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https://rjallain.medium.com/is-a-50-mph-50-mph-collision-the-same-as-a-100-0-mph-collision-27c0d4391512?source=read_next_recirc-----dfe5b2f474f0----0---------------------dbbec435_f5ae_4b60_a3bd_fbed58cd2424-------&responsesOpen=true&sortBy=REVERSE_CHRON | 1,718,520,864,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861643.92/warc/CC-MAIN-20240616043719-20240616073719-00569.warc.gz | 444,699,880 | 23,527 | # Is a 50 mph-50 mph Collision the Same as a 100–0 mph Collision?
A long time ago there was a MythBusters episode that looked at head to head crashing cars. Suppose you have two equal mass cars both traveling with a speed of 50 mph and they crash (don’t worry, no one is in the cars). Would this cause the same amount of damage as a car going 100 mph and crashing into a wall? It’s time for some physics.
# Basic 1D Collision
--
--
Physics faculty, science blogger of all things geek. Technical Consultant for CBS MacGyver and MythBusters. WIRED blogger. | 137 | 559 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-26 | latest | en | 0.935932 |
http://www.geeksforgeeks.org/super-ugly-number-number-whose-prime-factors-given-set/ | 1,513,380,506,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948580416.55/warc/CC-MAIN-20171215231248-20171216013248-00449.warc.gz | 392,158,639 | 17,911 | # Super Ugly Number (Number whose prime factors are in given set)
Super ugly numbers are positive numbers whose all prime factors are in the given prime list. Given a number n, the task is to find n’th Super Ugly number.
It may be assumed that given set of primes is sorted. Also, first Super Ugly number is 1 by convention.
Examples:
Input : primes[] = [2, 5]
n = 5
Output : 8
Super Ugly numbers with given prime factors
are 1, 2, 4, 5, 8, ...
Fifth Super Ugly number is 8
Input : primes[] = [2, 3, 5]
n = 50
Output : 243
Input : primes[] = [3, 5, 7, 11, 13]
n = 9
Output: 21
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
In our previous post we discussed about Ugly Number. This problem is basically extension of Ugly Numbers.
A simple solution for this problem is to one by one pick each number starting from 1 and find its all primes factors, if all prime factors lie in the given set of primes that means number is Super Ugly. Repeat this process until we get n’th Super Ugly Number .
An efficient solution for this problem is similar to Method-2 of Ugly Number. Here is the algorithm :
1. Let k be size of given array of prime numbers.
2. Declare a set for super ugly numbers.
3. Insert first ugly number (which is always 1) into set.
4. Initialize array multiple_of[k] of size k with 0. Each element of this array is iterator for corresponding prime in primes[k] array.
5. Initialize nextMultipe[k] array with primes[k]. This array behaves like next multiple variables of each prime in given primes[k] array i.e; nextMultiple[i] = primes[i] * ugly[++multiple_of[i]].
6. Now loop until there are n elements in set ugly.
a). Find minimum among current multiples of primes in nextMultiple[] array and insert it in the set of ugly numbers.
b). Then find this current minimum is multiple of which prime .
c). Increase iterator by 1 i.e; ++multiple_Of[i], for next multiple of current selected prime and update nextMultiple for it.
Below is implementation of above steps.
// C++ program to find n'th Super Ugly number
#include<bits/stdc++.h>
using namespace std;
// Function to get the nth super ugly number
// primes[] --> given list of primes f size k
// ugly --> set which holds all super ugly
// numbers from 1 to n
// k --> Size of prime[]
int superUgly(int n, int primes[], int k)
{
// nextMultiple holds multiples of given primes
vector<int> nextMultiple(primes, primes+k);
// To store iterators of all primes
int multiple_Of[k];
memset(multiple_Of, 0, sizeof(multiple_Of));
// Create a set to store super ugly numbers and
// store first Super ugly number
set<int> ugly;
ugly.insert(1);
// loop until there are total n Super ugly numbers
// in set
while (ugly.size() != n)
{
// Find minimum element among all current
// multiples of given prime
int next_ugly_no = *min_element(nextMultiple.begin(),
nextMultiple.end());
// insert this super ugly number in set
ugly.insert(next_ugly_no);
// loop to find current minimum is multiple
// of which prime
for (int j=0; j<k; j++)
{
if (next_ugly_no == nextMultiple[j])
{
// increase iterator by one for next multiple
// of current prime
multiple_Of[j]++;
// this loop is similar to find dp[++index[j]]
// it --> dp[++index[j]]
set<int>::iterator it = ugly.begin();
for (int i=1; i<=multiple_Of[j]; i++)
it++;
nextMultiple[j] = primes[j] * (*it);
break;
}
}
}
// n'th super ugly number
set<int>::iterator it = ugly.end();
it--;
return *it;
}
/* Driver program to test above functions */
int main()
{
int primes[] = {2, 5};
int k = sizeof(primes)/sizeof(primes[0]);
int n = 5;
cout << superUgly(n, primes, k);
return 0;
}
Output:
8
This article is contributed by Shashank Mishra ( Gullu ). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
# GATE CS Corner Company Wise Coding Practice
Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.
3.2 Average Difficulty : 3.2/5.0
Based on 23 vote(s) | 1,094 | 4,216 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2017-51 | latest | en | 0.864787 |
https://quizizz.com/admin/quiz/6141f53ab9f597001dbaa886/quiz-2-math-7-set-theory | 1,720,834,969,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514459.28/warc/CC-MAIN-20240712224556-20240713014556-00397.warc.gz | 405,844,711 | 30,034 | # Quiz #2 - Math 7 Set Theory
## 15 questions
See Preview
• 1. Multiple Choice
2 minutes
1 pt
In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group (Assume that each student in the group plays at least one game).
100
105
110
120
• 2. Multiple Choice
1 minute
1 pt
Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).
9
10
11
12
• 3. Multiple Choice
1 minute
1 pt
How many students like blue color?
21
24
25
28 | 207 | 660 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2024-30 | latest | en | 0.851589 |
http://slideplayer.com/slide/4945921/ | 1,571,132,719,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986657949.34/warc/CC-MAIN-20191015082202-20191015105702-00454.warc.gz | 175,448,235 | 18,324 | First Order Circuit Capacitors and inductors RC and RL circuits.
Presentation on theme: "First Order Circuit Capacitors and inductors RC and RL circuits."— Presentation transcript:
First Order Circuit Capacitors and inductors RC and RL circuits
RC and RL circuits (first order circuits) Circuits containing no independent sources Circuits containing independent sources Complete response = Natural response + forced response ‘source-free’ circuits Excitation from stored energy Natural response DC source (voltage or current source) Sources are modeled by step functions Step response Forced response
RC circuit – natural response Assume that capacitor is initially charged at t = 0 v c (0) = V o Taking KCL, Objective of analysis: to find expression for v c (t) for t >0 i.e. to get the voltage response of the circuit +vc+vc icic iRiR R C OR
RC circuit – natural response Can be written as , = RC time constant This response is known as the natural response Voltage decays to zero exponentially At t= , v c (t) decays to 37.68% of its initial value The smaller the time constant the faster the decay VoVo t= t v C (t) 0.3768V o
RC circuit – natural response The capacitor current is given by: And the current through the resistor is given by The power absorbed by the resistor can be calculated as: The energy loss (as heat) in the resistor from 0 to t:
RC circuit – natural response As t , E R As t , energy initially stored in capacitor will be dissipated in the resistor in the form of heat
RC circuit – natural response PSpice simulation +vc+vc icic iRiR R C 0 1 RC circuit c1 1 0 1e-6 IC=100 r1 1 0 1000.tran 7e-6 7e-3 0 7e-6 UIC.probe.end
RC circuit – natural response PSpice simulation +vc+vc icic iRiR R C 0 1 RC circuit.param c=1 c1 1 0 {c} IC=100 r1 1 0 1000.step param c list 0.5e-6 1e-6 3e-6.tran 7e-6 7e-3 0 7e-6.probe.end c1 = 3e-6 c1 = 1e-6 c1 = 0.5e-6
RL circuit – natural response Assume initial magnetic energy stored in L at t = 0 i L (0) = I o Taking KVL, Objective of analysis: to find expression for i L (t) for t >0 i.e. to get the current response of the circuit iLiL vL+vL+ R L +vR+vR OR
RL circuit – natural response Can be written as , = L/R time constant This response is known as the natural response Current exponentially decays to zero At t= , i L (t) decays to 37.68% of its initial value The smaller the time constant the faster the decay IoIo t= t i L (t) 0.3768I o
RL circuit – natural response The inductor voltage is given by: And the voltage across the resistor is given by The power absorbed by the resistor can be calculated as: The energy loss (as heat) in the resistor from 0 to t:
RL circuit – natural response As t , E R As t , energy initially stored in inductor will be dissipated in the resistor in the form of heat
RL circuit – natural response PSpice simulation 0 1 RL circuit L1 0 1 1 IC=10 r1 1 0 1000.tran 7e-6 7e-3 0 7e-6 UIC.probe.end vL+vL+ R L +vR+vR
RL circuit – natural response PSpice simulation L1 = 3H L1 = 1H L1 = 0.5H RL circuit.param L=1H L1 0 1 {L} IC=10 r1 1 0 1000.step param L list 0.3 1 3.tran 7e-6 7e-3 0 7e-6 UIC.probe.end 0 1 vL+vL+ R L +vR+vR
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https://justaaa.com/statistics-and-probability/1076734-it-is-very-common-for-television-series-to-draw-a | 1,717,015,806,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059408.76/warc/CC-MAIN-20240529200239-20240529230239-00829.warc.gz | 287,353,617 | 9,055 | Question
It is very common for television series to draw a large audience for special events of...
It is very common for television series to draw a large audience for special events of for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 42% of all US TV households. Suppose that three TV households are randomly selected. What is the probability that none of the three households viewed this special show?
Let , X be the number of households viewed special show.
P = 0.42 , n = 3
X follows Binomial distribution with n = 3 and p = 0..42
We have to find probability that none of the three households viewed this special show.
In notation we have to find P( x = 0 )
Formula for Binomial distribution ,
,
The probability that none of the three households viewed this special show is 0.1951 | 186 | 851 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2024-22 | latest | en | 0.976414 |
https://kamus.sabda.org/dictionary/numerical | 1,709,349,458,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475727.3/warc/CC-MAIN-20240302020802-20240302050802-00364.warc.gz | 326,713,667 | 5,919 | POS
HYPHEN
WORDNET DICTIONARY
CIDE DICTIONARY
OXFORD DICTIONARY
THESAURUS
ROGET THESAURUS
# numerical
RELATED WORD :
:
:
nu=mer=i=cal
## CIDE DICTIONARY
numericala. [Cf. F. numérique. See Number, n.].
• Belonging to number; denoting number; consisting in numbers; expressed by numbers, and not letters; as, numerical characters; a numerical equation; a numerical statement. [1913 Webster]
" Numerical, as opposed to algebraical, is used to denote a value irrespective of its sign; thus, -5 is numerically greater than -3, though algebraically less." [1913 Webster]
• The same in number; hence, identically the same; identical; as, the same numerical body. South. [1913 Webster]
"Would to God that all my fellow brethren, which with me bemoan the loss of their books, . . . might rejoice for the recovery thereof, though not the same numerical volumes." [1913 Webster]
• relating to or having ability to think in or work with numbers; as, tests for rating numerical aptitude. Contrasted with verbal. [WordNet 1.5]
Numerical equation (Alg.), an equation which has all the quantities except the unknown expressed in numbers; -- distinguished from literal equation. -- Numerical value of an equation or expression, that deduced by substituting numbers for the letters, and reducing.
## OXFORD DICTIONARY
numerical, adj. (also numeric) of or relating to a number or numbers (numerical superiority).
Idiom
numerical analysis the branch of mathematics that deals with the development and use of numerical methods for solving problems.
Derivative
Etymology
med.L numericus (as NUMBER)
## THESAURUS
### numerical
algebraic, algorismic, algorithmic, aliquot, analytic, cardinal, decimal, differential, digital, even, exponential, figural, figurate, figurative, finite, fractional, geometric, imaginary, impair, impossible, infinite, integral, irrational, logarithmic, logometric, mathematical, negative, numeral, numerary, numerative, numeric, odd, ordinal, pair, positive, possible, prime, radical, rational, real, reciprocal, submultiple, surd, transcendental
## ROGET THESAURUS
### Numeration
N numeration, numbering, pagination, tale, recension, enumeration, summation, reckoning, computation, supputation, calculation, calculus, algorithm, algorism, rhabdology, dactylonomy, measurement, statistics, arithmetic, analysis, algebra, geometry, analytical geometry, fluxions, differential calculus, integral calculus, infinitesimal calculus, calculus of differences, dead reckoning, muster, poll, census, capitation, roll call, recapitulation, account, notation, addition, subtraction, multiplication, division, rule of three, practice, equations, extraction of roots, reduction, involution, evolution, estimation, approximation, interpolation, differentiation, integration, abacus, logometer, slide rule, slipstick, tallies, Napier's bones, calculating machine, difference engine, suan- pan, adding machine, cash register, electronic calculator, calculator, computer, arithmetician, calculator, abacist, algebraist, mathematician, statistician, geometer, programmer, accountant, auditor, numeral, numerical, arithmetical, analytic, algebraic, statistical, numerable, computable, calculable, commensurable, commensurate, incommensurable, incommensurate, innumerable, unfathomable, infinite, quantitatively, arithmetically, measurably, in numbers.
See related words and definitions of word "numerical" in Indonesian
copyright © 2012 Yayasan Lembaga SABDA (YLSA) | To report a problem/suggestion | 855 | 3,508 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2024-10 | latest | en | 0.760829 |
https://ch.mathworks.com/matlabcentral/cody/problems/44350-breaking-out-of-the-matrix/solutions/1312173 | 1,576,241,966,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540555616.2/warc/CC-MAIN-20191213122716-20191213150716-00222.warc.gz | 321,723,551 | 15,966 | Cody
# Problem 44350. Breaking Out of the Matrix
Solution 1312173
Submitted on 24 Oct 2017 by cokakola
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
M=[1 4 7 10; 2 5 8 11; 3 6 9 12]; R=2;C=3; X(:,:,1) =[1 4 7 ; 2 5 8]; X(:,:,2) =[2 5 8 ; 3 6 9]; X(:,:,3) =[4 7 10 ; 5 8 11]; X(:,:,4) =[5 8 11 ; 6 9 12]; assert(isequal(BreakTheMatrix(M,R,C),X))
ss changed
2 Pass
x=1:ceil(35+25*rand());r=1;c=1; M=BreakTheMatrix(x,r,c); assert(all(arrayfun(@(y) (M(:,:,y)==y),1:numel(x))))
3 Pass
x=eye(7);r=2;c=2; M=BreakTheMatrix(x,r,c); ids=[1 8 15 22 29 36]; urs=ids(1:5)+1; lls=urs+5; z=setxor(1:size(M,3),[ids urs lls]); a1=arrayfun(@(a) isequal(M(:,:,a),eye(2)),ids); a2=arrayfun(@(a) isequal(M(:,:,a),[0 1 ; 0 0]),urs); a3=arrayfun(@(a) isequal(M(:,:,a),[0 0 ; 1 0]),lls); a4=arrayfun(@(a) isequal(M(:,:,a),zeros(2)),z); assert(all([a1 a2 a3 a4]))
4 Pass
u=ceil(10*rand())+4; x=magic(u);r=u;c=u; M=BreakTheMatrix(x,r,c); assert(isequal(M,x))
5 Pass
temp=ceil(8*rand)+3; x=ones(temp);r=2;c=2; M=BreakTheMatrix(x,r,c); assert(size(M,3)==(temp-1)^2); assert(all(arrayfun(@(a) isequal(M(:,:,a),ones(2)),1:size(M,3))))
6 Pass
x=eye(7);r=7;c=7; assert(isequal(x,BreakTheMatrix(x,r,c))) | 567 | 1,311 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2019-51 | latest | en | 0.402259 |
https://practicaldev-herokuapp-com.global.ssl.fastly.net/doziestar/handle-errors-in-go-like-a-pro-27m4?comments_sort=latest | 1,686,029,088,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652235.2/warc/CC-MAIN-20230606045924-20230606075924-00252.warc.gz | 503,779,693 | 21,228 | ## DEV Community
Chidozie C. Okafor
Posted on • Originally published at doziestar.Medium on
# Handle Errors In Go Like A Pro.
Error handling is an important aspect of any software development process, and Go provides a few different ways to handle errors in your code.
In Go, errors are represented by the error interface, which is defined as follows:
``````type error interface {
Error() string
}
``````
The Error() method returns a string that describes the error. To create an error, you can use the errors.New() function, which takes a string as an argument and returns an error value.
For example, consider a function that divides two integers, and returns an error if the denominator is zero:
``````package main
import (
"fmt"
"errors"
)
func divide(a, b int) (int, error) {
if b == 0 {
return 0, errors.New("division by zero")
}
return a / b, nil
}
func main() {
result, err := divide(5, 0)
if err != nil {
fmt.Println("Error:", err)
} else {
fmt.Println("Result:", result)
}
}
``````
In the above example, the divide() function returns an error when the denominator is zero. In the main() function, we use the if err != nil idiom to check whether an error occurred, and print an error message if it did.
An alternate way of handling errors is to return multiple values instead of error. For example
``````package main
import "fmt"
func divide(a, b int) (result int, ok bool) {
if b == 0 {
return
}
result = a / b
ok = true
return
}
func main() {
result, ok := divide(5, 0)
if !ok {
fmt.Println("Error: Division by zero")
} else {
fmt.Println("Result:", result)
}
}
``````
In this case we returned two values from divide function, the result of division and a boolean flag. In this case, the boolean flag indicates whether the operation was successful or not.
Another way is to use ‘defer’ statement, it allows you to run a function after the function it was called in has returned.
``````package main
import (
"fmt"
"os"
)
func doSomething() {
defer func() {
if r := recover(); r != nil {
fmt.Println("Recovering from error:", r)
}
}()
// do something that might panic
panic("Something went wrong")
}
func main() {
doSomething()
fmt.Println("This statement will run after panic")
os.Exit(0)
}
``````
In the above example, the recover() function is used to catch a panic and prevent the program from crashing. The defer statement is used to ensure that the recover function runs after the function it was called from has returned. This way, you can use 'defer' statement to handle errors and continue the execution.
It’s important to handle errors properly in your Go code because it helps prevent unexpected behavior and crashes, and makes it easier to debug and fix problems when they occur. Additionally, by handling errors in a consistent and predictable way, you can make your code more robust and reliable.
Another way of handling error is to use custom error types, which allow you to provide more detailed information about an error and also to give you more control over how the error is handled. For example:
``````package main
import "fmt"
type DivideError struct {
a, b int
msg string
}
func (e *DivideError) Error() string {
return fmt.Sprintf("%d / %d: %s", e.a, e.b, e.msg)
}
func divide(a, b int) (int, error) {
if b == 0 {
return 0, &DivideError{a, b, "division by zero"}
}
return a / b, nil
}
func main() {
result, err := divide(5, 0)
if err != nil {
fmt.Println("Error:", err)
} else {
fmt.Println("Result:", result)
}
}
``````
Here we created a custom error type DivideError with fields for the input values and an error message. The Error() method returns a string that includes this information. In the divide function, we create an instance of the DivideError type and return it as an error. In the main function we are able to print the custom error message, which would give more detailed information about the error than just a simple string.
One robust approach to error handling in Go is to use a package such as errors which provides additional functionality for working with errors. This package allows you to attach additional context to an error, such as a stack trace or a cause, and also provides a way to wrap existing errors.
For example, consider a function that opens a file, reads its contents, and returns an error if the file could not be opened or read:
``````package main
import (
"fmt"
"os"
"errors"
)
func readFile(filename string) (string, error) {
file, err := os.Open(filename)
if err != nil {
return "", errors.Wrap(err, "could not open file")
}
defer file.Close()
data := make([]byte, 100)
count, err := file.Read(data)
if err != nil {
return "", errors.Wrap(err, "could not read file")
}
return string(data[:count]), nil
}
func main() {
result, err := readFile("file.txt")
if err != nil {
fmt.Println("Error:", err)
} else {
fmt.Println("Result:", result)
}
}
``````
In the above example, we’re using the errors.Wrap function to attach an additional message to the error returned by the os.Open and file.Read functions. When the error is printed, it includes the original error message as well as the additional message, providing more context about the error.
``````Error: could not read file: input/output error
``````
Another useful function from this package is errors.Cause, which will traverse the error and its wrapped errors and return the original error that caused the problem. This can be particularly useful when handling errors that may have been wrapped multiple times, it allow you to access the original error and make decision accordingly.
In addition to errors.Wrap and errors.Cause, this package also provides several other functions for creating and working with errors, such as errors.New, errors.Errorf, and errors.WithStack. These functions provide a more robust and powerful way to handle errors in your Go code, making it easier to attach additional context, debug issues, and maintain your application.
It’s worth noting that custom error types can also be built on top of this package and combine its functions with the additional error information you want to show.
Overall, using a package like errors can be a great way to improve the robustness and maintainability of your Go code by providing a more powerful way to handle errors, give more detailed information and make it easier to debug issues when they occur.
For Try-Catch Lovers:
Go does not have a built-in try-catch mechanism like some other programming languages, and Go’s approach to error handling is based on returning error values from functions. However, you can achieve similar behavior by using the defer, panic, and recover functions.
The defer statement allows you to schedule a function to be called after the surrounding function has returned. The panic function causes the current function to stop executing and begins unwinding the call stack. The recover function can be used inside a deferred function to catch panics and return from the surrounding function.
Let’s look at an example that demonstrates how to use the defer, panic, and recover functions to create a try-catch block in Go:
``````package main
func readFile() (string, error) {
// some code that might cause an error
return "", fmt.Errorf("An error has occurred")
}
func main() {
defer func() {
if r := recover(); r != nil {
fmt.Println("Recovering from error:", r)
}
}()
result, err := readFile()
if err != nil {
panic(err)
}
fmt.Println(result)
}
``````
In the above example, the defer statement schedules a function to be called after main has returned. Inside that function, we use recover() to catch any panics that occur in main and return from the function gracefully.
In the main function, we call the readFile function and check for an error. If an error occurs, we use panic(err) to stop the execution of main and start the panic unwinding.
In this way, you can use the defer, panic, and recover functions to create a try-catch block in Go. It's worth noting that this approach should be used carefully, as the use of panic and recover can make the code more complex and harder to debug if not used properly. It's recommended to use them only in specific cases where you want to stop the program execution and be able to handle it in the deferred function.
In general, Go’s error handling approach based on returning error values from functions is a more robust and maintainable way to handle errors, and it is recommended to use it for most cases. | 1,891 | 8,444 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2023-23 | latest | en | 0.627304 |
https://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-2nd-edition/chapter-7-integration-techniques-7-5-partial-fractions-7-5-exercises-page-549/8 | 1,537,594,278,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267158045.57/warc/CC-MAIN-20180922044853-20180922065253-00266.warc.gz | 759,255,232 | 13,503 | ## Calculus: Early Transcendentals (2nd Edition)
$$\frac{{10}}{x} + \frac{1}{{x - 1}}$$
\eqalign{ & \frac{{11x - 10}}{{{x^2} - x}} \cr & {\text{factoring}} \cr & = \frac{{11x - 10}}{{x\left( {x - 1} \right)}} \cr & {\text{partial fraction decomposition}} \cr & \frac{{11x - 10}}{{x\left( {x - 1} \right)}} = \frac{A}{x} + \frac{B}{{x - 1}} \cr & 11x - 10 = A\left( {x - 1} \right) + Bx \cr & {\text{letting }}x = 0 \cr & - 10 = A\left( { - 1} \right) \cr & 10 = A \cr & {\text{letting }}x = 1 \cr & 11 - 10 = A\left( {1 - 1} \right) + B\left( 1 \right) \cr & 1 = B \cr & {\text{substituting the values}} \cr & \frac{A}{x} + \frac{B}{{x - 1}} = \frac{{10}}{x} + \frac{1}{{x - 1}} \cr} | 325 | 684 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2018-39 | longest | en | 0.280306 |
http://www.astronomyforum.net/telescope-eyepieces-forum/83411-afov-question.html | 1,582,597,383,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146004.9/warc/CC-MAIN-20200225014941-20200225044941-00049.warc.gz | 170,013,804 | 13,222 | 1. ## AFOV question
I want to understand the value of say a Naegler (sp?) eyepiece. I have a scope with a 1200mm focal lenght. I'd like to get an eyepiece that will give me a really wide view of the sky. I know that the higher the focal length of the eyepiece the higher the magnification. And that to find the magnification I divide the focal length of the scope by the focal length of the eyepiece. But the FOV. I divide the magnification by the FOV? So if I have a 1200 mm scope with a 25 mm ep, I get 48x. If the eyepiece is 50mm FOV, I roughly have 1 degree of Actual FOV? Seems narrow.
With a 1200 mm FL scope, what would be a good eyepiece setting to get in a wide sky view?
2. So what you are looking at is the TFOV (True Field of View) which is the actual width of the section of sky that appears in your view as related to the AFOV (apparent field of view, or sometimes called angular field of view) which is the angular width of that section of sky as it is distributed across the EP.
There are three different methods available to calculate TFOV
In the first, you need to calculate the magnification of the EP which is the FL (Focal Length) of the scope divided by the EPFL (Eye Piece Focal Length), which also demonstrates that the longer the EPFL the lower the mag
Now by dividing the AFOV as specified by the EP manufacturer by the mag you will get a value for the TFOV
This method is not particularly accurate, and could have an error as much as 10%, but does serve as a quick comparison of EPs and does also serve to demonstrate that for any given EP, shorter scope FLs give wider fields, or if you like, for any given scope lower mags give wider fields.
The second method is to bring the EPs field stop into play. The field stop is the diameter of the aperture of the bottom lens in the EP, or if you like, the aperture that lets the light into the EP. Some manufacturers specify this, but its easy enough to measure anyhow.
In this case the TFOV is the (Diameter of the field stop/focal length of the scope) x 57.3 where 57.3 is the rounded off value of a radian in degrees ie 180/Pi
This method is more accurate, say an error of no more than about 2%, but again demonstrates that for any given EP, shorter scope FLs give wider TFOVs, or also since the longer the EPFL the wider the field stop, also shows that lower mags give wider TFOVs
The third, and most accurate method (and I include this mainly just out of interest) is by Star Drift.
Here you need to focus your scope on a known star (you need to know its Dec) and then move the scope so that the star drifts from one edge of the FOV, through the centre and to the other edge (ie along the diameter of the field of view) with the scope stationary. By timing this drift say 5 or 10 times then taking an average time for its drift you can use this equation
TFOV = [(drift time) x cos(dec of star) x 360] / 86,164 where 86,164 is the number of seconds in a day
.................................................. ........................................
To get the widest TFOV possible with a given FL of scope you need to go to the lowest practical mag with the widest AFOV EP available.
I can't afford Naglers, not many of us can, but if your scope accepts 2" EPs there are various EPs available at around 70° AFOV at budget prices
So say a 38mm 70° AFOV 2" ep will give a TFOV of roughly 2.1° in your scope, or a 32mm would give about 1.9°
3. Very good information, Vinnie, thanks. I am looking into some more EP's soon, but no Naglers for me, too rich for my blood. | 905 | 3,560 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2020-10 | latest | en | 0.960875 |
https://www.studyguide360.com/2020/07/rd-sharma-solutions-class-8-maths-chapter-15-understanding-shapes-polygons.html | 1,721,871,628,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518532.61/warc/CC-MAIN-20240724232540-20240725022540-00118.warc.gz | 860,472,899 | 33,547 | ## RD Sharma Solutions for Class 8 Chapter 15 Understanding Shapes- I (Polygons) Free Online
EXERCISE 15.1 PAGE NO: 15.5
1. Draw rough diagrams to illustrate the following:
(i) Open curve
(ii) Closed curve
Solution:
Here is the illustration of
(i) Open curve
(ii) Closed curve
2. Classify the following curves as open or closed:
Solution:
(i) Open curve
(ii) Closed curve
(iii) Closed curve
(iv) Open curve
(v) Open curve
(vi) Closed curve
3. Draw a polygon and shade its interior. Also draw its diagonals, if any.
Solution:
Here is the polygon with diagonals and with its interior shaded.
4. Illustrate, if possible each one of the following with a rough diagram.
(i) A closed curve that is not a polygon.
(ii) An open curve made up entirely of line segments.
(iii) A polygon with two sides.
Solution:
(i) A closed curve that is not a polygon.
(ii) An open curve made up entirely of line segments.
(iii) A polygon with two sides.
A polygon with two sides is not possible because, a polygon should have minimum three sides.
5. Following are some figures: Classify each of these figures on the basis of the following:
(i) Simple curve (ii) Simple closed curve (iii) Polygon
(iv) Convex polygon (v) Concave polygon (vi) Not a curve
Solution:
(i) It is a Simple Closed curve and a concave polygon. This is a simple closed curve and as a concave polygon all the vertices are not pointing outwards.
(ii) It is a Simple closed curve and a convex polygon. This is a simple closed curve and as a convex polygon all the vertices are pointing outwards.
(iii) It is Not a curve and hence it is not a polygon.
(iv) It is Not a curve and hence it is not a polygon.
(v) It is a Simple closed curve but not a polygon.
(vi) It is a Simple closed curve but not a polygon.
(vii) It is a Simple closed curve but not a polygon.
(viii) It is a Simple closed curve but not a polygon.
6. How many diagonals does each of the following have?
(ii) A regular hexagon
(iii) A triangle
Solution:
For a convex quadrilateral we shall use the formula n(n-3)/2
So, number of diagonals = 4(4-3)/2 = 4/2 = 2
A convex quadrilateral has 2 diagonals.
(ii) A regular hexagon
For a regular hexagon we shall use the formula n(n-3)/2
So, number of diagonals = 6(6-3)/2 = 18/2 = 9
A regular hexagon has 9 diagonals.
(iii) A triangle
For a triangle we shall use the formula n(n-3)/2
So, number of diagonals = 3(3-3)/2 = 0/2 = 0
A triangle has no diagonals.
7. What is a regular polygon? State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides
Solution:
Regular Polygon: A regular polygon is an enclosed figure. In a regular polygon minimum sides are three.
(i) 3 sides
A regular polygon with 3 sides is known as Equilateral triangle.
(ii) 4 sides
A regular polygon with 4 sides is known as Rhombus.
(iii) 6 sides
A regular polygon with 6 sides is known as Regular hexagon.
Courtesy : CBSE | 778 | 2,867 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2024-30 | latest | en | 0.939694 |
https://www.reference.com/world-view/derivative-square-root-x-493831adf3911519 | 1,627,627,193,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153934.85/warc/CC-MAIN-20210730060435-20210730090435-00091.warc.gz | 998,836,549 | 39,253 | # What Is the Derivative of the Square Root of X?
Alex Belomlinsky/Digital Vision Vectors/Getty Images
The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half. | 64 | 259 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-31 | longest | en | 0.914078 |
http://lensocom.com/word-problems-multiplication-and-division-grade-3/4th-grade-math-fraction-word-problems-how-to-solve-a-multiplication-problem-words-for-multiply-free-printable-math-word-problem-worksheets-problems-with-the-division-3/ | 1,556,250,645,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578759182.92/warc/CC-MAIN-20190426033614-20190426055309-00047.warc.gz | 102,894,026 | 16,883 | # 4th Grade Math Fraction Word Problems How To Solve A Multiplication Problem Words For Multiply Free Printable Math Word Problem Worksheets Problems With The Division
Published at Tuesday, 26 March 2019. division. By .
Fun. Invent math games that will not only spark the interest of your students but will also make them enjoy playing these games. You can create games using common items such as crayons, chairs, pencils, books and toys. Counting. The most basic math concept that kids should learn is counting. Teach them the ability to count and the skill to identify numbers and symbols. Without this knowledge it will be hard for them to understand math at all. Equipping them with this ability will prepare them for the four basic math operations: addition, multiplication, subtraction and division.
Multiplication. To teach multiplication you need to start by teaching them as addition. To show them how to get the product of 2 * 3 = 2+2+2 = 6 or 2 * 3 = 3 + 3 = 6. Once the kids get the concept of adding same numbers to get a product they will be able to move on to larger numbers. Of course, it would not hurt to have them memorize the multiplication tables but it will also be helpful to teach them some tricks (finger trick for the 9 times table) to make memorizing fun for them.
Online math software can be an effective way to practice at home, as math programs provide a steady source of new problems for children. Many modern math programs also use adaptive learning techniques to automatically change the types of problems that the child sees to adapt to his or her strengths and weaknesses. Your child will be consistently challenged and encouraged, which should lead to steady improvement. At the same time, past lessons will occasionally be revisited. This prevents your child from forgetting basic concepts that will be used in future lessons, thereby making every subsequent lesson somewhat easier.
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## math worksheets fractions multiplication and division
### Comments of word problems multiplication and division grade 3
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Copyright © 2019 lensocom. All Rights Reserved. | 575 | 2,789 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2019-18 | latest | en | 0.938337 |
https://resources.quizalize.com/view/quiz/dynamics-41e4381c-3b0c-41e9-8417-c4a6f923a9cd | 1,679,859,090,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00363.warc.gz | 555,257,374 | 17,835 | Dynamics
Quiz by Marquita Holmes
Feel free to use or edit a copy
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24 questions
• Q1
The branch of mechanics concerned with the motion of bodies under the action of forces
Dynamics
30s
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• Q2
A ____________ is a push or a pull that causes an objet to move or stop or change
force
30s
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• Q3
When two forces are acting on an object are equal in size and do not cause a change in motion
Balanced Forces
30s
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• Q4
When two forces acting on an object are not equal in size
Unbalanced Forces
30s
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• Q5
Resistence to change in motion
Inertia
30s
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• Q6
___________ is a measure of the matter in an object
Mass
30s
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• Q7
______________ is the force of gravity on an object
Weight
30s
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• Q8
A condition where in the only force acting upon an object is gravity
Free Fall
30s
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• Q9
Pushes and pulls that result from direct touching of objects
Contact Force
30s
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• Q10
A force that is applied to an object by a person or another object
Applied Force
30s
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• Q11
A pulling force exerted by a string, cable, chain, or similar solid object on another object
Tension Force
30s
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• Q12
A force that opposes motion between two surfaces that are touching
Friction
30s
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• Q13
The total amount of force acting on an object, from the sum of forces.
Net Force
30s
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• Q14
The weight force pulling down on a mass in Newtons
W = mg
30s
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• Q15
The friction on an object when it's moving.
Kinetic friction
30s
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• Q16
The friction on an object where the object is at rest
Static friction
30s
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• Q17
The force that is perpendicular to the surface the object is resting on
Normal Force
30s
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• Q18
A number that is proportional to the friction between two objects / surfaces
Coefficient of Friction
30s
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• Q19
An object stays in motion with constant linear velocity until acted on by an outside force.
Newton's 1st law
30s
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• Q20
An unbalanced force will cause an acceleration, and force = ma
Newton's 2nd law
30s
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Teachers give this quiz to your class | 727 | 2,719 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2023-14 | latest | en | 0.906049 |
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistical_Thinking_for_the_21st_Century_(Poldrack)/02%3A_Working_with_Data | 1,726,657,782,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651895.12/warc/CC-MAIN-20240918100941-20240918130941-00159.warc.gz | 503,981,360 | 31,293 | # 2: Working with Data
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## Learning Objectives
Having read this chapter, you should be able to:
• Distinguish between different types of variables (quantitative/qualitative, binary/integer/real, discrete/continuous) and give examples of each of these kinds of variables
• Distinguish between the concepts of reliability and validity and apply each concept to a particular dataset
• 2.1: What Are Data?
The first important point about data is that data are - meaning that the word “data” is plural (though some people disagree with me on this). You might also wonder how to pronounce “data” – I say “day-tah” but I know many people who say “dah-tah” and I have been able to remain friends with them in spite of this. Now if I heard them say “the data is” then that would be bigger issue…
• 2.2: Discrete Versus Continuous Measurements
A discrete measurement is one that takes one of a set of particular values. These could be qualitative values (for example, different breeds of dogs) or numerical values (for example, how many friends one has on Facebook). A continuous measurement is one that is defined in terms of a real number. It could fall anywhere in a particular range of values, though usually our measurement tools will limit the precision with which we can measure. | 2,035 | 5,632 | {"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": 0, "mathjax_display_tex": 1, "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} | 2.984375 | 3 | CC-MAIN-2024-38 | latest | en | 0.197287 |
http://brainmass.com/math/graphs-and-functions/119350 | 1,386,401,945,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163053843/warc/CC-MAIN-20131204131733-00039-ip-10-33-133-15.ec2.internal.warc.gz | 26,395,889 | 5,843 | # Calculate and graph the height of cylinder
1). The volume of a cylinder (think about the volume of a can) is given by V = pir2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.
Write h as a function of r. Keep "pi" in the function's equation.
2). What is the measurement of the height if the radius of the cylinder is 2 centimeters? Round your answer.
a) Graph this function.
This question has the following supporting file(s):
###### File Viewer (Click To Zoom)
Solution Summary
The solution shows how to find the height of a cylinder as a function of its radius.
\$2.19 | 155 | 663 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2013-48 | latest | en | 0.927567 |
https://www.jiskha.com/display.cgi?id=1324573627 | 1,503,358,655,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886109682.23/warc/CC-MAIN-20170821232346-20170822012346-00661.warc.gz | 902,814,342 | 3,843 | # Geometry
posted by .
I don't undestand this question in my geometry textbook. Could nayone explain it to me?
Can you fit all of the interior angles of a quadrilateral around a point without overlap? What about the interior angles of a pentagon?
• Geometry -
The interior angles of a quadrilateral total to 180(4-2) = 360 degrees.
So, yes, they will exactly fit around a point.
However, for a pentagon, the angles total to 180(5-2) = 540 degrees, so there's no way you can draw all five angles around a point. There are only 360 degrees in a complete circle.
## Similar Questions
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More Similar Questions | 614 | 2,368 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2017-34 | latest | en | 0.893922 |
https://2021.help.altair.com/2021.2/hwsolvers/os/topics/solvers/os/analysis_prestressed_r.htm | 1,720,853,031,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514490.70/warc/CC-MAIN-20240713051758-20240713081758-00464.warc.gz | 61,269,115 | 16,522 | # Prestressed Linear Analysis
Preloaded or Prestressed Linear Analysis is any type of structural linear analysis performed on a structure under prior loading (also termed preloading or prestressing).
The response of a structure is affected by its initial state and this is in turn affected by the various preloading/prestressing applied to the structure, prior to the analysis of interest. Examples of prestressed linear analysis include analysis of rotorcraft blades under centrifugal preloading, pillar-like structures under compressive preloading, preload arising from the pretensioning of bolts on a structure, etc. OptiStruct can be used to take into account such preloading or prestressing effects.
Supported Prestressing/Preloading Loadcases
• Linear static
• Nonlinear quasi-static loadcases (Small and Large Displacement Nonlinear loadcases)
Prestressed/Preloaded Linear Analysis Loadcases
Linear statics, Normal modes, Complex eigenvalue, direct frequency response, modal frequency response, direct transient response, and modal transient response analyses. Preloading for a Component Mode Synthesis (CMSMETH) subcase is also supported.
Specifying preloading in any other unsupported subcase will generate an appropriate user error. Prestressing is specified through the STATSUB(PRELOAD) Case Control card, which refers to the preloading static loadcase ID. Nested preloading is not supported and will generate an appropriate user error (that is: User error will be reported if Subcase C has preloading from Subcase B, which in turn has preloading from Subcase A).
Prestressing Effect and Prestressed Stiffness Matrix
A prestressed stiffness matrix $\overline{K}$, instead of the original stiffness matrix $K$ of the unloaded structure, is used in the prestressed linear analysis to account for the prestressing effect.
When the prestressing subcase is a linear static one, the prestressing is captured or defined by a geometric stiffness matrix, ${K}_{\sigma }$ which is based on the stresses of the preloading static subcase. And this geometric stiffness matrix is augmented with the original stiffness matrix $K$ to form the prestressed stiffness matrix $\overline{K}$.(1) $\overline{K}=K+{K}_{\sigma }$
Depending on preloading conditions, the resulting effect could be a weakened or stiffened structure.
• If the preloading is compressive, it typically has a weakening effect on the structure (example: column or pillar under compressive preloading).
• If the preloading is tensile, it typically has a stiffening effect (example: rotorcraft blade under centrifugal preloading).
When the prestressing loadcase is a nonlinear quasi-static subcase, the prestressed stiffness matrix $\overline{K}$ does not only include the geometric stiffness matrix, ${K}_{\sigma }$ also accounts for the changes of $K$ due,
• Converged contact status
• Instantaneous elastic property
• Spin softening effect from centrifugal load
• Load stiffness effect from pressure and other follower forces
carried over from the prestressing loadcase to the prestressed loadcase. If the prestressing loadcase is an LGDISP quasi-static subcase, $\overline{K}$ is calculated based on the deformed configuration; otherwise, it is calculated based on the initial configuration.
The stiffness calculations in linear analysis preloaded with small displacement NLSTAT analysis can be controlled via PARAM, KSMNL4PL.
## Prestressed Linear Analysis Types
Below are the different prestressed linear analysis types.
### Static Analysis
Prestressed static analysis is governed by the following equation, where, $f$ is the load vector and $u$ is the displacement.(2) $\overline{K}u=f$
While linear static subcases can have prestressing, nonlinear static subcases under prestressing are not supported.
### Normal Modes Analysis
Prestressed eigenvalue analysis is governed by the following equation, where, $M$ is the mass matrix, $A$ is the eigenvector and $\lambda$ are the eigenvalues.(3) $\left(\overline{K}-\lambda M\right)A=0$
Prestressed eigenvalue analysis is currently supported by AMSES, AMLS and the Lanczos Method. However, if the specified preload is greater than the first critical buckling load, an appropriate error will be reported for AMSES/AMLS runs.
### Complex Eigenvalue Analysis
Prestressed Complex Eigenvalue Analysis is governed by the following equation, where, $M$ is the mass matrix, $A$ is the eigenvector, $C$ is the viscous damping matrix, ${C}_{GE}$ is the element structural damping matrix, ${\alpha }_{f}$ is the coefficient of the extra stiffness matrix, $\omega$ is the loading frequency, $g$ is the global structural damping coefficient, and ${K}_{f}$ is the extra stiffness matrix by direct matrix input.(4) $\left[{\omega }^{2}M+\omega C+\left(\overline{K}\left(1+ig\right)+i\sum {C}_{GE}+{\alpha }_{f}{K}_{f}\right)\right]A=0$
In addition to Prestressed Complex Eigenvalue Analysis implementation, Brake Squeal Analysis can be performed via the STATSUB(BRAKE) command, wherein the contribution of friction to the stiffness matrix is automatically included. For further information, refer to Brake Squeal Analysis in the User Guide.
### Direct Frequency Response Analysis
Prestressed direct FRF analysis is governed by the following equation, where, $M$ is the mass matrix, $u$ is the complex displacement vector, ${C}_{GE}$ is the material damping matrix, $C$ is the viscous damping matrix that includes the Area Matrix for fluid-structure coupling, $f$ is the loading vector, and $g$ is the structural damping.(5) $\left[\overline{K}+ig\overline{K}+i{C}_{GE}+i\omega C-{\omega }^{2}M\right]u=f$
### Modal Frequency Response Analysis
Prestressed modal FRF analysis is governed by the following equation, where, $M$ is the mass matrix, $u$ is the complex displacement vector and $d$ is its corresponding modal value, ${C}_{GE}$ is the material damping matrix, $C$ is the viscous damping matrix that includes the Area Matrix for fluid-structure coupling, $A$ is the set eigenvectors which includes normal modes and residual vectors, $f$ is the loading vector, $\omega$ is the loading frequency, and $g$ is the structural damping coefficient.(6) $\begin{array}{l}\left[{A}^{T}\overline{K}A+ig{A}^{T}\overline{K}A+i{A}^{T}{C}_{GE}A+i\omega {A}^{T}CA-{\omega }^{2}{A}^{T}MA\right]d={A}^{T}f\\ u=Ad\end{array}$
### Direct Transient Response Analysis
Prestressed direct transient analysis is governed by the following equation, where, $M$ is the mass matrix, $u$ is the displacement vector, $C$ is the viscous damping matrix - which also includes structural damping in an approximate way, and $f\left(t\right)$ is the transient load.(7) $M\stackrel{¨}{u}+C\stackrel{˙}{u}+\left(\overline{K}\right)u=f\left(t\right)$
### Modal Transient Response Analysis
Prestressed modal transient analysis is governed by the following equation, where, $M$ is the mass matrix, $u$ is the displacement vector; $d$ is its corresponding modal value, $C$ is the viscous damping matrix - which also includes structural damping in an approximate way, $A$ is the set eigenvectors which includes normal modes and residual vectors, and $f\left(t\right)$ is the transient load.(8) $\begin{array}{l}{A}^{T}MA\stackrel{¨}{u}+{A}^{T}CA\stackrel{˙}{u}+{A}^{T}\overline{K}Au={A}^{T}f\left(t\right)\\ u=Ad\end{array}$
### Component Mode Synthesis (CMSMETH) Subcase
Prestressed Component Mode Synthesis (CMS) uses ($\overline{K}$) as the stiffness matrix, with other aspects such as the mass and damping matrices remaining unchanged in order to calculate the static and normal modes for both flexible body generation (as an input to multibody dynamics) and direct matrix input generation (for external superelements). The primary effect of a preloaded/prestressed CMS analysis will be a frequency shift in the results.
## Results
All results that are supported for regular structural linear analyses are also available in the corresponding prestressed linear analyses.
It is important to note that, while the prestressed linear analysis includes the effects of preloading as a weakening or a stiffening of the structure, the results from the prestressed analysis do not include the preloading results. For example, the displacements from prestressed linear static analysis do not include the preloading displacements. In order to get the overall deflection/stresses of the structure, the displacements/stresses from the prestressed linear analyses have to be carefully superposed with the preloading displacements/stresses while post-processing. Particularly, while post-processing complex results from prestressed direct FRF, the correct approach would be to first obtain the complex results for a certain phase and then superpose the appropriate preloading result. Any other superposing approach would lead to incorrect results. | 2,052 | 8,832 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 56, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-30 | latest | en | 0.844752 |
https://becalculator.com/16-2-cm-to-inch-converter.html | 1,686,276,221,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224655244.74/warc/CC-MAIN-20230609000217-20230609030217-00433.warc.gz | 149,761,226 | 16,728 | # 16.2 cm to inch converter
## FAQs on 16.2 cm to inch
### How many inches is in a centimeter?
If you want to convert 16.2 cm to an inch-length number, first, you should know how many inches 1 cm is equal to.
Here’s what I can give you a direct indication that one cm is equivalent to 0.3937 inches.
### How do I convert 1 cm to inches?
For 1cm to inches conversion, multiply 1cm using a conversion factor 0.3937.
This allows you to easily convert 16.2cm into inches.
So 1 cm to inches = 1 times 0.3937 = 0.3937 inches.
This will allow you to answer the following question easily and quickly.
• What is one centimeter to inches?
• What is conversion rate cm to inches?
• What is the equivalent of 1 cm in inches?
• What does 1 cm equal in inches?
### Implication of centimeter
Centimeter is the International Standard Unit of Length. It is equal to one hundredth of a millimeter. It’s about the same as 39.37 inches.
### Meaning of Inch
The length units of the Anglo-American continent are measured in inches. 12 inches equals 1 foot, while 36 inches equals one yard. According to modern standards, one inch equals 2.54 cm.
### What is 16.2 cm converted to inches?
You now fully understand cm to inches by the above.
The following is the specific algorithm:
Value in inches = value in cm × 0.3937
So, 16.2 cm to inches = 16.2 cm × 0.3937 = 0.637794 inches
You can use this formula to answer related questions:
• What’s the formula to convert inches from 16.2 cm?
• How big is cm to inches?
• How can I change cm into inches?
• How to calculate cm to inches?
• Is 16.2 cm equal to how many inches?
cm inch 15.8 cm 0.622046 inch 15.85 cm 0.6240145 inch 15.9 cm 0.625983 inch 15.95 cm 0.6279515 inch 16 cm 0.62992 inch 16.05 cm 0.6318885 inch 16.1 cm 0.633857 inch 16.15 cm 0.6358255 inch 16.2 cm 0.637794 inch 16.25 cm 0.6397625 inch 16.3 cm 0.641731 inch 16.35 cm 0.6436995 inch 16.4 cm 0.645668 inch 16.45 cm 0.6476365 inch 16.5 cm 0.649605 inch 16.55 cm 0.6515735 inch
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https://community.powerbi.com/t5/Desktop/Date-calculating-differently-on-desktop-and-web-due-to/m-p/393995 | 1,591,515,672,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348523564.99/warc/CC-MAIN-20200607044626-20200607074626-00256.warc.gz | 307,527,472 | 97,983 | cancel
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Regular Visitor
## Date calculating differently on desktop and web due to formatting
I have a measure which calculates the number of working days within the current month (up to yesterday) with the following calculation:
Working Days = CALCULATE(SUM(Holidays[Working Day]), FILTER(Holidays, Holidays[Date] >= ([First date in slicer])),
FILTER(Holidays, Holidays[Date] <= [Latest Date in slicer]))
The Holiday's DB is stored online and has 3 columns, Day (this is a text field for an explanation of why a week day isn't a working day e.g. Christmas day etc.), Date (formatted in UK format) and Working Day (either 1 or 0) whereby 1 is a working day and 0 isn't.
The first date in slicer is the first of the current month: DATE(YEAR(TODAY()), MONTH(TODAY() -1), 1)
The latest date in slicer is yesterday (as we run the report for the last full day which will always be the day before it's ran: TODAY() - 1
When I run it in Power BI desktop, I get working days as 4. When I upload it and run it on Power BI Online, I get working days as 5. This then impacts a whole table as the table is divded by the number of working days.
Can anyone help? I have changed the Power BI online language settings to be default already and that has updated the date formats on the slicers from US to UK but it is still saying 5 working days and not 4.
1 ACCEPTED SOLUTION
Accepted Solutions
Highlighted
Community Support
## Re: Date calculating differently on desktop and web due to formatting
HI @aimsc,
First, if you direct use number to calculate with date, calculate time unit is days.
Second, utctoday not contains time part, so I think you can use utcnow.
Finally, BST timezone is utc +1, I think you should use + 1 hour instead -1.
```First date in slicer =
VAR bst =
UTCNOW () + TIME ( 1, 0, 0 )
RETURN
DATE ( YEAR ( bst ), MONTH ( bst ), 1 )
Latest Date in slicer =
UTCTODAY () + TIME ( 1, 0, 0 )
```
Regards,
Xiaoxin Sheng
Community Support Team _ Xiaoxin
If this post helps, please consider Accept it as the solution to help the other members find it more quickly.
8 REPLIES 8
Super User IV
## Re: Date calculating differently on desktop and web due to formatting
Is this in a dashboard tile or in a report that you see the 5?
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Regular Visitor
## Re: Date calculating differently on desktop and web due to formatting
Hi @Greg_Deckler I put it in a card on a report to view the number in both Desktop and Online.
I know it's wrong because when I manually calculate the average, it is using 5 and not 4 e.g. it is doing 964 / 5 to get 193 rather than 964 / 4 to get 241.
Community Support
## Re: Date calculating differently on desktop and web due to formatting
HI @aimsc,
AFAIK, current power bi service will analysis datetime as UTC format.
For UTC datetime, it equal to zero timezone datetime, it is different as local datetime. I think your issue is related to it.
Time in PBI Service is inconsistent with the local time (non-UTC time) displayed in PBI Desktop
Regards,
Xiaoxin Sheng
Community Support Team _ Xiaoxin
If this post helps, please consider Accept it as the solution to help the other members find it more quickly.
Regular Visitor
## Re: Date calculating differently on desktop and web due to formatting
I made the change as suggested, using +1 as I'm in BST, however, that now makes the desktop version incorrect too and today they are dividing by 6 working days rather than 5.
Community Support
## Re: Date calculating differently on desktop and web due to formatting
HI @aimsc,
I'd like to suggest you use UTCNOW and UTCTODAY function to use UTC format to deal with you records.
For detail information about these function, please refer to below link:
Power BI Desktop February Feature Summary
Spoiler
## UTCNOW() and UTCTODAY()
We've added two new DAX functions this month that help if you're working with date-time data across timezones. DAX has long supported the NOW() and TODAY() functions that return time and date in the timezone that the function's being used - so if a .pbix file is passed to someone in a different timezone they'll see different results. UTCNOW() and UTCTODAY() will always return the current time or date in UTC so you can guarantee consistent results wherever you are (and also when you upload the workbook to the Power BI service).
Regards,
Xiaoxin Sheng
Community Support Team _ Xiaoxin
If this post helps, please consider Accept it as the solution to help the other members find it more quickly.
Regular Visitor
## Re: Date calculating differently on desktop and web due to formatting
Hi @v-shex-msft
I updated the following and it still has 6 working days:
First date in slicer = DATE(YEAR(UTCTODAY()), MONTH(UTCTODAY() -1), 1)
Latest Date in slicer = UTCTODAY() - 1
Many thanks,
Aimee
Highlighted
Community Support
## Re: Date calculating differently on desktop and web due to formatting
HI @aimsc,
First, if you direct use number to calculate with date, calculate time unit is days.
Second, utctoday not contains time part, so I think you can use utcnow.
Finally, BST timezone is utc +1, I think you should use + 1 hour instead -1.
```First date in slicer =
VAR bst =
UTCNOW () + TIME ( 1, 0, 0 )
RETURN
DATE ( YEAR ( bst ), MONTH ( bst ), 1 )
Latest Date in slicer =
UTCTODAY () + TIME ( 1, 0, 0 )
```
Regards,
Xiaoxin Sheng
Community Support Team _ Xiaoxin
If this post helps, please consider Accept it as the solution to help the other members find it more quickly.
Regular Visitor
## Re: Date calculating differently on desktop and web due to formatting
Thanks @v-shex-msft that worked but with the -1 hour.
Thanks so much!!
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Top Kudoed Authors | 1,548 | 6,348 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-24 | latest | en | 0.906414 |
https://documen.tv/question/a-sound-source-producing-1-00-khz-waves-moves-toward-a-stationary-listener-at-one-half-the-speed-17310915-72/ | 1,632,058,364,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00397.warc.gz | 267,773,561 | 15,738 | ## A sound source producing 1.00 kHz waves moves toward a stationary listener at one-half the speed of sound. a) What frequency will the
Question
A sound source producing 1.00 kHz waves moves toward a stationary listener at one-half the speed of sound.
a) What frequency will the listener hear?
(b) Suppose instead that the source is stationary and the listener moves toward the source at one half the speed of sound. What frequency does the listener hear? How does your answer compare with that in par a? Did you expect to get the same answer in both cases? Explain on physical grounds why the two answers differ
in progress 0
2 months 2021-08-01T04:39:34+00:00 1 Answers 2 views 0
2000Hz and 1500Hz
Explanation:
Using
a) f = f0((c+vr)/(c+vs))
=>>> f0((c)/(c-0.5c))
=>>>1000/0.5 = 2000Hz
b) f = f0((c+vr)/(c+vs))
=>>>f0((c+0.5c)/(c))
=>>>>1000 x 1.5 = 1500Hz | 262 | 871 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2021-39 | latest | en | 0.847625 |
http://www.quantumtorah.com/pesach-sheini-in-a-state-of-superposition/ | 1,521,747,578,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257648000.93/warc/CC-MAIN-20180322190333-20180322210333-00022.warc.gz | 454,947,508 | 23,338 | In physics, we speak of systems and states. System is a collection of physical objects (particles, waves, etc.). A system can be in various states. For example, a coin could have two states – heads and tails. A top also has two possible states – it can be spinning clockwise or counterclockwise. Light can have two states too – being in vertical polarization or horizontal polarization. In classical mechanics a system can only be in a pure state, i.e., at any given point in time, a coin can be either in a state “Heads” or the alternative state “Tales”. A top can be spinning either clockwise or counterclockwise, each of which is a pure state.
In quantum mechanics, a system can be in a pure state or in a state of superposition. Let us say, the system has two possible states A and B. If a system is in a pure state it is either in state A or B. However, a system can be in a state of superposition of these two states – state aA + bB, where a2 and b2 are the probabilities of finding the system in state A or B. For example an electron can be in state Up – ↑ or state Down ↓, or it can be in a state of superposition of Up and Down – c1↑ + c2↓ – where c1 and c2 are coefficients that squared give us probabilities of finding the electron Up or Down: pup = |c1|2 and pdown = |c2|2. When we measure the state of the system, we collapse the wavefunction and find the system in one of the states.
When system is in a state of superposition, strange things can happen. For instance, an electron can be “spinning” clockwise and counterclockwise at the same time and Schrödinger cat can both dead and alive.
Today we read the Torah portion of Behaalotecha, which gives several examples of superposition of states. One example is manna, which was in a state of superposition of all possible tastes (whichever food a person eating manna would imagine, that is how it tasted).
Another example, which I want to focus on, is the commandment of Pesach Sheni – the Second Passover. Those people, who were unable to bring Passover sacrifice on time – on the 14th of Nissan – where given the second chance to bring the Korban Pesach (Passover sacrifice) a month later, on 14th of Iyar. The amazing thing, however, was that while eating Passover lamb with matzot, those who brought Korban Pesach on Pesach Sheini were allowed to eat bread. Let’s think about it. Usually, the whole year we eat leaven bread – chometz (let’s call this state Chometz) while on Passover we must remove all chometz from our houses and we are only allowed to each unleavened bread – matzah (let’s call this state Matzah). On Pesach Sheni, however, we are allowed to each chometz and matzah – in other words, we find ourselves in the state of superposition of (Chometz + Matzah)!
I grew up in Russia in secular family, which did not observe Jewish holidays. We didn’t have Jewish calendar and didn’t even know when the High Holidays – Rosh HaShanah and Yom Kippur – came about. We wouldn’t know about Passover either, if not for my uncle Yosef who lived in Zhitomir, Ukrain, where my mother’s family came from. Uncle Yosef was the only surviving brother of my grandmother Sarah. They had 11 siblings but most of them were murdered either by Kazaks during pogroms or Nazis during the World War II (may God avenge their blood!). My grandmother and uncle Yosef were the only ones who made it alive. Every year, in the spring, we would receive a package from Zhitomir from uncle Yosef with a box of matzahs. We didn’t know exactly when the Passover would start, but we knew it was close, so for a month or so we’d eat every day matzah… and bread. We didn’t know better. All my early Passovers were akin to Pesach Sheini – in a state of superposition (Chometz + Matzah). Growing up in a secular culture among Russians left me confused: was I a Jew or a Russian? I grew up in a mixed state of superposition (Jew + Russian). That is, until I collapsed my wavefunction and chose the state of being a Jew. This is my story told in quantum terms. Pesach Sheini, however, is a story of every ba’al teshuva who returns to his or her roots and who has to choose between two states. Luckily, the story of Pesach Sheini teaches that it is never too late. | 1,039 | 4,210 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2018-13 | longest | en | 0.929898 |
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# Finding a probability given Binomial and Poisson distributions
1.The Census Bureau reports that 55% of all 3-to-5-year-old children attended preschool programs at least a portion of the day. If 18 children are chosen at random, what is the probability that fewer than six children attend such a program?
2. Experimenters in ecology found that the average density of zooplankton in a pond where predators had been introduced was 4.60 individuals per centiliter. Assume a Poisson distribution applies. What is the probability that a centiliter of fluid from the pond contains no individuals?
#### Solution Summary
The problem below outlines the process of finding the probability of an event given a particular distribution (Binomial and Poisson)
\$2.19 | 164 | 783 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2017-13 | latest | en | 0.927033 |
http://docplayer.net/24160668-Conversions-in-the-metric-system.html | 1,545,197,859,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376831334.97/warc/CC-MAIN-20181219045716-20181219071230-00027.warc.gz | 73,581,573 | 22,996 | # Conversions in the Metric System
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1 The metric system is a system of measuring. It is used for three basic units of measure: metres (m), litres (L) and grams (g). Measure of Example Litres (L) Volume 1 L of juice Basic Units Grams (g) Mass 500 g of flour Metres (m) Length 1.74 m tall What makes the metric system so useful is that all three units of measure are based on the powers of ten (including , 0.001, 0.01, 0.1, 1, 10, 100, 1000). Let s examine the METRIC SYSTEM CONVERSION chart to understand this idea better. Units kilo- hecto- deka base deci centi- milli- micro Values 1, Prefix k- h- da- m g L d- c- m- mc- or μ- Values 1000x 100x 10x 10x 100x 1000x 1,000,000 (compa bigger bigger bigger red to 1 smaller smaller smaller x smaller base) In this chart, the metre (m), gram (g), and litre (L) have a value of 1. Units of measurement to the right of the base unit are becoming smaller and smaller. Units of measure to the left of the base unit are becoming larger and larger. For example, given a metre we notice the following unit conversions to the right of the base unit: There are 10 dm in a Thus, 1 dm = 1/10 m = 0.1 m There are 100 cm in a Thus, 1 cm = 1/100 m = 0.01 m There are 1000 mm in a Thus, 1 mm = 1/1000 m = m
2 Since the metric system of measurement is based on powers of ten (10) converting between units is a snap! PART A Ratio & Proportion Method Example 1: Convert 1.74 m into cm. To convert meters to centimeters we need to first identify the larger unit. Looking at the Metric System chart we notice that a centimeter is 100 times smaller than a meter. Thus, 1 m = 100 cm Knowing this we can set up a proportion to convert 1.74 m into cm. Remember! A proportion is a comparison of two equal ratios in which order matters. On the Left Hand Side (L.H.S.) of the proportion, list the ratio we know. On the Right Hand Side (R.H.S), list the ratio we are trying to find out. Solve for the unknown value using cross multiplication. ( ) ( ) Thus, there are 174 cm in 1.74 m.
3 Example 2: Convert 4 g into mg. First we need to identify the larger unit. Looking at the Metric System Chart we notice that a milligram is 1000 times smaller than a gram. Thus, 1 g = 1000 mg. Knowing this we can set up a proportion to convert 4 g into mg. On the Left Hand Side (L.H.S.) of the proportion, list the ratio we know. On the Right Hand Side (R.H.S), list the ratio we are trying to find out. Solve for the unknown value using cross multiplication. ( ) ( ) Thus, there are 4000 mg in 4 g. PART B Ladder Method For every step DOWN the staircase, move the decimal point to the right. For every step UP the staircase, move the decimal point to the left. Note: When moving down the stairs we are multiplying by 10, 100, or When moving up the stairs we are dividing by 10, 100, 1 000, or
4 Example 3: Convert L into ml. Beginning at the base unit litre (L), we have to take three steps DOWN the stairs to reach milliliters (ml). Thus, we will multiply by by moving the decimal point three spaces to the right x = Thus, there are 25.4 ml in L. Example 4: Convert mg into kg. Beginning at milligrams (mg), we have to take six steps up the stairs to reach kilograms (kg). Thus, we will divide mg by by moving the decimal point six spaces to the left = Thus, there is kg in mg. Notice that both starting units (mm and cm) cancel out and you are left with the desired unit (dm).
5 Exercises: 1. Convert the following larger units of the Metric System to the equivalent smaller units. a) 5 g = mg f) 1 g = mg b) 2 L = ml g) 54 g = mg c) 3.5 g = mg h) 2.5 L = ml d) 0.03 g = mg i) 3.6 cm = mm e) L = ml j) 18 cm = mm 2. Convert the following smaller units of the Metric System to the equivalent larger units. a) 610 ml = L f) 90 mg = g b) 306 mm = cm g) 115 ml = L c) 1520 g = kg h) 68 ml = L d) 890 mg = g i) 110 mg = g e) 2500 ml = L j) 500 mg = g Solutions: 1. a) 5 g = 5000 mg f) 1 g = 1000 mg b) 2 L = 2000 ml g) 54 g = mg c) 3.5 g = 3500 mg h) 2.5 L = 2500 ml d) 0.03 g = 30 mg i) 3.6 cm = 36 mm e) L = 2 ml j) 18 cm = 180 mm 2. a) 610 ml = 0.61 L f) 90 mg = 0.09 g b) 306 mm = 30.6 cm g) 115 ml = L c) 1520 g = 1.52 kg h) 68 ml = L d) 890 mg = 0.89 g i) 110 mg = 0.11 g e) 2500 ml = 2.5 L j) 500 mg = 0.5 g
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### KeyTrain Competencies Level 6
KeyTrain Competencies Level 6 Reduce Fractions 20 5 = 4 24 2 = 12 2 = 6 2 = 3 25 5 = 5 40 2 = 20 2 = 10 2 = 5 OR 24 4 = 6 2 = 3 40 4 = 10 2 = 5 To reduce fractions, you must divide the top number of the | 7,557 | 31,272 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2018-51 | latest | en | 0.878258 |
http://openstudy.com/updates/50f96af4e4b007c4a2ec0ef2 | 1,448,988,128,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398468396.75/warc/CC-MAIN-20151124205428-00244-ip-10-71-132-137.ec2.internal.warc.gz | 165,886,753 | 9,655 | ## quantaia 2 years ago find the slope for 1,6 and 6,8
• This Question is Open
1. Opcode
The formula to find slope is, $\huge\ slope=m=\frac{ y_2-y_1 }{ x_2-x_1 }$ Here, $\huge\ (x_1,y_1)=(1,6),(x_2,y_2)=(6,8)$ | 92 | 212 | {"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 | 3 | CC-MAIN-2015-48 | longest | en | 0.588386 |
http://mathproblems.info/prob31s.htm | 1,550,767,654,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247505838.65/warc/CC-MAIN-20190221152543-20190221174543-00275.warc.gz | 152,726,935 | 1,294 | # Problem 31 Solution
Let f(t) equal the money in the account at time t. Since the interest rate is 100% (compounded infinitely) f'(t) = f(t), in other words at any moment in time the money is doubling (which is not the case with simple interest). So for what function does f'(t)=f(t)? This answer is ex. So the value of the account after one year is f(1)=e1=e.
Below is another approach:
The value of \$1 invested for n years at interest rate i, compounded x times per year is (1+(i/x))nx.
In this case f(x) = the value of \$1 invested at 100% interest compounded n times per year = (1+(1/x))x, where x approaches infinity.
The following table shows values of f(x) for various values of x:
``` x f(x)
----------- ----------
1 2.00000000
4 2.44140625
12 2.61303529
52 2.69259695
365 2.71456748
1,000 2.71692393
10,000 2.71814593
100,000 2.71826824
1,000,000 2.71828047
10,000,000 2.71828169
100,000,000 2.71828180
```
As x approaches infinity it can be seen that f(x) approaches e =~ 2.71828182846.
Michael Shackleford, A.S.A. | 334 | 1,055 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2019-09 | latest | en | 0.827333 |
https://www.mql5.com/en/forum/391388 | 1,713,793,749,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818293.64/warc/CC-MAIN-20240422113340-20240422143340-00564.warc.gz | 782,086,028 | 16,314 | # Closest Low under current market price
Hello all,
I am new to EA progamming.
I need help with finding the previous low under the current price value like in the pictured represented by ( x )
do any of you know how to do this,
thank you very much
Files:
PreviousLow.png 16 kb
David Henriques:I am new to EA progamming. I need help with finding the previous low under the current price value like in the pictured represented by ( x ). do any of you know how to do this,
If you are new to MQL, then please first learn how to code the basics before attempting to code a specific task.
Take some of the examples in the codebase and study them, and then make small changes as you strive to reach your goal of a specific task, such as the one you describe.
Also, it is customary to first present your coding attempt at the task and then ask for advice.
MQL5 Code Base
• www.mql5.com
MQL5 Source Code Library for MetaTrader 5
Until you can state your want in concrete terms, it can not be coded.
1. You could go up hill, down, up, and down to find the second low.
``` INDEX iExtreme = iBeg++; Datatype extreme = arr[iExtreme], value;
INDEX iLimit = MathMin(iEnd, iExtreme + size);
for(; iBeg < iLimit; ++iBeg){
value = arr[iBeg];
if(comp.is_before(extreme, value) ){
iExtreme = iBeg; extreme = value;
iLimit = MathMin(iEnd, iExtreme + size);
} }
```
If you use a small window, you would find the local low between your x and current candles.
If you use a larger window, you would miss the local low and x and find the low at the left of your picture.
William Roeder #:
Until you can state your want in concrete terms, it can not be coded.
1. You could go up hill, down, up, and down to find the second low.
If you use a small window, you would find the local low between your x and current candles.
If you use a larger window, you would miss the local low and x and find the low at the left of your picture.
Thank you very much for you reply,
I am sorry if I didn't explain my self in a clear way
So in the picture I am including you can in green the Low I want to get, and marked with the red "X" are the one I want to not consider as the are above the current bid price.
I want to find the closest (in time) Low that is under the bid price.
I only need it's value, like in this case it would be 1.03050.
Once I have the value I can compare it with the current bid price and open my position.
Files:
David Henriques #: I want to find the closest (in time) Low that is under the bid price.
So do it. What's the problem?
Easiest is to using iFractal
Not compiled, not tested, just typed.
```int hFractal;
int OnInit(){ hFractal = iFractals(_Symbol,_Period); … }
void OnTick(){
MqlTick last_tick;
SymbolInfoTick(_Symbol,last_tick);
double Bid=last_tick.bid;
double down_arrows[];
int Bars=Bars(_Symbol,_Period);
if(CopyBuffer(hFractal,1,0,Bars,down_arrows)<0){
//--- if the copying fails, tell the error code
PrintFormat("Failed to copy data from the iFractals indicator to the FractalDownBuffer array, error code %d",
GetLastError());
return;
}
int iX=0; for(; iX < Bars; ++i) if(down_arrows[i] < Bid) break;
// Found bar X.```
Not compiled, not tested, just typed.
Reason: | 844 | 3,222 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-18 | latest | en | 0.90058 |
https://www.numwords.com/words-to-number/en/3082 | 1,563,667,663,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526799.4/warc/CC-MAIN-20190720235054-20190721021054-00131.warc.gz | 780,874,856 | 1,836 | NumWords.com
# How to write Three thousand eighty-two in numbers in English?
We can write Three thousand eighty-two equal to 3082 in numbers in English
< Three thousand eighty-one :||: Three thousand eighty-three >
Six thousand one hundred sixty-four = 6164 = 3082 × 2
Nine thousand two hundred forty-six = 9246 = 3082 × 3
Twelve thousand three hundred twenty-eight = 12328 = 3082 × 4
Fifteen thousand four hundred ten = 15410 = 3082 × 5
Eighteen thousand four hundred ninety-two = 18492 = 3082 × 6
Twenty-one thousand five hundred seventy-four = 21574 = 3082 × 7
Twenty-four thousand six hundred fifty-six = 24656 = 3082 × 8
Twenty-seven thousand seven hundred thirty-eight = 27738 = 3082 × 9
Thirty thousand eight hundred twenty = 30820 = 3082 × 10
Thirty-three thousand nine hundred two = 33902 = 3082 × 11
Thirty-six thousand nine hundred eighty-four = 36984 = 3082 × 12
Forty thousand sixty-six = 40066 = 3082 × 13
Forty-three thousand one hundred forty-eight = 43148 = 3082 × 14
Forty-six thousand two hundred thirty = 46230 = 3082 × 15
Forty-nine thousand three hundred twelve = 49312 = 3082 × 16
Fifty-two thousand three hundred ninety-four = 52394 = 3082 × 17
Fifty-five thousand four hundred seventy-six = 55476 = 3082 × 18
Fifty-eight thousand five hundred fifty-eight = 58558 = 3082 × 19
Sixty-one thousand six hundred forty = 61640 = 3082 × 20
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# Framerate independent friction
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36 replies to this topic
### #1BradDaBug Members - Reputation: 856
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Posted 28 April 2012 - 07:22 PM
I noticed that my game runs a bit differently when running at 60 FPS on my PC and 30 FPS on my phone, and I traced it down to the friction code. I'm applying friction like this:
`newVelocity = oldVelocity - oldVelocity * friction * elapsedTime`
The results are not consistent between 60 Hz and 30 Hz. But then I thought about how continuous compound interest is calculated, and I came up with this:
`newVelocity = oldVelocity * exp(-friction * elapsedTime)`
It works perfectly, at least on paper. Has anyone else ever used an approach like this? Or is there a better way to do it?
Edit: I should mention that the game is using a fixed time step. At 30 Hz it's 1/30 seconds and at 60 Hz it's 1/60.
Edited by BradDaBug, 28 April 2012 - 07:24 PM.
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### #2Álvaro Members - Reputation: 6171
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Posted 28 April 2012 - 10:50 PM
I think the better way to do it is to use a fixed time step for physics, independent of how fast the screen updates.
http://gafferongames.com/game-physics/fix-your-timestep/
### #3jefferytitan Members - Reputation: 1020
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Posted 28 April 2012 - 11:07 PM
Personally I think fixed timestep physics is good, but some accomodation for varying time delta is nice because schedulers are never 100% precise.
### #4SimonForsman Members - Reputation: 3814
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Posted 28 April 2012 - 11:41 PM
Personally I think fixed timestep physics is good, but some accomodation for varying time delta is nice because schedulers are never 100% precise.
what do schedulers have to do with a fixed timestep ?
If you use a fixed timestep you won't use elapsed time in the physics calculations.
updatePhysics(elapsedTime);
you do:
while (elapsedTime>timeStepSize) {
updatePhysics(timeStepSize);
elapsedTime-=timeStepSize;
}
where timeStepSize is constant so the physics calculations will be deterministics as you always give it the same delta to work with and instead call the physics update routine multiple times per frame if needed (or not at all if your framerate is higher than the physics update rate)
Edited by SimonForsman, 28 April 2012 - 11:44 PM.
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### #5japro Members - Reputation: 837
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Posted 29 April 2012 - 04:28 AM
It works perfectly, at least on paper. Has anyone else ever used an approach like this? Or is there a better way to do it?
It's the correct way of doing it... You are essentially multiplying with (1-friction) every time step so over multiple time steps the "correction" is (1-friction)^n and not n*(1-friction) (1-n*friction) as you would get with the first version when increasing the timestep n times.
Edit: n*(1-friction) would be totally off
Edited by japro, 29 April 2012 - 04:57 AM.
### #6jefferytitan Members - Reputation: 1020
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Posted 29 April 2012 - 04:09 PM
what do schedulers have to do with a fixed timestep ?
Say for example your physics engine runs at 50Hz, so 0.02s between executing physics. Due to the nature of a multitasking OS it won't be precisely 0.02s every time. One time it might be 0.018, another time 0.023. The difference may not be visible... or it may. Depending upon the nature of the physics and the speed of the objects involved. Also ignoring varying delta would be bad if there was a requirement for repeatability, such as in MMO games.
Using some game platforms the timing variation may be minimal, but some systems that I've tinkered with can have variations of up to 20%.
### #7SimonForsman Members - Reputation: 3814
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Posted 29 April 2012 - 04:37 PM
what do schedulers have to do with a fixed timestep ?
Say for example your physics engine runs at 50Hz, so 0.02s between executing physics. Due to the nature of a multitasking OS it won't be precisely 0.02s every time. One time it might be 0.018, another time 0.023. The difference may not be visible... or it may. Depending upon the nature of the physics and the speed of the objects involved. Also ignoring varying delta would be bad if there was a requirement for repeatability, such as in MMO games.
Using some game platforms the timing variation may be minimal, but some systems that I've tinkered with can have variations of up to 20%.
When you use a fixed timestep the delta is constant, you don't pass the actual elapsed time to the physics subsystem. (if you run the physics at 50hz with a fixed timestep you always pass 0.02 as the delta, if the elapsed time is 0.023 you still pass 0.02 as the delta and carry the 0.003 you have left (so the next update triggers after an additional 0.017s have passed), Therefore the scheduler has no impact on the simulation. (You can even run the simulation without measuring the actual elapsed time if the result doesn't have to be displayed in realtime (if you're making a movie for example))
If you need to compensate for a variable delta then you're not using a fixed timestep, you're using a variable timestep.
Edited by SimonForsman, 29 April 2012 - 04:50 PM.
I don't suffer from insanity, I'm enjoying every minute of it.
The voices in my head may not be real, but they have some good ideas!
### #8Cornstalks GDNet+ - Reputation: 5610
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Posted 29 April 2012 - 04:44 PM
Say for example your physics engine runs at 50Hz, so 0.02s between executing physics. Due to the nature of a multitasking OS it won't be precisely 0.02s every time. One time it might be 0.018, another time 0.023. The difference may not be visible... or it may. Depending upon the nature of the physics and the speed of the objects involved. Also ignoring varying delta would be bad if there was a requirement for repeatability, such as in MMO games.
Using some game platforms the timing variation may be minimal, but some systems that I've tinkered with can have variations of up to 20%.
Pseudo-code for which the scheduler doesn't matter:
```float timestep = 1.0f / 30.0f; // 30 updates per second
Clock clock;
clock.start();
while (runMainLoop)
{
if (clock.time() >= timestep)
{
clock.reset();
updateGame(timestep); // use the *fixed* timestep
}
renderGame();
}
```
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### #9jefferytitan Members - Reputation: 1020
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Posted 29 April 2012 - 05:02 PM
@Cornstalks: Very true. I wonder whether it might appear inconsistent or stuttery to a player when physics performed is constant but the real-time that it occurs in is not constant, but I really have no proof either way.
### #10Cornstalks GDNet+ - Reputation: 5610
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Posted 29 April 2012 - 05:19 PM
@Cornstalks: Very true. I wonder whether it might appear inconsistent or stuttery to a player when physics performed is constant but the real-time that it occurs in is not constant, but I really have no proof either way.
True. In a well done game, the rendering is often interpolated. So you don't just naively call renderGame(), but you give it the system time as well and it interpolates the rendering between the current system time and the game time.
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### #11Álvaro Members - Reputation: 6171
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Posted 29 April 2012 - 05:54 PM
You could read the link I posted, which explains exactly what fixing the timestep means, including interpolation. Just saying.
### #12Cornstalks GDNet+ - Reputation: 5610
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Posted 29 April 2012 - 06:00 PM
You could read the link I posted, which explains exactly what fixing the timestep means, including interpolation. Just saying.
I figured he didn't read it, so I'd summarize it here
@jefferytitan: Everything I've said in this thread comes from what alvaro linked to...
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### #13jefferytitan Members - Reputation: 1020
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Posted 29 April 2012 - 06:27 PM
You could read the link I posted, which explains exactly what fixing the timestep means, including interpolation. Just saying.
Nice article. I wish I'd had time to read it earlier. Work is inconsiderate like that.
### #14MrRowl Members - Reputation: 1108
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Posted 01 May 2012 - 11:20 AM
Your exponential form will give you timestep independent behaviour.
However, it's not correct for (what's usually called) friction, since the dry frictional force is independent of velocity. You'd normally call a force or acceleration that's proportional to the velocity, damping (e.g. a damped spring, and your equation is exponential damping). Aerodynamic drag results in the force/acceleration normally being approximately proportional to the velocity squared.
If you want more realistic friction - e.g. for one object sliding on top of another, then calculate:
- The force normal to the contact plane, Fn
- The maximum force that can be generated by friction Fmax = Fn * frictionCoefficient
- The force that would bring the relative tangential velocity v to zero in the following timestep dt: F0 = m * v / dt if your object is a point mass, or if you're apply the frictional force at its centre of mass, assuming you're using Euler integration.
Then you apply minimum(Fmax, F0) - though you need to get the signs right! Comparing Fmax with F0 means that the friction won't cause oscillation when the velocity is very small.
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Posted 01 May 2012 - 08:10 PM
Here is more information on fixing your time step that may be of use—maybe save you from falling into a few potholes.
http://lspiroengine.com/?p=378
Fixing your time step will solve all of your problems, but only if done correctly.
L. Spiro
It is amazing how often people try to be unique, and yet they are always trying to make others be like them. - L. Spiro 2011
I spent most of my life learning the courage it takes to go out and get what I want. Now that I have it, I am not sure exactly what it is that I want. - L. Spiro 2013
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### #16MrRowl Members - Reputation: 1108
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Posted 02 May 2012 - 05:27 AM
Fixing your time step will solve all of your problems, but only if done correctly.
I disagree If your code is written correctly, and implements good approximations to the real world, then it will handle variable timesteps, to within the approximations. It won't behave exactly the same with different sized timesteps, but the difference will just depend on how good your approximations are. It might be that you find that the variation in frame to frame of the approximation is just too much to put up with, in which case you can, if you wish, decide to use a fixed timestep and run multiple physics steps per render frame*. However, I'd maintain that it's better to start out with a physics system that is capable of handling a variable timestep (because that will likely expose incorrect implementations - like the OP saw), than to start with a system that is locked to one timestep (because that will cover up incorrect implementations).
Also, fixing the timestep won't solve the problem, if the problem is that the friction model is wrong!
Some games use a fixed timestep, and some a variable timestep. There are advantages and disadvantages to both choices.
* Another option might be: If you find your physics goes bad when dt > maxDt, you could split your physics update into N iterations such that dt/N < maxDt (choose N as small as possible!). This will result in the physics sim staying within the good-approximation range, without having to do interpolation between physics frames, or having the physics update time != render update time.
### #17japro Members - Reputation: 837
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Posted 02 May 2012 - 06:03 AM
A variable timestep introduces stability issues (as in numerical stability). Especially if there is any sort of collision involved...
### #18MrRowl Members - Reputation: 1108
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Posted 02 May 2012 - 07:27 AM
A variable timestep introduces stability issues (as in numerical stability). Especially if there is any sort of collision involved...
Only if you're solving collisions with spring-dampers (but nobody really does that these days, do they?). In a rigid body simulator, handling collisions with impulses, I don't see any reason why a variable timestep would lead to numerical instability*, as the collisions get handled outside of the integration of the equations of motion (because collisions introduce a discontinuity, and the response is independent of timestep).
Large timesteps can lead to jitter/approximation problems, but that's not numerical instability, or the same as variable timesteps.
Explicit spring/dampers are unstable at large timesteps (depending on the spring/damping values), but that's not the same as saying they're unstable with variable timesteps. Implicit formulations should be stable at large timesteps.
Fixed and variable timesteps have both got advantages and disadvantages - I'm just saying it's best to understand them rather than saying one is always better than the other, or saying that one always leads to problems, or that one will solve all your problems.
* Small timesteps can lead to problems if using Baumgarte stabilisation, where solver errors are corrected by introducing a bias that looks like error/timestep. This can be especially bad with a variable timestep: if a large timestep on one frame results in poor solver convergence, which is then "corrected" on the next frame with a small timestep, leading to excessive correction velocities. However, there are ways to fix this.
### #19Álvaro Members - Reputation: 6171
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Posted 02 May 2012 - 08:02 AM
I don't think it has been mentioned, but fixed timesteps allow easier reproduction of the results of the simulation, which can be really helpful in debugging. I imagine it also makes synchronization in multi-player games much easier, since there is a common discretization of time, although I don't have any real experience with that.
I can't think of any disadvantages of fixed timesteps. You mentioned something about using a fixed timestep masking problems, but I can't see that as a real problem. MrRowl, do you care to provide other disadvantages?
Edited by alvaro, 02 May 2012 - 08:03 AM.
### #20MrRowl Members - Reputation: 1108
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Posted 02 May 2012 - 08:35 AM
fixed timesteps allow easier reproduction of the results of the simulation
Indeed!
I can't think of any disadvantages of fixed timesteps. You mentioned something about using a fixed timestep masking problems, but I can't see that as a real problem. MrRowl, do you care to provide other disadvantages?
Here are some:
1. If you use a fixed physics timestep but a variable render frame time (or a render frame time that isn't a multiple of the physics timestep), but don't interpolate the physics results, then a smoothly moving physics object will not move smoothly across the screen, as sometimes it will experience N updates, and sometimes N+1 (for a fixed render frame time).
2. If you do interpolate between physics frames
2.1 that's an additional cost (which might be significant if you've got a lot of objects),
2.2 Also there's some "uncertainty" about where the object is - so when a user shoots an object, where is the impulse applied?
2.3 Debugging might be fun if your debug points etc don't match up with the interpolated object positions
2.4 If the ratio between the physics timestep and render timestep is such that sometimes you run 2 physics steps, and sometimes 1 (for example), and the physics simulation time is significant, then the frame rate can jitter from frame to frame (a lower, but rock steady, framerate is likely better than a high but variable framerate). If there's a spike in the render frame time (e.g. due to disk access), then a fixed physics timestep will result in a spike in the next frame time etc.
3 If the game allows running in slow motion (bullet time) you need to handle at least two, possibly very different timesteps, and the transition between them, otherwise either (a) you always update at the normal timestep, and the effects of interpolation will become obvious, or (b) you always run at the reduced timestep, with a cost that's excessive when running at the normal rate.
In my current home project (a flight sim for mobile devices), a smaller timestep always results in better physics quality. I just clamp the frame time to a max value (something like 0.1s), and always use N physics steps per frame. The user can choose N as a simulation quality setting - it's always at least 3 (or so). This way I get a constant physics simulation cost, so a really steady frame rate (depending on other stuff!), and I can check that everything will at least remain stable at the the maximum physics step time (0.033s). Faster devices get slightly better physics quality. This was originally my quick placeholder before moving to fixed physics timestep and interpolation (which I've done before), but actually I think it works great so don't intend to change!
I know some big commerical games use fixed, and some variable physics timesteps. There are problems to solve whichever way you go!
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PARTNERS | 4,538 | 18,440 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2013-20 | latest | en | 0.908026 |
https://www.physicsforums.com/threads/t-delta-rosette-strain-gauge.326595/ | 1,526,812,059,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863277.18/warc/CC-MAIN-20180520092830-20180520112830-00029.warc.gz | 821,935,097 | 15,519 | # Homework Help: T-delta rosette strain gauge
1. Jul 23, 2009
### jcurtis
1. The problem statement, all variables and given/known data For experimental validation of a design based on FEA, a prototype was tested using strain gauge rosettes at critical locations in a typical t-delta configurations, consisting of 3 gauges: A, B, C and fourth (extra) gauge D. D normally serves as a check on the strains recorded by the rosette arms. In this instance due to a fault in the measuring circuit, the strain response in gauge A could not be recorded the measured strains in the other three gauges were: eB = (-)135x10-6, eC=227x10-6 and eD= (-)63 x 10-6.
What would have been the strain recorded by gauge A?
2. Relevant equations
I found that J=eXX + eYY = eA + eC = eB + eD
3. The attempt at a solution I've looked in my notes that my lecturers put online and I've been searching on google all day and I can't find anything. I know it has something to do with the fourth gauge, but there's no information on the web about it that I could find. The equation I found seemed too simple as the question is worth 8 marks. Or is it more simple than I'm making out? Can anyone help please?
2. Jul 24, 2009
### nvn
jcurtis: As I currently see it, you have four equations and four unknowns. Your relevant equation is currently incorrect; eB and eD are not mutually perpendicular. Try it again. And, you need to list three more equations, for strain in a strain gauge leg. You must list relevant equations yourself. The angle from gauge A to gauge D is 90 deg; but I think you knew that, right? Hint: thetaA = 0 deg.
3. Jul 24, 2009
### jcurtis
Thanks for replying. So you're saying I should swap eB and eA around because a and d are perpendicular?
I can't find any other strain equations that aren't to do with resistance. other than principle strain equations which I need the value of A for, however I know it has to just do with the values of B, C and D as that's all they've given me.. Sorry I'm being a bit dense here, I'm just very confused.
4. Jul 24, 2009
### nvn
Yes, swap eB and eA, then omit eB + eC from your above equation, because gauges B and C are not mutually perpendicular.
5. Jul 25, 2009
### nvn
Hint 2: thetaYY = 90 deg. Do you have anything else at 90 deg? What does that tell you about the value of eYY? | 625 | 2,329 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2018-22 | latest | en | 0.968875 |
http://mathhelpforum.com/calculus/111099-solved-horizontal-vertical-asymptotes.html | 1,527,084,060,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865651.2/warc/CC-MAIN-20180523121803-20180523141803-00036.warc.gz | 181,699,924 | 9,010 | # Thread: [SOLVED] horizontal / vertical asymptotes
1. ## [SOLVED] horizontal / vertical asymptotes
Find the horizontal and vertical asymptotes of the curve.
after i factored it out and did cancellations I got x/x-6
idk why but i got the answer wrong for both asymptotes when i set x = 0. and y = 0
2. Hint: Where is $\displaystyle \frac{x}{x-6}$ undefined? Where does it approach infinity? Dividing the numerator and denominator by $\displaystyle x$, we obtain
$\displaystyle \frac{1}{1-\frac{6}{x}}.$
What happens as $\displaystyle x$ approaches $\displaystyle \infty$ or $\displaystyle -\infty$? | 168 | 605 | {"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} | 2.75 | 3 | CC-MAIN-2018-22 | latest | en | 0.789429 |
https://r-charts.com/distribution/cleveland-dot-plot/ | 1,721,491,109,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763515300.51/warc/CC-MAIN-20240720144323-20240720174323-00328.warc.gz | 421,787,925 | 18,538 | # Cleveland dot plot in R
## Sample data
The following variables represent the quantity sold of a product every month of the year, the month and the quarter of the year for each month.
``````# Sample dataset
set.seed(1)
sold <- sample(400:450, 12)
month <- month.name
quarter <- c(rep(1, 3), rep(2, 3),
rep(3, 3), rep(4, 3))``````
## Basic dot plot with `dotchart` function
Basic dot chart
A dot plot can be created with the `dotchart` function from base R graphics. You can pass a vector of numeric values to the function to create the most basic chart.
``dotchart(sold)``
Customization
There are several arguments that can be customized, such as `pch` to change the plotting character symbol, `col` to change the color of the symbols, `pt.cex` for the size of the symbols and `fram.plot`, which is a logical determining whether to draw a box around the plot or not.
``````dotchart(sold,
pch = 19, # Symbol
col = hcl.colors(12), # Colors
pt.cex = 1.5, # Symbol size
frame.plot = TRUE) # Plot frame``````
Labeling the observations
You can label each point with the `labels` argument. In this example we are passing the names of the months to represent each observation.
``````dotchart(sold,
pch = 19,
col = 4,
pt.cex = 1.5,
labels = month)``````
## Dot chart by group
Specifying groups
Given a variable representing groups it is possible to group the elements. In the following example we are passing the `quarter` variable to the `groups` argument to group the months by quarter.
``````dotchart(sold,
pch = 19, pt.cex = 1.5,
labels = month,
groups = rev(quarter))``````
Matrix as input
Note that the `dotchart` function also allows passing a matrix. In this scenario the groups will be the columns of the matrix by default and the rows the observations for each group.
``````# Matrix from the data
m <- matrix(sold, ncol = 4)
colnames(m) <- c("G1", "G2", "G3", "G4")
rownames(m) <- LETTERS[3:1]
dotchart(m, pch = 19, pt.cex = 1.5)``````
Color by group
If you have passed a grouping variable to `groups` you can also customize the colors for each group, passing a vector of the same length of the input data to the `color` argument.
``````# Colors for each group
cols <- c(rep("#56B4E9", 3), rep("#009E73", 3),
rep("#0072B2", 3), rep("#D55E00", 3))
dotchart(sold,
pch = 19, pt.cex = 1.5,
labels = month,
groups = rev(quarter),
color = cols)``````
Summary for each group
The `gdata` argument allows passing some measure for the groups, such as a statistical summary. In the example below we are calculating the mean of sells by quarter.
``````# Colors for each group
cols <- c(rep("red", 3), rep("blue", 3),
rep("green", 3), rep("orange", 3))
dotchart(sold,
pch = 19, pt.cex = 1.5,
labels = month,
groups = rev(quarter),
color = cols,
gdata = rev(tapply(sold, quarter, mean)))``````
The new points added with `gdata` can be customized with `gpch` and `gcolor` arguments, to modify the pch symbol and the color of the new points, respectively.
``````# Colors for each group
cols <- c(rep("#56B4E9", 3), rep("#009E73", 3),
rep("#0072B2", 3), rep("#D55E00", 3))
dotchart(sold,
pch = 19, pt.cex = 1.5,
labels = month,
groups = rev(quarter),
color = cols,
gdata = rev(tapply(sold, quarter, mean)),
gpch = 12,
gcolor = 1)``````
## Order the values
Finally, note that you can order the values and the labels based on the variable or other measure. In the following example we are ordering the months based on the amount of sales.
``````# Colors for each group
cols <- c(rep("#56B4E9", 3), rep("#009E73", 3),
rep("#0072B2", 3), rep("#D55E00", 3))
dotchart(sort(sold),
labels = month[order(sold)],
pch = 19, pt.cex = 1.5,
groups = rev(quarter),
color = cols)`````` | 1,104 | 3,713 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-30 | latest | en | 0.837911 |
http://meimei-love.info/rrrs/present-value-and-discount-rate-qid.php | 1,563,572,707,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526359.16/warc/CC-MAIN-20190719202605-20190719224605-00420.warc.gz | 97,974,965 | 8,588 | # Present value and discount rate
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## Present Value
The traditional method of valuing future income streams as a cash flow in the future time span might be used cash-flow by a multiple, known premium for long-term debt. An investor who has some money has two options: There of the overall interest rate environment in the economy. A dollar today is worth of moneyand can year from now, since an that is required of a rate of return or interest money from a lender. Currently, these bond rates are of cash flows takes as input the cash flows and positive cash flows for each. Interest that is compounded quarterly determined by calculating the costs 68, A Study of Order associated with interest rates:. By continuing to use our. The total present value of of money gained between the are several types and terms is three months. A cash flow today is more valuable than an identical bondsor through stockthe company is borrowing funds, and must pay interest begin earning returns, while a form of coupon payments, dividendsor stock price appreciation.
#### Calculator Use
Right now, year municipal bond by adding citations to reliable. Corporate finance and investment banking the investment information available. An investor, the lender of be evaluated regularly based on flows occurring further along the firm, the corporate reinvestment rate offers one method of deciding. If trying to decide between is the borrower of the maximize the value of the of Cost of Capital, whether the project can meet the. In this case, the bank present sum of money some funds and is responsible for both the Windows and the. This is described by economists rates are about 2.
In this case the organization would have to be extremely. Answer this question Flag as Karl Marx refers to NPV as fictitious capitaland the calculation as "capitalising," writing: After the cash flow for each period is calculated, the present value PV of each one is achieved by discounting its future value see Formula at a periodic rate of return the rate of return dictated by the market. An investor, the lender of money, must decide the financial determine whether a project or investment will result in a net profit or a loss. March Learn how and when rate is 1 percent, you'd. The initial amount of the flexibly for any cash flow is less than the total a schedule of different interest the lender. Refer to the tutorial article borrowed funds the present value and interest rate, or for their money, and present value rates at different times. Include your email address to is credited four times a question is answered. For example, if the discount get a message when this. Many financial arrangements including bonds, other loans, leases, salaries, membership project in which to invest annuity-due, straight-line depreciation charges stipulate offers one method of deciding.
By using this site, you less than or equal to the future value because money. NPV is an indicator of the following future cash flow. Using the discount rate to how much value an investment difficult to do in practice. Interest represents the time value adjust for risk is often of money-is called discounting how city or county should feel borrower in order to use. Re-investment rate can be defined as the rate of return for the firm's investments on. Ultimately, the discount rate should be evaluated regularly based on interest rate conditions and the especially internationally and is difficult comfortable with the rate. I've been throwing out a lot of my food because the Internet has exploded with. Articles needing additional references from agree to the Terms of such instruments exist.
Unsourced material may be challenged and removed. The interest rate used is the risk-free interest rate if in money of that period. Retrieved from " https: In economics and financepresent Value of a future cash as present discounted valueis the value of an the future that the cash flow occurs. For simplicity, assume the company will have no outgoing cash question is answered. This is because money can be put in a bank there are no risks involved investment that will return interest. More realistic problems would also need to consider other factors, value PValso known demonstrated as follows: Time value of money dictates that time affects the value of cash.
Appropriately risked projects with a March All articles needing additional. See "other factors" above that means the organization is very. To calculate NPV, you need positive NPV could be accepted. A positive net present value present sum of money some of the cash flows, the called a capitalization how much and number of years in 5 years. In mainstream neo-classical economicsNPV was formalized and popularized disregarded because investing in this his The Rate of Interest and became included in textbooks the NPV displays in red, in finance texts. The following equation can be used to calculate the Present by Irving Fisherin project is the equivalent of a loss of 31, If the future that the cash the investment's value is negative. Articles needing additional references from to know the annual discount. The initial amount of the value of future cash flows is based on a chosen rate of return or discount.
Views Read Edit View history. The NPV measures the excess that they should be undertaken in present value terms, above of capital may not account. The most commonly applied model for verification. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in. An investor, the lender of is a useful tool to project in which to invest their money, and present value for opportunity costi. The risk premium required can be found by comparing the determine whether a project or return required from other projects with similar risks. This does not necessarily mean money, must decide the financial since NPV at the cost investment will result in a net profit or a loss. A dollar today is worth more than a dollar tomorrow because the dollar can be believe that it is appropriate to use higher discount rates total accumulate to a value cost, or other factors. The best thing to go such results are usually incorporating. This article needs additional citations.
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In the case when all future cash flows are positive, or incoming such as the principal and coupon payment of and phase shift between commodity of cash is the purchase real parts are responsible for representing the effect of compound flows minus the purchase price. It is widely used throughout could affect the payment amount. Cookies make wikiHow better. Imaginary parts of the complex number s describe the oscillating behaviour compare with the pork cyclecobweb theorema bond the only outflow price and supply offer whereas price, the NPV is simply the PV of future cash interest compare with damping which is its own PV. Again there is a distinction the time value of money is to discount the flow of revenues and costs and and a perpetuity due - present value of a period.
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Where, as above, C is annuity payment, PV is principal, n is number of payments, believe that it is appropriate to use higher discount rates rate per period. For a riskier investment the purchaser would demand to pay. A compounding period can be adjust for risk is often in present value terms, above the future, taking inflation and. Contemporary Financial Management 12 ed. A firm's weighted average cost of capital after tax is often used, but many people starting at end of first period, and i is interest to adjust for risk, opportunity cost, or other factors. Bottom Line: Studies in rats show that the active ingredient years, starting in 1998 with a double-blind, placebo-controlled trial of and risks of raw milk, with no fillers today.
In financethe net higher rates applied to cash present worth NPW [1] is time span might be used now value of a series premium for long-term debt. The reverse operation-evaluating the present in both timing and amount of the cash flows, the may choose to use this years be worth today. Find the Present Value of the following future cash flow. Because NPV accounts for the time value of money NPV provides a method for evaluating and comparing products with cash flows spread over many years, as in loans, investments, payouts flows other applications. The forming of a fictitious. Uneven Cash Flow Stream Exercise.
##### Present Value Calculator
Time value of money dictates of the Excel window. The most commonly applied model that time affects the value. Formula 2 can also be already use a standard discount that at the given rate his The Rate of Interest rate to evaluate economic development value of the payments. For example, if the discount rate is 1 percent, you'd. In mainstream neo-classical economicsfor example by the English often used, but many people of Cost of Capital, whether positive sign, at the end cost of capital. A cash flow is an amount of money that is crown in setting re-sale prices differentiated by a negative or to use higher discount rates to adjust for risk, opportunity. The city or county may of cash flows takes as input the cash flows and for manors seized at the directly by summing the present. An alternative way of looking at Net Present Value is by Irving Fisherin perpetuity delayed n periods, or the project can meet the the early 16th century.
##### Present value
The traditional method of valuing future income streams as a Net cash in-flows and reduced multiply the average expected annual present value but in cases where the cash flows are. Fundamentals of Corporate Finance 9. Already answered Not a question is the sum of all. The forming of a fictitious payments, receivable indefinitely, although few. Mathematics of Investment and Credit. However, in practical terms a negative for outgoing cash flow, be thought of as rent represented asIt is borrower in order to use. Recall, a cost is a of money gained between the investment return, you won't be able to calculate NPV. In the case of this company's capital constraints limit investments present capital sum is to that is required of a some form of computing machinery. The above formula 1 for article, the wikiHow Tech Team insight for the average user rates are a good measure cash-flow by a multiple, known. | 2,369 | 11,972 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2019-30 | latest | en | 0.959675 |
https://www.wolfram.com/programming-lab/explorations/seashell-shapes/ | 1,726,023,470,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651343.80/warc/CC-MAIN-20240911020451-20240911050451-00147.warc.gz | 989,442,356 | 10,415 | Wolfram Archive
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# Seashell Shapes
Make an interactive widget for exploring the shapes of seashells.
Run the code to plot a circle:
As u goes from 0 to 1, {Cos[u 2π], Sin[u 2π]} traces out a circle:
ParametricPlot[{Cos[u 2 \[Pi]], Sin[u 2 \[Pi]]}, {u, 0, 1}]
ParametricPlot[{Cos[u 2 \[Pi]], Sin[u 2 \[Pi]]}, {u, 0, 1}]
Plot the circle in 3D:
Plot a circle in the x-z plane in 3D:
ParametricPlot3D[{Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}, {u, 0, 1}]
ParametricPlot3D[{Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}, {u, 0, 1}]
Plot a logarithmic helix:
Heres a plot of a 2D logarithmic spiral. Its radius increases exponentially:
ParametricPlot[.5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v]}, {v, 0, 4}]
Heres a plot of the 3D analog, a logarithmic helix. The spiral rises up the z axis as it unwinds:
ParametricPlot3D[.5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}, {v, 0, 4}]
ParametricPlot3D[.5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}, {v, 0, 4}]
Plot a shell shape:
Make a shell shape by sweeping a circle along a logarithmic helix. One side of the circle stays tangent to the z axis (drag the figure to view it from a different angle):
Well combine the following two plots to make the seashell shape. The parameter u controls the path around the circle, and v the progress along the helix:
{ ParametricPlot3D[{Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}, {u, 0, 1}], ParametricPlot3D[.5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}, {v, 0, 4}] }
As the circle sweeps out the shell shape, it rotates so that it stays orthogonal to the helix, its radius changes so that one side of the circle stays on the z axis, and its center follows the helix.
Heres the circle:
ParametricPlot3D[{Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}, {u, 0, 1}, {v, 0, 4}]
To make the center follow the path of the helix, translate it to the point on the helix by adding the expression for the helix to the expression for the circle. This doesnt yet look like a seashell because the circle is not yet rotating or changing radius:
ParametricPlot3D[{Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]} + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}, {u, 0, 1}, {v, 0, 4}]
Next, make the circle rotate as it follows the path of the helix. The helix point is at angle 2πv. RotationTransform[2πv,{0,0,1}] rotates the circle by 2πv about the z axis ({0,0,1}). Evaluate greatly speeds up the calculation by evaluating the rotation before its plotted:
ParametricPlot3D[ Evaluate[RotationTransform[2 \[Pi] v, {0, 0, 1}][{Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}], {u, 0, 1}, {v, 0, 4}]
Finally, scale the circle so that it stays tangent to the z axis as it rotates. The scale factor is the distance of the helix from the z axis, .5^v. PlotRangeAll ensures that the entire shell is plotted (try removing it to see what happens):
ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All]
To get a smoother shape, increase the number of plot points in the u and v directions with PlotPoints. Experiment with smaller values to see the effect:
ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}]
Remove the axes, box, and surface mesh:
ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None]
ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], 1}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None]
Make it interactive. Drag the slider to stretch the shell vertically:
Make the shell expression interactive by wrapping it with Manipulate, adding a stretch parameter, and letting the stretch vary from 0 to 4 with an initial value of 1. The stretch parameter effectively scales the helix along the z axis, compressing or stretching the shell:
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None], {{st, 1, "stretch"}, 0, 4} ]
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]], 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None], {{st, 1, "stretch"}, 0, 4} ]
Add a control for the width. Drag the slider to change the width of the shell:
Add a parameter that makes the circle move away from the z axis as it sweeps. The slider controls how quickly it moves away:
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4} ]
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[ 2 \[Pi] v, {0, 0, 1}][.5^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + .5^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4} ]
Add a control for scaling. Drag the slider to change how quickly the shell scales down:
Add a parameter that controls how quickly the circle scales down as it moves around the helix:
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[2 \[Pi] v, {0, 0, 1}][ sc^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + sc^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4}, {{sc, .5, "scaling"}, .1, 1} ]
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[2 \[Pi] v, {0, 0, 1}][ sc^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + sc^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4}, {{sc, .5, "scaling"}, .1, 1} ]
Add a control for transparency. Drag the slider to make the shell transparent:
Add a control for transparency. As the transparency goes from 0 to 1, the opacity goes from 1 to 0:
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[2 \[Pi] v, {0, 0, 1}][ sc^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + sc^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None, PlotStyle -> Opacity[1 - tr]], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4}, {{sc, .5, "scaling"}, .1, 1}, {{tr, 0, "transparency"}, 0, 1} ]
Manipulate[ ParametricPlot3D[ Evaluate[RotationTransform[2 \[Pi] v, {0, 0, 1}][ sc^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + sc^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None, PlotStyle -> Opacity[1 - tr]], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4}, {{sc, .5, "scaling"}, .1, 1}, {{tr, 0, "transparency"}, 0, 1} ]
Share ItMake an interactive website for exploring seashell shapes:
Deploy the Manipulate to the Wolfram Cloud where anyone with a browser can use it:
CloudDeploy[ Manipulate[ ParametricPlot3D[ Evaluate[ RotationTransform[2 \[Pi] v, {0, 0, 1}][ sc^v {Cos[u 2 \[Pi]] + w, 0, Sin[u 2 \[Pi]]}] + sc^v {Cos[2 \[Pi] v], Sin[2 \[Pi] v], st}], {u, 0, 1}, {v, 0, 4}, PlotRange -> All, PlotPoints -> {20, 40}, Axes -> None, Boxed -> False, Mesh -> None, PlotStyle -> Opacity[1 - tr]], {{st, 1, "stretch"}, 0, 4}, {{w, 0, "width"}, 0, 4}, {{sc, .5, "scaling"}, .1, 1}, {{tr, 0, "transparency"}, 0, 1} ], Permissions -> "Public" ]
Click on the link in the output to visit the site. | 3,349 | 8,583 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2024-38 | latest | en | 0.657528 |
https://www.hkbud.com/web/post-detail.php?lang=hk&id=4786&menu=1 | 1,603,335,443,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107878879.33/warc/CC-MAIN-20201022024236-20201022054236-00497.warc.gz | 742,560,103 | 20,185 | # Bianca
## 解答 0
• eric
2019-11-04 22:32:36
The answer is 2x+300, where x is sister saving which can be found through solving the equation: 300+x-450=2x/5
• eric
2019-11-04 22:47:05
Correction: The answer is 2x+300, where x is sister saving which can be found through solving the equation: 300+x-450=2(x+450)/5
jpg, gif, png, doc, docx, pdf, xls, mov, mp4, m4a, mp3 (檔案上限為50M) | 153 | 379 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2020-45 | latest | en | 0.830846 |
https://ru-facts.com/which-kurtosis-has-fat-tails/ | 1,719,303,961,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865694.2/warc/CC-MAIN-20240625072502-20240625102502-00783.warc.gz | 428,875,772 | 12,180 | # Which kurtosis has fat tails?
## Which kurtosis has fat tails?
Leptokurtic distributions are statistical distributions with kurtosis greater than three. It can be described as having a wider or flatter shape with fatter tails resulting in a greater chance of extreme positive or negative events.
## How do you calculate kurtosis?
Kurtosis = Fourth Moment / Second Moment2
1. Kurtosis = 313209 / (365)2
2. Kurtosis = 2.35.
Does high kurtosis mean fat tails?
Excess kurtosis. Kurtosis measures the “fatness” of the tails of a distribution. Positive excess kurtosis means that distribution has fatter tails than a normal distribution. Fat tails means there is a higher than normal probability of big positive and negative returns realizations.
### How do you determine if a distribution is heavy-tailed?
A heavy tailed distribution has a tail that’s heavier than an exponential distribution (Bryson, 1974). In other words, a distribution that is heavy tailed goes to zero slower than one with exponential tails; there will be more bulk under the curve of the PDF.
### Which distribution has fatter tails?
A leptokurtic distribution has excess positive kurtosis. The tails are “fatter” than the normal distribution, hence the term fat-tailed.
How do you find the kurtosis of a normal distribution?
The normal distribution has skewness equal to zero. The kurtosis of a probability distribution of a random variable x is defined as the ratio of the fourth moment μ4 to the square of the variance σ4, i.e., μ 4 σ 4 = E { ( x − E { x } σ ) 4 } E { x − E { x } } 4 σ 4 . κ = μ 4 σ 4 −3 .
## Why is high kurtosis bad?
The risk that does occur happens within a moderate range, and there is little risk in the tails. Alternatively, the higher the kurtosis, the more it indicates that the overall risk of an investment is driven by a few extreme “surprises” in the tails of the distribution.
## What causes fat tail distribution?
By definition, a fat tail is a probability distribution which predicts movements of three or more standard deviations more frequently than a normal distribution. Even before the financial crisis, periods of financial stress had resulted in market conditions represented by fatter tails.
What is the kurtosis of a normal distribution?
A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. An increased kurtosis (>3) can be visualized as a thin “bell” with a high peak whereas a decreased kurtosis corresponds to a broadening of the peak and “thickening” of the tails.
### What is kurtosis or fat tails?
When we speak of kurtosis, or fat tails or peakedness, we do so with reference to the normal distribution. We compare other distributions to the normal distribution, so it is important to be clear about the shape of the normal distribution. So let us spend a few minutes talking about the shape of the normal distribution.
### What is the kurtosis formula in statistics?
What is the Kurtosis Formula? The term “Kurtosis” refers to the statistical measure that describes the shape of either tail of a distribution, i.e. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution.
Which distribution has a large kurtosis?
A heavy-tailed distribution has large kurtosis. The canonical distribution that has a large positive kurtosis is the t distribution with a small number of degrees of freedom. Some heavy-tailed distributions have infinite kurtosis.
## What are the tails of a distribution curve?
The tails of a distribution measure the number of events that occurred outside of the normal range. Unlike skewness, kurtosis measures either tail’s extreme values. Excess kurtosis means the distribution of event outcomes have lots of instances of outlier results, causing fat tails on the bell-shaped distribution curve .
Begin typing your search term above and press enter to search. Press ESC to cancel. | 878 | 3,958 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2024-26 | latest | en | 0.911764 |
http://www.solve-variable.com/math-variable/cramers-rule/math-trivia-in-algebra-with.html | 1,521,928,079,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257651007.67/warc/CC-MAIN-20180324210433-20180324230433-00388.warc.gz | 464,229,949 | 11,184 | Free Algebra Tutorials!
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• conic graphing calculator online | 976 | 4,281 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-13 | latest | en | 0.91284 |
https://www.scribd.com/doc/56296621/Chap-03-Financial-Markets-and-Institutions | 1,448,542,901,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398447266.73/warc/CC-MAIN-20151124205407-00202-ip-10-71-132-137.ec2.internal.warc.gz | 898,035,678 | 22,955 | P. 1
Chap 03 - Financial Markets and Institutions
# Chap 03 - Financial Markets and Institutions
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# U9824613 阮德龍
Chapter 03
Interest rate and Security valuation
Question 22:
a.
t CFt PV of CFt Wt t × Wt
1 100 89.286 0.092 0.092
2 1100 876.913 0.908 1.816
total P0= 966.199 1 D = 1.908
The Duration is 1.908 years
b. Because the bond is zero-couon bond! the duration "ill e#ual to the nu\$ber o% eriods
until a bond \$atures.
&o! D = T = ' years.
c. The increasin( in the yield to \$aturity decreases the duration o% the bond. )ith the zero-
couon bond the yield to \$aturity increases \$a*e the duration o% zero-couon bond
increase in the sa\$e nu\$ber o% eriods.
Question 23:
a.
+or Ban* 1! an increase o% 100 basis oints in interest rate "ill cause the \$ar*et ,alues o%
assets and liabilities to decrease as %ollo"s-
• .oan-
/120!0000123+4n=10!i=135 6 /1!000!0000123+n=10!i=135 =/97'!737.'7.
• 8D-
/100!0000123+4n=10!i=115 6 /1!000!0000123+n=10!i=115 = /971!107.68.
Financial Markets and Institutions
U9824613 阮德龍
There%ore! the decrease in ,alue o% the asset "as /7!629.89 less than the liability.
+or Ban* 2-
• Bond-
/1!976!362.880123+n=7!i=135 = /870!077.08.
• 8D-
/82!7'00123+4n=10!i=115 6 /1!000!0000123+n=10!i=115 = /839!'18.73.
The bond ,alue decreased /'3!932.12! and the 8D ,alue %ell /'7!787.79. There%ore! the
decrease in ,alue o% the asset "as /'''.67 less than the liability.
b.
The assets and liabilities o% Ban* 4 chan(e in ,alue by di%%erent a\$ounts because the
durations o% the assets and liabilities are not the sa\$e! e,en thou(h the %ace ,alues and \$aturities
are the sa\$e. +or Ban* B! the \$aturities o% the assets and liabilities are di%%erent! but the current
\$ar*et ,alues and durations are the sa\$e. Thus! the chan(e in interest rates causes the sa\$e
9aro:i\$ate; chan(e in ,alue %or both liabilities and assets.
Question 24:
Financial Markets and Institutions
U9824613 阮德龍
a. T= ' years couon rate = 105 ar ,alue = /1!000
4ssu\$e < =105 se\$iannual
t CFt PV of CFt (PV of C! × t
0.' /'0 /77.62 /23.81
1 '0 7'.3' 7'.3'
1.' '0 73.19 67.79
2 '0 71.17 82.27
2.' '0 39.18 97.97
3 '0 37.31 111.93
3.' '0 3'.'3 127.37
7 '0 33.87 13'.37
7.' '0 32.23 17 '.07
' /10'0 /677.61 /3!223.07
total /1!000.00 /7!0'3.91
Duration is- D = /7!0'3.91=/1!000 = 7.0'391 years
b. < = 175 T= ' years se\$iannual couon rate = 105
1ar ,alue = /1!000
t CFt PV of CFt (PV of C! × t
0.' /'0 /76.73 /23.81
1 '0 7'.67 7'.3'
1.' '0 70.81 67.79
2 '0 38.17 82.27
2.' '0 3'.6' 97.97
3 '0 33.32 111.93
3.' '0 31.17 127.37
Financial Markets and Institutions
U9824613 阮德龍
7 '0 29.10 13'.37
7.' '0 27.20 17 '.07
' /10'0 /'33.77 /2!668.83
total /8'9.'3 /3!710.22
Duration is- D = /3!710.22=/8'9.'3 = 3.967'7 years
<= 165 T= ' couon rate = 105 ar ,alue = /1!000 se\$iannual
t CFt PV of CFt (PV of C! × t
0.' /'0 /76.29 /23.1'
1 '0 72.87 72.87
1.' '0 39.69 '9.'7
2 '0 36.7' 73.'
2.' '0 37.03 8'.08
3 '0 31.'1 97.'3
3.' '0 29.17 102.09
7 '0 27.02 108.08
7.' '0 2'.01 112.''
' /10'0 /786.3' /2!731.7'
total /798.69 /3!133.17
Duration is- D = /3!133.17=/798.69 = 3.9228 years.
c. 4s %ollo"-
>ield to \$aturity Duration
105 7.0'391 years
Financial Markets and Institutions
U9824613 阮德龍
175 3.967'7 years
165 3.9228' years
4s the yield to \$aturity increase! the duration "ill decrease.
Question 2":
a.
T = 7 years <= 105 couon rate = 105 ar ,alue = /1!000
se\$iannual
t
CFt
PV of CFt PV of CFt × t
0.' /'0 /77.62 /23.81
1 '0 7'.3' 7'.3'
1.' '0 73.19 67.79
2 '0 71.17 82.27
2.' '0 39.18 97.97
3 '0 37.31 111.93
3.' '0 3'.'3 127.37
7 /10'0 /710.'3 /2!872.73
total /1!000.00 /3!393.19
Duration is- D = /3!393.19= /1!000 = 3.3932 years
b.
8ouon rate = 105 ar ,alue = /1!000 < = 105 se\$iannual
Financial Markets and Institutions
U9824613 阮德龍
t
CFt
PV of CFt PV of CFt × t
0.' /'0 /77.62 /23.81
1 '0 7'.3' 7'.3'
1.' '0 73.19 67.79
2 '0 71.17 82.27
2.' '0 39.18 97.97
3 /10'0 /783.'3 /2!3'0.'9
total /1!000.00 /2!667.77
Duration is- D = /2!667.77=/1!000 = 2.66777 years.
c.
8ouon rate = 105 ar ,alue = /1!000 < = 105 se\$iannual
Duration is- D =
/1!861.62= /1!000 =
1.86162 years.
a.
4s the ti\$e to \$aturity decrease! the duration "ill decrease! too.
?aturity Duration
7 years 3.39319 years
3 years 2.66777 years
2 years 1.86162 years
Question 2#:
Financial Markets and Institutions
t
CFt
PV of CFt PV of CFt × t
0.' /'0 /77.62 /23.81
1 '0 7'.3' 7'.3'
1.' '0 73.19 67.79
2 /10'0 /863.87 /1!727.68
\$otal /1!000.00 /1!861.62
U9824613 阮德龍
Because the bond is zero-couon bond! the duration "ill be e#ual to the nu\$ber o% years to
\$aturity.
Then! the duration o% zero couon bond that has 8 years to \$aturity is D = 8 years
The duration o% zero couon bond i% the \$aturity increase to 10 years is D = 10 years.
The duration o% zero couon bond i% the \$aturity increases to 12 years is D = 12 years.
Question 2%-
a. 8ouon rate = 13.765 < = 105 T = ' years annual aid
1ar ,alue = /1!000
t CFt PV of CFt PV of CFt × t
1 /137.6 /12'.09 /12'.09
2 137.6 113.72 227.77
3 137.6 103.38 310.17
7 137.6 93.98 37'.92
' /1!137.6 /706.36 /3.'31.8
\$otal /1!172.'3 /7!'70.39
Duration is- /7!'70.39= /1!172.'3 = 7.0002 years or 7 years 9aro:i\$ately;
b. &ho" that! i% interest rates rise to 10 ercent "ithin the ne:t year and that i% your
in,est\$ent horizon is %our years %ro\$ today! you "ill still earn a 9 ercent yield on your
in,est\$ent.
2alue o% bond at end o% year %our- 12 = 9/137.66 /1!000; 1.11 = /1!027.86
+uture ,alue o% interest ay\$ents at end o% year %our-
/137.6@+23+ 97! 115; = /678.06
+uture ,alue o% all cash %lo"s at n = 7-
8ouon interest ay\$ents o,er %our years /''0.7
3nterest on interest at 11 ercent 97.66
2alue o% bond at end o% year %our /1!027.86
Total %uture ,alue o% in,est\$ent /1!672.92
>ield on urchase o% asset at /1!027.86 = /1!672.92@123+97! i; ⇒i = 10.00235.
Financial Markets and Institutions
U9824613 阮德龍
Question 2&:
a. ar ,alue = /10!000 couon rate = 85 < =105 T = ' years annual aid
t CFt PV of CFt PV of CFt × t
1 /800 /727.27 /727.27
2 800 661.16 1!322.31
3 800 601.16 1!803.16
7 800 '76.71 2!18'.67
' /10!800 /6!70'.9' /33!'29.7'
\$otal /9!271.87 /39!'68.17
Duration is- D = /39!'68.17=/9!271.87 = 7.28171years
b. 1ar ,alue = /10!000 couon rate = 105 < = 105 T= 'years annual aid
t CFt PV of CFt PV of CFt × t
1 /1000 /909.09 /909.09
2 1000 826.7' 1!6'2.89
3 1000 7'1.31 2!2'3.97
7 1000 683.01 2!732.0'
' /11!000 /6!830.13 /37!1'0.67
\$otal /10!000.00 /71!698.6'
Duration is- D = /71!698.6'= /10!000 = 7.1698 years
c. 1ar ,alue = /10!000 couon rate = 125 < = 105 T= ' annual aid
t CFt PV of CFt PV of CFt × t
1 /1200 /1!090.91 /1!090.91
2 1200 991.77 1!983.77
Financial Markets and Institutions
U9824613 阮德龍
3 1200 901.'8 2!707.73
7 1200 819.62 3!278.76
' /11!200 6!9'7.32 /37!771.'9
\$otal /10!7'8.16 /73!829.17
Duration is- D = /73!829.17=/10!7'8.16 = 7.07707 years
Question 2':
Ta*in( the %irst deri,ati,e o% a bondAs rice 91; "ith resect to the yield to \$aturity 9<; ro,ides
the %ollo"in(-
dPPd!1"# = - D
The econo\$ic interretation is that D is a \$easure o% the ercenta(e chan(e in the rice o% a
bond %or a (i,en ercenta(e chan(e in yield to \$aturity 9interest elasticity;. This e#uation can be
re"ritten to ro,ide a ractical alication-
d1 = - D \$d1" B1
3n other "ords! i% duration is *no"n! then the chan(e in the rice o% a bond due to s\$all chan(es
in interest rates! <! can be esti\$ated usin( the abo,e %or\$ula.
Question 30:
)e ha,e the e#uation-
-D = %PP%!1"# =- !&99'(&9)'#&9)'0.'*!1"9.)'+# = - 7.' years
&o! D = 7.' years
Financial Markets and Institutions
Thus.932.074.U9824613 阮德龍 Therefore.976.518. The bond value decreased \$53. • CD: \$82.08. but the current market values and durations are the same.629.89 less than the liability. The assets and liabilities of Bank A change in value by different amounts because the durations of the assets and liabilities are not the same.000.88*PVIFn=7. even though the face values and maturities are the same.67 less than the liability. Therefore.487. and the CD value fell \$54.i=11% + \$1. the maturities of the assets and liabilities are different. b. the change in interest rates causes the same (approximate) change in value for both liabilities and assets. Question 24: Financial Markets and Institutions .362.12. For Bank 2: • Bond: \$1.i=11% = \$839.i=13% = \$840. For Bank B.79. the decrease in value of the asset was \$4.750*PVIFAn=10.43.000*PVIFn=10. the decrease in value of the asset was \$555.
scribd
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https://physics.stackexchange.com/questions/337945/why-is-light-bent-but-not-accelerated/337952 | 1,623,915,024,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487629632.54/warc/CC-MAIN-20210617072023-20210617102023-00286.warc.gz | 395,690,869 | 42,370 | # Why is light bent but not accelerated?
Light is bent near a mass (for example when passing close to the sun as demonstrated in the famous sun eclipse of 1919). I interpret this as an effect of gravity on the light.
However, it seems (to me, at least) that light is not accelerated when it travels directly toward the (bary-)center of the sun. The same gravitational force applies yet the speed of light remains constant (viz. $c$).
What am I missing?
• Do you mean that the light does not change its speed or its momentum? Because the first one is simple: light travels always at the speed of light as it is mass-less (special theory of relativity). The bending due to the mass is a different effect. Do you mean: why does it not increase its momentum? – Mayou36 Jun 7 '17 at 17:37
• If it satisfy you, it "kind of" accelerates: light is blueshifted if shot directly into a massive body. Since light speed is fixed, it gains energy by increasing its frequency (or shortening its wavelenght). – lvella Jun 7 '17 at 19:07
• Wait a minute - isn't the OP asking precisely about this: wikipedia.org/wiki/Pound–Rebka_experiment physics.aps.org/story/v16/st1 The Pound–Rebka experiment. – Fattie Jun 8 '17 at 15:02
• I've removed some comments about "slow light" and "stopped light" in materials, which is a QED effect irrelevant to this question about general relativity. – rob Jun 8 '17 at 19:54
• It is light travelling in "curved" 4-dimensional space-time. Light travels straight (without any acceleration) but the space time is curved due to gravity, this makes it look like bending of light. – user92340 Jun 12 '17 at 4:13
One thing that the previous answers are missing -- the light is accelerated; it just is accelerated according to the rules of special relativity, which says that it cannot pick up speed when already travelling at the speed of light.
Instead, it gains kinetic energy the way a photon gains kinetic energy -- by being blueshifted to a higher frequency, which does translate to more energy, according to the Planck relation $E = h\nu$.
• Exactly. Of course the Energy–momentum relation for massless particles $E=pc$ means that the momentum of the photon also changes (in magnitude, not in direction) because of this acceleration. The photon gains momentum. This relates to the very first comment (to the question, not to the above answer), by Mayou36. – Jeppe Stig Nielsen Jun 11 '17 at 14:37
You missed a key aspect of general relativity (GR):
# Explanation
In general relativity, the presence of mass and energy warps four-dimensional space time, thereby inducing spatial curvature. The greater the presence of mass and energy in a given location, the greater the induced spatial curvature. When any particle (massless or not) travels into this curved space, the particle will continue to travel in a straight line (absent outside forces); but, since the space it is travelling upon is curved, its global path will be curved.
As an analogy, draw two straight lines on a sphere (a curved surface) travelling in different directions. Locally (at small two-dimensional distances), the lines travel in a straight direction, without veering. Globally (at three dimensions), we see that its path is curved and will inevitably intersect (on the other side of the sphere). We call these paths geodesics. The math concerning geodesics involves differential geometry which makes heavy use of multivariate calculus.
Now back to general relativity. GR predicts that the gravitational forces we observe are the manifestation of four-dimensional spacetime being warped by the presence of mass-energy. A common analogy made is the trampoline-well model shown below. A heavy mass sitting upon a trampoline curves the surface of the trampoline. Any objects then move towards the heavy mass has its path deflected towards it. Now, I must stress an important simplification made in such diagrams: these diagrams reduce four-dimensional spacetime to three spatial dimensions. The XY plane of the diagram represents the XYZ components of spacetime whereas the Z axis of the diagram represents the T component of spacetime. For math lovers, they are reducing $(\vec{X}, \vec{Y}, \vec{Z}, \vec{T})$ to $(\sqrt{\vec{X}^2 + \vec{Y}^2}, \vec{Z}, \vec{T})$
Now here's the cool part:
Now instead of its path curving along the $\vec{X}\vec{Y}$ plane as seen in the photo above, its path would curve against $\vec{Z}$ (vertical). In this context though, $\vec{Z}$ does not refer to the Z direction, but to $\vec{T}$. What this means is that, observers would see the particle 'accelerate' in through time and apparently 'slow down'. Namely, they will see gravitational time dilation.
EDIT. I made a mistake: the light does accelerate! It merely does so according to the rules of special relativity.* When objects (massless or not) pass near a gravitational well they pick up gravitational energy and accelerate, thereby gaining kinetic energy. For objects with mass, this means an increased velocity (hence gravitational sling shots). For massless particles (such as photons), this typically means an increased frequency or blue-shifting as Jeremy pointed out in a separate answer. (Thank you Peter, Rob, and Jeremy for pointing out this oversight.)
You may have noticed a contradiction here. According to special relativity and observations, objects in gravitational wells do accelerate. Case in point: gravitational sling-shooting. According to general relativity though, the 'gravitational force' we observe is a manifestation of four-dimensional space-time curvature. So which is it: is there a force or not? Not-really: it's a matter of frames-of-reference. From our reference frame we see acceleration; but, from the four-dimensional space-time reference we see pure geodesic motion.
# Hence, gravity isn't a force acting upon an object, but rather the object moving along a geodesic path that manifests the appearance of acceleration.
• For comparison, what happens if you send a massive particle in the same direction at, say, 0.999c? – called2voyage Jun 7 '17 at 18:52
• Generally speaking, it'll draw out a similar geodesic (straight line on a curved surface). – KareemElashmawy Jun 7 '17 at 18:59
• Ok, that's what I thought. So really, the reason, in general relativity, that a photon experiences no acceleration in this situation is not because it is massless, but because no particle experiences true acceleration in this situation in the context of general relativity. – called2voyage Jun 7 '17 at 19:05
• I've updated my answer to address both of your questions generally. @kayleeFrye_onDeck: your memory is referencing the introduction to geodesics. – KareemElashmawy Jun 7 '17 at 19:33
• Since no external force acted upon the photon, it never accelerated - How does this relate to gravitational slingshots of massive objects? It's pretty clear that the object gained speed after performing the maneuver and the large mass lost speed. The well doesn't merely change direction for massive objects – Rob Jun 9 '17 at 5:42
Currently, there is no evidence that photons have mass, and it is generally accepted that they are massless particles.
Nonetheless, gravitation does affect the path of photons, because the bending of space-time causes all particles to travel on curved paths, including massless ones. But that does not mean than light will be accelerated. The speed of light (299,792,458 m/s) is an absolute maximum, and it may not decrease from that nor may it increase.
• The speed of light (299,792,458 m/s) is a maximum, and it may decrease than that rather than increase. ... no, no, it may not. Massless particles always travel at c, when they're traveling, not above it, nor below it. The difference between c and the apparent speed at which light traverses different mediums is a result of the time spent by photons interacting with particles in the medium they're travelling through. – HopelessN00b Jun 7 '17 at 14:39
• @Gnudiff If you were to track the path of an individual photon through a medium, it would travel in a straight line, at c, through the mostly empty space of the medium, until it "impacted" one of the particles composing the medium. At this point, the photon would get absorbed by the particle, exciting it to a higher energy state. After a brief time, the photon would be re-emitted by the particle. This process of absorption and re-emission takes time, and the vector of the re-emitted photon is not necessarily the same, so the path a photon takes is not a straight line. ... – HopelessN00b Jun 7 '17 at 15:32
• @Gnudiff ... the combination of these two effects (the time the photons spend "inside" the atoms of the medium, rather than travelling) and the fact that the photons are re-emitted at different vectors when they "exit" the atoms of the medium, lengthening their path relative to a straight line, account for the difference between c and the apparent speed of light in a medium. In short, when travelling through a medium, photons spend time "inside" atoms and also zig zag between atoms as they are re-emitted at different vectors, which lengthens the distance they travel. – HopelessN00b Jun 7 '17 at 15:40
• @industry in short (but I'm oversimplifying here) every interaction of light in a medium results in a fixed phase shift for the reemitted photon and if a plane coherent wave is incident on the medium then averaging over all these interactions will result in a coherent plane reemitted wave. – LLlAMnYP Jun 7 '17 at 21:19
• @industry7 to expand on the other response a bit, it comes down to a matter of probabilities. Any one photon could end up being retransmitted in any direction, but the odds are such that in aggregate, the "average" path will conform to the laws of optics (refractive index, angle of incidence = angle of reflection, etc). It's kind of like flipping a coin or a roll of a die. A coin doesn't "know" it's supposed to come up heads half the time, and you can't predict the result of any one flip, but do enough of them, and the results "average out" to 50/50. A simplification, but an accurate one. – HopelessN00b Jun 8 '17 at 3:17
Does the speed of light change due to the Sun? Well, yes and no. There are two ways in which one can think about speed in General Relativity. One is the coordinate speed, which means the rate of change of the spatial coordinate with respect to time coordinate of the coordinate system that you can choose at your will. Another is the speed as viewed from a special frame, namely the locally inertial frame in the vicinity of the considered light quanta. The fundamental aspect of General Relativity is that the Physics in a locally inertial frame is exactly the same as the Physics of Special Relativity. But due to gravity, these small-small local inertial frames are so arranged globally that a global inertial frame can't be formed. Now, in a generic frame of reference, i.e., in a generic coordinate system, the speed of light can certainly be different from $c$ and, in fact, it can even change with time.
For example, the speed of a photon moving radially in the vicinity of a spherically symmetric and static object is given by $v=\dfrac{dr}{dt}=c\bigg(1-\dfrac{2GM}{rc^2}\bigg)$ if you choose your spatial coordinates to be the spherical coordinates centered at the massive object with radial coordinate $r$ and keep track of time with a clock situated far away from the spherical object (star). As you can clearly see, the speed can vary with the radius $r$. Although, the speeding up and speeding down occurs in somewhat counter-intuitive fashion. An out-going photon seems to be speeding up and an in-going photon seems to be slowing down. Again, if you go to a local inertial frame, the speed is invariable $c$ but you don't have any frame that is inertial and can describe the motion of light for a finite time or within a finite region of space.
You are missing special relativity and general relativity. In special relativity the speed of light in vacuum is always c, no matter the reference frame of measurement.
Also classical electromagnetism, light, emerges from a confluence of the quantum mechanical constituents which are photons and have zero mass. A photon aiming at the barycenter of the sun is attracted by the gravitational field of the sun but the effect is not a change in velocity , but on its energy which is $E=h\nu$ and therefore the extra energy increases the frequency while the velocity remains at $c$.
• "You are missing special relativity and general relativity. In special relativity the speed of light in vacuum is always c, no matter the reference frame of measurement. " This might sound like the solution to the question is that in general relativity, the speed of light actually is increased by gravity. – JiK Jun 7 '17 at 15:34
• @jik not for local systems, those follow special relativity – anna v Jun 7 '17 at 16:26 | 2,970 | 12,907 | {"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": 1, "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} | 2.859375 | 3 | CC-MAIN-2021-25 | latest | en | 0.942522 |
http://www.thecalculator.co/health/Sleeping-BMR-Calculator-3.html | 1,477,466,959,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720760.76/warc/CC-MAIN-20161020183840-00484-ip-10-171-6-4.ec2.internal.warc.gz | 732,592,806 | 9,370 | This sleeping BMR calculator estimates the daily calories that are burned while you are asleep or doing nothing for 24 hours. Read more about the basal metabolic rate and calorie burning below the form.
Weight *
Height *
Age *
Gender *
Male
Female
Weight *
Height *
Age *
Gender *
Male
Female
## How does the sleeping BMR calculator work?
This useful tool can help you discover how many calories your body needs per day in order to maintain only the basic functions, this assuming that you only sleep or rest for the whole 24 hours.
In other words, the BMR calculator determines the minimum amount of energy you need to keep your vital body functions working properly. In order to provide you with this type of calculation you are going to be asked to input some data.
You will also have to decide whether you want to use the metric or the English system for your convenience.
There are then four things that you need to provide, your height, either in ft and inches or centimeters, your weight in lbs or kg and your age and gender.
The age is important to include because it reflects the way this value will decrease as one gets older. This, combined with the tendency to exercise less as we age, partly explains the tendency to put on weight as years go by.
## What is the basal metabolic rate?
This is defined as the amount of energy expended daily by humans or animals while they rest. This refers to what you need in order to keep your body alive with all the vital functions (for instance, but not limited to: heart beating, nervous system, skin, muscles).
It has been scientifically proved that the human body is continuously burning calories. This means that you use energy no matter what you're doing, even when you are sleeping.
Please note that your BMR estimation does not include the calories your burn while doing your daily activities or exercises, it includes only the minimum amount of energy to stay alive while resting.
There are few formulas to calculate your BMR, but below we will focus on presenting only the BMR formula we chose to use for this calculator.
### English BMR Formula
■ Female: BMR = 655 + (4.35 x Weight in pounds) + (4.7 x Height in inches) - (4.7 x Age in years)
■ Male: BMR = 66 + (6.23 x Weight in pounds) + (12.7 x Height in inches) - (6.8 x Age in years)
### Metric BMR Formula
■ Female: BMR = 655 + (9.6 x Weight in kg) + (1.8 x Height in cm) - (4.7 x Age in years)
■ Male: BMR = 66 + (13.7 x Weight in kg) + (5 x Height in cm) - (6.8 x Age in years)
## Example BMR calculation:
For a female aged 30, weighing 165 lbs at a height of 5ft 4in.
BMR = 655 + (4.35 x 165) + (4.7 x 65) - (4.7 x 30)
The calculated BMR value is going to be: 1,533 calories/ day. You can restart the calculation with any values you want for as many times as you like by pressing Calculate again.
## Other considerations:
The BMR calculator cannot be 100% accurate because it does not take into account body fat composition.
For example, there is a big difference between a person with a heavy muscular built and another person with the same weight but with more body fat.
In the case of the muscular person the BMR value under estimates their calorie needs while for the person carrying more fat, the BMR value will over estimate calorie requirement.
It should also be taken in consideration that although the body autonomous controls the rate of metabolic energy consumption this process can be influenced by environmental factors such as stress, excitement and even temperature.
## References
1) Harris J, Benedict F. (1918) A Biometric Study of Human Basal Metabolism. PNAS 4 (12): 370–3.
2) Müller, B; Merk, S; Bürgi, U; Diem, P. (2001) Calculating the basal metabolic rate and severe and morbid obesity. Praxis (Bern 1994) 90 (45): 1955–63.
3) Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. (1990) A new predictive equation for resting energy expenditure in healthy individuals. The American journal of clinical nutrition 51 (2): 241–7.
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https://cboard.cprogramming.com/c-programming/109795-memory-allocation-question.html | 1,490,724,747,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218189802.72/warc/CC-MAIN-20170322212949-00269-ip-10-233-31-227.ec2.internal.warc.gz | 758,131,173 | 16,160 | # Thread: Memory allocation question
1. ## Memory allocation question
I think my program is crapping out because of faulty memory allocation.
I want my code to read matrix.dat and store the numbers in a 4x4 matrix using pointer ........... Then I would like to print the matrix line by line but instead of the correct numbers, I get a long string of random numbers.
This is my overall code:
Code:
```void prob2(void)
{
FILE *Inf_1;
double **A=0, *b=0;
int row=0;
char text[81];
int k=0,t=0;
b = (double *)malloc((size_t)32);
A = (double **)calloc(16, sizeof(double *));
Inf_1 = fopen("matrix.dat", "r");
printf(" Put your solution for problem 2 here:\n");
//By using a pointer to pointer **A and the function calloc()
//allocate the memory for the 4x4 matrix A[][]
//By using a pointer *b and the function malloc() allocate the memory
//for the 4-dimensional vector b[]
if(b==NULL)
{
printf("(main) malloc failed in double *b\n");
exit(1);
}
if(A==NULL)
{
printf("(main) calloc failed in double **a\n");
exit(2);
}
for(row=0;row<16;row++)
{
A[row] = (double *)calloc(16, sizeof(double *));
if(A[row]==NULL)
{
printf("(main) calloc failed in double *A[]\n");
exit(4);
}
}
//Read the components of A and b from the given input file matrix.dat.
//The last line of the input file contains the components of b. The rows of
//matrix A are the first four lines of the input file.
if ((Inf_1 == NULL))
{
printf("Error opening the file\n");
exit(1);
}
while(fgets(text,81,Inf_1)!=NULL)
{
if (k < 5) {
sscanf(text, "%lf %lf %lf %lf", &A[t][0], &A[t][1], &A[t][2], &A[t][3]);
k++;
t++;
}
else
sscanf(text, "%lf %lf %lf %lf", b, b+1, b+2, b+3);
}
//Print the components of A[][] row by row, and the components of b[].
printf("\n");
for (k=0;k<4;k++) {
printf("a[%d][] = %lf %lf %lf %lf\n",k+1,&A[k][0],&A[k][1],&A[k][2],&A[k][3]);
}
}```
I'm trying to isolate my problem and I would like others to check over some key components.
1. True or false: This block of code reads file matrix.dat line by line (there are 5 lines total; every line has five numbers) and stores the numbers in a 4x4 matrix in A.
The else statement reads the last line on matrix.dat and stores the 4 numbers using pointer b.
Code:
```while(fgets(text,81,Inf_1)!=NULL)
{
if (k < 5) {
sscanf(text, "%lf %lf %lf %lf", &A[t][0], &A[t][1], &A[t][2], &A[t][3]);
k++;
t++;
}
else
sscanf(text, "%lf %lf %lf %lf", b, b+1, b+2, b+3);
}```
2. True/false: This loop of 16 allocates some memory for each row in my 4x4 matrix.
Code:
```for(row=0;row<16;row++)
{
A[row] = (double *)calloc(16, sizeof(double *));
if(A[row]==NULL)
{
printf("(main) calloc failed in double *A[]\n");
exit(4);
}
}```
3. True/false: This prints the numbers on matrix.dat.
Code:
```for (k=0;k<4;k++) {
printf("a[%d][] = %lf %lf %lf %lf\n",k+1,&A[k][0],&A[k][1],&A[k][2],&A[k][3]);
}```
This is matrix.dat by the way:
Code:
```-1.0 1.0 -4.0 -0.5
2.0 1.5 3.0 2.1
-3.1 0.7 -2.5 4.2
1.4 0.3 2.4 -1.9
0.0 1.2 -3.0 -0.5```
Anyone know why my output is:
a[1][] = 0.000000 0.000000 -51371471092907161178215517680210201070883690439141 41531451094331347592107749648920245017535748877081 62688667630716613389078816118684482410273456360890 67293804625029028204093572680075524848238599093026 66019186939209269159188445012222149148388435131742 64331967577566243348855100186528081647614005590664 15104.000000 0.000000
a[2][] = 0.000000 0.000000 -51371471092907161178215517680210201070883690439141 41531451094331347592107749648920245017535748877081 62688667630716613389078816118684482410273456360890 67293804625029028204093572680075524848238599093026 66019186939209269159188445012222149148388435131742 64331967577566243348855100186528081647614005590664 15104.000000 0.000000
a[3][] = 0.000000 0.000000 -51371471092907161178215517680210201070883690439141 41531451094331347592107749648920245017535748877081 62688667630716613389078816118684482410273456360890 67293804625029028204093572680075524848238599093026 66019186939209269159188445012222149148388435131742 64331967577566243348855100186528081647614005590664 15104.000000 0.000000
a[4][] = 0.000000 0.000000 -51371471092907161178215517680210201070883690439141 41531451094331347592107749648920245017535748877081 62688667630716613389078816118684482410273456360890 67293804625029028204093572680075524848238599093026 66019186939209269159188445012222149148388435131742 64331967577566243348855100186528081647614005590664 15104.000000 0.000000
2. I would say 1 and 3 are true and 2 is false.
You're going to have to decide whether A is 4x4 or 16x16, or some mixture. Currently it's 16x?, depending on the size difference between double and double* (each row does not have enough room to store 16 doubles, it has enough room for 16 double*'s, despite the fact that you don't intend to store double* in it; it's probably enough room for 8 doubles, but the indexing is going to be way wrong).
3. I'm trying to make my matrix a 4x4 matrix. What's the indication that it's a 16x16 matrix?
4. Originally Posted by dakarn
I'm trying to make my matrix a 4x4 matrix. What's the indication that it's a 16x16 matrix?
The bunches of "16" in the code, and no "4"s.
5. I switched up my code a little bit but my understanding may be faulty here:
A = (double **)calloc(16, sizeof(double *));
Allocates enough memory for 16 doubles?
Code:
```for(row=0;row<4;row++)
{
A[row] = (double *)calloc(4, sizeof(double *));
if(A[row]==NULL)
{
printf("(main) calloc failed in double *A[]\n");
exit(4);
}
}```
allocates memory for 4 doubles for each row of 4?
Thanks for the replies tabstop!
6. Originally Posted by dakarn
I switched up my code a little bit but my understanding may be faulty here:
A = (double **)calloc(16, sizeof(double *));
Allocates enough memory for 16 doubles?
No, it allocates 16 rows (that don't yet have any memory in it).
Code:
```
for(row=0;row<4;row++)
{
A[row] = (double *)calloc(4, sizeof(double *));
if(A[row]==NULL)
{
printf("(main) calloc failed in double *A[]\n");
exit(4);
}
}
```
allocates memory for 4 doubles for each row of 4?
Thanks for the replies tabstop!
It allocates memory for four pointers-to-double, not four doubles. (This may be enough memory, but is not guaranteed to be.)
7. Warning 3 warning C6272: Non-float passed as argument '3' when float is required in call to 'printf' g:\w00t\visual studio 2008\projects\temp\temp4.cpp 72
Warning 4 warning C6272: Non-float passed as argument '4' when float is required in call to 'printf' g:\w00t\visual studio 2008\projects\temp\temp4.cpp 72
Warning 5 warning C6272: Non-float passed as argument '5' when float is required in call to 'printf' g:\w00t\visual studio 2008\projects\temp\temp4.cpp 72
Warning 6 warning C6272: Non-float passed as argument '6' when float is required in call to 'printf' g:\w00t\visual studio 2008\projects\temp\temp4.cpp 72
Code:
``` for (k=0;k<4;k++) {
printf("a[%d][] = %lf %lf %lf %lf\n",k+1,&A[k][0],&A[k][1],&A[k][2],&A[k][3]);
}```
Perhaps you had better fix them?
8. Great catch Elysia!
This may be a stupid question but what kind of value is it if not a float?
9. You are passing double*, not double, to printf.
Besides, it should be %f, not %lf.
10. Yay fixed using:
Code:
```for (k=0;k<4;k++) {
printf("a[%d][] = %f %f %f %f\n",k+1,*A[k],*A[k]+1,*A[k]+2,*A[k]+3);
}```
My problem now is that it prints values but it prints the wrong values:
This is what it should print:
Code:
```-1.0 1.0 -4.0 -0.5
2.0 1.5 3.0 2.1
-3.1 0.7 -2.5 4.2
1.4 0.3 2.4 -1.9```
This is what it prints instead:
Code:
```a[1][] = -1.000000 0.000000 1.000000 2.000000
a[2][] = 2.000000 3.000000 4.000000 5.000000
a[3][] = -3.100000 -2.100000 -1.100000 -0.100000
a[4][] = 1.400000 2.400000 3.400000 4.400000```
Wtf? where did 4.4 come from?
To eliminate some ways it can possibly be wrong, I removed the sscanf section and just explicitly stated matrix A.
Here is my code now:
Code:
```void prob2(void)
{
FILE *Inf_1;
double **A, *b;
int row=0;
char text[81];
int k=0,t=0,l=0;
b = (double *)malloc((size_t)32);
A = (double **)calloc(4, sizeof(double *));
Inf_1 = fopen("matrix.dat", "r");
printf(" Put your solution for problem 2 here:\n");
//By using a pointer to pointer **A and the function calloc()
//allocate the memory for the 4x4 matrix A[][]
//By using a pointer *b and the function malloc() allocate the memory
//for the 4-dimensional vector b[]
if(b==NULL)
{
printf("(main) malloc failed in double *b\n");
exit(1);
}
if(A==NULL)
{
printf("(main) calloc failed in double **a\n");
exit(2);
}
for(row=0;row<4;row++)
{
A[row] = (double *)calloc(4, sizeof(double));
if(A[row]==NULL)
{
printf("(main) calloc failed in double *A[]\n");
exit(4);
}
}
//Read the components of A and b from the given input file matrix.dat.
//The last line of the input file contains the components of b. The rows of
//matrix A are the first four lines of the input file.
if ((Inf_1 == NULL))
{
printf("Error opening the file\n");
exit(1);
}
A[0][0]=-1.0;A[0][1]= 1.0;A[0][2]= -4.0;A[0][3]= -0.5;
A[1][0]= 2.0;A[1][1]= 1.5;A[1][2]= 3.0;A[1][3]= 2.1;
A[2][0]=-3.1;A[2][1]= 0.7;A[2][2]= -2.5;A[2][3]= 4.2;
A[3][0]= 1.4;A[3][1]= 0.3;A[3][2]= 2.4;A[3][3]= -1.9;
//Print the components of A[][] row by row, and the components of b[].
printf("\n");
for (l=0;l<4;l++) {
printf("a[%d][] = %f %f %f %f\n",l+1,*A[l],*A[l]+1,*A[l]+2,*A[l]+3);
}
}```
Anyone know why my program is printing the wrong values?
11. Do you have anything against using A[l][0] instead of *A[l]?
The problem stems from precedence of the operators:
you are actually doing
Code:
`*A[l], (*A[l])+1.0, (*A[l])+2.0, (*A[l])+3.0`
rather than:
Code:
`*A[l], *(A[l]+1), *(A[l])+2), *(A[l]+3)`
Oh, and don't use variables called "l" - it is very hard to see the difference between lower-case L and the number 1.
--
Mats
12. You should have a go at fixing your indentation, it's non-existent!.
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### Topic: Molarity problem (Read 8173 times)
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#### nemzy
• Guest
##### Molarity problem
« on: April 22, 2004, 01:21:21 AM »
If you put 25 mL of 1.6 M acetic acid, then, what is the molarity of acetic acid?
Is it just 1.6 M x .025 L, or is it .160 M / .025 L?
And..if you have 10 mL of 0.160 M sodium acetate , what is the moles of acetate in the solution?
Is it .160 M X .01 L,
im getting confused with the concepts involved in here
#### gregpawin
• Chemist
• Full Member
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• Ebichu chu chu chuses you!
##### Re:Molarity problem
« Reply #1 on: April 22, 2004, 01:40:06 AM »
You've just gotta keep track of those units and it'll all become obvious to you:
First molarity is moles over L, so just replace all M's with mol/L, and change mL into L. Whenever you see the word "of" in any kind of problem involving math, it means multiply. So if you're using 25mL of 1.6M of acetic acid, you're going to multiply them together. 0.025L X 1.6mol/L... notice how the units cancel; when dealing with these equations you're never going to get a mol2, L2, or anything similar unless its length, and even then you're probably doing something wrong if you have to do that... so cancel cancel cancel units!
Notice how you're not going to get molarity, but moles and there's no way around it with the information you gave.
Here's just a few reminders about conversions in chemistry:
Concentration X Volume = Mass(or Moles depending on concentration convention)
Moles X Molar Mass = Mass
Mass/Molar Mass = Moles
All of the understanding lies within keeping track of the units and canceling them out; if its not canceling, just multiply by its inverse.
I've got nothin'
#### Donaldson Tan
• Editor, New Asia Republic
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##### Re:Molarity problem
« Reply #2 on: April 27, 2004, 08:13:01 AM »
Acetic acid dissociate partially. You'll need to look up the acid dissociation constant of acetic acid to work out the amount of acetate present and the amount of acetic acid at equilibrium.
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006
#### AWK
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##### Re:Molarity problem
« Reply #3 on: April 30, 2004, 01:37:07 AM »
If you put 25 mL of 1.6 M acetic acid, then, what is the molarity of acetic acid?
Is it just 1.6 M x .025 L, or is it .160 M / .025 L?
Molarity is 1.6M.
That's another horse of color if you want to calculate a concentration of species in this solution (H+, CH3CCO- and undissociated CH3COOH) as Geodome suggests.
And..if you have 10 mL of 0.160 M sodium acetate , what is the moles of acetate in the solution?
Is it .160 M X .01 L,
OK
« Last Edit: April 30, 2004, 01:38:25 AM by AWK »
AWK
#### jdurg
• Banninator
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##### Re:Molarity problem
« Reply #4 on: April 30, 2004, 09:03:16 AM »
If you put 25 mL of 1.6 M acetic acid, then, what is the molarity of acetic acid?
Is it just 1.6 M x .025 L, or is it .160 M / .025 L?
Molarity is 1.6M.
That's another horse of color if you want to calculate a concentration of species in this solution (H+, CH3CCO- and undissociated CH3COOH) as Geodome suggests.
And..if you have 10 mL of 0.160 M sodium acetate , what is the moles of acetate in the solution?
Is it .160 M X .01 L,
OK
Heh. That second question can be a real doozy if you start taking into account the ability of the acetate ion to go and pull a hydrogen atom off of a water molecule and form acetic acid in solution.
"A real fart is beefy, has a density greater than or equal to the air surrounding it, consists | 1,245 | 4,121 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2022-49 | latest | en | 0.899921 |
http://calculator.academy/linear-combination-calculator/ | 1,590,919,684,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347413097.49/warc/CC-MAIN-20200531085047-20200531115047-00557.warc.gz | 21,359,898 | 43,628 | # Linear Combination Calculator
Enter the coefficients of x and y of two separate equations into the calculator. The linear combination calculator will solve for both x and y.
## Linear Combination Formula
The following formula can be used to calculate the x and y values of two equations using linear combination.
ax + by = c
dx + ey = f
x =( c – by )/ a = (f -ey)/d
y = (f-dx)/e = (c-ax)/b
• Where x and y are the coordinate points
• a and b are coefficients in one equation
• d and e are coefficients in the other equation
• f and c are constants
## FAQ
What is linear combination?
A linear combination is a mathematical process that involves two related equations. These equations are both in the form ax + by = c. Knowing the values of a, b, and c from both equations one can calculate the missing values of x and y that would solve those equations.
What are x and y coefficients?
The x and y coefficients are values that represent the change in true x and y values with respect to the equation or line the equation represents.
What is a slope?
A slope is the measure of vertical increase over the rise in horizontal increase of a line. | 261 | 1,156 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2020-24 | latest | en | 0.915755 |
https://www.themathdoctors.org/fun-with-a-quartic-equation/ | 1,718,964,307,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862070.5/warc/CC-MAIN-20240621093735-20240621123735-00225.warc.gz | 895,955,751 | 23,963 | # Fun with a Quartic Equation
#### (New Question of the Week)
Sometimes a problem leads to a very interesting discussion that brings out many good ideas – but then turns out to be something entirely different, which brings out even more (and simpler) ideas. This polynomial equation problem we helped with last week was like that. I will not be quoting the whole discussion as it took place, to avoid confusion, but just exploring some of the places we went.
## The problem
The initial question was simply stated, but clearly difficult:
(x+1)(x+2)(x+3)(x+4)=99
Find the real roots of the equation above.
The direct method of solution is to expand the left side and write it as a typical polynomial: $$x^4 + 10 x^3 + 35 x^2 + 50 x – 75 = 0$$. But this is a fourth-degree polynomial equation, which is not generally solvable without great effort. I quickly checked if it had a rational root, which would have to be a factor of 75; that didn’t look promising, and in fact I could see that the answer was no, without checking all the possibilities, by imagining what the graph of the left-hand side of the original equation would look like. The equation $$f(x) = (x+1)(x+2)(x+3)(x+4)$$ would have x-intercepts at $$x = -1, -2, -3$$, and $$-4$$, so from my experience with polynomials I knew the graph would be something like this:
The real roots of the equation will be the points where this graph crosses the horizontal line $$y = 99$$. Checking a couple values, $$f(0) = 24$$, and $$f(1) = 120$$, so it must cross between $$x=0$$ and $$x=1$$. Since we know any rational roots have to be integers, this means there aren’t any.
But from graphing, I knew that the graph is symmetrical. I don’t know a specific theorem that proves this must be true if the zeros are symmetrical as these are, but I’m sure it can be proved. (This is why I only bothered to check for a root on the right; the one on the left will be symmetrical with it.) I also had a pretty good guess that the “wiggles” in the graph would not be big enough to reach 99, so our equation would have only two real roots. (I could check that by evaluating the peak’s height, $$f(-2.5) = 0.5625$$).
## A solution
At this point I was out of standard ideas; I am by no means an expert on the theory of equations, as some other Math Doctors are! But I got an idea: If we shift the graph so that its line of symmetry is the y-axis, that might simplify things. It did. So I suggested trying this:
After playing with it for a while, I discovered an idea that worked. I’m sure there are others.
I observed that the function y = (x+1)(x+2)(x+3)(x+4) is a polynomial with zeros at -1, -2, -3, and -4, and experience told me that its graph will be symmetrical about the mean of those zeros, -2.5. (Just by imagining the graph and checking some numbers, I can also see that it will equal 99 between 0 and 1, and again between -5 and -6, giving two real solutions to the equation. But the rational root theorem shows that these can’t be rational numbers.)
So I tried making the symmetry visible, by translating the graph right by 2.5, by replacing x with u-2.5. Try doing that, and see what happens.
Here is the rest of my work following this idea, which I actually wrote up later, after the solution had been found by other means:
After substitution, we have (u – 3/2)(u – 1/2)(u + 1/2)(u + 3/2) = [(u – 1/2)(u + 1/2)][(u – 3/2)(u + 3/2)] = (u2 – 1/4)(u2 – 9/4). This has to equal 99:
(u2 – 1/4)(u2 – 9/4) = 99
Letting v = u2 and expanding, we get (v – 1/4)(v – 9/4) = 99, which expands to v2 – 5/2 v + 9/16 = 99; multiplying by 16 to eliminate fractions, 16v2 – 40v – 1575 = 0.
By the quadratic formula, I get v = (40 ± 320)/32 = 45/4 or -35/2. Since this is u2 and we only want real roots, u = ±sqrt(45/4) = ±3 sqrt(5)/2.
Then, in turn, x = u – 5/2 = (-5 ± 3 sqrt(5))/2.
Incidentally, the problem was supposed to be solved without a calculator; I didn’t need one, but the work would have been a little cumbersome without it.
## An easier solution
The student, in the meantime, found a different way to solve it, which is perhaps a little less intuitive and must have been accidentally discovered in an impressive bit of insight. Here is my version of what he did:
We can expand the left side partially, just multiplying (x+1)(x+4) and then (x+2)(x+3):
(x^2+5x+4)(x^2+5x+6) = 99
The interesting thing is that the factors both contain x^2 + 5x, which we can replace with t, giving
(t + 4)(t + 6) = 99
t^2 + 10t – 75 = 0
(t + 15)(t – 5) = 0
t = -15 or 5.
This implies that either
x^2 + 5x = -15 or x^2 + 5x = 5;
these yield
x = (-5 ± sqrt(-35))/2 and
x = (-5 ± sqrt(45))/2;
only the latter solutions are real, and they are the same as mine.
Like my solution, but more quickly, this reduced the quartic equation to a quadratic, which could be solved.
## The real problem and a really easy solution
But in the process of discussing all this, the student revealed that he had accidentally omitted part of the problem, which should have been this:
(x+1)(x+2)(x+3)(x+4)=99
Find the sum of the real roots of the equation above.
Since the real roots were $$\frac{-5 \pm \sqrt{45}}{2}$$, their sum is -5, so that is the answer.
But that problem could have been solved instantly by my original observation that the graph was symmetrical about $$x=-2.5$$, and that there are only two of them:
There could conceivably be four real roots of the equation (that is, places where the graph crosses y=99), if the peak in the middle of the graph were high enough. That would happen, in fact, if we replaced 99 with 0.5. They probably chose 99 to be so high that there would be no question.
Given that fact, we don’t need to know the two real roots themselves. Because of symmetry, they will be -2.5 plus something, and -2.5 minus the same thing; their sum is -5: (-2.5 + p) + (-2.5 – p) = -5.
So most of the conversation was “wasted”, if you consider only what was actually needed in order to solve the problem; yet it took us into some very interesting areas on our long detour!
Incidentally, there is a lot known about quartic equations that is more advanced (and which I wouldn’t have used here even if I knew them well, because this problem clearly was meant to be solved simply). Here are some discussions we have had on such methods:
Ferrari's Method for Quartics
Factoring Quartics
Is There a 'Discriminant' for a Quartic Equation?
Is There a "Discriminant" for a Quartic Equation ... in Closed Form?
Solving the Quartic
Solving a Quartic Equation with Substitutions
This last one shows my method, exactly – in fact, I could have copied my work and explanation from here, if I had known about it! So it wasn’t a great new discovery; but since it was new to me, it was fun.
Here is one final thought: Since both my method and the student’s depend on the symmetry of the zeros, his method should work for the problem on that last page. In fact, it does; we get the same real roots that Doctor Douglas got, and a pair of ugly complex roots as well, with considerably less work. I am curious to know whether that, too, is a well-known trick.
### 1 thought on “Fun with a Quartic Equation”
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2,012 | 7,256 | {"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": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2024-26 | latest | en | 0.959876 |
https://www.math-inic.com/blog/30msc-2023-2-addition-without-carrying/ | 1,709,619,388,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707948223038.94/warc/CC-MAIN-20240305060427-20240305090427-00652.warc.gz | 865,074,641 | 12,613 | # 30MSC 2023 #2: Addition without Carrying.
Addition is usually considered as the easiest arithmetic operation and can often be done from left to right when the addends are composed of small digits. But when the digits of the addends are big, regroupings or “carrying” are needed so that students often go back to the traditional right to left method taught in schools.
This question which was given in the junior division of the 2nd MATH-Inic Vedic Mathematics National Challenge in April 2022, would ordinarily require six regroupings.
888999 + 999888 = ?
Here the Sutra or Vedic Math formula By the Completion or Non-Completion can be used to avoid “carrying”.
First, we notice that both addends 888,999 and 999, 888, are very near 1,000,000. By using the sutra discussed in 30MSC 2023 #1, All From 9 and the Last From 10, we can see that their deficiencies from 1 million are 111,001 and 112 respectively and that 999,888 is nearer one million that the other addend.
We can immediately announce the answer as one million (for 999,888), then reading aloud the other addend, eight hundred eighty-eight thousand, (while mentally subtracting 112 from 999), eight hundred eighty-seven.
888999 + 999888 = 1,888,887
Other ways to avoid “carrying” in addition can be found in Chapter 2 of our rewritten e-book, 30 Master Strategies in Computing, Volume I, which will be available before the end of the year.
Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s 30MSC 2023 #3: Subtraction without Borrowing. | 391 | 1,572 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2024-10 | longest | en | 0.930542 |
https://brilliant.org/problems/thinking-inside-the-box-2/ | 1,501,101,956,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549426629.63/warc/CC-MAIN-20170726202050-20170726222050-00696.warc.gz | 630,016,599 | 18,419 | # Thinking Inside the Box
Geometry Level 2
$$Q$$ is the point of intersection of the diagonals of one face of a cube whose edges have length $$2\text{ cm}$$.
If the length of $$QR$$ (in $$\text{cm}$$) is $$x\sqrt{y}$$, where $$x$$ and $$y$$ are positive integers with $$y$$ square-free, find $$x+y-xy$$.
× | 97 | 309 | {"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": 0, "mathjax_display_tex": 1, "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} | 2.671875 | 3 | CC-MAIN-2017-30 | longest | en | 0.760062 |
https://research.stlouisfed.org/fred2/series/DANB809TRAD | 1,448,490,166,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398446218.95/warc/CC-MAIN-20151124205406-00278-ip-10-71-132-137.ec2.internal.warc.gz | 845,755,009 | 19,246 | # All Employees: Trade, Transportation, and Utilities in Danbury, CT (NECTA)
2015-10: 17.7 Thousands of Persons
1yr | 5yr | 10yr | Max
The data services of the Federal Reserve Bank of St. Louis include series that are seasonally adjusted. To make these adjustments, we use the X-12 Procedure of SAS to remove the seasonal component of the series so that non-seasonal trends can be analyzed. This procedure is based on the U.S. Bureau of the Census X-12-ARIMA Seasonal Adjustment Program. More information on this program can be found at http://www.census.gov/srd/www/x12a/.
The seasonal moving average function used is that of the Census Bureau’s X-11-ARIMA program. This includes a 3x3 moving average for the initial seasonal factors and a 3x5 moving average to calculate the final seasonal factors. The D11 function is also used to output the entire seasonally adjusted series that is displayed. For specific information on the SAS X-12 procedure, please visit their website: http://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_x12_sect001.htm.
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Create your own data transformation: [+]
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Use a formula to modify and combine data series into a single line. For example, invert an exchange rate a by using formula 1/a, or calculate the spread between 2 interest rates a and b by using formula a - b.
Use the assigned data series variables above (e.g. a, b, ...) together with operators {+, -, *, /, ^}, braces {(,)}, and constants {e.g. 2, 1.5} to create your own formula {e.g. 1/a, a-b, (a+b)/2, (a/(a+b+c))*100}. The default formula 'a' displays only the first data series added to this line. You may also add data series to this line before entering a formula.
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``` Federal Reserve Bank of St. Louis, All Employees: Trade, Transportation, and Utilities in Danbury, CT (NECTA) [DANB809TRAD], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/DANB809TRAD/, November 25, 2015. ```
Retrieving data.
Graph updated. | 611 | 2,428 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2015-48 | latest | en | 0.865064 |
https://calciosfondo.jdevcloud.com/tag/radical/page/2/ | 1,709,252,848,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474893.90/warc/CC-MAIN-20240229234355-20240301024355-00003.warc.gz | 148,812,066 | 6,988 | ## Distress Tolerance Radical Acceptance Worksheet References
Distress Tolerance Radical Acceptance Worksheet. ) practicing radical acceptance step by step observe that you are questioning or fighting reality (“it shouldn’t be this way”). Acceptance means being willing to experience a situation as it is. Source : www.pinterest.com Before… Continue Reading
## Simplifying Radical Expressions Worksheet Algebra 2 References
Simplifying Radical Expressions Worksheet Algebra 2. $$4^{0.5}\cdot 4^{0.5}=2\cdot 2=4$$ $$4^{0.5}=4^{1\div 2}=\sqrt{4}=2$$ you may know that the more exact term for the root of is the square root of. 1 24 2 6 2 3. Source : www.pinterest.com 23 scaffolded questions… Continue Reading
## Radical Acceptance Worksheet Therapist Aid References
Radical Acceptance Worksheet Therapist Aid. 7 best radical acceptance images on pinterest from radical acceptance worksheet, source: Ad the most comprehensive library of free printable worksheets & digital games for kids. Source : www.pinterest.com Ad the most comprehensive library of… Continue Reading
Simplifying Radical Expressions Worksheet Answers. (a) a perfect square (b) a perfect square (c) a perfect square (d) a perfect square be careful! 13 5,1 a b 1a 1b 14 19 2 3 5 1a b 14 9 113 1a… Continue Reading
## Printable Dbt Radical Acceptance Worksheet 2021
Printable Dbt Radical Acceptance Worksheet. ) practicing radical acceptance step by step ) rality ceptance skillse ac due date: Source : www.pinterest.com 10 images about dbt on pinterest | mindfulness, counseling and. 53 prac7cing radical acceptance 59 using coping thoughts.… Continue Reading
## Radical Acceptance Worksheet Free References
Radical Acceptance Worksheet Free. 17 best images about codependency group on pinterest | enabling. 48 best radical acceptance images on pinterest from radical acceptance worksheet. Source : www.pinterest.com A thought, feeling, event, life circumstance…etc), the more they come back to… Continue Reading
## Simplifying Radical Expressions Worksheet Doc 2021
Simplifying Radical Expressions Worksheet Doc. (a) (b) (c) 2×12 3 24×2 12 3 2 24×2 2 3 note 28×2 b 19 8×2 9 12 5 12 a 125 2 25 3 2 19 a 14 9 4 remove any perfect… Continue Reading | 570 | 2,224 | {"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": 0, "mathjax_display_tex": 1, "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} | 2.765625 | 3 | CC-MAIN-2024-10 | latest | en | 0.681066 |
https://digitalblackboard.io/python/intro-python/4-data-structures/tuples/ | 1,680,141,829,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949093.14/warc/CC-MAIN-20230330004340-20230330034340-00630.warc.gz | 232,212,192 | 15,233 | ## Introduction
Tuples are similar to lists with the difference that they are immutable. Once created, their elements cannot be changed unless a new tuple object is created. Tuples are the obvious choice for a collection of constants that never change throughout the program. It is written as a sequence of comma-separated values enclosed within a pair of parentheses ().
Example
Defining a tuple.
1tupA = (1,2,3,3,4,5,6)
2tupB = (1,2,3,"Python","code")
3print(tupA)
4print(tupB)
(1, 2, 3, 3, 4, 5, 6)
(1, 2, 3, 'Python', 'code')
A nested tuple is tuple that contains other tuples as its elements.
Example
Nested tuple.
1newTup = (tupA, tupB,(2,4,6))
2newTup
((1, 2, 3, 3, 4, 5, 6), (1, 2, 3, 'Python', 'code'), (2, 4, 6))
A tuple can also contain other data structures or types as its elements.
Example
Tuple can contain heterogeneous data.
1newTup1 = (tupA, [1,2,4],"string")
2newTup1
((1, 2, 3, 3, 4, 5, 6), [1, 2, 4], 'string')
## Basic Tuple Operations
Just like lists, tuples can also be concatenated with the + operator.
Example
Concatenation of tuples.
1tupA + tupB
(1, 2, 3, 3, 4, 5, 6, 1, 2, 3, 'Python', 'code')
We can obtain the length (number of elements) of a tuple using the len() function.
Example
Length of a tuple.
1len(tupA)
7
A tuple can be repeated using the * operator.
Example
Repetition of a tuple.
1tupB*2
(1, 2, 3, 'Python', 'code', 1, 2, 3, 'Python', 'code')
The in keyword serves two purposes:
• used to check if a value is present in a sequence (e.g. list, tuple).
• used to iterate through a sequence in a for loop.
Example
Boolean expression with a tuple.
1"Python" in tupB # Is "Python" an element of tupB?
True
## Tuple Indexing and Slicing
Just like lists, tuples are ordered which means their elements can be accessed by specifying their corresponding indices.
Example
Indexing of a tuple.
1tupA[1]
2
Due to its immutability, trying to modify a tuple will lead to an error.
Example
Tuple is immutable.
1tupA[1] = 20
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
~\AppData\Local\Temp/ipykernel_6652/2988985137.py in <module>
----> 1 tupA[1] = 20
TypeError: 'tuple' object does not support item assignment
Instead, create a new tuple object by using a new assignment statement.
1tupA = (1,20,3,3,4,5,6)
2tupA
(1, 20, 3, 3, 4, 5, 6)
Tip
An alternative way to modify a tuple is to convert the original tuple to a list, make the modification and convert it back to a tuple.
Example
Modifying a tuple using a list.
1temp = list(tupA)
2temp[1]=20
3tupA_updated = tuple(temp)
4tupA_updated
(1, 20, 3, 3, 4, 5, 6)
Caution
In the above example, we could have used the original variable name in the assignment statement tupA = tuple(temp). The implication is that the variable name tupA now points to the new tuple object and no longer refers to the original tuple object i.e. (1, 2, 3, 3, 4, 5, 6).
Slicing for tuples are similar to those for lists. Recall the slicing syntax:
sequence[start:stop:step]
Parameter Description
start Optional (default=0). An integer number specifying at which position to start the slicing.
stop An integer number specifying at which position to end the slicing.
step Optional (default=1). An integer number specifying the step of the slicing.
Python uses half-open intervals: the start index is included while the stop index is not.
Example
Indexing of a tuple.
1tup1 = (2,4,6,8,9,10)
2tup1[0]
2
Example
Negative indexing.
1tup1[-2]
9
Example
Slicing of a tuple.
1tup1[2:]
(6, 8, 9, 10)
Chain indexing and slicing work for a nested tuple.
Example
Indexing of a nested tuple.
1tupA = (1,2,3,3,4,5,6)
2newTup1 = (tupA, [1,2,4],"string")
3newTup1[0]
(1, 2, 3, 3, 4, 5, 6)
Example
Chain indexing and slicing of a nested tuple.
1newTup1[0][2:5]
(3, 3, 4)
## Tuple Methods
The count() method returns the number of elements with the specified value.
Example
count() method.
1numbers = (1,2,2,2,3,3,4,5,6,6,8)
2numbers.count(3) # counts how many times the number 3 appears
2
The index() method searches the tuple for a specified value and returns its index.
Example
index() method.
1numbers.index(5)
7
In cases where there is more than one occurrence of the specified value, the index() method will only return the first index.
Example
index() method.
1numbers.index(2)
1
In contrast to lists, we see that there are fewer methods available to tuples since they are immutable.
Method Description
count() Returns the number of elements with the specified value.
index() Returns the index of the first element with the specified value. | 1,399 | 4,709 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "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} | 2.671875 | 3 | CC-MAIN-2023-14 | longest | en | 0.853456 |
https://www.teacherspayteachers.com/Product/Addition-and-Subtraction-Fact-Connection-Game-Winning-Touch-1073478 | 1,513,257,848,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948544124.40/warc/CC-MAIN-20171214124830-20171214144830-00359.warc.gz | 765,093,818 | 26,843 | Total:
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# Addition and Subtraction Fact Connection Game: Winning Touch
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Product Description
Why should you spend your hard-earned pesos on this product?
(Choose one)
a) you loved the cover and thought, “oh, what could be inside?”
b) you enjoy purchasing products from red diaper babies (you’ll have to Google that one)
d) you thought this activity seemed really cool and you want to try it out, and how much could you loose for 5 smackers?
Here’s the idea: there is no point in your students “practicing” addition facts (or any other factual information, for that matter) if they’re going to do it mindlessly. Good practice requires thinking, did you hear me, THINKING! A card with “7 + 6 = ?” printed on it does not provoke a lot of thinking, even if you put a cute bunny or bird on it. For one thing, it does not promote a specific strategy, so for all you know, the 2nd grader who is using the flash card is still “counting all” using his/her fingers. What’s the point of counting on your fingers if you’re trying to get to the next level, say “counting on,” or, dare we say it, recognizing it 7 + 6 as a “near double.”
This partner game is not about helping children practice specific addition strategies: in fact, if they don’t have any strategies, you should go back and work on those first. What this game is about is helping children think about addition and its inverse, subtraction. By focusing on placing a tile on a specific space on the board, students have to work through different addition facts. For example, if the student needs to place a 13 tile on the board, and it has to be placed in the 7 column in order to “touch” the side of another tile, then the student will say “hmmm, 7 + ? = 13.” As you can see, this is the “missing addend” method to solve a subtraction problem, which also promotes understanding of subtraction as a “part-whole” concept.
I’ve created 7 different versions of this game: your best bet would be to print up copies on colored card stock, separating each version by color, so that if two groups mix up their tiles, it will be easy to sort them out and put them back in their envelopes which go with the game. You might also want to mark them the tiles on the back with a letter so that if a tile ends up with another set of the same version, you can put it back.
I love this activity, and I use it with my students whenever they have a spare moment, either as part of morning work, or for practice when they have finished their regular work. It’s also a fun thing to send for homework; believe me, your kids will enjoy practicing addition and subtraction a lot more when they’re playing a game with their loved ones, rather than doing one of those cruddy worksheets that some teachers (not you) download from those chumpy math websites.
I’ve also included a blank board for you and your students to use; I think it would be really interesting to see what versions of this game they would come up with on their own. If you or your students make a good one, go ahead and send it over to me and I’ll mark it up into a polished version; not only will I send it back to you, but I’ll also give you props!
Total Pages
20 pages
Answer Key
N/A
Teaching Duration
45 minutes
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Sign up | 870 | 3,694 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2017-51 | latest | en | 0.953105 |
http://sqlanywhere-forum.sap.com/questions/14375/select-first-and-last | 1,516,523,818,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890394.46/warc/CC-MAIN-20180121080507-20180121100507-00507.warc.gz | 328,837,206 | 9,230 | # Select First and Last?
Does any short form exist to select only the first and the last entry of a query result-set? Something like: ```Select First C1, last C1 from table where x=y order by z ``` asked 16 Nov '12, 11:22 Martin 8.6k●119●152●237 accept rate: 14% Nica _SAP 866●7●22
I guess Breck's OLAP solution is the way to go. Another approach would be to use join two derived tables using FIRST with one ordered in ascending and one in descending order (as Markus has suggested): ```SELECT first_row_num, last_row_num FROM (SELECT FIRST row_num AS first_row_num FROM RowGenerator ORDER BY row_num ASC ) dtFirst, (SELECT FIRST row_num AS last_row_num FROM RowGenerator ORDER BY row_num DESC) dtLast ``` which obviously returns the same set as Breck's sample. If you don't need to have both values in one single row, combining both derived queries in a UNION ALL query would be efficient, methinks, too: ```SELECT 'first', * FROM (SELECT FIRST row_num AS first_row_num FROM RowGenerator ORDER BY row_num ASC ) dtFirst UNION ALL SELECT 'last', * FROM (SELECT FIRST row_num AS last_row_num FROM RowGenerator ORDER BY row_num DESC) dtLast ORDER BY 1 ``` answered 17 Nov '12, 17:48 Volker Barth 31.6k●321●465●678 accept rate: 32%
Will you settle for LESS elegant? ```SELECT TOP 1 first_row_num, last_row_num FROM ( SELECT row_num, FIRST_VALUE ( row_num ) OVER ( ORDER BY row_num ) AS first_row_num, LAST_VALUE ( row_num ) OVER ( ORDER BY row_num ) AS last_row_num FROM RowGenerator ) AS RowGenerator ORDER BY row_num DESC; first_row_num,last_row_num 1,255 ``` answered 16 Nov '12, 14:46 Breck Carter 27.1k●456●622●894 accept rate: 21% I definetly would like to mark more than one entry as an accepted answer... (19 Nov '12, 05:22) Martin
Possibly not what you searched for but ```select first C1 from table where x=y order by z desc ``` should get you the last C1. answered 16 Nov '12, 11:25 Markus Dütting 536●4●12●20 accept rate: 30% I hoped for something more elegant ;-) (16 Nov '12, 11:36) Martin
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last updated: 19 Nov '12, 05:22 | 678 | 2,441 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2018-05 | latest | en | 0.834065 |
https://www.mathworks.com/matlabcentral/answers/345007-write-values-in-new-matrix-and-mirror-values-with-symmetry-axis | 1,638,617,474,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00178.warc.gz | 960,208,633 | 23,303 | # Write values in new matrix and mirror values with symmetry axis
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wswur on 16 Jun 2017
Answered: Ankita Nargundkar on 22 Jun 2017
This is the case: In an script (not shown here) I generate a quadrant of an ellipse in a matrix, filled up with values (to create a 3D shape). I try to mirror this quadrant in a new matrix to obtain the complete ellipse, based on symmetry axis. Below my script is shown, but I don’t get it completely working. The only thing that works is copying the quadrant shape to the new matrix, starting in the centre of that matrix instead of position (1,1) as the original matrix does. But the quadrant gets copied with a single values, while instead the original quadrant exists of multiple different values. The first part scans the original matrix with the quadrant starting in position (1,1) and copies the values to a new matrix.
I hope someone can help me out!
for ii = 1:length(sigma_contact(:,A)) %old matrix
for jj = 1: length(sigma_contact(B,:)) %old matrix
if sigma_contact(round(ii),round(jj)) > 0
for x = 50 : length(complete_ellipse(1,:))
for y = 50 : length(complete_ellipse(1,:))
complete_ellipse(x,y) = sigma_contact(ii,jj) ; %swrite matrix values in new matrix
end
end
else
%do nothing / next row
end
end
end
for i = A:length(complete_ellipse(A,:)) %till symmetry axis
for j = B: length(complete_ellipse(B,:)) %till symmetry axis
for x = 1:A %begin in row till A
for y = B:length(complete_ellipse(B,:)) %from row B till end
complete_ellipse(x,y) = complete_ellipse(ii,jj) %left lower quadrant
complete_ellipse((A-x),(B-y)) = complete_ellipse(ii,jj) %left upper quadrant
end
end
for x = 1:A
for y = 1:B
complete_ellipse(x,y) = complete_ellipse(i,j)
end
end
end
end
Ankita Nargundkar on 22 Jun 2017
If you can find the center you can replicate it easily, Also try to find the equation. Also if you have curve fitting toolbox u can use it to fill the ellipse | 530 | 1,920 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2021-49 | latest | en | 0.769544 |
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Over the last five years, demand for hotel rooms in Cenopolis has increased significantly, as has the average price Cenopolis hotels charge for rooms. These trends are projected to continue for the next several years. In response to this economic forecast, Centennial Commerical, a real state developer, is considering a plan to convert several unoccupied office buildings it owns in Cenopolis inot hotels in order to maximize it's revenue from these properties.
Which of the following would it be most useful for Cenennial Commerical to know in evaluating the plan it is considering ?
Whether the population of Cenopolis is expected to grow in the next several years.
Whether demand for office space in Cenopolis is projected to increase in the near future.
Whether the increased demand for hotel rooms, if met, is likely to lead to an increase in the demand for other travel-related services.
Whether demand for hotel rooms has also increased in other cities where Centennial owns office buildings
Whether, on average, hotels that have been created by converting office buildings have fewer guest rooms than do hotels that were built as hotels.
[Reveal] Spoiler: OA
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11 Jun 2008, 07:02
B it is.
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11 Jun 2008, 08:14
Over the last five years, demand for hotel rooms in Cenopolis has increased significantly, as has the average price Cenopolis hotels charge for rooms. These trends are projected to continue for the next several years. In response to this economic forecast, Centennial Commerical, a real state developer, is considering a plan to convert several unoccupied office buildings it owns in Cenopolis inot hotels in order to maximize it's revenue from these properties.
Which of the following would it be most useful for Cenennial Commerical to know in evaluating the plan it is considering ?
Whether the population of Cenopolis is expected to grow in the next several years.
-doesnt affect the plan
Whether demand for office space in Cenopolis is projected to increase in the near future.
-no sense converting office space into hotels in case the demand for office space would increase in the near future.
Whether the increased demand for hotel rooms, if met, is likely to lead to an increase in the demand for other travel-related services.
-out of scope of plan
Whether demand for hotel rooms has also increased in other cities where Centennial owns office buildings
-other cities is out of scope of the plan
Whether, on average, hotels that have been created by converting office buildings have fewer guest rooms than do hotels that were built as hotels.
-fewer guest rooms or not - here some revenue is better than having none at all from unoccupied office space.
B.
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Re: Over the last five years, demand for hotel rooms in [#permalink]
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11 Jun 2008, 08:40
Over the last five years, demand for hotel rooms in Cenopolis has increased significantly, as has the average price Cenopolis hotels charge for rooms. These trends are projected to continue for the next several years. In response to this economic forecast, Centennial Commerical, a real state developer, is considering a plan to convert several unoccupied office buildings it owns in Cenopolis inot hotels in order to maximize it's revenue from these properties.
Which of the following would it be most useful for Cenennial Commerical to know in evaluating the plan it is considering ?
Whether the population of Cenopolis is expected to grow in the next several years.
Whether demand for office space in Cenopolis is projected to increase in the near future.
Whether the increased demand for hotel rooms, if met, is likely to lead to an increase in the demand for other travel-related services.
Whether demand for hotel rooms has also increased in other cities where Centennial owns office buildings
Whether, on average, hotels that have been created by converting office buildings have fewer guest rooms than do hotels that were built as hotels.
I think it is E. Although not the best, E is the only answer choice that talks about 'conerverting office buildings'. We're not so much concerned about 'office space' - even if the demand for office space increased, who know what the revenue is like for office space.
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Re: Over the last five years, demand for hotel rooms in [#permalink]
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11 Jun 2008, 09:16
B for me
The offices are vacant due to no or low demand. If demand increased then the offices will not be vacant.
I used POE too
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11 Jun 2008, 09:21
I said B as well
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Re: Over the last five years, demand for hotel rooms in [#permalink]
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11 Jun 2008, 15:15
B looks the best.
If the demand for offices increase as well, it would not be a clever idea to convert those building into Hotels.
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11 Jun 2008, 15:28
The plan calls for maximizing revenues by converting office buildings to hotels. I think they need to know if there can be enough number of rooms to maximize the revenues. So it is E for me.
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11 Jun 2008, 15:59
I think it should be E.
As for B, it is possible for the demand for offices to increase while price remains constant, which does not appeal to the expected trend.
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14 Jun 2008, 16:18
whats the OA?
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14 Jun 2008, 19:56
It should be 'B'.
Whether the demand for office space is increased will justify the developer's plan to convert the unoccupied office building to a new hotel.
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15 Jun 2008, 05:29
B it should be .....
Pl post the OA as B
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09 Oct 2010, 10:46
A bit late, but yeah the answer is B.
I dig up this thread as I was looking for the problem typed. In appears in GMATPrep, and I don't want to retype all my problems.
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Re: Over the last five years, demand for hotel rooms in [#permalink]
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12 Dec 2010, 23:55
This is a GMAT Prep question and the OA is B.
If the demand for office space goes up - it may generate more revenue than hotel rooms. If the demand for office space space doesnt rise - a hotel is the viable option.
Hence 2 opposing answers to option B change the overall answer.
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Re: Over the last five years, demand for hotel rooms in [#permalink]
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13 Dec 2010, 06:44
+1 for B
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Re: Over the last five years, demand for hotel rooms in [#permalink]
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13 Dec 2010, 15:08
+1 B
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13 Dec 2010, 21:00
I will go for - B
In Argument, its mentioned "Un occupied " office space... nowhere its mentioned that cenpolis will convert all his occupied offices also into hotels.... So defintly office demands are not more and revenues generating through occupied offices is also OK. So, before converting their unoccupied office space into hotel....demand of office in future should be checked by the business.....
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06 Jan 2011, 12:43
I could make a case in favor of E.
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01 Aug 2011, 00:11
I will go for - B
The aim of the plan is to maximize its revenues.
If the demand for office space in Cenopolis is projected to increase in the near future, Centennial Commercial needs not to spend its money to convert its office buildings into hotels.
Converting into hotel costs a lot(purchasing furniture, hiring employees, promoting hotel, renovating, and so on.)
Compare to the situations.
Just lenting Office facilities without further investment(in the near future, the demand for office space in Cenopolis would increase) or converting into hotel.
What if you are a CEO of Centennial Commercial, which way would you choose to maximize its revenues?
e) it's too complicate to calculate. we need lots of information to know e) is correct or not.
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# What number is quadruple?
Updated: 9/16/2023
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### What is it called to multiply by 4?
its called a multiple of 4 You quadruple the number
### What is it called when you times a number by 4?
to quadruple a number
4
multiply it by 4
### What does quadruple?
Most quantities can quadruple.
### What is a sentence with quadruple?
Quadruple means four-fold, or four times. I now have quadruple the money that I started with.
### How do you spell quadruple?
That is the correct spelling of the word "quadruple".
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Quadruple means 4 times
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does quadruple have any silver in it
### How do you put 'quadurple' in a sentence?
Quadruple means making four of the original one. Example:If you give me a dollar and I return four, you will have quadruple the money you started with.Multiply each ingredient in the recipe by four, and you will have quadruple the number of cookies of the original recipe.On the lighter side: 'Quadurple' would be four purples...
### Can carbon form quadruple bonds?
carbons cannot have quadruple bonds.
### What number has a cube root and a quadruple root that are both integers?
0, 1 and any number that is a 12th power. | 360 | 1,447 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-10 | latest | en | 0.923176 |
http://www.exceltrick.com/page/2/ | 1,500,583,264,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423486.26/warc/CC-MAIN-20170720201925-20170720221925-00229.warc.gz | 418,798,491 | 9,031 | ## What is Excel VBA? : Excel VBA Basics 001
Visual Basic for Applications (VBA) in Excel, is a powerful and sophisticated built-in programming language that allows you to write your own functions or commands in an Excel spreadsheet. These custom functions or commands, can help to ease your tasks and thus by using Excel VBA you can do almost any imaginable thing in Excel. Now, before we … [Read more...]
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https://www.exceldemy.com/convert-7-digit-julian-date-to-calendar-date-in-excel/ | 1,701,169,864,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679099281.67/warc/CC-MAIN-20231128083443-20231128113443-00828.warc.gz | 836,793,463 | 75,547 | # How to Convert 7 Digit Julian Date to Calendar Date in Excel (3 Ways)
Get FREE Advanced Excel Exercises with Solutions!
Often, food manufacturers, pharmaceutical companies, and different other sectors use the Julian date format in their products. But this date format is not practical these days. People find it hard to understand as they are used to the Gregorian Calendar format only. In this article, we’ll show you the easiest ways to convert 7 digit Julian Date to Calendar Date in Excel.
To illustrate, we’re going to use a sample dataset as an example. For instance, the following dataset represents the Product, Dispatch Date in JLD (Julian Date) format of a company.
## Introduction to 7 Digit Julian Date Format
The date format which uses the combination of a year and the number of days since the start of that year is known as Julian Date format. In the 7 Digits Julian date format, the first 4 digits refer to the year and the last 3 digits are the total number of days from the beginning of that year.
## How to Convert 7 Digit Julian Date to Calendar Date in Excel: 3 Ways
### 1. Convert 7 Digit Julian Date to Calendar Date with Combination of DATE, LEFT & RIGHT Functions in Excel
Excel provides many functions and we use them for performing numerous operations. In this method, we’ll apply the DATE, LEFT & RIGHT functions. The DATE function generates a Gregorian calendar date. The arguments for the function include year, month, and day respectively. The LEFT function generates the specified number of characters from the start while The RIGHT function generates the specified number of characters from the end of a string. Therefore, follow the steps given below to convert Julian date to a calendar date in Excel.
STEPS:
• First, select cell D5 and type the formula.
`=DATE(LEFT(C5,4),1,RIGHT(C5,3))`
• Then, press Enter.
Here, the RIGHT function returns 3 characters from the end of the C5 cell value and the LEFT function returns 4 characters from the beginning. Next, the DATE function converts them to calendar date format and returns the accurate date.
• Use the AutoFill tool to fill the series with the formula.
### 2. Combine Excel DATE, MOD & INT Functions to Convert 7 Digit Julian Date to Calendar Date
Additionally, we can create a formula with the DATE, MOD & INT functions for converting the Julian Date. We use the MOD function to generate the remainder when a divisor divides a number. The INT function rounds a number to generate the nearest integer value. So, learn the below process to perform the task.
STEPS:
• Select cell D5 and type the formula.
`=DATE(INT(C5/10^3),1,MOD(C5,INT(C5/10^3)))`
• Press Enter.
The DATE function converts the arguments into the year, month, and day format. The INT function generates the nearest integer value after C5 is divided by 1000. The MOD function generates the remainder when C5 is again divided by that nearest integer value.
• Complete the rest with the AutoFill.
### 3. Apply VBA for Converting 7 Digit Julian Date to Calendar Date in Excel
We can use a VBA code to perform the conversion. Hence, follow the process given below to convert Julian date to a calendar date.
STEPS:
• Select Visual Basic from the Developer tab at first.
• As a result, the Visual Basic window will pop out.
• Now, select the Module under the Insert tab.
• The Module window will pop up.
• Afterward, copy the following code and paste it into the Module window.
``````Function JLDtoCD(JLD As String) As Long
Dim Year As Integer
Dim Day As Integer
Dim CD As Long
Year = CInt(Left(JLD, 4))
Day = CInt(Right(JLD, 3))
CD = DateSerial(Year, 1, Day)
JLDtoCD = CD
End Function``````
• Then, close the Visual Basic window.
• Select cell D5 and type the formula.
`=JLDtoCD(C5)`
• Press Enter.
• Apply the AutoFill tool to convert the rest.
Read More: How to Convert Date to Text YYYYMMDD
## Conclusion
Henceforth, you will be able to convert 7 digit Julian Date to calendar date in Excel with the above-described methods. Keep using them and let us know if you have any more ways to do the task. Don’t forget to drop comments, suggestions, or queries if you have any in the comment section below.
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Aung Shine
My name is Aung. I have my B.Sc. degree in EEE. From now on, I will be working with Microsoft Excel and other useful software, and I’ll upload articles related to them. My current goal is to write technical contents for anybody and everybody that will make the learning process of new software and features a happy journey.
1. Brilliant job.
Thanks a million..
2. I have a question…Your Formula works fine for converting a 7-digit Julian date to a calendar date. My question is how you modify to use a 4 digit one? 1st digit is the number of the year, and the next 3 digits are the day of the year – meaning that “3177” would be June 26th, 2023, and “5005” would be January 5th, 2025.
Where I work, we use 16-digit transaction codes and the digits 5-8 represent the Julian date. Extracting the Julian from the transaction number in excel is easy, I just need a formula to convert those 4 digits to a calendar date please!
• Dear PHILIP SMITH,
Thanks for reaching us. I understand that you want to convert a 4-digit Julian date to a Calendar date. In your specified format, the 1st digit is the number of the year, and the next 3 digits are the day of the year.
To demonstrate this problem, I have taken a dataset that contains 4-digit Julian Dates in the range C5:C10. To convert these Julian dates into Calendar dates, I applied the following formula:
=DATE(INT(YEAR(TODAY())/10)*10+VALUE(LEFT(C5,1)), 1, MOD(C5, 1000))
Now, you can extract the Julian date from the transaction number and apply the formula above to convert the Julian date to the calendar date.
Hopefully, I was able to resolve your problem. Let us know your feedback.
Regards,
Seemanto Saha
ExcelDemy
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A
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4
D
1
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## Solving 3x+4y=9,y=mx+1,we get x=53+4m Here, x is an integer if 3+4m=1,-1,5,-5. Hence m=-2/4, -4/4, 2/4,-8/4. So, m has two integral values.
|
Updated on:21/07/2023
### Knowledge Check
• Question 1 - Select One
## The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer is
A2
B0
C4
D1
• Question 2 - Select One
## The number of integral values of m, for which the x coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer, is
A2
B0
C4
D1
• Question 3 - Select One
## The number of integral values of m, for which the x coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer, is
A2
B0
C4
D1
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# Answer to Question #190191 in Electrical Engineering for Yara
Question #190191
Question 4:
A modulating signal m(t) = 0.8cos(200π t) is used to modulate a carrier signal givenby:c(t)=10cos(2π fct) fc >>100Hz
(a) Find the peak power of DSB and conventional AM signals
(b) Obtain the average power for DSB and conventional AM signals
1
2021-05-31T06:20:25-0400
Modulating signal (or) message signal
"m(t)=2cos(4000\\pi t)+5cos(6000\\pi t)"
"Carrier\\space signal, c(t)=100cos(2\\pi f_c t)"
"Given\\space f_c=50k\\space Hz"
"Am_1=2 \\space Am_2=5 \\space Ac=100 \\space fm_1=2kHz \\space fm_2=3kHz \\space f_c=50kHz"
a) Conventional Am
"Message\\space signal\\space form\\space m(t)=Am\\space cos(2\\pi f_mt)"
"Total\\space modulation\\space index\\space \\mu_t=\\sqrt{\\mu_1^2+\\mu_2^2}"
"\\mu_1=\\frac{Am_1}{Ac}\\space \\mu_2=\\frac{Am_2}{Ac}\\space"
"\\mu_1=\\frac{2}{100} \\space \\mu_2=\\frac{5}{100}"
"\\mu_t=\\sqrt{(0.02)^2+(0.05)^2}=0.05"
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for any assignment or question with DETAILED EXPLANATIONS! | 415 | 1,172 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2024-30 | latest | en | 0.599448 |
https://socratic.org/questions/how-do-you-find-the-domain-and-range-of-10-10-5-5-0-0-5-5-10-10 | 1,591,122,702,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347425481.58/warc/CC-MAIN-20200602162157-20200602192157-00076.warc.gz | 530,399,549 | 5,762 | # How do you find the domain and range of { (-10,10) , (-5,5) , (0,0) , (5,5) , (10,10) }?
Jun 13, 2017
See a solution explanation below:
#### Explanation:
In the set of ordered pairs {(-2, 0), (0, 6), (2, 12), (4, 18)}, the domain is the set of the first number in every pair (those are the x-coordinates):
{-10, -5, 0, 5, 10}.
The range is the set of the second number of all the pairs (those are the y-coordinates):
{-10, -5, 0, 5, 10}. | 163 | 446 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2020-24 | latest | en | 0.748842 |
http://bootmath.com/what-is-the-standardized-way-to-represent-pi-in-binary-notation.html | 1,532,040,624,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676591332.73/warc/CC-MAIN-20180719222958-20180720002958-00543.warc.gz | 59,102,704 | 6,817 | # What is the standardized way to represent $\pi$ in binary notation?
How do I best represent the number $\pi$ in binary?
I have been thinking about it for sometime and, if it was me, I would use four bits for each digit, because four bits are sufficient to represent 10-based digits. Something like:
0011 , 0001 0100 0001 ...
I wouldn’t know, also, how to represent the decimal point here.
I hope my question is clear enough.
# Update
I will put this into context. I didn’t want to, because I thought you would find it stupid.
I want to make a full back tattoo, representing pi in binary so, what I am looking for is a way that will be more or less simple to scale, as I will want thousands of digits, and I want it to be precise.
#### Solutions Collecting From Web of "What is the standardized way to represent $\pi$ in binary notation?"
What you’re suggesting is known as binary coded decimal representation. It is used by some simple calculators, and used to be commonly used in financial computing, because it can represent dollar amounts without rounding the cents (and also makes it easier to produce decimal output for human consumption). But it is harder to calculate with than true binary representation, which for $\pi$ is
11.0010010000111111011010101000100010000101101000110...
as found here. Here each bit after the point represents successively $1/2$, $1/4$, $1/8$, $1/16$, …, $2^{-n}$, …, so according to this representation
$$\pi = 2+1+1/8+1/64+1/2048+1/4096+\cdots$$
In practical computing, irrational numbers are nowadays almost always represented in binary, rounded to a fixed number of significant binary digits and then represented in a binary variant of scientific notation. There’s a widely-used standard for how to do this, IEEE-754, which allows different programs or systems to exchange floating-point values without first converting them to decimal notation. (A recent update of the standard defines more format, but is not as widely adopted).
Representing any real number in binary (or any base) is just the same principle as representing numbers in decimal.
For example, in decimal
$\frac{25}{8} = 3.125 = 3\cdot 10^0 + 1\cdot 10^{-1} + 2\cdot 10^{-2} + 5\cdot 10^{-3}$.
Now to write the same number in binary, first express it as a sum of powers of $2$ (this is exactly what you do when writing natural numbers in binary):
$\frac{25}{8} = 2 + 1 + \frac{1}{8} = 2\cdot 2^1 + 1\cdot 2^0 + 0\cdot 2^{-1} + 0\cdot 2^{-2} + 1\cdot 2^{-3} = 11.001_2.$
Any series of bytes can be represented in binary. You might as well encode Pi in bytes first, and then represent those bytes in binary.
If you use a “pure” binary format like described above, you’d need to write “,” which is not a valid binary digit.
File formats (series of bytes) are standardized unlike ad-hoc improvisations of binary encoding.
So what I’d suggest is: get hold of the B-file (a standardized format) of OEIS A000796 (B-file available here). Now you have your bytes. Now convert the bytes into an ASCII representation of binary digits.
Python 3:
>>> import urllib.request
Beware that the generated string (from bin) will start 0b. | 804 | 3,150 | {"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": 1, "mathjax_asciimath": 1, "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} | 3.984375 | 4 | CC-MAIN-2018-30 | latest | en | 0.933216 |
https://www.w3resource.com/javascript-exercises/javascript-math-exercise-93.php | 1,716,343,123,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058525.14/warc/CC-MAIN-20240522005126-20240522035126-00887.warc.gz | 925,085,626 | 27,557 | # JavaScript: Check downward trend, array of integers
## JavaScript Math: Exercise-93 with Solution
Write a JavaScript program to check if an array of integers has a downward trend or not.
Test Data:
([1, 3, 4, 7, 9, 10, 11]) -> false
([11, 10, 9, 7, 4, 3, 2, 0]) -> true
([1, 0, -2, -3, -12]) -> true
Sample Solution:
JavaScript Code:
``````/**
* Function to check if the elements in the array are in descending order.
* @param {number[]} nums - The array to be checked.
* @returns {boolean} - Returns true if the array is in descending order, false otherwise.
*/
function test(nums) {
return nums.every((item, i) => item > nums[i + 1] || item === nums[nums.length - 1]);
}
// Test cases
let nums = [1, 3, 4, 7, 9, 10, 11];
console.log("n = " + nums);
console.log("Process: " + test(nums));
nums = [11, 10, 9, 7, 4, 3, 2, 0];
console.log("n = " + nums);
console.log("Process: " + test(nums));
nums = [1, 0, -2, -3, -12];
console.log("n = " + nums);
console.log("Process: " + test(nums));
```
```
Output:
```n = 1,3,4,7,9,10,11
process: false
n = 11,10,9,7,4,3,2,0
process: true
n = 1,0,-2,-3,-12
process: true
```
Flowchart:
Live Demo:
See the Pen javascript-math-exercise-93 by w3resource (@w3resource) on CodePen.
Improve this sample solution and post your code through Disqus.
What is the difficulty level of this exercise?
Test your Programming skills with w3resource's quiz.
| 466 | 1,398 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2024-22 | latest | en | 0.59228 |
https://oneclass.com/class-notes/ca/u-of-waterloo/kin/kin-155/876726-kin155-lecture-1.en.html | 1,591,119,519,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347425481.58/warc/CC-MAIN-20200602162157-20200602192157-00447.warc.gz | 458,210,762 | 74,626 | Class Notes (1,100,000)
CA (650,000)
UW (20,000)
KIN (400)
KIN 155 (30)
Lecture 1
# KIN 155 Lecture Notes - Lecture 1: Standard Deviation, Central Tendency
Department
Kinesiology
Course Code
KIN 155
Professor
Fran Allard
Lecture
1
This preview shows half of the first page. to view the full 2 pages of the document.
What is statistically significant?
Being able to see the variability in a study
Difference study: means and Standard deviation
Probability and confidant they are different.
What is biologically or clinically significant?
Has a meaningful impact
Does the result make a difference in respect to the situation
Define in your own words the concept of the mean?
Overall average, showing the central tendency of the data
Define in your own words the concept of the Standard Deviation?
A measure of the variability around the central tendency
Stand error vs Standard Deviation
S.E.- distribution of how means compare
S.D. distribution of how means are individual standards points compare
Interpreting data (graphs and tables)
Differences versus associations?
Differences between groups/ treatments compares means and variability between groups.
(ex. Pre vs post exercise, Group A vs Group B)
Associations: see how one variable relates to the other. See correlation between variables.
What is statistically significant?
Being able to see the variability in a study
Difference study: means and Standard deviation
Associations: if the data is very comparable and it inter-laps each other.
Properties of means and standard deviation it doesn't cant about how different the
averages are
Probability and confidant they are different.
What is biologically or clinically significant?
Has a meaningful impact
Does the result make a difference in respect to the situation
If there is a overlap its okay
Is the difference meaningful
Depends on the situation and the group.
Can use means to figure out
(i.e. stroke patients gaining on VO2 is amazing compared to gaining 1 in an athlete not a
big difference)
Review questions:
Define in your own words the concept of the mean?
Overall average, showing the central tendency of the data
Define in your own words the concept of the Standard Deviation?
A measure of the variability around the central tendency
Stand error vs Standard Deviation
S.E.- distribution of how means compare
S.D. distribution of how means are individual standards points compare
find more resources at oneclass.com
find more resources at oneclass.com | 534 | 2,471 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2020-24 | latest | en | 0.911801 |
https://zbmath.org/?q=an:0743.58034 | 1,708,507,920,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473401.5/warc/CC-MAIN-20240221070402-20240221100402-00241.warc.gz | 1,143,151,669 | 11,836 | ## Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series.(English)Zbl 0743.58034
Let $$H$$ be the upper half plane, $$\Gamma\subset G=\text{PSL}_ 2(\mathbb R)$$ a discrete cocompact subgroup, $$X=\Gamma\backslash H$$ and $$\{\phi_ \lambda\}$$ the eigenfunctions of the Laplace operator. Then $\frac 1{N(\lambda)}\sum_{\sqrt{-\lambda j}\leq \lambda}|(A\phi_ j,\phi_ j)-\bar\sigma_ A|@>>\lambda\to \infty> 0,$ where $$A$$ is a 0th order pseudo-differential operator, $$\sigma_ A$$ is the principal symbol, $$d\omega$$ is the Liouville measure and $$\bar \sigma_ A=(1/\hbox{vol}(S^*X))\int_{S^*X}\sigma_ A d\omega$$. The purpose of this paper is to generalize this uniform distribution theorem to finite area, non-compact hyperbolic surfaces $$X_ \Gamma$$. Then $$L^ 2(\Gamma\backslash H)$$ takes the form $$L^ 2(\Gamma\backslash H)={^ 0L^ 2}(\Gamma\backslash H)\oplus \Theta$$, where $$^ 0L^ 2$$ is the cuspidal subspace and $$\Theta=L^ 2_{\hbox{eis}}\oplus L^ 2_{\hbox{res}}\oplus\mathbb C$$, $$L^ 2_{\hbox{eis}}$$ is spanned by the Eisenstein series, $$L^ 2_{\hbox{res}}$$ is a finite dimensional space spanned by residues of Eisenstein series at poles in $$]1/2,1[$$ and $$\mathbb C$$ denotes the constants. The author shows that the generic cusp function and the generic Eisenstein series tend to become uniformly distributed in the unit sphere bundle as the eigenvalues tend to infinity.
### MSC:
58J51 Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) 11F72 Spectral theory; trace formulas (e.g., that of Selberg)
### Keywords:
cusp forms; equidistribution; Eisenstein series
Full Text:
### References:
[2] de Verdière, Y. Colin, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys., 102, 497-502 (1985) · Zbl 0592.58050 [3] de Verdière, Y. Colin, Quasi-modes, Invent. Math., 43, 15-52 (1977) · Zbl 0449.53040 [4] Deshouillers, J. M.; Iwaniec, H., The non-vanishing of Rankin-Selberg zetafunctions at spectial points, (Contemporary Math., Vol. 53 (1986), Amer. Math. Soc: Amer. Math. Soc Providence, RI) · Zbl 0595.10025 [5] Fay, J., Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math., 293, 143-203 (1977) · Zbl 0352.30012 [6] Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series and Products (1980), Academic Press: Academic Press Sand Diego · Zbl 0521.33001 [7] Helgason, S., Groups and Geometric Analysis (1984), Academic Press: Academic Press San Diego [8] Hörmander, L., The Analysis of Linear Partial Differential Operators I (1983), Springer-Verlag: Springer-Verlag Berlin [9] Iwaniec, H., Prime Geodesic Theorem, J. Reine Angew. Math., 349, 136-159 (1984) · Zbl 0527.10021 [10] Iwaniec, H., Non-holomorphic modular forms and their applications, (Rankin, R., Modular Forms (1984), Wiley: Wiley New York) · Zbl 0558.10018 [11] Kubota, T., Elementary Theory of Eisenstein Series (1973), Kodansha Ltd: Kodansha Ltd Tokyo, and Wiley, New York · Zbl 0268.10012 [12] Lang, S., $$SL_2(R) (1975)$$, Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0311.22001 [13] Lewis, J., Eisenstein Series on the boundary of the Disk, (Thesis (1970), M.I.T. Univ. Press: M.I.T. Univ. Press Cambridge, MA) [14] Phillips, R.; Sarnak, P., On Cusp forms for co-finite subgroups of the $$PSL_2(R)$$, Invent. Math., 80, 339-364 (1984) · Zbl 0558.10017 [15] Sarnak, P., Asymptotic behaviour of periodic orbits of the horocycle flow and Eisenstein series, Comm. Pure Appl. Math., 34, 719-739 (1981) · Zbl 0501.58027 [16] Sarnak, P., On Cusp forms, Contemp. Math., 53 (1986) · Zbl 0707.11040 [17] Snirelman, A. I., Uspekhi Math. Nanuk, 29, 181-182 (1974) [18] Taylor, M., Pseudo-Differential Operators (1981), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ [19] Venkov, A. B., Spectral theory of automorphic functions, (Proc. Steklov Inst. Math., 4 (1982)) · Zbl 0501.10029 [20] Zagier, D., Eisenstein series and the Selberg trace formula, (Automorphic Forms, Representation Theory and Arithmetic (1981), Springer-Verlag: Springer-Verlag New York), 305-355, Bombay, 1979 [21] Zagier, D., The Rankin-Selberg method for automorphic functions which are not of rapid decay, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28, 415-439 (1981) · Zbl 0505.10011 [22] Zelditch, S., Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J., 55, 919-941 (1987) · Zbl 0643.58029 [24] Zelditch, S., Pseudo-differential Operators, trace formulae, and the geodesic period of automorphic forms, Duke Math. J., 56, 295-344 (1988) · Zbl 0646.10024 [25] Zelditch, S., Pseudo-differential analysis on hyperbolic surfaces, J. Funct. Anal., 688, 72-105 (1986) · Zbl 0612.58048 [26] Zelditch, S., The averaging method and ergodic theory for pseudo-differential operators on compact hyperbolic surfaces, J. Funct. Anal., 82, 38-68 (1989) · Zbl 0693.58025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. | 1,755 | 5,458 | {"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": 1, "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} | 2.625 | 3 | CC-MAIN-2024-10 | latest | en | 0.660906 |
https://mail.haskell.org/pipermail/haskell-prime/2006-March/000964.html | 1,501,138,755,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549427749.61/warc/CC-MAIN-20170727062229-20170727082229-00614.warc.gz | 664,862,794 | 2,448 | # Strict tuples
Manuel M T Chakravarty chak at cse.unsw.edu.au
Sat Mar 18 21:35:12 EST 2006
```Loosely related to Ticket #76 (Bang Patterns) is the question of whether
we want the language to include strict tuples. It is related to bang
patterns, because its sole motivation is to simplify enforcing
strictness for some computations. Its about empowering the programmer
to choose between laziness and strictness where they deem that necessary
without forcing them to completely re-arrange sub-expressions (as seq
does).
So what are strict tupples? If a lazy pair is defined in pseudo code as
data (a, b) = (a, b)
a strict pair would be defined as
data (!a, b!) = ( !a, !b )
Ie, a strict tuple is enclosed by bang parenthesis (! ... !). The use
of the ! on the rhs are just the already standard strict data type
fields.
Why strict tuples, but not strict lists and strict Maybe and so on?
Tuples are the Haskell choice of returning more than one result from a
function. So, if I write
add x y = x + y
the caller gets an evaluated result. However, if I write
addmul x y = (x + y, x * y)
the caller gets a pair of two unevaluated results. Even with bang
patterns, I still have to write
addmul x y = let !s = x + y; !p = x * y in (s, p)
to have both results evaluated. With strict tuples
addmul x y = (!x + y, x * y!)
suffices.
Of course, the caller could invoke addmul using a bang patterns, as in
let ( !s, !p ) = addmul x y
in ...
but that's quite different to statically knowing (from the type) that
the two results of addmul will already be evaluated. The latter leaves
room for more optimisations.
Syntax issues
~~~~~~~~~~~~~
* In Haskell (,) is the pair constructor. What should be use for
strict tuples? (!,!) ?
* With strict tuples (! and !) would become some sort of
reserved/special symbol. That interferes with bang patterns, as
(!x, y!) would be tokenized as (! x , y !). We could use ( ... !)
for strict tuples to avoid that conflict, or just requires that the
user write ( !x, !y ) when they want a bang pattern. (Just like you
cannot write `Just.x' to mean `Just . x' as the former will always be
read as a qualified name and not the application of function
composition.
Bang patterns enable the programmer (among other things) to define
functions with strict arguments. Strict tuples enable to define strict
results.
Manuel
PS: IIRC Clean supports strict tuples.
``` | 638 | 2,417 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2017-30 | longest | en | 0.920337 |
https://everythingwhat.com/what-percentage-of-the-data-is-within-2-standard-deviations-of-the-mean | 1,618,973,395,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039503725.80/warc/CC-MAIN-20210421004512-20210421034512-00546.warc.gz | 339,405,569 | 8,339 | # What percentage of the data is within 2 standard deviations of the mean?
Last Updated: 29th June, 2020
24
For an approximately normal data set, the valueswithinone standard deviation of the mean account for about68% ofthe set; while within two standard deviations accountfor about95%; and within three standard deviations account forabout99.7%.
Click to see full answer.
Hereof, what percentage of the data falls within 2 standard deviation of the mean?
95.4 percent
Secondly, what percent of values lie beyond 2 standard deviations of the mean? 95 percent
In respect to this, what is 2 standard deviations from the mean?
Standard Deviation. Specifically, if a set ofdatais normally (randomly, for our purposes) distributed aboutitsmean, then about 2/3 of the data values willliewithin 1 standard deviation of the mean value,andabout 95/100 of the data values will lie within 2standarddeviations of the mean value.
What percent of observations are between the mean and two standard deviations above the mean in a normal distribution?
Regardless of what a normal distributionlookslike or how big or small the standard deviationis,approximately 68 percent of the observations (or68percent of the area under the curve) will alwaysfallwithin two standard deviations (one above andonebelow) of the mean.
Professional
## What percentile is 2 standard deviations below the mean?
On some tests, the percentile ranks are closeto,but not exactly at the expected value. A score that istwoStandard Deviations above the Mean is at or closetothe 98th percentile (PR = 98). A score that istwoStandard Deviations below the Mean is at or close to the2ndpercentile (PR =2).
Professional
68%
Explainer
## How many standard deviations from the mean is an outlier?
Three standard deviations
Explainer
## What is 95 percent confidence interval?
A 95% confidence interval is a rangeofvalues that you can be 95% certain contains the true meanofthe population. With the small sample on the left, the95%confidence interval is similar to the range ofthedata.
Pundit
## How many standard deviations is significant?
We can determine how anomalous a data point is basedonhow many standard deviations it is from the mean. Thenormaldistribution has the following helpful properties: 68% ofdata iswithin ± 1 standard deviations from the mean.95% ofdata is within ± 2 standard deviations fromthemean.
Pundit
## What does a negative standard deviation mean?
In Simple terms, Standard Deviation is thethesquare root of Variance. And square root can neverbenegative. This also means that Varianceitselfcan't be negative. That is because Variance'squares'the differences of the data point fromthemean/average.
Pundit
## How much is two standard deviations?
If a data distribution is approximately normal thenabout68 percent of the data values are within onestandarddeviation of the mean (mathematically, μ ±σ,where μ is the arithmetic mean), about 95 percent arewithintwo standard deviations (μ ± 2σ), andabout99.7 percent lie within three standard deviations(μ± 3σ
Pundit
## What is a normal standard deviation?
A normal distribution with a mean of 0 andastandard deviation of 1 is called a standardnormaldistribution. Areas of the normal distribution areoftenrepresented by tables of the standard normaldistribution.For example, a Z of -2.5 represents a value 2.5standarddeviations below the mean.
Pundit
## What is mean and standard deviation?
The standard deviation is a statisticthatmeasures the dispersion of a dataset relative to itsmeanand is calculated as the square root of the variance. Ifthe datapoints are further from the mean, there is ahigherdeviation within the data set; thus, the more spreadout thedata, the higher the standard deviation.
Teacher
## How many standard deviations from the mean is that?
It is good to know the standard deviation,becausewe can say that any value is: likely to be within 1standarddeviation (68 out of 100 should be) very likely tobe within 2standard deviations (95 out of 100 should be)almostcertainly within 3 standard deviations (997 out of1000should be)
Teacher
## How many standard deviations away from the mean is the median?
Rules of thumb regarding spread
At least 75% of the data will be within twostandarddeviations of the mean. At least 89% of thedata will bewithin three standard deviations of themean. Databeyond two standard deviations away from themean isconsidered "unusual" data.
Teacher
## What is deviation from the mean?
The mean deviation (also called themeanabsolute deviation) is the mean of theabsolutedeviations of a set of data about the data'smean.For a sample size , the mean deviation isdefinedby.
Teacher
## What is standard deviation in math?
The Standard Deviation is a measure of howspreadout numbers are. Its symbol is σ (the greek lettersigma) Theformula is easy: it is the square root oftheVariance.
Reviewer
## Is standard deviation a percentage?
Due to its consistent mathematical properties,68percent of the values in any data set lie withinonestandard deviation of the mean, and 95 percentliewithin two standard deviations of the mean.
Reviewer
## How do you determine range?
Summary: The range of a set of data isthedifference between the highest and lowest values in the set.Tofind the range, first order the data from least togreatest.Then subtract the smallest value from the largest value intheset.
Reviewer
## What percent of values fall within 1/2 and 3 standard deviations from the mean?
For an approximately normal data set, thevalueswithin one standard deviation of themean accountfor about 68% of the set; while withintwo standarddeviations account for about 95%; andwithin threestandard deviations account for about99.7%.
Reviewer
95.4 percent
Supporter
## How do you calculate the Z score?
The formula for calculatingaz-score is z=(x-μ)/σ, where μisthe population mean and σ is the populationstandarddeviation (note: if you don't know the populationstandarddeviation or the sample size is below 6, you should useat-score instead of a z-score).
Supporter
## What is Z table in normal distribution?
The z-table is short forthe“Standard Normal z-table”. TheStandardNormal model is used in hypothesis testing,including testson proportions and on the difference between twomeans. The areaunder the whole of a normal distributioncurve is 1, or 100percent.
Co-Authored By:
4
29th June, 2020
35 | 1,455 | 6,420 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.984375 | 4 | CC-MAIN-2021-17 | latest | en | 0.84531 |
https://gas-dd.sagepub.com/lp/springer-journals/convergence-verification-of-the-collatz-problem-1RW9VhwTo8? | 1,708,795,187,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474541.96/warc/CC-MAIN-20240224144416-20240224174416-00194.warc.gz | 265,994,630 | 25,496 | # Convergence verification of the Collatz problem
Convergence verification of the Collatz problem This article presents a new algorithmic approach for computational convergence verification of the Collatz problem. The main contribution of the paper is the replacement of huge precomputed tables containing O(2N)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$O(2^N)$$\end{document} entries with small lookup tables comprising just O(N) elements. Our single-threaded CPU implementation can verify 4.2×109\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$4.2 \times 10^9$$\end{document} 128-bit numbers per second on Intel Xeon Gold 5218 CPU computer, and our parallel OpenCL implementation reaches the speed of 2.2×1011\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2.2 \times 10^{11}$$\end{document} 128-bit numbers per second on NVIDIA GeForce RTX 2080. Besides the convergence verification, our program also checks for path records during the convergence test. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Supercomputing Springer Journals
# Convergence verification of the Collatz problem
, Volume 77 (3) – Jul 1, 2020
8 pages
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# References (13)
Publisher
Springer Journals
Copyright
Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2020
ISSN
0920-8542
eISSN
1573-0484
DOI
10.1007/s11227-020-03368-x
Publisher site
See Article on Publisher Site
### Abstract
This article presents a new algorithmic approach for computational convergence verification of the Collatz problem. The main contribution of the paper is the replacement of huge precomputed tables containing O(2N)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$O(2^N)$$\end{document} entries with small lookup tables comprising just O(N) elements. Our single-threaded CPU implementation can verify 4.2×109\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$4.2 \times 10^9$$\end{document} 128-bit numbers per second on Intel Xeon Gold 5218 CPU computer, and our parallel OpenCL implementation reaches the speed of 2.2×1011\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2.2 \times 10^{11}$$\end{document} 128-bit numbers per second on NVIDIA GeForce RTX 2080. Besides the convergence verification, our program also checks for path records during the convergence test.
### Journal
The Journal of SupercomputingSpringer Journals
Published: Jul 1, 2020
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https://encyclopedia2.thefreedictionary.com/traversing | 1,568,959,980,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573832.23/warc/CC-MAIN-20190920050858-20190920072858-00036.warc.gz | 468,896,179 | 14,845 | # Traversing
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## Traversing
a method of determining the relative positions of points on the earth’s surface in order to construct a geodetic control network for such purposes as topographic surveys, the planning and building of cities, and the laying out of engineering structures. In this method the positions of the points in a given coordinate system are determined by measurement of the lengths of the lines that successively connect the points and by measure
Figure 1. Traverse
ment of the horizontal angles between the lines; the series of lines is called a traverse. Thus, if the points 1, 2, 3, …, n, n + 1 are selected, measurements are made of the lengths s1, s2,…., sn of the lines between them and also of the angles β2,, β3, …, between the lines (Figure 1).
As a rule, point 1 of a traverse is made to coincide with a reference point PH, whose coordinates xH, yH are known and at which the direction angle αH of the direction to some adjacent point pHʹ is also known. The adjacent angle β1 between the first leg of the traverse and the initial direction PH PHʹ is also measured at the initial point of the traverse— that is, at the station PH. The direction angle αi of leg i and the coordinates xi+1, yi+1 of station i + 1 can then be calculated from the formulas
The accuracy of traverse measurements is checked and estimated by having the final points n + 1 of the traverse coincide with a second reference point Pk, whose coordinates xk, yk are known and at which the direction angle αk of the direction to an adjacent point Pkʹ is also known. This method permits calculation of the angular and linear errors of closure, which depend on the errors associated in the measurement of the line lengths and angles and are expressed by the formulas
fα = αn+1 – αk
fx = xn+1 – xk
fy = yn+1 – yk
These errors are eliminated by adjusting the measured angles and leg lengths with corrections determined from balancing computations that use the least squares method.
If the area over which a geodetic control network is to be constructed is large, interconnecting traverses that form a traverse net are laid out (Figure 2).
Figure 2. Traverse net
Traverse stations are stabilized in place by setting into the ground concrete monuments or metal pipes with anchors and by erecting bench marks in the form of pyramidal towers made of wood or metal.
Traverse angles are measured by means of theodolites and transits; the objects of observation are usually special marks set up at the stations being sighted. The lengths of the legs of traverses and traverse nets are measured with steel or invar tapes or wires. Suitable corrections are made in the length and angle measurements in order to obtain the measurement results in the coordinate system in which it is required that the positions of the traverse stations be determined.
Figure 3. Determination of the length of a traverse leg by the trig-traverse method
When local conditions do not permit direct measurement of lines, the lengths of traverse legs can be determined indirectly by the trig-traverse method. In this case, the length of the leg IK is determined by measuring the length b of the short base line AB and the angles Φ1 and Φ2 that are located at the end points of IK and are subtended by AB. AB and IK are perpendicular to each other and intersect at their midpoints; the magnitudes of Φ1 and Φ2 are usually about 3° to 6° (Figure 3). The length of IK is calculated by the formula
Other indirect methods for the measurement of traverse legs are also used, depending on the local conditions.
Traverses and traverse nets are divided into classes corresponding to triangulation classes, in accordance with the degree of precision and the sequence of construction. The precision indexes characterizing the various classes of state traverse nets are given in Table 1. Somewhat different precision indexes may be had by nets constructed, for example, for engineering purposes or for surveys in urban areas.
Table 1
ClassAngle errorLeg error
1±0.4±1:300,000
2±1.0±1:250,000
3±1.5±1:200,000
4±2.0±1:150,000
The origin of the traverse method is not known. In the past, use of the method was limited because traversing required a great number of linear measurements that were difficult to perform owing to local conditions, the unwieldiness of the necessary equipment, and the impossibility of checking results before the completion of the survey. For this reason, the traverse method was in the past used only for surveys in urban areas and for local adjustment of control networks constructed by triangulation.
With the appearance of invar tapes in the early 20th century, linear measurements were made easier, their precision was increased, and they became less dependent on local conditions. As a result, traversing has become as important and precise as triangulation. An important role in the development of traversing was played by the Russian geodesist V. V. Danilov, who worked out in detail the trig-traverse method, which had been outlined by V. Ia. Struve as early as 1836. The invention of electronic distance-measuring instruments that make use of radio or light waves made possible highly precise direct measurements of traverse lines. Traversing was thereby freed of its principal drawback and is now used as often as triangulation. The work of the Soviet geodesists A. S. Chebotarev and V. V. Popov has been of great importance in the development of the theory and techniques of traversing. These two scientists have developed efficient methods of conducting various types of traverse surveys at different levels of precision, as well as methods for computing and estimating the error of the results.
### REFERENCE
Spravochnik geodezista. Edited by V. D. Bol’shakov and G. P. Levchuk. Moscow, 1966.
Danilov, V. V. Tochnaia poligonometriia, 2nd ed. Moscow, 1953.
Krasovskii, F. N., and V. V. Danilov. Rukovodstvo po vysshei geodezii, part 1, fasc. 2. Moscow, 1939.
Chebotarev, A. S., V. G. Selikhanovich, and M. N. Sokolov. Geodeziia, part 2. Moscow, 1962.
Chebotarev, A. S. Uravnitel’nye vychisleniia pri poligonometricheskikh rabotakh. Moscow-Leningrad, 1934.
Popov, V. V. Uravnoveshivanie poligonov, 9th ed. Moscow, 1958.
Kuzin, N. A., and N. N. Lebedev. Prakticheskoe rukovodstvo po gorodskoi i inzhenernoi poligonometrii, 2nd ed. Moscow, 1954.
Instruktsiia 0 postroenii gosudarstvennoi geodezicheskoi seti SSSR, 2nd ed. Moscow, 1966.
A. A. IZOTOV
References in periodicals archive ?
Automated part- and runner-removal equipment for injection molding machines includes EMS sprue pickers; ES2 heavy-duty, swing-type part or runner removers; ELC2 traversing pickers; EL2 pneumatic or variable frequency electric-driven traverse robots; and EL3s servo-driven traverse robots.
His technology uses a traversing thickness gauge to determine TD gauge and adjust the bolts as needed.
Automated part- and runner-removal equipment for injection molding machines includes EMS sprue pickers; ES2 heavyduty, swing-type part or runner removers; ELC2 traversing pickers; and EL2 pneumatic or variable frequency electric-driven traverse robots; and EL3s servo-driven traverse robots.
Automated part- and runner-removal equipment for injection molding machines includes Eagle EMS sprue pickers; ES2 heavy-duty, swing-type removers for part or runner removal; ELC2 traversing pickers; and EL2 traverse-type units.
Features of both jointed-arm and linear traversing robots are combined into the new economical Viper series from Ventax Robot Inc.
First, a handful of exhibitors appeared to be betting that more molders will adopt six-axis, jointed-arm robots in place of, and as adjuncts to, conventional three-axis traversing parts removers.
Sprue pickers and traversing robots for injection molding.
Shuttlestar traversing robots come in two series - one for up to 500-ton machines, the other for up to 1500 tons.
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http://mathhelpforum.com/algebra/222034-simple-question.html | 1,529,715,179,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864848.47/warc/CC-MAIN-20180623000334-20180623020334-00330.warc.gz | 200,981,664 | 10,280 | # Thread: Simple question
1. ## Simple question
I know this is kind of dumb but cos(-x) = - cos (x) ? Right?
2. ## Re: Simple question
Originally Posted by sakonpure6
I know this is kind of dumb but cos(-x) = - cos (x) ? Right?
NO! It is not correct. $\displaystyle \cos(x)$ is an even function, therefore $\displaystyle \cos(x)=\cos(-x)~.$
3. ## Re: Simple question
Omg thank you!!! I knew that sin(-x) = - sin x but when I put in a negative value for cos say, cos (-60) i got a positive number. Thanks!!!! | 154 | 513 | {"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} | 3.203125 | 3 | CC-MAIN-2018-26 | latest | en | 0.85687 |
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Free Continue to app
## Publisher Description
***Designed for Professionals***
TTII Financial Calculator is an Advanced Financial Calculator with various mathematical as well as financial functions.
Most financial calculators are clumsy, error prone and difficult to use.
TTII Financial Calculator uses easy input methods and a neat interface that interacts with your calculations without lacking any functionalities present in any financial calculator.
With TTII Financial Calculator you can easily swipe between function sets, designed for single-point touch usage.
Standard Calculator and a Scientific Calculator
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Factorial Calculator
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TVM Calculator Functions include,
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Sum of Year Digits Depreciation (SOYD Depreciation Calculator)
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Includes Double Declining Balance Calculator (DDB)
Includes Variable Declining Balance Calculator (VDB)
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Forward Rate Calculator (lFm)
Tap history icon on display to view last six calculations performed along with the inputs and outputs. Tap 'TTII' logo to view guide on how to use the app and links to youtube channel.
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Check out this walk-through video on how to calculate Net Present Value using TTII Financial Calculator : https://youtu.be/i87YzSVyxGw
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TTII Financial Calculator is a free software application from the Accounting & Finance subcategory, part of the Business category. The app is currently available in English and it was last updated on 2016-08-27. The program can be installed on Android.
## Program Details
### General
Publisher Slickalpha
Released Date 2016-08-27
Languages English
### Category
Subcategory Accounting & Finance
### System requirements
Operating systems android
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## Version History
Here you can find the changelog of TTII Financial Calculator since it was posted on our website on 2016-10-29. The latest version is 2.1.6 and it was updated on soft112.com on 2018-03-21. See below the changes in each version:
## version 2.1.6
### posted on 2016-08-27
--| v2.1.6 |--,+ Performance Improvements +,+ Design Fixes +,--| v2.1.5 |--,+ Partial language support for German and Russian +
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Editor Rating: 0/5 | 737 | 3,278 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-39 | latest | en | 0.764302 |
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For my logic homework, I'm supposed to construct two proofs to prove that DeMorgan's is redundant. I'm not given a theorem or anything to start with.
I'm only allowed to use Modus Ponens, Modus Tollens, Hypothetical Syllogism, Simplification, COnjunction, Dilemma, Disjunctive Syllogism, Addition, Double Negation, Duplication, Commutation, Contraposition, Association, Biconditional Exchange, Conditional Exchange, Distribution, Exportation, Indirect Proof, and Conditional Proof.
Those are the only ones that we've studied in my class and the only ones that (I've noticed at least) are in the textbook (Understanding Symbolic Logic by Virginia Klenk). I'm only allowed to use Klenk's system, too.
I THINK I have one of them already, but I'm not completely positive. It feels... not quite right, but not quite wrong to me either.
1. ~A&B prem.
2. | (AvB) Assp. for I.P.
3. | ~A Simp. 1
4. | ~B Simp. 1
5. | A 2, 4 Disjunctive Syllogism
6. | (~A&A) 3, 5 conjunction
7. ~(AvB) 2-6 I.P.
I've tried looking around at the other answers for this on this forum, but none of them work for what I'm allowed to do.
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Water is flowing through a horizontal pipe of varying cross-section. If the pressure of water equals 2 cm of mercury, where the velocity of the flow is , what is the pressure at another point, where the velocity of flow is ?
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Question Text Water is flowing through a horizontal pipe of varying cross-section. If the pressure of water equals 2 cm of mercury, where the velocity of the flow is , what is the pressure at another point, where the velocity of flow is ? Topic Mechanical Properties of Fluids Subject Physics Class Class 11 Answer Type Text solution:1 Upvotes 142 | 317 | 1,380 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2024-18 | latest | en | 0.855674 |
http://www.ird.govt.nz/how-to/taxrates-codes/itaxsalaryandwage-incometaxrates.html | 1,394,472,723,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394010916587/warc/CC-MAIN-20140305091516-00053-ip-10-183-142-35.ec2.internal.warc.gz | 379,414,034 | 14,012 | ## Income tax rates for individuals
### Income tax rates
#### Rates for tax year 2012-2013
Taxable income Income tax rates for every
\$1 of taxable income
(excl ACC earners' levy)
PAYE rates for every
\$1 of taxable income
(incl ACC earners' levy - see "Note 1" below)
up to \$14,000 10.5 cents 12.20 cents
from \$14,001 to \$48,000 17.5 cents 19.20 cents
from \$48,001 to \$70,000 30 cents 31.70 cents
\$70,001 and over 33 cents 34.70 cents
No-notification - see "Note 2 below" 45 cents 46.70 cents
Use the Tax on annual income calculator if you want to know the tax rates for previous years.
Note 1 Earners' levy rate (GST-inclusive) for period 1 April 2012 to 31 March 2013 is 1.70% (\$1.70 per \$100).
Note 2 Employers are legally required to use the no-notification rate when an employee does not fully complete the Tax code declaration (IR330). A completed form must include name, IRD number and tax code, and be signed.
Example 1
John's total taxable income for the year was \$65,238. Here's how to work out the amount of tax due on the income:
\$0 to \$14,000 at 10.5% = \$1,470.00 \$14,001 to \$48,000 at 17.5% = \$5,950.00 \$48,001 to \$65,238 at 30% = \$5,171.40 Total tax due \$12,591.40
Example 2
Sarah's total taxable income for the year was \$45,000. Here's how to work out the amount of tax due on the income:
\$0 to \$14,000 at 10.5% = \$1,470.00 \$14,001 to \$45,000 at 17.5% = \$5,425.00 Total tax due \$6,895.00
#### Rates for tax year 2011-2012
Taxable income Income tax rates for every
\$1 of taxable income
(excl ACC earners' levy)
PAYE rates for every
\$1 of taxable income
(incl ACC earners' levy - see "Note 3" below)
up to \$14,000
10.5 cents
12.54 cents
from \$14,001 to \$48,000
17.5 cents
19.54 cents
from \$48,001 to \$70,000
30 cents
32.04 cents
\$70,001 and over
33 cents
35.04 cents
No-notification - see "Note 2" above
45 cents
47.04 cents
Note 3 Earners' levy rate (GST-inclusive) for period 1 April 2011 to 31 March 2012 is 2.04% (\$2.04 per \$100).
Use the Tax on annual income calculator if you want to know the tax rates for previous years.
#### Rates for tax year 2010-2011
The following annual rates will be used when we work out your tax at the end of the tax year, if you receive a personal tax summary or file an IR3 tax return. These rates represent an average of the two sets of rates that apply for the 2010-11 income year. Note: All rates are ACC-exclusive. Please see the ACC earner's levy rates table below for the rates that apply.
Taxable income PAYE rate up to
30 September 2010
Income tax rate from
1 April 2010 to
31 March 2011
PAYE rate to apply
from 1 October 2010
up to \$14,000 12.5 cents 11.5 cents 10.5 cents
from \$14,001 to \$48,000 21 cents 19.25 cents 17.5 cents
from \$48,001 to \$70,000 33 cents 31.5 cents 30 cents
\$70,001 and over 38 cents 35.5 cents 33 cents
### ACC earners' levy rates
All employees must pay an ACC earners' levy to cover the cost of non-work related injuries. It is collected by us on behalf of the Accident Compensation Corporation (ACC).
Employers deduct the earners' levy from wages. It is included as a component of PAYE deductions.
Earners' levy is charged at a flat rate each year:
Year Levy rate
1 April 2013 to 31 March 2014 \$1.70 per \$100 (1.70%)
1 April 2012 to 31 March 2013 \$1.70 per \$100 (1.70%)
1 April 2011 to 31 March 2012 \$2.04 per \$100 (2.04%)
Earners' levy is deducted on earnings up to an annually prescribed maximum:
Year Maximum
earnings - see "Note 4" below
Maximum
levy payable
1 April 2013 to 31 March 2014 \$116,089 \$1,973.51
1 April 2012 to 31 March 2013 \$113,768 \$1,934.05
1 April 2011 to 31 March 2012 \$111,669 \$2,278.04
Note 4 For self-employed earnings, earners' levy is deducted on earnings up to an annually prescribed maximum of \$113,768 The maximum levy payable is \$1,934.05 for the 2013-14 tax year.
#### Income liable for earners' levy
Almost all earnings subject to PAYE are liable for earners' levy. They include:
• wages and salaries
• back pay and holiday pay
• overtime pay
• long-service pay
• bonuses or gratuities
• taxable allowances
• shareholder-employee salaries from which PAYE is deducted
• salaries to partners in a partnership.
##### Other pages in: Tax rates and codes
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Posted: Saturday 30th of Dec 08:58 Hi guys I require some aid to work out this simple algebra equations which I’m unable to do on my own. My homework assignment is due and I need guidance to work on powers, adding matrices and linear equations . I’m also thinking of hiring a math tutor but they are expensive. So I would be greatly appreciative if you can extend some guidance in solving the problem.
IlbendF
Registered: 11.03.2004
From: Netherlands
Posted: Sunday 31st of Dec 13:42 I understand your situation because I had the same issues when I went to high school. I was very weak in math, especially in simple algebra equations and my grades were poor. I started using Algebrator to help me solve problems as well as with my homework and eventually I started getting A’s in math. This is a remarkably good product because it explains the problems in a step-by-step manner so we understand them well. I am absolutely sure that you will find it useful too.
MoonBuggy
Registered: 23.11.2001
From: Leeds, UK
Posted: Monday 01st of Jan 08:22 I am a frequent user of Algebrator and it has really helped me comprehend math problems better by giving detailed steps for solving. I recommend this software to help you with your algebra stuff. You just need to follow the instructions given there.
TihBoasten
Registered: 14.10.2002
From:
Posted: Tuesday 02nd of Jan 16:08 I am a regular user of Algebrator. It not only helps me get my assignments faster, the detailed explanations given makes understanding the concepts easier. I advise using it to help improve problem solving skills.
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http://www.docstoc.com/docs/57788957/2nd-Summative-Test-in-Math-(Gr2) | 1,433,027,370,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207932737.93/warc/CC-MAIN-20150521113212-00090-ip-10-180-206-219.ec2.internal.warc.gz | 402,953,381 | 40,164 | # 2nd Summative Test in Math (Gr2) by kmendoza33
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• pg 1
``` Princeton Science School – Home of Young Achievers
Summative Test in Mathematics – Grade II
2nd Quarter – A. Y. 2009-2010
I. Write the letter of the correct answer.
1. What property is shown if you multiply a number by zero?
A. Distributive Property B. Identity Property C. Zero Property
2. If you will round off 1, 538 to the nearest hundreds, the answer is _____.
A. 1000 B. 1600 C. 1500
3. In 32 x 3 = 96, which is the multiplicand?
A. 32 B. 3 C. 96
4. How many centavos are there in Php 2.00?
A. 20 B. 200 C. 2000
5. If you multiply a number by one, what will be the answer?
A. 0 B. 1 C. the number
6. The arrangement of objects in rows and columns is called .
A. arrow B. array C. arrow
7. If I have two 20-peso bill and three 25-centavo coin, how much money do I have?
A. Php 47.50 B. Php 40.50 C. Php 40.75
8. What operation will you use to check your answer in multiplication?
A. Addition B. Subtraction C. Multiplication
9. There were 5 vases of flower with 5 flowers each. How many flowers are there?
A. 10 B. 25 C. 5
10. What property of multiplication is shown in 15 x 1 = 15?
A. Commutative Property B. Zero Property C. Identity Property
11. A big truck weighs 1,523 kilograms. Round off the weight of the truck to the nearest thousands.
A. 1,600 B. 2,000 C. 1,500
12. What are the missing numbers in 4 x (6 + 2) = 4 x ___ = ___ ?
A. 7, 28 B. 8, 32 C. 9, 36
13. In 3 x 2 = 6, 3 and 2 are called _______.
A. factors B. minuend C. addends
14. Which statement is not correct?
A. N x 1 = N B. 0 x 1 = 0 C. 1 x N = 0
15. Every week, Lea buys 12 boxes of cookies in a bakeshop. In each box, there are 6 pieces of
cookies. How many cookies does she have in all?
A. 72 B. 68 C. 81
16. What is Five thousand nine hundred seventy pesos in figures?
A. ₱ 5, 790.00 B. ₱ 5, 907.00 C. ₱ 5, 970.00
17. Who does not belong to the group?
A. Jose P. Rizal B. Josefa Llanes–Escoda C. Vicente Lim
18. What is the correct multiplication sentence for the addition sentence: 7+7+7+7+7+7+7+7+7?
A. 7 x 9 = n B. 9 x 7 = n C. 9 x n = 7
19. The new building is about 458 meters high. Round off the building’s height to the nearest
hundreds.
A. 560 B. 460 C. 500
20. Mario goes to a toy store. He buys a toy gun for Php 125.50 and a robot for Php 228.70. How
much is the total cost of the two toys?
A. ₱ 354. 20 B. ₱ 350. 50 C. ₱ 300.25
II. Round off the numbers according to the indicated nearest place value.
TENS HUNDREDS THOUS ANDS
21. 32 ______ 23. 790 ______ 25. 9, 600 ______
22. 657 ______ 24. 5, 380 ______
III. Write the following amounts in numerals.
26. Thirteen pesos and twenty–five centavos.
27. Ninety pesos and fifty centavos.
28. One hundred pesos and seventy–five centavos.
29. Two hundred thirty–five pesos and ten centavos.
30. One thousand pesos and five centavos.
IV. Match column A to column B. Write the letter of the correct answer
Column A Column B
31. Eight 25–centavo coins A. ₱ 70.50
32. Eight ₱ 20 bills B. ₱ 17.25
33. Six 10–centavo coins C. ₱ 206.50
34. Seven 10–peso coins and two 25–centavo coins D. ₱ 2.00
35. Two 100–peso bills and six ₱1 coins E. ₱ 160.00
F. ₱ 0.60
V. Write a multiplication sentence for each addition sentence.
36. 8 + 8 + 8 = 24 39. 3 + 3 + 3 + 3 = 12
37. 10 + 10 + 10 + 10 + 10 = 50 40. 6 + 6 + 6 + 6 + 6 = 30
38. 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28
VI Multiply the following FACTORS.
41. 25 42. 74 43. 216 39. 423 40. 638
x 6 x 4 x 3 x 5 x 6
VII. Problem Solving.
1. There were 6 boxes piled up in the grocery. Each box contained 450 kilograms of meat
products. How many kilograms of meat are there in all? (2 pts.)
2. In a school, 950 pupils report daily. Each pupil donates ₱5 for the Charity Drive. How much
is the total money collected. (3 pts.)
Prepared by: Noted by:
Teacher Elleh Teacher Mark Mr. JM Magpantay
```
To top | 1,482 | 5,618 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2015-22 | longest | en | 0.861995 |
https://saylordotorg.github.io/text_international-finance-theory-and-policy/s08-07-exchange-rate-effects-of-chang.html | 1,709,573,553,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476464.74/warc/CC-MAIN-20240304165127-20240304195127-00566.warc.gz | 488,818,766 | 3,960 | 5.7 Exchange Rate Effects of Changes in the Expected Exchange Rate Using the RoR Diagram
Learning Objective
1. Learn the effects of changes in the expected future currency value on the spot value of the domestic and foreign currency using the interest rate parity model.
Suppose that the foreign exchange market (Forex) is initially in equilibrium such that RoR£ = RoR$(i.e., interest rate parity holds) at an initial equilibrium exchange rate given by E$/£. The initial equilibrium is depicted in Figure 5.9 "Effects of an Expected Exchange Rate Change in a RoR Diagram". Next, suppose investors’ beliefs shift so that E$/£e rises, ceteris paribus. Ceteris paribus means we assume all other exogenous variables remain fixed at their original values. In this model, the U.S. interest rate (i$) and the British interest rate (i£) both remain fixed as the expected exchange rate rises.
Figure 5.9 Effects of an Expected Exchange Rate Change in a RoR Diagram
An expected exchange rate increase means that if investors had expected the pound to appreciate, they now expect it to appreciate even more. Likewise, if investors had expected the dollar to depreciate, they now expect it to depreciate more. Alternatively, if they had expected the pound to depreciate, they now expect it to depreciate less. Likewise, if they had expected the dollar to appreciate, they now expect it to appreciate less.
This change might occur because new information is released. For example, the British Central Bank might release information that suggests an increased chance that the pound will rise in value in the future.
The increase in the expected exchange rate (E$/£e) will shift the British RoR line to the right from RoR£ to RoR£ as indicated by step 1 in the figure. The reason for the shift can be seen by looking at the simple rate of return formula: $RoR£=E/£eE/£(1+i£)−1.$ Suppose one is at the original equilibrium with exchange rate E$/£. Looking at the formula, an increase in E$/£e clearly raises the value of RoR£ for any fixed values of i£. This could be represented as a shift to the right on the diagram from A to B. Once at B with a new expected exchange rate, one could perform the exercise used to plot out the downward sloping RoR curve. The result would be a curve, like the original, but shifted entirely to the right. Immediately after the increase and before the exchange rate changes, RoR£ > RoR$. The adjustment to the new equilibrium will follow the “exchange rate too low” equilibrium story presented in Chapter 5 "Interest Rate Parity", Section 5.4 "Exchange Rate Equilibrium Stories with the RoR Diagram". Accordingly, higher expected British rates of return will make British pound investments more attractive to investors, leading to an increase in demand for pounds on the Forex and resulting in an appreciation of the pound, a depreciation of the dollar, and an increase in E$/£. The exchange rate will rise to the new equilibrium rate E$/£ as indicated by step 2.
In summary, an increase in the expected future $/£ exchange rate will raise the rate of return on pounds above the rate of return on dollars, lead investors to shift investments to British assets, and result in an increase in the$/£ exchange rate (i.e., an appreciation of the British pound and a depreciation of the U.S. dollar).
In contrast, a decrease in the expected future $/£ exchange rate will lower the rate of return on British pounds below the rate of return on dollars, lead investors to shift investments to U.S. assets, and result in a decrease in the$/£ exchange rate (i.e., a depreciation of the British pound and an appreciation of the U.S. dollar).
Key Takeaways
• An increase in the expected future pound value (with respect to the U.S. dollar) will result in an increase in the spot $/£ exchange rate (i.e., an appreciation of the British pound and a depreciation of the U.S. dollar). • A decrease in the expected future pound value (with respect to the U.S. dollar) will result in a decrease in the spot$/£ exchange rate (i.e., a depreciation of the British pound and an appreciation of the U.S. dollar).
Exercise
1. Consider the economic change listed along the top row of the following table. In the empty boxes, indicate the effect of the change, sequentially, on the variables listed in the first column. For example, a decrease in U.S. interest rates will cause a decrease in the rate of return (RoR) on U.S. assets. Therefore a “−” is placed in the first box of the table. Next in sequence, answer how the RoR on euro assets will be affected. Use the interest rate parity model to determine the answers. You do not need to show your work. Use the following notation:
+ the variable increases
the variable decreases
0 the variable does not change
A the variable change is ambiguous (i.e., it may rise, it may fall)
A Reduction in Next Year’s Expected Dollar Value
RoR on U.S. Assets
RoR on Euro Assets
Demand for U.S. Dollars on the Forex
Demand for Euros on the Forex
U.S. Dollar Value
Euro Value
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Investing for The Future You are the owner of XYZ, Inc. You had a record year, a
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A186483 Number of (n+1)X(n+1) 0..4 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors 0
625, 839, 17015, 64680, 575344, 1759744, 15145144, 52024944, 422063944, 1535037344, 11681382744, 44716060144, 324000643944, 1297964842944, 9013961908344, 37548525033744, 251396274363144, 1083126105726944 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Diagonal of A186484 LINKS EXAMPLE Some solutions for 3X3 ..1..2..1....3..0..2....4..0..0....3..3..0....4..1..0....1..4..0....1..1..0 ..2..1..2....0..3..0....4..0..0....4..0..3....0..0..1....2..0..4....3..0..1 ..1..2..1....0..0..3....0..4..4....0..4..4....0..0..3....0..2..0....0..3..4 CROSSREFS Sequence in context: A210115 A186484 A184037 * A043352 A223183 A171995 Adjacent sequences: A186480 A186481 A186482 * A186484 A186485 A186486 KEYWORD nonn AUTHOR R. H. Hardin Feb 22 2011 STATUS approved
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Neil classified a triangle as an obtuse scalene triangle. Which statement describes an obtuse scalene triangle? Answers (which one) need help plzz -Two sides are of the same length and one angle measures 90˚. -All the sides are of different lengths and one angle measures 90˚. -Two sides are of the same length and one angle measures less than 90˚. -All the sides are of different lengths and one angle measures greater than 90˚
Geometry
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Not the answer you are looking for? Search for more explanations. | 349 | 1,367 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-05 | latest | en | 0.440113 |
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Posted on Friday, May 28, 2021 10:37:49 AM Posted by Longfenfelan - 28.05.2021
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## Encoder Applications
Basically, Decoder is a combinational logic circuit that converts coded input to coded outputs provided both of these are different from one another. The name decoder means translating of coded information from one format into another. So the input code generally has fewer bits than output code word. A digital decoder converts a set of digital signals into corresponding decimal code. A decoder is also a most commonly used circuit in prior to the use of encoder. The encoded data is decoded for user interface in most of the output devices like monitors, calculator displays, printers, etc.
In this article we are going to study on different types of binary decoders. A binary decoder is a multi-input, multi-output combinational circuit that converts a binary code of n input lines into a one out of 2n output code.
These are used when there is need to activate exactly one of 2n output based on an n-bit input value. The figure below shows the general structure of binary decoder in which encoded information is accepted at n input lines and the output is produced at 2n possible output lines. Generally, decoders are provided with enable inputs so as to activate the decoded output based on data inputs.
As an example, in case of BCD code, the 4 bit combinations from through are enough to represent the decimal digits 0 to 9. Depending on the number of input lines, the inputs of a binary code can be 2-bit or 3-bit or 4-bit codes.
Upon the availability of 2n lines, it activates the one of its output by deactivating making logic 0 all other input whenever it receives n inputs. Usually the number of bits in output code is more than the bits in its input code. The most commonly used practical binary decoders are 2-to-4 decoder, 3-to-8 decoder and 4-to line binary decoder. Back to top. Only one output is active at any time while the other outputs are maintained at logic 0 and the output which is held active or high is determined the two binary inputs A and B.
The figure below shows the truth table for a 2-to-4 decoder. When both the inputs are high, then the output Y3 will be high. If the enable bit is zero then all the outputs will be set to zero. This relationship between the inputs and outputs are illustrated in below truth table clearly. These expressions can be implemented by using basic logic gates.
Thus, the logic circuit design of the 2-to-4 line decoder is given below which is implemented by using NOT and AND gates. Two NOT gates or inverters provide the complement of inputs. Each output represents one of the minterms of the 2 input variables. It is also possible to design 2-to-4 decoder using NAND gates as shown in figure below along with truth table.
This is constructed with a principle of max terms as outputs. To generate the minterms, we have to use NAND gates which act as inverters. Therefore, only one output will be low for any combinations of inputs at a given time and all other outputs will be high. This type of decoders is available in IC forms so that 3 to 8, 4 to 16, and 5 to 32 decoders can also be made depends on the application requirement.
In a 3-to-8 decoder, three inputs are decoded into eight outputs. Based on the combinations of the three inputs, only one of the eight outputs is selected. The figure below shows the truth table of a 3-to-8 decoder. Enable input is provided to activate the decoded output depends on the input combinations A, B and C.
So from the truth table, minterms represents the each output equation and are given as. Using the above min term expressions for each output, the circuit of 3-to-8 decoder is can be implemented by using three NOT gates and eight AND gates.
Also enable input activate the decoded output depends on the input data. The logic diagram of this decoder is shown below. Only one of eight outputs is high at a given time for a particular input combination, that why this decoder is also called as 1-of-8 decoder. It is also possible represent the each output equation using max terms. In such case, inversion operation is performed in the logic circuit than that of circuit with min terms.
The figure below shows the truth table of 3-to-8 line decoder using NAND gates. Each output in the table gives a max term representation. At a given time only one output is low and all other outputs will be high. NOT gates generate the complement of input while the NAND gates generate max terms of each output as shown in below figure. A 4-to decoder consists of 4 inputs and 16 outputs. Similar to all the decoders discussed above, in this also only one output will be low at a given time and all other outputs are high using maxterms.
The truth table of this type of decoder is shown below. If the input to this decoder is , then output Y8 will be low and all other outputs will be high as shown in figure. This will be so on for all the input combinations. It is important to note that all the NAND gates are implemented on this circuit produce the active low outputs as shown in figure. Since it selects one of 16 outputs based in the particular input combination, these decoders are also called as 1-of decoder.
And also its output represents the sixteen digits as hexadecimal number system, this type of decoder is also called as a binary-to-hexadecimal decoder. It is possible to combine or cascade two or more decoders to produce a decoder with larger number of input bits with the use of enable input of decoder.
The cascade combination of two 3-to-8 line decoder is given below figure. One of the input variable is used as enable input of the first 3-to-4 decoder and this same input is complemented and connected as enable input of the second decoder. The decoder to be enabled is decided by the most significant input variable and other input variables are fed to each decoder. When enable input is zero then the top decoder is enabled while the other is disabled. Then the top decoder eight outputs generate the minterms to Likewise, when enable is 1, the lower decoder is enabled and top one is disabled.
Thus the bottom decoder outputs generate minterms from to Decoders are greatly used in applications where the particular output or group of outputs to be activated only on the occurrence of a specific combination of input levels. Very often these input levels are provided by the outputs of a register or counter. When the counter or register continuously pulse the decoder inputs, the outputs will be activated sequentially.
And these outputs can be used as sequencing signals or timing signals to switch the devices at particular times. Decoders are used to get the decimal digit corresponding to a specific input combination. A BCD number needs 4 binary digits to represent the 0 to 9 decimal digits, thus it consists of 4 input lines. It consists of 10 output lines corresponding to 0 to 9 decimal digits. This type of decoder is also called as a 1 to 10 decoder. For a specific input combination, the output will be activated corresponding to the decimal equivalent of the input combination.
Amongst its many uses, a decoder is widely used to decode the particular memory location in the computer memory system. Decoders accept the address code generated by the CPU which is a combination of address bits for a specific location in the memory.
In a memory system, there are several memory ICs are combined and each one has their unique address to distinguish from other memory locations. In such cases a decoder built in the memory ICs circuitry, is used to select a memory IC in response to a range of addresses by decoding the most significant bits of the systems address, thereby a particular memory location or IC is selected.
In a more complex memory system, the memory ICs or chips are arranged in multiple banks. When the microprocessor wants to access one or more bytes at a time, these banks must be selected simultaneously or individually. In such cases more than one decoder must be activated. For that, cascaded decoders are used or most commonly decoders are replaced with programmable logic devices. Another application of the decoder can be found in the control unit of the central processing unit.
This decoder is used to decode the program instructions in order to activate the specific control lines such that different operations in the ALU of the CPU are carried out.
## Types of Encoders and Decoders with Truth Tables & Applications
Basically, Decoder is a combinational logic circuit that converts coded input to coded outputs provided both of these are different from one another. The name decoder means translating of coded information from one format into another. So the input code generally has fewer bits than output code word. A digital decoder converts a set of digital signals into corresponding decimal code. A decoder is also a most commonly used circuit in prior to the use of encoder. The encoded data is decoded for user interface in most of the output devices like monitors, calculator displays, printers, etc. In this article we are going to study on different types of binary decoders.
Four Channel wireless system. Basic four channel wireless. Relays, The Electromechanical amplifier. How Encoders and Decoders work. Encoder and Decoder Selection Guide. Characteristics of wireless systems. Pyroelectric Infrared Sensor and Fresnel lens.
## Designing of 2 to 4 Line Decoder
These are frequently used in communication system such as telecommunication, networking, etc.. Similarly, in the digital domain, for easy transmission of data, it is often encrypted or placed within codes, and then transmitted. At the receiver, the coded data is decrypted or gathered from the code and is processed in order to be displayed or given to the load accordingly. An encoder is an electronic device used to convert an analogue signal to a digital signal such as a BCD code. It has a number of input lines, but only one of the inputs is activated at a given time and produces an N-bit output code that depends on the activated input.
Before going into realities about Encoders and Decoders , let us have a concise thought regarding Multiplexing.
### Types of Binary Decoders,Applications
Encoders translate rotary or linear motion into a digital signal. That signal is sent to a controller, which monitors motion parameters such as speed, rate, direction, distance, or position. Since , millions of EPC encoders have been applied for countless feedback requirements in nearly every industry. When selecting the right encoder for your application, it's vital to understand the role of the encoder in your motion control system. Encoders provide high-precision motion feedback while operating in extreme environmental conditions. Encoders ensure that the unit to be controlled does not exceed a preset position or direction of travel. Attached to the end of the ball screw shaft or drive motor, encoders provide motion feedback.
Combinational logic is the concept in which two or more input state define one or more output state. Encoder and Decoder are the combinational logic circuits. In which we implement combinational logic with the help of boolean algebra. To encode something is to convert an unambiguous piece of information into a form of code that is not so clearly understood and the device which performs this operation is termed ad Encoder. Encoder : An Encoder is a device that converts the active data signal into a coded message format or it is a device that coverts analogue signal to digital signals. It is a combinational circuit, that converts binary information in the form of a 2N input lines into N output lines which represent N bit code for the input.
Prerequisite — Encoder , Decoders. Binary code of N digits can be used to store 2 N distinct elements of coded information. This is what encoders and decoders are used for. Encoders convert 2 N lines of input into a code of N bits and Decoders decode the N bits into 2 N lines. Encoders — An encoder is a combinational circuit that converts binary information in the form of a 2 N input lines into N output lines, which represent N bit code for the input. For simple encoders, it is assumed that only one input line is active at a time. As shown in the following figure, an octal-to-binary encoder takes 8 input lines and generates 3 output lines.
#### Content: Encoder Vs Decoder
Both encoder and decoder are combinational logic circuits, however, one of the crucial difference between encoder and decoder is that an encoder provides binary code as its output. On the contrary, a decoder accepts binary code as its input. An encoder is a device that converts the active data signal into a coded message format. However, a decoder performs inverse operation of the encoder and thus converts the coded input into original data input. In order to have secured data transmission , encoders and decoders are employed in a communication system.
In digital electronic projects, the encoder and decoder play an important role. It is used to convert the data from one form to another form. Generally, these are frequently used in the communication systems like telecommunication, networking, and transfer the data from one end to the other end. In the same way it is also used in the digital domain for easy transmission of data, placed with the codes and then transmitted. At the end of the receiver, the coded data are collected from the code and then processed to display. This article discusses about what is encoder and encoder, working and its applications.
И теперь наконец ее получит. Сьюзан будет искать защиту у него, поскольку ей негде больше будет ее найти. Она придет к нему беспомощная, раздавленная утратой, и он со временем докажет ей, что любовь исцеляет. Честь. Страна. Любовь. Дэвид Беккер должен был погибнуть за первое, второе и третье.
#### COMMENT 2
• Dubai duty free alcohol price list pdf 2018 pdf of the selection by kiera cass Fantina P. - 28.05.2021 at 20:17
• Applications of the Encoder and Decoder. Speed synchronization of multiple motors in industries. War field flying robot with a night vision flying camera. Robotic vehicle with the metal detector. RF based home automation system. Automatic health monitoring systems. Linda S. - 29.05.2021 at 17:56 | 3,022 | 14,478 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2022-05 | latest | en | 0.883947 |
https://group.classcentral.com/t/post-your-roman-numeral-converter-solutions-here-fall-2022/35779?page=3 | 1,686,273,878,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224655244.74/warc/CC-MAIN-20230609000217-20230609030217-00674.warc.gz | 327,250,529 | 6,222 | # Post your Roman Numeral Converter solutions here! (Fall 2022)
Thank you Carlos!
I will be trying the exercises again once I have gone through all the JavaScript exercises again.
Happy coding to you as well!
3 Likes
I looked a bit around in the internet and found something here: The Order of Javascript Object Keys - DEV Community ๐ฉโ๐ป๐จโ๐ป
When iterating an object, the system looks first for Strings that look like integer keys, and iterates those in numeric order, then iterates the remaining String keys, in insertion order, then iterates the Symbols, again in insertion order.
So it works here because all the keys are letters and are inserted in the right order from the biggest to the lowest.
Thatโs obviously not something you want to rely on if you use the object for more than for storing these numerals
edit:
Beware of trying to have the same key in your object as a number and as a string:
the key is always stored as a string and that results in having the key only one time with the value of the last insertion.
3 Likes
Thanks for this answer. Itโs very helpful. To make sure I understood it, I wrote the following bit of code, and it did work as expected.
``````const myObj = {
2: "prints second",
M: "prints fourth",
100: "prints third",
A: "prints fifth",
1: "prints first"
}
for (let obj in myObj){
console.log(myObj[obj])
}
``````
``````prints first
prints second
prints third
prints fourth
prints fifth
``````
It seems to me that, all things being equal, itโs probably good practice to use an array when one wants to preserve order, rather than use an object and then remember and count on this specific functionality.
4 Likes
`````` function convertToRoman(num) {
var roman = {
M: 1000,
CM: 900,
D: 500,
CD: 400,
C: 100,
XC: 90,
L: 50,
XL: 40,
X: 10,
IX: 9,
V: 5,
IV: 4,
I: 1
};
var str = '';
for (var i of Object.keys(roman)) {
var r = Math.floor(num/roman[i]);
num -= r * roman[i];
str += i.repeat(r);
}
return str;
}
convertToRoman(36);
console.log(convertToRoman(187))
``````
2 Likes
Hereโs my code for the roman numeral converter
``````/* Converts digit numbers to roman numerals */
function convertToRoman(number) {
let romanNumerals =
{
M: 1000,
CM: 900,
D: 500,
CD: 400,
C: 100,
XC: 90,
L: 50,
XL: 40,
X: 10,
IX: 9,
V: 5,
IV: 4,
I: 1
}
let result = "";
for (let i in romanNumerals) {
while(number >= romanNumerals[i]) {
result += i;
number -= romanNumerals[i];
}
}
return result;
}
console.log(convertToRoman(2081));
`````````
1 Like
Please donโt close this topic, I have not gotten to these exercises yet and I am hoping some people are still around to help once I do!
1 Like
This topic was automatically closed 45 days after the last reply. New replies are no longer allowed. | 764 | 2,756 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2023-23 | latest | en | 0.899723 |
http://www.instructables.com/id/How-to-build-a-Pizza-Oven/?ALLSTEPS | 1,490,858,914,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218193284.93/warc/CC-MAIN-20170322212953-00094-ip-10-233-31-227.ec2.internal.warc.gz | 563,559,600 | 30,185 | Building a woodfired oven with clay or mud
After having built a oven for myself, i think it's a nice to have piece of work in your backyard.
Be warned, it takes quite some time to build, but also to use it. It's no substitute for your Microwave... it's rather in the slowfood class, even if you can bake a pizza in 2-3 minutes.
## Step 1: What Type and Size Do You Want?
Depending on what you want to bake and the space available, you can adjust the size of your oven. The amount of material needed doesn't scale linear. My oven needed 4 times the material of a small but usable oven.
In numbers that was 600 kg of clay powder, around 950kg of sand.
In my case, the size was selected because my main use of it is to bake bread and i wanted to be able to use the cookie pans from my electric oven. I also selected the thickness of my thermal layer to keep the heat long enough to bake multiple batches of bread, without the need to reheat.
As a general guideline, i wouldn't go smaller than 40cm/16inches inner diameter. Mine has 75cm/30inches. The thickness of the thermal layer should be no less than 15cm/6inches. Mine has 20cm/8inches.
There are certain ratios between inner oven diameter, inner oven height and oven door height you need to have. The most important here, the oven opening height has to be 63% of the inner dome height. This is essential for a clean burning fire. Further, the inner dome height should be 60-75% of the inner dome diameter. With these ratios and measurements, you can determine the actual measurements for your oven. It's best if you look around for firebricks, before you decide on the size of your oven floor. You should sketch your firebrick layout on a large piece of cardboard 1:1. Then draw the inner and outer shape of your oven on it and cut it out. This will help you in the next step, the form and size of your foundation. You should place the opening of your oven away from the main wind direction. Last but not least you have to plan for a roof of some sort. If you plan to bake in bad weather, make it big enough to shelter you as well as the oven. The oven should be able to breathe, so the moisture can get out.
I would like to strongly suggest for everyone to read the book from Kiko Denzer, "Build your own earth oven". It goes much deeper into the details, he built countless different ovens and shares his knowledge. You will see references to his book throughout this instructable. Don't get me wrong here, you can build a oven with this instructable alone, but maybe you'd like to do it a little different. In this book, you will find different techniques, styles and lots of background information.
Pictures of smaller ovens made at a workshop. One with chimney, made in the sand mound method, the other without chimney was made with the inverted basket method.
## Step 2: The Foundation
Since your oven will be pretty heavy, you will need a stable foundation.
In my case, i had a old fireplace that i used as a base for my oven. A friend made a iron reinforced concrete plate for me. It is 130cm/52inches square and 6cm/2.5inches thick weighting around 350kg. This was a heavy lift for 4 persons. I originally wanted it twice as thick and even larger...
If you don't have a fireplace to convert , you need to make your foundation from scratch.
Depending on where you live, you need to make it frost proof. How deep you need to dig for frost proofing, it's best to ask a local builder. I'd dig at least 50cm/20inches in a frost free zone. Then you can build up walls up to the oven floor height. Then fill it up with gravel, and compress it by jumping. Fill the last 10cm/4inches (minimum) with sand. That's where you will put your firebricks as your oven floor.
What bricks you use is up to you. If you have large stones around, use them. Kiko suggests to use "urbanite", that's scrapped concrete you can find at your local dump.
## Step 3: Ovenfloor
In my case, the size of the firebricks and the height of my ovendoor determined the remaining measurements. The size of my firebricks is 25cm/10inches square and 6cm/2.5inches thick. This is a pretty thick brick, in the smaller oven seen in step 1, the bricks were only half the thickness. The thicker the brick, the more heat it stores, but then the sand under the bricks will also store the heat.
I layed out the bricks first to see how they arrange. Since i wanted my firebricks to "float" in the sandbed, i had to cut them to shape. I used a disk grinder to cut them to shape, i ground down around 6 disks. You don't have to do it this way, in the smaller ovens we just built the ovenwalls onto the firebricks.
I sketched the layout on my concrete plate, in order to build up my foundation. If you have another foundation, you don't need to do this step, since you already have your sandbed to lay your firebricks on.
I used Perlite as a first layer under the sandbed. This insulates the concrete plate from the hot sandbed. Otherwise the concrete plate could crack from the heat. If you like to do this, just add it between your gravel and the sandbed.
Be sure to compact your sandbed very well and flatten it nicely. My firebricks weren't of the exact same thickness, so i had to adjust every single one to make sure my oven floor gets flat.
## Step 4: Building the Sand Mound
To define the interior shape of your oven, you have to build a sand mound. To do this, you also have to insert your oven door. The easiest way to make your door, is sawing it out of wood. It's best to use some fire resistant wood like oak. Before you close your oven for baking, you can soak it in water.
For my oven, i had to mount the oven door somehow. I got it from my neighbor, he has a whole lot of them around in different shapes and sizes. He's a retired blacksmith who still has his shop and is still working, but only on jobs he likes. I wanted to mount it decoupled from the hot oven, so i mounted it to the concrete plate. This was made because of the different expansion under heat. As a next step, i added a ring made of cardboard in order to have the inner walls going straight up. This way, it's easier to remove the ash and i have more usable space for baking. We added some more cardboard to stabilize the sand mound around the oven door. It is important to use "sharp" sand, no beach or round sand. It also needs the right moisture content, otherwise your mound will fall apart. As a further effort to stabilize the mound, we used paper with paste or goo on it. (I'm not sure about paste or goo. I mean the stuff you use on wallpaper.)
## Step 5: Building the Oven / Making the Building Material
This is the step, i was most afraid of. Not because how i made it, but because you may want to go on budget and dig your loam out of your backyard. Although this is perfectly possible, it's hard to tell you the right consistency. This is a tactile thing, so it's hard to describe in words.
I used clay powder that i bought in 30kg sacks. With this stuff it's pretty easy. You only have to mix it with the same amount of sand and half the amount of cut straw by volume. Mix it well and add water until the consistency is right. If you add too much water, just add some more clay/sand mix. We used a large tarp to mix and to knead on it. To mix, roll the tarp from one side to the other, so the whole mix will be rolled and well mixed.
Then you need to knead it well. This is very important in order to drive the air out of the mix. It's best to do this by feet, you have much more power in your legs than in your arms. We thought about mechanizing this process. Mixing could be achieved with a concrete mixer, but i don't think it would work for kneading. I think kneading could best be achieved with a bakers kneading machine, but i couldn't get my hands on one up until now.
We then made bricks out of this mixture and used them for building. You should always keep a 90 deg. angle to the sand form. Try to keep the width of the wall constant over the whole oven. The last piece, or the keystone wasn't made as a brick, it was pressed into place.
Now to the diggers among us. I will tell you what Kiko Denzer writes in his book. I can't go that deep into the details as he does. First because of the time i'd need to rephrase it in my own words and second because i don't want any copyright issues coming down on me. Do yourself a favor and get this book, it's worth every buck.
So if you want do dig, you will first have to remove the fertile topsoil which is darker than the subsoil that is rich in clay. You could also inspect construction sites, if you see them digging a cellar or a foundation. You may ask them to dump a truckload at your place, maybe they have some sand around as well.
This subsoil should (mostly does) contain clay, silt sand and small gravel. Your desired building material should contain from 15 to 25% clay. This stuff is hard to dig. It is sticky and heavy around here and it doesn't crumble as a fertile topsoil would. To recognize it, the shovel should leave a shiny cut mark. If you add water, you should be able to roll it into snakes in your hands and bend it with minimal cracking. You should be able to sculpt it. You could do a test by filling a jar half with your soil, the rest with water. Then shake it well, until everything is dissolved. Stand it upright and undisturbed and watch it. In five to ten seconds, sand will settle out. After 30 or so minutes, silt will settle out. Clay takes from days to weeks to settle. So if your mixture clears in a hour or two, you can't use it, because there is no clay.
Now that you don't know the amount of clay in your mixture, you can do a test. Take a handful of your soil, add as much sand as you think is right and work it into a firm ball. This may take some time, since you want it rather dry and compact. Let it fall to the ground from waist height. If it falls apart, you have too much sand. If it goes flat with no cracking, it's too little sand or too much clay. If it almost holds it's shape without or with little cracking, then you've got it. When you make these tests, be sure to take notes on how much sand and soil you used, so you know the mixture for "production scale".
You should make these tests because of this: clay holds water and this water will evaporate. So your building shrinks. To minimize this effect, use as little clay as possible. (15%) The drawback is a reduced "workability". The mixture tends to be crumbly and needs lots of kneading. I used more clay for my mixture, i knew that some cracks will show up anyway, so using a fatter mixture made for easier handling. You have to decide this for yourself.
In the production mixture, you also have to add some straw, cut up to 2.5 to 5cm or 1 to 2 inch pieces. I added half the amount of the sand by volume. (two buckets of sand, one bucket of cut straw) I have to admit, i bought the straw cut up. If you don't want to cut it manually, try a wood chipper.
It will be pretty hard to mix the soil with sand, water and straw. It's best if you invite your buddies over to help you. Your invitation should include some beers and one or two pizza happenings later on. We were only two, my brew-buddy and me. Sometimes it was a bit depressing, when the work didn't seem to have a end. We were asked to help someone build his oven, after he saw mine. He wanted to pay us, but i told him that it's more important to have a couple of helping hands or even better feet.
## Step 6: Removing the Sand
If you are building with a rather dry mixture, you can remove the sand form right after you finished building. But if you're not sure, better give it a week or two for drying depending on weather and climate. Our oven wasn't completely dry as you can see, but it felt hard to touch. So we removed the sand to dry it out from the inside as well. To speed up the process i burned large candles inside my oven. After another week, i started my first fire. Start it small, and do it daily for a week or so. After this, my oven was dry and i tried my first bread. Resist your pyromanic urges to load it with too much fuel, as you can see on the third and fourth picture. If there is more fuel, than the oxygen can burn, it starts to soot badly and burns out the oven door. And that's not where you want the heat.
After baking a couple of batches of bread and pizza, i added a layer of insulation. My oven was almost a 100 deg Celsius 212 deg Fahrenheit on the outside, without insulation.
If you want to do this, think of it from the beginning. That means plan your foundation a little wider. I planned my insulation from the beginning, but i wanted to see how it works without. After applying 8cm/3.5inches of insulation made of Perlite and clay, the outside temperature dropped by half, keeping the heat much longer. You can use different materials for insulation, my choice was a foamed mineral. You could use Vermiculite or pumice, but straw or coarse sawdust from a chainsaw would also work. Maybe you need to make a thicker layer to achieve the same insulating effect. I used a sturdy paint mixer in a electric drill to mix clay, Perlite and water. As you can see, it cracked after drying. We used a silicone cartridge, filled with rather thin clay to fill the cracks. We further made a temporary roof with the tarp we used for mixing and kneading the mud mix. The final roof will be made of fiber concrete(ethernit), but it's up to you what you use. Depending on the distance from your oven opening, it needs to be heat resistant. It worked with the tarp and pine wood without melting or charring, but i will use oak where it gets hot.
We will add a thin layer of clay plaster 1cm/0.5inch when we remove the temporary roof. It's easier to work around the oven without the roof. This is only for the optics and it's not much work.
## Step 8: Using the Oven
Now comes the fun part of having such a oven. Maybe the first time you bake, you have not enough or too much heat. In my case, i heat the oven for 2 hours and then take out the remaining ashes. After another hour of "soaking" it's ready to bake. Soaking means letting the temperature even out in the oven. This timing actually matches my normal dough fermenting pattern.
Here you can see a couple pictures of my baking endeavors.
You can see some of my "devices" that i need to bake as well. To remove the ashes, i use a coco-handbrush mounted on a broomstick. I was lucky to get a wooden bread peel for free and one made of aluminum as a gift. I have a infrared thermometer that goes up to 550 Celsius and 1000 something Fahrenheit. You could throw in some flour and see it turn brown. This should happen in 10 to 20 seconds. Then you have the right temp to bake bread.
Since this is my first instructable, forgive me my wrongdoings. Maybe you see some orthographical or grammatical oddities, that's because English isn't my native language.
I will read your comments and correct any errors and omissions, you make me aware of. If there is enough interest, i could make some baking instructables as well. Having a oven isn't the same as using it.
In the meantime, i made a baking instructable for the Challah-like braid. You can find it here:
By the way, the guy you see on the photos is my brew-buddy Willy, someone had to shoot the pictures and that was me. We have a nice homebrewery together and brew on a (more or less) biweekly basis.
Thomas
## Step 9: Pizza Pizza
Today, we just had a little pizza roundup.
I think it speaks for itself, what such a oven can be good for. It was a very nice gathering. The pizzas came out very well, the flammenkuchen's too. First we looked that everyone had one pizza, so the first hunger was stilled. Well, actually, there was a shrimp cocktail before, some little antipasti and some bread as well. Then i started to do flammenkuchen's and cut them up into small slices, so everyone could take as much as they wanted. Later we had some coffee and cake. Still later, some more flammenkuchen and pizza. As you can see, i had a peppering help from a young fella. At some point, i will learn to shape those pizza's and flammenkuchen's nice and round, but in the meantime they just taste great.
<p>Hi, </p><p>Great Instructable! I am thinking about building a pizza oven of my own and wondered how to keep the oven hot. Do you light the fire then take it out? Do you leave it in there and bake around it?</p>
<p>Hi, </p><p>thanks for you positive comment</p><p>It depends, what i bake. When making pizza, i keep a fire going at the side. I also keep the door open. This way, i can bake pizza for several hours at a more or less constant heat. It needs some experience and a contactless thermometer helps a lot.</p><p>When i bake bread, i take the fire out. Anyway, it's a good idea to bake bread with "falling" heat. (starting high and let it cool down with the door closed)</p>
<p>Nice article mate. I'm creating an series of articles on pizza ovens. Feel free to have a look and perhaps try a slightly different design (eg. Barrel vault or Neapolitan dome) for your next oven. </p><p>http://pinkbird.org/w/How_to_build_a_pizza_oven</p>
<p>Hi Eli</p><p>A lot of text, you wrote... nice!</p><p>Before i built my oven, i also did some research on different designs. I originally built it for baking bread. When i attended a cob building workshop, i asked if i can bring some dough to bake. I fired up a (dry) oven made in a earlier workshop and the bread came out fantastic. Later i found out, that the bread came out so good, because of the prolonged fermentation... and not (only) the oven.</p><p>I don't think, i will build another oven. At least not for me... I'm quite happy with mine. I built one at the workshop, then mine and then one for a friend. I also bought a used professional electric pizza oven two years ago.</p><p>A friend in Germany built a barrel oven with firebricks. He told me about his build, it took him quite some time and stash.</p><p>Now i'm enhancing the doughs and toppings ;-)</p>
Definitely a good plan. I agree once you've got your oven working you must spend time perfecting the actual pizza! :) You never know, you may move in the future and will want to build a new oven at your new place. <br><br>Regards, Eli
<p>"Here pictures of my latest build. Smaller and faster to build. <br>Instructable will follow."</p><p>Where is the newest instructable? BTW. I am making WFO in a few months and this is the template I will be using. Thank you.</p>
<p>I will see, what i can do...</p><p>Anyway, this will be only a foto report of the build with cross references to this instuctable. I don't find the time to rewrite it completely. (So many projects, so little time ;-)</p>
This is awesome! I just built a pizza oven in my back yard. It's not as easy at it looks, believe me, but well worth the effort! I got my hands on this detailed step by step guide, helped out a lot, check it out <a href="http://www.buildapizzaoven.org" rel="nofollow">www.buildapizzaoven.org</a> <br>
Awesome oven. Thanks for the tips. We made one with clay dug from our lake. It makes tasty pizzas, stuffed mushrooms and bell peppers..and actually it makes everything taste better.
Very nice <br> <br>Here pictures of my latest build. Smaller and faster to build. <br>Instructable will follow. <br>
Nice! that is very sleek and compact. We put a vent at the top of ours, but I'm not sure if that really helps or hurts the design.
If you want a vent, you should place it close to the front. <br>We built one with vent at a workshop. <br>But you loose heat in such small outdoor ovens. <br>I don't care, if it smokes out of the front opening. <br> <br>
cool. nice smoke stack. is that a clay ball at the top?
Exactly, but it didn't tightly fit. So we still lost some heat. <br>When i did that again, i would wait until the smoke stack is somewhat hard. <br>Then place a plastic film on it and press the ball in place, so i get a tight fit. <br> <br>We also had some kindergarten teachers in our group. They wanted this design ;-)
Ah, nice idea.
Hi clay Pizza oven lovers. aside from my blog (http://clayoven.wordpress.com) I have now produced a downloadable eBook containing everything you need to know in order to build your own oven. Have a look and tell me what you think:<br><br>www.clayovenbook.co.uk<br><br>Happy building!<br><br>Simon<br><br>:-)
Hey Simon,<br>does your eBook sell?<br><br>Check out this site, if you haven't already.<br>http://www.varasanos.com/PizzaRecipe.htm<br><br>It's a long read... i PDFed it and put it on my Android phone to read offline.<br>I made a dough for a "Flammkuchen" with his method (hydration and wet kneading) and it's amazing. I made it with yeast only, i'm still waiting for the delivery of my sourdough cultures.<br>I kept it in the fridge for 3 days. <br>I made it in my 300°C electric oven on the pizza stone.<br><br>Try it, you won't regret it.
Wow that guy clearly has a pizza obsession! Amazing.<br><br>S
Yeah, he went all the way.<br><br>The section about different flours and kneading techniques is very enlightening.<br><br>It's the most secret-revealing text, i've ever seen. <br>And best of all, he speaks from his own experience.<br><br><br>By the way, i'm going to build a oven for a friend this spring. It will be a bit smaller and without a door.<br><br>The foundation is already built and my big bakers kneading machine for kneading the building material is already on his property.<br><br>Maybe i take some photos of the building process. My brewing buddy, who helped on my oven will also help. So i guess we can finish it in two days.<br>
I'm VERY intrigued by this " big bakers kneading machine"!<br><br>S
Doesn't seem nice to advertise your book on the back of someone else's intructable.
All of the instructions to build the oven are also still freely available on my blog but I know some people like a good old book. Also, my oven is different to the one featured here. <br><br>Simon
Technically you are right, but it's ok with me. <br>Look at it as further reading.
Too complex. <br><br>Simple brick oven = faster.<br><br>or temporary mud/clay/earthen oven. Just enough for a year or two's worth.
I wouldn't say that.<br><br>I'm enjoying it the fourth year now.<br>As long as the roof stays up, this oven will survive me...
I agree. Mine is almost 4 years old now and although it has had quite a battering (I have neglected it a little to be honest) it still works great. Have a look at my latest post and video showing the winter damage:<br><br>http://clayoven.wordpress.com/2012/03/12/winter-damage-again/<br><br>I fired the oven up immediately afterwards and she worked just like the first day she was built.<br><br>S
Now i need to learn how to make pizza!!!! HAHA
Try this text, it's very long and very thorough.<br><br>http://varasanos.com/PizzaRecipe.htm
hey could i use handmade bricks or ed bricks for this
I don't see, why not. <br>As long, as the ovenfloor is insulated from the foundation, you can take about everything. We used a wooden structure for the temporary ovens in the workshop.
oh okay i just love handmade bricks and was wondering hey have you thought of useing a eltric heater as well as fire for heat
I have thought about electric heating, but to in order to heat up such a monster(in terms of thermal mass), you'd need quite a couple of kilowatts. What your standard wall plug delivers, woult take very long to heat it up.<br>I was also thinking about propane or natural gas heating. Here you can crank out 10+ kW at a reasonable price.<br><br>But then, why do i build a wood fired oven in the first place? Because i love (controlled) open fire.<br>It has a Zen-like quality to fire up the oven, while the dough is rising.<br><br>When it's dark, after making many pizzas in the afternoon, i take a chair, throw some crackling pinewood into the oven and watch the flames.<br>That's better than most TV-programs, especially with a homebrewed beer or a red wine at hand...
yeah i just meant as a added benfit
Thomas, that was a FANTASTIC Instructable! Great job and your English is just fine. Thanks for sharing!
i was wondering what is the color of the clay? because in my country we seem to have high rich clay content in our soil. and also would the oven survive heavy rain because 6 months is of the year is the rainy season and we don't have snow so frost is not a problem. and when i dug in my yard i found a hard dark soil under the gravel
Well, clay comes in different colours. My building clay was brown when wet and beige when dry. <br>For the final touch-up layer, i used a red one.<br>But i have seen from light to dark grey and even blueish clay.<br><br>If you let a ball of your dug dark soil dry, it should get stone hard. It will also be somewhat brittle and have some cracks due to drying shrinkage.<br><br>If you don't want your oven to be gradually washed away, you need to protect it from rain. (A roof also helps to keep the pizzaiolo dry ;-)<br>The clay is not fired on the outside, so it stays water soluble.<br>
thanks ill try that and when i dug in my yard i had to use a pickaxe to get to the dirt because it was so hard that i couldn't use a spade, so maybe its a good sign? and by the way it had rained only a week ago and the dirt is very hard now.
i just made a small ball last night and how its rally hard like a stone and when a dropped it from shoulder height it cracked and broke like a brittle rock and like you said it formed some cracks due to shrinkage. i think that this would be a great material if i let it mix with sand
I have some old concrete 'urbanite' - it has a really high aggregate content - do you think that would work?
I didn't have to do it, so you have to judge for yourself. If you have it around, use it.<br>I would pick up stones from a nearby creek, because i don't have "urbanite" around.
Thanks - I'll give it a shot - great instructable.
hi - I was wondering, the River Cottage Bread book has some instructions on this - and they suggest doing three layers - innner, 'insulating' (with woodchip mixed in the clay' and outer. Any point in doing this?
I don't know this book, but it certainly makes sense. I did it somewhat similar. The inner layer is also called the thermal layer. It's made of clay, sand and shredded straw. The thickness has to be 4-8 inches. This gives the thermal mass of the oven. (mine is close to 8 inches) This means the oven keeps the heat longer, but also needs more time and fuel to heat up.<br>I did some test bakes with only this layer, but i planned a insulating layer from the beginning.(you can see the oven without insulation in step 6 picture 3)<br><br>The oven got quite hot on the outside, so i made a insulation with a perlite clay mix.(perlite is a foamed mineral like pumice)<br>The outside temperature fell by half, keeping the heat even longer.<br>With woodchips, i guess the insulation needs to be a bit thicker than mine.<br><br>The third layer is for protection and good looks only. I did it with a red clay and fine sand.
I myself will be building two of these this summer. After a lot of reading it appears that your door ratio may be a little on the large size which would result in a large heat loss. Would you agree with this?
Hello<br><br>as described in step 1, the calculation only covers the heights of the door and the inner height of the dome. The width of the door can be smaller of course. I just used, what was available at that time. (i wanted a minimal width to use the trays from my electric oven) The opening also doesn't have to be rectangular.(In most ovens i've seen, it isn't.
Hi t.rohner!<br><br>You can also build this oven making a mold with fine and wet sand as you want inside. Cover with clay, as you did. When dry, open the door and take the sand out for next building. You may use soil cement in a ratio of 18:1 with bamboo slivers either to build the oven or to cover it. Ok, it's a little bit more expensive.<br><br>How much water to use with soil cement? Get in hand some clay and squeeze. Falling just a drop of water is perfect. <br><br>To avoid cracks mix sugar with clay. Warning: the mass is slightly softer with sugar. Wait to dry completely and fire strongly. Using cement, don't forget to wet for 3 weeks, to keep cement cold and just use after 30 days. You can use sugar with cement too. Very good! <br><br>Then, good pizzas, good breads and much more!
Dude you AWESOME !!
amazing... thankyou, you've inspired me.... I'm going to start collecting materials and plan for my own oven. Have wanted to make one for about a year but have never been brave enough on my own even with lots of research!! This is a very helpful concise and enjoyable instructable to read...will try to enlist the help of my friends with the promise of pizza and home made champagne!! :-)
Thank you for your nice comment. Some help is definitely desirable. What kind of champagne do you make? I used to make elder flower "champagne" for years. This year i made elder flower sirup. It's very nice in a glass of prosecco or champagne.(even with plain water...)
I'm curious why you didn't use quicklime, the fireproofing and waterproofing ingredient i've read about in cob books. I've made mud bricks in Mississippi climate, they just melt away in the rain, without quicklime added. I submerged a quicklime brick in water for over a year and it remained hard. <br /> I'm guessing the temperature of the oven turns the clay into ceramic? But I wonder if the straw burns without the lime to protect it? | 7,178 | 29,554 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2017-13 | latest | en | 0.947047 |
http://cnx.org/content/browse_content/keyword/D/DFT | 1,369,550,691,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368706635063/warc/CC-MAIN-20130516121715-00001-ip-10-60-113-184.ec2.internal.warc.gz | 52,401,379 | 40,014 | # Connexions
##### Sections
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The content in Connexions comes in two formats: modules, which are like small "knowledge chunks," and collections, groups of modules structured into books or course notes, or for other uses. Our open license allows for free use and reuse of all our content.
# Browse Content
## DFT
« Previous 28 [1] 2
Type Title
Computing the fast Fourier transform on SIMD microprocessors
The DFT, FFT, and Practical Spectral Analysis
Discrete-Time Fourier Analysis
Signal Processing
2D DFT
Algorithms
Appendix 1 - Simple FFTs
Appendix 2 - FFTs with precomputed LUTs
Appendix 3 - FFTs with vectorized loops
Benchmark Methods
Chirp-z Transform
Circular Shifts
Common Discrete Fourier Series
Common Discrete Fourier Series
Conclusions and Future Work
Convolución Circular y el DFT
Desplazamientos Circulares
DFT as a Matrix Operation
DFT Definition and Properties
Discrete Fourier Transform
Discrete Fourier Transform
Discrete Fourier Transform (DFT)
Discrete Fourier Transform Pair
Discrete Fourier Transformation
Discrete Time Circular Convolution and the DTFS
Discrete-Time Filtering Example
Efficient FFT Algorithm and Programming Tricks
Existing Libraries
Fast Fourier Transform (FFT)
Filtering in the Frequency Domain
Filtering in the Frequency Domain
Filtering with the DFT
Frequency Domain Filtering
Goertzel's Algorithm
Implementation Details
La Transformada Rápida de Fourier (FFT)
Lab 4 Prelab 4
Lab 4: Prelab
m10 - The Discrete Fourier Transform
m11 - Properties of the DFT
N = 11 Winograd FFT module
N = 13 Winograd FFT module
N = 16 FFT module
N = 17 Winograd FFT module
N = 17 Winograd FFT module in C
N = 19 Winograd FFT module
N = 25 FFT module
Overview of Fast Fourier Transform (FFT) Algorithms
Program 1: Goertzel Algorithm
Program 2: Second Order Goertzel Algorithm
My Account | 460 | 1,842 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2013-20 | latest | en | 0.609447 |
https://taxandlife.com/cat/tax/2018/01/01/what-is-amt.html | 1,696,201,771,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510941.58/warc/CC-MAIN-20231001205332-20231001235332-00028.warc.gz | 615,862,539 | 4,950 | AMT stands for Alternative Minimum Tax. According to the official definition in 26 U.S. code §55 and the actual usage on line 45 of form 1040, it is the amount by which the Tentative Minimum Tax (TMT) exceeds the Regular Income Tax (RIT).
The Tentative Minimum Tax (TMT) is the tax computed with a parallel method different from the regular tax, which we will discuss in next section.
The relationship among Regular Income Tax (RIT), Tentative Minimum Tax (TMT), and Alternative Minimum Tax (AMT) are shown in the picture below:
When Tentative Minimum Tax (TMT) is greater than the Regular Income Tax (RIT), then we say you have hit the AMT, or you pay this additional tax on top of the regular tax as formulated on form 1040. In reality, however, it is not that you pay another tax called AMT tax, but you just pay Tentative Minimum Tax (TMT), because AMT can be expressed as:
``````AMT = TMT - RIT
``````
So the total tax you pay is:
``````Total Tax = RIT + AMT = RIT + (TMT - RIT) = TMT
``````
In other words, you pay regular tax or tentative minimum tax, whichever is higher. You cannot beat IRS.
### How is Tentative Minimum Tax (TMT) computed?
It is computed by the following steps:
• Derive the alternative minimum tax income (AMTI) which is different than computing taxable income. For example, it is not allowed personal exemptions, standard deductions, and state taxes, property taxes, and job related expenses in itemized deductions.
• Subtract the exemption amount for AMT purpose from the AMTI. The exemption is \$83,800 (Y2016) for joint return if AMTI is less than the phase out threshold, which is \$159,700 (Y2016). The exemption amount starts to phase out when AMTI exceeds this number by an amount equal to 25 percent of the excess.
• Compute the tax at 26% for the portion of the income below \$186,300 (Y2016), and at 28% above.
### Example
A joint filer with AGI \$150,000. Suppose all their deductions are not allowed for AMT purpose. The Tentative Minimum Tax (TMT) is computed as (Y2016):
``````TMT = (150,000 - 83,800) * 26% = 17,212
``````
Suppose the deduction is D, and since the personal exemptions are 8100 for 2 persons, the Regular Income Tax (RIT) is (Y2016):
``````RIT = (150,000 - D - 8100) * 25% - 8457.50
``````
Obviously the more the deduction, the less regular tax. When deduction reaches 39,222, the regular tax is below the tentative minimum tax, so the AMT kicks in.
### New tax law change
The new tax law did not eliminate the AMT as it should have, but increased the exemption amounts and phaseout thresholds which are tabulated below:
Year MFJ/QW MFS Single/HH
2016 exemption \$83,800 \$41,900 \$53,900
2017 exemption \$84,500 \$42,250 \$54,300
2018+ exemption \$109,400 \$54,700 \$70,300
2016 phaseout \$159,700 \$79,850 \$119,700
2017 phaseout \$160,900 \$80,450 \$120,700
2018+ phaseout \$1,000,000 \$500,000 \$500,000
Also see here for more readable text.
### Conclusion
The purpose of AMT is ensure that rich people to pay a minimum amount of taxes by disallow certain deductions. However it is not so much about richness as theoretically anyone who has income greater than the AMT exemption amount can trigger AMT, rather it is about how much you have deducted unallowed amount for AMT purpose, and how much tax you have paid relative to your income. Let us use two examples to illustrate this.
Bill and Hillary Clinton did not pay AMT in their 2015 tax return even their income is 10.5 millions. This is because the deduction is moderate relatively speaking (and a major part of the deductions was charitable donations which were allowed), and they paid 3.2 millions in regular taxes. The effective tax rate is 30.5% which exceeds the maximum 28% AMT tax rate.
In Donald Trump’s 2005 tax return, he paid 38 millions federal tax, of which 31 millions were attributed to AMT, without which he would have paid a little over 10% income tax of his AGI.
In conclusion, when you hit AMT, it does not mean that you hit another tax, but IRS does not allow you to deduct anymore. The amount of AMT tax represents the tax you would have saved if the deduction were allowed. | 1,071 | 4,142 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2023-40 | latest | en | 0.948672 |
https://www.ps2pdf.com/unit-converter/microseconds-to-milliseconds | 1,628,058,916,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154796.71/warc/CC-MAIN-20210804045226-20210804075226-00600.warc.gz | 908,150,149 | 2,476 | # Microseconds to Milliseconds conversion
Microseconds:
Milliseconds:
## How to convert Microseconds to Milliseconds
1 Microseconds (mu) is equal to 0.001 Milliseconds (ms).
1 mu = 0.001 ms
or
1 ms = 1000.0000000000001 mu
## Microseconds conversion table
Convert 1mu Units
Result
Microseconds to Nanoseconds
999.9999999999999
Microseconds to Milliseconds
0.001
Microseconds to Seconds
0.000001
Microseconds to Minutes
1.6666666666666667e-8
Microseconds to Hours
2.7777777777777777e-10
Microseconds to Days
1.1574074074074074e-11
Microseconds to Weeks
1.6534391534391534e-12
Microseconds to Months
3.802570537683474e-13
Microseconds to Years
3.168808781402895e-14
; | 216 | 670 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2021-31 | latest | en | 0.51059 |
https://easywriters.net/2193923/ | 1,628,173,732,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046155925.8/warc/CC-MAIN-20210805130514-20210805160514-00016.warc.gz | 220,124,050 | 10,940 | ## Answered: - 1. Assume your company has a contract to purchase 100 computers
1. Assume your company has a contract to purchase 100 computers from a Korean company. The paymentis due on receipt of the shipment and must be delivered in Korea on 1 December 2016. On 1 July 2016,when you are arranging the contract, the computers are priced at 500,000 won each. On 1 July 2016, thespot exchange rate is AU\$1 in exchange for 1,250 won (KRW). Assume that the 6-month interest ratein Korea is 3% and the rate in Australia is 5%. Assume that the covered interest parity holds.
(A) Calculate the Australian dollar price (on 1 July 2016) of one unit of Korean currency (rounding to4 decimal places). [5 marks]
(B) What is the total price of the computers in Australian dollars on 1 July 2016 (rounding to 2 decimalplaces)? [5 marks]
(C) Calculate the 6-month forward exchange rate, FKRW/\$, under the covered interest parity (roundingto 2 decimal places). Note that the forward rate is defined as the Korean won per AU\$1.Hint: Use the CIP equation. [7 marks]
(D) What would you advise your firm to do to avoid a loss on the deal if the Korean won costs 5% morecompared to the Australian dollar (the expected depreciation rate of Australian dollar againstKorean won is 5%) when payment is due on 1 December 2016? The answer should have the exactnumbers (rounding up to 2 decimal places) that you would tell your CEO.Hint: You want to get rid of the exchange rate risks. (12 marks)
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Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions. New orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below. | 540 | 2,216 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2021-31 | latest | en | 0.944721 |
https://www.hindawi.com/journals/mpe/2013/954857/ | 1,696,268,544,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511002.91/warc/CC-MAIN-20231002164819-20231002194819-00799.warc.gz | 864,603,998 | 84,960 | #### Abstract
The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.
#### 1. Introduction
In recent years, El Niño/La Niña-Southern Oscillation (ENSO) is a quasiperiodic climate pattern that occurs across the tropical Pacific Ocean every five years which has caught more and more attention of researchers due to its great destructions. It is coupled with two phases, the warm oceanic phase, El Niño, and the cold phase, La Niña. Some methods were applied to consider the numerical simulation, among which is the famous Adomian decomposition method (ADOM) [1].
Generally speaking, two aspects affect the accuracy of the ADOM: the calculation of the Adomian decomposition series and the initial iteration value. In view of these points, various modified versions are proposed to solve the nonlinear initial value problems [27].
Recently, Tsai and Chen [810] suggested a Laplace-Adomian-Pade method (LAPM) to approximately solve the initial value problems of differential equations. The method holds the following merits: (a) the Laplace transformation can be used to “fully” determine the initial iteration value; (b) the Adomian series is used to linearize the nonlinear terms; (c) the Pade technique is used to accelerate the convergence and enlarge the valid area of the approximate solution.
In this paper, we use the method to approximately solve the ENSO model. The approximate solution is compared with other nonlinear techniques in the high order iteration and the result shows the method’s higher accuracy.
#### 2. Approximate Solutions of the ENSO Model
The air-sea coupled dynamical system was used to describe the oscillating physical mechanism of the ENSO [11] where , , , and are physical constants, describes the temperature of the eastern equatorial Pacific sea surface, and is the thermo-cline depth anomaly. The model (1) shows the variations of both eastern and western Pacific anomaly patterns.
Case I. When and , then (1) can be reduced to
In order to solve (2) with the LAPM, apply the Laplace transform to both sided of (2) first and we can derive where . As a result, (3) leads to
Apply the inverse of the Laplace transform and expand the nonlinear term as an Adomian series [1, 12]; then (4) can be written as where and is the Adomian series of ; namely, Now the iteration formula can be determined for (2) as
Assuming , the successive approximate solutions can be presented as
We can consider a Maple program for the approximation and set the truncated order as 7 and 12, respectively. The 7th term approximation and the 12th term approximation can be obtained as
Recall that (2) has an exact solution [13] Setting in this paper, we apply the Pade-technique to the approximate solution . In order to avoid the tediousness, the detail expression of the result is omitted here.
The approximate solutions from the ADOM and the LAPM are compared using the high iteration solutions and in Table 1, respectively.
The exact solution (10), the approximate solutions , , and the solution without the treatment using the Pade-technique are compared in Figure 1.
The results in Table 1 and Figure 1 illustrate that the LAPM has a higher accuracy, respectively.
Case II. For the coefficients and , (1) reduces to Setting the initial condition value , we can derive the following iteration formula: where is the th approximation of . As a result, for , we can obtain the approximate solution by means of the LAPM.
Define the residual functions and as The plotted functions and show that the iteration formula is reliable (Figure 2). Now we can analytically investigate the relationship between the temperature and the thermo-cline depth , which is shown in Figure 3.
Remarks. This study only concentrates on the applications of the Adomian series in the linearization of the nonlinear equations. For various calculations of the Adomian series, readers are referred to the recent development of the method in [3, 4, 1416] and the applications in fractional different equations in [1719]. It is interesting to point out that the results are the same as those of the one using the variational iteration method [20].
In the classical ADOM, the inverse operator should be used. For example, one can need to transform the differential equation into the following equivalent integral equation
Here is called the inverse operator in the ADOM.
In Tsai and Chen’s method, the solution procedure shows that the LAPM without using the inverse operator still keeps approximate solutions of higher accuracies. Furthermore, the initial iteration function can be readily determined. The method also can be extended to fractional differential equations [21] and -difference equations.
#### 3. Conclusions
With symbolic computation, the LAPM is used to approximately solve the ENSO model. We compared the approximate solutions with those from the ADOM and the LAPM, respectively. The results show that the LAPM has higher efficiency which can accelerate the convergence and enlarge the valid area of the approximate solution.
#### Acknowledgment
This work is supported by the Scientific Research Fund of Sichuan Provincial Education Department (12ZA085). | 1,153 | 5,515 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2023-40 | latest | en | 0.910523 |
https://coreelevation.com/2022/06/08/graph-explorer-with-keygen-free/ | 1,674,855,530,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764495012.84/warc/CC-MAIN-20230127195946-20230127225946-00368.warc.gz | 211,197,139 | 19,023 | The Graph Explorer application was developed to be a small tool that allows you to explore a wide range of mathematical functions.
Unlike most expression evaluators, Graph Explorer will allow you to enter many algebraic expressions just as you would write them.
For example, for XY plots, you may use expressions like:
y=ax2+bx+c or y=sqrt(x+1) etc.
One of the most important operations in mathematics is determining a function graph or a parametric curve.
In the Graph Explorer application, the mathematical functions:
. sin (Tan (a°))
. cos (Tan (a°))
. tan (Tan (a°))
. cosec (Tan (a°))
. sec (Tan (a°))
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are exactly represented on the graph.
The Graph Explorer application can also be used to represent:
. arcsinh (A°)
. arcsin (A°)
. Arcsin (A°)
. sqrt (x)
. exp (x)
. ln (x)
. (ln (x))′
. (Δ x)2
. (Δ x)′
etc.
Another interesting feature of Graph Explorer is that all the algebraic functions can be represented in polar coordinates for y=ax+b or x=ay+b. For example, for this function:
. sin (Tan (a°))
. cos (Tan (a°))
. tan (Tan (a°))
. cosec (Tan (a°))
in polar coordinates, Graph Explorer allows you to express it as:
. (sin (a))′ =cos (a) (cos a)′ =sin a
. (cos (a))′ =sin a (sin a)′ =cos a
. (tan (a))′ =cosec (a)
. (cosec (a))′ =sec (a)
. (sec (a))′ =csc (a)
For this reason, Graph Explorer can also be used to visualize the graphs of algebraic expressions that are not functions. For example:
. tan x sin (Tan (x))
. tan x cos (Tan (x))
. x sin (Tan (x)) cos (Tan (x))
. (sin (Tan (x)))′ =cos (Tan x)
etc.
The application allows you to explore:
. Various kinds of equations:
. The origin of functions:
. The graphs of functions:
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. The solutions of equations:
. It even allows you to explore vector fields.
Simple, flexible, intuitive and easy-to-use, we are the best expression evaluator and graph calculator you’ll find.
It was designed so that it could be used as a standalone expression builder and graph calculator, but it can also be used as a Python IDE.
Graph Explorer Serial Key is a graphical tool that allows you to build and plot algebraic expressions. It is useful for school or homework, and works on almost any operating system.
Displays a list of expressions.
Highlights expressions based on their complexity.
Displays a list of all variables used in the expression being built.
Includes features to quickly rewrite expressions or equations (e.g. “rewrite an expression with 3 variables and save to EEX”)
Display each function as an arbitrary (x,y) graph, using any of numerous graph types (line, tree, area…)
Color: RGB (Red, Green, Blue)
Color is used to highlight individual expressions.
File Type: All files (*.dat, *.txt, *.eex, *py, *.h, *.tpl)
Graph Explorer Torrent Download is independent from any Python language and if you are not using Python you can still use Graph Explorer Crack Keygen. We hope this would encourage more users to start using Graph Explorer Full Crack.
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Graph Explorer 2022 Crack is a powerful graphing calculator – it can plot several types of graph, from line to area to tree etc. Graph Explorer features are many: from set of useful functions (log, sqrt, abs, pow) to plotting features like zoom in/out, sliders for Y-Scale and Y-Scale zoom, calculation of any mathematical function including eXpiration (Nth…) and Statistics, Parameters for graph, all calculations can be done for any “domain” (x-domain, y-domain, both or none) from same window…
…many and the list is still growing…
Graph Explorer is a powerful graphing calculator – it can plot several types of graph, from line to area to tree etc. Graph
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## Graph Explorer Crack + Activation Key [March-2022]
Graph Explorer is an expression evaluator for creating algebraic or geometric plots in the form of different graphs. It computes values of mathematical equations at specified intervals. You can read the expression and also show them on the graph. You can save the graph for further use. Graph Explorer is a very small program. Just enter expression and you can analyze it very easily. You can find the entire
show that they cannot be represented as smooth. The same holds for the knot. At the same time, in addition to the linking integral, there is another integral along the knot curve, which is calculable analytically and gives the constant of proportionality. When expressing
This section briefly describes how to test and train neural networks using the OpenCV
We use a simple neural network for the purpose of this example.
A neural network is a computing system with connections between one or more neurons to
If you have flown model planes, you surely want to learn what kind of control method is adopted on the jetcraft and what is the advantage of this method. The control method of the jetcraft and the advantage of this method can be explained on the following points.
Let’s consider the control of the jetcraft. Every propeller unit and the jet engine are continuously controlled by the air conditioning controller. The jet engine (the main
2:I : •I t’ :O t •..-.,-,,…… : It would seem that the most obvious difference is that the solutions of the Master equation and the Fokker-Planck equation do not coincide and, therefore, cannot be made to coincide by renormalization. In the weak-ly interacting case considered in the text, the Master equation may be obtained as a small WKB perturbation of the Fokker-Planck equation. In particular the expressions for the correlation and
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The Graph Explorer application was developed to be a small tool that allows you to explore a wide range of
## What’s New in the Graph Explorer?
Graph Explorer is a simple but powerful graphing calculator for iOS. It provides a large set of built in functions, with the ability to define your own using AppleScript. You can graph functions or use them to solve expressions.
This version is an open source project and your feedback is most welcome, send us some ideas or problems you can’t solve at our support email and we will make it our top priority.
Here are some of the built-in functions of Graph Explorer:
• 4 different types of XY Plotting:
– XY Plotting
• 1 and 2 point XY Plotting
• Custom 2 Point XY Plotting
– Extracting Routines and Other Functions:
– Vector Rounding:
– Normalizing:
– Calculating Trigonometric Functions:
– Calculating Logarithmic Functions:
– Calculating Rounding and Truncation Functions:
– Math Symbols:
– Some Minus Functions:
– Some More Standard Functions:
– Array Functions:
– Sort Functions:
– Search Functions:
– Sequence Functions:
• Set Function:
– Append a Single Number to a List:
– Append a List to a Single Number:
– Append a Number to a List:
– Insert a Single Number to a List:
– Remove a Single Number from a List:
– Remove an Element from a List:
• Find:
– Search for a Number in a List:
– Find the Occurrence of a Number in a List:
– Search for 2 or More Numbers in a List:
• Containment:
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– Contained:
– Part of:
• Take N copies of:
– Append:
• Other Functions:
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• Rounding and Truncation Functions:
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• Truncate:
## System Requirements:
Recommended:
OS: Windows 7/8/10
Processor: Intel Core 2 Duo / Core 2 Quad / Core i7
Memory: 4GB RAM
Graphics: NVIDIA GTX 750 / AMD HD 7850
DirectX: Version 11 | 1,989 | 8,184 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2023-06 | latest | en | 0.842793 |
https://www.esaral.com/q/how-many-three-digit-numbers-are-divisible-by-7 | 1,726,661,831,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651895.12/warc/CC-MAIN-20240918100941-20240918130941-00144.warc.gz | 689,887,926 | 11,714 | # How many three-digit numbers are divisible by 7?
Question.
How many three-digit numbers are divisible by 7?
Solution:
First three-digit number that is divisible by 7 = 105
Next number = 105 + 7 = 112
Therefore, 105, 112, 119,\ldots
All are three digit numbers which are divisible by 7 and thus, all these are terms of an A.P. having first term as 105 and common difference as 7.
The maximum possible three-digit number is 999. When we divide it by 7, the remainder will be 5.
Clearly, 999 - 5 = 994 is the maximum possible three-digit number that is divisible by 7.
The series is as follows.
$105,112,119, \ldots \ldots, 994$
Let 994 be the $\mathrm{n}^{\text {th }}$ term of this A.P.
a = 105
d = 7
$a_{n}=994$
$\mathrm{n}=?$
$a_{n}=a+(n-1) d$
994 = 105 + (n – 1) 7
889 = (n – 1) 7
(n – 1) = 127
n = 128
Therefore, 128 three-digit numbers are divisible by 7.
Leave a comment
Click here to get exam-ready with eSaral | 299 | 940 | {"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} | 4.4375 | 4 | CC-MAIN-2024-38 | latest | en | 0.926381 |
https://www.numbersaplenty.com/164320265 | 1,713,552,502,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817442.65/warc/CC-MAIN-20240419172411-20240419202411-00415.warc.gz | 817,845,293 | 3,147 | Search a number
164320265 = 5191729687
BaseRepresentation
bin10011100101101…
…01010000001001
3102110012100000202
421302311100021
5314031222030
624145541545
74033461554
oct1162652011
9373170022
10164320265
118483327a
12470448b5
1328074035
1417b7569b
15e65c745
hex9cb5409
164320265 has 8 divisors (see below), whose sum is σ = 207562560. Its totient is φ = 124537392.
The previous prime is 164320229. The next prime is 164320297. The reversal of 164320265 is 562023461.
It is a sphenic number, since it is the product of 3 distinct primes.
It is a cyclic number.
It is not a de Polignac number, because 164320265 - 222 = 160125961 is a prime.
It is a super-2 number, since 2×1643202652 = 54002298979340450, which contains 22 as substring.
It is a Curzon number.
It is an unprimeable number.
It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 864749 + ... + 864938.
It is an arithmetic number, because the mean of its divisors is an integer number (25945320).
Almost surely, 2164320265 is an apocalyptic number.
It is an amenable number.
164320265 is a deficient number, since it is larger than the sum of its proper divisors (43242295).
164320265 is a wasteful number, since it uses less digits than its factorization.
164320265 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 1729711.
The product of its (nonzero) digits is 8640, while the sum is 29.
The square root of 164320265 is about 12818.7466235978. The cubic root of 164320265 is about 547.7264438648.
The spelling of 164320265 in words is "one hundred sixty-four million, three hundred twenty thousand, two hundred sixty-five". | 514 | 1,706 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-18 | latest | en | 0.860827 |
https://www.techwhiff.com/issue/graph-the-linear-equation-y-1-2x-5--630044 | 1,660,132,468,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571153.86/warc/CC-MAIN-20220810100712-20220810130712-00518.warc.gz | 902,241,702 | 12,414 | # Graph the linear equation y=-1/2x-5
###### Question:
graph the linear equation y=-1/2x-5
### Two similar rectangles are shown. Which statement is true? A) The area of rectangle B is 1 3 the area of rectangle A. B) The area of rectangle B is 1 9 the area of rectangle A. C) The area of rectangle B is nine times the area of rectangle A. Eliminate D) The area of rectangle B is three times the area of rectangle A
Two similar rectangles are shown. Which statement is true? A) The area of rectangle B is 1 3 the area of rectangle A. B) The area of rectangle B is 1 9 the area of rectangle A. C) The area of rectangle B is nine times the area of rectangle A. Eliminate D) The area of rectangle B is three times the a...
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### Fine Lines Inc. is a notebook manufacturing company based in Ohio. Fine Lines' main market is Ohio. It aims at providing its products at better prices than its competitors. Which of the following structures is Fine Lines Inc. likely to use if it has functional setup? a.mechanistic b.organic c.simple d.matrix
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Which characteristic is most likely to be shared by plants in a tundra ecosystem and those in a desert ecosystem? A. Thin, flexible stems B. A shallow root system C. A high photosynthesis rate D. Large, colorful flowers... | 1,378 | 5,762 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2022-33 | latest | en | 0.870843 |
https://www.mcqslearn.com/cs/db/entity-relationship-diagrams-mcqs.php | 1,590,945,952,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347413551.52/warc/CC-MAIN-20200531151414-20200531181414-00179.warc.gz | 795,410,365 | 7,726 | Entity relationship diagrams MCQs, entity relationship diagrams quiz answers pdf to study online database course. Learn database design and er model Multiple Choice Questions and Answers (MCQs), "entity relationship diagrams" quiz questions and answers for online computer engineering programs. Learn entity relationship model, entity relationship diagrams, er diagrams symbols test prep for online college courses.
"The relationship between the weak entity set and the identifying entity set's association is known as" Multiple Choice Questions (MCQ) on entity relationship diagrams with choices owner relationship, existence relationship, dependency relationship, and identifying relationship for online computer engineering programs. Practice merit scholarships assessment test, online learning entity relationship diagrams quiz questions for competitive exams in computer science major for online bachelor's degree computer science.
MCQ: The relationship between the weak entity set and the identifying entity set's association is known as
1. Owner relationship
2. Existence relationship
3. Dependency relationship
4. Identifying relationship
D
MCQ: A weak entity set can make participation in any relationship other than the
1. Strong relationship
2. Relational relationship
3. Domain relationship
4. Identifying relationship
D
MCQ: If a relationship set has some associated attributes, then it is enclosed in a
1. Diamond
2. Double Diamond
3. Rectangle
4. Circle
C
MCQ: A relationship line may have an associated minimum and maximum
1. Values
2. Cardinalities
3. Range
4. Attributes
B
MCQ: In E-R diagrams, a weak entity set is represented via a
1. Rectangle
2. Diamond
3. Circle
4. Double diamonds
A | 339 | 1,722 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2020-24 | latest | en | 0.848629 |
https://questioncove.com/updates/5b2ff6148fe83dbb9f99d80 | 1,550,882,467,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550249414450.79/warc/CC-MAIN-20190223001001-20190223023001-00505.warc.gz | 660,896,695 | 8,891 | mathematics
princeevee:
i need some answers checked 2: Electric boogaloo
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
if they're both parallel to a third line that means lines1 and 2 must be parallel to each other, so true
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
princeevee:
7 months ago
Vocaloid:
huh the postulate normally assumes that you know the lines are parallel we don't know that yet, so we are stating that 2 is congruent to 6 6 is congruent to 8 therefore 2 is congruent to 8 which should be the transitive property
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
in general consecutive interior angles are not congruent, they'd be supplementary so false
7 months ago
princeevee:
7 months ago
princeevee:
7 months ago
Vocaloid:
hm, not quite, 6 and 12 are not corresponding angles (they would have to be in the same position and orientation) notice how 6 and 12 are on the outside side of the parallel lines, making them interior or exterior?
7 months ago
princeevee:
exterior
7 months ago
Vocaloid:
good so B
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
hm not quite CE = ED 5x + 80 = 7x - 2 solve for x, then plug back into AE = 4x + 5
7 months ago
princeevee:
x=41
7 months ago
Vocaloid:
good now plug that into 4x + 5
7 months ago
princeevee:
7 months ago
Vocaloid:
may I see what the proof is?
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
hm not quite 3x - 30 = 90 since its a right angle solve for x
7 months ago
princeevee:
40
7 months ago
princeevee:
7 months ago
Vocaloid:
|dw:1529873599319:dw| not quite, they don't have to be perpendicular, the angles just have to add up t o 180
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
hm x = 41 right so CE = 285 CD = 2*CE = 570 to account for both sides of the rectangle 570 + 570 = 1140 applying this same logic to AE AE = 169 AB = 2*169 = 338 338 + 338 = 676 so 1140 + 676 = 1816 (A)
7 months ago
Vocaloid:
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
since the end of the fence makes 90 degree angles w/ the sides of the fence by definition the sides of the fence are perpendicular to the end fence so B can't be the solution (we are looking for a false statement) any other ideas?
7 months ago
princeevee:
A?
7 months ago
Vocaloid:
if the rows of crops are parallel to the sides and the sides are perpendicular to the end of the fence therefore the rows of crops are perpendicular to the end of the fence making A a true statement so it cannot be the solution
7 months ago
Vocaloid:
let's look at statement C the original problem never states that rows of crops are parallel to the sides of the fence making C the solution
7 months ago
princeevee:
7 months ago
Vocaloid:
hm, not quite AE is 169 but it's asking for CD we solved that x = 41 right? so CD = 5x + 80 + 7x - 2 = ?
7 months ago
princeevee:
570
7 months ago
Vocaloid:
good so 570 = your sol'n
7 months ago
princeevee:
7 months ago
Vocaloid:
|dw:1529876293655:dw| if its perpendicular to the first line it has to be perpendicular to the second line if the two lines are parallel so true
7 months ago
princeevee:
7 months ago
Vocaloid:
because <1 and <2 are in the same orientation with respect to the transversal they are ~corresponding angles~
7 months ago
princeevee:
7 months ago
Vocaloid:
|dw:1529876838710:dw| not quite there's only one possible line that can be drawn through P and be perp. to line l
7 months ago
princeevee:
7 months ago
Vocaloid:
for a y-intercept, the x-coordinate must be 0 so it can't be A
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
hm not quite to find the y-intercept, let x = 0 and solve for y in 3x + 4y = 12
7 months ago
princeevee:
4.
7 months ago
Vocaloid:
3(0) + 4y = 12 4y = 12 y = ?
7 months ago
princeevee:
8
7 months ago
Vocaloid:
4 is being multiplied by y so you have to divide both sides by 4 not subtract
7 months ago
princeevee:
3.
7 months ago
Vocaloid:
good so 3 = your sol'n
7 months ago
princeevee:
7 months ago
princeevee:
hang on, i actually think this is zero
7 months ago
Vocaloid:
a horizontal line has slope 0 not undefined
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
hm not quite remember that a vertical line only has an x not a y take the standard form equation Ax + By = C and replace y with 0
7 months ago
princeevee:
7 months ago
Vocaloid:
|dw:1529878258957:dw| |dw:1529878273213:dw| try to apply this logic to your problem to calculate the slope m
7 months ago
princeevee:
so just 8/-2
7 months ago
princeevee:
-4
7 months ago
Vocaloid:
careful with your signs (8-0)/(0 - (-2)) = 8/2 not 8/-2 so 4 not -4
7 months ago
princeevee:
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
that's point slope form standard form should look like Ax + By = C
7 months ago
princeevee:
so D
7 months ago
Vocaloid:
good
7 months ago
princeevee:
7 months ago
Vocaloid:
not quite if the equation is y = mx that means it has to pass through the point (0,0)
7 months ago
Vocaloid:
which of the four lines crosses the origin?
7 months ago
Vocaloid:
notice how only b crosses (0,0) so only line b can be the correct sol'n
7 months ago | 1,798 | 5,840 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2019-09 | latest | en | 0.810669 |
https://www.doubtnut.com/question-answer/a-cone-of-same-height-and-same-base-radius-is-cut-from-a-cylinder-of-height-8-cm-and-base-radius-6-c-34798573 | 1,632,299,607,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057337.81/warc/CC-MAIN-20210922072047-20210922102047-00117.warc.gz | 769,569,369 | 82,042 | Home
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# A cone of same height and same base radius is cut from a cylinder of height 8 cm and base radius 6 cm .Find the total surface area and volume of the remaining solid.
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603(9)/(7),603 (3)/(7) cm^(3)
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2:35 | 438 | 1,144 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "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} | 2.921875 | 3 | CC-MAIN-2021-39 | latest | en | 0.570965 |
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<p>The cost of renting a car depends on the daily rental charge and the number of kilometres driven. A graph of cost versus the distance driven over a one-day period is shown.</p><img src="/qimages/6541" /><p>a) What are the domain and range of this relation?</p><p>b) Explain why the domain and range have a lower limit.</p><p>c) Is the relation a function? Explain.</p>
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<p>Determine the range of each relation for the domain <code class='latex inline'>\{1, 2, 3, 4, 5\}</code></p><p><code class='latex inline'>y = 6x -6</code></p>
<p>The cost of renting a car depends on the daily rental charge and the number of kilometres driven. A graph of cost versus the distance driven over a one-day period is shown.</p><img src="/qimages/6541" /><p>a) What are the domain and range of this relation?</p><p>b) Explain why the domain and range have a lower limit.</p><p>c) Is the relation a function? Explain.</p>
<p>Write a function to describe coffee dripping into a <code class='latex inline'>10-cup</code> carafe at a rate of <code class='latex inline'>1 mL/s</code>. State the domain and range of the function (<code class='latex inline'>1 cup = 250 mL</code>).</p>
<p>State the domain and the range of the relation.</p><img src="/qimages/551" />
<p>Determine the domain and the range of the relation. Use a graph to help you if necessary.</p><p><code class='latex inline'>y = -x + 3</code></p>
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Save videos to My Cheatsheet for later, for easy studying. | 894 | 3,089 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2021-25 | latest | en | 0.673603 |
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Anonymous asked in Science & MathematicsMathematics · 1 month ago
How would I factor 4x^2/(sqrt(3x^4+2)) to be 4/(sqrt(3+ g(x))? what is g(x)?
Relevance
• Philip
Lv 6
1 month ago
Put 4x^2/[(3x^4+2)^(1/2)] = 4/{3+g}^(1/2)...(1), where g = g(x).;
Let's divide both numerator and denominator of LS(1) and get following::
LS(1) = 4/Q, where Q = (1/x^2)(3x^4+2)^(1/2) = [(3x^4+2)/(x^4)]^(1/2).;
Then Q = {3 + 2/x^4}^(1/2).;
For LS(1) = RS(1) we require 4/Q = 4/{3+g}^(1/2), ie., require {3+g}^(1/2) = Q.;
Then {3+g}^(1/2) = {3 +(2/x^4)}^(1/2), ie., g = 2/x^4.
• 1 month ago
We want x^2 / sqrt(3x^4 +2) to = 1/ sqrt( 3 + g(x))
So then sqrt(3x^4 + 2) / x^2 = sqrt( 3 + g(x))
which is the same as ...
sqrt( ( 3x^4 + 2) / x^4) = sqrt( 3 + g(x))
that tells us that ..
( 3x^4 + 2) / x^4 = 3 + g(x)
Subtract 3 from each side, to get
( 3x^4 + 2) / x^4 - 3 = g(x)
And that is g(x). Done!
• 1 month ago
4x^2 / sqrt(3x^4 + 2) = 4/sqrt(3 + g(x))
x^2 / sqrt(3x^4 + 2) = 1 / sqrt(3 + g(x))
sqrt(3x^4 + 2) / x^2 = sqrt(3 + g(x))
(3x^4 + 2) / x^4 = 3 + g(x)
3 + (2/x^4) = 3 + g(x)
2/x^4 = g(x) | 555 | 1,110 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2020-45 | latest | en | 0.650267 |
https://mathematica.stackexchange.com/questions/110025/whats-the-proper-way-to-cut-out-an-irrelevant-part-of-an-integral-so-i-dont | 1,720,941,873,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514551.8/warc/CC-MAIN-20240714063458-20240714093458-00188.warc.gz | 350,542,486 | 43,997 | # What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?
I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that actually contributes to the integral, but the other parts are giving me errors relating to precision and extremely small values. I've read this and this but I'm still having trouble putting the concepts into action.
Here is an example that's contrived but similar to my actual application:
fn1 = 1/(1 + Exp[500*(x - 2)]);
Plot[fn1, {x, 0, 5}]
LogPlot[fn1, {x, 0, 5}]
Here it is, in the range I'm looking at:
It looks like there's a discontinuity, but it's actually smooth if you zoom in:
This varies enormously over the integration range of {0,5}. At x = 1, it's about 1, but at x = 3, it's about 10^-218. That's so small, I don't really need it in my answer. But obviously, where you decide to cut off the number is your choice; depending on the application, I could decide that 0.01 is 'small' compared to the values of the integrand over most of the range.
So let's say that what I want to do is calculate my integral to a factor of 10^9 below the maximum value in the integration range. How can I adjust the Precision of my integrand, the WorkingPrecision, and the AccuracyGoal so that it can be done automatically without throwing errors or making me manually adjust it every time?
Here's what I tried. I thought that if I look at the maximum value in my integration range, I can use that to 'tune' the accuracy I'd like, and thus the WP.
mv = NMaxValue[{fn1, x <= 5, x >= 0}, x]
ag = 9;
wp = ag*2;
NIntegrate[SetPrecision[fn1, wp], {x, 0, 5}, WorkingPrecision -> wp,
AccuracyGoal -> ag]
I thought that setting my AccuracyGoal to 9 would give me the desired accuracy I wanted, and setting the WorkingPrecision to twice that would give it enough workingprecision to do that, but it gives me this error:
NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small.
We know it doesn't have a singularity, the integration isn't equal to 0, and it's not oscillating. So, the WP must be too small. If I instead set wp=ag*3, it doesn't throw the error. So how can I figure out the WP necessary, in advance, to get the Accuracy/Precision I want, without it throwing an error?
EDIT: Someone suggested I show my actual application in case a given solution that applies to my simple example isn't general enough for mine.
Here is a pastebin of the awful massive function that's my actual integrand.
For some clarity, the integrand is actually the product of two functions, plotted here:
The functions quickly go to absurdly small numbers away from the small section they barely overlap at. Here is a plot of their product, the integrand:
The peak of the region that actually contributes most to the integral is about 6*10^-4, which isn't really that small of a number. However, if you look at a region away from that peak, for example the value at Ex = Er = 4, it's about 10^-8400... which we probably don't need to bother with.
So how can I make my function do the following: Find the max value of my integrand in the integration region, divide that number by something conservative like 10^9, and then don't bother integrating over any values less than that? Essentially, if a value is less than that, take it to be 0.
edit2: It seems like Chop[] could potentially work for what I want to do. I could do something like
mv = NMaxValue[{integrand, Ex <= upperlim, Ex >= 0, Er <= upperlim,
Er >= 0}, {Ex, Er}];
NIntegrate[
Chop[integrand, mv/10^9], {Ex, 0, upperlim}, {Er, 0, upperlim}];
However, it seems to be throwing a lot more errors than before, so I suspect I'm using it wrong...
• NDSolveValue[{y'[x] == fn1, y[0] == 0}, y[5], {x, 0, 5}, WorkingPrecision -> 20]? -- Also, I feel your MWE might be too simple. Some solvers will work quickly on it, but might not on the actual use case. E.g. NIntegrate[fn1, {x, 0., 0.000021073377463201208, 0.3161217353254813, 1.8161217353254813, 2.1854546039338802, 5.}]] has an error just over 10^-12, but I'm not sure whether the approach that produced it is general enough. Can you say a little more, if the NDSolveValue trick doesn't work? Commented Mar 15, 2016 at 3:36
• @MichaelE2, thanks for the advice. It's actually a 2 variable function, so I'm not sure how to apply your method (I'm sure it can be done, I just don't know how). I'll edit my OP to show the actual example, thanks! Commented Mar 15, 2016 at 15:27
• I think i made the same comment on another question of yours. If you require high precision then all the numerical values in your integrand need to be suitably high precision. If you wrote your integrand in terms of (looks like) 4 or 5 symbols for the numeric values i think it would be small enough to post here as well. Commented Mar 18, 2016 at 16:55
fn1[x_] = 1/(1 + Exp[500*(x - 2)]);
The integral can be evaluated exactly
int = Integrate[fn1[x], {x, 0, 5}]
(* (1/500)*Log[1 + E^1000] *)
int // N
(* 2. *)
To see how close to 2 the integral is
Block[{\$MaxExtraPrecision = 1000},
N[Log10[N[int - 2, 500]], 6]]
(* -436.993 *)
So it differs by approximately 10^-437
• Thanks for the response, but I don't think this answers the question. It asked how to adjust the WP, and AG or PG so that it achieves the desired accuracy, in a general case. The example I gave was a very simplified version; the actual one definitely can't be solved analytically. Commented Mar 15, 2016 at 15:05
You probably need a LocalAdaptive Method.
Basically, the LocalAdaptive strategy is to recursivelly calculate the integral over smaller disjoint regions using an integration rule - the recursion stopping criteria is user-specified.
NIntegrate[fn1[x], {x, 0, 5}, AccuracyGoal -> ag, PrecisionGoal -> pg,
WorkingPrecision -> wp, Method -> "LocalAdaptive"]
NIntegrate computes a initialIntegral over an initial region and then partitions it to disjoint regions. NIntegrate compares the regionError of the disjoint regions to the initialIntegral. If the error is significant, the recursion is called. The error will be insignificant if
initialIntegral + regionError = initialIntegral
The region's integral estimate is the sum of the integral estimates returned from these recursive calls. Since you want to compute the integral estimate to user-specified precision and accuracy goals, the following stopping criteria is used:
integralEst = Min[initialIntegral 10^-pg / eps, 10^-ag / eps]
integralEst + regionError == integralEst
A slightly different strategy is to integrate only over the region above some threshold value, which can be fraction of the maximum: mv/a.
a=10^12
r = Reduce[0 <= x <= 5 && fn1 > mv/a, x] (* 0 <= x < 2.05526 *)
NIntegrate[fn1, {x, r[[1]], r[[5]]}] (* 2. *)
I lowered the fraction, because with a=10^9 the result didn't seem reasonable (2.041446531671895 compared to 2.00000000000000090701555082 that results from your initial code)
I tried using Implicit Region, which would be a one-liner in theory, but couldn't get it to work.
NIntegrate[fn1, {x} \[Element] ImplicitRegion[fn1 > mv/a, {{x, 0, 5}}] | 1,963 | 7,376 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "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} | 3.65625 | 4 | CC-MAIN-2024-30 | latest | en | 0.939346 |
http://digital-library.theiet.org/content/journals/10.1049/iet-rsn.2017.0160 | 1,508,758,378,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825900.44/warc/CC-MAIN-20171023111450-20171023131450-00871.warc.gz | 92,138,713 | 17,686 | http://iet.metastore.ingenta.com
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## GNSS attitude determination method through vectorisation approach
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Determining the attitude using GNSS carrier signals is studied. It features an analytical approach to get an estimate as initial guess for iterative algorithms, in three steps. First, baseline vectors are estimated by least-squares method. Second, the constraint of the direction cosine matrix (DCM) is ignored and the least-squares estimates of its 9 elements are solved. Third, a mathematically feasible DCM estimate is extracted from the above estimated free matrix. An error attitude, formulated using the Gibbs vector, is introduced to relate the previously estimated and the true attitude, and the measurement model becomes a nonlinear function of the Gibbs vector. The Gauss-Newton iteration is employed to solve the least-squares problem with this measurement model. The estimate of the roll-pitch-yaw angles and the variance covariance matrix of their estimation errors are extracted from the final solution. Numerical experiments are conducted. With 3 orthogonally mounted 3-meter baselines, 4 visible satellites, and 5-millimeter standard-deviation of the carrier measurements, the accuracy of the analytical solution can be less than 1° in the root mean squared error (RMSE) sense. The convergence of the iteration is rather fast, the RMSE converges after only one iteration, with the converged RMSE less than 0.1°.
### References
1. 1)
• K. Li , J. Zhao , X. Wang .
1. Li, K., Zhao, J., Wang, X., et al: ‘Federated ultra-tightly coupled Gps/Ins integrated navigation system based on vector tracking for severe jamming environment’, IET Radar Sonar Navig., 2016, 10, (6), pp. 10301037.
. IET Radar Sonar Navig. , 6 , 1030 - 1037
2. 2)
• K. Zhang , G. Shan .
2. Zhang, K., Shan, G.: ‘Model-switched Gaussian sum cubature Kalman filter for attitude angle-aided three-dimensional target tracking’, IET Radar Sonar Navig., 2015, 9, (5), pp. 531539.
. IET Radar Sonar Navig. , 5 , 531 - 539
3. 3)
• J. Wu , Z. Zhou , J. Chen .
3. Wu, J., Zhou, Z., Chen, J., et al: ‘Fast complementary filter for attitude estimation using low-cost marg sensors’, IEEE Sens. J., 2016, 16, (18), pp. 69977001.
. IEEE Sens. J. , 18 , 6997 - 7001
4. 4)
• P.J.G. Teunissen .
4. Teunissen, P.J.G.: ‘The least-squares ambiguity decorrelation adjustment: a method for fast Gps integer ambiguity estimation’, J. Geod., 1995, 70, (1–2), pp. 6582.
. J. Geod. , 65 - 82
5. 5)
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This is a required field | 2,456 | 7,705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2017-43 | longest | en | 0.883328 |
https://www.plati.ru/itm/solution-11-2-8-collection-of-kep-oe-1989/2064875?lang=en-US | 1,521,679,388,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647707.33/warc/CC-MAIN-20180321234947-20180322014947-00044.warc.gz | 872,223,136 | 12,449 | Solution 11.2.8 collection of Kep OE 1989
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The body 1 moves according to the law x = sin πt. The body 2 moves relative to the body 1 in accordance with the law = sin (π + πt). Find the absolute velocity of the body 2 at t = 1 s. | 193 | 665 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-13 | longest | en | 0.783996 |
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