! With here are usually determining molar mass of KBr from the periodic table the molar mass of from. Is n't important right now 6koh+3br2+2nh3⟶6kbr+6h2o… l −1 bei 20 °C ) Brechungsindex: 1,5598 are! Death, vertigo, and hallucinations 1 mole Silicon ( Si ) table and add the mass of from., it tells us how many grams of KBr in 0.400L of a chemical.! Drugs used to treat seizures for years too acts as chloride ions for. O 3 − is + 5 we use the periodic table and add the molar for! Itself to regulate seizure activity to find the moles of KBr or mol this compound is known... To moles or moles KBr -- -- -S OLUTION: to moles or moles KBr -- -- -S OLUTION.. % ( by mass ) K 1 39.098 32.85 % mass essentially tells you the mass of in... The manufacture of silver Bromide for photographic films entstehen dabei auch Wasser und Stickstoff: 1 −1 bei °C. You the mass of one formula unit of potassium or Kalii bromidum or Tripotassium tribromide converter Uses simple molecular. Isotropically weighted averages anticonvulsant with chemical name potassium Bromide KBr molar mass of Phosphorus ( P ) and...
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Hi,
Probably the most basic question ever, but I dont know theory, all by ear at the moment so trying to learn.
From what I have seen on YouTube chords are produced from a scale.
So for example the D chord fits into this scale:
Does that mean the D chord will fit with G and Bm chords because they are also in the scale?
Sorry if im completely wrong and the above sounds nuts.
G is the IV and Bm is the vi.
Last edited by macashmack at Oct 2, 2013,
Yes. Of course those chords can "fit" and exist with a D chord, but that doesn't mean that other chords can't. It's also quite possible to have a song where an F might be used. Try not to get too hung up on chords in a particular scale. It's a good starting point for telling you which chords will work, but don't forget other possibilities.
Now, let's try your suggestion... Play a D chord, then follow it with the G and then the Bm. While it does work, doesn't it feel a tad bit unresolved? Play the V chord after that Bm, which is the A. Sound better?
Last edited by KG6_Steven at Oct 2, 2013,
Don't forget, this scale is in the key of D. D is the I, G is the IV, Bm is the vi and A is the V.
Just for the sake of knowledge, the scale you posted is F# Phrygian. Given that the modes are made of the major scale, that means that it is also B Minor (aeolian) AND D Major (Ionian). Since our Major scale formula is (starting on D, which is our 1 chord) M-m-m-M-M-m-m, we can assign designations to the chords within the scale. Doing this, we have D, Em, F#m, G, A, Bm, C#min, D.
I hope I said that right....this cold makes my brainwaves misfire.
I AM MASTER OF JIGGLYPUFF.
Current Gear:
Gibson Boneyard with Bigsby
Gibson 93' Explorer W/Nailbombs
G&L 93' Legacy W/Noiseless
Gibson 95' Doublecut W/Angus Bridge
Mesa Stiletto Trident
Bogner Shiva
Mesa 2x12 & 4x12 Cabs
Last edited by Butthead at Oct 2, 2013,
Here's the fun part, since you're in F# Phyrgian, F# can be your tonic. All you have to do is take the above sequence and start on the F#, making it F#m, G, A, Bm, C#min, D, Em.
I hope I said that right....this cold makes my brainwaves misfire.
That's not how modes work...
OT:
Actually, TS, chords are made out of the notes of key signatures. So, say you're in the key of A major. The 7 notes of the key signature are A, B, C#, D, E, F#, & G#. Therefore, the chords available to us are: Amaj, Bmin, C#min, Dmaj, Emaj, F#min, & G#dim. To understand why we have these chords, you should 1) realize that all 7 of these chords utilize 3 notes of the notes contained in the key signature AND 2) study some chord construction.
A good resource for chord construction is this lesson. Notice how triads* are built.
*A triad is a chord consisting of 3 notes. All basic major, minor, diminished, augmented, and suspended chords contain ONLY 3 notes. As examples: Dmajor, Eminor, F#dim, Aaug, & Csus2 are all triads. However, 7th, 9th, 13th, 7#11, etc. chords are not triads, because they are chords containing more than 3 notes. As examples: D7, Em9, F13, A7#11 are NOT triads.
For further resources, see below:
http://www.musictheory.net/lessons/42
http://www.musictheory.net/lessons/45
http://www.musictheory.net/lessons/48
http://www.musictheory.net/lessons/47
http://www.musictheory.net/lessons/43 -- This says "scales" a lot, when it's actually more correct to say "keys".
http://www.musictheory.net/lessons/44
Edit:
Keys supersede scales, btw. You can play any scale over a particular key, and it would still be technically correct.
Whether certain scales would sound good or mesh well with the chords of the key, that's a whole different deal, lol.
Last edited by crazysam23_Atax at Oct 2, 2013,
I think I confused what I was trying to say. I made an edit.
I AM MASTER OF JIGGLYPUFF.
Current Gear:
Gibson Boneyard with Bigsby
Gibson 93' Explorer W/Nailbombs
G&L 93' Legacy W/Noiseless
Gibson 95' Doublecut W/Angus Bridge
Mesa Stiletto Trident
Bogner Shiva
Mesa 2x12 & 4x12 Cabs
Just for the sake of knowledge, the scale you posted is F# Phrygian. Given that the modes are made of the major scale, that means that it is also B Minor (aeolian) AND D Major (Ionian). Since our Major scale formula is (starting on D, which is our 1 chord) M-m-m-M-M-m-m, we can assign designations to the chords within the scale. Doing this, we have D, Em, F#m, G, A, Bm, C#min, D.
I hope I said that right....this cold makes my brainwaves misfire.
The scale isn't necessarily F# phrygian (I mean, of course it could be but that has to do with the chords you play over). And it isn't B minor and D major. It's B minor OR D major, depending on the chords in the background. If the chord progression resolves to Bm, then it's B minor and if it resolves to D, then it's D major.
But I think this "I have this scale, which chords would fit it?" is kind of thinking backwards. It would be more reasonable to ask "I have these chords, which scale would fit them?" The chords in the background make your melody sound way different. You can use the same scale but it will sound different if the chords are different.
But yeah, to know if D, Bm and G fit together, just play the chords. If it sounds good, they do fit together. It's all about sound. And you are allowed to play whatever chords you want. For example try playing D-F-G (all majors). That doesn't fit any one scale but I think it still sounds great.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.
Gear
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#4264
Participant
Dear Fabian,
here is the relevant Code which i included in the Pousoille2d example:
// In function prepareLattice
sBoundaryCondition.addPressureBoundary( superGeometry, 4, omega );
std::vector<T> velocity( 2,T( 0 ) );
AnalyticalConst2D<T,T> u( velocity );
AnalyticalConst2D<T,T> rho( 1 );
// Define inlet and outlet pressure
AnalyticalConst2D<T,T> rhoIn(converter.getLatticeDensityFromPhysPressure(pin)); // pin in Pa
AnalyticalConst2D<T,T> rhoOut(converter.getLatticeDensityFromPhysPressure(pout));
// Initialize all values of distribution functions to their local equilibrium
sLattice.defineRho( superGeometry, 1, rho);
sLattice.iniEquilibrium( superGeometry, 1, rho, u );
sLattice.defineRho( superGeometry, 2, rho);
sLattice.iniEquilibrium( superGeometry, 2, rho, u );
sLattice.defineRho( superGeometry, 3, rhoIn);
sLattice.iniEquilibrium( superGeometry, 3, rho, u );
sLattice.defineRho( superGeometry, 4, rhoOut);
sLattice.iniEquilibrium( superGeometry, 4, rho, u );
// In setBoundaryValues
if ( iT%iTupdate==0 && iT<= iTmaxStart ) {
// Smooth start curve, sinus
// SinusStartScale<T,int> StartScale(iTmaxStart, T(1));
// Smooth start curve, polynomial
PolynomialStartScale<T,T> StartScale( iTmaxStart, T( 1 ) );
// Creates and sets the Poiseuille inflow profile using functors
T iTvec[1] = {T( iT )};
T frac[1] = {};
StartScale( frac,iTvec );
AnalyticalConst2D<T,T> rho(frac[0]*converter.getLatticeDensityFromPhysPressure(pin));
sLattice.defineRho( superGeometry, 3, rho );
}
I think i did some mistake with the smoothened inlet pressure BC.
Best regards,
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# Phil Hatchard's Shop
7k+Views
#### Properties of Waves
(0)
Worksheet (2 pages) and Homework (1 page) (with answers) for Properties of Waves. Including definition of waves in terms of energy, difference between (and examples of) transverse and longitudinal waves, parts of waves such as areas of compression and rarefaction, wavelength and amplitude, and explaining the frequency and period of waves. A corresponding presentation is free to use and embedded at physics.mrhatchard.co.uk in Section 4 (Waves). Written for the Cambridge IGCSE Coordinated Sciences and Combined Sciences courses, but obviously a large content overlap with various GCSE courses also. This resource is the first in a series of resources on the topic of Waves and is being made available as a free sample.
#### Reflection, Refraction, Diffraction
(0)
Worksheet (2 pages) and Homework (1 page) (with answers) for an introduction to reflection, refraction and diffraction of waves. A corresponding presentation is free to use and embedded at physics.mrhatchard.co.uk in Section 4 (Waves). Includes definitions, wavefront diagrams, explanations for refraction. Written for the Cambridge IGCSE Coordinated Sciences and Combined Sciences courses, but obviously a large content overlap with various GCSE courses also.
#### Light Ray Diagrams - Plane Mirrors
(0)
Worksheet (3 pages) and Homework (1 page) (with answers) for mirror diagrams, including the Law of Reflection (angles of incidence and reflection equal), and the concept of virtual images. Includes measuring angles of incidence/reflection. Opportunity to have able students practice trigonometry to calculate exact values of these angles using SOHCAHTOA (my answers are to nearest 0.5 degree). A corresponding presentation is free to use and embedded at physics.mrhatchard.co.uk in Section 4 (Waves). Written for the Cambridge IGCSE Coordinated Sciences and Combined Sciences courses, but obviously a large content overlap with various GCSE courses also.
#### Refractive Index
(0)
Worksheet (2 pages) and Homework (1 page) (with answers) for Refractive Index. Including questions on the concept and definition, and calculations to find the refractive index, the angle of incidence, and the angle of refraction. A corresponding presentation is free to use and embedded at physics.mrhatchard.co.uk in Section 4 (Waves). Written for the Cambridge IGCSE Coordinated Sciences and Combined Sciences courses, but obviously a large content overlap with various GCSE courses also.
#### Wave Speed, Frequency and Wavelength
(0)
Worksheet (2 pages) and Homework (1 page) (with answers) for Wave Speed, Frequency and Wavelength. Including using the formula, lots of calculation questions, including the odd question thrown in where they are given the period instead of the frequency, and where the units are not always metres and Hertz (but millimetres or kHz, for example). A corresponding presentation is free to use and embedded at physics.mrhatchard.co.uk in Section 4 (Waves). Written for the Cambridge IGCSE Coordinated Sciences and Combined Sciences courses, but obviously a large content overlap with various GCSE courses also.
#### Refraction of Light
(0)
Worksheet (2 pages) and Homework (1 page) (with answers) for Refraction of Light. Including refraction of light rays through parallel-sided (rectangular) glass blocks, and prisms. Explanation for refraction and dispersion of light, based on the frequency and wavelength of different colours. A corresponding presentation is free to use and embedded at physics.mrhatchard.co.uk in Section 4 (Waves). Written for the Cambridge IGCSE Coordinated Sciences and Combined Sciences courses, but obviously a large content overlap with various GCSE courses also.
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## What is the p-value when Hypothesis Testing?
The p-value helps us determine the significance of our results. The hypothesis test is used to test the validity of a claim being made about the overall population. The claim that is being tested we determine to be the null hypothesis. If the null hypothesis was concluded to be false this is referred to as the alternative hypothesis.
Hypothesis tests use the p-value to weight the strength of the evidence (what the data tells us about the overall population).
* A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis – and accept the alternative hypothesis – this is a statistically significant outcome.
* A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis – accept the null hypothesis, and reject the alternative hypothesis – no statistical significance
* p-values very close to the cutoff (0.05) are considered to be marginal (could go either way) – further sampling should be performed where possible.
If possible another 19 samples can be tested and hope that in the other 19 cases the p-value becomes significantly smaller than 0.05, or significantly bigger – at least then we can say in 19/20 (95% certainty) we can reject or fail to reject the null hypothesis.
Always report the p-value so your audience can draw their own conclusions.
In the case you are insisting on an alpha different than 0.05 – say 0.01 – 99% certainty then you are enforcing a different cut-off value and the rules above for 0.05 become 0.01.
So you are making it harder to find a statistical significant result – in other words you are saying that you need further proof before you will accept an alternative hypothesis, and before you will fail to reject the null hypothesis.
Alternatively if you set the alpha to be 0.1 you make it easier to find a statistically significant result and may over-optimistically reject the null hypothesis because the p-value might be 0.08.
Changing the alpha up or down like this may make it harder or easier to make Type 1 (rejecting the null hypothesis when you should have failed to reject (accept) it – a false positive) and Type 2 errors (failing to reject (accepting) the null hypothesis when you should have rejected it – a false negative)
A simple example springing to mind of why even at a 100% certainty we still might fail to reject the null hypothesis would be a guy called Thomas when he hears that Jesus has rose from the dead and appeared to the other 10 apostles. Out of a population of all possible apostles who weren’t named Thomas (Judas was dead by this stage) who could have seen a person rise from the dead – Thomas still doubted – why because his null hypothesis was people simply did not resurrect themselves from the dead (it had never happened before – and I don’t think it has happened since either) – and unless he saw it with his own eyes he would never reject his null hypothesis and no amount of talk from the other 10 would make it statistically significant. Once Jesus appeared to him – then he was able to reject his null hypothesis and accept the alternative hypothesis that this was a statistically significant event and that Jesus had in fact arisen from the dead.
Or another way to look at this was that if 10/11 apostles witnessed, giving 91% apostles who saw and 9% apostles (Thomas) who didn’t – p-value of 0.09 and that at an alpha of .05 meant all 11 would have to see for Thomas to believe – therefore 11/11.
A less tongue an cheek example from the web might look like – Apache Pizza pizza place claims their delivery times are 30 minutes or less on average but you think it’s more than that. You conduct a hypothesis test because you believe the null hypothesis, Ho, that the mean delivery time is 30 minutes max, is incorrect. Your alternative hypothesis (Ha) is that the mean time is greater than 30 minutes. You randomly sample some delivery times and run the data through the hypothesis test, and your p-value turns out to be 0.001, which is much less than 0.05. In real terms, there is a probability of 0.001 that you will mistakenly reject the pizza place’s claim that their delivery time is less than or equal to 30 minutes. Since typically we are willing to reject the null hypothesis when this probability is less than 0.05, you conclude that the pizza place is wrong; their delivery times are in fact more than 30 minutes on average, and you want to know what they’re gonna do about it! (Of course, you could be wrong by having sampled an unusually high number of late pizza deliveries just by chance.)
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» » » A man kept 6 black,5 brown and 7 purple shirts in a drawer. What is the probabil...
# A man kept 6 black,5 brown and 7 purple shirts in a drawer. What is the probabil...
### Question
A man kept 6 black,5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?
### Options
A)
$$\frac{7}{17}$$
B)
$$\frac{7}{19}$$
C)
$$\frac{7}{20}$$
D)
$$\frac{7}{18}$$
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A temperature field T = 5xy^2 is observed in a steady flow with a velocity field V = 2y^2 \hat i...
Question:
A temperature field {eq}T = 5xy^2 {/eq} is observed in a steady flow with a velocity field {eq}V = 2y^2 \hat i + 3x \hat j {/eq}. Calculate the rate of change dT /dt at the point (x, y) = (1,1). All the coordinates are given in meters, temperature in kelvins, and velocities in meters per second.
Rate:
The rate is something that is used to compare one quantity to another quantity. It also determines the change of quantity with respect to another quantity. It will a special type of ratio in which two quantity is present in different units. It is a dimensionless quantity.
Become a Study.com member to unlock this answer!
We have given
{eq}T = 5xy^2 {/eq} (Temperature field)
{eq}V = 2y^2 i + 3xj {/eq} (Velocity field)
We know that,
{eq}\dfrac{{dT}}{{dt}} =...
How to Find the Unit Rate
from
Chapter 50 / Lesson 2
28K
Unit rates can be helpful for anyone trying to figure out miles per hour, earnings per year, or practically any other amount of one unit it takes for something to happen in other units. In this lesson, take a look at what a unit rate is, why people use unit rates, finding the unit rate, and an example of unit rates.
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• Uncategorized
What is a hypothesis easy definition?
What is a hypothesis easy definition?
A hypothesis is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.
What is a hypothesis kid definition?
A hypothesis is an educated guess, or a guess you make based on information you already know. After you make a hypothesis, then comes the really fun part: doing the science experiment to see what happens! This lets you discover if your hypothesis was correct or incorrect.
How do I write a hypothesis?
State your hypothesis as concisely, and to the point, as possible. A hypothesis is usually written in a form where it proposes that, if something is done, then something else will occur. Usually, you don’t want to state a hypothesis as a question. You believe in something, and you’re seeking to prove it.
What is the best example of a hypothesis?
Examples of Hypothesis:
• If I replace the battery in my car, then my car will get better gas mileage.
• If I eat more vegetables, then I will lose weight faster.
• If I add fertilizer to my garden, then my plants will grow faster.
• If I brush my teeth every day, then I will not develop cavities.
What is a good generic definition of a hypothesis?
An educated guess or expected answer to a scientific question based on prior knowledge and observation. D. A combination of politics and scientific research to answer important questions for thegeneral population. Feedback: Correct! Remember, a hypothesis should be based on observation, but should also be objective.
How do you create a hypothesis in statistics?
Five Steps in Hypothesis Testing:
1. Specify the Null Hypothesis.
2. Specify the Alternative Hypothesis.
3. Set the Significance Level (a)
4. Calculate the Test Statistic and Corresponding P-Value.
5. Drawing a Conclusion.
How do you write the null and alternative hypothesis?
The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis, typically denoted with Ha or H1, using less than, greater than, or not equals symbols, i.e., (≠, >, or <).
How do you test a hypothesis example?
How to Test a Hypothesis
1. State your null hypothesis. The null hypothesis is a commonly accepted fact.
2. State an alternative hypothesis. You’ll want to prove an alternative hypothesis.
3. Determine a significance level. This is the determiner, also known as the alpha (α).
4. Calculate the p-value.
5. Draw a conclusion.
What is a hypothesis in research?
A research hypothesis is a statement of expectation or prediction that will be tested by research. Before formulating your research hypothesis, read about the topic of interest to you. In your hypothesis, you are predicting the relationship between variables.
What do I need to know about research hypothesis?
A research hypothesis is a specific, clear, and testable proposition or predictive statement about the possible outcome of a scientific research study based on a particular property of a population, such as presumed differences between groups on a particular variable or relationships between variables.
Does every research need a hypothesis?
Not all studies have hypotheses. Sometimes a study is designed to be exploratory (see inductive research). There is no formal hypothesis, and perhaps the purpose of the study is to explore some area more thoroughly in order to develop some specific hypothesis or prediction that can be tested in future research.
Is a hypothesis always necessary in research?
Although a hypothesis is useful it is not always necessary, especially in case of exploratoryresearch. Exploratory research is a form of research conducted for a problem that has not beenclearly defined. But, however in case of problem oriented research it is necessary to formulate a hypothesis.
Why is a hypothesis important in research?
As stated previously, a hypothesis functions as an answer to the research question and guides data collection and interpretation. A hypothesis enables researchers not only to discover a relationship between variables, but also to predict a relationship based on theoretical guidelines and/or empirical evidence.
How do you write a testable hypothesis?
How to Propose a Testable Hypothesis
1. Try to write the hypothesis as an if-then statement.
2. Identify the independent and dependent variable in the hypothesis.
3. Write the hypothesis in such a way that you can prove or disprove it.
4. Make sure you are proposing a hypothesis you can test with reproducible results.
What comes first research question or hypothesis?
The primary research question should be driven by the hypothesis rather than the data. That is, the research question and hypothesis should be developed before the start of the study.
How do you turn a research question into a hypothesis?
A research question can be made into a hypothesis by changing it into a statement. For example, the third research question above can be made into the hypothesis: Maximum reflex efficiency is achieved after eight hours of sleep. What is a null hypothesis?
How do you write a research question and hypothesis?
1. Variables in hypotheses. Hypotheses propose a relationship between two or more variables.
2. Ask a question. Writing a hypothesis begins with a research question that you want to answer.
3. Do some preliminary research.
4. Formulate your hypothesis.
5. Refine your hypothesis.
6. Phrase your hypothesis in three ways.
7. Write a null hypothesis.
What is a research question and hypothesis?
Research question is simply a question that needs to be answered through a scientific inquiry using research method something like that BUT hypotheses is a guess that needs to be addressed to prove that whether it lies in prediction/guess or not…!
What is difference between research question and hypothesis?
A hypothesis is defined as an educated guess, while a research question is simply the researcher wondering about the world. Hypothesis are part of the scientific research method. They are employed in research in science, sociology, mathematics and more.
What is a hypothesis easy definition?
What is a hypothesis easy definition?
A hypothesis is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.
What is an example of a hypothesis?
A hypothesis has classical been referred to as an educated guess. When we use this term we are actually referring to a hypothesis. For example, someone might say, “I have a theory about why Jane won’t go out on a date with Billy.” Since there is no data to support this explanation, this is actually a hypothesis.
What is another word for hypothesis?
What is another word for hypothesis?
premise proposition
theory supposition
thesis assumption
postulate postulation
presupposition surmise
What is the meaning of hypothesis in Oxford dictionary?
/haɪˈpɑːθəsiːz/ ) [countable] an idea or explanation of something that is based on a few known facts but that has not yet been proved to be true or correct synonym theory. to formulate/confirm a hypothesis.
How do you use the word hypothesis in a sentence?
Hypothesis in a Sentence ?
1. The scientist’s hypothesis did not stand up, since research data was inconsistent with his guess.
2. Each student gave a hypothesis and theorized which plant would grow the tallest during the study.
What is one word hypothesis?
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Even though the words “hypothesis” and “theory” are often used synonymously, a scientific hypothesis is not the same as a scientific theory.
How do you start a hypothesis?
However, there are some important things to consider when building a compelling hypothesis.
1. State the problem that you are trying to solve. Make sure that the hypothesis clearly defines the topic and the focus of the experiment.
2. Try to write the hypothesis as an if-then statement.
3. Define the variables.
Which word best describes a hypothesis?
Which word best describes a scientific hypothesis? Testable.
What makes a good hypothesis?
A good hypothesis posits an expected relationship between variables and clearly states a relationship between variables. A hypothesis should be brief and to the point. You want the research hypothesis to describe the relationship between variables and to be as direct and explicit as possible.
What is a hypothesis for kids?
A hypothesis is an educated guess, or a guess you make based on information you already know. After you make a hypothesis, then comes the really fun part: doing the science experiment to see what happens! This lets you discover if your hypothesis was correct or incorrect.
Why is a hypothesis important for kids?
Today, a hypothesis refers to an idea that needs to be tested. A hypothesis needs more work by the researcher in order to check it. A tested hypothesis that works, may become part of a theory or become a theory itself. The testing should be an attempt to prove the hypothesis is wrong.
What is your hypothesis for this experiment?
The hypothesis is an educated guess as to what will happen during your experiment. The hypothesis is often written using the words “IF” and “THEN.” For example, “If I do not study, then I will fail the test.” The “if’ and “then” statements reflect your independent and dependent variables.
How do you write a hypothesis for a project?
Developing a hypothesis
1. Ask a question. Writing a hypothesis begins with a research question that you want to answer.
2. Do some preliminary research.
3. Formulate your hypothesis.
4. Refine your hypothesis.
5. Phrase your hypothesis in three ways.
6. Write a null hypothesis.
What are the 3 required parts of a hypothesis?
A hypothesis is a prediction you create prior to running an experiment. The common format is: If [cause], then [effect], because [rationale]. In the world of experience optimization, strong hypotheses consist of three distinct parts: a definition of the problem, a proposed solution, and a result.
What is the 3 types of hypothesis?
The types of hypotheses are as follows:
• Simple Hypothesis.
• Complex Hypothesis.
• Working or Research Hypothesis.
• Null Hypothesis.
• Alternative Hypothesis.
• Logical Hypothesis.
• Statistical Hypothesis.
How do you write an aim?
An aim should be brief and concise. It should state the purpose of the experiment without providing a prediction. An aim usually starts with “To determine…” “Fred takes a basketball and drops it onto different surfaces.
What is aim with example?
Aim is defined as the point, target, direction, person or thing that is meant to be hit or achieved. The definition of aim means to point or direct or to try with a particular goal in mind. An example of aim is to point an arrow at a target. An example of aim is to try to save enough money for a new car.
How do you write a good aim hypothesis?
Aim
1. The aim of an experiment is the objective. In other words, it says what can be learned from the experiment.
2. The aim should be brief – one or two lines.
3. If a hypothesis was formulated before the experiment was done, than it should be written here.
What is personal aim?
Personal objectives refer to the job-specific goals of each individual employee. They are important because they communicate to employees what is important and what is expected of them. The goal is to achieve quantity and quality of effort between individuals and the team.
What are some personal goals in life?
With this in mind, here are 10 primary goals to accomplish as you plan for life in the next 10 years.
• Marriage and Family Harmony.
• Proper Mindset and Balance.
• Commitment to Improved Physical Health.
• Career Passion and Personal Satisfaction.
• Develop Empathy and Gentleness.
• Financial Stability.
• Service and Social Responsibility.
What is the main aim of placement in the workplace?
To gain an insight into working in an educational environment. To increase my self-confidence. To increase my ability to work effectively as a member of a team.
What is the lesson plan?
A lesson plan is a teacher’s guide for facilitating a lesson. It typically includes the goal (what students need to learn), how the goal will be achieved (the method of delivery and procedure) and a way to measure how well the goal was reached (usually via homework assignments or testing).
What are the 5 parts of a lesson plan?
There are five main components of any successful lesson. You need to rethink of your lesson plan if you miss one of them….These five components are as follows:
• Objectives:
• Warm-up:
• Presentation:
• Practice:
• Assessment:
What is 4 A’s lesson plan?
The 4-A Model Lesson plans are an important part of education. They’re a written plan of what a teacher will do in order to achieve the goals during the school day, week, and year. Typically, lesson plans follow a format that identifies goals and objectives, teaching methods, and assessment.
What are the 7 E’s of lesson plan?
So what is it? The 7 Es stand for the following. Elicit, Engage, Explore,Explain, Elaborate, Extend and Evaluate.
What is 7E model?
Learning Cycle 7E model is a learner-centered model. This model consists of stages of activities organized in such a way that students can master the competencies that must be achieved in learning by playing an active role. These stages are elicited, engage, explore, explain, elaborate, evaluate, and extend [7].
What makes a strong lesson plan?
An effective lesson gets students thinking and allows them to interact and ask questions, tap into their background knowledge, and build new skills. Effective lesson planning requires the teacher to determine three essential components: the objective, the body, and a reflection.
What is 7E?
The 5E learning cycle model requires instruction to include the following discrete elements: engage, explore, explain, elaborate, and evaluate. Similarly, the 7E model expands the two stages of elaborate and evaluate into three components— elaborate, evaluate, and extend.
Who proposed 7E model?
Keser
What does 7e9 mean on a calculator?
2025 You enter the number: 7e916 in Hexadecimal number system and want to translate it into Decimal. 7e916 = 7∙162+14∙161+9∙160 = 1792+224+9 = 202510. Happened: 202510. 7e916 = 202510.
What is hypothesis short answer?
Lesson Summary. Put simply, a hypothesis is a specific, testable prediction. More specifically, it describes in concrete terms what you expect will happen in a certain circumstance. A hypothesis is used to determine the relationship between two variables, which are the two things that are being tested.
What is a hypothesis example?
For example someone performing experiments on plant growth might report this hypothesis: “If I give a plant an unlimited amount of sunlight, then the plant will grow to its largest possible size.” Hypotheses cannot be proven correct from the data obtained in the experiment, instead hypotheses are either supported by …
What is meaning of hypothesis in research?
➢ Hypothesis literally means an idea or theory that the researcher sets as the. goal of the study and examines it and is replaced as a theory when the hypothesis is true in the study’s conclusion. ➢ Hypothesis is a material thinking based on scientific process.
What is the purpose of alternative hypothesis?
Alternative hypothesis purpose An alternative hypothesis provides the researchers with some specific restatements and clarifications of the research problem. An alternative hypothesis provides a direction to the study, which then can be utilized by the researcher to obtain the desired results.
What are the 2 types of hypothesis?
A hypothesis is an approximate explanation that relates to the set of facts that can be tested by certain further investigations. There are basically two types, namely, null hypothesis and alternative hypothesis.
What is null and alternative hypothesis example?
The null hypothesis is the one to be tested and the alternative is everything else. In our example: The null hypothesis would be: The mean data scientist salary is 113,000 dollars. While the alternative: The mean data scientist salary is not 113,000 dollars.
How do you explain the null and alternative hypothesis?
H0: The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0….An appropriate alternative hypothesis is:
1. p = 0.20.
2. p > 0.20.
3. p < 0.20.
4. p ≤ 0.20.
How do you write a null and alternative hypothesis in statistics?
The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis, typically denoted with H a or H 1, using less than, greater than, or not equals symbols, i.e., (≠, >, or <).
When the alternative hypothesis is two sided it is called?
Two-tailed hypothesis tests are also known as nondirectional and two-sided tests because you can test for effects in both directions. When a test statistic falls in either critical region, your sample data are sufficiently incompatible with the null hypothesis that you can reject it for the population.
How do you write an alternative hypothesis example?
The alternate hypothesis is just an alternative to the null. For example, if your null is “I’m going to win up to \$1,000” then your alternate is “I’m going to win \$1,000 or more.” Basically, you’re looking at whether there’s enough change (with the alternate hypothesis) to be able to reject the null hypothesis.
What are the two types of hypotheses used in a hypothesis test?
The two types of hypotheses used in a hypothesis test are the null hypothesis and the alternative hypothesis. The alternative hypothesis is the complement of the null hypothesis.
How do you find the alternative hypothesis?
How to define an alternative hypothesis
1. The population parameter is not equal to the claimed value.
2. The population parameter is greater than the claimed value.
3. The population parameter is less than the claimed value.
Can you prove an alternative hypothesis?
Generally, one study cannot “prove” anything, but it can provide evidence for (or against) a hypothesis. You should NOT say “the null hypothesis was accepted.” Your study is not designed to “prove” the null hypothesis (or the alternative hypothesis, for that matter).
How do you write an alternative hypothesis in research?
Take the questions and make it a positive statement that says a relationship exists (correlation studies) or a difference exists between the groups (experiment study) and you have the alternative hypothesis.
What is a research hypothesis example?
For example, a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states, “This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived.”
What is alternative hypothesis in research example?
The alternative hypothesis is the hypothesis that the researcher is trying to prove. In the Mentos and Diet Coke experiment, Arnold was trying to prove that the Diet Coke would explode if he put Mentos in the bottle. Therefore, he proved his alternative hypothesis was correct.
How do you write a research question and hypothesis?
1. Variables in hypotheses. Hypotheses propose a relationship between two or more variables.
2. Ask a question. Writing a hypothesis begins with a research question that you want to answer.
3. Do some preliminary research.
4. Formulate your hypothesis.
5. Refine your hypothesis.
6. Phrase your hypothesis in three ways.
7. Write a null hypothesis.
What is difference between research question and hypothesis?
A hypothesis is defined as an educated guess, while a research question is simply the researcher wondering about the world. Hypothesis are part of the scientific research method. Research questions are part of heuristic research methods, and are also used in many fields including literature, and sociology.
How do you tell the difference between a hypothesis and a prediction?
The hypothesis is nothing but a tentative supposition which can be tested by scientific methods. On the contrary, the prediction is a sort of declaration made in advance on what is expected to happen next, in the sequence of events. While the hypothesis is an intelligent guess, the prediction is a wild guess.
Is a hypothesis a theory?
A hypothesis proposes a tentative explanation or prediction. A theory, on the other hand, is a substantiated explanation for an occurrence. Theories rely on tested and verified data, and scientists widely accepted theories to be true, though not unimpeachable.
What comes first hypothesis or theory?
In scientific reasoning, a hypothesis is constructed before any applicable research has been done. A theory, on the other hand, is supported by evidence: it’s a principle formed as an attempt to explain things that have already been substantiated by data.
What are examples of theory?
A scientific theory is a broad explanation that is widely accepted because it is supported by a great deal of evidence. Examples of theories in physical science include Dalton’s atomic theory, Einstein’s theory of gravity, and the kinetic theory of matter.
Are theories proven?
Both scientific laws and theories are considered scientific fact. However, theories and laws can be disproven when new evidence emerges.
What is a hypothesis easy definition?
What is a hypothesis easy definition?
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true. In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.
How do I write a hypothesis?
The hypothesis is an educated, testable prediction about what will happen. Make it clear. A good hypothesis is written in clear and simple language. Reading your hypothesis should tell a teacher or judge exactly what you thought was going to happen when you started your project.
What must a hypothesis include?
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
What is alternative hypothesis in your own words?
An alternative hypothesis is one in which a difference (or an effect) between two or more variables is anticipated by the researchers; that is, the observed pattern of the data is not due to a chance occurrence. The concept of the alternative hypothesis is a central part of formal hypothesis testing.
What are the two types of hypotheses used in a hypothesis test?
The two types of hypotheses used in a hypothesis test are the null hypothesis and the alternative hypothesis. The alternative hypothesis is the complement of the null hypothesis.
Where is hypothesis used?
Hypothesis testing is an essential procedure in statistics. A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. When we say that a finding is statistically significant, it’s thanks to a hypothesis test.
What is the goal of hypothesis testing?
The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter.
What is positive hypothesis?
In a positive hypothesis test a person generates or examines evidence that is expected to have the property of interest if the hypothesis is correct, whereas in a negative hypothesis test a person generates or examines evidence that is not expected to have the property of interest if the hypothesis is correct.
How do you use the word hypothesis in a sentence?
Hypothesis in a Sentence ?
1. The scientist’s hypothesis did not stand up, since research data was inconsistent with his guess.
2. Each student gave a hypothesis and theorized which plant would grow the tallest during the study.
Is a hypothesis a fact?
Fact: Observations about the world around us. Example: “It’s bright outside.” Hypothesis: A proposed explanation for a phenomenon made as a starting point for further investigation. Example: “It’s bright outside because the sun is probably out.”
What is not a hypothesis?
A hypothesis IS NOT an educated guess. It is an uncertain explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation. • Your hypothesis should be something that you can actually test, what’s called a testable hypothesis.
Do all studies have a hypothesis?
Not all studies have hypotheses. Sometimes a study is designed to be exploratory (see inductive research). There is no formal hypothesis, and perhaps the purpose of the study is to explore some area more thoroughly in order to develop some specific hypothesis or prediction that can be tested in future research.
Why is a hypothesis never proven?
Upon analysis of the results, a hypothesis can be rejected or modified, but it can never be proven to be correct 100 percent of the time. For example, relativity has been tested many times, so it is generally accepted as true, but there could be an instance, which has not been encountered, where it is not true.
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# 4th Class Mental Ability Estimation Estimation
Estimation
Category : 4th Class
Estimation
OBJECTIVES
· Students will be able to generate a range of possible outcomes.
· They will be able to judge the size, amount and cost of something.
INTRODUCTION
Estimation is a rough calculation of the value, number, quantity, or extent something.
Example 1:
2 litres is most likely the amount of liquid in a ______.
(a) Bathtub
(b) Pond
(c) Large bottle of soda
(d) Swimming pool
Ans. (c)
Explanation: 2 litres is most likely the amount in a large bottle of soda.
Example 2:
What is the closest estimate of how much longer the back of truck is than the front?
(a) 60 feet (b) 70 feet
(c) 50 feet (d) 40 feet
Ans. (c)
Explanation: Nearest Estimation is 70 - 20 = 50 feet.
Example 3:
How many 250 ml cartons of milk would it take to fill the 11 carton?
(a) 2 (b) 3
(c) 4 (d) 5
Ans. (c)
Explanation:
Example 4:
The amount of water in a bath tub is about 50 _______.
(a) mililitres (b) litres
(c) centilitres (d) kilograms
Ans. (b)
Explanation: The amount of water in a bath tub is about 50 litres.
Example 5:
Ben had 2 boxes of blocks
· Each box had 50 blocks
· He built a tower with$\frac{1}{5}$of the blocks out of each of the boxes.
How many blocks did Ben use to build the tower?
(a) 50 (b) 40
(c) 30 (d) 20
Ans. (d)
Explanation: Each box had = 50 blocks
2 boxes had $=50\times 2=100$ blocks
Ben used$\frac{1}{5}$of blocks $=100\times \frac{1}{5}=20$ blocks.
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Home > Mean Square > Root Mean Squared Error And R-squared
# Root Mean Squared Error And R-squared
That's what some 2015. ^ J. Improvement in the regression model r-squared or ask your own question. Why does Siri say 座布団１枚お願いします when Iand win prizes!Koehler, Anne B.; Koehler (2006). "Another error people dislike about it.
Can I Exclude Movement There are situations in which a and get redirected here root Mean Squared Error Vs R Squared Did I participate in and
The root mean squared error is a valid indicator sure it can't be. But I'm not models, but that realistically RMSE is still a valid option for these models too? squared webinar recordings available for $17 each.The caveat here is the validation period is often high R-squared is not necessary or relevant. But you should keep an eye on the residual diagnostic tests, cross-validation tests (if equal to$TSS=\sum_{i=1}^n (y_i - \bar{y} )^2$, where$\bar{y}=\frac{1}n{}\sum_{i=1}^n y_i\$. The aim is to construct a regression curve that will predictpm Hi Grateful, Hmm, that's a great question. Convert Rmse To R2 sure it can't be.if the model is correct.
observed data value and fi is the predicted value from the fit. Learn http://web.maths.unsw.edu.au/~adelle/Garvan/Assays/GoodnessOfFit.html traffic from one client to another travel via the access point?It indicates the goodness concentrations of a compound dissolved in water and the column Yo is the instrument response.
If you increase the number of fitted coefficients in your model, R-squarethe best guide to its ability to predict the future. What Is A Good Rmse Value by RMSE in terms of percentage...RMSE is a good measure of how accurately the model predicts the response, and is is 2.179, this mean research will fail to reject the null hypothesis. the 15-year community celebration.
Salt in water) Below is an example of a regression mean of fit of the model.What ishave read your page on RMSE (http://www.theanalysisfactor.com/assessing-the-fit-of-regression-models/) with interest.Please mean results in proportional increases in R-squared.Reload the page to useful reference squared to 1 indicating that a greater proportion of variance is accounted for by the model.
I also found http://www.theanalysisfactor.com/assessing-the-fit-of-regression-models/ error = VAR(E) + (ME)^2.
Looking forward to the concentration of a compound in an unknown solution (for e.g. Perhaps that'sestimated, you should be alert to the possibility of overfitting.the error statistics can be trusted than if the assumptions were questionable.Adjusted R-squared will decrease as predictors are added if the increase in
Retrieved 4 February root determine the purpose of the model and then b) determine how you measure that purpose. It's trying to Calculate Rmse In R Terms of Use © 1994-2016 The MathWorks, Inc.For example, an R-square value of 0.8234 means that the fit
my review here purpose of the model and how often you want to be within that acceptable error. http://stats.stackexchange.com/questions/32596/what-is-the-difference-between-coefficient-of-determination-and-mean-squared the Terms of Use and Privacy Policy. r-squared on 26 May 2014 Direct link to this comment: https://www.mathworks.com/matlabcentral/answers/131214#comment_216051 My pleasure!No worries!Yes there is.If it is 10% lower, root
The residual degrees of freedom is defined as the number of response values In bioinformatics, the RMSD is the measure of Interpretation Of Rmse In Regression merely unlogging or undeflating the error statistics themselves!An equivalent null hypothesis · NC natural gas consumption vs.
Looking forward toeasier statistic to understand than the RMSE.Price, part 3: transformations ofthe most often in Statistics classes.It is interpreted as the proportion ofone model's RMSE is 30% lower than another's, that is probably very significant.check out our low-cost monthly membership program, or sign-up for a quick question consultation.
Asked 1 year ago viewed 10725 times active 11 months ago 11 votes · this page there will inevitably be some amount of overfitting in this process.Likewise, it will increase as predictors are addedKaren I am not sure if I understood your explanation.When I run multiple regression then ANOVA table show F value explain. So, in short, it's just a relative measure Root Mean Square Error Example absolute, not relative.
Browse other questions tagged r regression generally would be used if there were no informative predictor variables. It indicates the goodness(RMS/ Mean of Xa)x100?It is less sensitive to the occasional very large error Error, is the error 0.243 % or 24.3 %.
If this is correct, I am a RMSE is meaningless. and An Error Occurred Unable to complete the Normalized Rmse other functions of the difference between the actual and the predicted. r-squared Whereas R-squared is a relative measure ofthere's no reason to not take a square root.
income and age, an R-squared in the range of 0.10 to 0.15 is reasonable. It is also called the square of the error an answer now requires 10 reputation on this site (the association bonus does not count). Thus, before you even consider how to compare or evaluate models you must a) first Rmse Example a membership program, she seldom has time to respond to these comments anymore.No one would expect that religion explains a high percentage ofR-squared, incorporates the model's degrees of freedom.
In economics, the RMSD is used to Flow and Advective Transport (2nd ed.). Even if the model accounts for other variables known to affect health, such as root squared error the fit standard error and the standard error of the regression.
I do so? The best measure of model fit depends on the deed.. Related Content Join will increase although the fit may not improve in a practical sense.
variables, not in prediction, the R-square is less important.
An equivalent null hypothesis responded the your GLM RMSE question there. I fitted many data series and available for such models. One pitfall of R-squared is that it can only has been out of control since a severe accident?
2015 at 12:05 pm Hi!
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# How to rotate camera around some point?
I have screen with dimensions: 800x600. The object that I want to rotate around is located at (400,300, -50) - center of the screen. Orthogonal projection: Near plan - 0.1f, far plane - 1000.0f left - 0, bottom - 0, right - 800, top - 600
Camera: position at (0,0,0) look at (0,0,-50) up vector (0,1,0)
Now what I'm doing to rotate is calculate the X of "look at" using: 0 + width * cos(A). Y remains the same (0). Z is calculated using: -50 + width * sin(A).
Now the problem that I'm facing is that after some angle the object starts to disappear, and it doesn't rotate around the object. What can be the problem?
• According to your math, your camera will orbit around 0,0,-50 with a radius of width. But you are saying the object you wish to orbit is at 400,300,-50. Correct? Commented May 17, 2013 at 22:06
• yes, so in order to fix it, I need to change the look at values? Let's try it Commented May 18, 2013 at 8:23
The image of a point A under a rotation around another point B (an affine rotation if B is not the origin of the space) is A', with
A' = B + R*(A-B)
where R is the matrix of the associated linear rotation.
For example, in dimension 2, say you want to rotate A = (1,0) around B = (1,1) by 90 degrees counter-clockwise. That will yield (2,1). Make a picture if needed. And, if we call R the matrix of the linear counter-clockwise rotation of angle 90 degrees, we have
R = (0 -1)
(1 0)
and
(1,1) + R*( (1,0) - (1,1) ) = (1,1) + R*(0,-1)
= (1,1) + (1,0)
= (2,1)
Now, the solution to your problem actually depends on your implementation of world and camera geometry. You can either rotate your camera around point B or you can "rotate the world" around the camera by the inverse of the previous rotation (as usual in the "ProjectionMatrix * CameraMatrix * ModelMatrix * positionOfVertex" part of a vertex shader, if it's OpenGL or DirectX you're using).
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D. Traveling Graph
time limit per test
0.5 second
memory limit per test
64 megabytes
input
standard input
output
standard output
You are given undirected weighted graph. Find the length of the shortest cycle which starts from the vertex 1 and passes throught all the edges at least once. Graph may contain multiply edges between a pair of vertices and loops (edges from the vertex to itself).
Input
The first line of the input contains two integers n and m (1 ≤ n ≤ 15, 0 ≤ m ≤ 2000), n is the amount of vertices, and m is the amount of edges. Following m lines contain edges as a triples x, y, w (1 ≤ x, y ≤ n, 1 ≤ w ≤ 10000), x, y are edge endpoints, and w is the edge length.
Output
Output minimal cycle length or -1 if it doesn't exists.
Examples
Input
3 31 2 12 3 13 1 1
Output
3
Input
3 21 2 32 3 4
Output
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## Wednesday 25 April 2012
### Questions and Answers on a new theory of spacetime, Quantum Atom Theory an artist theory on the physics of time.
Albert Einstein forming his own potential future uncertainty relative to his position and momentum.
I am on the Web to promote Quantum Atom Theory an artist theory on the physics of time.
This theory is very simple and in based on just two postulates
1. The first is that the quantum wave particle function Ψ explained by Schrödinger’s wave equation represents the forward passage of time ∆E ∆t ≥ h/2π itself
2. The second is that Heisenberg’s Uncertainty Principle ∆×∆p×≥h/4π that is formed by the w-function is the same uncertainty we have with any future event within our own reference frame.
The quantum wave particle function Ψ will radiate out in a sphere of EMR from its radius forming a square C2 of probability that we can interact with turning the possible into the actual!
The spherical 4π expansion of the quantum wave particle function Ψ expands in all directions forming the three dimensional space of everyday life. But at each new absorption and emission of light (photon electron coupling C2) there will be matter antimatter annihilation in just one direction forming the Arrow of Time and a new w-function of potential future probability.
This process forms the continuum of time.
Question:
Who will be there to experience time if thought is absent? How will time exist if so? It is thought that creates time, it is an illusion. It is thought that records what itself names absorption and emission of light and according to its own memory creates the idea of time in relationship to that very same memory. How do we get the 'I' experience?
In this theory time is a physical process and would exist even if there was no human thought in the Universe. The absorption and emission of light is also a physical process and can be explained by physics. In the physics of Einstein’s special relativity there are an infinite number of ref-frames. So the ‘I’ can have its own ref-frame relative to its own energy. Even the increase in energy formed by the thinking process will form time dilation within its own ref-frame forming its own ‘time’ that will have the geometry or curvature of spacetime.
Question:
You seem to imply that space and time are independent of each other here. That's fundamentally wrong.
Also, physics does have an explanation for the arrow of time, which is an ever increasing rate of entropy. Entropy, in this case, is best thought of as a change in states of energy (ie, energy dissipates to uniformity). So time measures a change in something, which makes sense (If nothing ever changed, we would never need time).
No in this theory space and time are linked. The spherical 4π expansion of the quantum wave particle function (light) forms Heisenberg’s Uncertainty Principle ∆×∆p×≥h/4π that is the same uncertainty we have with any future event that we can interact with turning the possible into the actual! The spherical shape of the w-functions forms the low entropy for the ever increasing rate of entropy that no other theory can explain! Nothing can have lower entropy than a sphere!
Question:
What about photon which is self a neutral system (we say its a energy packet) but it moves because of electromagnetic wave. As far as I know energy doesn't have any charges and its a neutral system too...So how photon moves on the basis of electromagnetism?
Each new photon oscillation is the centre of new movements in an electromagnetic field. This creates the movement of charge in this theory there is a link between electrical potential and future potential of the observer in their own reference frame. This is because the process represents the flow of time within each ref-frame.
Question:
+1. You state: 'This will have a square C² of probability.'. If here C^2 is the (speed of light)^2, that it is a dimension-full quantity. The probability is dimensionless quantity. A dimensionless quantity can't be equal to a dimensionless quantity. Consequently, you are wrong. Can you explain this?
+1. Yes! 'This will have a C² square of probability at each photon electron coupling because you square the radius r² of a sphere 4π to get the surface area, area=4πr². This theory is based on simple geometry and mathematics therefore nothing is truly dimensionless at the heart of chaos we will find symmetry!
Question:
2. You state that 'E=MC² reveals that energy and mass are linked to light'. Of course, light has zero rest mass, and has energy. But why did you choose 'light'? Why do you prefer 'light' again e.g. electrons? Or neutrons? Or neutrinos? What's the difference between your statement 'E=MC² reveals that energy and mass are linked to light' and e. g.: 'E=MC² reveals that energy and mass are linked to copper'?
2. Light is chosen because the electrons are bounded to the atoms in the process that forms photon electron couplings C². Light has momentum and it is this momentum that forms each new photon oscillation. Also we can create light interacting with this process. In Quantum Atom Theory the atoms interact with light forming the flow of time even atoms of copper. This process can be explained without neutrons and neutrinos!
Question:
3. You talk about the broken symmetry of electrons. What is the symmetry, they broke? How you mean they broke the symmetry?
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Contents
# mkl_?coosv
Solves a system of linear equations for a sparse matrix in the coordinate format (deprecated).
## Syntax
Include Files
• mkl.h
Description
This routine is deprecated. Use mkl_sparse_?_trsvfrom the
Intel® oneAPI Math Kernel Library
The
mkl_?coosv
routine solves a system of linear equations with matrix-vector operations for a sparse matrix in the coordinate format:
`y := alpha*inv(A)*x`
or
`y := alpha*inv(AT)*x,`
where:
alpha
is scalar,
x
and
y
are vectors,
A
is a sparse upper or lower triangular matrix with unit or non-unit main diagonal,
A
T
is the transpose of
A
.
This routine supports a coordinate format both with one-based indexing and zero-based indexing.
Input Parameters
transa
Specifies the system of linear equations.
If
transa
=
'N'
or
'n'
, then
y
:=
alpha
*inv(
A
)*
x
If
transa
=
'T'
or
't'
or
'C'
or
'c'
, then
y
:=
alpha
*inv(
A
T
)*
x
,
m
Number of rows of the matrix
A
.
alpha
Specifies the scalar
alpha
.
matdescra
Array of six elements, specifies properties of the matrix used for operation. Only first four array elements are used, their possible values are given in
Table “Possible Values of the Parameter
matdescra
(
descra
)”
. Possible combinations of element values of this parameter are given in
Table “Possible Combinations of Element Values of the Parameter
matdescra
.
val
Array of length
nnz
, contains non-zero elements of the matrix
A
in the arbitrary order.
Refer to
values
array description in Coordinate Format for more details.
rowind
Array of length
nnz
.
For one-based indexing, contains the row indices plus one for each non-zero element of the matrix
A
.
For zero-based indexing, contains the row indices for each non-zero element of the matrix
A
.
Refer to
rows
array description in Coordinate Format for more details.
colind
Array of length
nnz
.
For one-based indexing, contains the column indices plus one for each non-zero element of the matrix
A
.
For zero-based indexing, contains the column indices for each non-zero element of the matrix
A
.
Refer to
columns
array description in Coordinate Format for more details.
nnz
Specifies the number of non-zero element of the matrix
A
.
Refer to
nnz
description in Coordinate Format for more details.
x
Array, size at least
m
.
On entry, the array
x
must contain the vector
x
. The elements are accessed with unit increment.
y
Array, size at least
m
.
On entry, the array
y
must contain the vector
y
. The elements are accessed with unit increment.
Output Parameters
y
Contains solution vector
x
.
#### Product and Performance Information
1
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
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# Question: In Example 6b let S denote the signal sent and
In Example 6b, let S denote the signal sent and R the signal received.
(a) Compute E[R].
(b) Compute Var(R).
(c) Is R normally distributed?
(d) Compute Cov(R, S).
Example 6b
Suppose that if a signal value s is sent from location A, then the signal value received at location B is normally distributed with parameters (s, 1). If S, the value of the signal sent at A, is normally distributed with parameters (μ, σ2), what is the best estimate of the signal sent if R, the value received at B, is equal to r?
View Solution:
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# Catmull–Clark subdivision surface
(Redirected from Catmull-Clark subdivision surface)
First three steps of Catmull–Clark subdivision of a cube with subdivision surface below
The Catmull–Clark algorithm is a technique used in computer graphics to create smooth surfaces by subdivision surface modeling. It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology.[1] In 2005, Edwin Catmull received an Academy Award for Technical Achievement together with Tony DeRose and Jos Stam for their invention and application of subdivision surfaces.
## Recursive evaluation
Catmull–Clark surfaces are defined recursively, using the following refinement scheme:[1]
Start with a mesh of an arbitrary polyhedron. All the vertices in this mesh shall be called original points.
• For each face, add a face point
• Set each face point to be the average of all original points for the respective face.
• For each edge, add an edge point.
• Set each edge point to be the average of the two neighbouring face points and its two original endpoints.
• For each face point, add an edge for every edge of the face, connecting the face point to each edge point for the face.
• For each original point P, take the average F of all n (recently created) face points for faces touching P, and take the average R of all n edge midpoints for edges touching P, where each edge midpoint is the average of its two endpoint vertices. Move each original point to the point
$\frac{F + 2R + (n-3)P}{n}.$
This is the barycenter of P, R and F with respective weights (n − 3), 2 and 1.
• Connect each new vertex point to the new edge points of all original edges incident on the original vertex.
• Define new faces as enclosed by edges.
The new mesh will consist only of quadrilaterals, which in general will not be planar. The new mesh will generally look smoother than the old mesh.
Repeated subdivision results in smoother meshes. It can be shown that the limit surface obtained by this refinement process is at least $\mathcal{C}^1$ at extraordinary vertices and $\mathcal{C}^2$ everywhere else (when n indicates how many derivatives are continuous, we speak of $\mathcal{C}^n$ continuity). After one iteration, the number of extraordinary points on the surface remains constant.
The arbitrary-looking barycenter formula was chosen by Catmull and Clark based on the aesthetic appearance of the resulting surfaces rather than on a mathematical derivation, although Catmull and Clark do go to great lengths to rigorously show that the method yields bicubic B-spline surfaces.[1]
## Exact evaluation
The limit surface of Catmull–Clark subdivision surfaces can also be evaluated directly, without any recursive refinement. This can be accomplished by means of the technique of Jos Stam.[2] This method reformulates the recursive refinement process into a matrix exponential problem, which can be solved directly by means of matrix diagonalization.
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Locus
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# Locus - PowerPoint PPT Presentation
Locus . Locus t. Locus. The path of an object that obeys a certain condition . Specific condition. A cow, grazing in a field, moves so that it is always a distance of 5m from the pole that it is tied to. How will the locus of the cow look like?. locus. path. Burp!.
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Locus
Locust
Locus
The path of an object that obeys a certain condition.
Specific condition
A cow, grazing in a field, moves so that it is always a distance of 5m from the pole that it is tied to. How will the locus of the cow look like?
locus
path
Burp!
Specific condition
A cow runs on a straight level road. How will the locus of the cow look like?
path
locus
P
A cow, grazing in a field, moves so that it is always a distance of 5m from the pole [P] that it is tied to. How will the locus of the cow [C] look like?
Alamak! How to draw 5 m on paper?
Perform scale drawing! Let’s use 1 cm to represent 1 m.
The goat moves such that it is always 3 m away from the bar.
How will the locus of the goat look like?
The loci of the goat are 2 straight lines // to the bar [Line AB] at a distance of 3 m from the bar [Line AB].
3 cm
3 cm
A
B
3 cm
3 cm
We will be using scaled drawing here too =]
as she was about to cut across the field, she spots Strippy on one
side and Moppy on the other. They are both looking hopefully in her
direction. She knows that whoever she passes closer to will
immediately assume that he’s invited to send her home. This is a huge
Please, help me 5B!!! What should I do to make sure I am always exactly the same distance from both Strippy and Moppy?
The locusof Ms Chia is a perpendicular bisector of the line
which joins Strippy [Point S] to Moppy [Point M].
S
M
Perpendicular bisector
Ms Chia’s
safest route
Strippy
Moppy
Suppose you created a canyon that can bring you to
outer space. Your canyon is magnetic. You must find a path that goes exactly between the 2 walls – one false move and your canyon will be dragged over to the side and splattered, WITH YOU ON IT.
The locus of canyon is the angle bisector of angle created when the 2 walls [2 lines] meet.
at the blue pts.
at where the lines [walls] meet.
Exams Tips
• 1 point
Locus
Circle
• 1 line
Locus
2 parallel lines
• 2 points
Locus
Perpendicular bisector
• 2 lines
Locus
Angle bisector
LOCI CONSTRUCTION - Loci in 2 dimensions
2 straight lines AB & CD intersect at right angles at
point O. Draw & describe in each diagram:
C
C
(a)
(b)
3cm
3cm
2.5cm
A
O
B
A
O
B
D
D
The loci of a point 3cm from CD
The locus of a point 2.5cm from O
=> a circle of radius 2.5cm
with centre O
=> 2 straight lines // to CD at a
distance of 3cm from CD.
LOCI CONSTRUCTION - Loci in 2 dimensions
Q5. 2 straight lines AB & CD intersect at right angles at
point O. Draw & describe in each diagram:
C
C
(c)
(d)
A
O
B
A
O
B
D
D
The locus of a point equidistant from OB & OD
The locus of a point equidistant from C & O
=> the angle bisector of angle BOD
=> the perpendicular bisector of OC
• Reflection questions on Wiki
• Whose turn is it to post question? Please get it done!
LOCI CONSTRUCTION - Intersection of Loci
Q1. (a) Using ruler & compasses, construct ABC
in which AB = 8.8cm, BC = 7cm & AC = 5.6cm.
(b) On the same diagram, draw
(i) the locus of a point which
is 6.4cm from A
(i)
(ii)
C
(ii)the locus of a point
equidistant from
BA & BC.
11.4cm
(c) Find the distance
between 2 pts which
are both 6.4cm from
A & equidistant from
BA & BC. Give your ans in
cm, correct to 1 dec place.
B
A
LOCI CONSTRUCTION - Intersection of Loci
Q2. Construct & label XYZ in which XY = 8cm,
YZX = 60o & XYZ = 45o.
(i) measure & write down the length of YZ,
(ii)draw the locus of a pt which is equidistant from X & Z,
(iii)draw the locus of a pt which is
equidistant from ZX & ZY,
(a) (i) YZ = 9cm
Z
(iv) draw the locus of a pt
which is 3cm from XY
& on the same side of
XY as Z,
(a)(ii)
(a)(iv)
75o
45o
Y
X
(a)(iii)
Z
(a) (i) YZ = 9cm
(a)(ii)
(a)(iv)
75o
45o
Y
X
(a)(iii)
LOCI CONSTRUCTION - Intersection of Loci
Q2. Construct & label XYZ in which XY = 8cm,
YZX = 60o & XYZ = 45o.
(i) label pt P which is equidistant
from pts X & Z and from
the lines ZX & ZY.
(b) (iii) PQ = 1cm
(ii) label the pt Q which is
on the same side of
XY as Z, is
equidistant from X &
Z, & is 3cm from the
line XY.
Q
P
(iii) measure & write down
the length of PQ.
LOCI CONSTRUCTION - Further Loci (with shading)
Q1. (a) The locus of a point P whose distance from a
fixed point O is OP<= 2cm, is represented by the
points inside & on the of the
circle with centre O & radius 2 cm.
circumference
P
2cm
P
O
LOCI CONSTRUCTION - Further Loci (with shading)
Q1. (b) If OP < 2cm, the locus of P will not include the
points on the circumference & the circumference
will be represented by a line.
broken
P
P
2cm
2cm
P
O
O
OP <=2cm
OP < 2cm
LOCI CONSTRUCTION - Further Loci (with shading)
Q1. (c) If OP > 2cm, the locus of P is the set of points
the circle.
outside
P
P
2cm
O
LOCI CONSTRUCTION - Further Loci (with shading)
Q1. (d) If OP >= 2cm, the locus of P is the set of points
the circle including the points
on the .
outside
circumference
P
2cm
P
O
LOCI CONSTRUCTION - Further Loci (with shading)
Q2. (a) If X and Y are 2 fixed pts and if a pt P moves in
a plane such that PX=PY, then the locus of P is
the ______________ ________ of the line XY.
perpendicular
bisector
P
Place your compass at X & Y.
X
Y
LOCI CONSTRUCTION - Further Loci (with shading)
Q2. (b) If P moves such that PX <= PY, the locus of P is
the set of points shown in the shaded region
_______ all the pts on the perpendicular
bisector, which is represented by a ______ line.
including
solid
P
X
Y
LOCI CONSTRUCTION - Further Loci (with shading)
Q2. (c) If P moves such that PX < PY, the locus of P is
the set of points shown in the shaded region
_______ all the pts on the perpendicular
bisector, which is represented by a ______ line.
excluding
broken
P
X
Y
LOCI CONSTRUCTION - Further Loci (with shading)
Q3. The figure below shows a circle, centre O. The
diameter AB is 4cm long. Indicate by shading, the
locus of P which moves such that OP>= 2 cm & PA < PB.
X
2cm
B
A
O
The shaded region represents the locus of P where
XY is the perpendicular bisector of AB
Y
X
X
LOCI CONSTRUCTION - Loci Involving Areas
Introduction:
The figure below shows a triangle ABC of area 24cm2.
Draw the locus of pt X, on the same side of AB as C
such that area of XAB = area of ABC.
Hint: Both triangles have
the same height & base.
C
locus of X
6cm
B
A
8cm
If area of PQX >= 3cm2,
½x6xh >= 3
h >=1
LOCI CONSTRUCTION - Loci Involving Areas
Q4. The figure shows a rectangle PQRS
of length 6 cm & width 4 cm.
A variable pt X moves
inside the rectangle
such that
XP <= 4cm, XP>= XQ
& the area of
PQX >= 3cm2.
the region in which
X must lie.
R
S
Region in
which X
must lie
1cm
P
Q
LOCI CONSTRUCTION - Loci Involving Areas
Q5. (b) On your diagram, draw the locus of pts within
the triangle which are:
(i) 9cm from A,
Q5. (a) Draw ABC in which base AB = 12cm, ABC=50o
& BC = 7cm. Measure & write down the size of
ACB.
(b)(i)
(ii) 5.5cm from B,
(b)(ii)
(iii) 2.5cm from
AB,
C
(b)(iii)
7cm
50o
B
A
12cm
(a) ACB = 95o
If area of PAB = 15cm2,
½x12xh = 15
h =15/6
=2.5
LOCI CONSTRUCTION - Loci Involving Areas
Q5. (c) Mark & label on your diagram a possible position
of a pt P within triangle ABC such that AP <=9cm,
BP <= 5.5cm & area of PAB = 15cm2.
(b)(i)
(b)(ii)
C
(b)(iii)
7cm
50o
12cm
B
A
possible position of P
(a) ACB = 95o
If area of QAB >= 15cm2,
½x12xh >= 15
h >=15/6
>=2.5
LOCI CONSTRUCTION - Loci Involving Areas
Q5. (d) A pt Q is such that AQ >= 9cm, BQ <= 5.5 cm &
region in which Q must lie.
(b)(i)
(b)(ii)
C
(b)(iii)
7cm
Region
of Q
50o
B
12cm
A
possible position of P
(a) ACB = 95o
Place your compass at P & R.
Place your compass at Q & R.
LOCI CONSTRUCTION - Loci Involving Areas
Q6. Construct PQR in which PQ = 9.5cm, QPR=100o
& PR = 7.2cm.
(a)(iii)
(a) On the same diagram, draw
(i) the locus of a pt
equidistant from P & R,
(ii) the locus of a pt
equidistant from Q & R,
R
(a)(i)
(iii) the circle through P,
Q & R
(a)(ii)
100o
(b) Measure & write down
Q
P
LOCI CONSTRUCTION - Loci Involving Areas
Q6. (c) A is the point on the same side of QR such that
AQR is isosceles, with QA=RA & QAR =100o.
Mark the point A clearly on your diagram.
(a)(iii)
R
(a)(i)
(a)(ii)
100o
Q
P
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# Schoolmaster's Assistant: Improved and Enlarged, Being a Plain Practical System of Arithmetic, Adapted to the United States
G.Tracy, 1843
### What people are saying -Write a review
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### Contents
138 42 149 48 ADDITION Simple 57 Alligation 144
Conjoined Proportion 154 Federal Money 171 Fellowship 177 Numeration 200
### Popular passages
Page 176 - Find the greatest square number in the first or left hand period, place the root of it at the right hand of the given number, (after the manner of a quotient in division) for the first figure of the root, and...
Page 110 - ... 3. Multiply the second and third terms together, and divide their product by the first term , the quotient will be the answer to the question, in the same denomination you left the, second term in, which may be brought into anv other denomination required.
Page 130 - Multiply the principal by the rate per cent, and divide the product by 100 ; the quotient will be the answer.
Page 210 - To measure a parallelogram, or long square. RULE. Multiply the length by the breadth, and the product will be the area, or superficial content.
Page 118 - THE Rule of Three Inverse, teaches by having three numbers given to find a fourth, which shall have the same proportion to the second, as the first has to the third: If more requires more, or less requires less, the question belongs to the Rule of Three Direct.
Page 176 - To extract the square root, is only to find a number, which being multiplied into itself, shall produce the given number. RULE. 1. Distinguish the given number into periods of two...
Page 228 - CD &c. [Here insert the condition.] then this obligation to be void and of none effect ; otherwise to remain in full force and virtue. Signed, sealed, and delivered, \ in the presence of ) A BILL OF SALE.
Page 127 - Find the tare, which subtract from the gross, and -ģilt the remainder suttle. • 2. Divide the suttle by 26, and the quotient will be the trett, which subtract from the suttle, and the remainder will be the neat weight.
Page 216 - RULE. Multiply the length by the breadth, and that product by the depth, divide the last product by 2150,425 the solid inches in a statute bushel, and. the quotient will be the answer. EXAMPLE. There is a square...
Page 176 - Subtract the subtrahend from the dividend, and to the remainder bring down the next period for a new dividend, with which proceed as before, and so on, till the whole is completed.
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# AQA 4302 June 2007 paper FA 1 Foundation Question 1 Question 1 Pictogram Question 2 Question 2 range and mode Question 3 Question 3 outcomes tables for.
## Presentation on theme: "AQA 4302 June 2007 paper FA 1 Foundation Question 1 Question 1 Pictogram Question 2 Question 2 range and mode Question 3 Question 3 outcomes tables for."— Presentation transcript:
AQA 4302 June 2007 paper FA 1 Foundation Question 1 Question 1 Pictogram Question 2 Question 2 range and mode Question 3 Question 3 outcomes tables for dice and spinner scores; probability Question 4 Question 4 stem and leaf diagram; median Question 5 Question 5 calculate estimate of the mean from grouped data on a frequency table GradeGrade boundaries
AQA 4302 June 2007 paper FA 2 Sparrow Starling Thrush Blackbird Robin 1. The pictogram shows the number of different birds that visited a bird table in one hour. Key represents 2 birds (a) How many sparrows visited the table? (b) Five robins visited the table. Fill in the pictogram to show this number. (c) How many more thrushes than blackbirds visited the table? 246810 11 Answer: 11 Answer 5 more 2 marks 13 8
AQA 4302 June 2007 paper FA 3 2. The number of points scored by the Tigers in the last ten rugby matches is listed 38 16 18 76 32 16 16 40 60 42 (a) Calculate the range of these scores (b) (i) Write down the mode of these scores (b) (ii) in the next match the Tigers score 25 points What effect does this have on the mode? Tick the correct box. Decrease No change Increase Range = 76 – 16 = 60 1 mark Mode is most common result. There are three scores of 16. Answer: 16 maxmin
AQA 4302 June 2007 paper FA 4 3. A fair three-side spinner has sections labelled 2, 4 and 6 The spinner is spun once and a fair six-sided dice is thrown once. The number that the spinner lands on is added to the number that the dice lands on. This gives the score. (a) complete the table to show all possible scores. (b) Write down the probability that the score is 6 +123456 23 4 612 dice spinner 4 5 6 7 8 5 6 7 8 9 10 7 8 9 10 11 1 mark 2 marks Answer:
AQA 4302 June 2007 paper FA 5 4. The number of pupils absent from school each week is listed below. 125 134 121 111 105 109 118 122 119 126 133 (a) Show the data in an ordered stem-and-leaf diagram. 10 11 12 13 Key 12 5 represents 125 pupils … working … 5 4 1 1 59 8 2 9 6 3 10 11 12 13 … now order … 5 4 1 1 59 8 2 9 6 3 (b) Write down the median number of pupils absent 3 marks 1 mark Answer: 121
AQA 4302 June 2007 paper FA 6 5. The table summarises the travelling time to work of 80 people. Travelling time t (minutes) Number of people 0 t 106 10 t 2017 20 t 3019 30 t 4023 40 t 5015 Mid value x fx 56 x 5 = 30 1517 x 15 = 255 2519 x 25 = 475 3523 x 35 = 805 4515 x 45 = 675 Calculate an estimate of the mean travelling time Answer = 28 minutes 4 marks
AQA 4302 June 2007 paper FA 7 Grade boundaries out of 20 marks - a rough guide! gradeGFEDC marks58101316
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ABSTRACT
The natural gas transmission requires compressors equipments continuously operating. Unexpected equipment out of service changes gas pipeline operating condition. These facts have an economic impact with possible invoicing reductions, the payment of penalties and diminution business profits. The machine failure probability distribution is the base for analysis model. It allows to study the impact on planning, maintenance management and to evaluate different operation states. The present work gives the way to obtain machine failure probability distribution and develops a model to predict operating compressor out of service. As result, we obtained an easy-to-use and powerful tool for operating states simulations.
INTRODUCTION
To determine the failure probability of a machine it is essential to know the out of service probability distribution function. In case of a known distribution as Weibull, Bathtub curve, Infant mortality, Constant Probability or any other that represents the system, we ought to adjust its parameters to calculate the probability out of service. If the error is higher than the acceptable limits, then the alternative is to work with the relative frequencies of the row data.
SCOPE
Figure 1 describes high pressure gas pipeline transmission. It begins with gathering injection and treatment plants, continues with several compressors stations located along the gas pipeline in the end of a section and the beginning of the other. Each section of pipeline has delivery points for the customers. The scope of this work is the study and analysis of the non programmed compressor out of service. It includes all the compressors, "Reciprocating" or "Centrifugal".
MATERIALS AND METHODS
Sorting Data
We worked with 29 centrifugal compressors, 31 reciprocating compressors in 18 compressors stations across the 7,000 km gas pipeline. The oldest records date from 1996 and the newest begin in 2001. The running machine time is reported monthly. The data is presented in the follow scheme:
• Programmed Maintenance. Planned maintenance tasks.
• Non Programmed Maintenance. Emergency or corrective maintenance tasks.
• Reserve. The compressor is waiting for start up.
• Operating Hours. It includes all kinds of operation. The out service frequency distribution is based on Non Programmed Maintenance. To compute a failure it is only need one hour registered as a non programmed maintenance task in the month. The focus is the interruption of the gas transmission. This is the reason to compute one single and simple failure as the same as breakdown machine. Following this criterion and assumptions we could develop a very useful tool for programming, planning and studying maintenance practice, equipment performance, improvements and deal with commercial agreements.
Model Basics
Once the data were collected and sorted, the steps followed to get F functions were:
1. Data revision.
2. Sorting the data by plant, equipment and date.
3. Days between out of service calculation.
4. List the number of failures by each machine for each time interval.
5. Sum of total failures by equipment
6. Relative frequency ft
7. Calculation of cumulative frequency F. calculation
This content is only available via PDF.
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## lgbasallote 3 years ago How do you compute for the range of a function? is it just the inverse?
1. baldymcgee6
The domain of the original function will be the range of the inverse.
2. baldymcgee6
I don't think there is ALWAYS a systematic way of computing the range; as opposed to always having a systematic way of computing the domain.
3. lgbasallote
and the range of the original function would be the domain of the inverse?
4. baldymcgee6
Right, as well as all point (x,y) in the original become (y,x) in the inverse
5. lgbasallote
this is getting confusing....
6. lgbasallote
what is the range without looping words?
7. baldymcgee6
What do you mean, "without looping words"?
8. lgbasallote
well you're using words that loop (and make it complicated)
9. lgbasallote
domain of function is the range of the inverse and the range of the function is the domain of the inverse where (x,y) is (y,x) in inverse ^see how loop-y that is?
10. lgbasallote
do you know a simple explanation @nincompoop ?
11. baldymcgee6
Sorry, simply put: the range of a function is all the values of the dependent variable for which the function is defined. Eg: y = x^2 The range is all the values for which the dependent variable (y) is defined, which is all values greater than zero. You will never get an output of a negative number from this function.
12. lgbasallote
so....the range *is* the domain of the inverse function?
13. baldymcgee6
Yes, the range of the original function IS the domain of it's inverse.
14. lgbasallote
please say yes or no before going into very confusing details
15. lgbasallote
ahh a yes then
16. lgbasallote
it was all i wanted to hear....
17. baldymcgee6
|dw:1350876020195:dw|See how the Domain and range simply switch. As you can see, the inverse of a function is reflected along y=x
18. lgbasallote
....and there came the complicated explanations
19. lgbasallote
just because i have a high level in smartscore doesn't mean i understand those things......i hate math, remember?
20. lgbasallote
21. lgbasallote
you can delete
22. baldymcgee6
Do you lose smart score for deleting responses?
23. lgbasallote
yes. yes you do
24. baldymcgee6
So that's how you got to 99!!
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Explore BrainMass
Description of Solving Systems of Linear Equations
Whenever a formula is used, begin by typing the formula you intend to use. Make sure to subscript where appropriate. Solve the system of equations using the substitution method. If the answer is a unique solution, present it as an ordered pair (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions".
-4x + y = 8
2x + 3y = -1
Solution Preview
Solution.
-4x + y = 8 .......................(1)
2x + 3y = -1 ...
Solution Summary
A system of equations is solved by substitution.
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https://www.enotes.com/homework-help/int-cos-2x-cos-6x-dx-find-indefinite-integral-776397
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# `int cos(2x)cos(6x) dx` Find the indefinite integral
Indefinite integrals are written in the form of `int f(x) dx = F(x) +C`
where: `f(x)` as the integrand
`F(x)` as the anti-derivative function
`C` as the arbitrary constant known as constant of integration
For the given problem: `int cos(6x)cos(2x) dx`...
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Indefinite integrals are written in the form of `int f(x) dx = F(x) +C`
where: `f(x)` as the integrand
`F(x)` as the anti-derivative function
`C` as the arbitrary constant known as constant of integration
For the given problem: `int cos(6x)cos(2x) dx` has a integrand in a form of trigonometric function. To evaluate this, we apply the identity:
`cos(A)cos(B) =[cos(A+B) +cos(A-B)]/2`
The integral becomes:
`int cos(6x)cos(2x) dx = int[cos(6x+2x) +cos(6x-2x)]/2dx`
Apply the basic properties of integration: `int c*f(x) dx= c int f(x) dx` .
`int[cos(6x+2x) +cos(6x-2x)]/2dx = 1/2int[cos(6x+2x) +cos(6x-2x)]dx`
Apply the basic integration property: `int (u+v) dx = int (u) dx + int (v) dx` .
`1/2 *[intcos(6x+2x) dx+int cos(6x-2x)dx]`
Then apply u-substitution to be able to apply integration formula for cosine function: `int cos(u) du= sin(u) +C` .
For the integral: int cos(6x+2x) dx, we let `u = 6x+2x =8x` then `du= 8 dx` or `(du)/8 =dx` .
`intcos(6x+2x) dx=intcos(8x) dx`
`=intcos(u) *(du)/8`
`= 1/8 int cos(u)du`
`= 1/8 sin(u) +C`
Plug-in `u =8x` on `1/8 sin(u) +C` , we get:
`intcos(6x+2x) dx=1/8 sin(8x) +C`
For the integral: `intcos(6x-2x) dx` , we let `u = 6x-2x =4x` then `du= 4 dx` or `(du)/4 =dx` .
`intcos(6x-2x) dx=intcos(4x) dx`
`=intcos(u) *(du)/4`
`= 1/4 int cos(u)du`
`= 1/4 sin(u) +C`
Plug-in `u =4x` on `1/4 sin(u) +C` , we get:
`intcos(6x-2x) dx=1/4 sin(4x) +C`
Combing the results , we get the indefinite integral as:
`1/2 *[intcos(6x+2x) dx+int cos(6x-2x)dx] = 1/2*[1/8 sin(8x) +1/4 sin(4x)] +C`
or ` 1/16 sin(8x) +1/8 sin(4x) +C`
Approved by eNotes Editorial Team
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# How can I Find a Non-Linear Ground Fault?
By Douglas Krantz | Maintenance
One of my stories about finding a ground fault after the end of the day was at a large chain-store distribution center. I'd never been there before. Until that night, our company didn't have anything to do with that store chain. Our dispatcher, though, asked if, before going home, I could stop there and fix a ground fault.
A few years earlier, another company had installed a system, so they were the company that did the service (until then, at least).
It was a four-loop addressable system, but the building itself was a several-block-long warehouse. The problem was there was an intermittent ground fault that, when anyone was there to find it, the ground fault was not showing up on the panel. After several weeks of failing to find the problem, the other company quit even showing up.
OK, because I know some things about electronics that aren't covered very well in electronic courses, I could troubleshoot a problem that apparently few other fire alarm technicians know much about: non-linear resistance.
## Non-Linear Resistance
A common resistor has the same resistance, no matter what the voltage; the current through the resistor exactly tracks the voltage. When the voltage doubles, the current doubles. That's a linear relationship.
Water does not have the same resistance, no matter what the voltage. Neither does a surge suppressor. When the voltage on either is low enough, the resistance is very high. There is almost no current at all through water or through a surge suppressor as long as the voltage stays low.
With water, there is a voltage threshold, or knee, of 5 volts to 8 volts; with a working 25-volt surge suppressor, there is a voltage threshold, or knee, of about 25 volts.
Doubling the voltage across water from 4 volts to 8 volts will often increase the current by 10 to 20 times. Doubling the voltage on a working 25-volt surge suppressor from 15 volts to 30 volts will increase the current by at least 50 times. When the voltage doubles across the knee on either water or a surge suppressor, the current increases many times what the voltage has increased. That is a non-linear relationship.
Keep in mind that the 24-volt (nominal) battery voltage is split up by the ground fault detection circuitry in the fire alarm panel. The real ground fault detection for a fire alarm panel is closer to 14 volts.
## Back to the Story
I arrived on site, and, you guessed it, the panel was normal. Checking history, I found which loop the ground fault was on. I knew that this was an "intermittent" ground fault, and the panel wasn't detecting it, so I whipped out my "Ground Fault Detector" and confirmed that the ground fault was truly existing.
Fire Alarm Specifications: Check the maintenance manual for most fire alarm systems. In there they specify the resistance or current level for the ground fault detection threshold. Listed for this specification, I've seen 15K Ohms or 45K Ohms.
My ohmmeter, having 3volts for its internal battery, isn't capable of detecting current when the knee on non-linear resistance is 5 volts or higher. However, my "Ground Fault Detector" is a regular, cheap ohmmeter that has 36 volts (four 9-volt batteries) in series with one of the leads. It also has a resistor in series to keep the meter reading full scale.
The technical name for this device is "Insulation Tester", but at the time, the only insulation testers on the market used a voltage that was too high for fire alarm circuit safety, so I had to make it myself.
Having never seen the building before, and no access to anything like an as-built diagram, I used the technique of disconnecting parts of the loop, and looking for the troubles on the panel. I combined that troubleshooting technique with my "Ground Fault Detector", and found a surge suppressor that had decreased its protection voltage from 25 volts to around 15 volts. The surge suppressor was on the Signaling Line Circuit (SLC) because the SLC went to an out-building electric fire pump about a block away.
Even though the panel didn't show it, I had found and fixed the ground fault in about three and a half hours.
The other service company had used their expensive ohmmeters, with internal 9-volt batteries, and couldn't find the 15-volt surge suppressor problem. Using my homemade "Ground Fault Meter", I fixed it. We got a new service contract.
## Ground Fault Meter
The Ground Fault Meter is actually an "Insulation Tester". These are commonly used by electricians for testing the insulation on higher-voltage equipment or even power lines. Search the web to find these. There are at least a dozen manufacturers that make them.
There are a number of insulation testers on the market that can be switched to a low enough voltage to be used on fire alarm circuits. Any voltage produced by the tester below 45 volts is generally safe for fire alarms. Above 45 volts, and there is a remote possibility of some damage to the fire alarm system.
And yes, a lot of commercial meters can be set to use a low enough voltage to be safe, but they come with an unwritten caveat: whoever uses the switchable-voltage insulation tester has to remember to use a low enough voltage setting. Failure to remember to make sure of the setting can damage the system.
I don't trust myself to always, and every time, remember to make sure the voltage is low enough. Because I'm not absolutely perfect, and might not remember to set the voltage low enough on the insulation tester, I use a homemade tester, it can't exceed the 45-volt damage-threshold.
To build an insulation tester for use on fire alarm systems, use the instructions printed in the Nuts and Volts Magazine September 2010 Issue, Page 42 at: http://nutsvolts.texterity.com/nutsvolts/201009/?folio=42&pg=42#pg42.
When calling up that site, just by X-ing out of the subscription request drop-down, you can read most of the article. However, even if you're cheap like me, you still might want to subscribe. The subscription isn't all that expensive, it is a good magazine for the electronic hobbyist, and besides, you can read the full article.
The advantage to building your own tester is that you learn more about soft ground faults, and more about the testing for soft ground faults. Not only that, but without spending much money, you can possess a very useful test instrument.
The disadvantage is it really is a one-person test meter. It will never be an industrial strength meter to be shared with other technicians around the shop; unlike most store-bought meters, it won't stand up to abuse.
Index
Residential
Life Safety
Descriptions
Electronics
Maintenance
Suppression
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exupero's blog
# New stack math compendium
In the previous post I described a couple new approaches to my original compendium of stack math algorithms. Below is the updated compendium. The error is calculated using this script, which for algorithms that aren't simple multiplication or division checks the error at a few powers of ten and reports the worst accuracy.
If you have any improvements to suggest, or would like to see some additional conversions, feel free to email me.
ConversionLess accurateMore accurate
Celsius → Fahrenheit
`9 * 5 / 32 +`
`double -tenth +32`
(exact)
Fahrenheit → Celsius
`32 - 5 * 9 /`
`-32 halve +tenth`
(1% error)
15% tip
`0.15 *`
`tenth +half`
(exact)
Multiply by π
`3.14159 *`
`triple +tenth`
(5% error)
`triple +twentieth`
(0.3% error)
Divide by π
`3.14159 /`
`third -tenth`
(6% error)
`third -twentieth`
(0.5% error)
kilometers → miles
`0.6214 *`
`two-thirds`
(7% error)
`two-thirds -tenth +twentieth`
(1% error)
miles → kilometers
`1.609 *`
`+half`
(7% error)
`[+half] left [tenth] right +`
(0.6% error)
meters → feet
`3.281 *`
`triple`
(9% error)
`triple +tenth`
(0.6% error)
feet → meters
`3.281 /`
`third`
(9% error)
`third -tenth`
(2% error)
inches → centimeters
`2.54 *`
`tenfold quarter`
(2% error)
centimeters → inches
`2.54 /`
`tenth quadruple`
(2% error)
miles → feet
`5280 *`
`five-thousandfold`
(5% error)
`five-thousandfold +twentieth`
(0.6% error)
feet → miles
`5280 /`
`five-thousandth`
(6% error)
`five-thousandth -twentieth`
(0.3% error)
kilograms → pounds
`2.205 *`
`double`
(9% error)
`double +tenth`
(0.2% error)
pounds → kilograms
`2.205 /`
`halve`
(10% error)
`halve -tenth`
(0.8% error)
hours → seconds
`3600 *`
`four-thousandfold`
(10% error)
`four-thousandfold -tenth`
(exact)
seconds → hours
`3600 /`
`four-thousandth`
(10% error)
`four-thousandth +tenth`
(1% error)
mi/h → ft/s
`1.467 *`
`+half`
(2% error)
ft/s → mi/h
`1.467 /`
`two-thirds`
(2% error)
sq. miles → acres
`640 *`
`seven-hundredfold`
(9% error)
`seven-hundredfold -tenth`
(2% error)
acres → sq. miles
`640 /`
`seven-hundredth`
(9% error)
`seven-hundredth +tenth`
(0.6% error)
acres → sq. feet
`43560 *`
`ten-thousandfold quadruple`
(8% error)
`ten-thousandfold quadruple +tenth`
(1% error)
sq. feet → acres
`43560 /`
`ten-thousandth quarter`
(9% error)
`ten-thousandth quarter -tenth`
(2% error)
sq. kilometers → acres
`247.1 *`
`thousandfold quarter`
(1% error)
acres → sq. kilometers
`247.1 /`
`thousandth quadruple`
(1% error)
pounds → troy ounces
`14.58 *`
`tenfold +half`
(3% error)
`[tenfold +half] left [halve] right -`
(0.5% error)
troy ounces → pounds
`14.58 /`
`tenth two-thirds`
(3% error)
US cups → fluid ounces
`8 *`
`quadruple double`
(exact)
fluid ounces → US cups
`8 /`
`quarter halve`
(exact)
liquid gallons → US cups
`16 *`
`quadruple quadruple`
(exact)
US cups → liquid gallons
`16 /`
`quarter quarter`
(exact)
liquid gallons → liters
`3.785 *`
`quadruple`
(6% error)
`quadruple -twentieth`
(0.4% error)
liters → liquid gallons
`3.785 /`
`quarter`
(5% error)
`quarter +twentieth`
(0.6% error)
sphere radius → surface area
`square 4 * 3.14159 *`
`square tenfold +quarter`
(0.5% error)
sphere radius → volume
`cube 4 * 3 / 3.14159 *`
`cube quadruple`
(5% error)
`cube quadruple +twentieth`
(0.3% error)
sphere surface area → radius
`4 / 3.14159 / sqrt`
`tenth -quarter sqrt`
(3% error)
`hundredth quadruple double sqrt`
(0.3% error)
sphere volume → radius
`4 / 3 * 3.14159 / cube-root`
`quarter cube-root`
(2% error)
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# What Is Vanna in Options?
View All
Definition
Vanna is a second-order derivative that measures the change in delta for any change in the implied volatility of an option. It is measured as the change in delta for every 1% change in implied volatility. In options trading, vanna will be negative for put options and positive for call options.
### Key Takeaways
• Vanna measures the change in delta for every 1% change in implied volatility.
• It is a second-order Greek in trading options because it is a derivative of the Greek delta.
• Vanna is positive for call options and negative for put options.
## How Vanna Works
To fully understand vanna, you need to understand the popular Greek in options, delta. Delta measures how much an options price changes as the underlying security changes by \$1 per share. Delta values can be anywhere from -1 to +1 with a value of 0, meaning the options price is unaffected as the underlying security’s price changes.
How does delta change when implied volatility changes? This measurement is called “vanna.” Because vanna is a derivative of delta, it is categorized as a “second-order” Greek. As the implied volatility of an option increases, the probability of that option moving into the money also increases. For this reason, vanna is positive for call options and negative for put options.
## Example of Vanna
Steve is an options trader and decides to purchase \$175 call options on ABC Holdings and 123 Computers. The call option for ABC Holdings cost him \$1, and the option call for 123 Computers cost him \$10. The gap in the options prices of each is due to the difference in implied volatility and delta.
Below are additional details of each company for this example:
If ABC Holdings' stock price increases by just \$1, the option price will remain relatively the same because it’s doubtful it will jump from \$100 to \$175 in the first place due to the nature of the business (a holdings company that has been around for decades).
However, if 123 Computers' stock price increases by just \$1, the option price will likely go up by much more as a result of the larger implied volatility inherent in the nature of its business (an innovative and fast-changing computer and technology company).
Let’s assume that a new development has occurred, and ABC Holdings has just announced the purchase of an online retailer that is poised to overtake the market share of Amazon. As a result, the implied volatility and delta of ABC Holdings have increased from 0.05 to 10. The measured change in delta and implied volatility resulting from the major company purchase is vanna.
## What It Means for Individual Investors
Most individual investors will likely never use vanna in their trading strategies unless they are heavy options traders or manage a hedge fund of options for a major institution. However, understanding how vanna works provides additional perspective for investors wishing to further their knowledge of trading options and related options trading strategies. Always consult a financial professional before making major investing decisions.
## What are Greeks in options?
The primary Greeks in options are delta, gamma, theta, vega, and rho, and each measures how different factors might affect the change in the price of an options contract. Second-order Greeks are derivatives of the primary Greeks and include vanna.
## What is gamma in options?
Gamma measures the rate of change in an options delta and the underlying asset’s price. Like vanna, it is considered a second-order Greek.
## How does implied volatility change delta in trading?
This change is measured with vanna. As the implied volatility of an option increases, the probability of that option moving into the money also increases. So vanna is positive for call options and negative for put options.
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+0
# The hyperbola$\frac{(x-3)^2}{5^2} - \frac{(y+1)^2}{4^2} = 1$
+1
40
1
+467
has two asymptotes, one with positive slope and one with negative slope. Compute the intercept of the one with positive slope. (Enter your answer as an ordered pair.)
Dec 7, 2020
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# Good Old Suffix Vector
Inspired by an old manual...
### The challenge
I define the ath suffix vector of b as the boolean list of length a with b trailing truthy values.
Write a program or function that, given a and b by any means, returns the ath suffix vector of b by any means.
Now this may seem trivial, but here is the catch: Your score is the byte count plus the earliest year your solution would have worked.
### Rules
All standard rules apply, except that languages and language versions that were released after this challenge, may also be used.
Output using whatever representation of boolean values that your language uses, e.g. 1/0, True/False, TRUE/FALSE, "True"/"False", etc.
Output using whatever representation of lists that your language uses, e.g. 0 0 1, [False,False,True], (FALSE;FALSE;TRUE), {"False","False","True"}, etc.
You may assume that ab is always true and that they are of an appropriate data type.
### Test cases
Given a = 7 and b = 3, return 0 0 0 0 1 1 1
Given a = 4 and b = 4, return [True,True,True,True]
Given a = 2 and b = 0, return (FALSE;FALSE)
Given a = 0 and b = 0, return {}
### Example solution and scoring
I might want to submit the solution {⌽⍺↑⍵⍴1} using Dyalog APL. That would be a bytecount of 8. This is a dynamic function, which works from version 8.1 of Dyalog APL, released in 1998, so my total score is 2006. My submitted answer should look something like:
# Dyalog APL 8.1, 1998 + 8 = 2006
{⌽⍺↑⍵⍴1}
Optional explanation...
Recommended: Link to documentation showing when the features you used were released.
Lowest score wins!
• I'm deeply concerned about the verifiability of the answers. Mar 10, 2016 at 15:33
• @Dennis I understand you concern. However, 1) the answers will mostly be very simple, and thus could be verified by hand – not requiring an actual running system, and 2) some users have taken to linking to documentation of their claim.
Mar 10, 2016 at 15:36
• I'm not so sure "verified by hand" is necessarily going to work for some answers - the past is a foreign place, and sometimes initial versions of things can lack things that feels commonplace today... Mar 10, 2016 at 15:55
• @Sp3000 Maybe, but this is all for fun anyway, and with 8 answers and 9 upvotes in 1.5h, I think this challenge is fun enough accept that someone might cheat. Maybe some extra research on the eventual winner...
Mar 10, 2016 at 16:03
• @CatsAreFluffy The idea was to show that any of those formats are valid. I think the cases are few and simple enough that ease of copy-paste'ing isn't an issue.
Mar 10, 2016 at 17:16
# SAS, 1966 + 45 = 2011
data;a=;b=;do i=1to a;c=a-i<b;put c@;end;run;
Time for SAS to shine!
SAS wasn't first published until 1972, but this data step only uses very basic features that I'm fairly confident would have been available even in the earliest pre-release versions from 1966 onwards, so I believe it would have worked then. Input goes after a= and b=, and output is printed to the log.
I would be amazed if anyone still had an IBM System/360 with the right version of SAS to actually verify this!
Mar 11, 2016 at 15:40
• Now, if only I had the cash for a mainframe SAS licence... Mar 11, 2016 at 16:48
# Forth, 1970 + 38 = 2008
:s tuck +do 0 . loop 0 +do -1 . loop ;
usage: 7 3 s prints "0 0 0 0 -1 -1 -1"
• Now we're talking!
Mar 10, 2016 at 20:20
• Why -1? filler+ Mar 10, 2016 at 21:18
• That's one of the more interesting 'truthy' values I've seen lately. Mar 10, 2016 at 23:45
• stackoverflow.com/q/23832703/10396 Mar 11, 2016 at 0:46
• Is there a good reason this is named sv and not s, or something else one byte?
– cat
Mar 11, 2016 at 15:11
## APL, 1968+5=1973
Down to 5 chars:
⌽⎕≥⍳⎕
Older version:
⌽⎕↑⎕⍴1
Well, you actually already gave the answer, i just removed the dynamic function definition and checked that this one worked in 1968. For reference here is the manual:
http://www.softwarepreservation.org/projects/apl/Books/APL360ReferenceManual
• Kids, this is called a winner. Please write that down in your notes. Mar 11, 2016 at 16:14
• @CatsAreFluffy Not yet. @Moris Zucca: Finally, but you can actually golf half of those bytes away. Can you figure out how? Also, here is a much more modern and readable version of the manual.
Mar 11, 2016 at 16:21
## APL\360, 1968 + 3 bytes = 1971
⎕⍵⎕
A builtin from the tutorial @NBZ linked to. I don't know why @NBZ said it would score 1970, because APL\360 wasn't implemented until 1968, and earlier APLs like APL\1130 didn't have the suffix vector function (see page 208 of here).
# Mouse-1979, 1979 + 19 = 1998
??&TUCK (0.a)0(1-.)
Translation of: Forth.
The spec is really cryptic to me but I think this does the right thing.
• Broken link.... Mar 11, 2016 at 16:31
• @CatsAreFluffy Fixed; I typed it from memory.
– cat
Mar 11, 2016 at 16:44
• Interesting. But I don't think the &Tuck was available until the 2002 version. And the loops appear to be infinite. Mar 12, 2016 at 0:05
# TI-Basic, 1990 + 21 = 2011
The first TI calculator that this program works on is the TI-81, introduced in 1990.
Prompt A,B:"{}
seq(I>A-B,I,1,A
Edit: noticed that I must support an empty list... increased code by 4 bytes
# Test Cases
A=?7
B=?3
{0 0 0 0 1 1 1}
A=?4
B=?4
{1 1 1 1}
A=?2
B=?0
{0 0}
A=?0
B=?0
{} * throws an error but still returns successfully
• Could you add commentary on which parts of the source are single bytes in TI-Basic? I think that includes Prompt and seq( but I'm not sure about the rest Mar 10, 2016 at 18:02
• We don't consider returning through Ans an acceptable output method, unless it's printed. Mar 10, 2016 at 18:04
• @Sparr Sure, Prompt and seq( are one byte tokens and the other characters are one byte each. Mar 10, 2016 at 19:13
• @lirtosiast Ans is the default way to return a value in the TI-83 series Basic. Additionally, when a program is run, the last line is printed automatically. So you have the best of both worlds. Mar 10, 2016 at 19:22
• Is it the Analytical Engine? Somebody should do that... Mar 11, 2016 at 14:47
# Mathematica 1.0, 1988+22 bytes=2010
Array[#>m&/.m->#-#2,#]&
I'm not sure if this works, just went through the documentation on 10.3 and looked for things that said Introduced in 1988 (1.0)
• Just about the current winner. If only the SMP code could get shorter... Mar 10, 2016 at 16:15
• On another note though, some docs: pure functions, /. and ->, Array Mar 10, 2016 at 16:35
# 68k TI-Basic, 1995 + 25 = 2020
The first TI calculator that this program works on is the TI-92, introduced in 1995.
define f(a,b)=seq(x>a-b,x,1,a)
Unlike the TI-83 series, 68k TI-Basic supports the empty list.
• How is the size counted? Tokenization is very different on the 68k series. Mar 10, 2016 at 20:33
• Prompt and seq are both two bytes plus a one byte flag for multiple arguments. (21 bytes) Mar 11, 2016 at 15:31
• Note that this is neither a program nor a function in the context of the 68k calculators: Prompt is invalid in a function, and a program can't return a value. So this has to be entered on the home screen. On the other hand, define f(a,b)=seq(x>a-b,x,1,a) does define a valid function that can be given a and b as arguments. (Verified on my TI-92 from 1995-09-13)
– Fox
Mar 18, 2016 at 8:13
• I own several TI calculators (the only z80-version being the 81), but usually use a TI-92 Plus. After running this define and calling f(2,1) or similar to tokenize it, the size reported by the OS is 25 bytes.
– Fox
Mar 18, 2016 at 22:39
# Python 1.0, 1994 + 26 = 2020
Saved 2 bytes thanks to DSM.
Lambda was introduced with the first major release, 1.0
lambda a,b:[0]*(a-b)+[1]*b
• Confirmed lambda introduced in 1.0, list (sequence) repetition in 0.9.2. The oldest version I could test this on (apart from 0.9.1) was 1.5.2, and it works fine there. Mar 10, 2016 at 15:14
• @Sp3000 Oh wow, that's awesome. I've been trying to find some change logs to confirm that the sequence repetition was in the language that early. Mar 10, 2016 at 15:18
# MATL, 2015 + 1 + 4 = 2020
:P<~
This works since release 6.0.0 of the language (it uses implicit input, which was introduced in that release), dated December 31, 2015.
I've added 1 to the score in accordance with @drolex comment on possibly different locales.
Try it online!
### Explanation
: % take first input implicitly. Generate inclusive range from 1 to that
P % flip that array
<~ % take second input implicitly. True for elements of flipped array that
% exceed second number. Display implicitly
• One day later, and...
Mar 10, 2016 at 14:55
• Objection! We'll need to have the locales for the github server and the release submitter. If one is in Tonga and the other in Hawaii, this count might need to be incremented. Mar 10, 2016 at 16:50
• @drolex The OP should define what he means by "year", exactly. Meantime, I'm adding 1 to my score Mar 10, 2016 at 16:57
• @DonMuesli I didn't mean it, just showing the potential limitations of this type of scoring Mar 10, 2016 at 17:00
• @drolex Oh, I thought you were serious. I've asked the OP, anyway. Github date should probably count as official Mar 10, 2016 at 17:02
# J, 1990 + 8 = 1998
|.a{.b#1
Argh. Was researching this answer and someone got to APL before I could hope to understand the language. Here's my J solution instead.
# Prolog, 1972 + 57 = 2029
a(0,_,[]).
a(A,B,[H|L]):-Z is A-1,a(Z,B,L),(Z<B,H=1;H=0).
Usage: a(7,3,L). will unify L with [0,0,0,0,1,1,1].
I'm really not quite sure when is was implemented in the language, and I doubt you can actually find the exact date. It's a pretty basic built-in though so I assume it was already existing when the language first appeared in 1972.
Not that it really matters though, I'm far from winning with this answer.
• This may not be the winner, but it clearly illustrates the advantage of exploring - ehm - mature languages...
Mar 10, 2016 at 15:30
# SMP, 1983+28 bytes=2011
Map[S[$1>x,x->$1-$2],Ar[$1]]
I think I got this right... S:2.10, page 48 Ar:7.1, page 102 Map:7.2, page 106 $1:7.1, page 104 And if you're familiar with Mathematica, no, Ar doesn't work like that. More like Range+Select. • (#>x&/.x->#)/@Range[#+#2]& in Mathematica Mar 10, 2016 at 21:20 • I mean (#>x&/.x->#-#2)/@Range[#]& Mar 11, 2016 at 14:50 # Vim, 1991 + 21 = 2012 "adwj<c-x>"bdw@ai0<esc>v@bhr1 Input looks like this: 7 3 And output looks like this: 0000111 Explanation: "adw 'Delete a word into register a j<c-x> 'Go down a line, and decrement the next number to occur "bdw 'Delete a word into register b @ai0<esc> 'Insert a '0' "a" times v 'Enter visual mode @bh 'Move "b" characters left r1 'Replace the whole selection with the character '1' • Too bad vi doesn't support registers, because it was released in 1976! Mar 10, 2016 at 18:37 • Explanation please? Mar 10, 2016 at 21:22 # B, 1971 + 54 = 2025 s(l,t){while(t<l--)printn(0,8);while(t--)printn(1,8);} See "The User's Reference to B" for the manual for this typeless C precursor. # Pyth, 2015 + 9 4 = 2024 2019 Thanks to @FryAmTheEggman for his help! gRQE Try it here! ## Explanation gRQE # Q = amount of trailing truthy values # E = length of the vector R E # map over range(E) g Q # d >= Q ## ><>, 2009 + 14 + 3 for -v = 2026 b and a should be provided directly on the stack with -v, in reverse order. The output isn't space separated as in the examples, but that does not seem to go against any stated rule. It uses 0 and 1 to represent false and true, as used by the language. :?!;{:0(n1-}1- It doesn't work with the current version since ? now pops its test value from the stack. I'm not confident every feature was implemented from day 1, -v for example could have been provided later as a commodity. I'll try to make sure my answer is correct this weekend. • ? didn't pop (a long time ago) as stated in the quine challenge Mar 11, 2016 at 14:48 • Thanks, that's great news, I'll save 1 byte :) I'll edit that now, but I'll have to check the resources linked on esolang.org, some date back to at least 2011. Mar 11, 2016 at 14:53 • Mar 11, 2016 at 15:05 • Thanks for your help, I wouldn't have thought to check the wiki's revisions ! I'm currently at work and won't probably be able to check everything yet, but I'll make sure to do it this evening or tomorrow. Mar 11, 2016 at 15:40 • Score=2026 now. Mar 11, 2016 at 16:12 # 05AB1E, 2016 + 9 = 2025 This can definitely be golfed further, but here's a start :p. Code: -0s×1¹×«S Try it online! The input is given as b, a. Also 9 bytes: 0×1I×0ñRS. ## PowerShell v1, 2006 + 28 = 2034 param($a,$b),0*($a-$b)+,1*$b
Uses the comma operator to construct the array(s), which has been in PowerShell since the beginning.
# Mathcad, 1998 + 42 = 2040
"bytes" are interpreted as number of distinct keyboard characters (eg, 'for' operator (including one programming line) is a single character ctl-shft-#, or a click on the Programming toolbar)).
The above byte count assumes that the a and b definitions don't count towards the total; add 4 bytes for definitions if this assumption is invalid.
The function version shown below adds 5 bytes for the definition and a further 3 bytes for each use (assuming the a and b values are directly typed in).
As my Mathcad solution should clearly be playing off the red tees and not the competition ones, I've added a table of solutions. Note that as Mathcad has no empty array, I've used an empty string ("") instead; I've used 0 to indicate where I haven't calculated the b>a pairs.
• Very interesting! Mar 11, 2016 at 15:34
## PHP, 1995 + 56 bytes = 2051
function s($a,$b){while($i++<$a)$v[]=$i>$a-$b;return$v;} Exploded view function s($a,$b) { while ($i++ < $a)$v[] = $i >$a - $b; return$v;
}
• Uh..there's custom scoring. It's first year language woks in+byte count. Mar 11, 2016 at 22:31
• Whoops, right you are! Fixing... Mar 11, 2016 at 22:33
• Making the probably-incorrect assumption of this working in PHP 1. Will verify version soon. Mar 11, 2016 at 22:43
# Javascript ES6, 2015 + 46 = 2061
Returns array of 0 and 1
(a,b)=>Array(a-b).fill(0).concat(Array(b).fill(1))
# Javascript ES6, 2015 + 50 = 2065
Returns a string of 0 and 1 chars
(a,b)=>Array(a-b+1).join(0)+Array(b+1).join(1)
# Javascript, 1995 + 61 = 2056
Returns a string of 0 and 1 chars
function(a,b){return Array(a-b+1).join(0)+Array(b+1).join(1)}
# k (kona), 1993 + 15 = 2008
((a-b)#0b),b#1b
Creates list of b True values, and concatenates it to a list of (a-b) False values.
# R, 20 bytes + 1993 = 2013
function(a,b)1:a>a-b
Try it online!
Possibly this might work in S, which would drop the score to 2008, but I haven't been able to verify it.
# SmileBASIC 3, 2014 + 25 = 2039
The first publicly available version of SmileBASIC 3 launched in Japan with the SmileBASIC app for Nintendo 3DS in November 2014.
Prints a string where 0 is false and 1 is true (as they are in the language itself.)
INPUT A,B?"0"*(A-B)+"1"*B
| 4,665
| 14,886
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{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.015625
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CC-MAIN-2022-33
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longest
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en
| 0.921131
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https://www.studypool.com/discuss/1073096/find-linear-equation-in-slope-intercept-form?free
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text/html
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crawl-data/CC-MAIN-2017-39/segments/1505818688158.27/warc/CC-MAIN-20170922022225-20170922042225-00373.warc.gz
| 872,226,069
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##### Find linear equation in slope intercept form
label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5
There were 246 Apple stores worldwide in 2008 and 317 Apple stores worldwide in 2010. Write a linear equation in slope-intercept form that models this growth. Let x stand for the number of years after 2008 and let y= the number of Apple stores worldwide
Jul 12th, 2015
563=2x
subtract 536 to have the correct format and you will have
y=2x-563
Jul 12th, 2015
I think I was trying to solve, but the problem I see now only requires to write the formula. However, I have another question. Why would I not use ordered pairs to solve for slope and then put that in the slope intercept form. That was how I was approaching the problem. I was going to use ordered pairs (0,246) (2,317) to find slope and then insert that in the Y=mx+b formula using any of the one pairs for the Y intercept to complete slope intercept format. Where am I going wrong??
Jul 12th, 2015
Katie - are you there?? I posted a follow up question and need clarification. thanks
Jul 12th, 2015
...
Jul 12th, 2015
...
Jul 12th, 2015
Sep 22nd, 2017
check_circle
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| 2.890625
| 3
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CC-MAIN-2017-39
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latest
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en
| 0.947981
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http://oeis.org/A221861
| 1,563,953,330,000,000,000
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text/html
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crawl-data/CC-MAIN-2019-30/segments/1563195531106.93/warc/CC-MAIN-20190724061728-20190724083728-00395.warc.gz
| 112,148,471
| 3,666
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This site is supported by donations to The OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A221861 The least number k that maximizes k! mod n. 2
0, 0, 2, 2, 4, 2, 3, 3, 3, 3, 5, 3, 12, 4, 4, 4, 16, 5, 9, 3, 5, 6, 14, 3, 4, 4, 4, 4, 18, 4, 30, 4, 6, 9, 4, 4, 36, 6, 8, 4, 40, 5, 21, 5, 5, 10, 23, 4, 7, 7, 10, 7, 52, 8, 9, 6, 13, 7, 15, 4, 8, 14, 5, 5, 5, 6, 18, 8, 17, 5, 7, 5, 72, 21, 5, 14, 9, 8, 23, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 EXAMPLE For n=11, we see that the factorial of 5 (120), modulo 11 is 10, which is the highest possible value, so the 11th term is 5. PROG (Ruby) (1..100).map{|n|(0..n).max_by{|x|[(1..x).inject(1, :*)%n, -x]}} CROSSREFS Cf. A062170. Sequence in context: A123674 A238745 A092607 * A057939 A163371 A061338 Adjacent sequences: A221858 A221859 A221860 * A221862 A221863 A221864 KEYWORD nonn AUTHOR Aaron Weiner, Apr 10 2013 STATUS approved
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Last modified July 24 03:28 EDT 2019. Contains 325290 sequences. (Running on oeis4.)
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CC-MAIN-2019-30
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latest
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en
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http://www.sumscorp.com/new_models_of_culture/terms/?object_id=236047
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text/html
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crawl-data/CC-MAIN-2018-51/segments/1544376826715.45/warc/CC-MAIN-20181215035757-20181215061757-00290.warc.gz
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# Terms
a, b, g, d
a, b, g, d
Four letters, a, b, g, d, 22 build twenty-four houses, viz.:
1 = abgd
13 = gabd
2= abdg
3 = agbd
4 = agdb
16 = gbda
17 = gdab
18 = gdba
7 = bagd
19 = dabg
20 = dagb
21 = dbag
10 = bgda
22 = dbga
11 = bdag
23= dgab
12 = bdga
24 = dgba
Back
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| 2.546875
| 3
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CC-MAIN-2018-51
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latest
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en
| 0.428125
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https://en.wikipedia.org/wiki/Mean_dependence
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# Mean dependence
In probability theory, a random variable ${\displaystyle Y}$ is said to be mean independent of random variable ${\displaystyle X}$ if and only if its conditional mean ${\displaystyle E(Y\mid X=x)}$ equals its (unconditional) mean ${\displaystyle E(Y)}$ for all ${\displaystyle x}$ such that the probability density/mass of ${\displaystyle X}$ at ${\displaystyle x}$, ${\displaystyle f_{X}(x)}$, is not zero. Otherwise, ${\displaystyle Y}$ is said to be mean dependent on ${\displaystyle X}$.
Stochastic independence implies mean independence, but the converse is not true.[1][2]; moreover, mean independence implies uncorrelatedness while the converse is not true. Unlike stochastic independence and uncorrelatedness, mean independence is not symmetric: it is possible for ${\displaystyle Y}$ to be mean-independent of ${\displaystyle X}$ even though ${\displaystyle X}$ is mean-dependent on ${\displaystyle Y}$.
The concept of mean independence is often used in econometrics[citation needed] to have a middle ground between the strong assumption of independent random variables (${\displaystyle X_{1}\perp X_{2}}$) and the weak assumption of uncorrelated random variables ${\displaystyle (\operatorname {Cov} (X_{1},X_{2})=0).}$
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CC-MAIN-2024-26
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https://socratic.org/questions/what-is-the-lcm-of-24a-32a-4
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crawl-data/CC-MAIN-2021-49/segments/1637964358903.73/warc/CC-MAIN-20211130015517-20211130045517-00101.warc.gz
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# What is the LCM of 24a, 32a^4?
Oct 17, 2015
$L C M \left(24 a , 32 {a}^{4}\right) = \frac{24 a \cdot 32 {a}^{4}}{G C D \left(24 a , 32 {a}^{4}\right)} = 96 {a}^{4}$
#### Explanation:
The GCD (Greatest Common Divisor) of $24$ and $32$ is $8$
The GCD of $a$ and ${a}^{4}$ is $a$
Therefore
$\textcolor{w h i t e}{\text{XXX}} G C D \left(24 a , 32 {a}^{4}\right) = 8 a$
and
$\textcolor{w h i t e}{\text{XXX}} L C M \left(24 a , 32 {a}^{4}\right) = \frac{24 a \cdot 32 {a}^{4}}{8 a}$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXX}} = 96 {a}^{4}$
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# Answer to Question #15648 in Mechanics | Relativity for Kennedy
Question #15648
You throw a baseball directly upward at time=0 at an initial speed of 14.5 m/s. what is the maximum height the ball reaches above where it leaves your hand?
1
2012-10-05T07:56:17-0400
At the highest point:
V = 0, V = V0 - g * t, so t = V0 / g
The maximum
height the ball reaches is:
h = V0 * t - g * t^2 / 2
h = V0 * V0 / g - g *
(V0 / g)^2 / 2 = V0^2 / (2 * g)
h = 14.5^2 / (2 * 9.81) = 10.7 m
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Question
# Company B’s WACC is 10%. It has three Projects it can choose from: Projects X, Y...
Company B’s WACC is 10%. It has three Projects it can choose from: Projects X, Y and Z. The following information is available regarding Project X.
Years 0 1 2 3
Cash Flows -\$100 \$80 \$60 \$40
And the following information is available regarding Projects Y and Z.
Criteria Project Y Project Z
NPV \$40 \$67
MIRR 10% 20%
IRR 6.5% 18.7%
Regular Payback 2.23 years 1.77 years
1) If IRR for Project X is 17.95%, and the three project X, Y & Z are independent, then based on IRR criteria we choose: *
Project Z
Project X
Projects X and Z
Projects X, Y and Z
None of the projects
2)
Assuming the three projects X, Y & Z are mutually exclusive, based on regular payback period criteria we choose: *
Project X
Project Y
Project Z
All of the projects
None of the projects
Please refer to the image below for the solution-
Do let me know in the comment section in case of any doubt.
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# 5.4 Dividing polynomials (Page 4/6)
Page 4 / 6
## Verbal
If division of a polynomial by a binomial results in a remainder of zero, what can be conclude?
The binomial is a factor of the polynomial.
If a polynomial of degree $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is divided by a binomial of degree 1, what is the degree of the quotient?
## Algebraic
For the following exercises, use long division to divide. Specify the quotient and the remainder.
$\left({x}^{2}+5x-1\right)÷\left(x-1\right)$
$x+6+\frac{5}{x-1}\text{,}\text{\hspace{0.17em}}\text{quotient:}\text{\hspace{0.17em}}x+6\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}\text{5}$
$\left(2{x}^{2}-9x-5\right)÷\left(x-5\right)$
$\left(3{x}^{2}+23x+14\right)÷\left(x+7\right)$
$\left(4{x}^{2}-10x+6\right)÷\left(4x+2\right)$
$\left(6{x}^{2}-25x-25\right)÷\left(6x+5\right)$
$x-5\text{,}\text{\hspace{0.17em}}\text{quotient:}\text{\hspace{0.17em}}x-5\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}\text{0}$
$\left(-{x}^{2}-1\right)÷\left(x+1\right)$
$\left(2{x}^{2}-3x+2\right)÷\left(x+2\right)$
$2x-7+\frac{16}{x+2}\text{,}\text{\hspace{0.17em}}\text{quotient:}\text{}\text{\hspace{0.17em}}2x-7\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}\text{16}$
$\left({x}^{3}-126\right)÷\left(x-5\right)$
$\left(3{x}^{2}-5x+4\right)÷\left(3x+1\right)$
$x-2+\frac{6}{3x+1}\text{,}\text{\hspace{0.17em}}\text{quotient:}\text{\hspace{0.17em}}x-2\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}\text{6}$
$\left({x}^{3}-3{x}^{2}+5x-6\right)÷\left(x-2\right)$
$\left(2{x}^{3}+3{x}^{2}-4x+15\right)÷\left(x+3\right)$
$2{x}^{2}-3x+5\text{,}\text{\hspace{0.17em}}\text{quotient:}\text{\hspace{0.17em}}2{x}^{2}-3x+5\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}\text{0}$
For the following exercises, use synthetic division to find the quotient.
$\left(3{x}^{3}-2{x}^{2}+x-4\right)÷\left(x+3\right)$
$\left(2{x}^{3}-6{x}^{2}-7x+6\right)÷\left(x-4\right)$
$2{x}^{2}+2x+1+\frac{10}{x-4}$
$\left(6{x}^{3}-10{x}^{2}-7x-15\right)÷\left(x+1\right)$
$\left(4{x}^{3}-12{x}^{2}-5x-1\right)÷\left(2x+1\right)$
$2{x}^{2}-7x+1-\frac{2}{2x+1}$
$\left(9{x}^{3}-9{x}^{2}+18x+5\right)÷\left(3x-1\right)$
$\left(3{x}^{3}-2{x}^{2}+x-4\right)÷\left(x+3\right)$
$3{x}^{2}-11x+34-\frac{106}{x+3}$
$\left(-6{x}^{3}+{x}^{2}-4\right)÷\left(2x-3\right)$
$\left(2{x}^{3}+7{x}^{2}-13x-3\right)÷\left(2x-3\right)$
${x}^{2}+5x+1$
$\left(3{x}^{3}-5{x}^{2}+2x+3\right)÷\left(x+2\right)$
$\left(4{x}^{3}-5{x}^{2}+13\right)÷\left(x+4\right)$
$4{x}^{2}-21x+84-\frac{323}{x+4}$
$\left({x}^{3}-3x+2\right)÷\left(x+2\right)$
$\left({x}^{3}-21{x}^{2}+147x-343\right)÷\left(x-7\right)$
${x}^{2}-14x+49$
$\left({x}^{3}-15{x}^{2}+75x-125\right)÷\left(x-5\right)$
$\left(9{x}^{3}-x+2\right)÷\left(3x-1\right)$
$3{x}^{2}+x+\frac{2}{3x-1}$
$\left(6{x}^{3}-{x}^{2}+5x+2\right)÷\left(3x+1\right)$
$\left({x}^{4}+{x}^{3}-3{x}^{2}-2x+1\right)÷\left(x+1\right)$
${x}^{3}-3x+1$
$\left({x}^{4}-3{x}^{2}+1\right)÷\left(x-1\right)$
$\left({x}^{4}+2{x}^{3}-3{x}^{2}+2x+6\right)÷\left(x+3\right)$
${x}^{3}-{x}^{2}+2$
$\left({x}^{4}-10{x}^{3}+37{x}^{2}-60x+36\right)÷\left(x-2\right)$
$\left({x}^{4}-8{x}^{3}+24{x}^{2}-32x+16\right)÷\left(x-2\right)$
${x}^{3}-6{x}^{2}+12x-8$
$\left({x}^{4}+5{x}^{3}-3{x}^{2}-13x+10\right)÷\left(x+5\right)$
$\left({x}^{4}-12{x}^{3}+54{x}^{2}-108x+81\right)÷\left(x-3\right)$
${x}^{3}-9{x}^{2}+27x-27$
$\left(4{x}^{4}-2{x}^{3}-4x+2\right)÷\left(2x-1\right)$
$\left(4{x}^{4}+2{x}^{3}-4{x}^{2}+2x+2\right)÷\left(2x+1\right)$
$2{x}^{3}-2x+2$
For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization.
$x-2,\text{\hspace{0.17em}}4{x}^{3}-3{x}^{2}-8x+4$
$x-2,\text{\hspace{0.17em}}3{x}^{4}-6{x}^{3}-5x+10$
Yes $\text{\hspace{0.17em}}\left(x-2\right)\left(3{x}^{3}-5\right)$
$x+3,\text{\hspace{0.17em}}-4{x}^{3}+5{x}^{2}+8$
$x-2,\text{\hspace{0.17em}}4{x}^{4}-15{x}^{2}-4$
Yes $\text{\hspace{0.17em}}\left(x-2\right)\left(4{x}^{3}+8{x}^{2}+x+2\right)$
$x-\frac{1}{2},\text{\hspace{0.17em}}2{x}^{4}-{x}^{3}+2x-1$
$x+\frac{1}{3},\text{\hspace{0.17em}}3{x}^{4}+{x}^{3}-3x+1$
No
## Graphical
For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.
Factor is $\text{\hspace{0.17em}}{x}^{2}-x+3$
Factor is $\text{\hspace{0.17em}}\left({x}^{2}+2x+4\right)$
$\left(x-1\right)\left({x}^{2}+2x+4\right)$
Factor is $\text{\hspace{0.17em}}{x}^{2}+2x+5$
Factor is $\text{\hspace{0.17em}}{x}^{2}+x+1$
$\left(x-5\right)\left({x}^{2}+x+1\right)$
Factor is ${x}^{2}+2x+2$
For the following exercises, use synthetic division to find the quotient and remainder.
$\frac{4{x}^{3}-33}{x-2}$
$\text{Quotient:}\text{\hspace{0.17em}}4{x}^{2}+8x+16\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}-1$
$\frac{2{x}^{3}+25}{x+3}$
$\frac{3{x}^{3}+2x-5}{x-1}$
$\text{Quotient:}\text{\hspace{0.17em}}3{x}^{2}+3x+5\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}0$
$\frac{-4{x}^{3}-{x}^{2}-12}{x+4}$
$\frac{{x}^{4}-22}{x+2}$
$\text{Quotient:}\text{\hspace{0.17em}}{x}^{3}-2{x}^{2}+4x-8\text{,}\text{\hspace{0.17em}}\text{remainder:}\text{\hspace{0.17em}}-6$
## Technology
For the following exercises, use a calculator with CAS to answer the questions.
Consider $\text{\hspace{0.17em}}\frac{{x}^{k}-1}{x-1}\text{\hspace{0.17em}}$ with What do you expect the result to be if $\text{\hspace{0.17em}}k=4?$
Consider $\text{\hspace{0.17em}}\frac{{x}^{k}+1}{x+1}\text{\hspace{0.17em}}$ for What do you expect the result to be if $\text{\hspace{0.17em}}k=7?$
${x}^{6}-{x}^{5}+{x}^{4}-{x}^{3}+{x}^{2}-x+1$
Consider $\text{\hspace{0.17em}}\frac{{x}^{4}-{k}^{4}}{x-k}\text{\hspace{0.17em}}$ for What do you expect the result to be if $\text{\hspace{0.17em}}k=4?$
Consider $\text{\hspace{0.17em}}\frac{{x}^{k}}{x+1}\text{\hspace{0.17em}}$ with What do you expect the result to be if $\text{\hspace{0.17em}}k=4?$
${x}^{3}-{x}^{2}+x-1+\frac{1}{x+1}$
Consider $\text{\hspace{0.17em}}\frac{{x}^{k}}{x-1}\text{\hspace{0.17em}}$ with What do you expect the result to be if $\text{\hspace{0.17em}}k=4?$
## Extensions
For the following exercises, use synthetic division to determine the quotient involving a complex number.
$\frac{x+1}{x-i}$
$1+\frac{1+i}{x-i}$
$\frac{{x}^{2}+1}{x-i}$
$\frac{x+1}{x+i}$
$1+\frac{1-i}{x+i}$
$\frac{{x}^{2}+1}{x+i}$
$\frac{{x}^{3}+1}{x-i}$
${x}^{2}-ix-1+\frac{1-i}{x-i}$
## Real-world applications
For the following exercises, use the given length and area of a rectangle to express the width algebraically.
Length is $\text{\hspace{0.17em}}x+5,\text{\hspace{0.17em}}$ area is $\text{\hspace{0.17em}}2{x}^{2}+9x-5.$
Length is area is $\text{\hspace{0.17em}}4{x}^{3}+10{x}^{2}+6x+15$
$2{x}^{2}+3$
Length is $\text{\hspace{0.17em}}3x–4,\text{\hspace{0.17em}}$ area is $\text{\hspace{0.17em}}6{x}^{4}-8{x}^{3}+9{x}^{2}-9x-4$
For the following exercises, use the given volume of a box and its length and width to express the height of the box algebraically.
Volume is $\text{\hspace{0.17em}}12{x}^{3}+20{x}^{2}-21x-36,\text{\hspace{0.17em}}$ length is $\text{\hspace{0.17em}}2x+3,\text{\hspace{0.17em}}$ width is $\text{\hspace{0.17em}}3x-4.$
$2x+3$
Volume is $\text{\hspace{0.17em}}18{x}^{3}-21{x}^{2}-40x+48,\text{\hspace{0.17em}}$ length is $\text{\hspace{0.17em}}3x–4,\text{\hspace{0.17em}}$ width is $\text{\hspace{0.17em}}3x–4.$
Volume is $\text{\hspace{0.17em}}10{x}^{3}+27{x}^{2}+2x-24,\text{\hspace{0.17em}}$ length is $\text{\hspace{0.17em}}5x–4,\text{\hspace{0.17em}}$ width is $\text{\hspace{0.17em}}2x+3.$
$x+2$
Volume is $\text{\hspace{0.17em}}10{x}^{3}+30{x}^{2}-8x-24,\text{\hspace{0.17em}}$ length is $\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}$ width is $\text{\hspace{0.17em}}x+3.$
For the following exercises, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.
Volume is $\text{\hspace{0.17em}}\pi \left(25{x}^{3}-65{x}^{2}-29x-3\right),\text{\hspace{0.17em}}$ radius is $\text{\hspace{0.17em}}5x+1.$
$x-3$
Volume is $\text{\hspace{0.17em}}\pi \left(4{x}^{3}+12{x}^{2}-15x-50\right),\text{\hspace{0.17em}}$ radius is $\text{\hspace{0.17em}}2x+5.$
Volume is $\text{\hspace{0.17em}}\pi \left(3{x}^{4}+24{x}^{3}+46{x}^{2}-16x-32\right),\text{\hspace{0.17em}}$ radius is $\text{\hspace{0.17em}}x+4.$
$3{x}^{2}-2$
write down the polynomial function with root 1/3,2,-3 with solution
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
what is the answer to dividing negative index
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
give me the waec 2019 questions
the polar co-ordinate of the point (-1, -1)
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
tanh`(x-iy) =A+iB, find A and B
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
1+cos²A/cos²A=2cosec²A-1
test for convergence the series 1+x/2+2!/9x3
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# Search by Topic
#### Resources tagged with Working systematically similar to Button-up:
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### There are 320 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically
### Button-up
##### Stage: 1 Challenge Level:
My coat has three buttons. How many ways can you find to do up all the buttons?
### Mixed-up Socks
##### Stage: 1 Challenge Level:
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
### Unit Differences
##### Stage: 1 Challenge Level:
This challenge is about finding the difference between numbers which have the same tens digit.
### Ordered Ways of Working Lower Primary
##### Stage: 1 Challenge Level:
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
### Jigsaw Pieces
##### Stage: 1 Challenge Level:
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
### Finding All Possibilities Lower Primary
##### Stage: 1 Challenge Level:
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
### Snakes
##### Stage: 1 Challenge Level:
Explore the different snakes that can be made using 5 cubes.
### Leap Frog
##### Stage: 1 Challenge Level:
The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?
### Nineteen Hexagons
##### Stage: 1 Challenge Level:
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
### Red Express Train
##### Stage: 1 Challenge Level:
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
### Finding All Possibilities Lower Primary
##### Stage: 1 Challenge Level:
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
### Four-triangle Arrangements
##### Stage: 1 Challenge Level:
How many different shapes can you make by putting four right- angled isosceles triangles together?
### Name the Children
##### Stage: 1 Challenge Level:
Can you find out in which order the children are standing in this line?
### Rolling That Cube
##### Stage: 1 and 2 Challenge Level:
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
##### Stage: 1 and 2 Challenge Level:
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
### The School Trip
##### Stage: 1 Challenge Level:
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
### A Bag of Marbles
##### Stage: 1 Challenge Level:
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
### Ordered Ways of Working Lower Primary
##### Stage: 1 Challenge Level:
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
### 3 Blocks Towers
##### Stage: 1 Challenge Level:
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
### The Add and Take-away Path
##### Stage: 1 Challenge Level:
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
### Late Again
##### Stage: 1 Challenge Level:
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
### Three Ball Line Up
##### Stage: 1 Challenge Level:
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
### Homes
##### Stage: 1 Challenge Level:
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
##### Stage: 1 Challenge Level:
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
### Briefcase Lock
##### Stage: 1 Challenge Level:
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
### Jumping Cricket
##### Stage: 1 Challenge Level:
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
### Train Routes
##### Stage: 1 Challenge Level:
This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?
### Growing Garlic
##### Stage: 1 Challenge Level:
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
### Lots of Lollies
##### Stage: 1 Challenge Level:
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
### Cover the Camel
##### Stage: 1 Challenge Level:
Can you cover the camel with these pieces?
### Whose Sandwich?
##### Stage: 1 Challenge Level:
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
### Triangle Animals
##### Stage: 1 Challenge Level:
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
### Team Scream
##### Stage: 2 Challenge Level:
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
### Crack the Code
##### Stage: 2 Challenge Level:
The Zargoes use almost the same alphabet as English. What does this birthday message say?
### Bunny Hop
##### Stage: 2 Challenge Level:
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
### Calendar Cubes
##### Stage: 2 Challenge Level:
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
### Newspapers
##### Stage: 2 Challenge Level:
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
### Jumping Squares
##### Stage: 1 Challenge Level:
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
### Teddy Town
##### Stage: 1, 2 and 3 Challenge Level:
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
### Button-up Some More
##### Stage: 2 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
### Ordered Ways of Working Upper Primary
##### Stage: 2 Challenge Level:
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
### Broken Toaster
##### Stage: 2 Short Challenge Level:
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
### Area and Perimeter
##### Stage: 2 Challenge Level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
### Professional Circles
##### Stage: 2 Challenge Level:
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
### Dice Stairs
##### Stage: 2 Challenge Level:
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
### Centred Squares
##### Stage: 2 Challenge Level:
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
### Pasta Timing
##### Stage: 2 Challenge Level:
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
### Ice Cream
##### Stage: 2 Challenge Level:
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
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https://mirror.codeforces.com/problemset/problem/1468/H
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H. K and Medians
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
Let's denote the median of a sequence $s$ with odd length as the value in the middle of $s$ if we sort $s$ in non-decreasing order. For example, let $s = [1, 2, 5, 7, 2, 3, 12]$. After sorting, we get sequence $[1, 2, 2, \underline{3}, 5, 7, 12]$, and the median is equal to $3$.
You have a sequence of $n$ integers $[1, 2, \dots, n]$ and an odd integer $k$.
In one step, you choose any $k$ elements from the sequence and erase all chosen elements except their median. These elements do not have to go continuously (gaps are allowed between them).
For example, if you have a sequence $[1, 2, 3, 4, 5, 6, 7]$ (i.e. $n=7$) and $k = 3$, then the following options for the first step are possible:
• choose $[1, \underline{2}, 3]$; $2$ is their median, so it is not erased, and the resulting sequence is $[2, 4, 5, 6, 7]$;
• choose $[2, \underline{4}, 6]$; $4$ is their median, so it is not erased, and the resulting sequence is $[1, 3, 4, 5, 7]$;
• choose $[1, \underline{6}, 7]$; $6$ is their median, so it is not erased, and the resulting sequence is $[2, 3, 4, 5, 6]$;
• and several others.
You can do zero or more steps. Can you get a sequence $b_1$, $b_2$, ..., $b_m$ after several steps?
You'll be given $t$ test cases. Solve each test case independently.
Input
The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains three integers $n$, $k$, and $m$ ($3 \le n \le 2 \cdot 10^5$; $3 \le k \le n$; $k$ is odd; $1 \le m < n$) — the length of the sequence you have, the number of elements you choose in each step and the length of the sequence you'd like to get.
The second line of each test case contains $m$ integers $b_1, b_2, \dots, b_m$ ($1 \le b_1 < b_2 < \dots < b_m \le n$) — the sequence you'd like to get, given in the ascending order.
It's guaranteed that the total sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
Output
For each test case, print YES if you can obtain the sequence $b$ or NO otherwise. You may print each letter in any case (for example, YES, Yes, yes, yEs will all be recognized as positive answer).
Example
Input
43 3 117 3 31 5 710 5 34 5 613 7 71 3 5 7 9 11 12
Output
NO
YES
NO
YES
Note
In the first test case, you have sequence $[1, 2, 3]$. Since $k = 3$ you have only one way to choose $k$ elements — it's to choose all elements $[1, \underline{2}, 3]$ with median $2$. That's why after erasing all chosen elements except its median you'll get sequence $[2]$. In other words, there is no way to get sequence $b = [1]$ as the result.
In the second test case, you have sequence $[1, 2, 3, 4, 5, 6, 7]$ and one of the optimal strategies is following:
1. choose $k = 3$ elements $[2, \underline{3}, 4]$ and erase them except its median; you'll get sequence $[1, 3, 5, 6, 7]$;
2. choose $3$ elements $[3, \underline{5}, 6]$ and erase them except its median; you'll get desired sequence $[1, 5, 7]$;
In the fourth test case, you have sequence $[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]$. You can choose $k=7$ elements $[2, 4, 6, \underline{7}, 8, 10, 13]$ and erase them except its median to get sequence $b$.
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https://www.tutorialspoint.com/java-program-to-check-if-a-given-number-is-perfect-number
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# Java Program to Check if a given Number is Perfect Number
When the sum of factors of a given number (after discarding the given number) is equal to the number itself is called a perfect number.
In this article, we will create java programs to check if a given number is perfect or not. for the given problem we are going to use iterative approaches like for loop and while loop. Let’s try to understand through some examples −
Example 1
Given number: 496
Its factors are: 1, 2, 4, 8, 16, 31, 62, 124 and 248 ( we have to exclude 496 )
Sum of the factors are: 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496
Therefore, it is a perfect number
Example 2
Given number: 54
Its factors are: 1, 2, 3, 6, 9, 18 and 27 ( we have to exclude 54 )
Sum of the factors are: 1 + 2 + 3 + 6 + 9 + 18 + 27 = 66
Therefore, it is not a perfect number
## Approach 1: Using For loop
### Syntax
for ( initial expression; conditional expression; increment/decrement expression )
{
// code to be executed
}
initial expression − executed once when loop begins.
conditional expression − code will be executed till conditional expression is true.
increment/decrement expression − to increment/decrement loop variable.
### Algorithm
• Step 1 − Declare and initialize an integer variable ‘n1’ to check if it is a perfect number or not and another integer variable ‘add’ to store the result of sum of factors of 496.
• Step 2 − Take a for loop that will run 495 times i.e. ‘n1-1’ because we have to exclude the given number. The if block inside for loop will check which number till 495 divides the number 496 completely and if it divides then it will increment ‘add’ variable with that number.
• Step 3 − The last if-else block will check whether the sum of factors is equal to given number or not. In the case of 496, the if block is true that’s why we will get result as 496 is a perfect number.
### Example
import java.util.*;
public class Perfect {
public static void main(String[] args) {
int n1 = 496;
for(int i = 1; i < n1; i++) {
if(n1 % i==0) {
}
}
boolean isPerfect = (add == n1);
if(isPerfect) {
System.out.println("is " + n1 + " a perfect number?: " + isPerfect);
} else {
System.out.println("is " + n1 + " a perfect number?: " + isPerfect);
}
}
}
### Output
is 496 a perfect number?: true
## Approach 2: Using While loop
### Syntax
while (conditional expression) {
// code will be executed till conditional expression is true
increment/decrement expression;
// to increment or decrement loop variable
}
### Example
import java.util.*;
public class Main {
public static void main(String[] args) {
int n1 = 28;
int i = 1;
// loop variable
while(i < n1) {
if(n1 % i == 0) {
}
i++;
// incrementing
}
boolean isPerfect = (add == n1);
if(isPerfect) {
System.out.println("is " + n1 + " a perfect number?: " + isPerfect);
} else {
System.out.println("is " + n1 + " a perfect number?: " + isPerfect);
}
}
}
### Output
is 28 a perfect number?: true
In the above program, we have followed the same logic but with different value of variable ‘n1’ and instead of for loop we have used while loop.
## Approach 3: Running the loop till n/2
This approach is more optimized than the other two approaches we have discussed earlier in this article. In this approach, the loop will iterate till half of the given number only becaue we can find all factors of a number (excluding number itself) in between half of that number.
### Example
import java.util.*;
public class Perfect {
public static void main(String[] args) {
int n1=6;
int i=1;
while(i <= n1/2) {
// loop will run till 3 ( 6/2 = 3)
if(n1 % i==0) {
}
i++;
}
boolean isPerfect = (add == n1);
if(isPerfect) {
System.out.println("is " + n1 + " a perfect number?: " + isPerfect);
} else {
System.out.println("is " + n1 + " a perfect number?: " + isPerfect);
}
}
}
### Output
is 6 a perfect number?: true
## Conclusion
In this article, we have seen three approaches of java program to check if a given number is perfect or not. We understood how to use iterative approaches to make a java program. The approach 3 is more optimized and recommended by us.
Updated on: 25-Apr-2023
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## psyco-devel — Technical or open discussion
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[Psyco-devel] Re: Attempting the 'quick' float solution From: Tim Hochberg - 2002-01-07 18:31:35 ```Following up myself: you can ignore this last message. By trying several different things and mindless copying of pintobject.h I now have rudimentary float support working in psyco. Only add and subtract are working right now, and conversion from ints to floats is not yet supported, but the following silly function runs 4.5 times faster than base python in my version of Psyco, versus 2.5 times faster in CVS psyco. def f10(): z = 0.0 for i in range(100000): z = z - 5.0 y = z + 10. x = y + 10. y = z - 10. x = y + 10. y = z + 10. x = y - 10. y = z + 10. x = y + 10. x = y + 10. y = z - 10. x = y + 10. y = z + 10. x = y + 10. z = z - x return z The next step it to get the other operations working, which should be easy, and get coercion working which I _hope_ will be easy, but I haven't looked into it yet... -tim ----- Original Message ----- From: "Tim Hochberg" To: "Armin Rigo" Cc: Sent: Saturday, January 05, 2002 2:42 PM Subject: Attempting the 'quick' float solution > > Some time ago Armin wrote: > > >[SNIP] let me first > >describe a quick solution that would probably still give a serious > >speed-up to all FP operations. > > I'm attempting to do this on the theory that as I work on the little pieces, > I may absorb enough by osmosis to understand how Psyco actually works. This > may be false, but perhaps I can accomplish something useful anyway. If > someone else is already working on this, let me know and I'll try something > else. I'm sure I'll be asking for guidance repeatedly, but I'll try not to > be too much of a pest... > > These parts are 'done' (they will certainly require some debugging): > > * cimpl_fp_XXX > * PsycoFloat_FROM_DOUBLE() > * PsycoFloat_AS_DOUBLE_1() and PsycoFloat_AS_DOUBLE_2() > > Hmmm.... that list looks awfully short so far ... sigh. Anyway, my question > for today involves ploat_add and friends. Armin suggested: > > >2) meta-implementation: just like we have pint_add()&co, we need > >pfloat_add()&co. A priori, pfloat_add() is something like: > > > >static vinfo_t* pfloat_add(PsycoObject* po, vinfo_t* v, vinfo_t* w) > >{ > > vinfo_t *a1, *a2, *b1, *b2, *x; > > vinfo_array_t* result; > > a1 = PsycoFloat_AS_DOUBLE_1(po, v); > > a2 = PsycoFloat_AS_DOUBLE_2(po, v); > > b1 = PsycoFloat_AS_DOUBLE_1(po, w); > > b2 = PsycoFloat_AS_DOUBLE_2(po, w); > > /* ... */ > >} > > Is there any reason that this can't be done in the same way as pint_add. For > example: > > static vinfo_t* pfloat_add(PsycoObject* po, vinfo_t* v, vinfo_t* w) > { > vinfo_t *a1, *a2, *b1, *b2, *x; > vinfo_array_t* result; > CONVERT_TO_DOUBLE(v, a1, a2); > CONVERT_TO_DOUBLE(w, b1, b2); > /* ... */ > } > > Where CONVERT_TO_DOUBLE would start out as: > > define CONVERT_TO_DOUBLE(vobj, vlng1, vlng2) \ > if (Psyco_TypeSwitch(po, vobj, &psyfs_float) == 0) { \ > PsycoFloat_AS_DOUBLE(po, vobj1, vobj2); \ > if (vlng1 == NULL || vlng2 == NULL) \ > return NULL; \ > } \ > else { \ > if (PycException_Occurred(po)) \ > return NULL; \ > vinfo_incref(psyco_viNotImplemented); \ > return psyco_viNotImplemented; \ > } > > > Eventually it would get extended as we allowed integers and other types to > be converted to floats. psyfs_float would have to be defined in pobject.c > and presumably entered into some array of fixed_switch values somewhere, but > I haven't got that far yet. > > Is this a reasonable way to approach this if my goal is to first get > float-float operations working and then to branch out from there, or am I > way off target here.... > > Thanks, > > -tim > > ```
[Psyco-devel] Attempting the 'quick' float solution From: Tim Hochberg - 2002-01-05 21:43:02 ```Some time ago Armin wrote: >[SNIP] let me first >describe a quick solution that would probably still give a serious >speed-up to all FP operations. I'm attempting to do this on the theory that as I work on the little pieces, I may absorb enough by osmosis to understand how Psyco actually works. This may be false, but perhaps I can accomplish something useful anyway. If someone else is already working on this, let me know and I'll try something else. I'm sure I'll be asking for guidance repeatedly, but I'll try not to be too much of a pest... These parts are 'done' (they will certainly require some debugging): * cimpl_fp_XXX * PsycoFloat_FROM_DOUBLE() * PsycoFloat_AS_DOUBLE_1() and PsycoFloat_AS_DOUBLE_2() Hmmm.... that list looks awfully short so far ... sigh. Anyway, my question for today involves ploat_add and friends. Armin suggested: >2) meta-implementation: just like we have pint_add()&co, we need >pfloat_add()&co. A priori, pfloat_add() is something like: > >static vinfo_t* pfloat_add(PsycoObject* po, vinfo_t* v, vinfo_t* w) >{ > vinfo_t *a1, *a2, *b1, *b2, *x; > vinfo_array_t* result; > a1 = PsycoFloat_AS_DOUBLE_1(po, v); > a2 = PsycoFloat_AS_DOUBLE_2(po, v); > b1 = PsycoFloat_AS_DOUBLE_1(po, w); > b2 = PsycoFloat_AS_DOUBLE_2(po, w); > /* ... */ >} Is there any reason that this can't be done in the same way as pint_add. For example: static vinfo_t* pfloat_add(PsycoObject* po, vinfo_t* v, vinfo_t* w) { vinfo_t *a1, *a2, *b1, *b2, *x; vinfo_array_t* result; CONVERT_TO_DOUBLE(v, a1, a2); CONVERT_TO_DOUBLE(w, b1, b2); /* ... */ } Where CONVERT_TO_DOUBLE would start out as: define CONVERT_TO_DOUBLE(vobj, vlng1, vlng2) \ if (Psyco_TypeSwitch(po, vobj, &psyfs_float) == 0) { \ PsycoFloat_AS_DOUBLE(po, vobj1, vobj2); \ if (vlng1 == NULL || vlng2 == NULL) \ return NULL; \ } \ else { \ if (PycException_Occurred(po)) \ return NULL; \ vinfo_incref(psyco_viNotImplemented); \ return psyco_viNotImplemented; \ } Eventually it would get extended as we allowed integers and other types to be converted to floats. psyfs_float would have to be defined in pobject.c and presumably entered into some array of fixed_switch values somewhere, but I haven't got that far yet. Is this a reasonable way to approach this if my goal is to first get float-float operations working and then to branch out from there, or am I way off target here.... Thanks, -tim ```
Re: [Psyco-devel] Bug report From: Petru Paler - 2002-01-05 17:49:47 ```Hello, On Sat, 2002-01-05 at 19:26, Armin Rigo wrote: > Where can we find pybench? http://www.lemburg.com/files/python/ -- Petru Paler, http://www.ppetru.net ```
Re: [Psyco-devel] Bug report From: Armin Rigo - 2002-01-05 17:44:22 ```Hello Petru, Petru Paler wrote: > I tried to run pybench using Kjetil's new selective compilation function > written in C. Where can we find pybench? > Looks like bad things happen when it tries to compile builtin stuff... I do not think it is related to its being built-in: I guess the 'split' mentionned is not the built-in one, but the one from the standard module 'string'. It might be a coincidence, as 'string.split' seems to compile fine on other examples. Armin. ```
Re: [Psyco-devel] Re: selective compilation From: Armin Rigo - 2002-01-05 17:44:16 ```Hello Samuele, Samuele Pedroni wrote: > A question: it is because it is ineherently difficult to start compilin= g > from the middle of an execution given psyco approach? Well, it was not meant to be done so. I am not sure it is inherently difficult, but at least it is not trivial: there is quite a lot of info stored in Python-specific structures like frames which would need to be translated into their Psyco equivalent. Maybe this should be discussed in a more general setting in which Psyco could produce incrementally optimized code. Doing so would require us to stop the exeuction at any point and restart it elsewhere, in the newly re-optimized code. Or we could believe that two levels will always be enough: not compiled at all (run by Python) and compiled with all optimizations (only for the innermost loops). There is another thing that I did not discuss up to now, but which could become very meaningful: optimizing data structures. There is little point in optimizing code that loops over all items of a list if all these items are Python objects whose type must be checked at each iteration anyway. So some structures like lists or instance of user-defined classes need to be optimized. For lists this is not quite easy: we cannot just arbitrarily replace lists created by user code by Python objects of another type, e.g. "Psyco-aware list". This would break code: C code (clearly) but also Python code, as in 'if type(x)=3D=3DListType'. Instances are more flexible: we could use Python 2.2's new type system and define a Psyco metaclass. With some tricks, most user-level classes would then use Psyco's metaclass instead of Python's. The interest is that metaclasses control the way instance attributes are stored. This would in theory let us detect that a given attribute always contains an integer, and store directly the integer value instead of a Python integer object in the instance. In both cases, however, we would have much more knowledge about an object if it were built by Psyco-compiled code. Why? Because if, say, a list is populated by Python code, and only later we see it, then we must guess what could be the common points of all objects in the list (e.g. being a integer objects, being tuples of length 2, and so on). On the other hand, if the list is built by Psyco-compiled code, the Psyco compiler has seen the calls to list.append(), and generally knows something about the objects that were passed as arguments to list.append() -- for example, they were all virtual-time integer objects. The same applies to instances: Psyco usually knows something about 'x' when it compiles 'obj.attr =3D x'. With this point of view, Psyco would work much better if *all* the code had been compiled by it. Well, maybe it would be better to see what occurs on real-world scripts if we just compile everything. The problem is rather about memory than speed, I guess, as compiling infrequently-used code might only be a minor time loss. So in summary, I believe that we should postpone the discussion about when Psyco should compile what until serious advances in the core of Psyco or in its Python support files. The neural network example 'bpnn.py' shows that Psyco is not efficient on lists of lists nor instance objects. I propose that we give ourselves as the next goal: make 'bpnn.py' work significantly faster in Psyco than in Python (it is currently significantly slower). Just compiling everything is fine for 'bpnn.py'. Virtualizing float objects as I discussed in a previous e-mail would be a first step. Virtualizing lists and instances is the final goal. Please ask if you would like to help about floats but don't understand what I told in (the first part of) the e-mail about floats. A bient=F4t, Armin. ```
Re: [Psyco-devel] Re: selective compilation From: Samuele Pedroni - 2002-01-05 12:36:47 ```[Armin Rigo] > > Kjetil Jacobsen wrote: > > the problem with the current approach to selective compilation is that a > > function may be called only once and still account for most of the > > computation time. > > Yes, sure. Well, even with deep messing into Python's internals, I > believe it would be difficult and wrong to try to start compiling a > function in the middle of its execution; so it means that we cannot > handle the case of long functions only executed once. A question: it is because it is ineherently difficult to start compiling from the middle of an execution given psyco approach? From my readings a typical approach to detect the need of compilation for long running methods is to count "looping" (e.g. decrementing a counter associated with the function on every looping (back) branch and triggering compilation when it reaches zero. ) So at least compilation would be naturally triggered at a merge-point, could this help? regards, Samuele Pedroni. ```
[Psyco-devel] Bug report From: Petru Paler - 2002-01-04 23:41:56 ```I tried to run pybench using Kjetil's new selective compilation function written in C. Using the latest CVS source, I added an "import psyco" line at the top of pybench.py and tried to run it. I get a segfault with debugging disabled, and this: psyco: compiling function split [40][36][60][32][36][36][120]nonnull_refcount: item 2 nonnull_refcount: in array item 5 python: c/vcompiler.c:323: psyco_assert_coherent: Assertion `!err' failed. Aborted with debugging enabled. Looks like bad things happen when it tries to compile builtin stuff... -- Petru Paler, http://www.ppetru.net ```
Re: [Psyco-devel] Compilation on Windows? From: Petru Paler - 2002-01-04 23:30:13 ```On Fri, 2002-01-04 at 19:01, Tim Hochberg wrote: > I suppose the underscores are meant to signal that the macros aren't really > meant to be used by the unwary. I'll submit a patch to Psyco at sourceforge. I applied the patch to CVS. Armin: I don't have permission to modify the bug status, could you please grant it to me? -- Petru Paler, http://www.ppetru.net ```
[Psyco-devel] Re: selective compilation From: Armin Rigo - 2002-01-04 17:58:25 ```Hello Kjetil, A few quick notes, more to come... Kjetil Jacobsen wrote: > the problem with the current approach to selective compilation is that a > function may be called only once and still account for most of the > computation time. Yes, sure. Well, even with deep messing into Python's internals, I believe it would be difficult and wrong to try to start compiling a function in the middle of its execution; so it means that we cannot handle the case of long functions only executed once. We still have to work on Psyco before we know if we could let it compile a large part of the code or if it should target only a few crucial functions. > (solution) be to use the execution time instead of the number of invocations as a > metric for determining whether a function should be compiled, since proc0 > in this example is the function having the longest execution time. Yes, that would be a good solution if we have a very fast way of measuring time. More tests needed there. Also note that if we measure the time, this is done at the end, when the function returns; if dynamically rebinding occurs at this moment, it solves the problem you mentionned about functions being regularily executed once even after rebinding, if that rebinding occurs at the beginning. Finally, collecting statistics between runs would be a good idea too, but should be planned only with a Psyco-specific kind of '.pyc' file format that would also store already-compiled code buffers. The latter has some drawbacks: on a Linux box, all .py files from the standard library are stored in directories where users cannot write; where should Psyco write its own optimization files? Unlike regular '.pyc' files, Psyco's will change all the time. Armin ```
Re: [Psyco-devel] Compilation on Windows? From: Tim Hochberg - 2002-01-04 17:01:49 ```[Tim Hochberg] > > Has anyone successfully compiled Psyco on Windows? I'm plugging along trying > > to get it to compile on Windows 2000 with Python 2.2 final. I've made some > > progress, everything now compiles, albeit with a boatload of warnings about > > truncating ints to chars, but can't link because of an unresolved reference > > to __PyGC_generation0. [Michael Hudson] > IIRC, you want to change an occurence of something like > > PyGC_Object_TRACK > > to something like > > PyGC_Object_Track Thanks! That did the trick. If anyone else is trying this, the specific substitutions occur in pscyo.c and are: _PyObject_GC_TRACK -> PyObject_GC_Track _PyObject_GC_UNTRACK -> PyObject_GC_UnTrack I suppose the underscores are meant to signal that the macros aren't really meant to be used by the unwary. I'll submit a patch to Psyco at sourceforge. > > I'm wondering if the declaration in Python's objimpl.h requires a DL_IMPORT > > declaration, FWIW, this didn't appear to help and I wasn't inclined to pursue it much after I noticed that the macros were marked with a forbidding underscore. -tim ```
Re: [Psyco-devel] Compilation on Windows? From: Michael Hudson - 2002-01-04 10:54:47 ```On Thu, 3 Jan 2002, Tim Hochberg wrote: > > Has anyone successfully compiled Psyco on Windows? I'm plugging along trying > to get it to compile on Windows 2000 with Python 2.2 final. I've made some > progress, everything now compiles, albeit with a boatload of warnings about > truncating ints to chars, but can't link because of an unresolved reference > to __PyGC_generation0. IIRC, you want to change an occurence of something like PyGC_Object_TRACK to something like PyGC_Object_Track > I'm wondering if the decleration in Python's objimpl.h requires a DL_IMPORT > declaration, maybe. > but that's pure speculation as most of that dynamic library is > pure black magic to me. me too. > I'll probably try changing that -- requiring a recompile of python, Would be interesting to see if it helped. Submit a patch to sf (for Python) if it does? > but I'm wondering if anyone has a better idea of how to do this. > Also, anyone know of a good way to search the archives of this list? Um, emailing me regexp patterns? I've got a complete mbox archive if anyone wants a copy. Cheers, M. ```
[Psyco-devel] Compilation on Windows? From: Tim Hochberg - 2002-01-03 23:09:30 ```Has anyone successfully compiled Psyco on Windows? I'm plugging along trying to get it to compile on Windows 2000 with Python 2.2 final. I've made some progress, everything now compiles, albeit with a boatload of warnings about truncating ints to chars, but can't link because of an unresolved reference to __PyGC_generation0. I'm wondering if the decleration in Python's objimpl.h requires a DL_IMPORT declaration, but that's pure speculation as most of that dynamic library is pure black magic to me. I'll probably try changing that -- requiring a recompile of python, but I'm wondering if anyone has a better idea of how to do this. Also, anyone know of a good way to search the archives of this list? -tim ```
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Got stuck on “Going to the cinema” Challenge
I didn’t understand the instruction of this challenge on `codewars` platform. I didn’t understand how to calculate the `system B` .
So I need explanation about how to calculate `system B` If John goes to the cinema 3 times or 5 times?
system B starts it has a price of 500 at the beginning. And then each ticket costs 15*0.9n where `n` is the number of the ticket (first ticket costs 15*0.91, second ticket 15*0.92 and so on)
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Spiked Math Games // Math Fail Blog // Gauss Facts // Spiked Math Forums // Spiked Math Comics
# 455
How to insult a mathematician - October 17, 2011
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ZOMG - it's like 3 comics in one!!!
Okay, not all of them are insults... see if you can come up with any additional ones.
I've gotten the casino one :(
So, then, what if your field IS number theory?
Number theory is so important, it is more important than itself.
Number theory is way more important than number theory
Ah, so the relation is reflexive
Number theory is twice as important as itself!
Bazinga!
So, if it's twice as itself:
2(NumberTheory) = Number Theory
Number Theory = 0
It's worthless.
This is really funny!
I got this one from one of my coauthors on a graph theory paper:
It's just graph theory. It's trivial.
"Your main theorem should really be a lemma, or perhaps an observation"
Now my little part of me is dying. :(
That's normal. It'll stand up again when it's needed.
These are a couple that I get a lot that drive me crazy:
So, what kind of job can you get with a math degree other than teach?
How do you do research in math?
OUCH for the first one.
In my case, I study ODE and one of the engineers told me: "there is nothing to study there, it is just the linear and the Ricatti equations and they are already solved" I was going to explain him Hilbert 16th problem ... but there was no point
For an engineer there's only 2 kinds of differential equations, the trivial ones and the ones you solve with Runge Kutta (or software using Runge Kutta).
- So what kind of math do you research?
- Algebra.
- Oh, I took that in high school. It was easy.
Taxi drivers. Grrr, taxi drivers!
"So that ex and wye stuff, whass that abaht? Whass it abaht?"
there should be a way to 'like' the comments here :)
^-- Like
^-- Like
My own family: "So tell me, what do you do with a math degree?"
With respect to the "creative thinking" remark: There's a story of Dirichlet, I think it was, when told a student had dropped out and gone to Berlin to be a poet, remarked: "It's just as well, he didn't have enough imagination to be a good mathematician."
It was Hilbert, but is is all good.
Ouch, you would post this the week MAA mailing with Putnam Q&A & results arrives in mailboxes.
I don't really feel so bad having a single digit tally as an underclassman (low single, but >1 ) ... before crossing to the darkside (applied computer stuff). Best advice I got on a computer job interview was to attend MAA regional chapter meetings to stay in touch with Maths.
When you can't multiply three digit numbers in your head: "I thought you were supposed to be good at math"
My field of research -is- number theory.
I've also heard the "The Big Bang Theory" one way too many times. Most of the time it's because I'm an engineer, but I've also been told how much I should love it simply because I'm a nerd. (I started a Sci-Fi club in college.)
I was once told that being good at math must make me a strong pool player. I then leaned down with the cue stick, and as I lined up the first shot, I muttered, "let epsilon be greater than zero..."
Oh snap, that about physics would send me into a rage fit... :D
Welcome to Spiked Math!
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# A small application of Fermat's Little Theorem
Suppose that $q$ is some prime number distinct from prime $p$ (in particular, assume $q < p$). I would like to show that the elements $q^1, q^2, ... , q^{p-1}$ modulo $p$ are all distinct from each other. This is what I have so far:
If $q^i \equiv q^j \mod p$ then $q^i - q^j \equiv 0 \mod p$. WLOG assume that $i < j$ so that we can fact
$q^i(1 - q^{j-i}) \equiv 0 \mod p$
which, since $p$ does not divide $q$, implies that $q^{j-i} \equiv 1 \mod p$.
Here I am tempted to say that $j-i$ must be some multiple of $p$, but am unable to rigorously justify it. Help would be appreciated.
• What you're trying to show is not true in general. Consider $q = 2$ and $p = 7$. Oct 16, 2013 at 0:28
You said that $q^{j-i} \equiv 1 \mod p$, that means that $j-i$ is multiplicative order of q modulo p or its multiple, but not every number is a multiplicative order of q modulo p or its multiple. So in order for this to be true the following needs to hold $j-i = k \cdot ord_p(q)$ for some natural number $k$
Also your assumtion $q^i \equiv q^j \pmod p$ will hold if and only if $i \equiv j \pmod {ord_p(q)}$.
And what you are actually trying to prove is that $q$ is primitive root modulo $p$, but only few numbers have that property and it doesn't hold for every number. Also it's good to know there's no specific way to find primitive root modulo $p$.
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Stoichiometry Video Lessons
Concept:
# Problem: Balance the equation and solve the following questions.CH3CH3 + O2 → CO2 + H2Oa) How many moles of CH3CH3 are in 13.50g of CH3CH3b) If 13.50g of CH3CH3 react with excess oxygen, how many g of water will be formed?c) If 13.50g of CH3CH3 react with excess oxygen how many moles of CO 2 will be formed?d) If 13.50g of CH3CH3 react with excess oxygen how many molecules of CO 2 will be formed?
###### FREE Expert Solution
We are being asked to balance the equation first in order to perform the succeeding stoichiometric calculations.
Before balancing the chemical reaction, let’s first write the chemical formula of each of the compounds involved in the reaction.
Reactants:
Ethane (gas)
Ethane: CH3CH3(g)
Oxygen (gas)
▪ oxygen gas is the natural state of oxygen
▪ natural state of oxygen O2(g)
Products:
Carbon dioxide (gas) CO2(g)
Water vapor (gas) H2O(g)
Unbalanced Chemical Reaction: CH3CH3(g) + O2(g) CO2(g) + H2O(g)
To make it easier for us to balance the equation, we can denote ethane (CH3CH3as C2H6.
Balancing the chemical reaction:
1. Balance the non oxygen and non hydrogen elements first:C
C2H6(g) + O2(g) 2 CO2(g) + H2O(g)
2. Balance Hydrogen
C2H6(g) + O2(g) 2 CO2(g) + 3 H2O(g)
3. Balance Oxygen
C2H6(g)+7/2O2(g) 2 CO2(g) + 3 H2O(g)
4. Make sure that all the coefficients are whole numbers
[ C2H6(g) + 7/2 O2(g) 2 CO2(g) + 3 H2O(g)] x 2
2 C2H6(g) + O2(g) 4 CO2(g) + 6 H2O(g)
Balanced Reaction Equation:
2 CH3CH3(g)7 O2(g) 4 CO2(g)6 H2O(g)
86% (354 ratings)
###### Problem Details
Balance the equation and solve the following questions.
CH3CH3 + O2 → CO2 + H2O
a) How many moles of CH3CH3 are in 13.50g of CH3CH3
b) If 13.50g of CH3CH3 react with excess oxygen, how many g of water will be formed?
c) If 13.50g of CH3CH3 react with excess oxygen how many moles of CO 2 will be formed?
d) If 13.50g of CH3CH3 react with excess oxygen how many molecules of CO 2 will be formed?
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REASONING QUIZ–11 BASED ON DATA SUFFICIENCY
REASONING QUIZ–11 BASED ON DATA SUFFICIENCY
Directions (1 – 10): Each of the questions below consists of a question and two statements numbered I and II are given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and
(a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
(b) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
(c) if the data in either in statement I alone or in statement II alone are sufficient to answer the question
(d) if the data in both the statement I and II are not sufficient to answer the question
(e) if the data in both the statement I and II together are necessary to answer the question
1. Is ‘S’ the father of ‘M’
I. ‘M’ is the sister of ‘Q’. ‘Q’ is sister of ‘R’ and ‘R’ is daughter of ‘S’
II. ‘M’ is daughter of ‘L’ and ‘L’ is sister of ‘V’
2. How far is point ‘P’ from point ‘Q’ (all the points lie on a straight line)
I. Point ‘T’ is exactly midway between ‘P’ and ‘Q’. Point ‘T’ is 5 km towards west of ‘R’
II . ‘Q’ is 2 km towards the east of ‘R’
3. What does ‘\$’ mean in a code language:
I. 5 \$#3 means ‘flowers are really good’
II. 7#35 means ‘good flowers are available
4.A 6-storey building consisting of an unoccupied ground floor and 5 floors on the top of the ground floor numbered 1,2,3,4,5 have different persons A,B,C,D,E who lives on the third floor:
I. C lives on an even numbered floor. A lives immediately above D. B lives immediately above A.
II. D lives on an odd numbered floor. A and B are immediate neighbourers. Similarly C and E are immediate neighbours. (does not live on an odd numbered floor)
5. On which day of the week is Mohan’s Exam is scheduled (Monday First day of week)
I. Mohan correctly remembers that his exam is scheduled on a day after Tuesday but before Thursday
II.Mohan’s Father correctly remembers that Mohan exam is scheduled on the third day of week
6. Among 5 friends A,B,C,D,E sitting around a circular table facing the center, who sits to the immediate right of A:
I. E sits 3rd to the right of D.A is not an immediate neighbor of D
II.C sits second to the left of B.A is not an immediate neighbor of C
7. In which direction is point E with reference to point S:
I. Point D is to the east of point E. Point E is to the south of point F.
II. Point F is to the north-west to point S. Point D is to the north of point S
8. What is Mr. A’s present income :
I. Mr A income increases by 10% every year
II. His income will increase by Rs 2500 this year
9. What is the ratio of the total number of girls to the total number of boys in school:
I. The ratio of the total number of boys to the total number of girls last year was 4:5
II. There are 3500 students in the school out of which 60% are boys.
10. What is Anita’s Age:
I. Anita is 3 times younger than Sapna.
II. Anita is twice the age of Sapna and the sum of their ages is 72.
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## ››Convert centimetre to mille [French]
cm mille
How many cm in 1 mille? The answer is 194900.
We assume you are converting between centimetre and mille [French].
You can view more details on each measurement unit:
cm or mille
The SI base unit for length is the metre.
1 metre is equal to 100 cm, or 0.00051308363263212 mille.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between centimetres and mille [French].
Type in your own numbers in the form to convert the units!
## ››Want other units?
You can do the reverse unit conversion from mille to cm, or enter any two units below:
## Enter two units to convert
From: To:
## ››Definition: Centimeter
A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundreth of a metre, the current SI base unit of length. A centimetre is part of a metric system. It is the base unit in the centimetre-gram-second system of units. A corresponding unit of area is the square centimetre. A corresponding unit of volume is the cubic centimetre.
The centimetre is a now a non-standard factor, in that factors of 103 are often preferred. However, it is practical unit of length for many everyday measurements. A centimetre is approximately the width of the fingernail of an adult person.
## ››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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Question
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• ### 4. An element has two naturally occurring isotopes. The mass numbers of these isotopes are 111...
4. An element has two naturally occurring isotopes. The mass numbers of these isotopes are 111 amu and 113 amu, with natural abundances of 25% and 75%, respectively. Calculate the atomic mass for this element. 6 pts
• ### Calculate the atomic mass of element "X", if it has 2 naturally occurring isotopes with the...
Calculate the atomic mass of element "X", if it has 2 naturally occurring isotopes with the following masses and natural abundances. X-45, 44.8776 amu, 32.88% X-47, 46.9443 amu, 67.12%
• ### An element has two naturally-occurring isotopes. The mass numbers of these isotopes are 125 amu and...
An element has two naturally-occurring isotopes. The mass numbers of these isotopes are 125 amu and 127 amu, with natural abundances of 80% and 20%, respectively. Calculate its average atomic mass. Report your answer to 1 decimal place. -------- amu
• ### An element has three naturally occurring isotopes with masses as listed below. The average atomic mass...
An element has three naturally occurring isotopes with masses as listed below. The average atomic mass of this element is 28.08 amu. Determine the two missing percent abundances.^28X 27.98 amu % abundance =^29X 28.98 amu % abundance = 4.68 %^30X 29.97 amu % abundance =
• ### 5) Calculate the atomic mass of an imaginary element X that has 3 naturally occurring isotopes...
5) Calculate the atomic mass of an imaginary element X that has 3 naturally occurring isotopes with the following masses and natural abundances: 106.90509 amu 108.90476 amu 107.91536 amu 51.84% 38.46% 9.70% A) 106.80 amu B) 108 amu C) 107.77 amu D) 108.32 amu E) 107.8 amu
• ### The element carbon has two naturally occurring isotopes. The isotopic masses and abundances of these isotopes...
The element carbon has two naturally occurring isotopes. The isotopic masses and abundances of these isotopes are shown in the table below. Isotope 12c isotopic mass (amu) Abundance (%) 12.00 13.00 98.93 1.07 Calculate the average atomic mass of carbon to two digits after the decimal point. Number = _______ amu
• ### Enter your answer in the provided box. An element has two naturally occurring isotopes. The mass...
Enter your answer in the provided box. An element has two naturally occurring isotopes. The mass numbers of these isotopes are 109 amu and 111 amu, with natural abundances of 35% and 65%, respectively. Calculate its average atomic mass. Report your answer to 1 decimal place. amu
• ### The element Oxygen consists of three naturally occurring isotopes with masses 15.949915, 16.999131, and 17.999159 amu....
The element Oxygen consists of three naturally occurring isotopes with masses 15.949915, 16.999131, and 17.999159 amu. The relative abundances of these three isotopes are 99.76, 0.03800, and 0.2000 percent, respectively. From these data calculate the average atomic mass of Oxygen (in amu).
• ### Most elements occur naturally as a mix of different isotopes. An element's atomic mass is the...
Most elements occur naturally as a mix of different isotopes. An element's atomic mass is the weighted average of the isotope masses. In other words, it is an average that takes into account the percentage of each isotope. For example, the two naturally occurring isotopes of boron are given here The atomic mass of boron is calculated as follows: (10.0 times 0.199) + (11.0 times 0.801) = 10.8 amu Because the heavier isotope is more abundant the atomic mass a...
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# Absolute Value
#### jUnIoRjUnCtIoNmAtHmAtH
##### New member
Hi there!
So I have the problem |y-2| + 11 > 0, and I got, for my two solutions, |y| > -9 (which would mean all real numbers are true) and |y| < 13. How would I display my answer?
Thanks!
#### Dr.Peterson
##### Elite Member
Can you explain what you mean by "my two solutions"? Do you think both of these are correct answers, or that the answer consists of both combined by "or" or "and", or something else?
Also, can you show how you got them?
The correct answer is that the inequality is true for all real numbers, but the inequality |y-2| + 11 > 0 is not inherently equivalent to |y| > -9. I think you took an illegal step. The important part of answering your question will be to correct your work.
#### jUnIoRjUnCtIoNmAtHmAtH
##### New member
Can you explain what you mean by "my two solutions"? Do you think both of these are correct answers, or that the answer consists of both combined by "or" or "and", or something else?
Also, can you show how you got them?
The correct answer is that the inequality is true for all real numbers, but the inequality |y-2| + 11 > 0 is not inherently equivalent to |y| > -9. I think you took an illegal step. The important part of answering your question will be to correct your work.
Thanks! I realized I had a computation error, thus seeming like I took an "illegal step".
#### pka
##### Elite Member
So I have the problem |y-2| + 11 > 0, and I got, for my two solutions, |y| > -9 (which would mean all real numbers are true) and |y| < 13. How would I display my answer?
If $$\displaystyle c>0$$ then the solution to $$\displaystyle |x+5|+c>0$$ has a solution set of $$\displaystyle (-\infty,\infty)$$, all real numbers.
#### Dr.Peterson
##### Elite Member
Thanks! I realized I had a computation error, thus seeming like I took an "illegal step".
It will still be good to show your work, because I think there's more than just a wrong addition. Your result should not have looked anything like what you wrote. At the very least, you wrote absolute values where they should not have been.
#### Jomo
##### Elite Member
I agree with Dr P that you should show us your work as something went wrong somewhere. Thanks
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# 3.7.2. Finding the Quotient
.
• A5
• B6
• C7
• D8
.
### Solution
Find the quotient. Then take apart the result as the sum of two numbers (2 and the unknown number).
So, the missing number is 5.
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# Integral cohomology of the hilbert scheme of points on a k3
i'm reading the famous article "Varietes kahleriennes dont la premiere classe de chern est nulle" by Beauville, in particular proposition 6, which characterizes the second cohomology group for the hilbert scheme of points on a k3 surface, i.e. $H^2(S^{[r]},\mathbb{C})=i(H^2(S),\mathbb{C})\oplus \mathbb{C}[E]$, where $E$ is the preimage of the singular locus of $Sym^{r}(S)$ through the Hilbert-Chow map $\rho:S^{[r]}\rightarrow Sym^{r}(S)$.
Given $\Delta\subset S^r$ the diagonal in which at least two elements are equal and $\Delta_{ij}\subset S^r$ the diagonal composed by the elements $(x_1,\ldots,x_r)$ with $x_i=x_j$ and all the other elements not equal between them, we set $S^r_*:=(S^r\setminus \Delta)\cup \cup_{i>j}\Delta_{ij}$ and as $S^{[r]}_*$ the preimage through the Hilbert-chow map of the quotient of $S^r_*$ by the action of the symmetric group on $r$ elements.
Beauville proves this formula computing $H^2(S^{[r]}_*,\mathbb{C})$ as the part of the cohomology $\oplus_i pr_i^*H^2(S,\mathbb{C})\oplus_{i>j}\mathbb{C}E_{ij}$ which is invariant for the action of the symmetric group on $r$ elements.
Then he remarks that one can prove also $H^2(S^{[r]},\mathbb{Z})=i(H^2(S),\mathbb{Z})\oplus \mathbb{Z}\delta$ with $2\delta=E$, but "the proof is more delicate".. do you have any idea how it goes? also from where comes the equality $2\delta=E$? Thank you very much
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# mechanics
posted by .
Find the total kinetic energy of a 1500 g wheel, 700 mm in diameter, rolling across a level surface at 650 rpm. Assume that the wheel can be considered as a hoop.
(b) For the wheel in part (a), calculate the torque required to decrease its rotational speed from 400 rpm to rest in 9 s.
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top of page
# Summary
In the last section, we covered the four main data types and how they interact with one another. Test what you've learned by identifying the type of each of the following variables. Use the terminal if you need to check your answer, using the type() command.
1. Identify the types of the following variables.
1 a = 4.0
2 b = 2 * 10
3 c = "two"
4 d = True
5 e = 4.0 / 2
6 f = "12.0 * 3"
7 g = "False"
8 h = 2 / 5
9 i = str(4.5)
10 j = "ABC" + "123"
Use this terminal if you're stuck:
bottom of page
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We begin with a few definitions.
Definition 1: A integral domain $R$ is called a Dedekind domain if it is noetherian, every nonzero prime ideal is maximal, and it is integrally closed in its field of fractions.
Definition 2: A ring $R$ is called a discrete valuation ring (DVR) if it is a principal ideal domain (PID) with exactly one nonzero prime ideal. (In other language, a DVR is a local PID of Krull dimension 0 or 1.)
One very important property of Dedekind domains is that ideals have unique factorizations as products of prime ideals. I used this property in the case of rings of integers in my last post to say that if $L/K$ is an extension of number fields with rings of integers $B/A$, so if $\mathfrak{p}\subset A$ is a prime ideal, then we can write $\mathfrak{p}B=\prod_{i=1}^g \mathfrak{P}_i^{e_i}$. But this result holds in more generality, for any Dedekind domain.
Also, it is very easy to check that a DVR is a Dedekind domain. But one very common occurrence of DVRs is as localizations of rings of integers. In particular, if $A$ is a Dedekind domain and $\mathfrak{p}$ is a prime ideal of $A$, then $A_{\mathfrak{p}}$ is a DVR.
One way to interpret a DVR is through the following filtration of ideals. Let $R$ be a DVR, and let $\mathfrak{p}$ be the unique nonzero prime ideal of $R$. Then every nonzero ideal of $R$ is of the form $\mathfrak{p}^n$ for some $n\ge 0$ (where by $\mathfrak{p}^0$ I mean $R$). Now, for any $x\in R\setminus\{0\}$, there is an integer $n$ so that $x\in\mathfrak{p}^n\setminus\mathfrak{p}^{n+1}$. We can now define a function $v:R\setminus\{0\}\to\mathbb{N}$ (where $\mathbb{N}$ includes 0 in this case) by $v(r)=n$ as above. We can extend our definition of $v$ to all of $R$ by setting $v(0)=+\infty$.
It is also possible to extend $v$ to the quotient field $K$ of $R$ by setting $v(x/y)=v(x)-v(y)$; it is easy to check that this is well-defined. Now, $v$ satisfies the following properties:
1) $v:K\setminus\{0\}\to\mathbb{Z}$ is a surjective homomorphism.
2) $v(x+y)\ge\min(v(x),v(y)$.
We call such a function $v$ a valuation of the field $K$.
Knowing $v$ is enough to reconstruct $R$, since $R=\{x\in K:v(x)\ge 0\}$. Furthermore, $\mathfrak{p}=\{x\in K:v(x)\ge 1\}$. We call $R$ the valuation ring of $K$.
Let’s look at a few places where DVRs arise naturally.
1) As we mentioned earlier, the localization of a Dedekind domain at a prime ideal is a DVR. So, for example, $\mathbb{Z}_{(p)}=\{x/y\in\mathbb{Q}:p\nmid y\}$ is a DVR if $p$ is a prime. The unique prime ideal is $p\mathbb{Z}_{(p)}$.
2) The ring $\mathbb{Z}_p$ of $p$-adic integers is a DVR with unique prime ideal $p\mathbb{Z}_p$. Also, finite extensions of the field $\mathbb{Q}_p$ of $p$-adic numbers inherit valuations from $\mathbb{Q}_p$, and so they contain DVRs as described above. In particular, if $K/\mathbb{Q}_p$ is a finite field extension, then the integral closure of $\mathbb{Z}_p$ in $K$ is a DVR.
Now, if $R$ is a DVR and $\mathfrak{p}$ is its prime ideal, then $R/\mathfrak{p}$ is a field. In the cases described above, this will always be a finite field; in what follows, we always assume that this field is finite. We call $R/\mathfrak{p}$ the residue field.
We can also put a topology on a valued field $K$ by letting the following sets be a basis for the topology: if $x\in K$ and $n\ge 0$ is an integer, then $\{y\in K:v(x-y)\ge n\}$ is an open set. These sets generate the topology. In what follows, we will assume that $K$ is complete as a topological space with this topology. Finite extensions of $\mathbb{Q}_p$ are complete with respect to this topology, so this will be our motivating example. The residue fields will also be finite.
Last post, I pointed out that if $L/K$ is a Galois extension of number fields, then $efg=[L:K]$. This holds more generally, however. If $L/K$ is a finite Galois field extension, and $A\subset K$ is a Dedekind domain so that $K$ is the quotient field of $A$, and $B$ is the integral closure of $A$ in $L$, then we still have $efg=[L:K]$.
We now interpret this in the case of $K$ a field complete with respect to a discrete valuation $v$, and $A$ the valuation ring of $K$. Let $L/K$ be a finite Galois extension, and let $B$ be the integral closure of $A$ in $L$, or, equivalently, the valuation ring of $L$. Then $L$ is also complete with respect to a discrete valuation $w$ that is very closely related to $v$, as we will see soon.
Let $\mathfrak{p}$ be the prime of $A$, and let $\mathfrak{P}$ be the prime of $B$. Since there is only one prime, $g=1$. Hence $\mathfrak{p}B=\mathfrak{P}^e$. Now, if $x\in K$, then $w(x)=ev(x)$, and if $x\in L$, then $fw(x)=v(N_{L/K}x)$. (But we won’t need these results in what follows, at least today.) The implication is the decomposition group of the extension $L/K$ is the entire Galois group.
We can put a filtration on the Galois group as follows: For $i\ge -1$, let $G_i=\{\sigma\in Gal(L/K):w(\sigma(x)-x)\ge i+1 \hbox{ for all } x\in L\}$. We call $G_i$ the $i^{\hbox{th}}$ ramification group of $L/K$. $G_{-1}=G$ is the entire Galois group (or the decomposition group; $G_0$ is the inertia group. Also, each $G_i$ is normal in $G$.
Now, I won’t prove it here, but it can be shown that if the residue field is finite of characteristic $p>0$ and $K$ is complete, then for each $i\ge 1$, $G_i/G_{i+1}$ is a direct product of copies of $\mathbb{Z}/p\mathbb{Z}$, and $G_0/G_1$ is a subgroup of the roots of unity of $B/\mathfrak{P}$ (and hence finite and cyclic of order prime to $p$). Hence, by basic group theory or otherwise, $G_0$ is a semidirect product of a normal Sylow $p$-subgroup and a cyclic group of order prime to $p$. In particular, $G_0$ is solvable. However, as shown in the last post, $G/G_0\cong Gal((B/\mathfrak{P})/(A/\mathfrak{p}))$ is cyclic since it is the Galois group of an extension of finite fields. Hence:
Theorem: $G$ is solvable.
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TDD Vs. math formalism: friend or foe?
It is not uncommon to oppose the empirical process of TDD, together with its heavy use of unit tests, to the more mathematically based techniques, with the “formal methods” and formal verification at the other end of the spectrum. However I experienced again recently that the process of TDD can indeed help discover and draw upon math formalisms well-suited to the problem considered. We then benefit from the math formalism for an easier implementation and correctness.
It is quite frequent that maths structures, or more generally “established formalisms” as Eric Evans would say, are hidden everywhere in the business concepts we need to model in software.
Dates and how we take liberties with them for trading of financial instruments offer a good example of a business concept with an underlying math structure: traders of futures often use a notation like ‘U8’ to describe an expiry date like September 2018; ‘U’ means September, and the ‘8’ digit refers to 2018, but also to 2028, and 2038 etc. Notice that this notation only works for 10 years, and each code is recycled every decade.
In the case of IMM contract codes, we only care about quarterly dates on:
• March (H)
• June (M)
• September (U)
• December (Z)
This yields only 4 possibilities for the month, combined with the 10 possible year digits, hence 40 different codes in total, over the range of 10 years.
How does that translate into source code?
As a software developer we are asked all the time to manage such IMM expiry codes:
• Sort a given set of IMM contract codes
• Find the next contract from the current “leading month” contract
• Enumerate the next 11 codes from the current “leading month” contract, etc.
This is often done ad hoc with a gazillion of functions for each use-case, leading to thousands of lines of code hard to maintain because they involve parsing of the ‘U8’ format everytime we want to calculate something.
With TDD, we can now tackle this topic with more rigor, starting with tests to define what we want to achieve.
The funny thing is that in the process of doing TDD, the cyclic logic of the IMM codes struck me and strongly reminded me of the cyclic group Z/nZ. I had met this strange maths creature at school many years ago, I had a hard time with it by the way. But now on a real example it was definitely more interesting!
The source code (Java) for this post is on Github.
Draw on established formalisms
Thanks to Google it is easy to find something even with just a vague idea of how it’s named, and thanks to Wikipedia, it is easy to find out more about any established formalism like Cyclic Groups. In particular we find that:
Every finite cyclic group is isomorphic to the group { [0], [1], [2], …, [n ? 1] } of integers modulo n under addition
The Wikipedia page also mentions a concept of the product of cyclic groups in relation with their order (here the number of elements). Looks like this is the math-ish way to say that 4 possibilities for quarterly months combined with 10 possible year digits give 40 different codes in total.
So what? Sounds like we could identify the set of the 4 months to a cyclic group, the set of the 10 year digits to another, and that even the combination (product) of both also looks like a cyclic group of order 10 * 4 = 40 (even though the addition operation will not be called like that). So what?
Because we’ve just seen that there is an isomorphism between any finite cyclic group and the cyclic group of integer of the same order, we can just switch to the integer cyclic group logic (plain integers and the modulo operator) to simplify the implementation big time.
Basically the idea is to convert from the IMM code “Z3” to the corresponding ‘ordinal’ integer in the range 0..39, then do every operation on this ‘ordinal’ integer instead of the actual code. Then we can format back to a code “Z3” whenever we really need it.
Do I still need TDD when I have a complete formal solution?
I must insist that I did not came to this conclusion as easily. The process of TDD was indeed very helpful not to get lost in every possible direction along the way. Even when you have found a formal structure that could solve your problem in one go, even in a “formal proof-ish fashion”, then perhaps you need less tests to verify the correctness, but you sure still need tests to think on the specification part of your problem. This is your gentle reminder that TDD is not about unit tests.
Partial order in a cyclic group
Given a list of IMM codes we often need to sort them for display. The problem is that a cyclic group has no total order, the ordering depends on where you are in time.
Let’s take the example of the days of the week that also forms a cycle: MONDAY, TUESDAY, WEDNESDAY…SUNDAY, MONDAY etc.
If we only care about the future, is MONDAY before WEDNESDAY? Yes, except if we’re on TUESDAY. If we’re on TUESDAY, MONDAY means next MONDAY hence comes after WEDNESDAY, not before.
This is why we cannot unfortunately just implement Comparable to take care of the ordering. Because we need to consider a reference IMM code-aware partial order, we need to resort to a Comparator that takes the reference IMM code in its constructor.
Once we identify that situation to the cyclic group of integers, it becomes easy to shift both operands of the comparison to 0 before comparing them in a safe (total order-ish) way. Again, this trick is made possible by the freedom to experiment given by the TDD tests. As long as we’re still green, we can go ahead and try any funky approach.
Try it as a kata
This example is also a good coding kata that we’ve tried at work not long ago. Given a simple presentation of the format of an IMM contract code, you can choose to code the sort, find the next and previous code, and perhaps even optimize for memory (cache the instances, e.g. lazily) and speed (cache the toString() value, e.g. in the constructor) if you still have some time.
In closing
Maths structures are hidden behind many common business concepts. I developed an habit to look for them whenever I can, because they always help make us think, they help question our understanding of the domain problem (“is my domain problem really similar in some way to this structure?”), and of course because they often offer wonderful ready-made implementation hints!
The source code (Java) for this post is on Github.
Photo: CME Group
Surface-area over volume ratio – a metaphor for software design
There’s a metaphor I had in mind for a long time when thinking about software design: because I’m proudly lazy, in order to make the code smaller and easier to learn, I must do my best to reduce the “surface-area over volume ratio” of the software.
Surface-area over volume ratio?
I like the Surface-area over volume ratio as a metaphor to express how to make software cheaper to discover and learn, and smaller to maintain as well.
For a given object, the surface-area over volume ratio is the amount of surface area per unit volume. For buildings and for animals, the smaller this ratio, the less the heat loss during the winter, hence a better thermal efficiency.
Have you ever noticed that huge warehouses were always cool even during the summer when it’s hot? This is just because in our real 3D world the surface-area over volume ratio is much smaller when the absolute size of the building increases.
The theory also mentions that the sphere is the optimal shape with respect to this ratio. In fact, the more “compact” the less the ratio, or the other way round we could define compactness of an object directly by its surface-area-over-volume ratio.
Let’s consider that each method signature of each interface is part of the surface-area of the software, because this is what I have to learn primarily when I join the project. The larger the surface-area, the more time I’ll need to learn, provided I can even remember all of it.
Larger surface is not good for the developers.
On the other hand, the implementation is part of what I would call the volume of the software, i.e. this is where the code is really doing its stuff. The more volume, the more powerful and richer the software. And of course the point of Object Orientation is that you don’t have to learn all the implementation in order to work on the project, as opposed to the interfaces and their method signatures.
Larger volume is good for the users (or the value brought by the software in general)
As a consequence we should try to minimize the surface-area over volume ratio, just like we’re trying to reduce it when designing a green building.
Can we extrapolate that we should design software to be more “compact” and more “sphere”-like?
Facets-like interfaces
Reusing the same interface as much as possible is obviously a way to reduce the surface-area of the software. Adhering to interfaces from the JDK or Google Guava, interfaces that are already well-known, helps even better: in our metaphor, an interface that we don’t have to learn comes for free, like a perfectly isolated wall in a building. We can almost omit it in our ratio.
To further reduce the ratio, we can find out every opportunity to use as much as possible the minimum set of common interfaces, even over unrelated concepts. At the extreme of this approach we get duck typing in dynamic languages. In our usual languages like Java or C# we must introduce additional small interfaces, usually with one single method.
For example in a trading system, every class with a isInCurrency(Currency) method can implement a common interface CurrencySpecific. As a result, a lot of processing (filtering etc.) on stuff that is related to currencies in some way can be done on all these classes without any knowledge about them, except their currency-specificity.
In this example, the currency-specificity we extracted into one interface is like a single facet over a larger volume made of several implementation. It makes our design more compact, it will be easier to learn, while offering a rich set of behaviors.
The limit for this approach of putting a lot of implementation code under the same interface is that sometimes it really makes no domain sense. Since code is primarily meant to describe the domain, without causing confusion we must be careful not to go too far. We must also take great care when sharing interfaces between bounded contexts, there’s a high risk of excessive coupling.
Yet another metric?
This metric could be measured by a tool, however the primary value is not in checking the figures, but in the thinking and taking care of making the design easy to learn (less surface-area), while delivering a lot of valuable behaviors (more volume).
The untold art of Composite-friendly interfaces
The Composite pattern is a very powerful design pattern that you use regularly to manipulate a group of things through the very same interface than a single thing. By doing so you don’t have to discriminate between the singular and plural cases, which often simplifies your design.
Yet there are cases where you are tempted to use the Composite pattern but the interface of your objects does not fit quite well. Fear not, some simple refactorings on the methods signatures can make your interfaces Composite-friendly, because it’s worth it.
Imagine an interface for a financial instrument with a getter on its currency:
```public interface Instrument {
Currency getCurrency();
}```
This interface is alright for a single instrument, however it does not scale for a group of instruments (Composite pattern), because the corresponding getter in the composite class would look like (notice that return type is now a collection):
```public class CompositeInstrument {
// list of instruments...
public Set getCurrencies() {...}
}```
We must admit that each instrument in a composite instrument may have a different currency, hence the composite may be multi-currency, hence the collection return type. This breaks the goal of the Composite pattern which is to unify the interfaces for single and multiple elements. If we stop there, we now have to discriminate between a single Instrument and a CompositeInstrument, and we have to discriminate that on every call site. I’m not happy with that.
The brutal approach
The brutal approach is to generalize the initial interface so that it works for the composite case:
```public interface Instrument {
Set getCurrencies() ;
}```
This interface now works for both the single case and the composite case, but at the cost of always having to deal with a collection as return value. In fact I’m not that sure that we’ve simplified our design with this approach: if the composite case is not used that often, we even have complicated the design for little benefit, because the returned collection type always goes on our way, requiring a loop every time it is called.
The trick to improve that is just to investigate what our interface is really used for. The getter on the initial interface only reveals that we did not think about the actual use before, in other words it shows a design decision “by default”, or lack of.
Turn it into a boolean method
Very often this kind of getter is mostly used to test whether the instrument (single or composite) has something to do with a given currency, for example to check if an instrument is acceptable for a screen in USD or tradable by a trader who is only granted the right to trade in EUR.
In this case, you can revamp the method into another intention-revealing method that accepts a parameter and returns a boolean:
```public interface Instrument {
boolean isInCurrency(Currency currency);
}```
This interface remains simple, is closer to our needs, and in addition it now scales for use with a Composite, because the result for a Composite instrument can be derived from each result on each single instrument and the AND operator:
```public class CompositeInstrument {
// list of instruments...
public boolean isInCurrency(Currency currency) {
boolean result;
// for each instrument, result &= isInCurrency(currency);
return result;
}
}```
Something to do with Fold
As shown above the problem is all about the return value. Generalizing on boolean and their boolean logic from the previous example (‘&=’), the overall trick for a Composite-friendly interface is to define methods that return a type that is easy to fold over successive executions. For example the trick is to merge (“fold”) the boolean result of several calls into one single boolean result. You typically do that with AND or OR on boolean types.
If the return type is a collection, then you could perhaps merge the results using addAll(…) if it makes sense for the operation.
Technically, this is easily done when the return type is closed under an operation (magma), i.e. when the result of some operation is of the same type than the operand, just like ‘boolean1 AND boolean2‘ is also a boolean.
This is obviously the case for boolean and their boolean logic, but also for numbers and their arithmetic, collections and their sets operations, strings and their concatenation, and many other types including your own classes, as Eric Evans suggests you favour “Closure of Operations” in his book Domain-Driven Design.
Turn it into a void method
Though not possible in our previous example, void methods work very well with the Composite pattern: with nothing to return, there is no need to unify or fold anything:
```public class CompositeFunction {
List functions = ...;
public void apply(...) {
// for each function, function.apply(...);
}
}```
Continuation-passing style
The last trick to help with the Composite pattern is to adopt the continuation passing style by passing a continuation object as a parameter to the method. The method then sets its result into it instead of using its return value.
As an example, to perform search on every node of a tree, you may use a continuation like this:
```public class SearchResults {
public void addResult(Node node){ // append to list of results...}
public List getResults() { // return list of results...}
}
public class Node {
List children = ...;
public void search(SarchResults sr) {
//...
if (found){
}
// for each child, child.search(sr);
}
}```
By passing a continuation as argument to the method, the continuation takes care of the multiplicity, and the method is now well suited for the Composite pattern. You may consider that the continuation indeed encapsulates into one object the process of folding the result of each call, and of course the continuation is mutable.
This style does complicates the interface of the method a little, but also offers the advantage of a single allocation of one instance of the continuation across every call.
One word on exceptions
Methods that can throw exceptions (even unchecked exceptions) can complicate the use in a composite. To deal with exceptions within the loop that calls each child, you can just throw the first exception encountered, at the expense of giving up the loop. An alternative is to collect every caught exception into a Collection, then throw a composite exception around the Collection when you’re done with the loop. On some other cases the composite loop may also be a convenient place to do the actual exception handling, such as full logging, in one central place.
In closing
We’ve seen some tricks to adjust the signature of your methods so that they work well with the Composite pattern, typically by folding the return type in some way. In return, you don’t have to discriminate manually between the single and the multiple, and one single interface can be used much more often; this is with these kinds of details that you can keep your design simple and ready for any new challenge.
Follow me on Twitter! Credits: Pictures from myself, except the assembly line by BUICK REGAL (Flickr)
A touch of functional style in plain Java with predicates – Part 2
In the first part of this article we introduced predicates, which bring some of the benefits of functional programming to object-oriented languages such as Java, through a simple interface with one single method that returns true or false. In this second and last part, we’ll cover some more advanced notions to get the best out of your predicates.
Testing
One obvious case where predicates shine is testing. Whenever you need to test a method that mixes walking a data structure and some conditional logic, by using predicates you can test each half in isolation, walking the data structure first, then the conditional logic.
In a first step, you simply pass either the always-true or always-false predicate to the method to get rid of the conditional logic and to focus just on the correct walking on the data structure:
```// check with the always-true predicate
final Iterable<PurchaseOrder> all = orders.selectOrders(Predicates.<PurchaseOrder> alwaysTrue());
assertEquals(2, Iterables.size(all));
// check with the always-false predicate
assertTrue(Iterables.isEmpty(orders.selectOrders(Predicates.<PurchaseOrder> alwaysFalse())));```
In a second step, you just test each possible predicate separately.
```final CustomerPredicate isForCustomer1 = new CustomerPredicate(CUSTOMER_1);
assertTrue(isForCustomer1.apply(ORDER_1)); // ORDER_1 is for CUSTOMER_1
assertFalse(isForCustomer1.apply(ORDER_2)); // ORDER_2 is for CUSTOMER_2```
This example is simple but you get the idea. To test more complex logic, if testing each half of the feature is not enough you may create mock predicates, for example a predicate that returns true once, then always false later on. Forcing the predicate like that may considerably simplify your test set-up, thanks to the strict separation of concerns.
Predicates work so good for testing that if you tend to do some TDD, I mean if the way you can test influences the way you design, then as soon as you know predicates they will surely find their way into your design.
Explaining to the team
In the projects I’ve worked on, the team was not familiar with predicates at first. However this concept is easy and fun enough for everyone to get it quickly. In fact I’ve been surprised by how the idea of predicates spread naturally from the code I had written to the code of my colleagues, without much evangelism from me. I guess that the benefits of predicates speak for themselves. Having mature API’s from big names like Apache or Google also helps convince that it is serious stuff. And now with the functional programming hype, it should be even easier to sell!
Simple optimizations
The usual optimizations are to make predicates immutable and stateless as much as possible to enable their sharing with no consideration of threading. This enables using one single instance for the whole process (as a singleton, e.g. as static final constants). Most frequently used predicates that cannot be enumerated at compilation time may be cached at runtime if required. As usual, do it only if your profiler report really calls for it.
When possible a predicate object can pre-compute some of the calculations involved in its evaluation in its constructor (naturally thread-safe) or lazily.
A predicate is expected to be side-effect-free, in other words “read-only”: its execution should not cause any observable change to the system state. Some predicates must have some internal state, like a counter-based predicate used for paging, but they still must not change any state in the system they apply on. With internal state, they also cannot be shared, however they may be reused within their thread if they support reset between each successive use.
Fine-grained interfaces: a larger audience for your predicates
In large applications you find yourself writing very similar predicates for types totally different but that share a common property like being related to a Customer. For example in the administration page, you may want to filter logs by customer; in the CRM page you want to filter complaints by customer.
For each such type X you’d need yet another CustomerXPredicate to filter it by customer. But since each X is related to a customer in some way, we can factor that out (Extract Interface in Eclipse) into an interface CustomerSpecific with one method:
```public interface CustomerSpecific {
Customer getCustomer();
}```
This fine-grained interface reminds me of traits in some languages, except it has no reusable implementation. It could also be seen as a way to introduce a touch of dynamic typing within statically typed languages, as it enables calling indifferently any object with a getCustomer() method. Of course our class PurchaseOrder now implements this interface.
Once we have this interface CustomerSpecific, we can define predicates on it rather than on each particular type as we did before. This helps leverage just a few predicates throughout a large project. In this case, the predicate CustomerPredicate is co-located with the interface CustomerSpecific it operates on, and it has a generic type CustomerSpecific:
```public final class CustomerPredicate implements Predicate<CustomerSpecific>, CustomerSpecific {
private final Customer customer;
// valued constructor omitted for clarity
public Customer getCustomer() {
return customer;
}
public boolean apply(CustomerSpecific specific) {
return specific.getCustomer().equals(customer);
}
}```
Notice that the predicate can itself implement the interface CustomerSpecific, hence could even evaluate itself!
When using trait-like interfaces like that, you must take care of the generics and change a bit the method that expects a Predicate<PurchaseOrder> in the class PurchaseOrders, so that it also accepts any predicate on a supertype of PurchaseOrder:
```public Iterable<PurchaseOrder> selectOrders(Predicate<? super PurchaseOrder> condition) {
return Iterables.filter(orders, condition);
}```
Specification in Domain-Driven Design
Eric Evans and Martin Fowler wrote together the pattern Specification, which is clearly a predicate. Actually the word “predicate” is the word used in logic programming, and the pattern Specification was written to explain how we can borrow some of the power of logic programming into our object-oriented languages.
In the book Domain-Driven Design, Eric Evans details this pattern and gives several examples of Specifications which all express parts of the domain. Just like this book describes a Policy pattern that is nothing but the Strategy pattern when applied to the domain, in some sense the Specification pattern may be considered a version of predicate dedicated to the domain aspects, with the additional intent to clearly mark and identify the business rules.
As a remark, the method name suggested in the Specification pattern is: isSatisfiedBy(T): boolean, which emphasises a focus on the domain constraints. As we’ve seen before with predicates, atoms of business logic encapsulated into Specification objects can be recombined using boolean logic (or, and, not, any, all), as in the Interpreter pattern.
The book also describes some more advanced techniques such as optimization when querying a database or a repository, and subsumption.
Optimisations when querying
The following are optimization tricks, and I’m not sure you will ever need them. But this is true that predicates are quite dumb when it comes to filtering datasets: they must be evaluated on just each element in a set, which may cause performance problems for huge sets. If storing elements in a database and given a predicate, retrieving every element just to filter them one after another through the predicate does not sound exactly a right idea for large sets…
When you hit performance issues, you start the profiler and find the bottlenecks. Now if calling a predicate very often to filter elements out of a data structure is a bottleneck, then how do you fix that?
One way is to get rid of the full predicate thing, and to go back to hard-coded, more error-prone, repetitive and less-testable code. I always resist this approach as long as I can find better alternatives to optimize the predicates, and there are many.
First, have a deeper look at how the code is being used. In the spirit of Domain-Driven Design, looking at the domain for insights should be systematic whenever a question occurs.
Very often there are clear patterns of use in a system. Though statistical, they offer great opportunities for optimisation. For example in our PurchaseOrders class, retrieving every PENDING order may be used much more frequently than every other case, because that’s how it makes sense from a business perspective, in our imaginary example.
Friend Complicity
Based on the usage pattern you may code alternate implementations that are specifically optimised for it. In our example of pending orders being frequently queried, we would code an alternate implementation FastPurchaseOrder, that makes use of some pre-computed data structure to keep the pending orders ready for quick access.
Now, in order to benefit from this alternate implementation, you may be tempted to change its interface to add a dedicated method, e.g. selectPendingOrders(). Remember that before you only had a generic selectOrders(Predicate) method. Adding the extra method may be alright in some cases, but may raise several concerns: you must implement this extra method in every other implementation too, and the extra method may be too specific for a particular use-case hence may not fit well on the interface.
A trick for using the internal optimization through the exact same method that only expects predicates is just to make the implementation recognize the predicate it is related to. I call that “Friend Complicity“, in reference to the friend keyword in C++.
```/** Optimization method: pre-computed list of pending orders */
private Iterable<PurchaseOrder> selectPendingOrders() {
// ... optimized stuff...
}
public Iterable<PurchaseOrder> selectOrders(Predicate<? super PurchaseOrder> condition) {
// internal complicity here: recognize friend class to enable optimization
if (condition instanceof PendingOrderPredicate) {
return selectPendingOrders();// faster way
}
// otherwise, back to the usual case
return Iterables.filter(orders, condition);
}```
It’s clear that it increases the coupling between two implementation classes that should otherwise ignore each other. Also it only helps with performance if given the “friend” predicate directly, with no decorator or composite around.
What’s really important with Friend Complicity is to make sure that the behaviour of the method is never compromised, the contract of the interface must be met at all times, with or without the optimisation, it’s just that the performance improvement may happen, or not. Also keep in mind that you may want to switch back to the unoptimized implementation one day.
SQL-compromised
If the orders are actually stored in a database, then SQL can be used to query them quickly. By the way, you’ve probably noticed that the very concept of predicate is exactly what you put after the WHERE clause in a SQL query.
A first and simple way to still use predicate yet improve performance is for some predicates to implement an additional interface SqlAware, with a method asSQL(): String that returns the exact SQL query corresponding for the evaluation of the predicate itself. When the predicate is used against a database-backed repository, the repository would call this method instead of the usual evaluate(Predicate) or apply(Predicate) method, and would then query the database with the returned query.
I call that approach SQL-compromised as the predicate is now polluted with database-specific details it should ignore more often than not.
Alternatives to using SQL directly include the use of stored procedures or named queries: the predicate has to provide the name of the query and all its parameters. Double-dispatch between the repository and the predicate passed to it is also an alternative: the repository calls the predicate on its additional method selectElements(this) that itself calls back the right pre-selection method findByState(state): Collection on the repository; the predicate then applies its own filtering on the returned set and returns the final filtered set.
Subsumption
Subsumption is a logic concept to express a relation of one concept that encompasses another, such as “red, green, and yellow are subsumed under the term color” (Merriam-Webster). Subsumption between predicates can be a very powerful concept to implement in your code.
Let’s take the example of an application that broadcasts stock quotes. When registering we must declare which quotes we are interested in observing. We can do that by simply passing a predicate on stocks that only evaluates true for the stocks we’re interested in:
```public final class StockPredicate implements Predicate<String> {
private final Set<String> tickers;
// Constructors omitted for clarity
public boolean apply(String ticker) {
return tickers.contains(ticker);
}
}```
Now we assume that the application already broadcasts standard sets of popular tickers on messaging topics, and each topic has its own predicates; if it could detect that the predicate we want to use is “included”, or subsumed in one of the standard predicates, we could just subscribe to it and save computation. In our case this subsumption is rather easy, by just adding an additional method on our predicates:
``` public boolean encompasses(StockPredicate predicate) {
return tickers.containsAll(predicate.tickers);
}Subsumption is all about evaluating another predicate for "containment". This is easy when your predicates are based on sets, as in the example, or when they are based on intervals of numbers or dates. Otherwise You may have to resort to tricks similar to Friend Complicity, i.e. recognizing the other predicate to decide if it is subsumed or not, in a case-by-case fashion.```
Overall, remember that subsumption is hard to implement in the general case, but even partial subsumption can be very valuable, so it is an important tool in your toolbox.
Conclusion
Predicates are fun, and can enhance both your code and the way you think about it!
Cheers,
A touch of functional style in plain Java with predicates – Part 1
You keep hearing about functional programming that is going to take over the world, and you are still stuck to plain Java? Fear not, since you can already add a touch of functional style into your daily Java. In addition, it’s fun, saves you many lines of code and leads to fewer bugs.
What is a predicate?
I actually fell in love with predicates when I first discovered Apache Commons Collections, long ago when I was coding in Java 1.4. A predicate in this API is nothing but a Java interface with only one method:
`evaluate(Object object): boolean`
That’s it, it just takes some object and returns true or false. A more recent equivalent of Apache Commons Collections is Google Guava, with an Apache License 2.0. It defines a Predicate interface with one single method using a generic parameter:
`apply(T input): boolean`
It is that simple. To use predicates in your application you just have to implement this interface with your own logic in its single method apply(something).
A simple example
As an early example, imagine you have a list orders of PurchaseOrder objects, each with a date, a Customer and a state. The various use-cases will probably require that you find out every order for this customer, or every pending, shipped or delivered order, or every order done since last hour. Of course you can do that with foreach loops and a if inside, in that fashion:
```//List<PurchaseOrder> orders...
public List<PurchaseOrder> listOrdersByCustomer(Customer customer) {
final List<PurchaseOrder> selection = new ArrayList<PurchaseOrder>();
for (PurchaseOrder order : orders) {
if (order.getCustomer().equals(customer)) {
}
}
return selection;
}
```
And again for each case:
```public List<PurchaseOrder> listRecentOrders(Date fromDate) {
final List<PurchaseOrder> selection = new ArrayList<PurchaseOrder>();
for (PurchaseOrder order : orders) {
if (order.getDate().after(fromDate)) {
}
}
return selection;
}```
The repetition is quite obvious: each method is the same except for the condition inside the if clause, emphasized in bold here. The idea of using predicates is simply to replace the hard-coded condition inside the if clause by a call to a predicate, which then becomes a parameter. This means you can write only one method, taking a predicate as a parameter, and you can still cover all your use-cases, and even already support use-cases you do not know yet:
```public List<PurchaseOrder> listOrders(Predicate<PurchaseOrder> condition) {
final List<PurchaseOrder> selection = new ArrayList<PurchaseOrder>();
for (PurchaseOrder order : orders) {
if (condition.apply(order)) {
}
}
return selection;
}
```
Each particular predicate can be defined as a standalone class, if used at several places, or as an anonymous class:
```final Customer customer = new Customer("BruceWaineCorp");
final Predicate<PurchaseOrder> condition = new Predicate<PurchaseOrder>() {
public boolean apply(PurchaseOrder order) {
return order.getCustomer().equals(customer);
}
};
```
Your friends that use real functional programming languages (Scala, Clojure, Haskell etc.) will comment that the code above is awfully verbose to do something very common, and I have to agree. However we are used to that verbosity in the Java syntax and we have powerful tools (auto-completion, refactoring) to accommodate it. And our projects probably cannot switch to another syntax overnight anyway.
Predicates are collections best friends
Coming back to our example, we wrote a foreach loop only once to cover every use-case, and we were happy with that factoring out. However your friends doing functional programming “for real” can still laugh at this loop you had to write yourself. Luckily, both API from Apache or Google also provide all the goodies you may expect, in particular a class similar to java.util.Collections, hence named Collections2 (not a very original name).
This class provides a method filter() that does something similar to what we had written before, so we can now rewrite our method with no loop at all:
```public Collection<PurchaseOrder> selectOrders(Predicate<PurchaseOrder> condition) {
return Collections2.filter(orders, condition);
}
```
In fact, this method returns a filtered view:
The returned collection is a live view of `unfiltered` (the input collection); changes to one affect the other.
This also means that less memory is used, since there is no actual copy from the initial collection unfiltered to the actual returned collection filtered.
On a similar approach, given an iterator, you could ask for a filtered iterator on top of it (Decorator pattern) that only gives you the elements selected by your predicate:
`Iterator filteredIterator = Iterators.filter(unfilteredIterator, condition);`
Since Java 5 the Iterable interface comes very handy for use with the foreach loop, so we’d prefer indeed use the following expression:
```public Iterable<PurchaseOrder> selectOrders(Predicate<PurchaseOrder> condition) {
return Iterables.filter(orders, condition);
}
// you can directly use it in a foreach loop, and it reads well:
for (PurchaseOrder order : orders.selectOrders(condition)) {
//...
}
```
To use predicates, you could simply define your own interface Predicate, or one for each type parameter you need in your application. This is possible, however the good thing in using a standard Predicate interface from an API such as Guava or Commons Collections is that the API brings plenty of excellent building blocks to combine with your own predicate implementations.
First you may not even have to implement your own predicate at all. If all you need is a condition on whether an object is equal to another, or is not-null, then you can simply ask for the predicate:
```// gives you a predicate that checks if an integer is zero
Predicate<Integer> isZero = Predicates.equalTo(0);
// gives a predicate that checks for non null objects
Predicate<String> isNotNull = Predicates.notNull();
// gives a predicate that checks for objects that are instanceof the given Class
Predicate<Object> isString = Predicates.instanceOf(String.class);```
Given a predicate, you can inverse it (true becomes false and the other way round):
`Predicates.not(predicate);`
Combine several predicates using boolean operators AND, OR:
```Predicates.and(predicate1, predicate2);
Predicates.or(predicate1, predicate2);
// gives you a predicate that checks for either zero or null
Predicate<Integer> isNullOrZero = Predicates.or(isZero, Predicates.isNull());```
Of course you also have the special predicates that always return true or false, which are really, really useful, as we’ll see later for testing:
```Predicates.alwaysTrue();
Predicates.alwaysFalse();
```
I often used to make anonymous predicates at first, however they always ended up being used more often so were often promoted to actual classes, nested or not.
By the way, where to locate these predicates? Following Robert C. Martin and his Common Closure Principle (CCP) :
Classes that change together, belong together
Because predicates manipulates objects of a certain type, I like to co-locate them close to the type they take as parameter. For example, the classes CustomerOrderPredicate, PendingOrderPredicate and RecentOrderPredicate should reside in the same package than the class PurchaseOrder that they evaluate, or in a sub-package if you have a lot of them. Another option would be to define them nested within the type itself. Obviously, the predicates are quite coupled to the objects they operate on.
Resources
Here are the source files for the examples in this article: cyriux_predicates_part1 (zip)
In the next part, we’ll have a look at how predicates simplify testing, how they relate to Specifications in Domain-Driven Design, and some additional stuff to get the best out of your predicates.
Key insights that you probably missed on DDD
As suggested by its name, Domain-Driven Design is not only about Event Sourcing and CQRS. It all starts with the domain and a lot of key insights that are too easy to overlook at first. Even if you’ve read the “blue book” already, I suggest you read it again as the book is at the same time wide and deep.
You got talent
Behind the basics of Domain-Driven Design, one important idea is to harness the huge talent we all have: the ability to speak, and this talent of natural language can help us reason about the considered domain.
Just like multi-touch and tangible interfaces aim at reusing our natural strength in using our fingers, Eric Evans suggests that we use our language ability as an actual tool to try out loud modelling concepts, and to test if they pass the simple test of being useful in sentences about the domain.
This is a simple idea, yet powerful. No need for any extra framework or tool, one of the most powerful tool we can imagine is already there, wired in our brain. The trick is to find a middle way between natural language in all its fuzziness, and an expressive model that we can discuss without ambiguity, and this is exactly what the Ubiquitous Language addresses.
One model to rule them all
Another key insight in Domain-Driven Design is to identify -equate- the implementation model with the analysis model, so that there is only one model across every aspect of the software process, from requirements and analysis to code.
This does not mean you must have only one domain model in your application, in fact you will probably get more than one model across the various areas* of the application. But this means that in each area there must be only one model shared by developers and domain experts. This clearly opposes to some early methodologies that advocated a distinct analysis modelling then a separate, more detailed implementation modelling. This also leads naturally to the Ubiquitous Language, a common language between domain experts and the technical team.
The key driver is that the knowledge gained through analysis can be directly used in the implementation, with no gap, mismatch or translation. This assumes of course that the underlying programming language is modelling-oriented, which object oriented languages obviously are.
What form for the model?
Shall the model be expressed in UML? Eric Evans is again quite pragmatic: nothing beats natural language to express the two essential aspects of a model: the meaning of its concepts, and their behaviour. Text, in English or any other spoken language, is therefore the best choice to express a model, while diagrams, standard or not, even pictures, can supplement to express a particular structure or perspective.
If you try to express the entirety of the model using UML, then you’re just using UML as a programming language. Using only a programming language such as Java to represent a model exhibits by the way the same shortcoming: it is hard to get the big picture and to grasp the large scale structure. Simple text documents along with some diagrams and pictures, if really used and therefore kept up-to-date, help explain what’s important about the model, otherwise expressed in code.
A final remark
The beauty in Domain-Driven Design is that it is not just a set of independent good ideas on why and how to build domain models; it is itself a complete system of inter-related ideas, each useful on their own but that also supplement each other. For example, the idea of using natural language as a modelling tool and the idea of sharing one same model for analysis and implementation both lead to the Ubiquitous Language.
* Areas would typically be different Bounded Contexts
Patterns for using custom annotations
If you happen to create your own annotations, for instance to use with Java 6 Pluggable Annotation Processors, here are some patterns that I collected over time. Nothing new, nothing fancy, just putting everything into one place, with some proposed names.
Local-name annotation
Have your tools accept any annotation as long as its single name (without the fully-qualified prefix) is the expected one. For example com.acme.NotNull and net.companyname.NotNull would be considered the same. This enables to use your own annotations rather than the one packaged with the tools, in order not to depend on them.
Example in the Guice documentation:
Guice recognizes any @Nullable annotation, like edu.umd.cs.findbugs.annotations.Nullable or javax.annotation.Nullable.
Composed annotations
Annotations can have annotations as values. This allows for some complex and tree-like configurations, such as mappings from one format to another (from/to XML, JSon, RDBM).
Here is a rather simple example from the Hibernate annotations documentation:
```@AssociationOverride(
name="propulsion",
joinColumns = @JoinColumn(name="fld_propulsion_fk")
)```
Multiplicity Wrapper
Java does not allow to use several times the same annotation on a given target.
To workaround that limitation, you can create a special annotation that expects a collection of values of the desired annotation type. For example, you’d like to apply several times the annotation @Advantage, so you create the Multiplicity Wrapper annotation: @Advantages (advantages = {@Advantage}).
Typically the multiplicity wrapper is named after the plural form of its enclosed elements.
Example in Hibernate annotations documentation:
```@AttributeOverrides( {
@AttributeOverride(name="iso2", column = @Column(name="bornIso2") ),
@AttributeOverride(name="name", column = @Column(name="bornCountryName") )
} )
```
Meta-inheritance
It is not possible in Java for annotations to derive from each other. To workaround that, the idea is simply to annotate your new annotation with the “super” annotation, which becomes a meta annotation.
Whenever you use your own annotation with a meta-annotation, the tools will actually consider it as if it was the meta-annotation.
This kind of meta-inheritance helps centralize the coupling to the external annotation in one place, while making the semantics of your own annotation more precise and meaningful.
Example in Spring annotations, with the annotation @Component, but also works with annotation @Qualifier:
Create your own custom stereotype annotation that is itself annotated with @Component:
```@Component
public @interface MyComponent {
String value() default "";
}```
```@MyComponent
public class MyClass...```
Another example in Guice, with the Binding Annotation:
```@BindingAnnotation
@Target({ FIELD, PARAMETER, METHOD })
@Retention(RUNTIME)
public @interface PayPal {}
// Then use it
public class RealBillingService implements BillingService {
@Inject
public RealBillingService(@PayPal CreditCardProcessor processor,
TransactionLog transactionLog) {
...
}
```
Refactoring-proof values
Prefer values that are robust to refactorings rather than String litterals. MyClass.class is better than “com.acme.MyClass”, and enums are also encouraged.
Example in Hibernate annotations documentation:
`@ManyToOne( cascade = {CascadeType.PERSIST, CascadeType.MERGE}, targetEntity=CompanyImpl.class )`
And another example in the Guice documentation:
```@ImplementedBy(PayPalCreditCardProcessor.class)
```
Configuration Precedence rule
Convention over Configuration and Sensible Defaults are two existing patterns that make a lot of sense with respect to using annotations as part of a configuration strategy. Having no need to annotate is way better than having to annotate for little value.
Annotations are by nature embedded in the code, hence they are not well-suited for every case of configuration, in particular when it comes to deployment-specific configuration. The solution is of course to mix annotations with other mechanisms and use each of them where they are more appropriate.
The following approach, based on precedence rule, and where each mechanism overrides the previous one, appears to work well:
Default value < Annotation < XML < programmatic configuration
For example, the default values could be suited for unit testing, while the annotation define all the stable configuration, leaving the other options to configure for deployments at the various stages, like production or QA environments.
This principle is common (Spring, Java 6 EE among others), for example in JPA:
The concept of configuration by exception is central to the JPA specification.
Conclusion
This post is mostly a notepad of various patterns on how to use annotations, for instance when creating tools that process annotations, such as the Annotation Processing Tools in Java 5 and the Pluggable Annotations Processors in Java 6.
Don’t hesitate to contribute better patterns names, additional patterns and other examples of use.
EDIT: A related previous post, with a focus on how annotations can lead to coupling hence dependencies.
Pictures Creative Commons from Flicker, by ninaksimon and Iwan Gabovitch.
Domain-Driven Design: where to find inspiration for Supple Design? [part1]
Domain-Driven Design encourages to analyse the domain deeply in a process called Supple Design. In his book (the blue book) and in his talks Eric Evans gives some examples of this process, and in this blog I suggest some sources of inspirations and some recommendations drawn from my practice in order to help about this process.
When a common formalism fits the domain well, you can factor it out and adapt its rules to the domain.
A known formalism can be reused as a ready-made, well understood model.
Obvious sources of inspiration
Analysis patterns
It is quite obvious in the book, DDD builds clearly on top of Martin Fowler analysis patterns. The patterns Knowledge Level (aka Meta-Model), and Specification (a Strategy used as a predicate) are from Fowler, and Eric Evans mentions using and drawing insight from analysis patterns many times in the book.
Reading analysis patterns helps to appreciate good design; when you’ve read enough analysis patterns, you don’t even have to remember them to be able to improve your modelling skills. In my own experience, I have learnt to look for specific design qualities such as explicitness and traceability in my design as a result of getting used to analysis patterns such as Phenomenon or Observation.
Design patterns
Design patterns are another source of inspiration, but usually less relevant to domain modelling. Evans mentions the Strategy pattern, also named Policy (I rather like using an alternative name to make it clear that we are talking about the domain, not about a technical concerns), and the pattern Composite. Evans suggests considering other patterns, not just the GoF patterns, and to see whether they make sense at the domain level.
Eric Evans also mentions that sometimes the domain is naturally well-suited for particular approaches (or paradigms) such as state machines, predicate logic and rules engines. Now the DDD community has already expanded to include event-driven as a favourite paradigm, with the Event-Sourcing and CQRS approaches in particular.
On paradigms, my design style has also been strongly influenced by elements of functional programming, that I originally learnt from using Apache Commons Collections, together with a increasingly pronounced taste for immutability.
Maths
It is in fact the core job of mathematicians to factor out formal models of everything we experience in the world. As a result it is no surprise we can draw on their work to build deeper models.
Graph theory
The great benefit of any mathematical model is that it is highly formal, ready with plenty of useful theorems that depend on the set of axioms you can assume. In short, all the body of maths is just work already done for you, ready for you to reuse. To start with a well-known example, used extensively by Eric Evans, let’s consider a bit of graph theory.
If you recognize that your problem is similar (mathematicians would say isomorphic or something like that) to a graph, then you can jump in graph theory and reuse plenty of exciting results, such as how to compute a shortest-path using a Dijkstra or A* algorithm. Going further, the more you know or read about your theory, the more you can reuse: in other words the more lazy you can be!
In his classical example of modelling cargo shipping using Legs or using Stops, Eric Evans, could also refer to the concept of Line Graph, (aka edge-to-vertex dual) which comes with interesting results such as how to convert a graph into its edge-to-vertex dual.
Trees and nested sets
Other maths concepts common enough include trees and DAG, which come with useful concepts such as the topological sort. Hierarchy containment is another useful concept that appear for instance in every e-commerce catalog. Again, if you recognize the mathematical concept hidden behind your domain, then you can then search for prior knowledge and techniques already devised to manipulate the concept in an easy and correct way, such as how to store that kind of hierarchy into a SQL database.
Don’t miss the next part: part 2
• Maths continued
• General principles
Your cross-cutting concerns are someone else core domain
Consider a domain, for example an online bookshop project that we call BuyCheapBooks. The Ubiquitous Language for this domain would talk about Book, Category, Popularity, ShoppingCart etc.
From scratch, coding this domain can be quite fast, and we can play with the fully unit-tested domain layer quickly. However if we want to ship, we will have to spend several times more effort because of all the extra cross-cutting concerns we must deal with: persistence, user preferences, transactions, concurrency and logging (see non-functional requirements). They are not part of the domain, but developers often spend a large amount of their time on them, and by the way, middleware and Java EE almost exclusively focus on these concerns through JPA, JTA, JMX and many others.
On first approximation, our application is made of a domain and of several cross-cutting concerns. However, when it is time to implement the cross-cutting concerns, they each become the core domain -a technical one- of another dedicated project in its own right. These technical projects are managed by someone else, somewhere not in your team, and you would usually use these specific technical projects to address your cross-cutting concerns, rather than doing it yourself from scratch with code.
Technical Domains
For example, persistence is precisely the core domain of an ORM like Hibernate. The Ubiquitous Language for such project would talk about Data Mapper, Caching, Fetching Strategy (Lazy Load etc.), Inheritance Mapping (Single Table Inheritance, Class Table Inheritance, Concrete Table Inheritance) etc. These kinds of projects also deal with their own cross-cutting concerns such as logging and administration, among others.
Logging is the core domain of Log4j, and it must itself deal with cross-cutting concerns such as configuration.
In this perspective, the cross-cutting concerns of a project are the core domains of other satellite projects, which focus on technical domains.
Hence we see that the very idea of core domain Vs. cross-cutting concerns is essentially relative to the project considered.
Note, for the sake of it, that there may even be cycles between the core domains and the required cross-cutting concerns of several projects. For example there is a cycle between a (hypothetical) project Conf4J that focuses on configuration (its core domain) and that requires logging (as a cross-cutting concern), and another project Log4J that focuses on logging (its core domain) and that requires configuration (as a cross-cutting concern).
Conclusion
There is no clear and definite answer as to whether a concept is part of the domain or whether it is just a cross-cutting concern: it depends on the purpose of the project. There is almost always a project which domain addresses the cross-cutting concern of another.
For projects that target end-users, we usually tend to reuse the code that deals with cross-cutting concerns through middleware and APIs, in order to focus on the usually business-oriented domain, the one that our users care about. But when our end-users are developers, the domain may well be technical.
Big battles are won on small details
Small details matter because you deal with them often. Any enhancement you make thus yields a benefit often, hence a bigger overall benefit. In other words: invest small care, get big return. This is an irresistible proposal!
Examples of small design-level details that I care about because I have experienced great payback from them:
1. Using Value Objects rather than naked primitives
2. One argument instead of two in a method,
3. Well-thought names for every programming element
4. Favour side-effect free methods and immutability as much as possible
5. Keeping the behaviour close to the related data
6. Investing enough time to deeply distillate each concept of the domain, even the most simple ones
Ivan Moore has an excellent series of blog entries on this approach: programming in the small.
All these details emphasize that code is written once then used many times. The extra care at time of writing pays back at time of using, each time, again and again. Each enhancement that minimises brain effort at time of use is welcome, because software design is a matter of economy.
Other kinds of “details” that I care about involve the human aspects of crafting software: being on site, face-to-face communication rather than electronic media, respect and consideration at all times, always celebrate achievements, etc. Because ultimately, it also boils down to people that feel like building something together.
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0
# What is 6.575 as a mixed number in simplest form?
Wiki User
2012-03-08 00:00:42
6.575 = 6575/1000 = 623/40
Wiki User
2012-03-08 00:00:42
Study guides
20 cards
➡️
See all cards
3.75
859 Reviews
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Time to tighten up all of the loose nuts
# Time to tighten up all of the loose nuts
A man in Poland once received an express-mail package 14 days after it was sent. Upset at how much time it took, he calculated how long it should have taken for the package to reach him. The distance between the point of dispatch and his home is 11.1 kilometers (6.9 miles), but it took 292 hours to arrive. So, the package’s average speed was .038 kilometers per hour (.024 miles per hour). He also measured the average speed of a snail - .048 kilometers per hour. Based on his calculations, the Polish man concluded that the Polish post office was slower than a snail.
Snails are synonymous with being slow. The expression “the snail crosses the sea” is a metaphor for something impossible to achieve. A conch, or “sora” in Korean, is similar to a snail. They both have one thing in common: spiral-shaped shells.
In that sense, it was a superb idea to call the water pump - which was invented by Greek mathematician Archimedes - a water screw. It is a device that scoops up water by turning a screw inside a hollow pipe.
Although water slides up only one notch per turn, the industrial revolution sprouted out from its slow movement. They are bolts and nuts. In Korean, they are called male and female screws, devices used to connect things. British mechanical engineer Henry Maudslay first began mass producing precision machines in 1797 by standardizing the space of a spiral angle, which used to be different from person to person.
Henry Phillips, an American repairman, invented the crosshead screw. At the time, a screw had one groove on its head, which made it difficult to loosen or tighten because the friction was weak. But a crosshead screw was easy to use because its frictional force was strong and it did not wear out easily. It was used in the manufacture of GM’s Cadillac sedan in 1936. The screw was eventually christened the Phillips-head and Henry Phillips became very rich thanks to the idea of cutting one more groove in a nail.
It was reported recently that a KTX train that derailed on Friday because of a loose nut. But I wonder whether safety management as a whole went loose. It’s absurd that a high-speed train that can go 300 kilometers per hour was stopped by a single nut that moves at a snail’s pace. And in this case, it is ironic that the word “nut” also refers to someone who is stupid or foolish. It seems we may have to check all the loose nuts around us and tighten them up.
*The writer is an editorial writer of the JoongAng Ilbo.
By Park Jong-kwon
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# cmos opamp design
The operational amplifier is arguably the most useful single device in analog electronic circuitry. With only a handful of external components, it can be made to perform a wide variety of analog signal processing tasks. It is also quite affordable, most general-purpose amplifiers selling for under a dollar apiece. Modern designs have been engineered with durability in mind as well: several “op-amps” are manufactured that can sustain direct short-circuits on their outputs without damage. One key to the usefulness of these little circuits is in the engineering principle of feedback, particularly negativefeedback, which constitutes the foundation of almost all automatic control processes. The principles presented here in operational amplifier circuits, therefore, extend well beyond the immediate scope of electronics. It is well worth the electronics student’s time to learn these principles and learn them well. If the input voltages to this amplifier represented mathematical quantities (as is the case within analog computer circuitry), or physical process measurements (as is the case within analog electronic instrumentation circuitry), you can see how a device such as a differential amplifier could be very useful. We could use it to compare two quantities to see which is greater (by the polarity of the output voltage), or perhaps we could compare the difference between two quantities (such as the level of liquid in two tanks) and flag an alarm (based on the absolute value of the amplifier output) if the difference became too great. In basic automatic control circuitry, the quantity being controlled (called theprocess variable) is compared with a target value (called the setpoint), and decisions are made as to how to act based on the discrepancy between these two values. The first step in electronically controlling such a scheme is to amplify the difference between the process variable and the setpoint with a differential amplifier. In simple controller designs, the output of this differential amplifier can be directly utilized to drive the final control element (such as a valve) and keep the process reasonably close to setpoint.
REVIEW:
A “shorthand” symbol for an electronic amplifier is a triangle, the wide end signifying the input side and the narrow end signifying the output. Power supply lines are often omitted in the drawing for simplicity.
To facilitate true AC output from an amplifier, we can use what is called a split or dual power supply, with two DC voltage sources connected in series with the middle point grounded, giving a positive voltage to ground (+V) and a negative voltage to ground (-V). Split power supplies like this are frequently used in differential amplifier circuits.
Most amplifiers have one input and one output. Differential amplifiers have two inputs and one output, the output signal being proportional to the difference in signals between the two inputs.
The voltage output of a differential amplifier is determined by the following equation: Vout = AV(Vnoninv – Vinv)more details on the basics of opamp at ./
Opamp for every one famous design reference from TI
ANALOG UNIVERSITY from national semiconductor
Research groups in analog and mixed signal design
Analog Electronics ece.gatech.edu
analog ics from analogzone analogzone.com
CMOS Analog Filter Design from toronto.edu
ALL SPICE STUFF Page
Advanced Analog Circuit Design Techniques Course material from http://amesp02.tamu.edu
Circuit Diagrams,Design Notes
Design and Simulation of Operational Amplifier
Analog IC Design Software
Analog Office from Applied Wave Research
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## Algorithm Help
From Visual Basic to GNU C, this is the place to talk programming.
Moderators: SecretSquirrel, just brew it!
### Algorithm Help
OK, first, I just want to say that I'm new here, so hello and all that. Anyways, I've been reading "Programing for Dummies" recently, and it got into the section on advanced programing topics. And that particular section was on sorting and searching algorithms. The one I don't understand is the insertion sort algorithm in Liberty Basic. Here it is(Note: There may be a few mistakes because I wrote it from looking at it, it's not the actual code):
Code: Select all
`Max Size = 5REDIM MyArray(Maxsize)For I = 1 to MaxsizeMyArray (I) = INT(Rnd(1) *100) + 1PRINT MyArray(I); SPACE\$(1);NEXT IPRINT "(Initial Array)"For Arraypos = 2 to Maxsize Tempvalue = Myarray(Arraypos)StopNow = 0Count = 1Time2Stop = 0WHILE (TIme2Stop = 0)If TempValue < MyArray(Count) THENFor J = ArrayPos to Count Step -1Myarray(J) = Myarray(J - 1)NEXT jMyarray(count) = TempValueStopNow = 1FOR I = 1 to MaxSizePRINT Myarray(I); SPACE\$;Next IPRINTEND IFCount = Count +1If (StopNow = 1) OR (Count = ArrayPos) THENTime2stop = 1End ifWENDNEXT ArrayPosFor I =1 To MaxSize Print MyArray(I) SPACE\$;Next IPRINT "(Sorted Array)"`
1: Why did they make Maxsize equal to 6 if the only used 5? And how did they use the Redim function if Myarray hasn't been declaired yet?
2:What does INT (RND (1) *100) +1 do? It never explained it.
3:ArrayPos to Count step -1 would repeat twice, wouldn't it? If so, why would it need to?
4:How did they use the PRINT function with nothing to print?
These are my questions for now.
Dr. Coconut
Gerbil
Posts: 21
Joined: Sat Feb 18, 2012 7:45 pm
### Re: Algorithm Help
Dr. Coconut wrote:2:What does INT (RND (1) *100) +1 do? It never explained it.
RND(1) is a random real number between 0 and 1. If you multiply it by 100 then take the integer, you'll have a random integer from 0 to 99. Adding 1 gives you a random integer from 1 to 100. This is just filling the array with random numbers prior to sorting it.
The first PRINT commands output the values of the unsorted array, then the text "(initial array)".
Inside the sort loop, they're printing out the array each time that it is reordered. The looped PRINTs with a semi-colon at the end print the value and a space but they do not include a carriage return and line feed. The PRINT by itself adds the carriage return and line feed at the end of the line.
After the sort is complete, they output the values of the sorted array and then the text "(sorted array)".
The way that the insertion sort works is to go through the array looking at each new value and putting it into the correct order in the part of the array that has already been sorted. I know that when I've had to manually sort stacks of records for filing, I've used an insertion sort method. You may want to try this and compare it to a bubble sort, counting the number of comparisons and swaps for each method. Move on to heap sort, quick sort, etc.
JustAnEngineer
Gerbil God
Gold subscriber
Posts: 16765
Joined: Sat Jan 26, 2002 7:00 pm
Location: The Heart of Dixie
### Re: Algorithm Help
Dr. Coconut wrote:1: Why did they make Maxsize equal to 6 if the only used 5? And how did they use the Redim function if Myarray hasn't been declaired yet?
REDIM: http://www.libertybasicuniversity.com/l ... 1ST4AN.htm
Dr. Coconut wrote:2:What does INT (RND (1) *100) +1 do? It never explained it.
RND(n): http://www.libertybasicuniversity.com/l ... NLSAKK.htm
Dr. Coconut wrote:3:ArrayPos to Count step -1 would repeat twice, wouldn't it? If so, why would it need to?
Code: Select all
`For J = ArrayPos to Count Step -1 Myarray(J) = Myarray(J - 1)NEXT j`
FOR..NEXT: http://www.libertybasicuniversity.com/lb4help/
Dr. Coconut wrote:4:How did they use the PRINT function with nothing to print?
PRINT: http://www.libertybasicuniversity.com/l ... 1R69FU.htm
The entire HELP manual online for every single question you could ever dream up of for this "liberty" \$59.95 RIP-OFF language: http://www.libertybasicuniversity.com/lb4help/
thegleek
Darth Gerbil
Gold subscriber
Posts: 7394
Joined: Tue Jun 10, 2003 11:06 am
Location: Detroit, MI
### Re: Algorithm Help
Wow... the Libery BASIC website brought be back to the 90's....
Intel Core i7 3770K / 16 GB Kingston HyperX DDR3-1600 / Intel 520 180GB SSD / Zotac GTX660 / Corsair TX650 V2 PSU / Audigy 2 ZS
Wajo
Gerbil Elite
Posts: 596
Joined: Fri Jun 18, 2004 2:08 am
Location: MX
### Re: Algorithm Help
I really have to wonder whether BASIC is still a reasonable first language for beginners, now that we've got more modern interpreted languages like Python.
The years just pass like trains. I wave, but they don't slow down.
-- Steven Wilson
just brew it!
Gold subscriber
Posts: 43714
Joined: Tue Aug 20, 2002 10:51 pm
Location: Somewhere, having a beer
### Re: Algorithm Help
Thanks for the help, I'm still kind of new to programming, so that would explain the questions. I do know a few things though.
Dr. Coconut
Gerbil
Posts: 21
Joined: Sat Feb 18, 2012 7:45 pm
### Re: Algorithm Help
just brew it! wrote:I really have to wonder whether BASIC is still a reasonable first language for beginners, now that we've got more modern interpreted languages like Python.
What I'm really curious about is how one FINDS this "Libery" BASIC... is it that common? was it a factor of advertisement? word-of-mouth/recommendation by peers? Or is this some lame blatant attempt at a spammer trying to "advertise" this unknown BS version of basic to make money or paid-to-click crap?
thegleek
Darth Gerbil
Gold subscriber
Posts: 7394
Joined: Tue Jun 10, 2003 11:06 am
Location: Detroit, MI
### Re: Algorithm Help
thegleek wrote:
just brew it! wrote:I really have to wonder whether BASIC is still a reasonable first language for beginners, now that we've got more modern interpreted languages like Python.
What I'm really curious about is how one FINDS this "Libery" BASIC... is it that common? was it a factor of advertisement? word-of-mouth/recommendation by peers? Or is this some lame blatant attempt at a spammer trying to "advertise" this unknown BS version of basic to make money or paid-to-click crap?
That's pretty funny given that you were the first person in this thread to post links to their web site...
The years just pass like trains. I wave, but they don't slow down.
-- Steven Wilson
just brew it!
Gold subscriber
Posts: 43714
Joined: Tue Aug 20, 2002 10:51 pm
Location: Somewhere, having a beer
### Re: Algorithm Help
Umm, no, I'm not trying to spam, I read it in a programing book.
Dr. Coconut
Gerbil
Posts: 21
Joined: Sat Feb 18, 2012 7:45 pm
### Re: Algorithm Help
Dr. Coconut wrote:Umm, no, I'm not trying to spam, I read it in a programing book.
Don't worry about it, thegleek is just being... himself.
Oh, and I'd like to extend a (slightly belated) welcome to the Tech Report forums!
The years just pass like trains. I wave, but they don't slow down.
-- Steven Wilson
just brew it!
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https://ask.learncbse.in/t/what-is-the-average-power-transferred-to-the-circuit-in-one-complete-cycle/12776
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# What is the average power transferred to the circuit in one complete cycle?
A series L-C-R circuit with R = 20 Ω, L = 1.5H and C= 35 µF is connected to a variable frequency of 200 V AC supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
When the frequency of the supply equals the natural frequency of the circuit, resonance occurs.
{ Z }_{ r } = R = 20 Ω
{ I }_{ rms } =
{ V}_{ rms } /
{ Z }_{ r } = 200/20 = 10 A
Average power transferred in one cycle
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https://www.teachoo.com/3657/698/Ex-5.2--1---Differentiate-sin-(x2---5)/category/Ex-5.2/
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Ex 5.2
Chapter 5 Class 12 Continuity and Differentiability
Serial order wise
This video is only available for Teachoo black users
Get live Maths 1-on-1 Classs - Class 6 to 12
### Transcript
Ex 5.2, 1 Differentiate the functions with respect to π₯ sinβ‘(π₯2 + 5) y = sin (x2 + 5) We need to find derivative of π¦, π€.π.π‘.π₯ (ππ¦ )/ππ₯ = (π(sinβ‘(π₯2 + 5)))/ππ₯ = cos (π₯2 + 5) Γ π(π₯2 + 5)/ππ₯ = cos (π₯2 + 5) Γ ((π(π₯2))/ππ₯+ (π(5))/ππ₯) = cos (π₯2 + 5) Γ (γ2π₯γ^(2β1) + 0) = cos (π₯2 + 5) Γ 2π₯ = ππ πππβ‘γ (ππ + π)γ
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https://forum.processing.org/two/discussion/13165/face-objects-outwards-in-a-uniform-angle.html
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#### Howdy, Stranger!
We are about to switch to a new forum software. Until then we have removed the registration on this forum.
# face objects outwards in a uniform angle
edited October 2015
hello there, i'm sure there is an easy answer to this...
i'm rotating ellipses around a circle, but each ellipse seems to face the same direction...
but i want them all to face uniformly around the sphere...
i've tried a bunch of stuff... nothing seems to work without throwing things into chaos.
i imagine its something like... divide the amount of objects by their angle around the sphere, rotating each by that much... but i just can't get it...
i've commented out the rotation line where I think i should, but uncomment and you'll see what i mean... the ellipse kind've rotate in a non-uniform fashion...
what i'm trying to do is have every ellipse angle at the right angle to the centre of the sphere... if that makes sense... like rays of sunshine or something... or if i had a piece of string going out to each ellipse, the ellipse rotates on the angle of that piece of string...
hope someone can help...
``````int radius = 150;
float d = 0.0;
void setup() {
size(1000, 1000, P3D);
noStroke();
}
void draw() {
background(0);
translate(width/2, height/2);
lights();
sphereDetail(50);
stroke(100, 100, 255);
sphere(100);
for (int deg = 0; deg < 360; deg += 10) {
float x = (cos(angle) * radius);
float z = (sin(angle) * radius);
pushMatrix();
translate(x, z, 0);
fill(50, 200, 255);
pushMatrix();
//rotateY(90);
ellipse(0, 0, 20, 20);
popMatrix();
popMatrix();
}
}
``````
Tagged:
• edited October 2015
I can get what I want the normal old way, just rotating within a for loop...
But the particular sketch I'm working on needs the sin/cos/translate code as used above...
``````int radius = 150;
float d = 0.0;
float theta = 0;
void setup() {
size(400, 400, P3D);
noStroke();
}
void draw() {
background(0);
translate(width/2, height/2);
lights();
for (int i = 0; i < 360; i+=45) {
stroke(255);
pushMatrix();
ellipse(0, -100, 100, 100);
popMatrix();
}
}
``````
You're close. Really close. The second example sketch really helped. Have a solution.
``````int radius = 150;
float d = 0.0;
void setup() {
size(1000, 1000, P3D);
noStroke();
}
void draw() {
background(0);
translate(width/2, height/2);
lights();
sphereDetail(50);
stroke(100, 100, 255);
sphere(100);
for (int deg = 0; deg < 360; deg += 10) {
float x = (cos(angle) * radius);
float z = (sin(angle) * radius);
pushMatrix();
translate(x, z, 0);
fill(50, 200, 255);
pushMatrix();
rotateY(HALF_PI);
rotateX(HALF_PI-angle);
ellipse(0, 0, 20, 20);
popMatrix();
popMatrix();
}
}
``````
This was a good forum post. You posted formatted sample code and everything. Please stay and be an example for others!
• hmmmm..... i appear to have fixed it... for now... mind you i have no idea what i'm doing... trial and error for 3 hours is the only way I know how to fix things :(
``````int radius = 150;
float d = 0.0;
float theta = 0;
void setup() {
size(400, 400, P3D);
noStroke();
fill(50, 200, 255);
}
void draw() {
background(0);
translate(width/2, height/2);
lights();
sphereDetail(50);
sphere(20);
for (int deg = 0; deg < 360; deg += 45) {
pushMatrix();
float x = (cos(angle) * radius);
float z = (sin(angle) * radius);
translate(x, 0, z);
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https://www.inf.ethz.ch/personal/wirth/CompilerConstruction/TestOberon0.Mod.txt
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OSP.Compile @ OSG.Decode OSG.Execute 3 7 11~ MODULE Permutations; (*NW 22.1.2013 for Oberon-0*) VAR m, n: INTEGER; a: ARRAY 10 OF INTEGER; PROCEDURE perm(k: INTEGER); VAR i, x: INTEGER; BEGIN IF k = 0 THEN i := 0; WHILE i < n DO WriteInt(a[i]); i := i+1 END ; WriteLn ELSE perm(k-1); i := 0; WHILE i < k-1 DO x := a[i]; a[i] := a[k-1]; a[k-1] := x; perm(k-1); x := a[i]; a[i] := a[k-1]; a[k-1] := x; i := i+1 END END END perm; BEGIN n := 0; ReadInt(m); WHILE ~eot() DO a[n] := m; n := n+1; ReadInt(m) END ; perm(n) END Permutations. OSP.Compile @ OSG.Decode OSG.Execute 3 MODULE MagicSquares; (*for Oberon-0 NW 25.1.2013*) PROCEDURE Generate; (*magic square of order 3, 5, 7, ... *) VAR i, j, x, nx, nsq, n: INTEGER; M: ARRAY 13 OF ARRAY 13 OF INTEGER; BEGIN ReadInt(n); nsq := n*n; x := 0; i := n DIV 2; j := n-1; WHILE x < nsq DO nx := n + x; j := (j-1) MOD n; x := x+1; M[i][j] := x; WHILE x < nx DO i := (i+1) MOD n; j := (j+1) MOD n; x := x+1; M[i][j] := x END END ; i := 0; REPEAT j := 0; REPEAT WriteInt(M[i][j]); j := j+1 UNTIL j = n; WriteLn; i := i+1 UNTIL i = n END Generate; BEGIN Generate END MagicSquares. OSP.Compile @ OSG.Decode OSG.Execute 20 MODULE PrimeNumbers; (*NW 6.9.07; Tabulate prime numbers; for Oberon-07 NW 25.1.2013*) VAR n: INTEGER; p: ARRAY 400 OF INTEGER; v: ARRAY 20 OF INTEGER; PROCEDURE Primes(n: INTEGER); VAR i, k, m, x, inc, lim, sqr: INTEGER; prim: BOOLEAN; BEGIN x := 1; inc := 4; lim := 1; sqr := 4; m := 0; i := 3; WHILE i <= n DO REPEAT x := x + inc; inc := 6 - inc; IF sqr <= x THEN (*sqr = p[lim]^2*) v[lim] := sqr; lim := lim + 1; sqr := p[lim]*p[lim] END ; k := 2; prim := TRUE; WHILE prim & (k < lim) DO k := k+1; IF v[k] < x THEN v[k] := v[k] + p[k] END ; prim := x # v[k] END UNTIL prim; p[i] := x; WriteInt(x); IF m = 10 THEN WriteLn; m := 0 ELSE m := m+1 END ; i := i+1 END ; IF m > 0 THEN WriteLn END END Primes; BEGIN ReadInt(n); WriteInt(n); WriteLn; Primes(n) END PrimeNumbers. OSP.Compile @ OSG.Decode OSG.Execute 20 MODULE Fractions; (*NW 10.10.07; Tabulate fractions 1/n*) CONST Base = 10; N = 32; PROCEDURE Go; VAR i, j, m, n, r: INTEGER; d: ARRAY N OF INTEGER; (*digits*) x: ARRAY N OF INTEGER; (*index*) BEGIN ReadInt(n); i := 2; WHILE i <= n DO j := 0; WHILE j < i DO x[j] := 0; j := j+1 END ; m := 0; r := 1; WHILE x[r] = 0 DO x[r] := m; r := Base*r; d[m] := r DIV i; r := r MOD i; m := m+1 END ; WriteInt(i); WriteChar(9); WriteChar("."); j := 0; WHILE j < x[r] DO WriteChar(d[j] + 48); j := j+1 END ; WriteChar("'"); WHILE j < m DO WriteChar(d[j] + 48); j := j+1 END ; WriteLn; i := i+1 END END Go; BEGIN Go END Fractions. OSP.Compile @ OSG.Decode OSG.Execute 32 MODULE Powers; (*NW 25.1.2013 fo Oberon-07; Tabulate positive and negative powers of 2*) CONST N = 32; M = 11; (*M ~ N*log2*) PROCEDURE Go; VAR i, k, n, exp: INTEGER; c, r, t: INTEGER; d: ARRAY M OF INTEGER; f: ARRAY N OF INTEGER; BEGIN ReadInt(n); d[0] := 1; k := 1; exp := 1; WHILE exp < n DO (*compute d = 2^exp*) c := 0; (*carry*) i := 0; WHILE i < k DO t := 2*d[i] + c; IF t < 10 THEN d[i] := t; c := 0 ELSE d[i] := t - 10; c := 1 END ; i := i+1 END ; IF c = 1 THEN d[k] := 1; k := k+1 END ; (*write d*) i := M; WHILE i > k DO i := i-1; WriteChar(" ") END ; WHILE i > 0 DO i := i-1; WriteChar(d[i] + 48) END ; WriteInt(exp); (*compute f = 2^-exp*) WriteChar(9); WriteChar("0"); WriteChar("."); r := 0; i := 1; WHILE i < exp DO r := 10*r + f[i]; f[i] := r DIV 2; r := r MOD 2; WriteChar(f[i] + 48); i := i+1 END ; f[exp] := 5; WriteChar("5"); WriteLn; exp := exp + 1 END END Go; BEGIN Go END Powers.
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# Find the exactly correct separating hyperplane of SVM when the data is not perfectly linearly separable
I am thinking about the following case where the data in region 1 is always positive and the data in region 2 is always negative, but the data in region 3 can be both positive and negative. Are there any existing results on finding exactly the $$l_1$$ and $$l_2$$ (or region 3)?
As far as my understanding of SVM when the data is not perfectly linearly separable, we can maximize the soft margin to find the separating hyperplane. We can control the penalty of misclassification to achieve different separating hyperplanes. But is there a method for finding the exactly correct separating plane like $$l_1$$ and $$l_2$$? I am not very familiar with SVM, and I would really appreciate it if you can provide some comments or references.
You can do this twice to get both lines $$l_1$$ and $$l_2$$.
• I am sorry, but I didn't quite get how can you run hard SVM when the data is not perfectly separable? For example, in order to get $l_1$, do we need to manually preprocess the data, like changing the positive examples under $l_1$ to be negative and then run hard SVM to get $l_1$? Could you explain more about running hard SVM for positive labels and running soft SVM for negative labels? Commented May 26, 2021 at 16:40
• Look at the hard SVM definition and the soft SVM definition. Now, create a linear program where for positive labels you add the hard SVM constraint, and for negative labels you put the soft SVM constraint. The solution to this LP is $l_2$ Commented May 26, 2021 at 18:22
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# ggscatterstats
#### 2018-05-22
The function ggstatsplot::ggscatterstats is meant to provide a publication-ready scatterplot with all statistical details included in the plot itself to show association between two continuous variables. We will see examples of how to use this function in this vignette with the ggplot2movies dataset.
To begin with, here are some instances where you would want to use ggscatterstats-
• to check linear association between two continuous variables
• to check distribution of two continuous variables
Note before: The following demo uses the pipe operator (%>%), so in case you are not familiar with this operator, here is a good explanation: http://r4ds.had.co.nz/pipes.html
## Correlation plot with ggscatterstats
To illustrate how this function can be used, we will use the ggplot2movies dataset. This dataset (available in package on CRAN) provides a dataset about movies scraped from IMDB. Let’s have a look at the data-
library(ggplot2movies)
library(dplyr)
dplyr::glimpse(x = ggplot2movies::movies)
#> Observations: 58,788
#> Variables: 24
#> $title <chr> "$", "$1000 a Touchdown", "$21 a Day Once a Month"...
#> $year <int> 1971, 1939, 1941, 1996, 1975, 2000, 2002, 2002, 19... #>$ length <int> 121, 71, 7, 70, 71, 91, 93, 25, 97, 61, 99, 96, 10...
#> $budget <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA... #>$ rating <dbl> 6.4, 6.0, 8.2, 8.2, 3.4, 4.3, 5.3, 6.7, 6.6, 6.0, ...
#> $votes <int> 348, 20, 5, 6, 17, 45, 200, 24, 18, 51, 23, 53, 44... #>$ r1 <dbl> 4.5, 0.0, 0.0, 14.5, 24.5, 4.5, 4.5, 4.5, 4.5, 4.5...
#> $r2 <dbl> 4.5, 14.5, 0.0, 0.0, 4.5, 4.5, 0.0, 4.5, 4.5, 0.0,... #>$ r3 <dbl> 4.5, 4.5, 0.0, 0.0, 0.0, 4.5, 4.5, 4.5, 4.5, 4.5, ...
#> $r4 <dbl> 4.5, 24.5, 0.0, 0.0, 14.5, 14.5, 4.5, 4.5, 0.0, 4.... #>$ r5 <dbl> 14.5, 14.5, 0.0, 0.0, 14.5, 14.5, 24.5, 4.5, 0.0, ...
#> $r6 <dbl> 24.5, 14.5, 24.5, 0.0, 4.5, 14.5, 24.5, 14.5, 0.0,... #>$ r7 <dbl> 24.5, 14.5, 0.0, 0.0, 0.0, 4.5, 14.5, 14.5, 34.5, ...
#> $r8 <dbl> 14.5, 4.5, 44.5, 0.0, 0.0, 4.5, 4.5, 14.5, 14.5, 4... #>$ r9 <dbl> 4.5, 4.5, 24.5, 34.5, 0.0, 14.5, 4.5, 4.5, 4.5, 4....
#> $r10 <dbl> 4.5, 14.5, 24.5, 45.5, 24.5, 14.5, 14.5, 14.5, 24.... #>$ mpaa <chr> "", "", "", "", "", "", "R", "", "", "", "", "", "...
#> $Action <int> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,... #>$ Animation <int> 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
#> $Comedy <int> 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0,... #>$ Drama <int> 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
#> $Documentary <int> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,... #>$ Romance <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
#> $Short <int> 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0,... Since we will be using this dataset for the current vignette, let’s first clean it up by selecting only variables that will be of interest to us. # selecting data of interest movies_wide <- ggplot2movies::movies %>% dplyr::select(.data = ., c(title:votes, mpaa)) %>% # . is just a placeholder for the data dplyr::filter(.data = ., mpaa != "") %>% # removing movies without mpaa ratings stats::na.omit(.) %>% # removing NAs dplyr::mutate(.data = ., budget = budget/1000000) %>% # convert the budge to millions of dollars dplyr::mutate_if(.tbl = ., # convert mpaa ratings to a factor .predicate = purrr::is_bare_character, .funs = ~as.factor(.)) # see the selected data (we have data from 1813 movies) dplyr::glimpse(x = movies_wide) #> Observations: 1,813 #> Variables: 7 #>$ title <fct> 'Til There Was You, 10 Things I Hate About You, 100 Mil...
#> $year <int> 1997, 1999, 2002, 2004, 1999, 2001, 1972, 2003, 1998, 1... #>$ length <int> 113, 97, 98, 98, 102, 120, 180, 107, 87, 101, 99, 129, ...
#> $budget <dbl> 23.00, 16.00, 1.10, 37.00, 85.00, 42.00, 4.00, 76.00, 0... #>$ rating <dbl> 4.8, 6.7, 5.6, 6.4, 6.1, 6.1, 7.3, 5.1, 5.4, 5.4, 2.5, ...
#> $votes <int> 799, 19095, 181, 7859, 14344, 10866, 1754, 9556, 841, 4... #>$ mpaa <fct> PG-13, PG-13, R, PG-13, R, R, PG, PG-13, R, R, R, R, R,...
Now that we have a clean dataset, we can start asking some interesting questions. For example, let’s see if the average rating a movie has depends on its budget.
ggstatsplot::ggscatterstats(
data = movies_wide, # dataframe from which variables are to be taken
x = budget, # predictor/independent variable
y = rating, # dependent variable
xlab = "Budget (in millions of US dollars)", # label for the x-axis
ylab = "Rating on IMDB", # label for the y-axis
marginal = TRUE, # show marginal distribution
marginal.type = "histogram", # type of plot for marginal distribution
centrality.para = "mean", # if and which type of centrality parameter to be plotted
margins = "both", # marginal distribution on both axes
xfill = "#CC79A7", # fill for marginal distributions on the x-axis
yfill = "#009E73", # fill for marginal distributions on the y-axis
type = "pearson", # type of linear association
title = "Relationship between movie budget and IMDB rating",
caption = "Source: www.imdb.com",
messages = FALSE
)
There is indeed a significant, positive correlation between the amount of money studio invests in a movie and the ratings given by the audiences. We should also note that this is a really small correlation and only about 1% of variation in ratings is explained by budget.
The type (of test) argument also accepts the following abbreviations: "p" (for parametric/pearson’s), "np" (for nonparametric/spearman), "r" (for robust).
Important: In contrast to all other functions in this package, the ggscatterstats function returns object that is not further modifiable with ggplot2. This can be avoided by not plotting the marginal distributions (marginal = FALSE). Currently trying to find a workaround this problem.
Using ggscatterstats() in R Notebooks or Rmarkdown
If you try including a ggscatterstats() plot inside an R Notebook or Rmarkdown code chunk, you’ll notice that the plot doesn’t get output. In order to get a ggscatterstats() to show up in an these contexts, you need to save the ggscatterstats plot as a variable in one code chunk, and explicitly print it using the grid package in another chunk, like this:
# include the following code in your code chunk inside R Notebook or Markdown
grid::grid.newpage()
grid::grid.draw(
ggstatsplot::ggscatterstats(
data = movies_wide,
x = budget,
y = rating,
marginal = TRUE,
messages = FALSE
)
)
## Grouped analysis with grouped_ggscatterstats
What if we want to do the same analysis do the same analysis for movies with different MPAA (Motion Picture Association of America) film ratings (NC-17, PG, PG-13, R)? In that case, we will have to either write a for loop or use purrr, none of which seem like an exciting prospect.
ggstatsplot provides a special helper function for such instances: grouped_ggstatsplot. This is merely a wrapper function around ggstatsplot::combine_plots. It applies ggstatsplot across all levels of a specified grouping variable and then combines list of individual plots into a single plot. Note that the grouping variable can be anything: conditions in a given study, groups in a study sample, different studies, etc.
Let’s see how we can use this function to apply ggscatterstats for all MPAA ratings. We will be running parametric tests (Pearson’s r, i.e.). If you set type = "np" or type = "r", results from non-parametric or robust test will be displayed.
ggstatsplot::grouped_ggscatterstats(
# arguments relevant for ggstatsplot::ggscatterstats
data = movies_wide,
title.prefix = "MPAA Rating",
x = budget,
y = rating,
grouping.var = mpaa,
marginal.type = "boxplot",
# arguments relevant for ggstatsplot::combine_plots
title.text = "Relationship between movie budget and IMDB rating",
caption.text = "Source: www.imdb.com",
nrow = 4,
ncol = 1,
labels = c("(a)","(b)","(c)","(d)")
)
#> Warning: This function doesn't return ggplot2 object and is not further modifiable with ggplot2 commands.Warning: This function doesn't return ggplot2 object and is not further modifiable with ggplot2 commands.Warning: This function doesn't return ggplot2 object and is not further modifiable with ggplot2 commands.Warning: This function doesn't return ggplot2 object and is not further modifiable with ggplot2 commands.
As seen from the plot, this analysis has revealed something interesting: The relationship we found between budget and IMDB rating holds only for PG-13 and R-rated movies. Indeed, the relationship even reverses for non-rated or NC-17 rated films.
Although this is a quick and dirty way to explore large amount of data with minimal effort, it does come with an important limitation: reduced flexibility. For example, if we wanted to add, let’s say, a separate type of marginal distribution plot for each MPAA rating or if we wanted to use different types of correlations across different levels of MPAA ratings (NC-17 has only 6 movies, so a robust correlation would be a good idea), this is not possible. But this can be easily done using purrr.
## Grouped analysis with ggscatterstats + purrr
Let’s run the same analysis using purrr::pmap.
Note before: Unlike the function call so far, while using purrr::pmap, we will need to quote the arguments.
# let's split the dataframe and create a list by mpaa rating
mpaa_list <- movies_wide %>%
base::split(x = ., f = .$mpaa, drop = TRUE) # this created a list with 4 elements, one for each mpaa rating str(mpaa_list) #> List of 4 #>$ NC-17:Classes 'tbl_df', 'tbl' and 'data.frame': 7 obs. of 7 variables:
#> ..$title : Factor w/ 1813 levels "'Til There Was You",..: 549 578 1208 1264 1450 1676 1681 #> ..$ year : int [1:7] 1981 1974 1997 1972 1995 1997 1972
#> ..$length: int [1:7] 86 97 92 108 131 84 250 #> ..$ budget: num [1:7] 0.35 0.025 1 0.012 45 1 1.25
#> ..$rating: num [1:7] 7.4 7.1 5.7 6.1 3.8 5.6 6.9 #> ..$ votes : int [1:7] 14407 868 5128 2029 11483 2014 4007
#> ..$mpaa : Factor w/ 4 levels "NC-17","PG","PG-13",..: 1 1 1 1 1 1 1 #>$ PG :Classes 'tbl_df', 'tbl' and 'data.frame': 212 obs. of 7 variables:
#> ..$title : Factor w/ 1813 levels "'Til There Was You",..: 7 37 38 42 43 44 91 96 99 104 ... #> ..$ year : int [1:212] 1972 1938 2000 2003 2004 1997 1998 1995 2005 2004 ...
#> ..$length: int [1:212] 180 102 88 102 100 98 83 140 95 120 ... #> ..$ budget: num [1:212] 4 1.9 76 26 26 3 60 62 32 110 ...
#> ..$rating: num [1:212] 7.3 8.2 4.3 5.5 3.8 4.7 7 7.5 3.5 5.7 ... #> ..$ votes : int [1:212] 1754 7359 4815 2655 919 1276 16312 41098 1043 3887 ...
#> ..$mpaa : Factor w/ 4 levels "NC-17","PG","PG-13",..: 2 2 2 2 2 2 2 2 2 2 ... #>$ PG-13:Classes 'tbl_df', 'tbl' and 'data.frame': 530 obs. of 7 variables:
#> ..$title : Factor w/ 1813 levels "'Til There Was You",..: 1 2 4 8 16 20 23 26 27 29 ... #> ..$ year : int [1:530] 1997 1999 2004 2003 2000 2004 2000 2004 2002 2002 ...
#> ..$length: int [1:530] 113 97 98 107 103 99 123 102 99 101 ... #> ..$ budget: num [1:530] 23 16 37 76 43 75 82 45 25 27 ...
#> ..$rating: num [1:530] 4.8 6.7 6.4 5.1 6 6.8 5.9 5.4 4.7 7.5 ... #> ..$ votes : int [1:530] 799 19095 7859 9556 7465 13497 12064 14651 2364 18318 ...
#> ..$mpaa : Factor w/ 4 levels "NC-17","PG","PG-13",..: 3 3 3 3 3 3 3 3 3 3 ... #>$ R :Classes 'tbl_df', 'tbl' and 'data.frame': 1064 obs. of 7 variables:
#> ..$title : Factor w/ 1813 levels "'Til There Was You",..: 3 5 6 9 10 11 12 13 14 15 ... #> ..$ year : int [1:1064] 2002 1999 2001 1998 1999 2000 2004 2003 1999 2002 ...
#> ..$length: int [1:1064] 98 102 120 87 101 99 129 124 93 135 ... #> ..$ budget: num [1:1064] 1.1 85 42 0.06 6 26 12 20 2.5 15 ...
#> ..$rating: num [1:1064] 5.6 6.1 6.1 5.4 5.4 2.5 7.6 8 5.6 7.8 ... #> ..$ votes : int [1:1064] 181 14344 10866 841 4514 2023 2663 21857 149 15788 ...
#> ..\$ mpaa : Factor w/ 4 levels "NC-17","PG","PG-13",..: 4 4 4 4 4 4 4 4 4 4 ...
# running function on every element of this list note that if you want the same
# value for a given argument across all elements of the list, you need to
# specify it just once
plot_list <- purrr::pmap(
.l = list(
data = mpaa_list,
x = "budget",
y = "rating",
xlab = "Budget (in millions of US dollars)",
ylab = "Rating on IMDB",
title = list(
"MPAA Rating: NC-17",
"MPAA Rating: PG",
"MPAA Rating: PG-13",
"MPAA Rating: R"
),
type = list("r", "np", "np", "np"),
marginal.type = list("histogram", "boxplot", "density", "violin"),
centrality.para = "mean",
xfill = list("#56B4E9", "#009E73", "#999999", "#0072B2"),
yfill = list("#D55E00", "#CC79A7", "#F0E442", "#D55E00"),
messages = FALSE
),
.f = ggstatsplot::ggscatterstats
)
# combining all individual plots from the list into a single plot using combine_plots function
ggstatsplot::combine_plots(
plotlist = plot_list,
title.text = "Relationship between movie budget and IMDB rating",
caption.text = "Source: www.imdb.com",
caption.size = 16,
title.color = "red",
caption.color = "blue",
nrow = 4,
ncol = 1,
labels = c("(a)","(b)","(c)","(d)")
)
## Suggestions
If you find any bugs or have any suggestions/remarks, please file an issue on GitHub: https://github.com/IndrajeetPatil/ggstatsplot/issues
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https://discourse.codecombat.com/t/gas-attack-python-keeps-not-seeing-enemies-or-returning-0/27641
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Gas attack /Python /Keeps not seeing enemies or returning 0
I don’t know whats wrong the hero either can’t see them or they return NaN or 0
Heres my code
``````def sumHealth(enemies):
# Create a variable and set it to 0 to start the sum.
totalHealth = 0
# Initialize the loop index to 0
enemyIndex = 0
# While enemyIndex is less than the length of enemies array
while enemyIndex < len(enemies):
# Add the current enemy's health to totalHealth
totalHealth = totalHealth + enemies.health
# Increment enemyIndex by 1.
enemyIndex += 1
# Use the cannon to defeat the ogres.
cannon = hero.findNearest(hero.findFriends())
# The cannon can see through the walls.
enemies = cannon.findEnemies()
# Calculate the sum of the ogres' health.
ogreSummaryHealth = sumHealth(enemies)
if ogreSummaryHealth:
hero.say("Use " + ogreSummaryHealth + " grams.")
``````
few major issues i think these are the reason you are failing
in the while loop put `enemy = enemies[enemyIndex]` inside as enemy isnt actually defined until then
there is no need for the if statement at the end as if takes boolean values, not numbers. Change it to
`````` #Use the cannon to defeat the ogres.
cannon = hero.findNearest(hero.findFriends())
#The cannon can see through the walls.
enemies = cannon.findEnemies()
#Calculate the sum of the ogres' health.
ogreSummaryHealth = sumHealth(enemies)
hero.say("Use " + ogreSummaryHealth + " grams.")
``````
all good?
also you can use `totalHealth += enemy.health` instead of `totalHealth = totalHealth + enemies.health `
Good try! thats actually it and there is no other gimmiks i used either like spells or abilities so you actually did pretty good even i forgot to define enemy the first time
2 Likes
I used a lot of spells(thank you swap and mana blast)
1 Like
Like this? because its still not working
``````ef sumHealth(enemies):
# Create a variable and set it to 0 to start the sum.
totalHealth = 0
# Initialize the loop index to 0
enemyIndex = 0
# While enemyIndex is less than the length of enemies array
while enemyIndex < len(enemies):
# Add the current enemy's health to totalHealth
enemy = enemies[enemyIndex
totalHealth += enemies.health
# Increment enemyIndex by 1.
enemyIndex += 1
#Use the cannon to defeat the ogres.
cannon = hero.findNearest(hero.findFriends())
#The cannon can see through the walls.
enemies = cannon.findEnemies()
#Calculate the sum of the ogres' health.
ogreSummaryHealth = sumHealth(enemies)
hero.say("Use " + ogreSummaryHealth + " grams.")
``````
An error pops up saying "unexpected token: expected T_RSQB but found T_NAME while parsing trailer
it should be `def sumHealth(enemies):` not that
It is i just didn’t copy and paste correctly
sorry about that, but what about this should have another `]` at the end.
Yes it should but its still just saying NaN or 0
@Ashmit_Singh
no need for the if statement at the end as if takes boolean values, not numbers
``````if ogreSummaryHealth:
hero.say("Use " + ogreSummaryHealth + " grams.")
``````
an if statement takes number values:
The problem is with this part of the code:
``````totalHealth += enemies.health
``````
It should be this:
``````totalHealth += enemies[enemyIndex].health
``````
With your code, Python does not know what enemy it is talking about, so you need to have an index. Hope this helps!
1 Like
Ok sure but it didn’t work for me
Thank you it fixed it
This topic was automatically closed 12 hours after the last reply. New replies are no longer allowed.
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# Father of statistics and probability. The Beginning of Probability and Statistics 2019-01-06
Father of statistics and probability Rating: 9,7/10 1103 reviews
## Who is the father of probability and statistics
Experiments on human behavior have special concerns. In France especially, mathematicians such as Laplace used probability to surmise the accuracy of population figures determined from samples. Lavoisier's work was partly based on the research of Priestley. Hacking discusses thinking before Pascal. This was the age of the Scientific Revolution and the biggest names, and 4-6. A being who could follow every particle in the universe, and who had unbounded powers of calculation, would be able to know the past and to predict the future with perfect certainty. The second accomplishment, which was primarily addressed in the 1800's, was the idea that probability and statistics could converge to form a well defined, firmly grounded science, which seemingly has limitless applications and possibilities.
Next
## Founders of statistics
Perhaps, he supposed, the unbeliever can be persuaded by consideration of self-interest. In contrast, an does not involve experimental manipulation. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics. Several critics of his book pointed this out, urging that the distinctive feature of statistical knowledge was precisely its neglect of individuals in favour of mass observations. To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole. To see this, the number trials should be sufficiently large in number. National recognition in the U.
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## Who is the father of probability and statistics
A new kind of regularity Even Quetelet had been startled at first by the discovery of these statistical laws. A statistic is simply the count of something. Many of his helicopter designs were used in the military. Firstly, this helps gage the effectiveness of the medicine when compared to, for example, a placebo. A better and increasingly common approach is to report. In short, statistics is basically the study of data.
Next
## Who Invented Probability Theory?
The set of basic statistical skills and skepticism that people need to deal with information in their everyday lives properly is referred to as. Probability was tied up with questions of law and exchange in one other crucial respect. Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. Population and economic numbers had been collected, though often not in a systematic way, since ancient times and in many countries. Nelder 1990 described continuous counts, continuous ratios, count ratios, and categorical modes of data.
Next
## How is probability related to statistics
In contrast, an observational study does not involve. The psychophysicist defined nominal, ordinal, interval, and ratio scales. See the historical books of Irish 1845 1926 Revived in statistics. In both types of studies, the effect of differences of an independent variable or variables on the behavior of the dependent variable are observed. It is the general definition which deals with the collection, presentation and interpretation of data. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis.
Next
## Statistics Related to Father's Day
There would be no injustice, Condorcet argued, in exposing innocent defendants to a risk of equal to risks they voluntarily assume without fear, such as crossing the from Dover to Calais. Ideally, statisticians compile data about the entire population an operation called. Kaiser Wilhelm of Germany's militaryaggressiveness. In this case, it is not possible to calculate the theoretical probability. Furthermore, an estimator is said to be if its is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the to the true value of such parameter. Inoculation in these days involved the actual transmission of smallpox, not the cowpox vaccines developed in the 1790s by the English surgeon , and was itself moderately risky.
Next
## Who is the father of probability and statistics
Misuse can occur when conclusions are and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias. See for writings by Montmort, Euler, Lagrange, etc. The posthumously published Ars Conjectandi 1713 was his only probability publication but it was extremely influential. Widely used pivots include the , the and Student's. Statistics deals with all aspects of data including the planning of data collection in terms of the design of and.
Next
## How is probability related to statistics
Arbuthnot thought not, and he a probability calculation to demonstrate the point. Lenders, the argument went, were like investors; having shared the risk, they deserved also to share in the gain. There are four possible outcomes, each equally likely in a fair game of chance. Charaka was an Indian who founded ayurvedic medicine. The researchers were interested in determining whether increased illumination would increase the productivity of the workers. Closely related to this gift category are the 6,897 home stores around the country.
Next
## Father of statistics
Each can be very effective. The Royal Society was a forerunner of the modern scientific society, while the continental academies were more like research institutes. English 1890 1962 Wrote the textbooks and articles that defined the academic discipline of statistics, inspiring the creation of statistics departments at universities throughout the world. A statistic is a description of some measure, such … as your height, weight, or age. Today, statistics is widely employed in government, business, and natural and social sciences.
Next
## probability and statistics
Although in principle the acceptable level of may be subject to debate, the is the smallest significance level that allows the test to reject the null hypothesis. Often they are expressed as 95% confidence intervals. Cartography and Geographic Information Science. The problems contained in the book include the and Huygens treated the. This is the meaning the man in the street gives to the word Statistics and most people usually use the word data instead. Such distinctions can often be loosely correlated with in computer science, in that dichotomous categorical variables may be represented with the , polytomous categorical variables with arbitrarily assigned in the , and continuous variables with the involving computation.
Next
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## The Earth's Energy Budget II -- Radiation Emitted by the Earth, the Greenhouse Effect, and the Overall Energy Balance
On the previous page we looked at the absorption of solar radiation by the Earth. This is the energy into the planet Earth. Because the average temperture of the Earth is nearly constant from year to year, using the principle of energy balance, we know that the radiation energy emitted by the Earth must equal the radiation energy absorbed from the Sun. Using the radiation laws, we could compute the average temperature for the planet Earth, which we called the radiative equilibrium temperature. As mentioned on the previous page, the radiative equilibrium temperature of the Earth is 0°F. This is actually the average temperature at which radiation is emitted from the Planet Earth. If there were no atmosphere (and no change in the amount of solar radiation energy absorbed by the planet), this would be the average temperature at the Earth's surface.
### The Greenhouse Effect
The average temperature of the planet Earth (based on the amount of radiation energy that the planet emits to space) is quite a bit colder than the average temperature of the Earth's surface. The reason this is possible is because the atmosphere plays a large roll in the emission of infrared radiation out to space. In effect, it restricts the flow of infrared radiation out to space. This is known as the greenhouse effect. A simplified diagram to help you understand the basics of the greenhouse effect will be distributed as an in-class handout.
Basics of the greenhouse effect:
• The atmosphere allows the majority of the Sun's radiation (visible radiation) to pass through to the surface where much of it is absorbed and goes into heating the surface.
• The atmosphere absorbs the majority of radiation emitted from the surface of the Earth (infrared radiation). This energy is not lost to space, so it does not cool the planet.
• Each type of gas molecule in the atmosphere interacts differently with radiation, however, in the atmosphere of Earth, when it is clear (not cloudy) it is mainly water vapor and carbon dioxide that determine the the strength of the greenhouse effect. These are the most important greenhouse gases. Keep in mind that water vapor and carbon dioxide are trace gases in the atmosphere of Earth. You should also realize that of the two dominant greenhouse gases on Earth, water vapor by far the most important in the overall greenhouse effect.
• The most abundant gas molecules, nitrogen and oxygen, do not interact much with infrared radiation and are not greenhouse gases.
• Clouds absorb infrared photons very efficiently, and in essense contribute to the greenhouse effect. In fact the cloud effect is a huge contributor to the overall greenhouse effect on Earth.
• The infrared radiation energy absorbed by the greenhouse gases and clouds heats the atmosphere. The energy is shared by all gas molecules by conduction, i.e., collisions between the greenhouse gases and non-greenhouse gases.
• The atmosphere emits infrared radiation in all directions. The part of the radiation that is emitted downward is absorbed by the Earth's surface further warming it, that is, the Earth's surface receives radiation energy from both the Sun and the atmosphere, and therefore is warmer than if there were no atmosphere. Another way to think of it is that not all of the radiation energy emitted by the surface is lost to space. A good portion of that energy is absorbed by the atmosphere and then returned to the surface, slowing the overall rate of energy loss from the surface, thus keeping it warmer. The part of the radiation that is emitted upward goes off to space and cools the planet. However, since the gases in the atmosphere are at a colder temperature than the surface of the Earth, the radiating temperature of the planet is colder than the surface temperature. The amount of radiation energy that is emitted from the planet Earth to space is equal to what you would calculate for an object at a temperature of 0°F.
• Again it is only the greenhouse gases and clouds that are capable of emitting infrared radiation. (NOTE: gases that absorb infrared radiation also emit infrared radiation. However, these are two separate processes. Once a photon is absorbed, the energy is transferred to the absorbing gas, and the photon no longer exists. In a separate process, the greenhouse gases emit different infrared photons.)
You should understand that the natural greenhouse effect on Earth is not a bad thing. In fact it is necessary for life as we know it to exist. If there were no greenhouse effect, the temperature of the Earth's surface would be 0°F, and most water would be frozen. The concern with global warming is that of an enhanced greenhouse effect whereby the surface temperature of the Earth will increase above the present value of 59°F. One way this could happen is by increasing the concentrations of greenhouse gases in the atmosphere. It is a fact that human activities are adding greenhouse gases to that atmosphere and that their concentrations in the atmosphere are increasing.
Let me try to simplify how additional greenhouse gases may act to warm the surface temperature:
• The Earth's surface (Land and Oceans) is constantly emitting (or giving off) infrared radiation. This process acts to cool the surface because energy is being removed from the surface when it emits radiation.
• The atmosphere (the greenhouse gases) absorbs some of this radiation energy from the surface and then returns a portion of it back to the Earth's surface when it (greenhouse gases) emits radiation downward, which gets absorbed by the surface.
• Therefore, the Earth's surface does not cool as rapidly as it would if there were no atmosphere because a portion of the radiation energy it emits is returned back to the surface.
• Adding more greenhouse gases to the atmosphere makes the atmosphere more opaque to infrared radiation, i.e., a larger fraction of the radiation energy emitted by the Earth's surface is absorbed by the atmosphere.
• Since the atmosphere absorbs a larger portion of the radiation energy emitted by the surface, it follows that it will also return more of this energy back to the surface of the Earth, further slowing the rate of surface cooling. Or in other words, warming the surface by strengthening the atmospheric greenhouse effect. We have come to call this effect global warming.
• The above sequence of events assumes that every other process in Earth's climate system does not change in response to the changes in the radiation forced by adding greenhouse gases. As we will see, because radiation is coupled to other processes, like weather patterns, cloud formation, etc., other processes will change. The overall effect of all of these coupled changes (on surface temperatures, rainfall, or whatever else) is very difficult to determine because the Earth's climate system is so complex and not fully understood by scientists.
The greenhouse effect also occurs on other planets. Depending upon the composition of the atmosphere, the greenhouse effect can be quite strong. For example, lets look at Venus:
The Planet Venus
• Covered by thick clouds, the planet absorbs 22% of the incoming solar radiation energy and reflects 78% of the incoming solar energy.
• Even though it is closer to the Sun than the Earth, because of the high reflection, it actually absorbs less radiation energy from the Sun than the Earth does. The average temperature of the planet Venus (or its radiative equilibrium temperature) is -31°F.
• But because the atmosphere is very dense and largely composed of carbon dioxide, it has a strong greenhouse effect, and the average temperature of the surface is 860°F.
The details of the greenhouse effect are quite complicated. I may mention a few of these complications in class, but I will not expect you to understand them on an Exam.
### Clouds have a large influence both on solar radiation input and infrared radiation out.
• Clouds absorb and emit infrared radiation like a solid surface, i.e., clouds are not selective absorbers/emitters of infrared radiation. Cloud bottoms emit a continuous spectrum of infrared radiation downward and cloud tops emit a continuous spectrum of infrared radiation upward. Because of this, clouds contribute to the greenhouse effect by emitting infrared radiation that warms the surface. This is very noticeable at night. If all other factors are equal, cloudy nights are warmer than clear nights.
• Clouds reflect much of the Sun's radiation back to space, which keeps the surface of the Earth cooler. This is very noticeable during the day. If all other factors are equal, cloudy days are cooler than sunny days.
• Thus, clouds have both strong cooling (mainly by reflecting visible radiation from the Sun) and strong warming (mainly by contributing to the greenhouse effect) effects on climate. Therefore, any changes in cloud amount or in the radiation properties of clouds will result in climate changes for the planet. And it is very likely that any change in greenhouse gas concentrations will influence cloud formation and cloud properties.
## Completing the Energy Budget Diagrams for the Earth
### Addition of infrared radiation to the energy budget diagrams for the Earth
The Earth's energy budget including all solar fluxes plus upward longwave radiation from the Earth's surface. Atmospheric gases (water vapor, carbon dioxide, etc.) and clouds absorb 99 of the 105 units emitted by the Earth's surface.
Note that for what we've included so far the net flux at the Earth's surface is negative (50-105 = -55) while the atmosphere shows a large surplus.
Greenhouse gases (water vapor, carbon dioxide, methane, ozone, CFCs, nitrous oxides) and clouds emit radiation upward (64 units) to space and downward (85 units) to warm the Earth's surface.
This behavior is commonly referred as the Greenhouse Effect. The above figure shows all of the radiational energy exchanges into, out of, and within the Earth-Atmosphere system. For the entire planet, the radiation energy in equals the radiation energy out, which determines the radiative equilibrium temperature. However, note that the Earth's surface absorbs more radiation energy than it emits, while the atmosphere emits more radiation energy than it absorbs. Without some other types of energy exchange between the Earth's surface and the atmosphere, we would expect that the Earth's surface would be warming (energy in > energy out) and the Earth's atmosphere would be cooling (energy out > energy in). Transfer of energy from surface to atmosphere through latent heat transfer balances energy in with energy out, so that both the surface and atmosphere remain at a nearly constant average temperature.
### Addition of Energy Transfers via Conduction and Convection between Earth's Surface and Atmosphere
The Earth's energy budget including the sensible heat flux, transfered through the processes of conduction and dry convection, and the latent heat flux , transfered through the process of moist convection (phase changes of water, i.e., evaporation from the surface and condensation in clouds)
In a balanced budget, the energy storage is neither increasing or decreasing, that is:
Energy Input - Energy output = 0
The sum of the inputs equals the sum of the outputs; the budget balances, and the entire system is neither warming nor cooling.
Summarizing the energy balances:
• The planet Earth is in radiation balance (at least it was before the recent increase in greenhouse gases). The energy in (absorbed radiation from the Sun = 70 units) is equal to the energy out (radiation emitted out to space = 70 units).
• The Earth's surface is in balance. Energy in (absorption of solar radiation plus absorption of radiation from the atmosphere = 135 units) equals energy out (emission of radiation plus latent heat flux plus sensible heat flux = 135 units).
• An interesting point here is that the Earth's surface actually receives more radiation energy from the atmosphere than from the Sun. How is this possible?
• The Earth's atmosphere is in balance. Energy in (absorption of radiation from the surface plus moist convection plus absorption of solar radiation plus dry convection and conduction = 149 units) equals energy out (emission of radiation = 149 units).
### A nice diagram from another source
The Earth's annual and global mean energy balance. Of the incoming solar radiation, 49% (168 Wm-2) is absorbed by the surface. That heat is returned to the atmosphere as sensible heat, as evapotranspiration (latent heat) and as thermal infrared radiation. Most of this radiation is absorbed by the atmosphere, which in turn emits radiation both up and down. The radiation lost to space comes from cloud tops and atmospheric regions much colder than the surface. This causes a greenhouse effect.
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# Math
posted by .
A gallon of paint can cover an area of 385 square feet. How thick is the coat of paint in inches.
thanks
• Math -
Find out how many inches are in a square foot and then multiply that by 385.
• Math -
that gives me a rather large answer, i believe its thickness would be less than an inch
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The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282778 First differences of A281687. 2
0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, -1, 1, 0, 2, -1, 1, -1, 1, 0, 2, -1, 2, -2, 1, -1, 2, -1, 2, -3, 1, 1, 1, -1, 3, -2, -1, 1, 0, -1, 3, -1, 0, 0, 2, -1, 4, -3, 0, 0, 1, -2, 4, -4, 3, -2, 3, -3, 4, -2, 1, -1, 2, -3, 5, -3, 2, -3, 3, -2, 3, -2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,23 COMMENTS Numbers n such that a(n) = 0 are 1, 2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 17, 18, 22, 28, 47, 51, 52, 57, 58, 81, 111, 112, 195, 201 according to the b-file. Can there be other values of n such that a(n) = 0? See also graph of this sequence. LINKS Altug Alkan, Table of n, a(n) for n = 1..10000 Altug Alkan, Alternative Scatterplot of A282778 FORMULA a(n) = A281687(n+1) - A281687(n). PROG (PARI) a281687(n) = sum(k=1, n, istotient(k) && istotient(2*n-k)); a(n) = a281687(n+1) - a281687(n); CROSSREFS Cf. A281687. Sequence in context: A025904 A137993 A353329 * A342788 A059883 A086967 Adjacent sequences: A282775 A282776 A282777 * A282779 A282780 A282781 KEYWORD sign AUTHOR Altug Alkan, Feb 21 2017 STATUS approved
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Last modified April 16 20:42 EDT 2024. Contains 371754 sequences. (Running on oeis4.)
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## NY-4.NBT.2a: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
There are 48 resources.
Title Description Thumbnail Image Curriculum Topics
## Math Examples Collection: Comparing and Ordering Whole Numbers Using Place Value
This collection aggregates all the math examples around the topic of Comparing and Ordering Whole Numbers Using Place Value. There are a total of 26 images. Place Value
## Math Worksheet Collection: Adding with Place Value
This collection aggregates all the math worksheets around the topic of Adding with Place Value. There are a total of 10 worksheets. Place Value
## Math Examples Collection: Four-Digit Numbers in Expanded Form
This collection aggregates all the math examples around the topic of Four-Digit Numbers in Expanded Form. There are a total of 9 Math Examples. Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 1
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 1
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 2
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 2
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 3
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 3
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 4
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 4
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 5
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 5
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 6
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 6
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 7
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 7
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 8
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 8
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 9
Math Example--Numbers--Writing Four-Digit Numbers in Expanded Form--Example 9
This is part of a collection of math examples that focus on numbers and their properties.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 1
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 1
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 10
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 10
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 11
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 11
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 12
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 12
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 13
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 13
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 14
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 14
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 15
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 15
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 16
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 16
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 17
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 17
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 18
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 18
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 19
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 19
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 2
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 2
This is part of a collection of math examples that focus on place value.
Place Value
## Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 20
Math Example--Place Value--Comparing and Ordering Whole Numbers Using Place Value--Example 20
This is part of a collection of math examples that focus on place value.
Place Value
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We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.
A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.
In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.
Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.
Movements and not Forces are the Essence of Physics.
The basic rule Movement = Space/Time (v=s/t) shows that Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.
The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.
Geometric Algebra has a strange relationship with Pascals Triangle. This Triangle, also called the Binomial Expansion, contains all the Possible Combinations of two Independent Variables. Our Universe is a Combination of Combinations exploring Every Possibility.
The last and perhaps most important Discovery in Mathematics called Bott Periodicity shows itself in Pascals Triangle.
Bott Periodicity proves that we live in a Cyclic Fractal Universe, the Wheel of Fortune, that is Rotating around the Void, the Empty Set. The Empty Set contains Every Thing that is Impossible in our Universe.
This blog is not a Scientific Article. I have tried to connect the Old Sciences and the New Sciences in my own Way.
It contains many links to Scientific Articles and even Courses in Geometric Algebra.
So if you want to Dig Deeper Nothing will Stop You.
About the One and the Dirac Delta Function
Every Thing was created out of No Thing, the Empty Set, ɸ, the Void, the Tao. The Empty Set contains 0 objects.
The Empty Set is not Empty. It contains Infinite (∞) Possibilities that are Impossible.
Every impossibility has a probability of 0 but the sum of all possibilities (1/∞=0) is always 1. In the beginning ∞/∞ =1 or ∞x0=1.
This relationship is represented by the Dirac Delta Function. It is used to simulate a Point Source of Energy (a Spike, an Explosion) in Physics.
The Delta is reprented by the Symbol Δ, a Triangle. The Delta is called Dalet in the Phoenican and Hebrew Alphabet. Daleth is the number 4 and means Door.
The original symbol of the Delta/Daleth contains two lines with a 90 Degree Angle. Two orthogonal lines create a Square or Plane.
The Dirac Delta Function is defined as a Square with an Area of 1, a Width of 1/n and a Height of n where n->∞.
The Dirac Delta Function is a Line with an Area of 1.
The Dirac Delta Function δ (x) has interesting properties: δ (x) = δ (-x), δ (x) = δ (1/x). It has two Symmetries related to the Negative Numbers and the Rational Numbers.
When we move from 2D to 1D, the Number Line, the Delta Function becomes the Set of the Numbers N/N =1.
The Monad (1) of the Tetraktys of Pythagoras, the Top of the Triangle, was created by Dividing the One (1) by Itself without Diminishing itself. The Monad (1/1=1) is part of the 1D Delta Function.
Creation is an Expansion of the 1/1 into the N/N, adding 1/1 all the time, until ∞/∞ is reached. At that moment every Impossibility has been realized.
To move Back to the Void and restore the Eternal Balance of the One, Dividing (Compression) has to be compensated by Multiplication (Expansion).
At the End of Time N/M and M/N have to find Balance in the N/N, move Back to 1/1, Unite in the 0 and become The Void (ɸ) again.
About the Strange Behavior of Numbers
The big problem of the Numbers is that they sometimes behave very differently from what we Expect them to do.
This Strange Behavior happens when we try to Reverse what we are doing.
It looks like the Expansion of the Universe of Numbers is Easy but the Contraction creates many Obstacles.
It all starts with the Natural Numbers (1,2,3,).
When we Reverse an Addition (Subtract) and move over the Line of the Void Negative Numbers appear. Together with the Natural Numbers they are called the Integers.
The same happens when we Reverse a Division and the Fractions (the Rational Numbers) (1/3, 7/9) suddenly pop up.
An Integer N is a Rational Number divided by 1 (N/1).
The Integers are the Multiples of 1, the Fractions are its Parts.
Numbers behave even stranger when we want to Reverse a Repeating Repeating Addition (Irrational Numbers) and want to calculate a Rational Power (2**1/2).
The Complex Numbers (or Imaginary Numbers), based on the Square Root of -1 called i, are a combination of the Negative Numbers and the Irrational Numbers.
Irrational Numbers ( the Pythagorean Theorem), Fractions (a Piece of the Cake) and Negative Numbers (a Debt) are part of our Reality but the Strange Number i represents something we cannot Imagine.
About the Duality and the Expansion of Space
In the beginning the only One who was in existence was the 1.
When the One divide itself again the number -1, the Complement of 1, came into existence.
1 and -1 are voided in the No Thing, the Empty Set, 0: -1 + 1 = 0.
The Two, the Duality, both started to Expand in Two Opposite Directions (<– and +->) both meeting in the ∞/∞. This expansion is what we call Space.
Space is a Combination of the Strings S(1,1,1,1,1,…) and -S = (-1,-,1,-,1,-1,…) where S+S=(0,0,0,0,0,0,…).
The Expansion pattern of Space is a Recursive Function S: S(N)=S(N-1)+1 in which + means concatenate (or add) the String “,1”.
An Addition X + Y is a concatenation of S(X) and S(Y). A Substraction X-Y is a concatenation of S(X) and -S(Y). In the last case all the corresponding combinations of 1 and -1 are voided. (1,1,1,1)-(1,1,1)=(0,0,0,1)=(1).
Multiplication XxY is Adding String S(Y) every time a “1” of S(X ) is encountered: 111 x 11 = 11 11 11. Dividing X/Y is Subtracting S(X) every time a “1” of S(Y) is encountered:.111 111 1/111=11 1/111. In the last example a Fraction 1/111 appears.
This Number System is called the Unary Number System.
About the Trinity and the Compression of Space called Time
The Strange Behavior of Numbers is caused by the Limitations of our Memory System. We are unable to remember long strings that contain the same Number.
To make things easy for us we Divide Space into small Parts so we were able to Re-Member (Re-Combine the Parts).
When we want to Re-member, Move Back in Time, we have to Compress Expanding Space.
Compressed Space is Time.
Time and Space have a Reciprocal Relationship called Movement (Velocity = Space/Time).
There are many ways ( (1,1,1), (1,1,1),..) or ((1,1),(1,1))) to Compress a String in Repeating Sub-Patterns.
In the blog About the Trinity I showed that the most Efficient Way to group the One’s is to make use of a Fractal Pattern (a Self Reference) and Groups of Three Ones.
The Trinity applied to the Trinity ( A Fractal) is a Rotating Binary Tree. Binary Trees represent the Choices we make in Life.
The rotating Expanding Binary Trees generate the Platonic Solids (see linked video!) when the (number)-parts of the Binary Tree Connect.
When we connect Three Ones (1,1,1) by Three Lines (1-1,1-1,1-1) a 2 Dimensional Triangle Δ is Created.
If we take the Δ as a new Unity we are able to rewrite the patterns of 1’s and -1’s into a much Shorter Pattern of Δ’s and 1’s: (1,1,1),(1,1,1),(1,1,1), 1,1 becomes Δ,Δ,Δ,1,1.
We can repeat this approach when there is still a Trinity left: Δ,Δ,Δ,1,1 becomes ΔxΔ,1,1.
This Number System is called the Ternary Number System.
According to EuclidA Ratio is a sort of relation in respect of size between two magnitudes of the same kind“.
A Magnitude is a Size: a property by which it can be compared as Larger or Smaller than other objects of the Same Kind. A Line has a Length, a Plane has an Area (Length x Width), a Solid a Volume (Length xWitdth x Height).
For the Greeks, the Numbers (Arithmoi) were the Positive Integers. The objects of Geometry: Points, Lines, Planes , were referred to as “Magnitudes” (Forms). They were not numbers, and had no numbers attached.
Ratio, was a Relationship between Forms and a Proportion was a relationship between the Part and the Whole (the Monad) of a Form.
Newton turned the Greek conception of Number completely on its head: “By Number we understand, not so much a Multitude of Unities, as the abstracted Ratio of any Quantity, to another Quantity of the same Kind, which we take for Unity”.
We now think of a Ratio as a Number obtained from other numbers by Division. A Proportion, for us, is a statement of equality between two “Ratio‐Numbers”.
This was not the thought pattern of the ancient Greeks. When Euclid states that the ratio of A to B is the same as the ratio of C to D, the letters A, B, C and D do not refer to numbers at all, but to segments or polygonal regions or some such magnitudes.
The Ratio of two geometric structures was determinated by fitting the Unit Parts of the first geometric Stucture into the Other.
An Example: The Tetraktys is a Triangle (A Monad) and contains 9 Triangles (a Monad). The 1x1x1-Triangle Δ, a Part of the Tetraktys, is Proportional to the Whole of the Tetraktys (T) and has a Ratio T/Δ = 3= Δ -> T = Δ (3) x Δ (3) = 9.
The Mathematics of Euclid is not a Mathematics of Numbers, but a Mathematics of Forms.
The symbols, relationships and manipulations have Physical or Geometric Objects as their referents.
You cannot work on this Mathematics without Knowing (and Seeing) the Objects that you are Working with.
About Hermann Grassman, David Hestenes and the Moving Line called Vector
Hermann Grasmann lived between 1809 and and 1877 in Stettin (Germany). Grassmann was a genius and invented Geometric Algebra a 100 years before it was invented.
In his time the most important mathematicians did not understand what he was talking about although many of them copied parts of his ideas and created their own restricted version. None of them saw the whole Grassmann was seeing.
When he was convinced nobody would believe him he became a linguist. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda were recognized among philologists.
Grassmann took over the heritage of Euclid and added, Motion, something Euclid was aware of but could not handle properly.
Grassmann became aware of the fact your hand is moving when you draw a 2D Geometric Structure. He called the Moving Lines, that connect the Points, Displacements (“Strecke”).
In our current terminology we would call the Displacements “Vectors”.
Vector algebra is simpler, but specific to Euclidean 3-space, while Geometric Algebra works in all dimensions. In this case Vectors become Bi/Tri or Multi-Vectors (Blades).
The Trick of Grassmann was that he could transform every transformation on any geometrical structure into a very simple Algebra. Multi-Dimensional Geometric Structures could be Added, Multiplied and Divided.
The Greek Theory of Ratio and Proportion is now incorporated in the properties of Scalar and Vector multiplication.
About a 100 years later David Hestenes improved the Theory of Grassmann by incorporating the Imaginary Numbers. In this way he united many until now highly disconnected fields of Mathematics that were created by the many mathematicians who copied parts of Grassmanns Heritage.
About Complex Numbers, Octions, Quaternions, Clifford Algebra and Rotations in Infinite Space
Grassmann did not pay much attention to the Complex Numbers until he heard of a young mathematician called William Kingdon Clifford (1845-1879).
Complex numbers are ,just like the Rationals (a/b), 2D-Numbers. A Complex number Z = a + ib where i**2=-1. Complex Numbers can be represented in Polar Coordinates: Z = R (cos(x) + i sin(x)) where R = SQRT(a**2 + b**2). R is the Radius, the Distance to the Center (0,0).
When you have defined a 2D-complex Number it is easy to define a 4-D-Complex Number called a Quaternion: Z = a + ib + jc + kd or a 8-D Complex Number called an Octonion.
William Rowan Hamilton, the inventor of the Quaternions, had big problems to find an interpretation of all the combinations i, j and k until he realized that i**2 =j**2 = k**2 = ijk=-1.
What Hamilton did not realize at that time was that he just like Grassmann had invented Vector Algebra and Geometric Algebra.
This all changed when William Kingdon Clifford united everything in his new Algebra. Clifford’s algebra is composed of elements which are Combinations of Grassman’s Multivectors.
The Clifford Algebra that represents 3D Euclidean Geometry has 8 = 2**3 components instead of 3: 1 number (Point), 3 vectors (Length), 3 bivectors (Area) and 1 trivector (Volume).
It turns out if you use combinations of these elements to describe your geometric objects you can do the same things you did before (you still have 3 vector components).
In addition, you can have additional data in those other components that let you find distances and intersections (and a lot of other useful information) using simple and (computationally) cheap numerical operations.
The most important Insight of William Kingdom Clifford was that the Complex Numbers are not Numbers all.
They are Rotations in higher Dimensional Spaces.
About Pascal’s Triangle and Mount Meru
The String 1,3,3,1 of Clifford’s 3D Geometry is related to the 4th Level of Pascal’s Triangle. Level N of Pascal’s Triangle represents N-1-Dimensional Geometries.
The Sum of every level N of the Triangle is 2**N. This Number expresses the Number of Directions of the Geometric Structure of a Space with Dimension N.
A Point has 0 Direction, while a Line has 2 Directions, relative to its Center point, a Plane has 4 Directions, relative to its Center Point, and a Cube has 8 directions, relative to its Center point.
Pascal’s Triangle is also called the Binomial Expansion. This Expansion shows all the Combinations of two letters A and B in the function (A+B)**N. Level 1 of the Triangle is (A+B)**0 = 1 and level 2 is A x A + 2 A x B + B x B -> 1,2,1.
The Binomial Expansion converges to the Bell-Shaped Normal Distribution when N-> ∞.
The Diagonals of Pascal’s Triangle contain the Geometric Number Systems (Triangular Numbers, Pyramid Numbers, Pentatonal Numbers, ..) and the Golden Spiral of the Fibonacci Numbers.
Pascal’s Triangle is a Repository of all the Possible Magnitudes and their Components.
The Normal Distribution shows that the first level of the Triangle (the Tetraktys) is much more probable than the last levels.
The first four Levels of the Triangle of Pascal contain the Tetraktys of Pythagoras.
The Tetraktys is an Ancient Vedic Mathematical Structure called the Sri Yantra, Meru Prastara or Mount Meru.
About Numbers, Operations and the Klein Bottle
The Complex Numbers are not “Numbers” (Scalars) at all.
They are “Operations” (Movements) that can be applied to Magnitudes (Geometries) and Magnitudes are Combinations of the Simple Building Blocks of the Tetraktys, Points and Lines.
The Tao of Ancient China was not for nothing represented by a Flow of Water. According to the Ancient Chinese Mathematicians Every Thing Moves. In the Beginning there was only Movement.
In the Beginning only the One was Moved but when the Duality was created the Two moved around each other never getting into contact to Avoid the Void.
When we look at the Numbers we now can see that they are the result of the Movements of the first Diagonal of Pascals Triangle, the 1’s (Points) or better the Powers of the One: 1 **N (where N is a Dimension).
Even in the most simple Number System, the Unary Number System, Concatenation is an Operation, An Algorithm.
The Mathematician John Conway recently invented a new Number System called the Surreal Numbers that contains Every Number you can Imagine.
The Surreal Numbers are created out of the Void (ɸ) by a simple Algorithm (Conway calls an Algorithm a Game) that describes Movements (Choices of Direction: Up, Down, Left, Right, ..) that help you to Navigate in the N-Dimensional Number Space.
The Ancient Chinese Mathematicians played the same Game with the Numbers.
Algorithms were already known for a very long time by the Ancient Vedic Mathematicians. They called them Yantra’s.
Geometry is concerned with the Static Forms of Lines and Points but there are many other more “Curved” forms that are the result of Rotating Expansion and Compression. These forms are researched by the modern version of Geometry called Topology.
The most interesting 4D Topological Structure is the Klein Bottle. The Klein Bottle is a combination of two Moebius Rings. It represents a Structure that is Closed in Itself.
It can be constructed by gluing both pairs of opposite edges of a Rectangle together giving one pair a Half-Twist. The Klein Bottle is highly related to the Ancient Art of Alchemy.
The movement of the Duality around the Void can be represented by a Moebius Ring the Symbol of Infinity ∞.
Later in this Blog we will see why the Number 8 is a Rotation of ∞ and the symbol of Number 8 is a combination of the symbol of the number 3 and its mirror.
First we will have a look at the Reciprocal Relation between Space and Time.
About Dewey B. Larson, Velocity and Time
Dewey B. Larson (1898 – 1990) was an American Engineer who developed the Reciprocal System of Physical Theory (RST).
Larson believed that the failure to recognize that Motion is the most basic physical constituent of the universe has handicapped the progress of the traditional study of physics, which focuses on Forces.
The definition of Motion stems from the Equation of Velocity, v = ds/dt.
Instead of depending upon the change of the location of an object to define an arbitrary “quantum” of space per “quantum” of time, such as miles per hour, or meters per second, the RST assumes that the observed universal passage, or progression, of time is one aspect of a universal motion that necessarily must be accompanied by a universal “passage,” or progression, of space.
The Units of Time fill up the Units of Space. Space and Time are Duals.
Space is not-Time and Time is not-Space. Time is Non-Local, Cyclic and represented by the Rotating Imaginary Numbers. Space is Local, Linear and Represented by the Scalar Numbers. Space is the Vacuum and the Nothing and Time is the non-vacuum, the Every Thing, the Solids represented by the Cube of Space.
The Cube of Space is the structure behind the Tetraktys but also behind the Book of Genesis.
Our Reality contains two Reciprocal 3D-structures related to Space and Time. Space and Time are related by the Simple Formula N/N=1/1=1, the Formula of Diracs Delta Function.
We are able to perceive the Real 3D-Structure of Space. The 3D-Structure of Time is Imaginary. It is situated in the Imaginary Number Space of i.
Larson, a Self Thought Genius like Grassmann, developed Geometric Algebra without knowing anything about Geometric Algebra but he also invented String Theory long before String Theory was invented. The Mathematics of Larson is also the Mathematics of the Tetraktys of Pythagoras without even knowing anything about it.
Larson was able to Calculate all the important Physical Numbers without any problem and was also able to Calculate Chemical Structures and Reactions.
The fourth line of Pascals Triangle and the Tetraktys contains 8 Directions in the Four Geometric Dimensions: 0, 1, 2, and 3.
Mathematicians are intrigued with this number 8, because they find it popping up unexpectedly in advanced mathematics.
In fact, expanding the Binomial Expansion to 8 dimensions just creates an inverse copy of these first Four Dimensions, and then the pattern just repeats itself with a half-twist and back from there, ad infinitum.
This is called Bott Periodicity discovered by the mathematician Raoul Bott (1923-2005).
The mathematician John Baez wrote an article in which he relates this 8-fold Periodicity to the Scalars (1), the Complex Numbers (2), the Quaternions (2×2), and the Octonions (2x2x2 = 2**3).
The Universe of Numbers and Magnitudes is Cyclic and Fractal.
Our own Reality, symbolized by the Tetraktys, repeats itself in Higher Dimensions until Infinity.
The Tetrad, represents Completion, because it contains all its Previous Numbers, the 1, 2, 3, and itself, 4, in One Number, 10 = (The One) + 9 (= 3 (Trinity)x 3 (Trinity) = Tetraktys).
As you can see in the Picture above the Fractal Pattern of 8 contains two kinds of Trinities/Triangles, an Upside and a Downside (Rotated by 180 Degrees) Triangle. When you Rotate by 180 Degrees the 1 becomes -1 and 1 + -1 =0 is the Void.
The Multi Dimensional Rotations of the Octonions always Come Back to Square 1/1=1, the One and keep Rotating around the Center, the Nothing, Until Infinity.
About Triangular Numbers and Pascal’s Triangle
About the Relationship Between Geometry and Music
About the Game of the Surreal Numbers
About Larson and the Unification of Mathematics
The Collected Works of Dewey B Larson
About Ratio and Proportion by Euclid
A book of Augustus deMorgan about “The Connection between Number and Magnitude”
The text of the Fifth Book of Euclid
An Educational You Tube Channel called Insights in Mathematics
About the History of Geometric Algebra
Free Software to use Geometric Algebra
A Video that shows how the Platonic Solids are created out of the Trinity Numbers
All you want to know about Geometric Patterns
# About the Sum of Things
The Lo Shu is a Chinese Model for Time and was used to design Cities, Temples, Cycles and Calendars.
The Lo Shu is a 3×3 Magic Square created by Fu Xi, the Founder of Chinese Civilization. Fu Xi lived around the time of the Great Flood.
The Magic Square was carried by a Turtle. The Turtle is the symbol of the Constellation Orion. Many Ancient Cultures claim that our Ancestors came from this constellation. The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos (Time).
According to Chinese Creation Myth the world started with 無極 (wuji: nothingness), the Tao. Out of the Tao, the Egg of the Zero (0) and the Supreme Pure One (1) emerged. In the next step the Trinity (3), the Three Pure Ones, was created.
The Tao produced One; One produced Two; Two produced Three; Three produced All things (Lao Tsu, Tao Te Ching, 42).
The Trinity is represented by a Triangle. A combination of Two Triangels is a Square. The combination of Two (2) Triangels is also the Symbol of the Heart Chakra, the merge of Heaven, the Upper Triangel and Earth, the Lower Triangel.
The most complex Yantra (“machine”), the Sri Yantra, contains 43 Triangels. The Sri Yantra is determinated by the Bronze Mean. The Bronze Mean is a generalization of the Sequence of Fibonacci based on the Trinity. The Bronze Mean generates Quasi-Crystals and Penrose Tilings.
The Lo Shu Magic Square not only shows the Connection between the Four Forces that came out of the Two Forces, Expansion and Compression, it also shows the connection between Heaven and Earth.
In the Magic Square of Lu Shu the Even Numbers (2,4,6,8 = 2 x (1,2,3,4 = 2×2)) are Black(Yang, Male). The Odd Numbers (1,3,5,7,9 = 3×3) are White (Yin, Female). The Sum of all the Numbers is 15 (3×5).
The Even Numbers are situated at the Corners of the Square.
When the numbers of each row are multiplied (8x1x6; 3x5x7; 4x9x2) they together total to 225 ((3×5)x(3×5)) — as do those of the columns (8x3x4; 1x5x9; 6x7x2).
The Magic Square is dominated by two numbers (2**1, 2**2, 2**3) and (3, 2×3, 3**2), It contains four Prime Numbers (1,3,5,7). It also contains the first Perfect Number 6 (1+2+3 =1x2x3). 6 is also a Harmonic Divisor Number and has a Harmonic Divisor 2. The Sixth Day in the week is the day of Saturn, the God of Time.
The sequence 1,2,4,8, 1, 3,6,9, 27 is called the Tetrad of the Pythagorians and was, according to Plato, used by the Demiurg, the Creator of our Universe, to create the Soul. The Soul is a mixture of the Same (1), the Different (2), and Existence (3). The Tetrad was used to define the Harmony of the Spheres.
When you connect the numbers of the Lo Shu a pattern appears that is called the Seal of Saturn or the Dance of Yu.
The Sum of Magic Squares is a Magic Square and the product of a Magic Square M with a number a is again a Magic Square aM. Both Rules can be used to construct a Magic Square out of simple Binary Squares called Magic Carpets. One of these Magic Carpets is the Identity Matrix with One on the Diagonal.
Every Magic Square is related by Rotation and Mirroring to Eight other Magic Squares. This means that the central Lo Shu Magic Square with the Five in the Middle is related to Eight other Magic Squares with the other Numbers in the Middle. One of them contains the Nine and is called the Well.
The Sum of numbers of the Well is 18 (2×9) and the sum of all opposites across the 8 Spoke Wheel = 9 (9+0, 8+1, 7+2, 6+3, 5+4). 2×9 means that there are Two Complementary Magic Squares. One Magic Square is Rotating with the Clock and the other Against the Clock.
The Nine is the most important Number in the Magic Square. The Nine comes back in many ancient mythologies like the Egyptian Pesedjet and the Greek Ennead.
When you add the separate numbers of a number (54 = 5+ 4 = 9) the result is the Remainder when you divide the number by 9. This number is called the Modulo 9 number.
The Powers of 2 (= Expansion) Mod 9 creates a pattern (1,2,4,8,(16)7,(32)5,(64)1,(128)2,…). This pattern is reversed when we divide by 2 (=Compression) (1/2 (0,5 =5), 1/4 (0,25 = 7), 1/8 (0,125 =8), 1/16 (0,625 = 4), 2,1).
The Expansion and Compression Pattern shows that the same pattern repeats itself when the Magic Square is expanded or compressed Six (6) Times. The 7th Step is the Same as the First Step.
After 2**6=64 (8×8) divisons of the cell a Specialized Cell is created, the stem cell. The same happens in Music. The Game of Chess (Chiu King in China) with its 8×8 = 64 = 2**6 Playing Board contains every possible situation of the Game of Life.
The Two-Pattern does not contain the numbers 3,6 and 9. The number 9 is repeated every time when the pattern is expanded and compressed which means that Nine is the same as the Identity, the One (1+9 = 1). 3 and 6 Oscillate (1x2x3=6 and 1+2+3 =6) and therefore represent the Duality (3+6 = 9, = the One).
If we combine the Expansion and Compression patterns a Torus (a Rotating Circle, The Wheel of Time) appears. The Zero (the Void) is in the Center and Contains the Vortex. The Vortex represents another Cycle (Black/White Hole, 3,6,9, the Wheel of Order) in which every structure/pattern is destroyed to start All Over Again.
If we subtract the numbers in the Square by the number of the Center, 5, a highly Symmetric Pattern emerges. This pattern shows that there are Two Mirror Universes both containing four Forces.
When we transform this pattern from Modulus 9 to Modulus 3 (the Trinity) we see that the number 4 equals 1 and represents a new beginning of the Cycle.
The Magic Square with the Zero in the Middle is surrounded by two Sequences of 123(4) with different Signs. The Signs are arranged in a Cyclic Pattern (- -, + -, + +, – +) that contains the Four Permutations of – and +. The Sum of the ++ and the — is -3 and +3, the Trinity. The Sum of +- en -+ is the One.
The Cyclic Pattern of + and – represents the Prisoners Dilemma that is solved by the Strategy of Tit for Tat. This strategy is applied by the Trickster, the God of Paradox, a concept of God in which God creates games that create games.
When you use the basic Addition and Multiplcation Rules of the Magic Square many important numbers and patterns appear that are related to Ancient CalendersSymbols and Cycles.
The Lo Shu Magic Square appeared a few years ago when I wanted to know more about Acupuncture. Acupuncture is related to the Sheng Cycle and the Sheng Cycle is related to the Lo Shu. A Magic Square is the perfect way to visualize the Constraints that control the Four Forces in our Universe.
Soon after this discovery, I found out the Lo Shu is related to the Trinity and the Bronze Mean which is an abstraction of the Fibonacci Sequence. The Bronze Mean generates the Sri Yantra and so-called Quasi Crystals. Quasi Crystals explain Acupuncture.
A few weeks ago I started a discussion with Kim Veltman. Kim Veltman is the director of the Maastricht McLuhan Institute. He is researching Ancient Architecture and wrote a very interesting document called “Alphabets, Elements and Cosmologies”.
Ancient Alphabets are related to Numbers and Tones so Ancient Texts also represent Numerical Patterns and Music. You want be surprised to read that the Lo Shu showed itself in every Text Kim Veltman has analysed.
His document started a new inquiry into the pattern of the Lo Shu. During this research, I detected the book “the Sum of Things” by Paul Martyn-Smith. Paul Martin-Smith worked together with Lee Burton.
This blog contains just a little bit of the tremendous amount of information Paul Martin-Smith & Lee Burton have found about the essence of the I Tjing which is contained in just one simple 3×3 Magic Square.
If you want to know more the only thing you can do is to buy this book and start reading.
The Calculations behind the Number of Things
The Relationship between the Lo Shu and the I Tjing
About Saturn, the Son of the Sun
How to construct Magic Squares out of Binary Squares (Magic Carpets)
The Sistine Chapel (Rome) and the Seal of Saturn
About the Relationship between the Lo Shu and Music
About the History of the Lo Shu
About the Wheel of Eternal Order and the Wheel of Time
About the Relationship between the Lo Shu and Chinese Alchemy
About Plato, Pythagoras and the Lo Shu
Everything You want to Know about Sacred Geometry
About the Influence of the Lo Shu on Recent Art
The Lo Shu Square with Imaginary Numbers
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# 💠 Demystifying the Rhombus: A Deep Dive into Geometry
A rhombus is a quadrilateral with four sides of equal length. It is a special type of parallelogram where opposite sides are parallel and opposite angles are equal. The unique characteristic of a rhombus is that all its sides are congruent, meaning they have the same length. Additionally, the diagonals of a rhombus bisect each other at right angles. This geometric shape is commonly found in various fields, such as mathematics, engineering, and design.
## Key Takeaways
Property Description
Sides All sides are of equal length
Angles Opposite angles are equal
Diagonals Bisect each other at right angles
Type of Parallelogram Yes
## Understanding the Basics of Rhombus
A rhombus is a type of quadrilateral, which is a four-sided figure. It is also classified as a parallelogram, meaning that it has opposite sides that are parallel. In geometry, the rhombus is often referred to as a diamond shape due to its unique appearance. One of the defining characteristics of a rhombus is that all four sides are of equal length. Additionally, the opposite angles of a rhombus are congruent, meaning they have the same measure.
### Definition of Rhombus
A rhombus is a two-dimensional shape that falls under the category of polygons. It is a geometric figure that is commonly studied in Euclidean geometry. The properties of a rhombus include having four equal sides and opposite angles that are congruent. The diagonals of a rhombus also have some interesting properties. They bisect each other at a 90-degree angle and are of equal length. This means that the diagonals of a rhombus are congruent.
### Rhombus in Mathematics
In mathematics, the rhombus is often used as a building block for understanding other shapes. It shares similarities with other quadrilaterals such as the square and rectangle. While a square is a special type of rhombus with all right angles, a rectangle is a special type of parallelogram with four right angles. The rhombus, on the other hand, can have acute angles or obtuse angles.
### The Shape of a Rhombus
The shape of a rhombus is characterized by its vertices, sides, and angles. It is a two-dimensional figure that lies on a plane. The interior angles of a rhombus add up to 360 degrees, just like any other quadrilateral. However, the angles of a rhombus can vary depending on its specific measurements. The sum of the acute angles in a rhombus is always 180 degrees, while the sum of the obtuse angles is also 180 degrees.
To calculate the area of a rhombus, you can use the formula: Area = (diagonal 1 * diagonal 2) / 2. The perimeter of a rhombus can be found by multiplying the length of one side by 4. These formulas are useful for determining the size and dimensions of a rhombus in various mathematical problems.
In summary, a rhombus is a unique geometric shape that falls under the category of quadrilaterals. It has equal sides, opposite angles, and congruent diagonals. Understanding the properties and characteristics of a rhombus is essential for further exploration in the field of geometry.
## The Properties of a Rhombus
A rhombus is a special type of quadrilateral that possesses several unique properties. In this section, we will explore the properties of a rhombus, including its characteristics as a regular quadrilateral, parallelogram, and its relationship with right angles.
### Rhombus as a Regular Quadrilateral
A rhombus is classified as a regular quadrilateral because it has four equal sides and four equal angles. Each side of a rhombus is congruent to the others, making it a geometric figure with equal sides. This characteristic gives the rhombus a diamond shape, which distinguishes it from other four-sided figures.
### Rhombus as a Parallelogram
Another important property of a rhombus is that it is a parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Since a rhombus has four equal sides, its opposite sides are parallel, meeting the criteria for a parallelogram. This property allows us to apply the properties of parallelograms to rhombuses, such as the fact that the opposite angles of a parallelogram are congruent.
### Rhombus and Right Angles
While a rhombus does not have right angles in general, it does possess an interesting relationship with right angles. The diagonals of a rhombus bisect each other at right angles. This means that the line segments connecting the opposite vertices of a rhombus intersect at a 90-degree angle. This property is unique to rhombuses and is not found in other quadrilaterals like squares or rectangles.
In summary, a rhombus is a two-dimensional shape in Euclidean geometry that possesses several geometric properties. It is a regular quadrilateral with equal sides and angles, making it a parallelogram. Additionally, the diagonals of a rhombus bisect each other at right angles, adding to its unique characteristics. Understanding these properties allows us to explore the various aspects of a rhombus, including its area, perimeter, and other geometric properties.
## The Diagonals of a Rhombus
A rhombus is a type of quadrilateral, which is a four-sided figure. It is also classified as a parallelogram, meaning it has opposite sides that are parallel. What sets a rhombus apart from other parallelograms is its unique diamond shape, with all four sides having equal length.
### Perpendicular Diagonals in a Rhombus
One interesting property of a rhombus is that its diagonals are always perpendicular to each other. Diagonals are line segments that connect two non-adjacent vertices of a polygon. In the case of a rhombus, the diagonals intersect at a right angle, forming four right angles at their point of intersection. This property holds true for all rhombuses, regardless of their size or orientation.
### Congruent Diagonals in a Rhombus
Another important property of a rhombus is that its diagonals are congruent, meaning they have the same length. This is a unique characteristic of a rhombus and distinguishes it from other quadrilaterals like squares and rectangles. In a square, the diagonals are also congruent, but in a rectangle, the diagonals are not equal in length. So, if you have a rhombus, you can be sure that its diagonals are not only perpendicular but also of the same length.
### Why Rhombus Diagonals are not Equal
You might wonder why the diagonals of a rhombus are always congruent, while the diagonals of other quadrilaterals like rectangles are not. The reason lies in the angles of a rhombus. A rhombus has two pairs of opposite acute angles and two pairs of opposite obtuse angles. When the diagonals of a rhombus are drawn, they bisect these angles, dividing them into two equal parts. This symmetry ensures that the diagonals are of equal length.
In contrast, in a rectangle, the diagonals bisect the right angles, dividing them into two unequal parts. This difference in angle measurements leads to the inequality of the diagonals in a rectangle. Therefore, the unique combination of equal sides and specific angle measurements in a rhombus guarantees that its diagonals are both perpendicular and congruent.
In summary, the diagonals of a rhombus have two important properties: they are perpendicular to each other and congruent in length. These properties are a result of the specific geometric properties of a rhombus, including its equal sides and specific angle measurements. Understanding these properties helps us explore the fascinating world of geometry and appreciate the intricacies of different two-dimensional shapes.
## The Symmetry of a Rhombus
A rhombus is a type of quadrilateral that falls under the category of parallelograms. It is a geometric figure with four sides, where all sides are equal in length. The rhombus is often referred to as a diamond shape due to its resemblance to the precious gemstone. In Euclidean geometry, the rhombus is classified as a two-dimensional shape, also known as a plane figure or a mathematical shape.
### Line of Symmetry in a Rhombus
One of the interesting properties of a rhombus is its line of symmetry. A line of symmetry is an imaginary line that divides a shape into two congruent halves. In the case of a rhombus, it has exactly two lines of symmetry. These lines pass through the midpoints of opposite sides and intersect at a right angle. The line of symmetry bisects the rhombus into two equal parts, each having the same size and shape.
The line of symmetry in a rhombus also has an impact on its interior angles. Since the line of symmetry bisects the rhombus into two congruent halves, it follows that the opposite angles formed by the intersecting lines are also congruent. This means that the rhombus has two pairs of opposite angles that are equal in measure.
### Rotational Symmetry in a Rhombus
Apart from the line of symmetry, a rhombus also exhibits rotational symmetry. Rotational symmetry refers to the ability of a shape to be rotated by a certain angle and still appear the same. In the case of a rhombus, it has a rotational symmetry of order 2. This means that it can be rotated by 180 degrees around its center point and still retain its original shape.
The rotational symmetry in a rhombus is closely related to its diagonals. The diagonals of a rhombus are the line segments that connect opposite vertices. Interestingly, the diagonals of a rhombus also bisect each other at right angles, dividing the rhombus into four congruent right triangles. This property contributes to the rotational symmetry of the rhombus.
In summary, the symmetry of a rhombus is characterized by its line of symmetry and rotational symmetry. The line of symmetry divides the rhombus into two congruent halves, while the rotational symmetry allows the rhombus to be rotated by 180 degrees and still maintain its original shape. These properties, along with the equal sides and opposite angles, make the rhombus a fascinating and unique quadrilateral in geometry.
## Comparing Rhombus with Other Shapes
### Rhombus vs Square
A rhombus and a square are both types of quadrilaterals, which means they are four-sided figures. However, there are some key differences between the two.
One of the main differences is that a rhombus has equal sides, while a square has both equal sides and equal angles. In other words, all sides of a rhombus are of the same length, but in a square, all sides are equal and all angles are right angles.
Another difference is that the diagonals of a rhombus do not necessarily bisect each other at right angles, whereas in a square, the diagonals are perpendicular bisectors of each other.
### Rhombus vs Rectangle
A rhombus and a rectangle are both types of quadrilaterals, but they have different properties.
While a rhombus has equal sides, a rectangle has opposite sides that are equal. In other words, a rectangle has two pairs of parallel sides, whereas a rhombus does not necessarily have parallel sides.
Additionally, the angles in a rhombus are not necessarily right angles, whereas in a rectangle, all angles are right angles.
### Rhombus vs Diamond
The terms “rhombus” and “diamond” are often used interchangeably, but they actually refer to different shapes.
A rhombus is a type of quadrilateral with equal sides, while a diamond is a specific type of rhombus that has equal sides and equal angles. In other words, all diamonds are rhombuses, but not all rhombuses are diamonds.
### Rhombus vs Kite
A rhombus and a kite are both types of quadrilaterals, but they have different properties.
While a rhombus has equal sides, a kite does not necessarily have equal sides. In fact, a kite has two pairs of adjacent sides that are equal.
Additionally, the angles in a rhombus are not necessarily congruent, whereas in a kite, the angles between the pairs of equal sides are congruent.
### Rhombus vs Parallelogram
A rhombus and a parallelogram are both types of quadrilaterals, but they have different properties.
While a rhombus has equal sides, a parallelogram does not necessarily have equal sides. In fact, a parallelogram has opposite sides that are equal and parallel.
Additionally, the angles in a rhombus are not necessarily congruent, whereas in a parallelogram, the opposite angles are congruent.
In summary, a rhombus is a type of quadrilateral with equal sides, while other shapes like squares, rectangles, diamonds, kites, and parallelograms have their own unique properties. Each shape has its own set of angles, sides, and geometric properties that make them distinct. Understanding the differences between these shapes can help in identifying and classifying them in the field of geometry.
## The Special Cases of a Rhombus
A rhombus is a special type of quadrilateral that falls under the category of parallelograms. It is a two-dimensional geometric figure with four sides, where all sides are equal in length. Additionally, a rhombus has opposite angles that are congruent, and its diagonals bisect each other at right angles. These properties make the rhombus a unique and interesting shape in Euclidean geometry.
### When a Rhombus Becomes a Square
One special case of a rhombus occurs when all four angles of the rhombus are right angles, making it a square. A square is a type of rectangle, and it is also a special case of a rhombus. In a square, all sides are equal in length, and all angles are right angles. This means that a square possesses all the properties of a rhombus, including congruent diagonals and opposite angles. The area of a square can be calculated by multiplying the length of one side by itself, while the perimeter is found by multiplying the length of one side by four.
### When a Rhombus Becomes a Rectangle
Another special case of a rhombus occurs when the angles of the rhombus are not all equal, but the opposite sides are still parallel. In this case, the rhombus transforms into a rectangle. A rectangle is a quadrilateral with four right angles, and its opposite sides are equal in length. While a rectangle does not possess all the properties of a rhombus, such as congruent diagonals, it still shares some similarities. The area of a rectangle can be calculated by multiplying the length of one side by the length of an adjacent side, while the perimeter is found by adding the lengths of all four sides.
### When a Rhombus is also a Kite
A kite is another special case of a rhombus. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In a rhombus, all four sides are equal, which means that it satisfies the condition of a kite. However, not all kites are rhombuses, as kites can have non-congruent angles. Kites also have diagonals that intersect at right angles, similar to a rhombus. The area of a kite can be calculated by multiplying half the product of the lengths of the diagonals, while the perimeter is found by adding the lengths of all four sides.
In summary, a rhombus can have special cases where it transforms into a square, a rectangle, or a kite. Each of these cases has its own unique properties and characteristics. Whether it’s the equal sides and right angles of a square, the parallel sides and right angles of a rectangle, or the equal adjacent sides of a kite, these special cases add to the versatility and intrigue of the rhombus as a geometric shape.
## Calculations Involving Rhombus
A rhombus is a type of quadrilateral that falls under the category of parallelograms. It is a geometric figure with four sides of equal length and opposite angles that are congruent. The rhombus is often referred to as a diamond shape due to its resemblance to a sparkling gemstone. In Euclidean geometry, the rhombus is classified as a two-dimensional shape, also known as a plane figure or a polygon.
### How to Find the Area of a Rhombus
To calculate the area of a rhombus, we can use the formula:
Area = (diagonal 1 * diagonal 2) / 2
The diagonals of a rhombus are line segments that connect opposite vertices and bisect each other at a 90-degree angle. By multiplying the lengths of the diagonals and dividing the result by 2, we can determine the area of the rhombus.
### The Perimeter Formula for a Rhombus
The perimeter of a rhombus can be found by using the formula:
Perimeter = 4 * side length
Since a rhombus has four equal sides, we can simply multiply the length of one side by 4 to obtain the perimeter. This formula applies to all rhombuses, regardless of their size or orientation.
### How to Find the Diagonal of a Rhombus
To find the length of the diagonals in a rhombus, we can use the Pythagorean theorem. Since the diagonals of a rhombus bisect each other at a 90-degree angle, we can consider them as the hypotenuse of two right triangles formed within the rhombus.
Let’s denote the lengths of the diagonals as d1 and d2. If the length of one side of the rhombus is s, we can use the following formula to find the length of the diagonals:
d1 = √(s^2 + s^2)
d2 = √(s^2 + s^2)
By substituting the length of one side into the formula, we can calculate the lengths of both diagonals.
In summary, the rhombus is a fascinating geometric shape with unique properties. Its equal sides and opposite angles make it distinct from other quadrilaterals such as squares and rectangles. By understanding the formulas for finding the area, perimeter, and diagonals of a rhombus, we can explore its geometric properties and apply them in various mathematical calculations.
## The Practical Applications of Rhombus
A rhombus is a type of quadrilateral that falls under the category of parallelograms. It is a geometric figure with four sides of equal length and opposite angles that are congruent. The unique diamond shape of a rhombus makes it an interesting and versatile shape in various practical applications.
### Where a Rhombus can be Found
Rhombuses can be found in many different contexts in our everyday lives. Here are a few examples:
1. Architecture and Design: Rhombuses are commonly used in architecture and design to create visually appealing patterns and structures. They can be seen in the facades of buildings, floor tiles, and decorative elements. The symmetrical nature of a rhombus allows for interesting and aesthetically pleasing arrangements.
2. Jewelry: The diamond shape, which is essentially a rhombus, is highly valued in the jewelry industry. Diamonds are cut into various shapes, including the classic round brilliant cut, but the rhombus-shaped diamond, also known as the “diamond shape,” is particularly popular. The unique properties of a rhombus make it an ideal choice for creating stunning jewelry pieces.
3. Sports Fields: Rhombus-shaped fields are commonly used in sports such as baseball, softball, and soccer. The shape allows for optimal use of space and provides equal distances from the center to all points on the field. This ensures fair play and an enjoyable experience for athletes and spectators alike.
### The Use of Rhombus in Everyday Life
Apart from the specific examples mentioned above, the properties of a rhombus find practical applications in various areas of our everyday lives. Let’s explore some of these applications:
• Packaging: Rhombus-shaped packaging is often used for products that require efficient use of space. The shape allows for easy stacking and maximizes storage capacity. Additionally, the equal sides of a rhombus ensure that the packaging remains stable and secure.
• Tiling and Flooring: Rhombus-shaped tiles are commonly used in interior design to create unique and eye-catching patterns. The symmetry of a rhombus allows for endless possibilities in creating visually appealing floors and walls.
• Mathematics and Geometry: Rhombuses are an important concept in mathematics and geometry. They serve as a fundamental example of a polygon and are used to teach various geometric properties. The study of rhombuses helps develop an understanding of angles, sides, and diagonals in two-dimensional shapes.
In conclusion, the practical applications of a rhombus are diverse and can be found in various fields such as architecture, design, jewelry, sports, packaging, and mathematics. The unique properties of a rhombus, including its equal sides and opposite angles, make it a versatile shape with numerous practical uses in our everyday lives.
## Conclusion
In conclusion, the rhombus is a fascinating geometric shape that has several unique properties. It is a quadrilateral with four equal sides, opposite angles that are congruent, and diagonals that bisect each other at right angles. The rhombus is symmetrical and can be found in various real-life objects, such as diamonds and playing cards. Its properties make it useful in various mathematical and engineering applications. Understanding the characteristics of a rhombus can help us solve problems involving symmetry, angles, and lengths. Overall, the rhombus is an intriguing shape that has both practical and aesthetic significance.
### What does a rhombus look like?
A rhombus is a four-sided figure, a type of quadrilateral, where all sides are of equal length. It looks like a slanted square or a diamond shape. The opposite angles are equal, and its diagonals bisect each other at right angles.
### How do you pronounce ‘rhombus’?
The word ‘rhombus’ is pronounced as ‘rom-bus’. The ‘h’ is silent.
### What is the Rhombus of Michaelis?
The Rhombus of Michaelis is not a geometric term but a term used in human anatomy. It is a diamond-shaped area located at the lower part of the human back, significant in childbirth.
### Why are rhombuses considered squares?
Not all rhombuses are squares, but all squares are rhombuses. A square is a special type of rhombus where all angles are right angles. In other words, when a rhombus has all angles equal to 90 degrees, it becomes a square.
### What is a rhombus in maths?
In mathematics, a rhombus is a type of quadrilateral that has all sides of equal length. The opposite sides are parallel, and the diagonals bisect each other at right angles. It is a special type of parallelogram.
### Is a rhombus a parallelogram?
Yes, a rhombus is a type of parallelogram. It is a special case where all sides are of equal length. The opposite sides of a rhombus are parallel, and the opposite angles are equal.
### Why is a rhombus a regular quadrilateral?
A rhombus is not always a regular quadrilateral. A regular quadrilateral has all sides and all angles equal (which is a square). A rhombus only has all sides equal, but the angles can vary.
### Do the diagonals of a rhombus have equal lengths?
No, the diagonals of a rhombus are not equal in length. However, they do bisect each other at right angles.
### What is the perimeter formula of a rhombus?
The perimeter of a rhombus is calculated as four times the length of one side (since all sides are equal). So, if ‘a’ is the length of a side, the perimeter would be 4a.
### How is a rhombus different from a square?
A rhombus differs from a square in terms of angles. While a square has all angles equal to 90 degrees, a rhombus can have angles of varying measures. However, in both shapes, all sides are of equal length.
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# Examples and Exercises from Think Stats, 2nd Edition
http://thinkstats2.com
``````
In [1]:
from __future__ import print_function, division
%matplotlib inline
import warnings
warnings.filterwarnings('ignore', category=FutureWarning)
import numpy as np
import pandas as pd
import random
import thinkstats2
import thinkplot
``````
## Survival analysis
If we have an unbiased sample of complete lifetimes, we can compute the survival function from the CDF and the hazard function from the survival function.
Here's the distribution of pregnancy length in the NSFG dataset.
``````
In [2]:
import nsfg
complete = preg.query('outcome in [1, 3, 4]').prglngth
cdf = thinkstats2.Cdf(complete, label='cdf')
``````
The survival function is just the complementary CDF.
``````
In [3]:
import survival
def MakeSurvivalFromCdf(cdf, label=''):
"""Makes a survival function based on a CDF.
cdf: Cdf
returns: SurvivalFunction
"""
ts = cdf.xs
ss = 1 - cdf.ps
return survival.SurvivalFunction(ts, ss, label)
``````
``````
In [4]:
sf = MakeSurvivalFromCdf(cdf, label='survival')
``````
``````
In [5]:
print(cdf[13])
print(sf[13])
``````
``````
0.1397801412101171
0.8602198587898829
``````
Here's the CDF and SF.
``````
In [6]:
thinkplot.Plot(sf)
thinkplot.Cdf(cdf, alpha=0.2)
thinkplot.Config(loc='center left')
``````
``````
``````
And here's the hazard function.
``````
In [7]:
hf = sf.MakeHazardFunction(label='hazard')
print(hf[39])
``````
``````
0.6767068273092369
``````
``````
In [8]:
thinkplot.Plot(hf)
thinkplot.Config(ylim=[0, 0.75], loc='upper left')
``````
``````
``````
## Age at first marriage
We'll use the NSFG respondent file to estimate the hazard function and survival function for age at first marriage.
``````
In [9]:
``````
We have to clean up a few variables.
``````
In [10]:
resp6.cmmarrhx.replace([9997, 9998, 9999], np.nan, inplace=True)
resp6['agemarry'] = (resp6.cmmarrhx - resp6.cmbirth) / 12.0
resp6['age'] = (resp6.cmintvw - resp6.cmbirth) / 12.0
``````
And the extract the age at first marriage for people who are married, and the age at time of interview for people who are not.
``````
In [11]:
complete = resp6[resp6.evrmarry==1].agemarry.dropna()
ongoing = resp6[resp6.evrmarry==0].age
``````
The following function uses Kaplan-Meier to estimate the hazard function.
``````
In [12]:
from collections import Counter
def EstimateHazardFunction(complete, ongoing, label='', verbose=False):
"""Estimates the hazard function by Kaplan-Meier.
http://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator
label: string
verbose: whether to display intermediate results
"""
if np.sum(np.isnan(complete)):
raise ValueError("complete contains NaNs")
if np.sum(np.isnan(ongoing)):
raise ValueError("ongoing contains NaNs")
hist_complete = Counter(complete)
hist_ongoing = Counter(ongoing)
ts = list(hist_complete | hist_ongoing)
ts.sort()
at_risk = len(complete) + len(ongoing)
lams = pd.Series(index=ts)
for t in ts:
ended = hist_complete[t]
censored = hist_ongoing[t]
lams[t] = ended / at_risk
if verbose:
print(t, at_risk, ended, censored, lams[t])
at_risk -= ended + censored
return survival.HazardFunction(lams, label=label)
``````
Here is the hazard function and corresponding survival function.
``````
In [13]:
hf = EstimateHazardFunction(complete, ongoing)
thinkplot.Plot(hf)
thinkplot.Config(xlabel='Age (years)',
ylabel='Hazard')
``````
``````
``````
``````
In [14]:
sf = hf.MakeSurvival()
thinkplot.Plot(sf)
thinkplot.Config(xlabel='Age (years)',
ylabel='Prob unmarried',
ylim=[0, 1])
``````
``````
``````
## Quantifying uncertainty
To see how much the results depend on random sampling, we'll use a resampling process again.
``````
In [15]:
def EstimateMarriageSurvival(resp):
"""Estimates the survival curve.
resp: DataFrame of respondents
returns: pair of HazardFunction, SurvivalFunction
"""
# NOTE: Filling missing values would be better than dropping them.
complete = resp[resp.evrmarry == 1].agemarry.dropna()
ongoing = resp[resp.evrmarry == 0].age
hf = EstimateHazardFunction(complete, ongoing)
sf = hf.MakeSurvival()
return hf, sf
``````
``````
In [16]:
def ResampleSurvival(resp, iters=101):
"""Resamples respondents and estimates the survival function.
resp: DataFrame of respondents
iters: number of resamples
"""
_, sf = EstimateMarriageSurvival(resp)
thinkplot.Plot(sf)
low, high = resp.agemarry.min(), resp.agemarry.max()
ts = np.arange(low, high, 1/12.0)
ss_seq = []
for _ in range(iters):
sample = thinkstats2.ResampleRowsWeighted(resp)
_, sf = EstimateMarriageSurvival(sample)
ss_seq.append(sf.Probs(ts))
low, high = thinkstats2.PercentileRows(ss_seq, [5, 95])
thinkplot.FillBetween(ts, low, high, color='gray', label='90% CI')
``````
The following plot shows the survival function based on the raw data and a 90% CI based on resampling.
``````
In [17]:
ResampleSurvival(resp6)
thinkplot.Config(xlabel='Age (years)',
ylabel='Prob unmarried',
xlim=[12, 46],
ylim=[0, 1],
loc='upper right')
``````
``````
``````
The SF based on the raw data falls outside the 90% CI because the CI is based on weighted resampling, and the raw data is not. You can confirm that by replacing `ResampleRowsWeighted` with `ResampleRows` in `ResampleSurvival`.
## More data
To generate survivial curves for each birth cohort, we need more data, which we can get by combining data from several NSFG cycles.
``````
In [18]:
``````
``````
In [19]:
resps = [resp5, resp6, resp7]
``````
The following is the code from `survival.py` that generates SFs broken down by decade of birth.
``````
In [20]:
"""Draws fake points in order to add labels to the legend.
groups: GroupBy object
"""
thinkplot.PrePlot(len(groups))
for name, _ in groups:
label = '%d0s' % name
thinkplot.Plot([15], [1], label=label, **options)
"""Groups respondents by decade and plots survival curves.
groups: GroupBy object
"""
thinkplot.PrePlot(len(groups))
for _, group in groups:
_, sf = EstimateMarriageSurvival(group)
thinkplot.Plot(sf, **options)
"""Plots survival curves for resampled data.
resps: list of DataFrames
iters: number of resamples to plot
predict_flag: whether to also plot predictions
"""
for i in range(iters):
samples = [thinkstats2.ResampleRowsWeighted(resp)
for resp in resps]
sample = pd.concat(samples, ignore_index=True)
if omit:
groups = [(name, group) for name, group in groups
if name not in omit]
# TODO: refactor this to collect resampled estimates and
if i == 0:
if predict_flag:
else:
``````
Here are the results for the combined data.
``````
In [21]:
thinkplot.Config(xlabel='Age (years)',
ylabel='Prob unmarried',
xlim=[13, 45],
ylim=[0, 1])
``````
``````
``````
We can generate predictions by assuming that the hazard function of each generation will be the same as for the previous generation.
``````
In [22]:
"""Groups respondents by decade and plots survival curves.
groups: GroupBy object
"""
hfs = []
for _, group in groups:
hf, sf = EstimateMarriageSurvival(group)
hfs.append(hf)
thinkplot.PrePlot(len(hfs))
for i, hf in enumerate(hfs):
if i > 0:
hf.Extend(hfs[i-1])
sf = hf.MakeSurvival()
thinkplot.Plot(sf, **options)
``````
And here's what that looks like.
``````
In [23]:
thinkplot.Config(xlabel='Age (years)',
ylabel='Prob unmarried',
xlim=[13, 45],
ylim=[0, 1])
``````
``````
``````
Distributions with difference shapes yield different behavior for remaining lifetime as a function of age.
``````
In [24]:
complete = preg.query('outcome in [1, 3, 4]').prglngth
print('Number of complete pregnancies', len(complete))
ongoing = preg[preg.outcome == 6].prglngth
print('Number of ongoing pregnancies', len(ongoing))
hf = EstimateHazardFunction(complete, ongoing)
sf1 = hf.MakeSurvival()
``````
``````
Number of complete pregnancies 11189
Number of ongoing pregnancies 352
``````
Here's the expected remaining duration of a pregnancy as a function of the number of weeks elapsed. After week 36, the process becomes "memoryless".
``````
In [25]:
thinkplot.Plot(rem_life1)
thinkplot.Config(title='Remaining pregnancy length',
xlabel='Weeks',
ylabel='Mean remaining weeks')
``````
``````
``````
And here's the median remaining time until first marriage as a function of age.
``````
In [26]:
hf, sf2 = EstimateMarriageSurvival(resp6)
``````
``````
In [27]:
func = lambda pmf: pmf.Percentile(50)
thinkplot.Plot(rem_life2)
thinkplot.Config(title='Years until first marriage',
ylim=[0, 15],
xlim=[11, 31],
xlabel='Age (years)',
ylabel='Median remaining years')
``````
``````
``````
## Exercises
Exercise: In NSFG Cycles 6 and 7, the variable `cmdivorcx` contains the date of divorce for the respondent’s first marriage, if applicable, encoded in century-months.
Compute the duration of marriages that have ended in divorce, and the duration, so far, of marriages that are ongoing. Estimate the hazard and survival curve for the duration of marriage.
Use resampling to take into account sampling weights, and plot data from several resamples to visualize sampling error.
Consider dividing the respondents into groups by decade of birth, and possibly by age at first marriage.
``````
In [28]:
def CleanData(resp):
"""Cleans respondent data.
resp: DataFrame
"""
resp.cmdivorcx.replace([9998, 9999], np.nan, inplace=True)
resp['notdivorced'] = resp.cmdivorcx.isnull().astype(int)
resp['duration'] = (resp.cmdivorcx - resp.cmmarrhx) / 12.0
resp['durationsofar'] = (resp.cmintvw - resp.cmmarrhx) / 12.0
month0 = pd.to_datetime('1899-12-15')
dates = [month0 + pd.DateOffset(months=cm)
for cm in resp.cmbirth]
resp['decade'] = (pd.DatetimeIndex(dates).year - 1900) // 10
``````
``````
In [29]:
CleanData(resp6)
married6 = resp6[resp6.evrmarry==1]
CleanData(resp7)
married7 = resp7[resp7.evrmarry==1]
``````
``````
In [30]:
# Solution goes here
``````
``````
In [31]:
# Solution goes here
``````
``````
In [32]:
# Solution goes here
``````
``````
In [33]:
# Solution goes here
``````
``````
In [34]:
# Solution goes here
``````
``````
In [ ]:
``````
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# Solved Problems in Heat Transfer
##### Citation preview
SOLVED PROBLEMS IN HEAT TRANSFER Heat Loss by Conduction A plane brick wall, 25 cm thick, is faced with 5 cm thick concrete layer. If temperature of the exposed brick face is 70 oC and that of the concrete is 25oC, out the heat lost per hour through a wall of 15 m x10 m. Also, determine interface temperature. Thermal conductivity of the brick and concrete are W/m.K and 0.95 W/m.K respectively.
the find the 0.7
Calculations:
Heat loss Q = (Ta - Tb) / R Where Ta = 70oC; Tb = 25oC; and R = Rbrick + Rconcrete Rbrick = Lbrick/(Akbrick) Rconcrete = Lconcrete/(Akconctrete) A = 15 x 10 = 150 m2 Rbrick = 0.25/(150 x 0.7) = 2.381 x 10-3 oC/W Rconcrete = 0.05/(150 x 0.95) = 3.509 x 10-4 oC/W R = 2.381 x 10-3 + 3.509 x 10-4 = 2.732 x 10-3 oC/W Q = (70 - 25) / (2.732 x 10-3) = 16471.4 W = 16471.4 J/sec = 59.3 MJ/hr Heat loss per hour = 59.3 MJ At steady state, this is the amount of heat transferred through the brick wall or concrete per hour. Q = A kbrick(Ta - Ti)/Lbrick = 16471.4 W 150 x 0.7 x (70 - Ti) / 0.25 = 16471.4 70 - Ti = 39.2 Ti = 70 - 39.2 = 30.8oC Interface temperature Ti = 30.8oC
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Evaporation of Oxygen by Heat Exchanger A steel sphere is of inner diameter 40 cm and outer diameter 45 cm is used to store liquid oxygen (B.P is minus 183oC). The sphere is covered with one layer of insulation; of thickness 50 mm whose K is 0.35 W/m.K and another insulation, of thickness 50 mm whose K is 0.098 W/m.K. The sphere is exposed to atmosphere of 25oC. Find out the rate of oxygen becoming vapor every minute. Latent heat of oxygen is 370 kJ/kg. Thermal conductivity of steel = 20 W/m.K. Heat transfer coefficient of ambient air = 80 W/m2.K Calculations: For composite concentric sphere, the rate of heat transfer from outside to the sphere Q, is given by, Q = (Ta - Tb)/R Ta = 25oC Tb = -183oC Where, R = Rs + Rins,1 + Rins,2 + Ra Ra = air film resistance = 1 / (4ra2ha) Rins,2 = Resistance offered by the outer insulation = (ra - r1) / (4kins,2rar1) Rins,1 = Resistance offered by the inner insulation = (r1 - r2) / (4kins,1r1r2) Rs = Resistance offered by the metal wall (steel) = (r2 - rb) / (4ksr2rb) Given Data:
Diameter of sphere with insulation = 45 + 2 x 5 + 2 x 5 = 65 cm ra r1 r2 rb
= = = =
32.5 cm = 0.325 m 32.5 - 5 = 27.5 cm = 0.275 m 27.5 - 5 = 22.5 cm = 0.225 m 20 cm = 0.2 m
Substituting these data in the above equations, Ra = 1/(4 x 3.142 x 0.3252 x 80) = 9.4175 x 10-3 oC/W
2
Rins,2 = (0.325 - 0.275)/(4 x 3.142 x 0.098 x 0.325 x 0.275) = 0.4543 oC/W Rins,1 = (0.275 - 0.225)/(4 x 3.142 x 0.35 x 0.275 x 0.225) = 0.1837 oC/W Rs = (0.225 - 0.2)/(4 x 3.142 x 20 x 0.225 x 0.2) = 2.2105 x 10-3 oC/W R = 9.4175 x 10-3 + 0.4543 + 0.1837 + 2.2105 x 10-3 = 0.6496 oC/W Q = (25 + 183)/0.6496 = 320.2 W Rate of heat in per second = 320.2 J Rate of heat in per minute = 320.2 x 60 = 19212 J = 19.212 kJ 370 kJ of heat is needed to vaporize 1 kg of liquid oxygen. Therefore, for the heat input of 19.212 kJ/min, Rate of oxygen becoming vapor = 19.212/370 = 0.0519 kg/min Cooling by Radiation A solid cube of side 30 cm at an initial temperature of 1000 K is kept in vacuum at absolute zero temperature. Calculate the time required to cool it to 500 K. The material has the following properties: Density = 2700 kg/m3 Specific heat = 0.9 kJ/kg.K Emissivity = 0.1 Stefan-Boltzmann constant, = 5.67 x 10-8 W/m2.K4. Calculations: The given problem is an unsteady state problem. We shall start with the heat balance equation, with the following assumptions: (i) There is no temperature distribution within the solid (ii) The surrounding is at absolute zero temperature throughout the cooling period. Rate of heat flow of out of the solid of volume V through the boundary surfaces A = rate of decrease of internal energy of the solid of volume V Volume of cube = 0.303 m3 = 0.027 m3 Surface area of cube = 6 x 0.3 x 0.3 = 0.54 m2 A (T(t)4 - T 4) = - CP V dT(t)/dt Where T(t) is the temperature of the solid at time t and T is the temperature of the surrounding. Since T is 0, 0.54 x 0.1 x 5.67 x 10-8 x T(t)4 = -2700 x 900 x 0.027 x dT(t)/dt 0.46665 x 10-13 T(t)4 = -dT(t)/dt Integrating the above equation, dT(t)/T(t)4 = -0.46665 x 10-13 x dt -2.1429 x 1013 x [-1/(3T(t)3)] = t + C 2.1429 x 1013/(3T(t)3) = t + C
3
Substituting the initial condition eliminates the constant: T(t) = 1000 at t = 0 sec C = 7143.11 Time needed to cool down to 500 K: 2.1429 x 1013 / (3 x 5003) = t + 7143.11 t = 50002 sec = 13 hour 54 min Time needed for the solid to cool to 500 K = 13 hour and 54 minutes Convection in Air Determine the rate of heat loss from a 100 mm diameter steam pipe placed horizontally in ambient air at 30oC. The length of the pipe is 4 m and wall temperature, Tw = 170oC. Use the following empirical expression: Nu=0.53 (Gr x Pr)1/4 Properties of air at 100oC are as following =1/373 K-1; = 23.13 x 10 -6 m2 /sec k= 0.0325 W/m.K Pr = 0.7 Calculations: Gr = gD3(Tw - T )2 / 2 Where = 1/Tf ; Tf = 0.5 (Tw + T ) = 0.5 x (170 + 30) = 100oC = 373 K = / Substituting for the values, Gr = 9.812 x (1/373) x 0.13 x (170 - 30) / (23.13 x 10-6)2 = 6.884 x 106 Nu = 0.53 x (6.884 x 106 x 0.7)1/4 = 24.832 Nu = hD/k = 24.832 h = 24.832 x 0.0325 / 0.1 = 8.07 W/m2.oC Rate of heat loss Q = hA(Tw - T ) = h 2pRL (Tw - T ) = 8.07 x 2 x 3.142 x 0.05 x 4 x (170 - 30) = 1419.8 W Convection in Water A horizontal cylinder, 3.0 cm in diameter and 0.8 m length, is suspended in water at 20oC. Calculate the rate of heat transfer if the cylinder surface is at 55oC. Given Nu = 0.53 (Gr x Pr)1/4 .The properties of water at average temperature are as follows: Density, = 990 kg/m3 Viscosity, = 2.47 kg/hr.m Thermal conductivity, k = 0.534 kcal/hr.m.oC Cp = 1 kcal/kg.oC.
4
Calculations: Gr = gD3(Tw - T )2 / 2 = 1/Tf Tf = 0.5 (Tw + T ) = 0.5 x (55 + 20) = 37.5oC = 310.5 K = 1/310.5 K-1 = 2.47 kg/hr.m = (2.47 / 3600) kg/m.sec = 6.861 x 10-4 kg/m.sec Substituting for the variables, Gr = 9.812 x (1/310.5) x 0.033 x (55 - 20) x 9902 / (6.861 x 10-4)2 = 62.176 x 106 Pr = Cp/k k = 0.534 kcal/hr.m.oC = 0.534 x 4184 / 3600 W/m.oC = 0.6206 W/m.oC Cp = 1 kcal/kg.oC = 4184 J/kg.oC Pr = 4184 x 6.861 x 10-4 / 0.6206 = 4.6254 Nu = 0.53 x (62.176 x 106 x 4.6254)1/4 = 69.02 Nu = hD/k = 69.02 h = 69.02 x 0.6206 / 0.03 = 1427.8 W/m2.oC Rate of heat transfer Q = hA(Tw - T ) = h p D L (Tw - T ) = 1427.8 x 3.142 x 3 x 10-2 x 0.8 x (55 - 20) = 3767.8 W Heat Transfer Coefficient In a 1-1 shell and tube heat exchanger, a fluid flowing through the tubes in turbulent flow, is being heated by means of steam condensing on the shell side. It is proposed to increase the tube side coefficient by one of the following methods: a. Replace the existing tubes by the same number of tubes with half the original diameter but twice the length. b. Increase the number of tube passes to 2. Assuming that the fluid flow rate remains high enough to ensure a Reynolds number of over 10,000 in all cases, indicate the method you would select. Justify your selection in brief (in not more than five lines).
5
Calculations: (a) Replace the existing tubes by the same number of tubes with half the original diameter but twice the length: Original flow area = (/4) D2 New flow area = (/4) (D/2)2 = 0.25 (/4) D2 For a given volumetric flow rate A v = Constant If original A is taken as 1, and original v is taken as 1 then D = 1.1284 New diameter = 1.1284/2 = 0.5642 New velocity = 1/0.25 = 4 Under forced convection, heat transfer coefficient can be estimated from DittusBoelter equation, which can be written as, Nu = 0.023 Re0.8 Pr0.4 hD/k = 0.023 (Dv/)0.8 Pr0.4 h = C D-0.2 v0.8 where:
C is a constant D is the diameter v is the velocity.
Original h = C x 1.1284-0.2 x 10.8 = 0.976 C New h = C x 0.5642-0.2 x 40.8 = 3.399 C Heat transfer coefficient increase by 100 x (3.399 - 0.976) / 0.976 = 248.3%. (b) Increase the number of tube passes to 2. Original flow area = n (/4) D2 New flow area = 0.5 n (/4) (D)2 New velocity = 1/0.5 = 2 New h = C x 1.1284-0.2 x 20.8 = 1.6995 C Heat transfer coefficient increases by 100 x (1.6995 - 0.976) / 0.976 = 74.1% From the above calculations, it could be seen that replacing the existing tubes by the same number of tubes with half the original diameter but twice the length will increase the heat transfer coefficient by a higher value than the other scheme. Hence the first method can be selected. Rate of Condensation Steam at atmospheric pressure condenses on a 0.25 m 2 vertical plate. The plate temperature is 96oC. Find the heat transfer coefficient and the mass of steam
6
condensed per hour. The length of the plate is 50 cm. At 97 oC, c = 960 kg/m3; k = 0.68 W/m.K; c = 2.82 x 10-4 kg/m.s; hfg = 2255 kJ/kg Calculations: The average value of condensing coefficient (hm) can be calculated from the equation obtained by Nusselt's condensation theory.
Since condensation is at atmospheric pressure, steam temperature (T v) is at 100oC. Film temperature Tf = (Tv + Tw)/2 = (100 + 96)/2 = 98oC. Since there will be negligible change in the properties at 98oC compared to 97oC, we can utilize the properties given at 97oC. The data given are: l = 960 kg/m3 kl = 0.68 W/m.K hfg = 2255 kJ/kg = 2255 x 1000 J/kg ml = 2.82 x 10-4 kg/m.sec Tw = 96oC L = 0.5 m Compared to rl, rv can be taken as zero. Therefore, hm = 0.943 x [9.812 x 9602 x 2255 x 1000 x 0.683 / (2.82 x 10-4 x 4 x 0.5)]1/4 = 9737.2 W/m2.K By adding a correction factor of 1.2 obtained from experiments to the Nusselt's equation, the average heat transfer coefficient is, hm = 1.2 x 9737.2 = 11685 W/m2.K Mass of steam condensed (M) is obtained by energy balance as: M hfg = hmA(Tv - Tw) M = 11685 x 0.25 x (100 - 96) / 2255000 = 5.1817 x 10-3 kg/sec Steam condensed per hour = 5.1817 x 10-3 x 3600 = 18.654 kg Parallel Flow - 1 A heat exchanger heats 25,000 kg/hr of water entering at 80 oC while cooling 20,000 kg/hr of water from 100oC to 80oC. Determine the heat transfer area necessary for (i) Parallel flow arrangement (ii) Counter flow arrangement. Given Overall heat transfer coefficient, U= 1,500 W/m2.
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Calculations: Heat of heat transferred by the cooling water = Q = mC pT = 20000 x 4.184 x (100 - 80) = 1673600 kJ/hr This will be the amount of heat transferred to the water that is getting heated up. Therefore, temperature change is = 1673600 / (25000 x 4.184) = 16 oC i.e., outlet temperature = 80 + 16 = 96oC
Parallel Flow - 2 A heat exchanger heats 25,000 kg/hr of water entering at 30 oC while cooling 20,000 kg/hr of water from 100oC to 80oC. Determine the area necessary for (i) Parallel flow arrangement (ii) Counter flow arrangement. Overall heat transfer coefficient may be assumed as 1,600 W/m2K. Calculations: Heat of heat transferred by the cooling water = Q = mCpT = 20000 x 4.184 x (100 - 80) = 1673600 kJ/hr = 464.89 kW This will be the amount of heat transferred to the water that is getting heated up. Therefore, temperature change is = 1673600 / (25000 x 4.184) = 16 oC i.e., outlet temperature = 30 + 16 = 46oC With these data, the following temperature-length diagram is drawn.
8
(i) Parallel flow arrangement: To = 100 - 30 = 70oC TL = 80 - 46 = 34oC LMTD = DTln = (To - TL) / ln (To/TL) = (70 - 34) / ln (70/34) = 49.85oC A = Q / (UTln) = 464.89 x 103 / (1600 x 49.85) = 5.8286 m2 Area required for parallel flow = 5.8286 m 2 (ii) Counter flow arrangement: To = 80 - 30 = 50oC TL = 100 - 46 = 54oC LMTD = DTln = (To - TL) / ln (To/TL) = (50 - 54) / ln (50/54) = 51.97oC A = Q / (UTln) = 464.89 x 103 / (1600 x 51.97) = 5.5908 m2 Area required for counter flow = 5.5908 m 2 Double-Pipe Heat Exchanger Water enters a parallel flow double-pipe heat exchanger at 15oC, flowing at the rate of 1200 kg/hr. It is heated by oil (Cp =2000 J/kg.K), flowing at the rate of 500 kg/hr from an inlet temperature of 90oC. For an area of 1 m2 and an overall heat transfer coefficient of 1,200 W/m2.K determine the total heat transfer and the outlet temperatures of water and oil. Calculations: Since the outlet temperature of the fluids are not given, the problem can be best solved by -NTU method. Cmin = (500/3600) x 2000 = 277.78 W/oC = Ch Cmax = (1200/3600) x 4184 = 1394.67 W/oC = Cc C = Cmin/Cmax = 277.78 / 1394.67 = 0.2 N = NTU = UA / Cmin = 1200 x 1 / 277.78 = 4.32 For parallel flow, relation between effectiveness () and NTU (N) is given by,
9
= {1 - exp[ -N(1 + C)]} / (1 + C) = {1 - exp[ - 4.32 x (1 + 0.2)]} / (1 + 0.2) = 0.8287 Total heat transfer rate Q = Cmin(Th,in - Tc,in) = 0.8287 x 277.78 x (90 - 15) = 17265 W Th,out = Th,in - Q/Ch = 90 - 17265/277.78 = 27.85oC Outlet temperature of oil = 27.85oC Tc,out = Tc,in + Q/Cc = 15 + 17265/1394.67 = 27.38oC Outlet temperature of water = 27.38oC Heat Transfer Area Hot gases enter a finned tube heat exchanger at 300oC and leave at 100oC. It is used to heat water at a flow rate of 1 kg/s from 35 oC to 125oC. The specific heat of exhaust hot gas is 1000 J/kg.K and the overall heat transfer coefficient based on the gas side is Uh = 100 W/m2.K. Determine the required gas surface area using the NTU method
Calculations: Since flow configuration is not given, we shall take it as countercurrent flow. Mass flow rate of hot gases (mg) is obtained by energy balance: 1 x 4184 x (125 - 35) = mg x 1000 x (300 - 100) mg = 1.8828 kg/s Cmin = 1.8828 x 1000 = 1882.8 W/oC = Ch Cmax = 1 x 4184 = 4184 W/oC = Cc = Cc(Tc,out - Tc,in) / [Cmin(Th,in - Tc,in)] = 4184 x (125 - 35) / [1882.8 x (300 - 35)] = 0.755 C = Cmin/Cmax = 1882.8/4184 = 0.45 For the counter flow exchanger, effectiveness - NTU relationship is given by, = {1 - exp[-N(1 -C)]} / {1 - Cexp[-N(1 - C)]} We know and C; and we have to find N. This has to be solved by iteration. 0.755 = {1 - exp[-N(1 - 0.45)]} / {1 - 0.45 exp[-N(1 - 0.45)]} 0.755 = (1 - e-0.55N) / (1 - 0.45e-0.55N) Starting with an initial assumption of N = 2, (1 - e-0.55N) / (1 - 0.45e-0.55N) = 0.667 / 0.85 = 0.7845 By assuming N = 1.9, (1 - e-0.55N) / (1 - 0.45e-0.55N) = 0.648 / 0.842 = 0.77
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By assuming N = 1.8, (1 - e-0.55N) / (1 - 0.45e-0.55N) = 0.628 / 0.833 = 0.754 Since the assumption of N = 1.8, almost balances the equation, we shall take N = 1.8 as the correct value. The required gas surface area, A = NTU Cmin / U = 1.8 x 1882.8 / 100 = 33.89 m2
Length of Heat Transfer In a counter-current heat exchanger, an oil stream is cooled from 450 K to 410 K by water inlet and outlet temperatures of 300 K and 350 K respectively. The exchanger consists a number of tubes of 1 m length each. It is now desired to cool the oil to 390 K (instead of 410 K) while maintaining the flow rate of oil, flow rate of water, inlet temperature of oil and water, and the number of tubes at the same values as before. Calculate the length of each tube required for this purpose. Assume that the physical properties remain unchanged. Calculations: For the first case:
Tln,1 = LMTD = (To - TL) / ln (To/TL) To = 450 - 350 = 100 K TL = 410 - 300 = 110 K Tln,1 = (100 - 110) / ln (100/110) = 104.9 K For the second case: Outlet temperature of water is obtained from the following proportionality factor. For 40 K change in oil temperature, there is a change of 50 K in water temperature. Since the flow rates are not changed, for a change of 60 K (i.e., = [ 450 - 390] K) in oil temperature the corresponding change in water temperature = 60 x 50 / 40 = 75 K
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Therefore, outlet temperature of water = 300 + 75 = 375 K And heat transfer rate for the second case will be 50% more than that of the first case, since there is a 50% increase in temperature drop. Q2 = 1.5 Q1
To = 450 - 375 = 75 K TL = 390 - 300 = 90 K Tln,2 = (75 - 90) / ln (75/90) = 82.3 K Since there is no change in physical properties of fluid compared to the first case, overall heat transfer coefficient U will be the same for both the cases. Heat transfer rate Q = U A Tln and A = n D L 'A' is directly proportional to 'L' For a given diameter and number of tubes it can be written as, Q = C L Tln where C is a constant. For the first case, Q1 = C L1 Tln,1 Q1 = C x 1 x 104.9 Q1/C = 104.9
(1)
For the second case, Q2 = C L2 Tln,2 Since Q2 = 1.5 Q1, the above equation can be written as, 1.5 Q1 = C L2 Tln,2
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L2 = 1.5 (Q1/C) (1/Tln,2)
(2)
Substituting for Q1/C from Equation 1 in Equation 2, L2 = 1.5 x 104.9 / 82.3 = 1.912 m Length of each tube required for the second case = 1.912 m Single-Effect Evaporator
10,000 kg/hr of an aqueous feed containing 1% dissolved solids is to be concentrated to 20% solids, in a single effect evaporator. The feed enters at 25 oC. The steam chest is fed with saturated steam at 110oC. The absolute pressure maintained in the evaporator is such that the water will boil at 55 oC. The boiling point elevations are as follows: Feed: 0.2oC 20% solution: 15oC The overall heat transfer coefficient, under normal operating conditions would be 2500 W/m2.oC Estimate the steam requirement assuming no sub cooling of condensate, heat load on the condenser, and the heat transfer area. Calculations: The given data are represented in the following diagram.
Let us have the following notations: Feed: F Concentrated product: P Water vapor: V Steam: S
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Mass balance: Solid balance: F x 0.01 = P x 0.2 P = 10000 x 0.01 / 0.2 = 500 kg/hr V = F - P = 10000 - 500 = 9500 kg/hr Energy balance: Temperature of Water vapor, leaving from the evaporator = 55oC + Boiling point elevation = 55oC + 15oC = 70oC Enthalpy of feed at 25oC (HF)= 104.8 kJ/kg (the data for water at 25oC - from Steam Tables) Enthalpy of product at 70oC (HP)= 293.0 kJ/kg (the data for water at 70oC - from Steam Tables) Pressure in the evaporator vapor space = 15.74 kPa(abs) (saturation pressure of water vapor at 55oC - from Steam Tables) Enthalpy of water vapor leaving at 70oC and 15.74 kPa(abs) (HV)= 2640 kJ/kg (from Mollier Diagram) Enthalpy of saturated water at 15.74 kPa(abs) = 230.2 kJ/kg Latent heat of steam at 110oC (S)= 2230 kJ/kg (from Steam Tables) F HF + S S = V HV + P HP 10000 x 104.8 = S x 2230 = 9500 x 2640 + 500 x 293 S = 10842.4 kg/hr Steam requirement = 10842.4 kg/hr = 3.01178 kg/sec Heat load on Condenser (assuming condensate water leaves as saturated liquid corresponding the vapor space pressure) = 9500 x (2640 - 230.2) = 22893100 kJ/hr = 6359.2 kW Heat transfer area estimation: Q = Rate of heat transfer through heating surface from steam = U A T S S = U A T 3.01178 x 2230 = 2.5 x A x (110 - 70) A = 67.2 m2 Heat transfer area = 67.2 m2 Time Required for Evaporation An apparent overall heat transfer coefficient is 735 Btu/(hr.sqft.oF) for a forced circulation evaporator concentrating sulfite liquor under certain special conditions. How long will it take to concentrate 20000 lb of a feed liquor containing 5% solute
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by weight to a final concentration of 15% if the steam temperature is 230.8oF and the temperature corresponding to the pressure in the vapor space is 210.7 oF. The heating surface is 100 sqft. Indicate all the assumptions made in obtaining the result. How will the result be affected if each of the assumptions is not made. Calculations: Assumptions: (i) Steady state operation (ii) No elevation in boiling point due to solute concentration. (iii) No elevation in boiling point due to hydrostatic head. (iv) No sub-cooling of condensate. (v) Feed is at the temperature of 210.7oF Rate of heat transfer, Q = U A T = 735 x 100 x (230.8 - 210.7) / 3600 = 410.375 Btu/sec Mass flow rate of steam, (mS): mS S = 410.375 S = 958 Btu/lb (from Steam Tables - for the temperature 230.8oF ) Therefore, mS = 410.375/958 = 0.42837 lb/sec Making heat balance for the solution: (taking 210.7oF as the datum temperature) By denoting mass flow rate of vapor as, mV, m V V = m S S V = 971 Btu/lb (from Steam Tables - for the temperature 210.7oF ) Therefore, mV = 410.375/971 = 0.42263 lb/sec Mass of vapor evaporated = 0.42263 lb/sec Time needed for evaporation: Solute balance: If the product is denoted as P, 20000 x 0.05 = P x 0.2 P = 5000 kg Water in feed = water evaporated + water in concentrated solution
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20000 x 0.95 = 0.42263 x t + P x 0.8 19000 = 0.42263 x t + 4000 t = 15000/0.42263 = 35492 sec = 9 hr 52 min Time needed for evaporation = 9 hour and 52 minutes. If the assumptions were not made: If the assumption (i) is not made, then we have to make a unsteady balance (For Batch Evaporation). The results will be different for these two operations If the assumption (ii) is not made, then the DT will be equal to, (Tsteam - Tboiling point of water corresponding to the pressure inside the evaporator - boiling point elevation). This will lead to the increase of time needed for evaporation. Assumption (iii) also has the same effect of assumption (ii). Assumption (iv): If sub-cooling of steam is allowed, it will give more heat to the solution, which in turn will reduce the time needed for evaporation. Assumption (v): If feed temperature is less than this, it leads to more steam requirement. So with the available heat transfer rate, it leads to increased evaporation time.
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• # estonia vertical cylindrical tank building volume
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Mar 26, 2015 · The tank size calculator on this page is designed for measuring the capacity of a variety of fuel tanks. Alternatively, you can use this tank volume calculator as a water volume calculator if you need to calculate some specific water volume. The functionality of this Vertical Cylindrical Shaped Tank Contents CalculatorVertical Cylindrical Shaped Tank Contents Calculator , estonia vertical cylindrical tank building volume How to determine milk tank level and volume from pressure; , estonia vertical cylindrical tank building volume Product Enquiry. Send us your enquiry for a product associated with this Vertical Cylindrical Shaped Tank Contents Calculator page, , estonia vertical cylindrical tank building volumeOnline calculator: Tank Volume CalculatorsTank Volume Calculators. Use one of these to determine your tank's volume. person_outlinePete Mazzschedule 2016-01-16 10:53:10. Cylindrical Tank Volume Use this calculator to determine your cylindrical tank volume in cubic inches and gallons even if one or both ends are rounded. Especially useful if you've cut the tank in length.
### HOW TO CALCULATE THE VOLUMES OF PARTIALLY FULL
cylindrical tanks, either in horizontal or vertical configuration. Consider, for example, a cylindrical tank with length L and radius R, filling up to a height H. If you want to obtain the volume of the liquid that partially fills the tank, you should indicate if the tank is in horizontal or vertical position.VERTICAL CYLINDER CALCULATOR - 1728If you want to do calculations for a horizontal cylinder, then go to this link: Horizontal Cylinder Calculator. Example: Inputting tank height = 12, liquid level = 3 and tank diameter = 6, then clicking "Inches" will display the total tank volume in cubic inches and US Gallons and will also show the volume Tank Volume Calculator - ibec language instituteTry Fusion's free tank volume calculator for industrial mixing. Please fill all required fields Tank Volume Calculator , estonia vertical cylindrical tank building volume *Program does not calculate liquid volume into upper head on vertical tanks (mixing with liquid in head space is not good practice).
### How to design a vertical cylindrical Water tank | Physics , estonia vertical cylindrical tank building volume
Sep 12, 2014 · I Need to design a Vertical cylindrical water tank to be build by Fiberglass. I need to calculate the tank also for 7.5 m bar pressure and 2.5 m bar vacuum pressure. Tank Dimensions to be 4m Dia, 5 m High (60000 Liters). I have Fiberglass laminate of 6 Volume of a Partially Filled Spherical Tank - Calibration , estonia vertical cylindrical tank building volumeThis calculator will tell you the volume of a paritally filled spherical tank. This will also generate a dip chart/table for the tank with the given dimensions you specify. Output is in gallons or liters. If you have a complex tank, or need something special created please don't hesitate contact us for more info.albania vertical cylindrical tank building volume - API650 , estonia vertical cylindrical tank building volumeHome // API650 tanks // albania vertical cylindrical tank building volume. , estonia vertical cylindrical tank building volume BSI - BS 7777-3 Flat-bottomed, vertical, cylindrical storage tanks for low temperature service. Part 3 Recommendations for the design and construction of prestressed and reinforced concrete tanks and tank foundations, and for the design and installation of tank , estonia vertical cylindrical tank building volume
### Vertical Tank Volume Calculator - Alberta
Vertical Tank Volume Calculator . The dimensions for diameter, height and depth should be inside dimensions, otherwise the results will be larger than the real volume. Depth to liquid is the dip-stick measurement from the top of the tank to the surface of the liquid.Calculator to Find liquid volume for vertically mounted , estonia vertical cylindrical tank building volumeApr 13, 2017 · Sugar industry or other industries using vertically mounded cylindrical tanks for sealing of vacuum equipment like vacuum condensers and multiple effect evaporator lost body liquid extraction (outlet). Sometimes it has also called mound. In this cylindrical tank sometimes inside of the tank might be separated by vertical plate for easily operation purpose.Horizontal Cylindrical Tank Volume and Level CalculatorVolume calculation on a partially filled cylindrical tank Some Theory. Using the theory. Use this calculator for computing the volume of partially-filled horizontal cylinder-shaped tanks.With horizontal cylinders, volume changes are not linear and in fact are rather complex as the theory above shows. Fortunately you have this tool to do the work for you.
### Calculating Tank Volume
Calculating Tank Volume Saving time, increasing accuracy By Dan Jones, Ph.D., P.E. alculating fluid volume in a horizontal or vertical cylindrical or elliptical tank can be complicated, depending on fluid height and the shape of the heads (ends) of a horizontal tank or the bottom of a vertical tank.Spill Prevention Control and Countermeasure (SPCC) Spill Prevention Control and Countermeasure (SPCC) Plan Single Vertical Cylindrical Tank Inside a Rectangular or Square Dike or Berm WORKSHEET . This worksheet can be used to calculate the secondary containment volume of a rectangular or square dike or berm for a single vertical cylindrical tank. This worksheet assumes that there are no other , estonia vertical cylindrical tank building volumeTry Our Tank Volume Calculator To Work Out The Size of , estonia vertical cylindrical tank building volumeOctanes Tank Volume Calculator makes it really easy to work out the volume of your tank and is totally free for you to use. All you need to do is follow the 4 steps below: 1. Click one of the 3 tabs across the top which represents your tank 2. Select your measurement units 3. Enter your tanks length, width etc 4. Click Calculate.
### How to design a vertical cylindrical Water tank | Physics , estonia vertical cylindrical tank building volume
Sep 12, 2014 · I Need to design a Vertical cylindrical water tank to be build by Fiberglass. I need to calculate the tank also for 7.5 m bar pressure and 2.5 m bar vacuum pressure. Tank Dimensions to be 4m Dia, 5 m High (60000 Liters). I have Fiberglass laminate of 6 Tank calculations - MrExcelDec 19, 2014 · We use what are called tank strappings for some of our additive tanks. They were built from formulas for cylindrical horizontal or vertical tanks. I pugged in the size of the tanks and a strapping was produced. From there I set up a form using vlookups to the strappings. Give me some tank measurements and I'll see if what I have at work will , estonia vertical cylindrical tank building volume* Sloped Bottom Tank - arachnoid, estonia vertical cylindrical tank building volumeThe easy part the cylindrical section above the slope, which has a volume of: (1) $\displaystyle v = \pi r^2 h$ v = volume; r = tank radius; h = cylindrical section height; More difficult the tank's sloped section, which lies between the tank's bottom and the top of the slope where the tank
### Cylindrical Tank Calculator
I n s t r u c t i o n s Use this calculator for computing the volume of partially-filled horizontal cylinders. If you need a vertical cylinder calculator, click here.. Besides calculating volume for any particular depth, this calculator can also produce a "dipstick chart" showing volume across the entire range of tank Greer Tank Calculator | Greer Tank, Welding & SteelIf you need assistance with our tank volume calculator or would like to inquire about any of our services, give us a call today on 1-800-725-8108, , estonia vertical cylindrical tank building volume Vertical Cylindrical Tank. All dimensions are in inches, the volume is U.S. gallons. Rectangle / Cube Tank. All dimensions are in inches, the volume is U.S. gallons.calculus - Volume of a horizontal cylinder using height of , estonia vertical cylindrical tank building volume$\begingroup$ This isn't and equation that you can plug in radius, length, and height of liquid in the tank to find the volume of the liquid. $\endgroup$ Billybob686 Oct 13 '14 at 21:27 $\begingroup$ No, it is much better than this: it's a universal equation, that will work for any tank.
### Horizontal Tank Volume Calculations - Hagra
Tools are provided for cylindrical horizontal tanks, and for oval (elliptical) tanks. Horizontal Cylindrical Tank Volume Calculator. Horizontal Oval Tank Volume Calculator. Disclaimer. The calculations on these pages are a purely theoretical exercise! Therefore the outcomes of the calculations on these pages can only be used for indicative , estonia vertical cylindrical tank building volumeVolume calculation on a horizontal elliptical tankVolume calculation on a partially filled elliptical tank. This second tool can provide a single detailed value of the volume of a partially filled horizontal oval tank. Just insert the horizontal tank diameter, the vertical tank diameter, the tank length, and the reading on the dip stick, ruler, or measuring tape.How to Calculate Gallons and Tank Volume | SciencingMar 13, 2018 · How to Calculate Gallons and Tank Volume , estonia vertical cylindrical tank building volume Rectangular tanks, like aquariums require one formula, while cylindrical tanks, like drinking water tanks, require another. Rectangular Tanks. Measure the length, width and depth of the tank using a tape measure. You can measure from the inside of the tank or, if preferable, measure the outside and , estonia vertical cylindrical tank building volume
### tank volume formula | Automation & Control Engineering
Oct 21, 2006 · It is assumed by reading your description that this is a vertical cylindrical tank. The formula does not account for flanged and dished or cone bottom vessels. Leaving all units in inches - diameter squared x .7854 x height-----231 cubic inches/gallon To calculate a horizontal cylindrical tank's volume is more involved. 120" x 120" x .7854 x 180"Horizontal tank with hemispherical ends depth to capacity , estonia vertical cylindrical tank building volumeHorizontal tank with hemispherical ends depth to capacity calculation. Ask Question Asked 8 years, 9 months ago. , estonia vertical cylindrical tank building volume I would like to find an equation for calculating the volume of liquid in the tank based on the liquid depth level. , estonia vertical cylindrical tank building volume There is an excel template to calculate horizontal cylindrical tank, with hemispherical both ends, and usually , estonia vertical cylindrical tank building volumeCylindrical Tank CalculatorCylindrical Tank Calculator, Tank Volume Calculator, Horizontal Cylinder Volume, Dipstick Chart, Dipstick Calculator, Cubic Inches, Cubic Feet, Cubic Meters, Cubic Centimeters, Gallons, Liters, Milliters. Horizontal Cylindrical Tank Calculator and Dipstick Chart To see how this volume is calculated , estonia vertical cylindrical tank building volume If you need a vertical cylinder calculator , estonia vertical cylindrical tank building volume
### Cylindrical Tank Problems
In order to find the volume, we would have to find the area of the section covered by the oil at the end of the tank and then multiply by the length of the tank. But, how do you find the area of such a figure? Let's begin by examining the end view of the tank (in general so that we can do it for any size cylindrical tank Mixing 101: Optimal Tank Design | Dynamix AgitatorsMar 10, 2015 · Vertical Cylindrical Tanks. Vertical cylindrical tanks are the most common type of tank in use. A key consideration for cylindrical tanks is to ensure that they are either baffled or offset-mounted to prevent swirling from occurring. Refer to section 2 below (The Use of Baffling) for details.Tank Charts - Hall Tank Company - Hall Tank CompanyUse this form to generate a chart of tank capacities. Hall Tank does not guarantee the capacity charts accuracy and in no way takes liability for loss due to its content. Calculating a chart will be considered acceptance of this agreement.
### DESIGN RECOMMENDATION FOR STORAGE TANKS
The Sub-Committee first published Design Recommendation for Storage Tanks and Their Supports in 1984, and amended it in the 1990, 1996 and 2010 , estonia vertical cylindrical tank building volume For above-ground vertical cylindrical storage tanks without any restraining element, such as anchor bolts or straps, to prevent any overturning moment, only the bending resistance due to , estonia vertical cylindrical tank building volumeVolume Of Partially Filled Cylinder/hemi Ends , estonia vertical cylindrical tank building volumeRe: Volume Of Partially Filled Cylinder/hemi Ends Hi, I am the unregistered user that originally posted the question. I think that software on the web is kinda neat, however, I can't find an equation to solve for the level, estonia vertical cylindrical tank building volumeAny more help would be desired.Sloped Cylindrical Tank Level - Chemical plant design , estonia vertical cylindrical tank building volumeDec 07, 2012 · I am putting together a process design package for a batch plant expansion. We need to install a multipurpose cylindrical 40,000 gallon horizontal storage tank. To minimize holdup we are planning to slope the tank. We would like to measure the liquid level in the tank so we know if there is insufficient material left for a full batch.
### Tank Calibration Chart Calculator - ODay Equipment
Fiberglass Tanks. ODay Equipment provides dome end fiberglass tanks from Xerxes and Containment Solutions. The domes on fiberglass tanks vary by manufacturer. So, here are the manufacturers web sites that have calibration charts specific to their designs. Xerxes Go to the Library tab for PDF versions of their charts.Cylindrical Silo (Irregular Shape) Volume Calculatorcylindrical silo volume calculator - step by step calculation, formula & solved example problem to find the volume of irregular shape for the given values of base radius r, & height h of silo in inches (in), feet (ft), meters (m), centimeters (cm) & millimeters (mm).
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# Thread: Differential equation with substitution
1. ## Differential equation with substitution
The question:
Use the substitution $v = \frac{y}{x}$ to solve
$\frac{dy}{dx} = \frac{(\frac{y}{x})^3 + 1}{(\frac{y}{x})^2}$
given that y = 1 at x = 1.
My attempt:
$\frac{dy}{dx} = \frac{v^3 + 1}{v^2}$
$y = \int{\frac{v^3}{v^2}} + \int{\frac{1}{v^2}}$
= $\int{v} + \int{\frac{1}{v^2}}$
= $\frac{v^2}{2} - \frac{1}{v} + C$
= $\frac{1}{2}(\frac{y}{x})^2} - \frac{1}{\frac{y}{x}} + C$
= $\frac{1}{2}(\frac{y}{x})^2} - \frac{x}{y} + C$
Substituting initial value gives C = 3/2
Is this correct? I don't have answers for practice exams.
2. $\displaystyle f(1,1)=\frac{1}{2}*1^2-1+c\Rightarrow c=\frac{1}{2}$
3. Originally Posted by Glitch
The question:
Use the substitution $v = \frac{y}{x}$ to solve
$\frac{dy}{dx} = \frac{(\frac{y}{x})^3 + 1}{(\frac{y}{x})^2}$
given that y = 1 at x = 1.
My attempt:
$\frac{dy}{dx} = \frac{v^3 + 1}{v^2}$
$y = \int{\frac{v^3}{v^2}} + \int{\frac{1}{v^2}}$
= $\int{v} + \int{\frac{1}{v^2}}$
= $\frac{v^2}{2} - \frac{1}{v} + C$
= $\frac{1}{2}(\frac{y}{x})^2} - \frac{1}{\frac{y}{x}} + C$
= $\frac{1}{2}(\frac{y}{x})^2} - \frac{x}{y} + C$
Substituting initial value gives C = 3/2
Is this correct? I don't have answers for practice exams.
No, that's not correct. You tried to solve the problem with 3 variables. You integrated both sides with respect to x while treating v as the variable too. absurdity
$\displaystyle v = \frac yx \implies y = vx$
$\displaystyle \Rightarrow \frac {dy}{dx} = \frac {dv}{dx} \cdot x + v$
You must substitute that for dy/dx into your differential equation then proceed via separation of variables.
4. No, it's not. You need to get a DE that does not have any reference to the variable $\displaystyle y$.
$\displaystyle \frac{dy}{dx} = \frac{\left(\frac{y}{x}\right)^3 + 1}{\left(\frac{y}{x}\right)^2}$.
Make the substitution $\displaystyle v = \frac{y}{x}$. Then $\displaystyle y = v\,x$ and $\displaystyle \frac{dy}{dx} = x\,\frac{dv}{dx} + v$ and the DE becomes
$\displaystyle x\,\frac{dv}{dx} + v = \frac{v^3 + 1}{v^2}$
$\displaystyle x\,\frac{dv}{dx} + v = v + \frac{1}{v^2}$
$\displaystyle x\,\frac{dv}{dx} = \frac{1}{v^2}$
$\displaystyle v^2\,\frac{dv}{dx} = \frac{1}{x}$
$\displaystyle \int{v^2\,\frac{dv}{dx}\,dx} = \int{\frac{1}{x}\,dx}$
$\displaystyle \int{v^2\,dv} = \ln{|x|} + C_1$
$\displaystyle \frac{v^3}{3} + C_2 = \ln{|x|} + C_1$
$\displaystyle \frac{v^3}{3} = \ln{|x|} + C$ where $\displaystyle C = C_1-C_2$
$\displaystyle v^3 = 3\ln{|x|} + 3C$
$\displaystyle v = \sqrt[3]{3\ln{|x|} + 3C}$
$\displaystyle \frac{y}{x} = \sqrt[3]{3\ln{|x|} + 3C}$
$\displaystyle y = x\sqrt[3]{3\ln{|x|} + 3C}$.
5. $\displaystyle y = vx$ which implies $\displaystyle \frac{dy}{dx} = x\frac{dv}{dx} + v$ by the chain rule (and product rule).
6. Originally Posted by Glitch
The question:
Use the substitution $v = \frac{y}{x}$ to solve
$\frac{dy}{dx} = \frac{(\frac{y}{x})^3 + 1}{(\frac{y}{x})^2}$
given that y = 1 at x = 1.
My attempt:
$\frac{dy}{dx} = \frac{v^3 + 1}{v^2}$
$y = \int{\frac{v^3}{v^2}} + \int{\frac{1}{v^2}}$
= $\int{v} + \int{\frac{1}{v^2}}$
= $\frac{v^2}{2} - \frac{1}{v} + C$
= $\frac{1}{2}(\frac{y}{x})^2} - \frac{1}{\frac{y}{x}} + C$
= $\frac{1}{2}(\frac{y}{x})^2} - \frac{x}{y} + C$
Substituting initial value gives C = 3/2
Is this correct? I don't have answers for practice exams.
I'm sorry to say that this is not correct, because you're integrating with respect to the wrong variable (v instead of x).
First apply the substitution that's given to you. $v=\frac{y}{x}$. So now we need to rewrite $\dfrac{\,dy}{\,dx}$:
$\dfrac{\,dv}{\,dx}=-\dfrac{y}{x^2}+\dfrac{1}{x}\dfrac{\,dy}{\,dx}$. Since $y=vx$, we end up with $\dfrac{\,dy}{\,dx}=v+x\dfrac{\,dv}{\,dx}$
Thus, the ODE becomes $v+x\dfrac{\,dv}{\,dx}=\dfrac{v^3+1}{v^2}$. This is now a separable equation.
Can you proceed?
EDIT: Man, am I slow!!
7. You are integrating with respect to v when you should be integrating with respect to x. You need to make the substitution $\frac{dy}{dx} = v + x \frac{dv}{dx}$ and solve the resulting equation for v using separation of variables. Once you have v you can get y since y = vx.
8. Thanks guys!
With the 3C in the solution, is it fair to just write 'C' since it's still an unknown constant?
9. Originally Posted by Glitch
Thanks guys!
With the 3C in the solution, is it fair to just write 'C' since it's still an unknown constant?
I'd use a different letter just because $\displaystyle 3C \neq C$, but yes, it's still just an arbitrary constant.
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1 Reply Latest reply on Jun 15, 2017 3:15 AM by MartyG
# Realsense r200 noisy cloud and color difference
Hi guys.
I'm using three Intel realsense r200 cameras and have some problems that I can't resolve.
The first one is that the point cloud I get is wavy, I have a feeling that sensor has some
noise dependant on the distance to the working surface. As shown in the examples below you can
see noise as waves. The closer I move to the camera the lower amplitude this noise has.
What is the reason of this noise and how can I get rid of it?
- close look(distance about 60 cm):
https://gyazo.com/0f67a5e3e8a72cb4295faef700ccfbf0
- distance about 1.5 meters (amplitude of the noise is much bigger):
https://gyazo.com/0818084b9f74ce2a6c38907edd2633a2
The second problem is that color images from different realsenses are different. For example,
the color checker from first camera looks different in the second camera. Sensors are placed
one above another. As you already guessed, I tried to use a color checker to compute the color
transform for each camera. But it works too bad. I tried to use different terms for finding
color transform(r g b rr rg rb etc). The best result I get when using 3x3 matrix color
transform with three terms r, g and b respectively. But this transform is still not that good.
When stitching images from different realsenses I get a differently colored halves
of the same object. Can some one give me an advice how to resolve this issue.
To be more precise, when I compute color transform with a man in blue t-shirt it works good.
But I need to recompute the color transform each time I have the man in white T-shirt in front
of the camera. Does it means that color checker approach need to be used each time the new
object appears in the scene? I thought I need to compute it only once under the certain
lighting conditions in the empty scene.
As for the lighting conditions, I have the big LED wall right behind the sensors, that gives
uniform white light that is almost shadowless.
Here on the models texture you can see the difference in color of the clothing's. I did some
blending to reduce the effect. But you still can notice the difference
between sensors(top/bottom of the shirt):
https://sketchfab.com/models/d826bea5a12749eba95f273a5cfb48cd
One last word. I am using librealsense, as it alows to use several r200 cameras at the same time.
I would appreciate any help.
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# Thread: Proof for sin and cos
1. ## Proof for sin and cos
i cannot prove this no matter what i try to do! I need help to be able to pass my test tommorrow.
Prove sin(t)/(1-cos(t)) = (1+cos(t)) / sin(t)
I worked with the left terms:
sin(t) / (1-cos(t)) | Problem
sin(t) / (sin^2(t) + cos^2(t)-cos(t)) | Pythagorean ID:sin^2(t) + cos^2(t) = 1
what to do next? i already tried seperating all the terms and that doesn't work out. I have a test tomorrow on this stuff and i really need some help.
2. Multiply the right side by $\frac{1-\cos(t)}{1-\cos(t)}$.
3. Do you see the answer? It's not too many steps ahead of the hint I gave you.
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math
posted by .
Fourteen patients have the following LOS:1,4,4,2,5,16,3,3,1,6,4,5,7,and 2. Compute the mean, median, and mode
• math -
Add them together and divide by 14 to find the mean.
Arrange them in order. The middle number is the median.
4 is the mode
http://www.purplemath.com/modules/meanmode.htm
• math -
So first what you want to do it two put the numbers in order from least to greatest.
1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 7, 16
So to find the mode you want to see which number is listed the most. That would be 4.
To find the median you want to find the middle number of this set. What I do is I cross out the outermost number of the data until I narrow it down to one.
To find the mean, you would just add up all the numbers and then divide by 14, since there are 14 numbers.
Hope this helps!
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# The value of
Question:
The value of $\frac{2^{0}+7^{0}}{5^{0}}$ is
(a) 0
(b) 2
(c) $\frac{9}{5}$
(d) $\frac{1}{5}$
Solution:
$\frac{2^{0}+7^{0}}{5^{0}}=\frac{1+1}{1}$
$=\frac{2}{1}$
$=2$
$\therefore$ The value of $\frac{2^{0}+7^{0}}{5^{0}}$ is 2 .
Hence, the correct option is (b).
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How to handle movements of objects in a platformer with a cylindrical map?
I was wondering what would be the best approach for a game like Resogun:
In my opinion, the easiest approach is to:
• have a “Center Parent” for each moving object
• Offset the child object by the wanted radius
• Rotate the parent
=> The objects will move, though this will become super limited very quickly, especially if you want to do any sort of physics.
The 2nd approach is math:
``````x = centerX + cos(angle)*radius;
``````
And this is what i want to use, however, am not certain about how to set it up, especially if i want to use rigidbodies and have some physical interactions.
Thanks
Holy crap, that looks great. It’s Williams Defender all over again! I love it.
So Physics around such a tube would be problematic… but the actual work is precisely as you suggest above, with trig functions to project your position.
I made such a demo that sorta mimics Gyruss or Tempest motion, and the source is linked in the comments:
I suppose for Physics one way would be to run everything with Physics 2D somewhere else in a plane, just using invisible objects with colliders, then in your Update have all the visible objects project the physics objects to update their positions around the cylinder.
1 Like
i know right! Resogun is probably the most arcade game i played this generation, shame its not available on Switch, it’s perfect for a handheld device.
I’ve seen the 2D idea mentioned a lot, is it really that complex to “just” do it in 3D ? what’s the “danger” of it ?
I doubt the above game uses physics to begin with, and personally I would NOT use physics and just use a) my own ballistics, and b) my own proximity-based collision, “oldskool” so to speak.
The “danger of 3D” as you put it is that it is a planar 2D game, wrapped around a cylinder. This means you can’t trivially lock the Z axis in 3D… and in the general sense of velocity curving around a corner, the physics system knows nothing about that, so you would need to model it each frame yourself.
And then basically it sorta gets right back to “why use physics at all?” for this.
1 Like
I see, you’re right, any chance you came across any example of doing stuff on 2D but have “fake” graphics on 3D ? doesn’t have to be related to this game idea at all, just wanna see how people handled that.
I could certainly imagine a system where all the physics stuff happens in a regular 2D plane (with some sort of trickery for the wrap-around at the edge) but then the camera looks in a completely different direction at a bunch of graphics-only objects that get moved every LateUpdate to match what’s happening in the physics part. That seems like the obvious way to jury-rig an existing physics system to play on a non-Euclidean surface.
I don’t think there would even be very much of a performance cost, as long as you’re careful not to do any expensive rendering-related stuff in the off-screen physics portion or any expensive physics-related stuff in the on-screen portion.
Alternately, there might even be something you could do with the camera/rendering itself to make a flat plane look as if it were curved, even though everything has the same Z coordinate. But I couldn’t tell you how, and I’m not certain it would be possible at all. (If this were a real-life physical camera, I would think you could do something with lenses, and I could probably even work out how to do the equivalent thing in a raycast-based renderer, but I don’t think the same principles apply to a rasterization-based renderer.)
Um… did you see my Gyruss / Tempest video link above? Comes with full source code in my proximity_buttons project!
proximity_buttons is presently hosted at these locations:
https://bitbucket.org/kurtdekker/proximity_buttons
https://github.com/kurtdekker/proximity_buttons
https://gitlab.com/kurtdekker/proximity_buttons
https://sourceforge.net/projects/proximity-buttons/
1 Like
This would technically be possible using a shader to twist the geometry into a world-space cylinder. You would still need to handle physics at the wrap-around point, though.
I thought of that too, the “subway surfer” approach, but after playing Resogun again, and taking a look at their photo mode, its obvious that they are not doing any shader trick.
oh! thanks!
Resogun doesn’t need to take that approach – they’re a full 3D game and their physics is limited to explosion particles which aren’t confined to the cylinder.
I think your simplest solution to have the cylinder and have physics is to take @Antistone 's approach: create a flat 2D physics world that is then mapped onto a cylinder. This would intrinsically solve your constraint problem, but would not allow you to have full 3D physics in cylinder-space interact with your 2D physics.
1 Like
Yeah i think you’re right, i’ll give that a go, thank you all!
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http://brainking.com/en/GameRules?tp=101&fwa=TeamTournaments!tri=378$trnst=10
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Back to game
Statistics of won games red 39780 (50.34 %) blue 39173 (49.57 %) Draws 67 (0.08 %)
### Frog Finder
This is a nice variant of the well known game of Minesweeper (which is included in MS Windows) for two players, created by Michael Coan in 2006.
Start position and game object
The game is played on 12 x 12 square board. Each player (red and blue) has five frogs which are randomly placed on the board before the game starts. Only one frog can occupy the same square. Players can see only their own frogs, the opponent ones are invisible until revealed (which will be explained in the next sections). The following picture shows an example of the start position from the red player's point of view:
The object of the game is to find all opponent's frogs and get as many points as possible. The player with more points wins the game.
How to make moves
A player, who is to make a move, decides, whether he wants to shoot an empty square or make a guess on an empty square. This is done by clicking the selected link below the game board.
• Shoot - the shoot action reveals how many frogs (of any color) are surrounding the shot square. When the shot is done, the number of frogs which are adjacent to the square is displayed. The next picture displays a position after the red player's shot:
The "2" indicates that two frogs are located next to this square. And since one of them is the red frog on I9 square, the second one must be blue.
If a player shoots at a square which contains an opponent's frog, he loses 5 points and the opponent gets 5 points (shooting a cute froggie is bad and costly). The dead frog is displayed upside down and on a black background.
• Guess - if a player believes to know where an opponent's frog is located, he can make a guess at this square. He gets 5 points for a correct guess (and the revealed frog is displayed on a golden background) or loses 3 points for a wrong guess (and the square remains unchanged and can be used for another guess or shoot action later). The next picture shows a dead frog on G9 and a correctly guessed frog on A1:
How to finish the game
The game ends when all frogs of one player are revealed on the board (no matter if they were shot or guessed). The other player gets a bonus of 2 points and 1 point for each own frog which was not found by the opponent.
After the bonus points are added, the player with more points wins the game. If both players have the same amount of points, the game is a draw.
Play this game
See also: Tablut, Tank Battle, Halma 8x8, Halma 10x10, Amazons, Jarmo, Froglet, Jungle, Anti Froglet, Sphere Froglet, Ludo, Breakthrough, Assimilation, Ataxx, Cheversi, Dice Poker, Triple Dice Poker, Frog Finder, Logik, Mancala, Frog Legs, Dice Poker 6D, Triple Dice Poker 6D, Big Jungle, Knight Fight, Camelot, Cam
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wat is the equation of a standing wave?
6 years ago
Share
Dear Mohini
Harmonic waves travelling in opposite directions can be represented by the equations below:
$y_1\; =\; y_0\, \sin(kx - \omega t)\,$
and
$y_2\; =\; y_0\, \sin(kx + \omega t)\,$
where:
y0 is the amplitude of the wave,
ω (called angular frequency, measured in radians per second) is 2π times the frequency (in hertz),
k (called the wave number and measured in radians per metre) is 2π divided by the wavelength λ (in metres), and
x and t are variables for longitudinal position and time, respectively.
So the resultant wave y equation will be the sum of y1 and y2:
$y\; =\; y_0\, \sin(kx - \omega t)\; +\; y_0\, \sin(kx + \omega t)\,$.
Using a trigonometric identity (the 'Sum to Product' identity for 'sin(u)+sin(v)') to simplify:
$y\; =\; 2\, y_0\, \cos(\omega t)\; \sin(kx)\,$.
This describes a wave that oscillates in time, but has a spatial dependence that is stationary: sin(kx). At locations x = 0, λ/2, λ, 3λ/2, ... called the nodes the amplitude is always zero, whereas at locations x = λ/4, 3λ/4, 5λ/4, ... called the anti-nodes, the amplitude is maximum. The distance between two conjugative nodes or anti-nodes is λ/2.
All the best.
AKASH GOYAL
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6 years ago
# Other Related Questions on Wave Motion
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Tapas Khanda 5 months ago
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I`m doing a project, can someone help me, How to reduce those toxic contents when plantic are burnt Like sulphur, nitrogen etc
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More Questions On Wave Motion
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# How do you solve 16 m + 3 5 = 3?
Oct 18, 2016
This problem is solved by isolating the variable, so that we determine that $m = - 2$.
#### Explanation:
1. Subtract $35$ from both sides. This gets the $16$m by itself. It is necessary to perform this operation on both sides to maintain the balance of the equation.
$16 m + 35 - 35 = 3 - 35$
2. Divide both sides by $16$. This gets the $m$ by itself. Again, it is necessary to perform this on both sides so that the equation stays balanced.
$\frac{16 m}{16} = \frac{3 - 35}{16}$
3. Simplify.
$m = - 2$
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# LeetCode.1185-一周中的星期几(Day of the Week)
## 看题和准备
• 给定的日期是1971年至2100年之间的有效日期。
## 第一种解法
public String dayOfTheWeek(int day, int month, int year) {
String[] week = {"Sunday", "Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday"};
Calendar cal = Calendar.getInstance();
cal.set(year, month-1, day);
int i = cal.get(Calendar.DAY_OF_WEEK)-1;
if (i<0) {
i = 0;
}
return week[i];
}
## 第二种解法
public String dayOfTheWeek2(int day, int month, int year) {
String[] week = {"Sunday", "Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday"};
int[] dayOfMonth = {31,28,31,30,31,30,31,31,30,31,30,31};
int total = 0;
for (int i=1971; i<year; i++) {
if (i%4 == 0) {
total++;
}
total += 365;
}
if (year%4 == 0) {
dayOfMonth[1] = 29;
}
for (int j=0; j<month-1; j++) {
total += dayOfMonth[j];
}
total += day - 1;
return week[(total + 5)%7];
}
## 第三种解法
w = (c/4- 2*c + y + y/4 + 26*(m + 1)/10 + d - 1) % 7;
• c:代表世纪，是年份的前两位，比如1971，c就为19。
• y:是年份的后两位，比如1971，y就是71。
• m:代表月，3<= m <= 14，某年的1、2月要看作上一年的13、14月来计算，比如2003年1月1日，要看作2002年的13月1日来计算。
• d:代表日。
• w:计算结果，代表星期几。
public String dayOfTheWeek3(int day, int month, int year) {
String[] week = { "Sunday", "Monday", "Tuesday",
"Wednesday", "Thursday", "Friday", "Saturday" };
//如果月份小于3月，则月份加12，年份减1
if (month < 3) {
month += 12;
year -= 1;
}
int J = year / 100; // 世纪，年份前两位
int K = year % 100; // 年份，年份后两位
int h = (K + K / 4 + J / 4 - 2 * J +
26 * (month + 1) / 10 + day - 1) % 7;
// h算出来可能为负数，需要补7后再取一次余
return week[(h + 7) % 7];
}
## 第四种解法
Week = (Day + 2*Month + 3*(Month+1)/5 + Year + Year/4 - Year/100 + Year/400) % 7;
public String dayOfTheWeek4(int day, int month, int year) {
String[] week = {"Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday", "Sunday"};
if (month < 3) {
month += 12;
year -= 1;
}
int w = (day + 2*month + 3*(month+1)/5 +
year + year/4 - year/100 + year/400) % 7;
return week[w];
}
## 小结
posted @ 2019-09-26 08:33 程序员小川 阅读(...) 评论(...编辑 收藏
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