url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://cm-to.com/6.3-inch-to-cm/ | 1,718,674,679,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861746.4/warc/CC-MAIN-20240618011430-20240618041430-00018.warc.gz | 142,721,431 | 8,254 | # 6.3 Inch to Centimeter
Convert 6.3 (six) Inches to Centimeters (in to cm) with our conversion calculator.
6.3 Inches to Centimeters equals 16.0020 cm.
• Meter
• Kilometer
• Centimeter
• Millimeter
• Micrometer
• Nanometer
• Mile
• Yard
• Foot
• Inch
• Light Year
• Meter
• Kilometer
• Centimeter
• Millimeter
• Micrometer
• Nanometer
• Mile
• Yard
• Foot
• Inch
• Light Year
Convert 6.3 Inches to Centimeters (in to cm) with our conversion calculator.
6.3 Inches to Centimeters equals 16.0020 cm.
To convert 6.3 inches to centimeters, you use the conversion factor where 1 inch is equal to 2.54 centimeters. The calculation is straightforward: you simply multiply the number of inches you have (6.3) by the conversion factor (2.54 cm/inch).
So, the calculation would be 6.3 inches * 2.54 cm/inch = 16.002 cm. This calculation involves using the given value (6.3 inches), recognizing the relationship between inches and centimeters (where 1 inch equals to 2.54 centimeters), and applying basic multiplication to arrive at the converted value. This method offers a simple yet effective way to transform measurements from the imperial system to the metric system, allowing for easier comparison and application in a variety of contexts.
Items that are approximately 6.3 inches in length:
1. A large smartphone:
• Modern smartphones, especially the "Plus" or "Max" models, tend to have screen diagonals that approach or exceed 6.3 inches. This measurement typically does not include the phone's bezels.
2. A standard pencil at full length:
• Brand new, standard pencils are typically around 7.5 inches long but can be around 6.3 inches after some use.
3. A small ruler:
• While most rulers are 12 inches long, smaller versions intended for compact spaces or for carrying in a pencil case might measure around 6.3 inches.
4. A paperback book's height:
• Mass-market paperbacks vary in size, but many are around 6.3 inches tall, making them comfortable to hold and read.
5. A dollar bill:
• Although a US dollar bill is actually slightly shorter, at 6.14 inches long, it's quite close to this length.
6. A pair of eyeglasses:
• From one end of the frame to the other, a pair of eyeglasses can measure approximately 6.3 inches, depending on the style and brand.
7. A hand-held gaming console:
• Some portable gaming devices have widths or heights that approach 6.3 inches, making them just the right size for portability and playability. | 610 | 2,448 | {"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-2024-26 | latest | en | 0.840603 |
http://www.quantumstudy.com/practice-zone/numerical-kinematics-2/ | 1,585,440,626,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370493121.36/warc/CC-MAIN-20200328225036-20200329015036-00080.warc.gz | 280,170,864 | 9,432 | # Numerical Problems : Kinematics-II
#### LEVEL – II
1. Two particles are projected horizontally in opposite directions with v1 & v2 from the top of a pole. If the particles move perpendicular to each other just before striking the ground, find the height of the pole.
[Ans: v1v2 /2g ]
2. A cannon fires successively two shells with velocity vo = 250 m/s; the first at the angle α1 = 60° and the second at the angle α2 = 45° to the horizontal, the azimuth being the same. Neglecting the air drag, find the time interval between firings leading to the collision of the shells.
[Ans:10.7 sec]
3. An aeroplane flies in still air at a speed of 400 km/hr. Air is blowing from the south at a speed of 50 km/hr. The pilot wants to travel from point A to point B north-east of A and then to return.Calculate the direction he must steer
(a) on his onward journey (b) on his return journey.
If the distance AB is 1000 km then calculate the time taken in two journeys.
[Ans:(a) 390 56’ north of east, 2.3 hour (b) 390 56 ‘ west of south, 2.75 hour ]
4. Two particles move in a uniform gravitational field with an acceleration g. At the initial moment the particles were located at one point in space and moved with velocities v1 = 3.0 m/s and v2 = 4.0 m/s horizontally in opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutually perpendicular.
[Ans:2.5 m ]
5. A point moves rectilinearly with deceleration whose modulus depends on the velocity v of the particle as w = a √v , where ‘ a ‘ is a positive constant. At the initial moment the velocity of the point is equal to vo . What distance will it traverse before it stops? What time will it take to cover that distance?
6. Find the ratio between the normal and tangential acceleration of a point on the rim of a rotating wheel when at the moment when the vector of the total acceleration of this point forms an angle of 30° with the vector of the linear velocity.
[Ans: ar/at = 1/√3]
7. A fan rotates with a velocity corresponding to a frequency of 900 rev/min. When its motor is switched off, the fan uniformly slows down and performs 75 revolutions before it comes to a stop. How much time elapsed from the moment the fan was switched off to the moment it stopped ?
[Ans: 10 sec ]
8. A motor cyclist, going due east with a velocity of 10 m/s, finds that the wind is blowing directly from the north. When he doubles his speed, he finds that the wind is blowing from north east. In what direction and with what velocity is the wind blowin?.
[Ans: 10√2 m/s, from north west ]
9. The acceleration vector of a particle having initial speed Vo changes with distance as a = √x . Find the distance covered by the particle when its speed becomes twice the initial speed.
10. An observer in a train moving with a uniform velocity finds that a car moving parallel to the train has a speed of 10 km/h in the direction of motion of the train. An object falls from the car and the observer in the train notices that the car has moved on for one minute, turned back, and moved with a speed of 10 km/h and picked up the object two minutes after turning. Find
(a) the velocity of the train relative to the ground and
(b) the velocity of the car during its forward and reverse journeys.
Assume that the object comes to rest immediately on fall from the point of view of the observer on the ground.
[Ans:(a) 3.33 km/hr (b) 13 km/hr, 6.67 km/hr ]
<< Back Page Kinematics (Level) | 845 | 3,489 | {"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-2020-16 | latest | en | 0.905542 |
https://calculate.onl/perpetuity-present-value-calculator/ | 1,721,027,739,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514680.75/warc/CC-MAIN-20240715071424-20240715101424-00199.warc.gz | 144,962,547 | 23,540 | # Perpetuity Calculator: Present Value of Infinite Annuity + Growth Rate
A perpetuity is an infinite annuity, i.e. a never-ending series of payments. These cash flows can be even or subject to an even growth rate (source). You can use the present value of a perpetuity to determine the value of an endless series of cash flows, e.g. if you are evaluating assets such as real estate or companies. Read more about these uses in the dedicated section below.
## The Perpetuity Calculator – Calculate the Present Value of a Perpetuity (incl. Growth Rate)
Provide the requested values, i.e. the projected annuity, the discount rate as well as a growth rate (if applicable, fill in 0 otherwise). The calculator processes your input automatically and shows you the present value of a perpetuity.
## Input Data
In order to calculate the present value of a perpetuity, you will have to provide the following input parameters.
### Perpetuity or Infinite Annuity
The perpetuity or annuity can be negative or positive. However, if you are investing your money, you are most likely expecting a positive cash flow.
If you wish to calculate the present value of an infinite liability payment (e.g. from the perspective of a government that issues a perpetual bond).
### Discount Rate
Provide a discount rate for the calculation. This can be a market interest rate, your expected rate of return or – in case of company projects – the accounting interest rate or the weighted average cost of capital (WACC)
### Growth Rate
If you expect the annuity being subject to an even growth rate, enter the growth rate in this field. The growth rate is deducted from the discount rate which in turn leads to a higher present value.
## Calculating the Present Value of an Annual Perpetuity
The Formula for calculating the present value of an annual perpetuity is:
Present Value = Perpetuity / (Discount Rate – Growth Rate).
This is the formula implemented for the above calculator. Use the annual perpetuity as well as an annualized discount and growth rate to achieve valid results.
## Calculating the Present Value of Monthly or Quarterly Perpetuities
If you need to calculate the perpetuity based on monthly or quarterly infinite annuities, you can use the standard formula but insert monthly or quarterly values. The formulas read as follows:
Present Value of monthly perpetuity = Perpetuity_month / (DiscountRate_month – GrowthRate_month), and
Present Value of quarterly perpetuity = Perpetuity_quarterly / (DiscountRate_quarterly – GrowthRate_quarterly).
You can convert your annual discount and growth rate into monthly or quarterly compound rates using this formula:
Monthly rate = (1 + annual rate) ^ (1/12) – 1 and
Quarterly rate = (1 + quarterly rate) ^ (1/4) – 1.
## Uses of Perpetuity
Perpetuities can sometimes be found in financial markets, e.g. in the form of sovereign bonds with indefinite tenor. However, these instruments are not too common after all.
The present value of a perpetuity is most commonly used for the valuation of assets or investments. For real estate or land, for instance, it is not uncommon to calculate the market value by applying a multiplicator to the annual net returns. This multiplier is just another form of presentation of a perpetuity. In real estate markets, the multipliers used are typically in a range from 14 to 50 (depending on the region, type and condition of the object, interest rates, seller vs. buyer market etc.) which is equals the present value of a perpetuity using a discount rate between 2% and 7%.
Similar approaches are also popular in markets for websites, software, licenses and other rights of use.
Another typical use is the evaluation of companies or projects based on their cash flows. If a constant revenue or net profit is assumed, the company or the project can be evaluated using the present value of its infinite cash flows. More common though is using perpetuities in conjunction with the net present value. When calculating the net present value (NPV), the couple of cash flows are often subject to a detailed projection while long-term cash flows are hard to predict and prone to unforeseen developments. Therefore, the present value of a perpetuity can be used as residual value, representing the long-term cash flow and growth rate expectations.
## Final Thoughts
We hope that this calculator and article have helped you solve your perpetuity calculation. Take also a look at our other finance calculators that you might find useful as well. | 945 | 4,527 | {"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} | 3.3125 | 3 | CC-MAIN-2024-30 | latest | en | 0.901437 |
http://eclipseclp.org/doc/bips/lib/fd_global/sorted-3.html | 1,575,944,493,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540525781.64/warc/CC-MAIN-20191210013645-20191210041645-00171.warc.gz | 43,772,869 | 1,438 | [ library(fd_global) | Reference Manual | Alphabetic Index ]
# sorted(?List, ?Sorted, ?Positions)
Sorted is a sorted permutation (described by Positions) of List
List
List of domain variables or integers
Sorted
List of domain variables or integers
Positions
List of domain variables or integers
## Description
Declaratively: Sorted is a sorted permutation of List. Positions is a list whose elements range from 1 to N (where N is the length of the lists) indicating the position of each unsorted list element within the sorted list. The positions are all different. The three lists are constrained to have the same length.
Operationally: the elements in all three lists are constrained such that their domains are consistent with the declarative meaning.
Two of the three arguments can be uninstantiated or partial lists at call time.
Any input variables which do not already have finite bounds will be given default bounds of -10000000 to 10000000.
### Modes and Determinism
• sorted(+, ?, ?)
• sorted(?, +, ?)
• sorted(?, ?, +)
## Examples
``` ?- length(Xs,4), Xs::0..100, sorted(Xs,Ys,Ps), Xs = [8,20|_].
Xs = [8, 20, _346{[0..100]}, _359{[0..100]}]
Ys = [_445{[0..8]}, _427{[0..20]}, _537{[8..100]}, _635{[20..100]}]
Ps = [_882{[1..3]}, _895{[2..4]}, _908{[1..4]}, _921{[1..4]}]
``` | 365 | 1,301 | {"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} | 2.71875 | 3 | CC-MAIN-2019-51 | latest | en | 0.773652 |
http://docplayer.net/23860608-Q-price-elasticity-of-demand.html | 1,542,334,227,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039742968.18/warc/CC-MAIN-20181116004432-20181116030432-00164.warc.gz | 88,739,267 | 35,955 | # q PRICE ELASTICITY OF DEMAND:
Save this PDF as:
Size: px
Start display at page:
## Transcription
1 q PRICE ELASTICITY OF DEMAND: Definition of Price Elasticity of Demand m Price elasticity of demand is a measure of the effect of a change in price of a good/service in terms of quantity demanded. It measures the responsiveness of demand to a change in price. Definition: Earlier we discussed how changes in demand can occur as a result of a change in price. Looking at the price elasticity of demand involves looking at the degree to which a change in price can result in a change in demand. It is important that the term price elasticity of demand is understood properly, and should be precisely defined. The responsiveness of quantity demanded to price changes is the price elasticity of demand. Mathematically, it is expressed through the percentage change in quantity demanded, divided by the percentage change in price. If a firm raises its prices, revenue will be affected. However, whether total revenue rises or falls depends on the characteristics of the product and the attitudes of buyers. The word to describe the size of the change in price is elasticity. If the product is elastic, then the total revenue (price X quantity) will shift significantly when the price is changed. Just think of an elastic band - large change. However, if the product is inelastic, then the total revenue shift will be small following a change in price. Content: ELASTIC: Definition of Elastic m Elastic goods are those whereby a change in price will have a greater than proportional change in demand price changes have a significant influence on demand. Definition: A good has elastic demand when there is a strong response of the quantity demanded to a change in price. Elastic demand is sometimes written as relatively elastic demand. A good has relatively elastic demand when the increase in quantity demanded is proportionately greater than the fall in price. EXAMPLES: Luxury goods have an elastic demand. The price of airline tickets are considered elastic because price rises generally lead to more than Creative Classroom 151
2 proportionate decreases in demand. This means that an increase in price will result in considerably less of a fall in consumption of the good/ service. If the good being produced has an elastic demand then to increase revenue the business should lower price. This does not mean that profits will be higher. If the price of the good is increased the total revenue will fall. Diagram: For the INELASTIC: Definition of Inelastic m Inelastic goods are those whereby a change in price will have a less than proportional change in demand price changes do not have a considerable impact on demand. Definition: Conversely, a good is relatively inelastic if there is a less than proportionate change in the quantity demanded to a change in price. A good has inelastic demand if there is a weak response in demand to a change in price. If the good being produced has an inelastic demand then to increase revenue the business should increase the price. This means that profits will be higher. If the price of the good is decreased the total revenue will fall. Diagram: For the 152 Creative Classroom
3 EXAMPLES: Most necessities have an inelastic demand curve. Other examples of goods with inelastic demand include alcohol and cigarettes. These are both considered addictive (to differing extents), and thus any price change is unlikely to have a significant impact on the quantity demanded. This is because people who consume these products crave and demand the goods, and are willing to pay almost any reasonable price to do so. Hence, price increases and taxes (such as the recent alcopops and tobacco taxes) have a minimal impact on demand and increase the tax revenue for the government and higher revenue for firms. UNIT ELASTICITY: Definition of Unit elasticity m Unit elasticity refers to a particular impact of a change in price on demand. m Unit elastic goods are those whereby a change in price will have an equally proportional effect on demand. Definition: A good is unit elastic if there is a proportional change in demand to a change in price. For example, a price increase of 10% will mean demand will fall by 10%. If the price of the good is decreased or increased then the total revenue will remain the same. Unit/unitary elasticity is a theoretical point. Diagram: For the Creative Classroom 153
4 CALCULATIONS FOR ELASTICITY: There are three main methods used to calculate price elasticity, these are the total outlay, point, and arc methods. USING TOTAL OUTLAY METHOD: The total outlay method is the easiest way to calculate elasticity. Total outlay, or total expenditure, is calculated by multiplying the price by the quantity demanded at that price and then comparing revenues at different price levels. Relatively inelastic demand occurs when total outlay moves in the same direction as a price change. (Price up, TR up: Price down, TR down.) Relatively elastic demand occurs when total outlay moves the opposite direction to the price change. (Price up, TR down: Price down, TR up.) If total outlay remains the same despite a price change, then the good is unit elastic. (Price up, TR the same: Price down, TR the same.) Tip: Only the total revenue is identified in the syllabus. Price Quantity Total outlay/ expenditure \$20 8 \$160 - Elasticity \$30 6 \$180 Inelastic \$40 5 \$200 Inelastic \$50 4 \$200 Unit elasticity \$60 3 \$180 Elastic Example: A story to remember a specfic issue: ELASTICITY Meet the Price family: Story: there are three brothers, their surnames are Price (standing for prices), One brother is called Indiana Price The second brother is called Edward Price The second brother is called Unicorn Price (a half brother) There is a dance with girls, they symbolise, total price revenue. Meaning: Price standing up or down = price changes - up or down. Indiana Price = Inelastic demand Edward Price = Elastic demand Unicorn Price = Unit demand Girls = total revenue (price x quantity) 154 Creative Classroom
5 Scene 1: Inelastic demand Indiana Price goes to the dance and he stands up. then girls stand up to talk to Indiana. Indiana then sits down, the girls sit down. (total revenue down). Characteristics of Indiana, he is very small guy. Indiana is a chemist. Story: Meaning: Remembering the issues of inelastic demand Indiana Price stands up = The price of a good rises, then the Girls stand up = total revenue (price x quantity) Indiana Price sits down Girls sit down = The price of a good falls, then the = Total revenue falls He is a small guy = The figure for elasticity - less than 1 He is a chemist = Goods that have an inelastic demand are necessities. Indiana, you are a short guy, and all the girls love to be with you. Can we sit down now? Creative Classroom 155
6 Scene 2: Elastic demand Indiana goes home to tell his brother Edward that he should go to the dance. Edward Price then goes to the dance and stands up, sadly, the girls sit down. Edward is a big guy. Edward loves luxury items- he has sports cars and gold chains. Meaning: Remembering the issues of elastic demand Edward Price stands up = The price of a good rises, then the Girls sits down = total revenue falls Edward sits down Girls stand up = The price of a good falls, then the = Total revenue rises. He is a big guy = The figure for elasticity- greater than 1. He loves luxury items = Goods that have an elastic demand are luxuries. Why are the girls sitting down? I am on the dance floor. Eddie, you are a big guy, but the girls would prefer not to be with you. Please sit down so we can stand up. BIG EDDIE IS A LUXURY 156 Creative Classroom
7 Scene 2: Unit elasticity Edward goes home really sad, he tells his half-brother the unicorn that he should go to the dance. Unicorn Price enters the dance room, all the girls are petrified by the pet unicorn. Unicorn Price can stands up or fall to the ground, the girls do not move (Price up or price down, total revenue will remain the same). Unicorn Price yells out that he is Number 1. Tip: Only the total revenue is identified in the syllabus. Meaning: Remembering the issues of unit elasticity demand Unit Price stands up = The price of a good rises (demand is unit elasticity), then the Girls are petrified = total revenue stays the same Unit Price sits down = The price of a good falls, then Girls are petrified = Total revenue stays the same He is Number 1 = The figure for elasticity is equal to 1 The girls don t move even when I stand up or sit down. Girls, don t move, the unicorn is here! Creative Classroom 157
8 g Information overload: Additional details to enhance your extended response answers. USING POINT METHOD: The point method, specifically the midpoint method, uses three rules to determine elasticity. If elasticity of demand is greater than 1, then demand is price elastic. If elasticity is equal to 1, then demand is unit elastic. If elasticity is less than 1, then demand is price inelastic. Value of Elasticity of Demand Elasticity > 1 Elastic 1 Unit Elastic < 1 Inelastic The value of elasticity of demand is calculated by using the following formula: Elasticity = Q /Q P /P Elasticity = (Change in Quantity demanded Quantity demanded) All divided by (Change in Price Price) EXAMPLE: The price of chocolate rose from \$3 a block to \$5 a block, Consumption fell from 10,000 blocks to 5,000. The price elasticity of chocolate is: Quantity demanded = 10,000; Change in quantity demanded = 5,000; Price = \$3; Change in price = \$2 Using the formula, and substituting the above figures: Elasticity = (5,000 10,000) (2 3) = Tip: u Only the total revenue is identified in the syllabus. u Tip: Quantity is always on the top of the equation. Story: Remember Queensland is geographically on the top. Q Queensland is always on the top! As this value is less than 1, = 0.75 In this example, chocolate is price inelastic. Remember, Indiana Price is a small guy. g Information overload! If the answer was greater than 1, chocolate would be price elastic. Remember, Edward Price is a big guy. If the answer was equal to 1, chocolate would be price elastic. Remember, Edward Price is a big guy. Ignore this section if you are still coming to grips with the basics. 158 Creative Classroom
9 g Information overload: Additional details to enhance your extended response answers. USING ARC METHOD: Another method of calculating price elasticity is the arc method. The arc method follows the same rules as the point method Elasticity of demand greater than one is price elastic; Elasticity of demand less than one is price inelastic and Elasticity of demand is equal to 1 it is unit elastic. The arc method is more accurate than the point method. The arc method makes use of the following formula: Elasticity = [(Q2 Q1) (Q averaged)] ALL [(P2 P1) (averaged)] Q1 Q2 Q ave P1 P2 P ave = Initial Quantity Demanded = New Quantity Demanded = Average Quantity Demanded = Initial Price = New Price = Average Price EXAMPLE: The price of petrol rose from \$1 a litre to \$2 a litre and Consumption fell from 100,000 litres to 80,000 litres. Quantity figures: (The figures on the top of the equation) Change in Quantity = 20,000 Q1 = 100,000 Q2 = 80,000 Average Quantity Demanded = 90,000 Price figures: (The figures on the bottom of the equation) Change in Price = \$1 P1 = \$1 P2 = \$2 Average Price = \$1.50 Tip: u Only the total revenue is identified in the syllabus. u Tip: Quantity is always on the top of the equation. Story: Remember Queensland is geographically on the top. Q Queensland is always on the top! Using the formula, and substituting the above figures: 20,000 90,000 ALL Divided by ) = -1/3 = 1/3 (absolute values) As this value is less than 1, it can be seen that petrol is price inelastic. Remember, Indiana Price is a small guy. Creative Classroom 159
10 E EXTREME ELASTICITY POINTS: PERFECT ELASTICITY: A horizontal demand curve indicates a perfectly elastic demand. Consumers demand an endless quantity at a certain price, and nothing above this price. This is only theoretical, and very unlikely to occur in the market place. g Information overload! Ignore this section if you are still coming to grips with the basics. PERFECT INELASTICITY: A vertical demand curve indicates a perfectly inelastic demand, where consumers are willing to purchase the product at any price. Diagram: For the Creative approach: ELASTICITY: Key exam points to memorise: There are two extremes with elasticity. One is a vertical line showing perfectly inelasticity (for demand or supply), the other is a horizontal line which represents something that is perfectly elastic. Note: the word perfectly means vertical or horizontal. Under exam conditions you may get them confused. Perfectly inelastic: You must remember this line is vertical, not horizontal or downward sloping. Just remember the I in the word perfectly Inelastic Remember, when drawing perfectly inelasticity curve It looks like the capital letter I! I Perfectly inelastic: Remember, when drawing perfectly elasticity curve It looks like the capital E having a sleep. The word perfectly in front of inelastic or elastic helps you remember it is an extreme situation. Story: 160 Creative Classroom
13 OTHER EXAMPLES OF ELASTICITY: Elasticity is not limited to demand and supply. Other types of elasticity exist, namely cross-elasticity and income elasticity. Cross-elasticity refers to what are known as related goods (substitute and complementary goods), and the effect of price changes for these products. Income elasticity, however, is refers to the responsiveness of demand when consumer income changes. Both are linked to the demand curve. Q Queensland is always on the top! 1A. INCOME ELASTICITY OF DEMAND - FOR A NORMAL GOOD: Generally, demand for most goods increases (normal good) as consumer income rises. However, the percentage increase in demand is determined by income elasticity. For example, if income rises by 10%, it is highly unlikely that demand for water will rise by more than 10%. It is much more probable that demand for a product such as DVDs will rise by more than 10%. When a rise in income causes a greater percentage rise in demand, then the good is income elastic. However, if a rise in income causes a smaller percentage rise in demand, then the good is income inelastic. For example, if income rose by 10%, but demand for bottled water rose by 1%, then bottled water has income inelastic. The diagram shows demand for two goods. D1 is the original demand for both goods (assume income has increased by 10%). g Information overload! Ignore this section if you are still coming to grips with the basics. Diagram: For the The good represented by D3: It can be seen that demand has increased by more than D2. This indicates that D3 is more likely to be income elastic (large change in demand) compared with the good represented by D2. If D3 is income elastic the demand will increase by more than 10%. The good represented by D2: It can be seen that demand has increased by less than D3. This indicates that D2 is more likely to be income inelastic (small change in demand) compared with the good represented by D3. If D2 is income inelastic the demand will increase by less than 10%. Creative Classroom 163
14 A Creative Story: REMEMERING ISSUE ABOUT INCOME ELASTICITY: When I obtain an increase in income (as if), I will increase my demand for the goods. Look at the following three examples, all of which are based on a ten percent increase in income (as if that s going to happen!) Example 1, salt: It is possible that I will increase my demand for salt, but it is unlikely to be greater than a 10% increase. Therefore my income demand for salt is inelastic. (For Inelastic changes, think Indiana means small change ). The demand curve would move from D1 to D2 Example 2. Movie Tickets: If I receive a 10% increase in income I am likely to increase my expenditure on movie tickets by more than 10%. Note a larger change in demand has occurred as a result of a change in income. Movie tickets are income elastic. (For elastic changes, think Eddie (elastic) is a BIG guy ) BIG EDDIE IS A LUXURY The demand curve would move from D1 to D3. 1B. INCOME ELASTICITY - FOR AN INFERIOR GOOD: As income rises, the demand for a few goods decreases. The consumer views some goods as poor in quality. The consumer would prefer a higher quality good but cannot afford a superior good. Once income rises, the consumer buys the better product and the demand for the inferior good falls. Diagram: For the A Creative Story: REMEMERING ISSUE ABOUT INFERIOR GOODS: Example 3. I am a struggling teacher, so I am buying soup bones to feed my family. If I receive a 10% increase in income then my demand for these bones will decrease because soup bones are an inferior good. I will decrease the demand for soup bones and switch to steak. Steak is a normal good higher increase will cause an increase in demand. The diagram for the inferior good shows that the higher income will cause a decrease in demand, from D1 to D Creative Classroom
15 2. CROSS-ELASTICITY OF DEMAND: (CROSS-ELASTICITY): g Information overload: Additional details to enhance your extended response answers. Cross-elasticity refers to the responsiveness of one good in regards to a change in the price of a different, albeit related, product. Substitute and complement goods are included in this analysis, as these are considered related goods. The following formula is used to calculate cross-elasticity. If the resulting figure is positive, the good is a substitute. If it is negative, then the product is a complementary good. Cross-elasticity of Demand = Percentage change in Quantity demanded for good A Divided by Percentage change in Price of good B. g Information overload! u Tip: Quantity is always on the top of the equation. Story: Remember Queensland is geographically on the top. SUBSTITUTE GOODS: Substitute goods are those which are interchangeable, have the same (or similar) purpose, and can be consumed in place of each other. Examples include butter to margarine and tea to coffee. Generally, if the price of one substitute rises, then the demand for the other good will rise. Applying the example of butter and margarine, this means that if the price of butter rises, then the demand for margarine will also rise. This is shown by the diagram to the right of the text, the demand for margarine will rise because the price of butter has risen. Further, if the price of one substitute falls, then demand for the other good will fall. Again, using the butter and margarine example, if the price of butter falls, then the demand for margarine will decrease. Q Queensland is always on the top! Diagram: For the COMPLEMENTARY GOODS: Complementary goods are those which are consumed together these goods are not used in place of each other. Examples include petrol and cars, and washing machines and washing powder. Generally, if the price for one complement rises, then the demand for both goods falls. For example, if the price of petrol rose, then the demand for large cars would Content: Creative Classroom 165
16 fall. This is shown by the diagram below. If the price of petrol is increased, then the demand for large cars will fall. Conversely, if the price of one complement falls, then the demand for both goods will theoretically rise. The key concept regarding all complementary goods is the existence of a relationship between the goods. For example, it is obvious that cars and petrol have a relationship, yet milk and petrol do not have such a relationship. Diagram: For the A Story To Remember A Specfic Issue:s Complementary/ Substitutes 1. Substitute goods: STORY: When the substitute player (Michael Jordan) comes into the basketball game, people hold up positive signs. Meaning: When the price of Good B increases, then the demand for Good increases (a positive sign). N.B - The maths behind this concept: A positive dividing into a positive equals a positive sign. When the price of Good B is lowered, then the demand for Good A will decrease (a positive sign). N.B - The maths behind this concept: A negative dividing into a negative equals a positive sign. Content: 2. Complementary goods: STORY: Two friends are walking down the street, paying each other compliments but crossing their arms horizontally. The two arms are showing a negative sign. Meaning: If the price of Good B goes up, then the demand for Good A will decrease (positive dividing into a negative = negative sign). N.B - The maths behind this concept: A negative dividing into a positive = negative sign. If the price of Good B goes down, then the demand for Good A will increase (negative dividing into a positive = negative sign). N.B - The maths behind this concept: A negative dividing into a positive = negative sign. HSC Importance for the exams Content Markets- Demand No overlap Just know how to draw the Demand and Supply curves Rating 9/10 Short Answer questions Multiple Choice questions Extended Response questions 166 Creative Classroom
17 q PRICE ELASTICITY OF SUPPLY: CONCEPT OF PRICE ELASTICITY OF SUPPLY: Earlier, we discussed how changes in price impact on the quantity demanded. This involved looking at the degree to which a change in price can result in a change in demand. The same set of points relate to the elasticity of supply. The price elasticity of supply involves looking at the degree by which a change in price can result in a change in the quantity supplied. It is important that price elasticity of supply is understood properly. The responsiveness of quantity supply to price changes is known as the price elasticity of supply (PES). Mathematically, it is expressed through the percentage change in quantity supplied divided by the percentage change in price. The value of elasticity of supply is calculated by using the following formula: Elasticity = Q /Q P /P Elasticity = (Change in Quantity supplied Quantity supplied) All divided by (Change in Price Price) ELASTIC: Definition of Elastic Supply m Elastic goods are those goods for which a change in price will have a greater than proportional change in supplies, and for which price changes have a significant influence on the quantity of supply. Q Queensland is always on the top! Definition: If the supply is elastic (relatively elastic), then the quantity supplied will shift significantly when the price is changed. Just think of the elastic band story we looked at for the elasticity of supply- large change. Creative Classroom 167
18 INELASTIC: Definition of Inelastic Supply m Inelastic goods are those whereby a change in price will have a less than proportional change in supply price changes do not have a considerable impact on the quantity supplied. If the product is inelastic (relatively inelastic), then the shift in the quantity supplied will be small following a change in price. Diagram: EXTREME ELASTICITY POINTS: PERFECTLY ELASTIC: At one end of the spectrum, perfectly elastic supply is where an unlimited quantity of goods can be produced, at the current price. This is a theoretical point and not likely to exist in reality. The supply curve in this example is a horizontal line. Content: PERFECTLY INELASTIC: At the other end of the spectrum perfectly inelastic supply, which is where supply does not change regardless of the price offered. The supply curve is a vertical line. The price of this good is determined by the level of demand. Example: A piece of art from one on the great masters, such as a piece by the post-impressionist artist Vincent van Gogh. 168 Creative Classroom
19 FACTORS AFFECTING ELASTICITY OF SUPPLY: There are three main issues impacting on the elasticity of supply. These are: 1. Time / production period 2. Stock Levels 3. Excess Capacity Content: TIME PERIOD: The length of time after a price change impacts significantly on price elasticity of supply. A price rise will cause: 1. Immediately after an increase in price the quantity offered for sale will not change. Price elasticity of supply (PES) will be essentially perfectly inelastic (no increase in the supply of the goods). This is because suppliers are unable to increase supply immediately. This time period is known as the market period. 2. In the short term, suppliers will increase the resources allocated to their existing production capital, in the form of additional workers and raw material, causing a rise in quantity supplied. The producers are using the plant/equipment more efficiently. This time period is known as the short run. 2. In the long term suppliers will add to their existing production capital by increasing the size and number of factories, production lines, and other fixed methods of production. As these processes increase, the ability of suppliers to increase significantly the quantity supplied in response to price increases. Price elasticity of supply will become increasingly elastic. This time period is known as the long run. EXCESS (SPARE) CAPACITY: Excess capacity is a sitution where the resources used by a firm are not being used to the greatest level of efficiency. If this is the case, price elasticity of supply for that firm will be relatively elastic, as any increase in price can be met with increased production by using those resources more efficiently. LEVEL OF INVENTORIES: Some firms have the ability to store excess stock/inventory. The ability to hold this stock significantly affects the price elasticity of supply (PES) for that firm. For example, if the firm has a significant ability to hold over stock, the firm can significantly increase the amount of stock they offer for sale if prices increases. This represents a greatly elastic price elasticity of supply (PES). However, if a firm is unable to hold over stock, they cannot increase the Creative Classroom 169
20 quantity for sale if the price increases. This represents a greatly inelastic price elasticity of supply (PES). It should be noted that the type of good greatly affects storage for example, cars are often significantly dated, and its model and year greatly affects its selling price, thus firms aim to maintain low stock levels. On the other hand, housing materials do not significantly change, and can be stored for significant lengths of time easily. A STORY -THE FACTORS CAUSING AN ELASTIC SUPPLY: STORY: The elastic band business - Factors causing an elastic supply: I am looking inside a factory that produces elastic bands. There is a long clock (grandfather clock) and its going tick elastic tick. There are workers asleep (idle capacity) and the building is filled to the top with elastic bands (high level of stocks). 1. Elastic Band Company = Elasticity of supply. 2. Long clocks = Long time period. Tick elastic tick = Makes the same point again, that the longer the time period, the more elastic the supply. 3. Workers asleep = Idle or excess capacity including labour and machinery. 4. Room filled with elastic bands = High levels of stocks (inventories). Story: q MARKET STRUCTURES: Overview: There are four main types of market structures. They vary in the degree of market power each firm has, and consequently the level of competition in that market. PURE COMPETITION (PERFECT COMPETITION): NUMBER OF SELLERS: Perfect Competition is a market structure where there are so many firms, and they are all so small, that they are unable to affect the price of the goods or services they provide. In effect, they are price takers, as they would not be able to sell any product above the market price, and must sell all the products at the market price. Going below the market price would simply sacrifice profit needlessly. While perfect competition is a good academic model, it is unlikely to occur in real life, as in almost all markets, firms have some level of market power. Content: 170 Creative Classroom
21 PRODUCT (HOMOGENEOUS / DIFFERENTIATED): In perfect competition, all of the products sold in the market are the same. Buyers and sellers of the product know that the products sold by all the different firms are the same, and know that the price is the same. In perfect competition, the market provides all the competition for the firms. Firms cannot differentiate their products, as they are known to be the same, and they cannot change the price of their goods, as they are price takers. BARRIERS TO ENTRY: There are no barriers to entry. MONOPOLY: NUMBER OF SELLERS: A monopoly market structure is the market structure where there is only one firm selling the product in the market. Therefore, there is no competition in the market at all, and the firm enjoys complete market power. PRODUCT (HOMOGENEOUS / DIFFERENTIATED): To ensure that the firm enjoys this monopoly power, the product being sold must have no close substitutes. Content: BARRIERS TO ENTRY: There are significant barriers to entry into the market, which effectively means that no potential competitors are able to enter the market. REASONS FOR BARRIERS TO ENTRY: 1. In many modern economies, there is a belief that some areas of the economy should not be run for profit, but instead run by the government or government-run institutions. The government legislates that only one producer exists. A good example of this is Australia Post, which is the only company licensed to carry mail in Australia. The industry is not driven by competition and the profit motive, but instead continues to offer good quality of service in this important area. 2. The firm might hold a patent for the production of the good. A good example of this is the pharmaceutical industry. New pharmaceutical medications can take decades, and many hundreds of millions of dollars, to develop, without any guarantee of success. In order to make investments in such a risky venture attractive, the government guarantees that the company will be the only vendor of that product for an extended period of time, by allowing a company to patent their drug. This means that no other company is allowed to produce that drug for a length of time. Creative Classroom 171
22 The patent effectively creating a barrier to entry for other companies, creating a monopoly for the production of that drug. SUPER PROFITS IN THE LONG TERM: As the firm enjoys monopoly power, the firm also has complete market power. This means that the firm is a price setter, or can set the price of the goods at the profit-maximizing level. This means that the firm is able to make abnormal profits. Normally, in a market, if a firm is making abnormal profits in the short term, more firms will enter the market, until firms only make normal profits. However, due to the significant barriers to entry which exist in a monopoly market structure, it is impossible for other firms to enter into the marketplace. The monopolist is able to make abnormal profits in the long term. Oligopoly: NUMBER OF SELLERS: An oligopoly is where there are only a few large firms in the market. An oligopolistic market structure, or one where the firms are in an oligopoly, is a type of imperfect competition. This means that there is some competition, unlike in a monopoly, but there is not as much competition as appears in Perfect Competition. In an oligopolistic market, the few large firms sell a differentiated products. Firms in an oligopoly usually require significant start up costs in order to compete in the market. In this market, they each control a significant market share. A good example of an Australian oligopoly is the supermarket industry, which is dominated by Woolworths and Coles. Content: PRODUCT (HOMOGENEOUS / DIFFERENTIATED): The product is differentiated. There is usually an unspoken agreement in oligopolistic markets to compete on a product basis, rather than price. For this reason, oligopolies usually produce significant amounts of advertising, in an attempt to increase market share by increasing brand loyalty. BARRIERS TO ENTRY: The reasons there are only a few firms in the market due to significant barriers to entry: As there are few firms in an oligopolistic market, each firm closely monitors the behaviour of the other firms in the market. 172 Creative Classroom
23 As each firm has significant market power, if one firm decided to undercut its rivals by decreasing its prices, it could start a price war that would significantly lower the profits of the entire market. Oligopolies are usually tolerated by governments, as long as the firms do not abuse their market power. For this reason, any new mergers in oligopoly markets are usually not allowed by the competition watchdog. Any attempt at collusion, such as a synchronised increase in prices, is closely observed by the Australian Competition and Consumer Commission. Monopolistic Competition: NUMBER OF SELLERS: Monopolistic competition is a market structure where there are many firms that all have a small level of market power. A Monopolistic Competition market structure is the other type of imperfect competition. This means that there is some competition, unlike in a monopoly, but there is not as much competition as appears in perfect competition (see later). Firms in monopolistic competition are usually limited in the amount they can expand. A good example of a monopolistic market is the restaurant industry. This means that monopolistic competition usually needs little regulation for it to remain competitive, and as such is usually encouraged by the government. Content: PRODUCT (HOMOGENEOUS / DIFFERENTIATED): While the firms sell similar products, the products are not identical; the products are differentiated. Firms will use significant levels of product differentiation, or branding, to separate their product from other products. Having a degree of separation promotes brand loyalty, which increases the market power of the firm. Firms in monopolistic competition concentrate on product differentiation and brand loyalty. As they must, to a great extent, follow the market price level, their best way to increase profit is to increase the amount of people purchasing their product. As they are able to differentiate their product, they can create a form of brand loyalty which increases their level of sales. This product differentiation, usually based on advertising, becomes one of the key factors of the businesses success. BARRIERS TO ENTRY: There are no barriers to entry. Creative Classroom 173
24 SAMPLE ESSAY q SAMPLE ESSAY: Discuss the workings of the market, including concepts of elasticity, and how governments intervene. In discussing the market economy, the economist must look at both the strengths and weaknesses of the market and its processes, as well the ways in which governments can intervene. The market system involves the interaction of supply and demand to determine price. The responsiveness of quantity demanded and supplied to price changes are, respectively, the price elasticity of demand and price elasticity of supply. Governments intervene in the market through price floors and ceilings, quantity intervention, as well as subsidies and grants. The economic problem arises because of scarcity and finite resources. That is, we do not possess enough resources to satisfy our unlimited wants. The economic problem has generated significant debate amongst economists as to what is the best solution. Solving the economic problem involves acknowledging that finite economic resources must be used efficiently. Different economic models, such as capitalism and socialism, present differing ways to address the economic problem. A solution to the economic problem can lie with producing as many goods and services as possible, and the goods and services needed the most. A laissez faire free market allows the forces of supply and demand to solve the economic problem, ensuring greater allocative efficiency as resources are directed towards highly valued goods and services. A centrally planned economy solves the economic problem through allowing the government to control and prioritise the production of certain goods and services. One of the important components of the price mechanism is demand, the specific amount of a good or service that households are prepared and able to pay for at a specific time. Individual demand is concerned with the demand of each individual person. Market demand is concerned with the collective demand of all consumers, and this is what we are going to look at. Demand interacts with supply, which will be discussed later, to determine the price of a good or service. A demand schedule refers to a table that illustrates the demand for a good or service over a price range, often in constant increments. The law of demand states that an increase in the price of a good or service will result in a decrease in demand, and vice versa. An increase in the price of a good or service means that consumers will purchase less of the product because the product is more expensive compared to alternatives and they cannot afford to purchase as much of the product. Giffen goods represent a challenge to the law of demand, as demand increases when price increases. This is often because higher priced goods are seen as indicative of wealth FOCUS: Introducing the answer. FOCUS: Simple analysis. FOCUS: Key definition. 174 Creative Classroom
25 and prestige, meaning that people want to purchase the good. Price factors play an important role in influencing demand. Price factors only deal with the price of the good or service itself. If the price of a need increases, there will likely not be a significant decrease in demand because such products are required for daily life. However, more luxurious goods will see a decrease in demand when price increases. Ceteris paribus, changes in the price of a good or service, can result in a change in the quantity demanded, most often in the opposing direction of the price change. Only changes in the price of the good or service itself can lead to a contraction or expansion in demand (that is, movements along the demand curve). Several non-price factors can also lead to movements of the demand curve. Social movements, technological developments, and trends can lead to some goods being seen as more fashionable than others, leading to an increase in demand. If there is a rise in level of incomes, perhaps due to economic growth, then there will be a subsequent increase in demand, because consumers will be more willing and able to purchase certain goods and services. If the price of an alternative good or service decreases, and the alternative product is considered a close substitute, then the demand for the alternative product will likely increase whilst the demand for the original good will decrease. If consumers expect that prices will increase in the future, then consumers will increase their current demand. If there is a rise in the proportion of young people, then there will an increase in demand for youth-related products. Similarly, a rise in the proportion of old people will see an increased demand for aged care. The quantity of products demanded will increase if the population increases. The other important component of the price mechanism is supply; the specific amount of a good or service that firms in a specific industry are prepared and able to sell at various price levels at a specific time. Individual supply is concerned with the supply of each individual firm. Market supply is concerned with the cumulative supply of all firms. Supply interacts with demand, which was discussed earlier, to determine the price of a good or service. A supply schedule refers to a table that illustrates the supply of a good or service over a price range, often in constant increments. The following discussion rests under the assumption that there is pure competition and no government intervention in the market. This means that no firm in the market, or the government, has the power to determine prices. The price mechanism involves the interaction of supply and demand to determine the market price of a particular good or service and the quantity FOCUS: Simple examples. FOCUS: Simple analysis. FOCUS: Simple examples. SAMPLE ESSAY Creative Classroom 175
26 SAMPLE ESSAY of this good or service that is produced. The concept of market equilibrium involves looking at the price mechanism, and occurs when the quantity demanded and quantity supplied of a particular product is equal. As a result, the market clears as there is no excess supply or demand, and there is no tendency for price or quantity change. This concept is similar to the price elasticity of demand. Looking at the price elasticity of demand involves looking at the degree to which a change in price can result in a change in supply. A good has relatively elastic supply when the rise in quantity supplied is proportionately greater than the increase in price. Conversely, a good is relatively inelastic if there is a less than proportionate change in quantity supplied to a change in price. A good is unit elastic if there is a proportional change in supply to a change in price. Looking at the price elasticity of demand involves looking at the degree to which a change in price can result in a change in demand. It is important that price elasticity of demand is understood properly, and should be precisely defined. The responsiveness of quantity demanded to price changes is the price elasticity of demand. Mathematically, it is expressed through the percentage change in quantity demanded divided by the percentage change in price. A good has elastic demand when there is a strong response to a change in price. A good has relatively elastic demand when the increase in quantity demanded is proportionately greater than the fall in price. Conversely, a Key good is relatively inelastic if there is a less than proportionate change in quantity demanded to a change in price. A good is unit elastic if there is a proportional change in demand to a change in price. A good has inelastic demand if there is a weak response in demand to a change in price. Economists have debated endlessly about the level of government intervention that should be allowed in an economy. Often the prices of goods and services can be too high or low, and the quantity produced can be too little or too much. This revolves around how to address the problem of market failure, as the market by itself can lead to undesirable outcomes. Market failure refers to the situation in which the free market and price mechanism only considers private costs and advantages of production, without due consideration of the social costs such as environmental destruction and health problems. For example, the market may fail to take into account the damage caused by carbon emissions, which can worsen the problem of climate change. The market may also fail to take into account factors such as noise pollution caused by aeroplanes and industry. Market failure is a reason for government intervention, and this is why the Australian government intervenes in the market. Governments can intervene FOCUS: Simple analysis. FOCUS: Key definition. FOCUS: Simple examples. 176 Creative Classroom
27 in both price and quantity factors. There can be situations where the market price for a good or service is too high or too low. For example, the cost of public transport or solar panels may be too high, whilst the cost of polluting products may be too low. Consequently, the government may intervene in the price mechanism to address over pricing or under pricing. If a good or service is too expensive, then the government can impose a price ceiling, which is a maximum price that can be charged for a particular good or service. Conversely, if a good or service is too cheap, then the government can apply a price floor, which imposes a minimum price limitation upon a good or service. There are problems associated with the disequilibrium in such price interventions. A price ceiling can lead to under-production of the good, whereas a price floor can lead to over-production of the good. Therefore, price intervention is not a flawless way of addressing market failure. Governments also resort to quantity intervention as a way of addressing market failure. The quantity of certain products may be too high or low because of market failure, and there may be a limited consideration of social costs, such as environmental destruction. The unintended social costs and benefits of production are called externalities, and are not accounted for in the price mechanism. Governments are concerned with negative externalities, such as pollution. Governments intervene through taxes on firms and legislation to decrease the quantity produced of such goods, or to encourage more beneficial, less harmful forms of production. On the other hand, goods and services with positive externalities are often not appreciated fully by the public in terms of social benefits. Examples include parks, the arts and stage productions, as well as the defence force. Such goods are called merit goods and public goods. Merit goods are goods that are not produced enough by firms because consumers do not sufficiently value these goods, and therefore they are largely unprofitable. Public goods are different. Public goods are produced entirely by the government because firms cannot restrict the benefits of such goods to those who have paid for the good. In these cases, the government intervenes, often in the form of subsidies and the direct provision of such goods. As can be seen, the market is a complex system that involves issues of demand, supply, elasticity and government intervention. Imperfections in the market warrant intervention from the government, and appropriate measures need to be taken by decision makers through legislation and government policies. FOCUS: Key definition. FOCUS: Simple analysis. FOCUS: Simple examples. SAMPLE ESSAY Creative Classroom 177
### AS Economics Unit 1: Markets and Market Failure Syllabus, Key Terms & Charts
AS Economics Unit 1: Markets and Market Failure Syllabus, Key Terms & Charts 10.1 The Economic Problem The Nature and Purpose of Economic Activity The central purpose of economic activity is the production
### Elasticity. This will always be a negative number; we take the absolute value. Larger numbers (in absolute value) mean the demand is more elastic.
Elasticity Elasticity is the term economists use to measure the responsiveness of one variable to changes in another. We can measure the responsiveness of quantity demanded to changes in price, income,
### Introduction to microeconomics
RELEVANT TO ACCA QUALIFICATION PAPER F1 / FOUNDATIONS IN ACCOUNTANCY PAPER FAB Introduction to microeconomics The new Paper F1/FAB, Accountant in Business carried over many subjects from its Paper F1 predecessor,
### Price Elasticity of Demand and Supply
Supporting Teachers: Inspiring Students Economics Revision Focus: 2004 AS Economics Elasticity of Demand and Supply tutor2u (www.tutor2u.net) is the leading free online resource for Economics, Business
### The price mechanism. Chapter. Syllabus Content. B - The market system and the competitive process 40 %
Chapter 2 The price mechanism Syllabus Content B - The market system and the competitive process 40 % The price mechanism: the demand and supply model and its applications. Page 1 2.1 A market Buyers and
### Government Intervention
Government Intervention Deadweight Loss à the loss in economic surplus due to the market being prevented from reaching the equilibrium price and quantity where marginal benefit (MB) equals marginal cost
### Chapter 3 Demand and supply
Chapter 3 emand and supply emand is the amount of a product that consumers are willing and able to purchase at any given price. It is assumed that this is effective demand, i.e. it is backed by money and
### MARKET DEMAND &SUPPLY DEMAND
MARKET Market is a place where consumers meet sellers and the trading takes place. The consumers buy products at certain price, so money is exchanged for goods and services. We distinguish types of market
### Microeconomics Instructor Miller Practice Problems Monopolistic Competition
Microeconomics Instructor Miller Practice Problems Monopolistic Competition 1. A monopolistically competitive market is described as one in which there are A) a few firms producing an identical product.
### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MBA 640, Survey of Microeconomics Fall 2006, Final Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The "law of demand" states that, other
### Teaching- Learning Material
STATE COUNCIL OF EDUCATIONAL RESEARCH &TRAINING VARUN MARG, DEFENCE COLONY, NEW DELHI Teaching- Learning Material (On the basis of weekly syllabus for the Month of July 2011) For Class XII PGT (Economics)
### BASIC MARKET ELEMENTS. Supply Demand Price Competition
BASIC MARKET ELEMENTS Supply Demand Price Competition Supply Supply is the quantity of goods that firms are willing to produce and sale with respect to the market price when all other conditions (like
### CHAPTER 3 ELASTICITY (DEMAND AND SUPPLY)
CHAPTER 3 ELASTICITY (DEMAND AND SUPPLY) Elasticity Elasticity is a measure of responsiveness or sensitivity of a dependant variable to a percentage change in an independent variable. Elasticity is a measure
### CCEA GCE Economics Diagram Bank AS 1: Markets and Prices
CCEA GCE Economics iagram Bank AS 1: Markets and s Contents Page Introduction 1 iagram 1: The Production Possibility Frontier (1) 2 iagram 2: The Production Possibility Frontier (2) 3 iagram 3: Movements
### Chapter 7 Monopoly, Oligopoly and Strategy
Chapter 7 Monopoly, Oligopoly and Strategy After reading Chapter 7, MONOPOLY, OLIGOPOLY AND STRATEGY, you should be able to: Define the characteristics of Monopoly and Oligopoly, and explain why the are
### Chapter 4: Elasticity. McTaggart, Findlay, Parkin: Microeconomics 2007 Pearson Education Australia
Chapter 4: Elasticity Objectives After studying this chapter, you will be able to: Define, calculate, and explain the factors that influence the price elasticity of demand Define, calculate, and explain
### Perfect Competition. Perfect competition a pure market
We now move on to study the economics of different market structures. The spectrum of competition ranges from perfectly competitive markets where there are many sellers who are price takers to a pure monopoly
### 1.2 Elasticity: Price elasticity of demand (PED)
1.2 Elasticity: Price elasticity of demand (PED) Learning Outcomes Explain the concept of price elasticity of demand, understanding that it involves responsiveness of quantity demanded to a, along a given
ANSWERS TO END-OF-CHAPTER QUESTIONS 24-1 No firm is completely sheltered from rivals; all firms compete for the consumer dollars. Pure monopoly, therefore, does not exist. Do you agree? Explain. How might
### The formula to measure the rice elastici coefficient is Percentage change in quantity demanded E= Percentage change in price
a CHAPTER 6: ELASTICITY, CONSUMER SURPLUS, AND PRODUCER SURPLUS Introduction Consumer responses to changes in prices, incomes, and prices of related products can be explained by the concept of elasticity.
### SUPPLY AND DEMAND : HOW MARKETS WORK
SUPPLY AND DEMAND : HOW MARKETS WORK Chapter 4 : The Market Forces of and and demand are the two words that economists use most often. and demand are the forces that make market economies work. Modern
### Demand Equilibrium price Consumer sovereignty Elasticity Shortage Surplus
Social Studies AP Economics STANDARD SKILLS and CONCEPTS VOCABULARY Standard 1: Scarcity and Economic Reasoning Students will understand that productive resources are limited; therefore, people, institutions
### PROBLEM SET#3 PART I: MULTIPLE CHOICE
1 PROBLEM SET#3 PART I: MULTIPLE CHOICE 1. In general, elasticity is a measure of a. the extent to which advances in technology are adopted by producers. b. the extent to which a market is competitive.
### ECON 101 MIDTERM 1 REVIEW SESSION (WINTER 2015) BY BENJI HUANG
ECON 101 MIDTERM 1 REVIEW SESSION (WINTER 2015) BY BENJI HUANG TABLE OF CONTENT I. CHAPTER 1: WHAT IS ECONOMICS II. CHAPTER 2: THE ECONOMIC PROBLEM III. CHAPTER 3: DEMAND AND SUPPLY IV. CHAPTER 4: ELASTICITY
### AP Microeconomics Chapter 4 Outline
I. Introduction A. Learning Objectives In this chapter students should learn: 1. What price elasticity of demand is and how it can be applied. 2. The usefulness of the total revenue test for price elasticity
### UNIT 6 cont PRICING UNDER DIFFERENT MARKET STRUCTURES. Monopolistic Competition
UNIT 6 cont PRICING UNDER DIFFERENT MARKET STRUCTURES Monopolistic Competition Market Structure Perfect Competition Pure Monopoly Monopolistic Competition Oligopoly Duopoly Monopoly The further right on
### AP Microeconomics Chapter 12 Outline
I. Learning Objectives In this chapter students will learn: A. The significance of resource pricing. B. How the marginal revenue productivity of a resource relates to a firm s demand for that resource.
### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chap 13 Monopolistic Competition and Oligopoly These questions may include topics that were not covered in class and may not be on the exam. MULTIPLE CHOICE. Choose the one alternative that best completes
### Managerial Economics Prof. Trupti Mishra S.J.M School of Management Indian Institute of Technology, Bombay. Lecture - 10 Theory of Demand (Contd )
Managerial Economics Prof. Trupti Mishra S.J.M School of Management Indian Institute of Technology, Bombay Lecture - 10 Theory of Demand (Contd ) In continuation to our last session on theory of demand
### Income Elasticity and Cross-price Elasticity
Supporting Teachers: Inspiring Students Economics Revision Focus: 2004 AS Economics Income Elasticity and Cross-price Elasticity tutor2u (www.tutor2u.net) is the leading free online resource for Economics,
### 1. If the price elasticity of demand for a good is.75, the demand for the good can be described as: A) normal. B) elastic. C) inferior. D) inelastic.
Chapter 20: Demand and Supply: Elasticities and Applications Extra Multiple Choice Questions for Review 1. If the price elasticity of demand for a good is.75, the demand for the good can be described as:
### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MBA 640 Survey of Microeconomics Fall 2006, Quiz 6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A monopoly is best defined as a firm that
### Fundamentals of Economics. 01 June Marking Scheme
Fundamentals of Economics 01 June 2016 Marking Scheme This marking scheme has been prepared as a guide only to markers. This is not a set of model answers, or the exclusive answers to the questions, and
### The slope is calculated as the change in the vertical variable divided by the change in the horizontal variable (0.80 = 20/25).
1. A city's decision to limit smoking in public areas is an example of The invisible hand at work. The market mechanism at work. Market success. Government intervention. Governments can sometimes improve
### Perfect competition is a market structure in which a large number of firms all produce the same product.
The Four Conditions for Perfect Competition Perfect competition is a market structure in which a large number of firms all produce the same product. 1. Many Buyers and Sellers There are many participants
### 1 st Exam. 7. Cindy's cross-price elasticity of magazine demand with respect to the price of books is
1 st Exam 1. Marginal utility measures: A) the total utility of all your consumption B) the total utility divided by the price of the good C) the increase in utility from consuming one additional unit
### EC 480 SEMINAR 5 Revision: Costs, Revenues & Profit
EC 480 SEMINAR 5 Revision: Costs, Revenues & Profit Profit and the aims of a firm Profit is made by firms earning more from the sale of goods than the cost of producing the goods. A firm s total profit
### Test Yourself: Market Structures
Test Yourself: Market Structures To determine whether any industry is workably competitive, therefore, simply have a good graduate student write his dissertation on the industry and render a verdict. It
### Learning Objectives. Chapter 6. Market Structures. Market Structures (cont.) The Two Extremes: Perfect Competition and Pure Monopoly
Chapter 6 The Two Extremes: Perfect Competition and Pure Monopoly Learning Objectives List the four characteristics of a perfectly competitive market. Describe how a perfect competitor makes the decision
### 1. Supply and demand are the most important concepts in economics.
Page 1 1. Supply and demand are the most important concepts in economics. 2. Markets and Competition a. Market is a group of buyers and sellers of a particular good or service. P. 66. b. These individuals
### 2007 Thomson South-Western
Monopoly While a competitive firm is a price taker, a monopoly firm is a price maker. A firm is considered a monopoly if... it is the sole seller of its product. its product does not have close substitutes.
### 12 MONOPOLY. Chapter. Key Concepts
Chapter 12 MONOPOLY Key Concepts Market Power Monopolies have market power, the ability to affect the market price by changing the total quantity offered for sale. A monopoly is a firm that produces a
### Ch. 6 Lecture Notes I. Price Elasticity of Demand 4. CONSIDER THIS A Bit of a Stretch
Ch. 6 Lecture Notes I. Price Elasticity of Demand A. Law of demand tells us that consumers will respond to a price decrease by buying more of a product (other things remaining constant), but it does not
### A2 Economics. Perfect Competition. tutor2u Supporting Teachers: Inspiring Students. Economics Revision Focus: 2004
Supporting Teachers: Inspiring Students Economics Revision Focus: 2004 A2 Economics tutor2u (www.tutor2u.net) is the leading free online resource for Economics, Business Studies, ICT and Politics. Don
### Perfect Competition. Chapter 7 Section Main Menu
Perfect Competition What conditions must exist for perfect competition? What are barriers to entry and how do they affect the marketplace? What are prices and output like in a perfectly competitive market?
### Chapter 4 - Firms and Market Structures
Chapter 4 - Firms and Market Structures 1. a) True b) True c) True d) True e) False f) True g) False h) False I) True j) False k) False l) True m) False n) False 2. b) There is a single seller who can
### 23. If demand is perfectly inelastic, changes in price leave total revenue unchanged. A) True B) False. Page 4
1. Suppose the price of gasoline increases 10% and quantity demanded in Orlando drops 5% per day. The price elasticity of demand for gasoline in Orlando is: A) price elastic. B) price inelastic. C) price
### A2 Micro Business Economics Diagrams
A2 Micro Business Economics Diagrams Advice on drawing diagrams in the exam The right size for a diagram is ½ of a side of A4 don t make them too small if needed, move onto a new side of paper rather than
### a. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price elastic
Things to know about elasticity. 1. Price elasticity of demand a. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price
### Learning Objectives. Chapter 7. Characteristics of Monopolistic Competition. Monopolistic Competition. In Between the Extremes: Imperfect Competition
Chapter 7 In Between the Extremes: Imperfect Competition Learning Objectives List the five conditions that must be met for the existence of monopolistic competition. Describe the methods that firms can
### Monopoly. Monopoly. Monopoly. Monopoly. While a competitive firm is a price taker, a monopoly firm is a price maker. Chapter 15. Why Monopolies Arise
Chapter 15 While a competitive firm is a price taker, a monopoly firm is a price maker. Copyright 21 by Harcourt, Inc. All rights reserved. Requests for permission to make copies of any part of the work
### Chapter 5 Applications of Supply and Demand
1. Elasticity of Demand (E d ) Chapter 5 Applications of Supply and Demand Measures the responsiveness of Q d to a change in price. How much does Q d change (%) when P changes (%)? We can use a formula
### ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS
ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS Due the Week of June 23 Chapter 8 WRITE [4] Use the demand schedule that follows to calculate total revenue and marginal revenue at each quantity. Plot
### Chapter 20 Elasticity
Chapter 20 Elasticity How responsive are consumers to a change in price? Recall law of demand: As P increases, QD decreases. But how much does QD decrease? The answer to this question gives us elasticity
### Elasticity. Ratio of Percentage Changes. Elasticity and Its Application. Price Elasticity of Demand. Price Elasticity of Demand. Elasticity...
Elasticity and Its Application Chapter 5 All rights reserved. Copyright 21 by Harcourt, Inc. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department,
### Monopolistic Competition
Introduction to Microeconomics Monopolistic Competition Introduction In this document we refer to imperfect competition as monopolistic competition. Monopolistic competition is described as the situation
### Elasticity! Price, Income and Cross Elasticity
Elasticity! Price, Income and Cross Elasticity Elasticity the concept l The responsiveness of one variable to changes in another l When price rises what happens to quantity demanded? Demand falls BUT!
### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Four - Sample Questions Chapters 12-14 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) What is the difference between perfect competition
### Exam 3 Student Name: Microeconomics Exam Dates: Week 15, late April-early May, 2007
Exam 3 Student Name: Microeconomics Exam Dates: Week 15, late April-early May, 2007 Instructions: I) On your Scantron card you must print three things: 1) Print your full name clearly; 2) Print the day
### ADVANCED SUBSIDIARY (AS) General Certificate of Education Economics Assessment Unit AS 1. assessing. Markets and Prices [AE111]
ADVANCED SUBSIDIARY (AS) General Certificate of Education 2012 Economics Assessment Unit AS 1 assessing Markets and Prices [AE111] TUESDAY 12 JUNE, AFTERNOON MARK SCHEME 7395.01 General Marking Instructions
### J. K. SHAH CLASSES. (C) True or False : (i) True (ii) True (iii) False (iv) True. Ans.2. Give Reasons/ explain the following statement:
J. K. SHAH CLASSES QUESTION PAPER Date: 25/09/2016 Total Marks: 40 Total time: 2 hour Solutions Ans.1. (A) Fill in the Blank: 1) Ragner Frisch 2) Larger 3) Equilibrium 4) Monopolistic Competition (B) Match
### Unit 5.4: Monopoly. Michael Malcolm. June 18, 2011
Unit 5.4: Monopoly Michael Malcolm June 18, 2011 1 Price Making A firm has a monopoly if it is the only seller of some good or service with no close substitutes. The key is that this firm has the power
### 4 THE MARKET FORCES OF SUPPLY AND DEMAND
4 THE MARKET FORCES OF SUPPLY AND DEMAND IN THIS CHAPTER YOU WILL Learn what a competitive market is Examine what determines the demand for a good in a competitive market Chapter Overview Examine what
### Paper 1 (SL and HL) markschemes
Paper 1 (SL and HL) markschemes Examples of markschemes for Exam practice: paper 1 in the Economics for the IB Diploma CD-ROM are provided below. Paper 1 section A: Microeconomics Chapter 2 Competitive
### Elasticity. I. What is Elasticity?
Elasticity I. What is Elasticity? The purpose of this section is to develop some general rules about elasticity, which may them be applied to the four different specific types of elasticity discussed in
### Chapter 6. Non-competitive Markets 6.1 SIMPLE MONOPOLY IN THE COMMODITY MARKET
Chapter 6 We recall that perfect competition was theorised as a market structure where both consumers and firms were price takers. The behaviour of the firm in such circumstances was described in the Chapter
ANSWERS TO END-OF-CHAPTER QUESTIONS 23-1 Briefly indicate the basic characteristics of pure competition, pure monopoly, monopolistic competition, and oligopoly. Under which of these market classifications
### Practice Exam 1. 1. Economics is the study of choice under conditions of a. demand b. supply c. scarcity d. opportunity e.
Practice Exam 1 1. Economics is the study of choice under conditions of a. demand b. supply c. scarcity d. opportunity e. abundance 2. Suppose your friends take you out for dinner on your birthday and
### Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output.
Topic 8 Chapter 13 Oligopoly and Monopolistic Competition Econ 203 Topic 8 page 1 Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry
### Chapter 3 Market Demand, Supply, and Elasticity
Chapter 3 Market Demand, Supply, and Elasticity After reading chapter 3, MARKET DEMAND, SUPPLY, AND ELASTICITY, you should be able to: Discuss the Law of Demand and draw a Demand Curve. Distinguish between
### TOPIC III: ELASTICITY AS A MEASUREMENT OF DEGREE OF RESPONSE
TOPIC III: ELASTICITY AS A MEASUREMENT OF DEGREE OF RESPONSE I. Price Elasticity of Demand A. A measurement of the degree of responsiveness of quantity demanded of good X to a change in P x B. E D = measured
### CHAPTER-1 1. Whose definition of economics is classificatory? 2. Who is considered as the father of economics?
CHAPTER-1 1. Whose definition of economics is classificatory? (A)Adam Smith (B) Marshall (C) Pigou (D) Robbins 2. Who is considered as the father of economics? (A)Adam Smith (B) Marshall (C) Pigou (D)
### Chapter 13 Perfect Competition
Chapter 13 Perfect Competition 13.1 A Firm's Profit-Maximizing Choices 1) What is the difference between perfect competition and monopolistic competition? A) Perfect competition has a large number of small
### Elasticity and Its Uses
CHAPTER 4 Elasticity and Its Uses CHAPTER OVERVIEW One of the most practical uses of economic analysis is to predict the effects of changes in underlying conditions or policies on the prices and production
### ELASTICITY AND ITS APPLICATION
5 ELASTICITY AND ITS APPLICATION CHAPTER OUTLINE: I. The Elasticity of Demand A. Definition of elasticity: a measure of the responsiveness of quantity demanded or quantity supplied to one of its determinants.
### Midterm Exam #2. ECON 101, Section 2 summer 2004 Ying Gao. 1. Print your name and student ID number at the top of this cover sheet.
NAME: STUDENT ID: Midterm Exam #2 ECON 101, Section 2 summer 2004 Ying Gao Instructions Please read carefully! 1. Print your name and student ID number at the top of this cover sheet. 2. Check that your
### Monopolistic Competition
In this chapter, look for the answers to these questions: How is similar to perfect? How is it similar to monopoly? How do ally competitive firms choose price and? Do they earn economic profit? In what
### CHAPTER 12 MARKETS WITH MARKET POWER Microeconomics in Context (Goodwin, et al.), 2 nd Edition
CHAPTER 12 MARKETS WITH MARKET POWER Microeconomics in Context (Goodwin, et al.), 2 nd Edition Chapter Summary Now that you understand the model of a perfectly competitive market, this chapter complicates
### Price Theory Lecture 2: Supply & Demand
Price Theory Lecture 2: Supply & emand I. The Basic Notion of Supply & emand Supply-and-demand is a model for understanding the determination of the price of quantity of a good sold on the market. The
### Chapter 6 Elasticity
Goldwasser AP Microeconomics Chapter 6 Elasticity BEFORE YOU READ THE CHAPTER Summary This chapter develops the concept of elasticity, which provides a numerical measure of the responsiveness of quantity
### SAMPLE COURSE OUTLINE ECONOMICS ATAR YEAR 11
SAMPLE COURSE OUTLINE ECONOMICS ATAR YEAR 11 Copyright School Curriculum and Standards Authority, 2014 This document apart from any third party copyright material contained in it may be freely copied,
### BPE_MIC1 Microeconomics 1 Fall Semester 2011
Masaryk University - Brno Department of Economics Faculty of Economics and Administration BPE_MIC1 Microeconomics 1 Fall Semester 2011 Final Exam - 12.12.2011, 9:00-10:30 a.m. Test A Guidelines and Rules:
### BPE_MIC1 Microeconomics 1 Fall Semester 2011
Masaryk University - Brno Department of Economics Faculty of Economics and Administration BPE_MIC1 Microeconomics 1 Fall Semester 2011 Final Exam - 12.12.2011, 9:00-10:30 a.m. Test B Guidelines and Rules:
### Review Test Ch 9, 10, 11 2
Review Test Ch 9, 10, 11 2 Student: 1. A one-firm industry is known as: A. monopolistic competition. B. oligopoly. C. pure monopoly. D. pure competition. 2. Which of the following is not a basic characteristic
### Unit 7. Firm behaviour and market structure: monopoly
Unit 7. Firm behaviour and market structure: monopoly Learning objectives: to identify and examine the sources of monopoly power; to understand the relationship between a monopolist s demand curve and
### Pre-Test Chapter 23 ed17
Pre-Test Chapter 23 ed17 Multiple Choice Questions 1. The kinked-demand curve model of oligopoly: A. assumes a firm's rivals will ignore a price cut but match a price increase. B. embodies the possibility
### Recitation #5 Week 02/08/2009 to 02/14/2009. Chapter 6 - Elasticity
Recitation #5 Week 02/08/2009 to 02/14/2009 Chapter 6 - Elasticity 1. This problem explores the midpoint method of calculating percentages and why this method is the preferred method when calculating price
### Market Structure: Perfect Competition and Monopoly
WSG8 7/7/03 4:34 PM Page 113 8 Market Structure: Perfect Competition and Monopoly OVERVIEW One of the most important decisions made by a manager is how to price the firm s product. If the firm is a profit
### http://ezto.mhecloud.mcgraw-hill.com/hm.tpx
Page 1 of 17 1. Assume the price elasticity of demand for U.S. Frisbee Co. Frisbees is 0.5. If the company increases the price of each Frisbee from \$12 to \$16, the number of Frisbees demanded will Decrease
### Economics 103h Fall 2012: Part 1 of review questions for final exam
Economics 103h Fall 2012: Part 1 of review questions for final exam This is the first set of review questions. The short answer/graphing go through to the end of monopolistic competition. The multiple
### CHAPTER 18 MARKETS WITH MARKET POWER Principles of Economics in Context (Goodwin et al.)
CHAPTER 18 MARKETS WITH MARKET POWER Principles of Economics in Context (Goodwin et al.) Chapter Summary Now that you understand the model of a perfectly competitive market, this chapter complicates the
### 1 of 25 5/1/2014 4:28 PM
1 of 25 5/1/2014 4:28 PM Any point on the budget constraint Gives the consumer the highest level of utility. Represent a combination of two goods that are affordable. Represents combinations of two goods
### Chapter 11 Perfect Competition
These notes provided by Laura Lamb are intended to complement class lectures. The notes are based on chapter 11 of Microeconomics and Behaviour 2 nd Canadian Edition by Frank and Parker (2004). Chapter
### I. Features of Monopolistic Competition
University of Pacific-Economics 53 Lecture Notes #15 I. Features of Monopolistic Competition Like the name suggests, a monopolistically competitive industry has features from both a monopoly market structure
### Economics Basics Tutorial
Economics Basics Tutorial http://www.investopedia.com/university/economics/ Thanks very much for downloading the printable version of this tutorial. As always, we welcome any feedback or suggestions. http://www.investopedia.com/contact.aspx
### Chapter 15: Monopoly WHY MONOPOLIES ARISE HOW MONOPOLIES MAKE PRODUCTION AND PRICING DECISIONS
Chapter 15: While a competitive firm is a taker, a monopoly firm is a maker. A firm is considered a monopoly if... it is the sole seller of its product. its product does not have close substitutes. The
### CHAPTER 4 WORKING WITH SUPPLY AND DEMAND
CHAPTER 4 WORKING WITH SUPPLY AND DEMAND ANSWERS TO ONLINE REVIEW QUESTIONS 1. The rate of change along a demand curve measures how much one variable changes for every one-unit change in another variable.
### Microeconomics Required Graphs and Terms
Microeconomics Required Graphs and Terms Understanding and explaining the economic concepts required by the AP and IB exams rests on a solid knowledge of fundamental economic graphs and terms. In order | 15,686 | 73,053 | {"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-2018-47 | latest | en | 0.932062 |
https://theshippingforecastmusic.com/qa/quick-answer-what-is-the-smallest-seven-digit-number.html | 1,618,982,637,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039508673.81/warc/CC-MAIN-20210421035139-20210421065139-00009.warc.gz | 650,798,075 | 9,592 | # Quick Answer: What Is The Smallest Seven Digit Number?
## What is the difference between the largest number of four digit and the smallest number of 6 digit?
The difference is 9999- 1,00,000 is – 90001..
## How many 9 digit numbers are there?
1 billion 9There are 1 billion 9 digit numbers (000,000,000 through 999,999,999). There are 45 different combinations of two different numerals (10 x 9 divided by 2). There are 512 (2 to the 9th power) different permutations for any two numbers to be used in a 9 digit number. 45 x 512 = 23,040 – 10 = 23,030.
## Which is smallest 5 digit number?
10000The smallest 5 -digit number is 10000, while the largest 5 -digit number is 99999.
## What is largest 7 digit number having different digits?
9876543The greatest seven-digit number whose digits are all different is 9876543.
## How many zeros are there in the smallest 6 digit number?
5 zerosHow many 6-digit numbers are there? The smallest 6-digit number is 1 followed by 5 zeros. This number is called one hundred thousand.
## What is the 7 digit smallest number?
1000000The smallest 7-digit number is 1000000.
## Which is the smallest 9 digit number?
100,000,000The smallest 9-digit is 10,00,00,000 in Indian Numeric System. It is 100,000,000. Smallest 9 digit number is 100000000. the answer is 100,000,000 in international system.
## Which is smallest 8 digit number?
10 millionOur smallest eight-digit number is 10 million.
## Which is the largest 9 digit number?
987654321smallest 9digit number is 123456789 and the largest 9 digit number is 987654321.
## What is the number 2 more than the smallest 9 digit number?
Answer. Because the least 9 digit number is 100000000.
## What is 9 digit number called?
100,000,000 (one hundred million) is the natural number following 99,999,999 and preceding 100,000,001.
## What is the greatest and smallest 7 digit number?
The largest 7-digit number is 99,99,999. The successor of 99,99,999 = 99,99,999 + 1 = 1,00,00,000. 10000000 is the smallest 8-digit number.
## Which is smallest 6 digit number?
100000So, the smallest six digit number is 100000.
## What is the smallest and greatest 6 digit number?
Find the difference between the greatest 6-digit number and smallest 5-digit number formed by using the digits 9, 8, 3, 4 (each digit must be used at least once). greatest number is 999843 and smallest number is 33489.
## Is 0 a digit number?
0 (zero) is a number, and the numerical digit used to represent that number in numerals. It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems.
## What is the greatest 10 digit number?
This number is called one billion. The largest 10-digit number is 9 followed by another 9 nines. This number is called nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine. There are a total of nine billion different 10-digit numbers.
## Which will be the smallest number of 7 digit using 0123456?
The smallest 6th digit we can pick is 5. We have picked all different digits, and have 1 more digit to pick. The smallest 7th and last digit we can pick is 6. Answer: 1023456 is the smallest possible 7 digit number with all different digits.
## What is the greatest number of 6 digit?
999,999The largest (decimal) 6 digit number is obviously 999,999, and the smallest is 100,000, you should be able to make up the difference by yourself.
## What is the smallest digit number?
The smallest one-digit number is 1 and the largest one-digit number is 9.
## What is the 3 digit smallest number?
100The smallest 3 -digit number is 100, and the largest three digit number is 999.
## What is 8 digit number called?
10,000,000 (ten million) is the natural number following 9,999,999 and preceding 10,000,001.
## What is the greatest number?
The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That’s written as a one followed by googol zeroes.
## What is the 8 digit greatest number?
This number is called ten million. The largest 8-digit number is 9 followed by another 7 nines. This number is called ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine.
## What is the 4 digit greatest number?
9999The greatest 4-digit number = 9999. So, we say that we have 9000 four-digit numbers.
## What is the smallest 8 digit number is called?
The smallest 8 digit number is 1 followed by 7 zeroes and is written as 10000000.
## What is a 6 digit number called?
short codeA six-digit phone number is what’s known as a short code. Many businesses use short codes to send out marketing blasts or alerts. Short codes are also useful for anyone who’s set up two-step verification to log into their accounts on sites like Google or Twitter.
## What is greatest and smallest number?
We know that a four digit number has four places, i.e., thousands, hundreds, tens and ones or units from left to right as Th, H, T, O. If greatest to lowest digits are placed at these places in descending order, we get the greatest number and if placed in ascending order, we get the smallest number.
## How many 7 digit numbers are there?
All the digits after first digit can be anything between 0–9, including both. The easy answer to this is to subtract the value of the largest 6-digit number from the largest 7-digit number. 9,999,999 – 999,999 = 9,000,000. Therefore, there are nine million distinct 7-digit integers. | 1,415 | 5,575 | {"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} | 3.578125 | 4 | CC-MAIN-2021-17 | latest | en | 0.812741 |
http://questionpack.com/User/main/Lesson/e41a6cab-054e-4022-95a7-5243c4cdfea8/ | 1,618,650,761,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00113.warc.gz | 80,131,549 | 3,459 | Simple Interest
Tests
Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10
Sample
Simple Interest [Test 1]
1) Matt's current bank balance is \$9,600.00. Bank offers a simple interest with monthly rate of 1.67 %. Interest earned is computed and deposited every years. What was the bank balance years ago? \$
2) Jasmine's current bank balance is \$199,092.00. Bank offers a simple interest with monthly rate of 1.92 %. Interest earned is computed and deposited every years. What was the bank balance years ago? \$
3) Matt's current bank balance is \$70,272.00. Bank offers a simple interest with monthly rate of 1.00 %. Interest earned is computed and deposited every years. What was the bank balance years ago? \$
4) George lended \$111,600.00 to a friend with anual interest rate of 15.00 %. What is the total amount George will receive after 7 months. The interest is computed as simple interest and is not compunded. \$
5) Max borrowed \$27,600.00 from the bank with anual interest rate of 12.00 %. What would be the total amount that Max need to pay after 6 years. \$
6) A local bank offers a fix deposit scheme with maturity of 8 years and monthly interest rate of 1.83 %. Interest is computed only once at the maturity date as a simple interest. Mr. B deposited \$96,000.00 in that scheme. How much interest money would Mr. B earn? \$
7) Matt lended \$104,400.00 to a friend with anual interest rate of 15.00 %. What is the total amount Matt will receive after 3 months. The interest is computed as simple interest and is not compunded. \$
8) Jacob borrowed \$108,000.00 from the bank with anual interest rate of 5.00 %. What would be the total amount that Jacob need to pay after 7 years. \$
9) Mr. B received a total of \$17,280.00 from the bank. The bank paid the simple interest with yearly rate of 10.00 %. How many years ago did Mr. B deposited \$9,600.00?
10) Val received a total of \$95,040.00 from the bank. The bank paid the simple interest with yearly rate of 20.00 %. How many years ago did Val deposited \$39,600.00? | 570 | 2,101 | {"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-2021-17 | latest | en | 0.932683 |
https://www.jiskha.com/display.cgi?id=1399276521 | 1,503,365,011,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886109803.8/warc/CC-MAIN-20170822011838-20170822031838-00380.warc.gz | 906,285,680 | 4,102 | # physics
posted by .
a body of mass 5kg falls vertically against a resistance of x Newtons.The body passes through two points A and B, 2.5 METERS APART with A above B, WHEN TRAVELING WITH SPEED 2 METERS PER SECOND AND 6 METERS PER SECOND RESPECTIVELY. BY ENERGY CONSIDERATION , FIND THE VALUE OF X.
## Similar Questions
1. ### physics i suck
an antelope moving with constant acceleration covers the distance between two points that are 80 meters apart in 7 seconds. Its velocity as it passes the second point is 15 meters per second. What is the antelope's velocity at the …
2. ### physical science
A car with a mass of 1,200 kilograms is moving around a circular curve at a uniform velocity of 20 meters per second. The centripetal force on the car is 6,000 newtons. What is the radius of the curve?
3. ### related rate problem
A railroad track and a road cross at a right angle. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per second is the train moving …
4. ### physics
A body moves 6 meters north than 8 meters east than 10 meters vertically upward. What is its resultant displacement from initial position?
5. ### Math
For one pony, thecritical force was 1.16 times its body weight. It experienced a force of 0.75 times its body weight at a speed of 2 meters per second, and a force of 0.93 times its body weight at 3 meters per second. At what speed …
6. ### physics
A body is projected so that on its upward path it passes through a point x meters and y meters vertically from the point of projection. Show that if R is the range on the horizontal through point of projection the angle of elevation …
7. ### physics
A bicyclist moving at a constant speed takes 10.0 seconds to travel 500 meters down a path inclined 30.0° downward from the horizontal. What is the vertical velocity of this motion?
8. ### Physics
A baseball with a mass of 0.15 kilograms collides with a bat at a speed of 40 meters/second. The duration of the collision is 8.0 × 10-3 seconds. The ball moves off with a speed of 50 meters/second in the opposite direction. What …
9. ### physics
A friend is making an iMovie and wants your help designing a skateboard stunt. You estimate that your friend�s mass is four times greater than that of the skateboard. For the following questions, ignore friction. In one scenario, …
10. ### Physics
A two head collision. One car weighs 45000 newtons and going at 15 meters per second. The other car is traveling at 25 meters per second and weighs 9000 newtons. How would I calculate velocity?
More Similar Questions | 632 | 2,651 | {"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-2017-34 | latest | en | 0.917225 |
http://www.slideserve.com/gilead/properties-of-matter | 1,506,431,328,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818695726.80/warc/CC-MAIN-20170926122822-20170926142822-00072.warc.gz | 570,221,727 | 13,483 | 1 / 21
# Properties of Matter - PowerPoint PPT Presentation
Properties of Matter. Physical Properties, Phases of Matter, Chemical Properties. General (Physical) Properties. Physical properties may be observed without changing the nature of the matter. Boiling point is a physical property
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
### Properties of Matter
Physical Properties, Phases of Matter, Chemical Properties
• Physical properties may be observed without changing the nature of the matter.
• Boiling point is a physical property
• When a liquid boils, the vapor may be condensed to get the liquid back
• The liquid is still the same substance
• Properties you can see, such as color, shape, hardness, and texture
• Properties that are easily measured, such as mass, volume, density, melting point, boiling point
• Note! Freezing and melting point are the same temperature!
• Density = Mass ÷ Volume
• Is the ability to be attracted to a magnet a physical property?
• Mass is measured on a balance or scale. Common units are grams, milligrams, and kilograms
• Liquid volume is measured with a graduated cylinder. Common units are liters and milliliters
• Solid volumes may be calculated with formulas or by water displacement Common units are cm3 or milliliters.
• A wooden block raises the level of the liquid in the graduated cylinder from 150ml to 180ml. What is the volume of the block?
• 180ml
– 150ml
= 30ml
M D I V
• If the density of the block is 300g/ml, what is its mass? (remember, its volume was 30ml)
• M 300g/ml I 30ml
• 9000g
• A wood block as in the last example has sides that are 2cm wide, 5cm long, and 3cm high. What is the volume of the block?
• Use the formula l x w x h
• The answer will be in cm3
• If its mass is 90 grams, what is its density?
• 2cm x 5cm x 3cm = 30cm3
90g ÷ 30cm3 = 3g/cm3
1) If the mass of a rock is 500g and its volume is 25cm3, what is its density?
• If the density of a liquid is 1.2 g/ml, and its volume is 10ml, what is its mass?
• If Bob’s mass is 80kg and his density is 1.6kg/l, what is his volume?
M
• 1) 500g ÷ 25cm3 = 20g/cm3
• 2) 1.2g/ml x 10ml = 12g
• 3) 80kg ÷ 1.6kg/l = 50L
D
V
• Weight is the pull of gravity on mass.
• Weight changes in response to gravitational pull.
• A person’s mass will remain the same on the earth or on the moon, but she will only weigh 1/6 as much on the moon.
• The most common phases of matter are solid, liquid, and gas
• Plasma is a high energy phase found in stars
• When a substance changes phase, energy (heat) is lost or gained, but temperature remains the same.
the sun hitting our atmosphere. This causes electrons in
atmospheric gases to be excited to a higher energy level,
And when they drop back down, a photon of light is emitted.
• Solid to liquid:
Melting
• Liquid to gas:
Vaporization
• Gas to liquid:
Condensation
• Liquid to solid:
Freezing
• Solid to gas:
Sublimation
• Chemical properties describe a substances’ ability to change into a different substance. A chemical change is the process by which the substance changes.
• Flammability
• Ability to support burning
• Ability to combine with other chemicals in a chemical reaction.
• Rusting
• Photosynthesis
• Explosions
• Burning
• Digestion
• Baking food
• Fermentation
• Gas given off
• Heat absorbed or released
• Light given off
• Color change
• Oxidation of a metal
• New substances are formed | 1,036 | 3,982 | {"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 | 3 | CC-MAIN-2017-39 | latest | en | 0.886103 |
https://metanumbers.com/1531373 | 1,642,329,218,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320299852.23/warc/CC-MAIN-20220116093137-20220116123137-00406.warc.gz | 460,523,548 | 7,350 | # 1531373 (number)
1,531,373 (one million five hundred thirty-one thousand three hundred seventy-three) is an odd seven-digits prime number following 1531372 and preceding 1531374. In scientific notation, it is written as 1.531373 × 106. The sum of its digits is 23. It has a total of 1 prime factor and 2 positive divisors. There are 1,531,372 positive integers (up to 1531373) that are relatively prime to 1531373.
## Basic properties
• Is Prime? Yes
• Number parity Odd
• Number length 7
• Sum of Digits 23
• Digital Root 5
## Name
Short name 1 million 531 thousand 373 one million five hundred thirty-one thousand three hundred seventy-three
## Notation
Scientific notation 1.531373 × 106 1.531373 × 106
## Prime Factorization of 1531373
Prime Factorization 1531373
Prime number
Distinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 1.53137e+06 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 14.2417 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 1,531,373 is 1531373. Since it has a total of 1 prime factor, 1,531,373 is a prime number.
## Divisors of 1531373
2 divisors
Even divisors 0 2 2 0
Total Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 1.53137e+06 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 765687 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 1237.49 Returns the nth root of the product of n divisors H(n) 2 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 1,531,373 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 1,531,373) is 1,531,374, the average is 765,687.
## Other Arithmetic Functions (n = 1531373)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 1531372 Total number of positive integers not greater than n that are coprime to n λ(n) 1531372 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 116091 Total number of primes less than or equal to n r2(n) 8 The number of ways n can be represented as the sum of 2 squares
There are 1,531,372 positive integers (less than 1,531,373) that are coprime with 1,531,373. And there are approximately 116,091 prime numbers less than or equal to 1,531,373.
## Divisibility of 1531373
m n mod m 2 3 4 5 6 7 8 9 1 2 1 3 5 4 5 5
1,531,373 is not divisible by any number less than or equal to 9.
• Arithmetic
• Prime
• Deficient
• Polite
• Prime Power
• Square Free
## Base conversion (1531373)
Base System Value
2 Binary 101110101110111101101
3 Ternary 2212210122112
4 Quaternary 11311313231
5 Quinary 343000443
6 Senary 52453405
8 Octal 5656755
10 Decimal 1531373
12 Duodecimal 61a265
20 Vigesimal 9b88d
36 Base36 wtm5
## Basic calculations (n = 1531373)
### Multiplication
n×y
n×2 3062746 4594119 6125492 7656865
### Division
n÷y
n÷2 765686 510458 382843 306275
### Exponentiation
ny
n2 2345103265129 3591227822430392117 5499509324118696867386641 8421800092203621177900482588093
### Nth Root
y√n
2√n 1237.49 115.264 35.1779 17.259
## 1531373 as geometric shapes
### Circle
Diameter 3.06275e+06 9.6219e+06 7.36736e+12
### Sphere
Volume 1.50429e+19 2.94694e+13 9.6219e+06
### Square
Length = n
Perimeter 6.12549e+06 2.3451e+12 2.16569e+06
### Cube
Length = n
Surface area 1.40706e+13 3.59123e+18 2.65242e+06
### Equilateral Triangle
Length = n
Perimeter 4.59412e+06 1.01546e+12 1.32621e+06
### Triangular Pyramid
Length = n
Surface area 4.06184e+12 4.2323e+17 1.25036e+06
## Cryptographic Hash Functions
md5 e06e22754a5c74f284ca8324a7895b05 cedae1c7f94de26286bf13f212b843ea170e710b a20bd9689a4276750bad7e3a4cb279aa3130d1cc0506120c46d1c7561df84663 3afbdf15ac8f772f93915a2f1b5ac7902b0b5086800c113e7ec3ee4c4c8f2be681fb4f7481fc5e395ac69ff6b68fb6d8c8d8ffa66309e281c5d96fecfdc8439d 158fa4a242e1e134538646b9dc85c9087cfd5297 | 1,538 | 4,317 | {"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} | 3.53125 | 4 | CC-MAIN-2022-05 | latest | en | 0.820159 |
http://hackage.haskell.org/package/type-settheory-0.1.2/docs/Control-SMonad.html | 1,529,867,122,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267867050.73/warc/CC-MAIN-20180624180240-20180624200240-00251.warc.gz | 132,286,197 | 3,251 | Contents Variants using auto for the domain-membership proofs Derived combinators
Description
Example application of sets
This is quite similar to what the rmonad package does, but we use preexisting sets rather than an associated datatype
• The apostrophed variants take proof objects as arguments
• The plain variants use auto; that is, they assume that membership has been proved by an instance of Fact
Synopsis
class SFunctor dom f | f -> dom where
sfmap' :: (x :∈: dom) -> (y :∈: dom) -> (x -> y) -> f x -> f y
class SFunctor dom f => SApplicative dom f | f -> dom where
spure' :: (x :∈: dom) -> x -> f x sap' :: (x :∈: dom) -> (y :∈: dom) -> ((x -> y) :∈: dom) -> f (x -> y) -> f x -> f y
class SApplicative dom m => SMonad dom m | m -> dom where
sbind' :: (x :∈: dom) -> (y :∈: dom) -> m x -> (x -> m y) -> m y
sfmap :: (SFunctor dom f, Fact (x :∈: dom), Fact (y :∈: dom)) => (x -> y) -> f x -> f y
spure :: (SApplicative dom f, Fact (x :∈: dom)) => x -> f x
sap :: (SApplicative dom f, Fact (x :∈: dom), Fact (y :∈: dom), Fact ((x -> y) :∈: dom)) => f (x -> y) -> f x -> f y
sreturn' :: SMonad dom f => (x :∈: dom) -> x -> f x
sreturn :: (SMonad dom f, Fact (x :∈: dom)) => x -> f x
sbind :: (Fact (x :∈: dom), Fact (y :∈: dom), SMonad dom m) => m x -> (x -> m y) -> m y
sjoin' :: SMonad dom m => (m y :∈: dom) -> (y :∈: dom) -> m (m y) -> m y
sjoin :: (Fact (m y :∈: dom), Fact (y :∈: dom), SMonad dom m) => m (m y) -> m y
sfmap'Default :: SMonad dom m => (x :∈: dom) -> (y :∈: dom) -> (x -> y) -> m x -> m y
sap'Default :: SMonad dom m => (x :∈: dom) -> (y :∈: dom) -> ((x -> y) :∈: dom) -> m (x -> y) -> m x -> m y
sliftA2' :: SApplicative dom f => (x :∈: dom) -> (y :∈: dom) -> (z :∈: dom) -> ((y -> z) :∈: dom) -> (x -> y -> z) -> f x -> f y -> f z
sliftA2 :: (Fact ((x1 -> y) :∈: dom), Fact (y :∈: dom), Fact (x1 :∈: dom), SApplicative dom f, Fact (x :∈: dom)) => (x -> x1 -> y) -> f x -> f x1 -> f y
ssequence' :: SApplicative dom f => (a :∈: dom) -> ([a] :∈: dom) -> (([a] -> [a]) :∈: dom) -> [f a] -> f [a]
ssequence :: (Fact (a :∈: dom), Fact ([a] :∈: dom), Fact (([a] -> [a]) :∈: dom), SApplicative dom f) => [f a] -> f [a]
Documentation
class SFunctor dom f | f -> dom where Source
Methods
sfmap' :: (x :∈: dom) -> (y :∈: dom) -> (x -> y) -> f x -> f y Source
Instances
SFunctor OrdType Set SFunctor OrdType Set
class SFunctor dom f => SApplicative dom f | f -> dom where Source
Methods
spure' :: (x :∈: dom) -> x -> f x Source
sap' :: (x :∈: dom) -> (y :∈: dom) -> ((x -> y) :∈: dom) -> f (x -> y) -> f x -> f y Source
Instances
SApplicative OrdType Set SApplicative OrdType Set
class SApplicative dom m => SMonad dom m | m -> dom where Source
Methods
sbind' :: (x :∈: dom) -> (y :∈: dom) -> m x -> (x -> m y) -> m y Source
Instances
Variants using auto for the domain-membership proofs
sfmap :: (SFunctor dom f, Fact (x :∈: dom), Fact (y :∈: dom)) => (x -> y) -> f x -> f y Source
spure :: (SApplicative dom f, Fact (x :∈: dom)) => x -> f x Source
sap :: (SApplicative dom f, Fact (x :∈: dom), Fact (y :∈: dom), Fact ((x -> y) :∈: dom)) => f (x -> y) -> f x -> f y Source
sreturn' :: SMonad dom f => (x :∈: dom) -> x -> f x Source
sreturn :: (SMonad dom f, Fact (x :∈: dom)) => x -> f x Source
sbind :: (Fact (x :∈: dom), Fact (y :∈: dom), SMonad dom m) => m x -> (x -> m y) -> m y Source
Derived combinators
sjoin' :: SMonad dom m => (m y :∈: dom) -> (y :∈: dom) -> m (m y) -> m y Source
sjoin :: (Fact (m y :∈: dom), Fact (y :∈: dom), SMonad dom m) => m (m y) -> m y Source
sfmap'Default :: SMonad dom m => (x :∈: dom) -> (y :∈: dom) -> (x -> y) -> m x -> m y Source
sfmap' in terms of spure' and sbind'
sap'Default :: SMonad dom m => (x :∈: dom) -> (y :∈: dom) -> ((x -> y) :∈: dom) -> m (x -> y) -> m x -> m y Source
sap' in terms of spure' and sbind'
sliftA2' :: SApplicative dom f => (x :∈: dom) -> (y :∈: dom) -> (z :∈: dom) -> ((y -> z) :∈: dom) -> (x -> y -> z) -> f x -> f y -> f z Source
sliftA2 :: (Fact ((x1 -> y) :∈: dom), Fact (y :∈: dom), Fact (x1 :∈: dom), SApplicative dom f, Fact (x :∈: dom)) => (x -> x1 -> y) -> f x -> f x1 -> f y Source
ssequence' :: SApplicative dom f => (a :∈: dom) -> ([a] :∈: dom) -> (([a] -> [a]) :∈: dom) -> [f a] -> f [a] Source
ssequence :: (Fact (a :∈: dom), Fact ([a] :∈: dom), Fact (([a] -> [a]) :∈: dom), SApplicative dom f) => [f a] -> f [a] Source
Produced by Haddock version 2.4.2 | 1,805 | 4,385 | {"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} | 3.015625 | 3 | CC-MAIN-2018-26 | latest | en | 0.580886 |
http://slidegur.com/doc/70105/ppt---dr.-wissam-fawaz | 1,477,510,169,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720972.46/warc/CC-MAIN-20161020183840-00443-ip-10-171-6-4.ec2.internal.warc.gz | 228,578,468 | 10,897 | ### ppt - Dr. Wissam Fawaz
```M/M/1 queue
λ
μ
λ: arrival rate
μ: service rate
λn = λ, (n >=0); μn = μ (n>=1)
Pn
0 1 ... n 1
0 1 ... n
P0 Pn
Pn P0 ;
n
n
n
P0
P0 P1 ... Pn ... 1
P0 (1 ...) 1 P0 1
2
1
Traffic intensity
rho = λ/μ
It is a measure of the total arrival traffic to the system
Example: λ = 3/hour; 1/μ=15 min = 0.25 h
Represents the fraction of time a server is busy
In which case it is called the utilization factor
Example: rho = 0.75 = % busy
2
Queuing systems: stability
λ<μ
N(t)
busy
=> stable system
3
2
1
1
λ>μ
idle
2 3 4 5 6 7 8 9 10 11
Time
Steady build up of customers => unstable
N(t)
3
2
1
1
2 3 4 5 6 7 8 9 10 11
Time
3
Example#1
A communication channel operating at 9600 bps
Receives two type of packet streams from a gateway
Type A packets have a fixed length format of 48 bits
Type B packets have an exponentially distribution length
With a mean of 480 bits
If on the average there are
20% type A packets and 80% type B packets
Calculate the utilization of this channel
Assuming the combined arrival rate is 15 packets/s
4
Performance measures
L
Lq
Mean queue length in the queue space
W
Mean # customers in the whole system
Mean waiting time in the system
Wq
Mean waiting time in the queue
5
Mean queue length (M/M/1)
L E[n]
nP n
n0
n (1 )
n
n0
(1 ) ( n
n 1
n0
) (1 ) ( )'
n
n0
(1 ) ( )'
n
n0
(1 )(
L
1
1
)'
1
6
Mean queue length (M/M/1)
(cont’d)
Lq
( n 1) P
n
n 1
nP
n 1
n
P
n
n 1
L (1 P0 )
L (1 (1 ))
L
L Lq
7
Little’s theorem
This result
Existed as an empirical rule for many years
And was first proved in a formal way by Little in 1961
The theorem
Relates the average number of customers L
In a steady state queuing system
To the product of the average arrival rate (λ)
And average waiting time (W) a customer spend in a system
L .W
8
LITTLE’s Formula
=×
: average number of messages in system
: average delay
λ: arrival rate
Little’s relation holds for any
Service discipline
Arrival process
Holding area
Graphical Proof
A(t)
L(t)
Nb. of customers that left system up to t
=> N(t) = A(t) – L(t)
Cumulative arrival process
Nb. of customers in system at time t
di : interval between ith arrival and its departure
∆ = 1 + 2 + … +
Graphical Proof (continued)
Graphical Proof (continued)
=
()
, ()
⇒ × =
Now, let → ∞
=
∆()
()
∆()
= ()
lim = , lim =
→∞
→∞
⇒ lim = =
→∞
Mean waiting time (M/M/1)
Applying Little’s theorem
L .W
W
L
1
.
1
1
13
Z-transform: application in
queuing systems
X is a discrete r.v.
P(X=i) = Pi, i=0, 1, …
P0 , P1 , P2 ,…
g (z)
Pi z
i
i0
Properties of the z-transform
g(1) = 1, P0 = g(0); P1 = g’(0); P2 = ½ . g’’(0)
=
=1
,
2
=
2
2
=1
+
=1
14
M/M/1 Queue – Infinite Waiting Room
Probability generating function
Mean
=
∞
=0
=
(1−)
Variance
=
1− 2
1− =
1−
1−
M/M/S
n
n ; n s
n
s ; n s
n s
Pn
0 1 ... n 1
1 ... n
P0
n
. 2 . 3 ... n
n
1
. . P0
n!
16
M/M/S (cont’d)
n S
Pn
n
. 2 . 3 ... S . S . S ...
P0
n
1
P0
nS
S !. S
Pn
P0
n
1
P0 ; n S
n!
n
1
P0 ; n S
nS
S !. S
1
S 1
n
S
1 1
1
.
.
.
n! S !
n0
1
S .
17
S servers
μ
M/M/S
λ
n
n ; n S
n
S ; n S
n S , Pn
0 1 ... n 1
1 ... n
1
. P0 . . P0
. 2 . 3 ... n
n!
n
1
P0
P0
nS
. 2 . 3 ... S . S . S ...
S !. S
n S , Pn
Pn
P0
n
n
n
n
1
P0 ; n S
n!
n
1
P0 ; n S
nS
S !. S
18
M/M/S: normalizing equations
P0 P1 ... PS PS 1 ... Pn ... 1
n
1
n! P0
n0
S 1
n
1
S !. S n S P0 1
nS
S 1 n 1
P0
n 0 n!
n
1
S !. S n S
nS
n
1
n
1
1
1
S !. S n S S ! S n S
nS
nS
S
S 1
S2
1
1
1
. . 2 ...
S !
S
S
S
1
2
1 1
1
. 1 . . 2 ...
S!
S S
19
M/M/S: stable queue
is λ/Sμ < 1 ?
Otherwise you will not get a stable queue, as such
S
1
2
1 1
1
. 1 . . 2 ...
S!
S S
S
1
1
. .
S! 1
S
P0
1
S 1
n
S
1 1
1
. n! . S !.
n0
1
S .
20
M/M/S: performance measures
Mean queue length
Lq
S
.
(
n
S
)
P
S
nS
( / S )
S !. 1
S
2
Mean waiting time in the queue (Little’s theorem)
L q .W q W q
Lq
Mean waiting time in the system
W Wq
. P0
1
Mean # of customers in the whole system
L .W L .W q
21
Erlang C formula
A quantity of interest
Probability to find all s servers busy
∞
! ( − )
, =
=
−1
=
=0
! +
(! ( − ))
Ratio between Lq and Pc
=
⇒ =
( − )
−
22
M/M/S: stability revisited
Stable
If λ/Sμ < 1
Arrival rate to an individual server
S
Utilization of a server
1
.
S
Utilization of all servers
23
M/M/1/N
λ
% loss
μ
N
Birth and death equations
n ,n 0
; n N 1
n
0; n N
Pn
0 1 ... n 1
1 2 ... n
n
P0 n . P0 P0 , n 0 ,1,..., N
n
24
M/M/1/N: normalizing constant
Let ρ=λ/μ
P0 P1 ... PN 1
P0 . P0 .... . PN 1
N
P0 (1 ... ) 1
N
P0
(1
N 1
)
1
1 P0
1
1
N 1
As such
(1 )
n
Pn . P0
n
1
N 1
PN
(1 )
(1
N
N 1
)
Probability of arriving
to a full waiting room
25
M/M/1/N: what percent of λ
gets into the queue?
Percentage of time the queue is full
is equal to PN
.75
.25
Not full
full
Rate of lost customers = λ.PN
Rate of customers getting in : λ.(1-PN)
Often referred to as effective customer arrival rate
.(1 PN )
Utilization of server
.(1 PN )
26
M/M/1/N: performance
measures
Mean # of customers in the system
L
1
( N 1)
1
N 1
N 1
LM/M./1
Mean queue length
L q L (1 P0 )
Waiting time in system: W = L/λ
Waiting time in queue: Wq = Lq/λ
27
M/M/1/N: equivalent systems
When an M/M/1/N queue is full
Continuous arrival
A system with loss
is equivalent to shutting up the service
For the duration during which the queue is full
And starting it up again when system no longer ful
This system is called a shut down system
This equivalence holds only when
the inter-arrival is exponential
28
Proof: rate diagrams
M/M/1/N system with loss
Consider the special case where N = 5
0
λ
1
μ
λ
2
μ
λ
μ
3
λ
μ
4
λ
5
λ
μ
. P0 . P1
( ). P1 . P0 . P2
.
.
( ). P5 . P4 . P5 . P5 . P4
29
Proof: rate diagrams (cont’d)
M/M/1/N shut down system
Consider the special case where N = 5
0
λ
1
μ
λ
μ
2
λ
3
μ
λ
μ
4
λ
5
μ
. P0 . P1
( ). P1 . P0 . P2
.
.
. P5 . P4
30
M/M/infinity: birth and death
equations Infinite number of
servers
μ
λ
.
.
n
n n .
Pn
0 1 ... n 1
1 2 ... n
n
1
P0 n . . P0 . . P0
. P0
n!
n!
n!
n
1
n
31
M/M/infinity: normalizing
constant
Pn
n
n!
. P0
P0 P1 ... Pn ... 1
P0
1!
P0
2
2!
. P0 ...
n
n!
. P0 ... 1
2
P0 1
... 1 P0 .e 1 P0 e
1!
2!
Pn
n
.e
n!
32
Erlang system: M/M/S/S
Finite number of
Servers = S
μ
λ
.
.
Pn
n
n!
. P0
2
S
P0 1
...
1
1!
2!
S!
P0
1
n0
n
n!
33
Erlang loss formula
What percent gets in and
What percent gets lost
PS = prob S customers in system
/ S!
S
PS
S
n0
n
Erlang loss formula
n!
Effective arrival rate
.(1 PS )
Rate of lost customers = λ.PS
34
Erlang B formula
Probability of finding all s servers busy
, =
!
=0
!
In an iterative form:
( − 1, )
, =
+ ( − 1, )
0, = 1
35
``` | 6,134 | 8,305 | {"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-2016-44 | latest | en | 0.757447 |
https://studydaddy.com/question/phoebe-realizes-that-she-has-charged-too-much-on-her-credit-card-and-has-racked | 1,603,925,059,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107902038.86/warc/CC-MAIN-20201028221148-20201029011148-00006.warc.gz | 537,904,322 | 7,799 | Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
Phoebe realizes that she has charged too much on her credit card and has racked up \$6,400 in debt.
Phoebe realizes that she has charged too much on her credit card and has racked up \$6,400 in debt. If she can pay \$225 each month and the card charges 16 percent APR (compounded monthly), how long will it take her to pay off the debt? (Do not round intermediate calculations and round your final answer to 2 decimal places.) | 126 | 551 | {"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} | 2.9375 | 3 | CC-MAIN-2020-45 | latest | en | 0.979143 |
https://www.scaffoldedmath.com/2023/12/discovering-sum-of-interior-angles-polygons.html?m=0 | 1,709,591,527,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476532.70/warc/CC-MAIN-20240304200958-20240304230958-00011.warc.gz | 976,850,922 | 19,233 | ## Pages
### Sums of angles in polygons hands-on discovery
Ripping the corners off a triangle to prove the sum of its interior angles is 180 degree is my favorite visual proof. Over the weekend, I posted a couple short videos for finding the sum of interior angles in a polygon, so here I wanted to share the videos and the worksheets from the videos.
Sum of interior angles - triangle and quadrilateral video
Above is a short, 17-second video showing the sum of a triangle's interior angles is 180 degrees, and the sum of a quadrilateral's interior angles is 360 degrees.
Sum of interior angles of a pentagon video
This second short shows the sum of the interior angles of a pentagon is 540 degrees. The angles needed a bit of trimming to fit together, but clearly showed the "circle and a half". How cool is it that we can show these proofs using cut paper?
If you'd like the triangle, quadrilateral and pentagon shapes worksheets from the videos, they are here in my Google Drive.
Geometry Word Wall reference
A teacher emailed to ask if I had a math word wall reference for the sums of interior angles of polygons. I added the above reference to the Geometry Word Wall today.
Free math resource library | 258 | 1,220 | {"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} | 2.8125 | 3 | CC-MAIN-2024-10 | latest | en | 0.893928 |
https://www.calculatormix.com/calculators/depreciation/ | 1,721,631,718,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517833.34/warc/CC-MAIN-20240722064532-20240722094532-00107.warc.gz | 589,885,543 | 12,532 | # Depreciation Calculator
Year
1
2
3
4
5
Depreciation Amount
4000
2400
1440
864
518
Item Value
6000
3600
2160
1296
777
Depreciation Bar Chart:
Depreciation is the reduction of the value of an asset over a period of time. This calculator features two of the most popular ways of determining roughly how much something will depreciate on a yearly basis; straight-line and declining balance depreciation.
## The Straight Line Depreciation Method
The most popular and simple way of determining depreciation is with the straight-line formula. To calculate this, we subtract the final salvage cost from the asset cost then divide that by the number of years of ownership.
The formula for the straight line can be written like this:
`Depreciation per year = (asset cost - salvage value) / years`
This is a nice way of giving you an idea of total depreciation but doesn't take into account that newer assets tend to depreciate faster.
## Declining Balance Depreciation
Many assets depreciate faster when they are new. In those cases, it is better to use a declining balance formula, which uses a factor to determine the depreciation rate.
For each year, a double declining balance is calculated by multiplying the current asset value by the depreciation rate (factor).
`New value = current asset value * depreciation factor` | 291 | 1,327 | {"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} | 2.96875 | 3 | CC-MAIN-2024-30 | latest | en | 0.862622 |
https://www.physicsforums.com/threads/interference-of-different-lights.469375/ | 1,701,754,398,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100545.7/warc/CC-MAIN-20231205041842-20231205071842-00587.warc.gz | 1,058,418,667 | 16,232 | Interference of different lights
• Dimani4
In summary, two lasers of different wavelengths can produce interference when they are close together. This interference results in a different color being perceived.
Dimani4
Hi ppl,
I have a question to you. What happens if we approach two lasers with different wavelengths close together while they going in the same direction?
---------------->
-.-.-.-.-.-.-.-.-.>
did we get the interference between the different wave length of lasers result the different wavelength means different color?
as here: http://www.olympusmicro.com/primer/java/interference/index.html
what happens if we point these two lasers at one point? did we get the different color?
how close they should be to get the interference between them (minimum distance)?
thank you.
Last edited:
This is interesting! I have frequently read that in dual slit type experiments that individual photons only interfere with themselves, while the posted link suggests this not true.
yes for me it was also interesting. 2day I've asked some ppl about that question and I think that the interference of the two photons from the different lasers with different wavelength is possible from the theoretic point of view but very complicated practically because of of coherence length of the lasers. when we speak about two lasers with different phases when we try to add their electric field and find out the electric flux that will carry this wave we get just the sums of the two intensities of each wave. like this:
E1=A1exp(i(w1t-k1x));
E2=A2exp(i(w2t-k2x-phase));
Etotal=E1+E2 and Itotal=I1+I2 (I1=A1^2;I2=A2^2)and there is no interference between the two waves. All we get it's just a higher intensity because more photons are in the region when the two lasers together.
But in the case of the two equal lasers with the same phase we get real the intereference in the energy flux equation, like
E1=A1exp(i(wt-kx))
E2=A2exp(i(wt-kx))
Etotal=(A1+A2)exp(i(wt-kx))
Itotal=A1^2+A2^2+A1XA2*+A2XA1*, so here we see the interference pattern (A1XA2*+A2XA1*) that actually play significant role in the increasing of the energy flux of the additive waves.
Actually to get two lasers with the same phases almost impossible. As I know in practice the laser can be splited into the two waves with the beam splitter and afterwards these two equal waves can be added (holography).
Dimani4 said:
Hi ppl,
I have a question to you. What happens if we approach two lasers with different wavelengths close together while they going in the same direction?
---------------->
-.-.-.-.-.-.-.-.-.>
did we get the interference between the different wave length of lasers result the different wavelength means different color?
You don't have a single wavelenght anylonger, so you have a wave, no more sinusoidal (I assume both lasers are monochromatic) which Fourier spectrum is given by the sum of two Dirac Delta functions located in two different points (the two lasers' wavelenghts).
The colour, intended as perception, changes in a very simple way, known from the theory of colours, the same which allows you to see a yellow spot in you PC monitor as given by the mixing of green and red pixels. Blue+red = violet/magenta, blue+green = cyan, red+yellow = orange, and so on.
lightarrow said:
You don't have a single wavelenght anylonger, so you have a wave, no more sinusoidal (I assume both lasers are monochromatic) which Fourier spectrum is given by the sum of two Dirac Delta functions located in two different points (the two lasers' wavelenghts).
The colour, intended as perception, changes in a very simple way, known from the theory of colours, the same which allows you to see a yellow spot in you PC monitor as given by the mixing of green and red pixels. Blue+red = violet/magenta, blue+green = cyan, red+yellow = orange, and so on.
thanx man. very clear explanation. | 902 | 3,876 | {"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-2023-50 | latest | en | 0.916386 |
http://www.expertsmind.com/library/environmental-economics-5141.aspx | 1,524,586,753,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946807.67/warc/CC-MAIN-20180424154911-20180424174911-00020.warc.gz | 423,301,506 | 9,875 | +1-415-670-9189
info@expertsmind.com
# Get Solution
Environmental economics
Course:- Public Economics
Reference No.:- EM13141
Tweet
Expertsmind Rated 4.9 / 5 based on 47215 reviews.
Review Site
Assignment Help >> Public Economics
Use Excel formulas to calculate everything.
There are three alternative plans that indicate the benefits and costs associated with the construction of a Manitoba hazardous waste facility (see table on next page).
a. For the three alternatives calculate the net present value and benefit-cost ratio for four different discount rates (0%, 6%, 12%, 18%). You must use Excel or some other spreadsheet program and do not use the built in formula for net present value.
b. Create a ranking for each of the discount rates based on their net present values. Based on the ranking which alternative would you choose at each discount rate?
c. On a single graph show the impact of discount rates on net present value for each alternative. The vertical access should be net present value and on the horizontal access should be discount rate.
Indicate on the graph the lowest approximate discount rate where each alternative should not be undertaken.
Minimize
Ask Question & Get Answers from Experts
Browse some more (Public Economics) Materials
What is the empirical evidence regarding the usefulness of the expectations hypothesis of the term structure (EHTS) for explaining future spot interest rates? How well does th A generous university benefactor has agreed to donate a large amount of money for student scholarships. The money can be provided in one lump sum of \$12 million in Year 0 (t How could the Klamath Basin water shortage have been avoided? And how can we avoid this situation in the future and how do we decide between "fish vs farmers" in general? Oct. 17. Sold office equipment in exchange for \$135,000 cash plus receipt of a \$1,00,000, 90-day, 9% note. The equipment had a cost of \$320,000 and accumulated depreciation What are the key characteristics of a monopolistically competitive market? Some experts have argued that too many brands of breakfast cereal are on the market. Give an argum The GDP in country I is \$2,900 per capita-or about \$3.3 trillion for all of country I. If country I expect growth in GDP to be about 7% for next year, health expenditures sh List and briefly describe the dependent and independent variables. What theoretical basis or conceptual framework does the author utilize in framing an understanding of the p In a single posting, describe in detail how you would address this growing problem using each of the policing styles listed above. Explain which approach is best, using rese | 556 | 2,672 | {"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-2018-17 | longest | en | 0.909319 |
http://mathhelpforum.com/pre-calculus/168091-matrices-linear-equations.html | 1,481,445,612,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698544358.59/warc/CC-MAIN-20161202170904-00121-ip-10-31-129-80.ec2.internal.warc.gz | 173,198,702 | 12,401 | # Thread: Matrices - Linear equations
1. ## Matrices - Linear equations
I don't quite understand how to use that augmented matrix to prove anything about a, b and c.
Any ideas on where to start?
2. The above image seems a bit hard to read.
Here is another question similar in format, though, and it's clearer:
It's part of our matrices unit but I'm not sure how to incorporate that into this question.
3. 25. You know four points that lie on the curve, $\displaystyle (0, 10), (1, 7), (3, -11), (4, -14)$.
So that means they all satisfy the equation $\displaystyle y = a\,x^3 + b\,x^2 + c\,x + d$.
So
$\displaystyle 10 = a\cdot 0^3 + b\cdot 0^2 + c\cdot 0 + d$
$\displaystyle 7 = a\cdot 1^3 + b\cdot 1^2 + c\cdot 1 + d$
$\displaystyle -11 = a\cdot 3^3 + b\cdot 3^2 + c\cdot 3 + d$
$\displaystyle -14 = a\cdot 4^3 + b\cdot 4^2 + c\cdot 4 + d$.
So now you can set up your matrix equation...
$\displaystyle \left[\begin{matrix}0 & 0 & 0 & 1 \\ 1 & 1 & 1 & 1\\ 27 & 9 & 3 & 1 \\ 64 & 16 & 4 & 1\end{matrix}\right]\left[\begin{matrix}a \\ b\\ c\\d \end{matrix}\right] = \left[\begin{matrix}\phantom{-}10 \\ \phantom{-}7 \\ -11 \\ -14\end{matrix}\right]$
4. .I usually write the constants in the same brackets as the large matrix here (to the furthest right side of the matrix, since that's what we were taught). So:
0 0 0 1 10
1 1 1 1 7
27 9 3 1 -11
64 16 4 1 -14
Is that right?
Would I use Gauss-Jordan to reduce that into reduced row-echelon?
I'm still confused about how to find the variables from there.
5. .
6. [QUOTE=TN17;604092].I usually write the constants in the same brackets as the large matrix here (to the furthest right side of the matrix, since that's what we were taught). So:
0 0 0 1 10
1 1 1 1 7
27 9 3 1 -11
64 16 4 1 -14
Is that right?/[quote]
Yes, that is what is meant by the "augmented" matrix.
Would I use Gauss-Jordan to reduce that into reduced row-echelon?
I'm still confused about how to find the variables from there.
Yes, you certainly could use Gauss-Jordan. I would be inclined to swap the first row to the last initially to get
$\begin{bmatrix}1 & 1 & 1 & 1 & 7 \\ 27 & 9 & 3 & 1 & -11\\ 64 & 16 & 4 & 1 & -14 \\ 0 & 0 & 0 & 1 & -14\end{bmatrix}$
Then subtract 27 times the first row from the second, 64 times the first row from the third, etc.
7. If you have a CAS, it's quite simple if you know that the solution to the matrix equation
$\displaystyle \mathbf{A}\mathbf{x} = \mathbf{b}$
is
$\displaystyle \mathbf{x} = \mathbf{A}^{-1}\mathbf{b}$...
8. Originally Posted by Prove It
If you have a CAS, it's quite simple if you know that the solution to the matrix equation
$\displaystyle \mathbf{A}\mathbf{x} = \mathbf{b}$
is
$\displaystyle \mathbf{x} = \mathbf{A}^{-1}\mathbf{b}$...
On the other hand, if you want to actually learn some linear algebra there is no better way than doing it by hand!
9. Originally Posted by HallsofIvy
On the other hand, if you want to actually learn some linear algebra there is no better way than doing it by hand!
I disagree, using matrix algebra to solve matrix equations and then programming a computer/CAS to perform the tedious calculations that you are almost certain to make a mistake with is far more beneficial.
10. I'll meet you guys halfway. To maximise understanding the OP should know how to solve a system like the one above by hand. Once confident with such methods then use technology to save time. | 1,080 | 3,405 | {"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": 0, "img_math": 0, "codecogs_latex": 12, "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} | 4.5625 | 5 | CC-MAIN-2016-50 | longest | en | 0.884207 |
https://www.jiskha.com/display.cgi?id=1278349621 | 1,503,277,279,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107065.72/warc/CC-MAIN-20170821003037-20170821023037-00342.warc.gz | 919,778,245 | 4,223 | # Research and Statistics
posted by .
Here are heart rates for a sample of 30 students before and after a class break. At α = .05, was
there a significant difference in the mean heart rate? (a) State the hypotheses. (b) State the decision
rule and sketch it. (c) Find the test statistic. (d) Make a decision. (e) Estimate the p-value and
interpret it
Student Before After Student Before After
1 60 62 16 70 64
2 70 76 17 69 66
3 77 78 18 64 69
4 80 83 19 70 73
5 82 82 20 59 58
6 82 83 21 62 65
7 41 66 22 66 68
8 65 63 23 81 77
9 58 60 24 56 57
10 50 54 25 64 62
11 82 93 26 78 79
12 56 55 27 75 74
13 71 67 28 66 67
14 67 68 29 59 63
15 66 75 30 98 82
• Research and Statistics -
dlpjd
## Similar Questions
1. ### statistics
Does lovastatin reduce the risk of heart attack?
2. ### Statistics
In a test of hypotheses, the null hypothesis is that the mean is 100 and the alternate hypothesis is that the mean is greater than 100. The power of the test when the mean is 101 would be greatest for which of the following choices …
3. ### Statistics
Here are heart rates for a sample of 30 students before and after a class break. At รก = .05, was there a significant difference in the mean heart rate?
4. ### college
Here are heart rates for a sample of 30 students before and after a class break. At α = .05, was there a significant difference in the mean heart rate?
5. ### university of phoenix
Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack?
6. ### UOP
o test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of …
7. ### Statistics
The Deborah Heart Institute performs many open-heart surgery procedures. Recently research physicians at the Institute developed a new heart bypass procedure that they believe reduces the average length of recovery. The hospital board …
8. ### statistics
The Deborah Heart Institute performs many open-heart surgery procedures. Recently research physicians at the Institute developed a new heart bypass procedure that they believe reduces the average length of recovery. The hospital board …
9. ### Biology
Hey I am doing a lab, the link is down h t t p : //w w w . sd67 . bc . ca/schools/salc/biology%2012/module%20c%20-%20human%20biology/unit%2010%20-%20respiratory%20system/Homeostasis%20Lab .pdf And I really would like help with #1 My …
10. ### Health (Check)
1. Lucille has been told she needs to improve her heart health, and she is ready to get started. There are many activities she is considering for her new routine, but she knows she must first calculate her target heart rate zone. When …
More Similar Questions | 757 | 2,779 | {"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 | 3 | CC-MAIN-2017-34 | latest | en | 0.882098 |
https://www.slideshare.net/sadique_ghitm/a-study-on-face-recognition-technique-based-on-eigenface | 1,495,727,787,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608084.63/warc/CC-MAIN-20170525140724-20170525160724-00085.warc.gz | 945,105,387 | 37,041 | Upcoming SlideShare
Loading in …5
×
# A study on face recognition technique based on eigenface
1,384 views
Published on
A Study on Face Recognition Technique Based on Eigenface
0 Comments
2 Likes
Statistics
Notes
• Full Name
Comment goes here.
Are you sure you want to Yes No
Your message goes here
• Be the first to comment
No Downloads
Views
Total views
1,384
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
2
Embeds 0
No embeds
No notes for slide
### A study on face recognition technique based on eigenface
1. 1. A STUDY ON FACE RECOGNITION TECHNIQUE BASED ON EIGENFACE By: Sadique Nayeem Pondicherry University
2. 2. Outline Overview Eigenface Algorithm Implementation Image Database Experimental Result Future Enhancement Conclusions 2
3. 3. Overview Face recognition system consist of three component. Face Representation: How to model a face? Template-based approaches Feature-based approaches Appearance-based approaches Face Detection: To locate a face in image. Manipulation of images in “face space” Utilization of elliptical shape of human head Face Identification: Compare given image with database. Performance affected by scale, pose, illumination, facial expression, and disguise, etc. 3
4. 4. Eigenfaces Approach In the language of information theory… the main objective is to mine the relevant information in a face image, encode it as efficiently as possible and compare one face encoding with a database of face images encoded in the same process. In mathematical terms… Find the principal components of the face distribution, or the eigenvectors of the covariance matrix of the set of face images, called e ig e nface s. Eigenfaces are a set of features that characterize the variation between face images. Each training face image can be represented in terms of a linear combination of the eigenfaces, so can the new input image. Compare the feature weights of the new input image with those of the known individuals 4
5. 5. Eigenface Initialization The eigenfaces approach for face recognition involves the following initialization operations: Acquire a set of training images. Calculate the eigenfaces from the training set, keeping only the best M images with the highest eigenvalues. These M images define the “face space”. As new faces are experienced, the eigenfaces can be updated. Calculate the corresponding distribution in M-dimensional weight space for each known individual (training image), by projecting their face images onto the face space. 5
6. 6. Eigenface Recognition Having initialized the system, the following steps are used to recognize new face images: Given an image to be recognized, calculate a set of weights of the Meigenfaces by projecting it onto each of the eigenfaces. Determine if the image is a face at all by checking to see if the image is sufficiently close to the face space. If it is a face, classify the weight pattern as either a known person or as unknown. 6 Figure : Eigenfaces of Essex face database -'face94'
7. 7. Image Database Name of database Source Image format Image size Image type Number of unique individual Total numbe rof images Variations Sample Image IFD IIT Kanpur [3] JPG 110 X 75 Color 60 660 8 pose, 3 emotion Essex face databas e -face94 University of Essex, UK [4] JPG 90 X 100 Color 152 3040 facial expression, slight head tilt. Yale Yale university [5] GIF 320 X 243 Grey 15 165 facial expression, w/o glasses Face 1999 California Institute of Technolo gy [6] JPG 300X198 Color 26 450 lighting, expression, background 7
8. 8. Experimental Result 8 Eigenface face recognition with different sample images Name of databas e Total No. of unique person No. of samples of each image in training set No. of image in training set No. of False recognition Accuracy rate (%) IFD 60 1 60 31 49.18 2 120 25 59.01 3 180 16 73.77 4 240 16 73.77 5 300 12 80.32 6 360 8 86.88 7 420 3 95.08 8 480 2 96.72 9 540 1 98.36 10 600 1 98.36 11 660 1 98.36 Esse x face 152 1 152 47 69.07 2 304 29 80.92 3 456 12 92.10 4 608 11 92.76 5 760 11 92.76 6 912 10 93.42 7 1064 10 93.42 8 1216 9 94.07 9 1368 8 94.73 10 1520 8 94.73 11 1672 6 96.05 Yale 15 1 15 8 46.66 2 30 2 86.66 3 45 3 80.00 4 60 3 80.00 5 75 2 86.66 6 90 1 93.33 7 105 2 86.66 8 120 1 93.33 9 135 1 93.33 10 150 1 93.33 11 165 1 93.33 Face 1999 26 1 26 17 34.61 2 52 15 42.30 3 78 14 46.15 4 104 9 65.38 5 130 9 65.38 6 156 8 69.23 7 182 5 80.76 8 208 5 80.76 9 234 3 88.46 10 260 2 92.30 11 286 1 96.15 Eigenface face recognition with different sample images Name of databas e Total No. of unique person No. of samples of each image in training set No. of image in training set No. of False recognition Accuracy rate (%)
9. 9. Experimental Result (cont..) 9 Number of samples
10. 10. Future Enhancement According to the experimental result, recognition with one sample per person does not give better recognition rate in all cases. But, in real time application only one sample per person will be available ( as in case of voter card, Driving license, passport or ADHAAR Card). So, recognition from single sample per person is needed. One sample per person is easy to collect, save storage cost and save computational cost. 10 Courtesy: http://images.google.co.in/
11. 11. Problem Statement This problem can be defined as follows: “Given a stored database of faces with only one image per person, the goal is to identify a person from the database later in time in any different and unpredictable poses, lighting, disguise, etc from the individual image.” 11
12. 12. Proposed Idea 1.2 billion population of India is being enrolled for ADHAAR Card with different biometric. Face image is also being collected. The ADHAAR Card or UID no. can be used as a platform on which different application can be developed as under: 12 ADHAAR CARD or UID NUMBER
13. 13. Proposed Idea (contd.) To restrain the crime, ADHAAR Card can be the best source for identification. Individual images in ADHAAR Card may work as training set. CCTV images from crime scene can be used as test image. Procedure: Capture the video from the CCTV camera. Detect the human face in the CCTV video. Take the CCTV image as the test image. Do the preprocessing on the CCTV image i.e Crop both the eyes, eyebrow, nose, and mouth. Load the ADHAAR based Face image as the training image Crop both the eyes, eyebrow, nose, and mouth Apply the Eigenface PCA for the Recognition 13
14. 14. Conclusions Eigenface PCA is one of the most successful technique and it gives better result for more number of samples in training set. It does not produce good result for single sample per person. The need for real time application can be given by only single sample per person. Taking ADHAAR Card as a platform, Artificial Face Recognition system can be developed by using PCA on reconstructed image. 14
15. 15. Reference 1. “Eigenfaces for recognition”, M. Turk and A. Pentland, Jo urnalo f Co g nitive Ne uro scie nce , vo l. 3, No . 1 , 1 9 9 1 2. “Automatic recognition and analysis of human faces and facial expressions: A survey”, A. Samal and P. A. Iyengar, Patte rn Re co g nitio n, 25(1 ): 6 5-7 7 , 1 9 9 2 3. “The Indian Face Database”, Vidit Jain, Amitabha Mukherjee, 2002, http://vis- www. cs. um ass. e du/~ vidit/IndianFace Database / 4. “Essex face database -face94”, University of Essex, UK, http: //cswww. e sse x. ac. uk/m v/allface s/inde x. htm l 5. “Yale Database”, http: //cvc. yale . e du/pro je cts/yale face s/yale face s. htm l 6. “FACE 1999”, http: //www. visio n. calte ch. e du/htm l-file s/archive . htm l 15
16. 16. Thank You ! 16 | 2,228 | 7,691 | {"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-2017-22 | latest | en | 0.784972 |
http://oeis.org/A331613 | 1,606,403,536,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141188800.15/warc/CC-MAIN-20201126142720-20201126172720-00432.warc.gz | 66,957,080 | 4,566 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A331613 Odd exceptional numbers: odd k such that A005179(k) < A037019(k). 0
243, 729, 1215, 2187, 3645, 6561, 10935, 15309, 19683, 32805, 45927, 54675, 59049, 98415, 137781, 164025, 177147, 216513, 255879, 273375, 295245, 334611, 373977, 413343, 452709, 492075, 531441, 570807, 610173, 649539, 688905, 728271, 767637, 807003, 820125, 846369, 885735, 925101 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS This sequence is infinite, because 3^p is a term for all p >= 5. It seems that the smallest p-rough exceptional number (i.e., the smallest exceptional number whose smallest prime factor is p) is p^k, where k is the smallest number such that prime(k) > 2^p (p = 2 gives 2^3 = 8, p = 3 gives 3^5 = 243, p = 5 gives 5^12 = 244140625, ...). LINKS M. E. Grost, The smallest number with a given number of divisors, Amer. Math. Monthly, 75 (1968), 725-729. EXAMPLE The smallest number with 243 divisors is 2^8 * 3^2 * 5^2 * 7^2 = 2822400, while A037019(243) = 2^2 * 3^2 * 5^2 * 7^2 * 11^2 = 5336100 > A005719(243), so 243 is a term. PROG (PARI) isA331613(n) = (n%2) && A037019(n) > A005179(n) \\ See A005179 and A037019 for their programs CROSSREFS Cf. A072066 (exceptional numbers), A005179, A037019. Sequence in context: A232924 A067838 A255111 * A255626 A205049 A235540 Adjacent sequences: A331610 A331611 A331612 * A331614 A331615 A331616 KEYWORD nonn AUTHOR Jianing Song, Jan 22 2020 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.) | 742 | 2,188 | {"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} | 3.6875 | 4 | CC-MAIN-2020-50 | latest | en | 0.683925 |
https://chem.libretexts.org/Courses/University_of_California_Davis/Chem_107B%3A_Physical_Chemistry_for_Life_Scientists/Chapters/2%3A_Chemical_Kinetics/2.4B%3A_Steady-State_and_Pre-equilibrium_Approximations | 1,723,436,856,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641028735.71/warc/CC-MAIN-20240812030550-20240812060550-00594.warc.gz | 124,557,103 | 30,902 | # 2.4B: Steady-State and Pre-equilibrium Approximations
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vectorC}[1]{\textbf{#1}}$$
$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$
$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$
$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
The steady state approximation, occasionally called the stationary-state approximation, involves setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero. It is important to note that steady state approximation does not assume the reaction intermediate concentration to be constant (and therefore its time derivative being zero), it assumes that the variation in the concentration of the intermediate is almost zero: the concentration of the intermediate is very low, so even a big relative variation in its concentration is small, if considered quantitatively.
Its use facilitates the resolution of the differential equations that arise from rate equations, which lack an analytical solution for most mechanisms beyond the most simple ones. The steady state approximation is applied, for example in Michaelis-Menten kinetics. As an example, the steady state approximation will be applied to two consecutive, irreversible, homogeneous first order reactions in a closed system. If the rate constants for the following reaction are $$k_1$$ and $$k_2$$;
$A \rightarrow \; B \rightarrow \; C$
combining the rate equations with a mass balance for the system yields for following differential rate laws:
For species A:
$\dfrac{d[A]}{dt} = -k_1 [A]$
For species B:
$\dfrac{d[B]}{dt} = k_1 [A] - k_2 [B]$
For species C:
$\dfrac{d[C]}{dt} = k_2 [B]$
The analytical solutions for these equations (supposing that initial concentrations of every substance except for A are zero) are:
$[A]=[A]_0 e^{-k_1 t}$
$\left[ B \right]=\left\{ \begin{matrix} \left[ A \right]_{0}\dfrac{k_{1}}{k_{2}-k_{1}}\left( e^{-k_{1}t}-e^{-k_{2}t} \right);\,\,k_{1}\ne k_{2} \\ \left[ A \right]_{0}k_{1}te^{-k_{1}t}\;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{matrix} \right.$
$\left[ C \right]=\left\{ \begin{matrix} \left[ A \right]_{0}\left( 1+\dfrac{k_{1}e^{-k_{2}t}-k_{2}e^{-k_{1}t}}{k_{2}-k_{1}} \right);\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k_{1}\ne k_{2} \\ \left[ A \right]_{0}\left( 1-e^{-k_{1}t}-k_{1}te^{-k_{1}t} \right);\,\,\,\,\,\,\text{otherwise} \\ \end{matrix} \right.$
If the steady state approximation is applied, then the derivative of the concentration of the intermediate is set to zero.
$\dfrac{d[B]}{dt} = 0 = k_1 [A] - k_2 [B] \Rightarrow \; [B] = \dfrac{k_1}{k_2} [A]$
therefore
$\dfrac{d[C]}{dt} = k_1 [A] so [C]=[A]_0 \left (1- e^{-k_1 t} \right ).$
## Validity of Approximation
The analytical and approximated solutions should now be compared in order to decide when it is valid to use the steady state approximation. The analytical solution transforms into the approximate one when $$k_2 \gg k_1$$, because then $$e^{-k_2t} \ll e^{-k_1t}$$ and $$k_2-k_1 \approx \; k_2$$. Therefore it is valid to apply the steady state approximation only if the second reaction is much faster than the first one ($$k_2/k_1 > 10$$ is a right criterion), because that means that the intermediate forms slowly and reacts readily so its concentration stays low.
The graphs show concentrations of A (red), B (green) and C (blue) in two cases, calculated from the analytical solution:
• When the first reaction is faster it is not valid to assume that the variation of $$[B]$$ is very small, because $$[B]$$ is neither low or close to constant: first $$A$$ transforms into $$B$$ rapidly and $$B$$ accumulates because it disappears slowly. As the concentration of $$A$$ decreases its rate of transformation decreases, at the same time the rate of reaction of B into C increases as more B is formed, so a maximum is reached when
$t=\left\{ \begin{matrix} \dfrac{\ln \left( \dfrac{k_{1}}{k_{2}} \right)}{k_{1}-k_{2}} & \, k_{1} \ne k_{2} \\ \dfrac{1}{k_{1}} & \, otherwise \\ \end{matrix} \right..$
From then on the concentration of $$B$$ decreases.
• When the second reaction is faster, after a short induction period, concentration of $$B$$ remains low (and more or less constant) because its rate of formation and disappearance are almost equal and the steady state approximation can be used.
The equilibrium approximation can be used sometimes in chemical kinetics to yield similar results as the steady state approximation (Michaelis-Menten kinetics can be derived assuming equilibrium instead of steady state): it consists in assuming that the intermediate is at chemical equilibrium. Normally the requirements for applying the steady state approximation are laxer: the concentration of the intermediate is only needed to be low and more or less constant (as seen, this has to do only with the rates at which it appears and disappears), but it is not needed to be at equilibrium, which is usually difficult to prove and involves heavier assumptions.
## Contrbutors
• Sourced from World Heritage Encyclopedia
2.4B: Steady-State and Pre-equilibrium Approximations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. | 3,103 | 9,342 | {"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} | 3.546875 | 4 | CC-MAIN-2024-33 | latest | en | 0.199689 |
https://www.shaalaa.com/question-bank-solutions/solve-the-following-problem-if-laspeyre-s-and-dorbish-s-price-index-numbers-are-1502-and-1528-respectively-find-paasche-s-price-index-number-construction-of-index-numbers-weighted-aggregate-method_157563 | 1,695,535,622,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506623.27/warc/CC-MAIN-20230924055210-20230924085210-00434.warc.gz | 1,094,658,791 | 9,500 | # Solve the following problem : If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number. - Mathematics and Statistics
Sum
Solve the following problem :
If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number.
#### Solution
Given, P01(L) = 150.2, P01(D-B) = 152.8
Dorbish-Bowley’s Price Index Number:
P01(D-B) = ("P"_01("L") + "P"_01("P"))/(2)
∴ 152.8 = (150.2 + "P"_01("P"))/(2)
∴ 305.6 = 150.2 6 + P01(P)
∴ P01(P) = 305.6 – 150.2 = 155.4
Concept: Construction of Index Numbers - Weighted Aggregate Method
Is there an error in this question or solution?
Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]
#### APPEARS IN
Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.14 | Page 93
Share | 298 | 929 | {"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} | 4.0625 | 4 | CC-MAIN-2023-40 | latest | en | 0.680761 |
https://www.studypool.com/discuss/4852345/homework-for-physics-206-L- | 1,576,390,382,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575541301598.62/warc/CC-MAIN-20191215042926-20191215070926-00452.warc.gz | 872,653,541 | 27,423 | # homework for physics 206 L
Anonymous
### Question Description
the instructions on this file
### Unformatted Attachment Preview
PHYS 206L Magnetic Induction Homework (Due 10.26.17) 1) In a mass spectrometer, a single-charged particle (charge e) has a speed of 1.0 x 106 m/s and enters a uniform magnetic field of 0.20 T. The radius of the circular orbit is 0.020 m. What is the mass of the particle? 2) A beam of electrons is accelerated through a potential difference of 10 kV before entering a velocity selector. If the B-field of the velocity selector has a value of 0.010 T, what value of the E-field is required if the particles are to be un-deflected? 3) A solenoid with 500 turns is 0.10 m long and carries a current of 4.0 A. What strength of magnetic field will it have at its center? 4) How much current must pass through a 400 turn coil 4.0 cm long to generate a 1.0 T magnetic field at the center? 5) What is the strength of a magnetic field 5.0 cm from a long straight wire carrying 4.0 A of current? 6) A very long straight wire carries a current of 25 A. What is the magnitude of the magnetic field at a distance of 0.15 m from the wire? 7) A high power line carrying 1000 A generates what magnetic field at the ground, 10 m away? -3 8) How much current must flow for 1.0 x 10 T of magnetic field to be present 1.0 cm from a wire? 9) At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the -5 magnetic field due to the wire equal to the strength of the Earth's magnetic field of about 5.0 x 10 T? 10) What fundamental fact underlies the operation of essentially all electric motors? A) Opposite electric charges attract and like charges repel. B) A current-carrying conductor placed perpendicular to a magnetic field will experience a force. C) Alternating current and direct current are both capable of doing work. D) Iron is the only element that is magnetic. E) A magnetic north pole carries a positive electric charge, and a magnetic south pole carries a negative electric charge. ...
Purchase answer to see full attachment
School: University of Maryland
Please find the attached and go though it. In case of anything feel free to mention it.
Surname: 1
Name
Course
Tutor
Date
Magnetic Induction
1. In a mass spectrometer, a single charged particle (charge e) qhas a speed of 10*10^6m/s and
enters a uniform magnetic field of 0.20T.the radius of a circular orbit is 0.020m.What is the mass
of the particle?
Solution
Speed=10*10^6m/s
Magnetic field=0.20T
Mass of the particle
Magnetic field=u*3.142*pi*mass
0.20=1.0*10^6*3.142Pi*mass
0.20=3142000m
=0.637*10^-8kg
2. A beam of electrons is accelerated through a potential difference of 10KV before enteri...
flag Report DMCA
Review
Anonymous
The tutor was pretty knowledgeable, efficient and polite. Great service!
Anonymous
Heard about Studypool for a while and finally tried it. Glad I did caus this was really helpful.
Anonymous
Just what I needed… fantastic!
Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4
Brown University
1271 Tutors
California Institute of Technology
2131 Tutors
Carnegie Mellon University
982 Tutors
Columbia University
1256 Tutors
Dartmouth University
2113 Tutors
Emory University
2279 Tutors
Harvard University
599 Tutors
Massachusetts Institute of Technology
2319 Tutors
New York University
1645 Tutors
Notre Dam University
1911 Tutors
Oklahoma University
2122 Tutors
Pennsylvania State University
932 Tutors
Princeton University
1211 Tutors
Stanford University
983 Tutors
University of California
1282 Tutors
Oxford University
123 Tutors
Yale University
2325 Tutors | 970 | 3,645 | {"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} | 2.90625 | 3 | CC-MAIN-2019-51 | latest | en | 0.892987 |
https://www.solutioninn.com/let-a-and-b-be-n-n-matrices-with | 1,623,876,710,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487626008.14/warc/CC-MAIN-20210616190205-20210616220205-00611.warc.gz | 914,538,670 | 9,814 | # Let A and B be n × n matrices with
Let A and B be n × n matrices with eigenvalues λ and μ, respectively.
(a) Give an example to show that λ + μ need not be an eigenvalue of A + B.
(b) Give an example to show that λμ need not be an eigenvalue of AB.
(c) Suppose λ and μ correspond to the same eigenvector x. Show that, in this case, λ + μ is an eigenvalue of A + B and λμ is an eigenvalue of AB.
Members
• Access to 2 Million+ Textbook solutions
• Ask any question from 24/7 available
Tutors
\$9.99
OR
Non-Members
Get help from Linear Algebra Tutors
Ask questions directly from Qualified Online Linear Algebra Tutors .
Best for online homework assistance. | 178 | 662 | {"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-2021-25 | latest | en | 0.825905 |
https://www.activityshelter.com/odd-and-even-number-worksheets/ | 1,722,874,526,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640451031.21/warc/CC-MAIN-20240805144950-20240805174950-00620.warc.gz | 506,168,431 | 43,892 | Being able to determine a number as odd or even is one assessment that children or student have to pass. To make them understand the concept of odd and even numbers, they have to be exposed to the real problems of differentiating the odd numbers from the even ones.
Such experience in solving odd and even problems can be found in these odd and even number worksheets for students.
image via gopixpic.com
These odd and even number worksheets are purposed to train and test children’s knowledge and ability in determining the kind of numbers. These worksheets will help them in learning the basics of number’s classification in order to be able to recognize the kind of numbers once they see them. Moreover, the various exercises provided in these worksheets enable them to study the key concept of odd and even numbers. Check out the other worksheets in the images below!
image via mibb-design.com | 176 | 901 | {"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-2024-33 | latest | en | 0.956698 |
http://www.brightstorm.com/tag/exponential-growth/ | 1,432,300,045,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207925201.39/warc/CC-MAIN-20150521113205-00174-ip-10-180-206-219.ec2.internal.warc.gz | 350,024,164 | 12,928 | • #### Exponential Growth and Decay - Concept
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to use the exponential growth and decay formula.
• #### Exponential Growth and Decay - Problem 3
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to use exponential growth to find the size of a population.
• #### Exponential Growth and Decay - Concept
##### Math›Precalculus›Exponential and Logarithmic Functions
How to find the doubling time of a population when the growth rate is given.
• #### The Differential Equation Model for Exponential Growth - Problem 1
##### Math›Calculus›Antiderivatives and Differential Equations
How to solve a differential equation that describes exponential growth or exponential decay.
• #### The Differential Equation Model for Exponential Growth - Problem 3
##### Math›Calculus›Antiderivatives and Differential Equations
How to solve differential equations that are related to exponential growth or exponential decay.
• #### The Differential Equation Model for Exponential Growth - Concept
##### Math›Calculus›Antiderivatives and Differential Equations
How to use differential equations to represent exponential growth or exponential decay.
• #### Exponential Growth and Decay - Problem 1
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to solve a carbon-14 dating question.
• #### Exponential Growth and Decay - Problem 2
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to use exponential decay to find the amount of drug left in somebody's blood stream.
• #### Exponential Growth and Decay - Problem 5
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to use exponential decay to predict how much an item will be worth after a certain amount of time
• #### The Differential Equation Model for Exponential Growth - Problem 2
##### Math›Calculus›Antiderivatives and Differential Equations
How to use the general solution of the exponential growth equation to solve a similar differential equation.
• #### Exponential Growth and Decay - Problem 1
##### Math›Precalculus›Exponential and Logarithmic Functions
How to find the inflation rate of a tuition when the doubling time is given.
• #### Exponential Growth and Decay - Problem 4
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
Determine after how many years a product will be worth a certain amount.
• #### The Differential Equation Model for Exponential Growth - Problem 4
##### Math›Calculus›Antiderivatives and Differential Equations
How to find the temperature of cooling object by solving a differential equation.
• #### Exponential Growth and Decay - Problem 2
##### Math›Precalculus›Exponential and Logarithmic Functions
How to find the half-life of a radioactive substance when the decay rate is given.
• #### Exponential Growth and Decay - Problem 7
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to predict the age of a fossil with a known decay constant and exponential decay modeling.
• #### Exponential Growth and Decay - Problem 8
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
Application of Newton's Law of Cooling to show how long it takes an item to cool.
• #### Exponential Growth and Decay - Problem 6
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
Predict how many of a population will be present after a certain amount of time.
Tags:
• #### Exponential Functions and their Graphs - Problem 4
##### Math›Precalculus›Exponential and Logarithmic Functions
How to graph exponential growth functions.
• #### Exponential Functions and their Graphs - Problem 4
##### Math›Algebra 2›Inverse, Exponential and Logarithmic Functions
How to graph exponential growth functions.
• #### Exponential Functions and their Graphs - Problem 7
##### Math›Precalculus›Exponential and Logarithmic Functions
Examples of how to determine whether a function represents an exponential growth or decay model based on the value of the base | 886 | 4,039 | {"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} | 3.640625 | 4 | CC-MAIN-2015-22 | longest | en | 0.737557 |
http://fweb.wallawalla.edu/class-wiki/index.php?title=Chapter_6&diff=9426 | 1,601,195,310,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400265461.58/warc/CC-MAIN-20200927054550-20200927084550-00731.warc.gz | 50,088,155 | 14,836 | # Difference between revisions of "Chapter 6"
## Contents
### Digital Logic Gates
Boolean Algebra
A B NAND
$\overline{AB}$
NOR
$\overline{A+B}$
XOR
$A\oplus B$
0 0 1 1 0
0 1 1 0 1
1 0 1 0 1
1 1 0 0 0
### De Morgan Laws & NAND Equivalent Gates
• "If the variables in a logic expression are replaced by their inverses, and if the AND operation is replaced by OR, the OR operation is replaced by AND, and the expression is inverted, the resulting logic expression yields the same values as before the changes."<ref>Electronics p.353</ref>
• It is possible to create any combinatorial logic function with solely NAND (or NOR) gates
Gate Symbol NAND equivalent
Inverter $\overline{A}$ $\overline{AA}$
AND $AB$ $\overline{(\overline{A}+\overline{B})}$
OR $A+B$ $\overline{(\overline{A} \, \overline{B})}$
### Questions
• p.365: Why even have R_on?
<references/> | 271 | 863 | {"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": 0, "img_math": 9, "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} | 2.890625 | 3 | CC-MAIN-2020-40 | latest | en | 0.696748 |
http://financelearners.blogspot.com/2016/12/how-to-calculate-depreciation-expense.html | 1,503,012,111,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886104172.67/warc/CC-MAIN-20170817225858-20170818005858-00588.warc.gz | 154,581,366 | 7,367 | ### How to Calculate Depreciation Expense
Definition: Depreciation Expense (or annual depreciation) is the loss in value of a fixed asset in a year. There are several methods of calculating depreciation, including straight line method, declining balance method, sum-of-the-years'-digits method, etc.
Example 1:
An equipment which costs \$40,000 is expected to have a useful life of 5 years and a scrap value of \$5,000. Calculate the annual depreciation charge using straight line method.
Formula: Annual depreciation = (Cost - Scrap value)/Useful life
= (40000-5000)/5 = \$7,000
Example 2:
Calculate the annual depreciation of vehicle using declining balance method:
Cost of vehicle = \$40,000
Estimated useful life = 4 years
Expected disposal value at the end of useful life = \$2,500
Depreciation rate = 50%
Depreciation (year 1) = \$20,000
Depreciation (year 2) = (40000-20000)x50% = \$10,000
Depreciation (year 3) = (40000-30000)x50% = \$5,000
Depreciation (year 4) = (40000-35000)x50% = \$2,500
Reducing Balance Method of Depreciation
Straight-Line Method of Depreciation | 291 | 1,084 | {"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} | 3.796875 | 4 | CC-MAIN-2017-34 | latest | en | 0.851523 |
https://www.free-ebooks.net/ebook/The-Physics-of-Karate-Strikes/html/2 | 1,496,093,062,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463612553.95/warc/CC-MAIN-20170529203855-20170529223855-00097.warc.gz | 1,062,715,691 | 11,175 | # The Physics of Karate Strikes HTML version
Volume 1
JOURNAL OF HOW THINGS WORK
Fall, 1999
enough relative to other parts of the board (which are generally held still by the
cinderblocks on which the boards are placed), breakage occurs.
This same phenomenon can be analyzed in terms of energy transfer and resulting
deformation damage. Given and object with mass m1 at rest (the board) and another
object of mass m2 (the karateka’s hand) moving at velocity v upon impact and
ignoring the negligible amount of energy lost as thermal energy (heat), the amount of
energy in the system lost to deformation damage (
E) is given by the following:
(1
)
2(
2
mm
∆ =
1
2
v
2
mm
)
1
2
where e is the coefficient of restitution, which measures how elastic the collision is. It
is a function of the hardness or softness of the colliding objects, which along with
velocity determines impulse. If hard objects collide (for a perfectly inelastic collision,
e=0), they will accelerate one another quickly, transferring a large amount of force in
a small amount of time while soft objects colliding (for a perfectly elastic collision,
e=1) transfer smaller amounts of energy to one another for longer periods of time.
Difference in how long momentum takes to transfer and therefore in force at a given
instant is why hitting a pillow with the fleshy part of the hand hurts much less than
hitting a brick with the knuckles.
As
3 StrikingSurface
Any martial artist who has ever struck a board with improper hand technique can
attest to the physical pain associated with such impact. The human had is a complex
system of bones connected by tissue, and much can be said about the importance of
proper hand alignment in breaking. From the standpoint of physical science, however,
what is crucial about hand position upon impact is that all formulae for force,
momentum, and deformation energy are for a given unit of area. By minimizing the
amount of striking surface on the hand involved in collision with the board, a karateka
minimizes the area of the target to which force and energy are transferred and
therefore maximizes the amount of force and energy transferred per unit area.
Consider a martial artist capable of striking with 190 joules (J) of energy. A typical
human hand is about 6 inches long including the fingers and 4 inches across, which
means that a strike with the entire hand disperses those 190 J over 24 square inches,
about 7.92 J per square inch. If, however, the karateka strikes with only the fleshy part
of the palm, about 2 inches across and 1.5 inches long, the 190 J will be dispersed
over only 3 square inches. That strike will deliver about 63.3 J per square inch,
inflicting many times the amount of damage the whole hand could—the same amount
of energy dispersed over a smaller area delivers more energy per unit area. This is | 653 | 2,841 | {"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-2017-22 | latest | en | 0.937316 |
https://gillettestore.com/qa/question-is-current-used-up-in-a-circuit.html | 1,618,197,238,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038066568.16/warc/CC-MAIN-20210412023359-20210412053359-00224.warc.gz | 384,399,598 | 9,366 | # Question: Is Current Used Up In A Circuit?
## What does a current do in a circuit?
An electric current is a flow of electric charge around a circuit.
The charge is already in the wires (carried by billions of tiny particles called electrons).
This charge is evenly spread out through the wires.
So all the charge starts moving at once..
## Is voltage used up in a circuit?
Voltage, V Voltage is supplied by the battery (or power supply). Voltage is used up in components, but not in wires.
## Does current remain the same in a circuit?
For a series circuit with no branching locations, the current is everywhere the same. The current at the battery location is the same as the current at each resistor location. … There are three values left to be determined – the voltage drops across each of the individual resistors.
## Does current flow from negative to positive?
The flow of electrons is termed electron current. Electrons flow from the negative terminal to the positive. Conventional current or simply current, behaves as if positive charge carriers cause current flow. Conventional current flows from the positive terminal to the negative.
## Does electricity flow through or around a wire?
However, electrical energy does not travel though the wire as sound travels through air but instead always travels in the space outside of the wires. This is because electric energy is composed of electric and magnetic fields which are created by the moving electrons, but which exist in the space surrounding the wires.
## Why is the current the same in a circuit?
The amount of current in a series circuit is the same through any component in the circuit. This is because there is only one path for current flow in a series circuit.
## How does the current flow?
Current is flow of electrons, but current and electron flow in the opposite direction. Current flows from positive to negative and electron flows from negative to positive. Current is determined by the number of electrons passing through a cross-section of a conductor in one second.
## How do you reduce current in a circuit?
The current in a circuit is directly proportional to the electric potential difference impressed across the circuit and inversely proportional to the resistance of the circuit. Reducing the current can be done by reducing the voltage (choice A) or by increasing the resistance (choice D). 2.
## Why is the current in a series circuit the same everywhere?
You might think that the current gets less as it flows through one component after another, but it is not like this. The current is not used up by the components in a circuit. This means that the current is the same everywhere in a series circuit, even if it has lots of lamps or other components.
## How do you change the current in a circuit?
If you have an inductance in the circuit the current will rise until the emf generated by the inductance equals the applied voltage. The current will then continue at a rate determined by the circuit resistance. The current may be varied by varying the input voltage, or by varying the resistance of the circuit.
## Why does no current flow if there is no voltage?
When one point is more charged with electric than the other, that’s voltage. If the waterfall is dry and thee is no Current, the difference between two points is still there. One point is higher than the other (one point is more electrically charged than the other). … Still = no flow = no current without voltage.
## Can the current be negative?
Consequently, the reference directions of currents are often assigned arbitrarily. When the circuit is solved, a negative value for the current implies the actual direction of current through that circuit element is opposite that of the chosen reference direction.
## What happens to current as it flows through a circuit?
Current only flows when a circuit is complete—when there are no gaps in it. In a complete circuit, the electrons flow from the negative terminal (connection) on the power source, through the connecting wires and components, such as bulbs, and back to the positive terminal.
## Is current constant in parallel?
Components connected in parallel are connected along multiple paths so that the current can split up; the same voltage is applied to each component. … In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents flowing through each component.
## Do resistors decrease current?
Resistors don’t reduce current and voltage instead it opposes flow of current and produce drop in voltage across the terminals.
## What is the difference between voltage and current?
Voltage is the difference in charge between two points. Current is the rate at which charge is flowing.
## Why does current flow from negative to positive?
The flow of electric current occurs because we have a high potential of electrons gathered at the positive terminal and a low potential of electrons at the negative terminal.
## What two things does every circuit have?
All electric circuits have at least two parts: a voltage source and a conductor. They may have other parts as well, such as light bulbs and switches, as in the simple circuit seen in the Figure below. The voltage source of this simple circuit is a battery.
## How do you increase current in a circuit?
So to increase current of the circuit what you can do is :Use conductor of low resistivity, ¶.Use conductor of small length.Use thick wire.Decrease the temperature of the circuit.If operating temprature is high than use semiconductor, because it have negative temprature coefficient.Minimise the circuit losses.
## What does 0 volts mean?
When used while measuring potential difference, zero volt simply means the two points in measurement has same electric potential. … It is also measured in volts. If the source provides no energy then the emf of the source is zero volt. Also, the ground does not have zero voltage.
## Do electrons actually move in a circuit?
Electrons do not move along a wire like cars on a highway. Actually, Any conductor (thing that electricity can go through) is made of atoms. … If you put new electrons in a conductor, they will join atoms, and each atom will deliver an electron to the next atom. | 1,241 | 6,312 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-17 | latest | en | 0.942377 |
https://www.transtutors.com/questions/finance-98806.htm | 1,596,549,542,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735867.94/warc/CC-MAIN-20200804131928-20200804161928-00207.warc.gz | 885,267,421 | 13,236 | # finance 1 answer below »
Question 5 Question 4 Question 3 Question 2 Question 1 Possible Earned Question 6.00 6.00 7.00 9.00 36.00 0.00 8.00 Question 5 Question 4 Question 3 Question 2 Question 1 Possible Earned Question 6.00 6.00 7.00 9.00 36.00 0.00 8.00
Document Preview:
In Excel, use formulas in the spreadsheet to solve the problems so your instructor can see how you arrived at your answers. If your instructor cannot determine how an answer was calculated, no credit will be given for that answer. If a question calls for a text answer, such as a few sentences or a short paragraph, create a text box on the spreadsheet and enter your text in the box. In Word, be sure to show clearly how you arrived at your answers by entering the calculations as text. If your instructor cannot determine how an answer was calculated, no credit will be given for that answer. Question 1: (Cost of Capital) You are provided the following information on a company. The total market value is $40 million. The capital structure, shown here, is considered to be optimal. Accounting Value Market Value Bonds,$1000 par, 5% coupon, 5% YTM $10,000,000$10,000,000 Preferred Stock, 6%, $100 par, 100,000 shares$10,000,000 $8,000,000 Common Stock,$1 par, 100,000 shares $100,000 Capital in excess of par$400,000 $22,000,000 * Retained Earnings$13,500,000 * Total market value of common equity a. What is the after-tax cost of debt? (assume the company’s effective tax rate = 35%) b. Assuming a $6 dividend paid annually, what is the required return for preferred shareholders (i.e. component cost of preferred stock)? (assume floatation costs =$0.00) c. Assuming the risk-free rate is 2%, the expected return on the stock market is 8%, and the company's beta is 1.0, what is the required return for common stockholders (i.e., component cost of common stock)? d. What is the company's weighted average cost of capital (WACC)? Question 2: (Capital Budgeting) The Seattle Corporation has been presented with an investment opportunity which will yield end-of-year cash flows of $30,000 per year in Years 1 through 4,$35,000 per year in Years 5 through 9, and \$40,000 in...
Attachments: | 566 | 2,169 | {"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} | 2.8125 | 3 | CC-MAIN-2020-34 | latest | en | 0.906113 |
https://www.physicsforums.com/threads/torque-on-left-foot-of-man-in-rotating-system.991548/ | 1,720,815,802,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514452.62/warc/CC-MAIN-20240712192937-20240712222937-00890.warc.gz | 745,201,902 | 19,794 | # Torque on Left Foot of Man in Rotating System
• KDPhysics
In summary: I posted correct? I think it makes sense but you never know.Lets look at some limits: v=0 looks right, R gets large looks right, d gets large looks right, Units good. I think it is correct
KDPhysics
Homework Statement
A man of mass M stands on a railroad car that is rounding an unbanked turn of radius R at speed v. His center of mass is height L above the car, and his feet are a distance d apart. How much weight is on each of his feet?
Relevant Equations
Torque equation
I saw that the solution states that the torque about the center of mass is zero, since the man does not rotate about its center of mass.
However, I then thought about taking the torque about the left foot (so the right foot for the man's POV). Hence:
$$\tau_{left} = \tau_{0} + \textbf{R}\times \textbf{F}$$
where ##\textbf{R}## is the vector pointing from the left foot to the center of mass, ##\tau_{0}## is the torque about the center of mass (so zero) and ##\textbf{F}## is the net force on the man.Then:
$$N_R d - Mg\frac{d}{2}= 0 + \textbf{R}\times \textbf{F} \implies N_R=\frac{Mg}{2} + \frac{LMv^2}{Rd}$$
which is correct. However, I wrote that the torque about the left foot is ##\frac{d}{2}(2N_R-Mg)##, but clearly the man isn't rotating so shouldn't it be equal to zero? Then I would get that ##N_R = \frac{Mg}{2}##. So why isn't the torque about the left foot zero.
EDIT: thinking about it, perhaps this might have to do with the fact that the left foot is not an inertial frame of reference, and that therefore we have to take into consideration the centrifugal force acting on the man. Then. I find that:
$$\tau_{left}=N_R d - Mg\frac{d}{2} - L\frac{Mv^2}{R}$$
which when equated to zero gives the desired result. But then, is my previous method (where I wrote ##\tau_{left} = \frac{d}{2}(2N_R-Mg)## incorrect?
#### Attachments
• Schermata 2020-07-18 alle 19.42.06.png
34.8 KB · Views: 126
Last edited:
Any free body diagram with magnitudes and directions of forces as described in the problem?
The problem asks you about weight, which direction is vertical.
The weight distribution can only be between 50/50 and 100/0.
The centripetal effect tries tipping the man over and induces horizontal reactive forces at the feet, but the man is not skidding either.
Last edited:
Lnewqban said:
The weight distribution can only be between 50/50 and 100/0.
The solution to the problem (given by the book) is ##N_R=\frac{Mg}{2} + \frac{LMv^2}{Rd}##, so it is not a 50/50 nor a 100/0 distribution of weight.
Merlin3189
What happens after the curve ends and R becomes infinite?
Isn't the term ##2L/d## the cotangent of the angle formed between the horizontal and vertical forces acting upon the center of mass?
KDPhysics
the railroad is circular so the curve never ends
KDPhysics said:
the railroad is circular so the curve never ends
OK then.
What happens to the normal reaction on outside foot when ##mv^2/R##
(centrifugal force/weight) ratio equals ##d/2L## ratio?
Last edited:
it doesn't make sense since ##\frac{d}{L}## is unitless whereas ##\frac{mv^2}{R}## has units Newtons.
For anyone interested, I believe I have found an answer to my question. It turns out that the formula I suggested:
$$\tau_{left} = \tau_{0} + \textbf{R}\times \textbf{F}$$
is only correct when "left" is an inertial frame of reference. If instead we choose a point P that is accelerating, so that it is not inertial, then:
$$\frac{d\textbf{L}_P}{dt}=\tau_{ext, P} - \underbrace{M(\textbf{R}_{CM}-\textbf{R}_P)\times \ddot{\textbf{R}}_P}_{\text{pseudo-force torque}}$$
where ##\textbf{L}_P## is the angular momentum about P, and ##\tau_{ext, P}## is the net external torque about P, and ##\textbf{R}_{CM}-\textbf{R}_P## is just the vector displacement between P and the center of mass.
In the previous exercise, we have that ##\frac{d\textbf{L}_P}{dt}=0##, so:
$$0 = Mg\frac{d}{2} + N_R d - L\frac{Mv^2}{R} \implies N_R = =\frac{Mg}{2} + \frac{LMv^2}{Rd}$$
as was found previously.
So, in conclusion, just because the object is not rotating about a moving point P does not mean that the net torque about P is zero, since the pseudo-force torque must be taken into account. The only exception is when the moving point is the center of mass, in which case the pseudo-force torque is zero (##\textbf{R}_{CM}-\textbf{R}_P = 0##) and therefore the the net torque is also zero.
Lnewqban said:
The weight distribution can only be between 50/50 and 100/0.
KDPhysics said:
not a 50/50 nor a 100/0
I believe @Lnewqban did not say "either/or". He said "in the range between". I think you are talking past each other!
KDPhysics
I believe @Lnewqban did not say "either/or". He said "in the range between". I think you are talking past each other!
Oh, that makes much more sense...
hutchphd said:
I believe @Lnewqban did not say "either/or". He said "in the range between". I think you are talking past each other!
also is the explanation I posted correct? I think it makes sense but you never know.
Lets look at some limits: v=0 looks right, R gets large looks right, d gets large looks right, Units good. I think it is correct
great!
## 1. What is torque on the left foot of a man in a rotating system?
Torque on the left foot of a man in a rotating system refers to the twisting force that is applied to the left foot when the man is standing on a rotating platform or surface. It is a vector quantity that is measured in units of Newton-meters (Nm).
## 2. How is torque on the left foot calculated?
The torque on the left foot can be calculated by multiplying the force applied to the foot by the distance from the point of rotation to the foot. This is known as the lever arm or moment arm. The formula for torque is T = F x r, where T is torque, F is force, and r is the lever arm.
## 3. What factors affect the torque on the left foot in a rotating system?
The torque on the left foot in a rotating system is affected by the magnitude of the force applied to the foot, the angle at which the force is applied, and the distance from the point of rotation to the foot. The mass and speed of the rotating system can also affect the torque.
## 4. How does torque on the left foot impact balance and stability?
The torque on the left foot can impact balance and stability by causing the foot to rotate or twist, which can lead to loss of balance and stability. This is especially important in activities such as skating or skiing, where maintaining balance and stability is crucial for performance and safety.
## 5. What are some real-life examples of torque on the left foot in a rotating system?
Some real-life examples of torque on the left foot in a rotating system include ice skating, rollerblading, skiing, and riding a bike. In all of these activities, the left foot is constantly applying torque to maintain balance and stability while the body is in motion on a rotating surface or object.
• Introductory Physics Homework Help
Replies
7
Views
508
• Introductory Physics Homework Help
Replies
7
Views
411
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
287
• Introductory Physics Homework Help
Replies
335
Views
9K
• Introductory Physics Homework Help
Replies
19
Views
965
• Introductory Physics Homework Help
Replies
29
Views
2K
• Introductory Physics Homework Help
Replies
97
Views
3K | 2,038 | 7,513 | {"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": 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} | 4.0625 | 4 | CC-MAIN-2024-30 | latest | en | 0.929213 |
https://cracku.in/99-which-one-of-the-following-will-come-next-in-the-g-x-sbi-clerk-2016-2 | 1,726,523,306,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651714.51/warc/CC-MAIN-20240916212424-20240917002424-00087.warc.gz | 157,508,981 | 26,509 | Instructions
Answer the questions based on the given arrangement:
D L J # 3 P + A W Z R E 8 G 2 N S = T 6 & Y 9 @ X 4 H U 5 ^ 7 B
Question 99
# Which one of the following will come next in the given sequence ? D#L PW+ E28 TY6 ?
Solution
Series : D L J # 3 P + A W Z R E 8 G 2 N S = T 6 & Y 9 @ X 4 H U 5 ^ 7 B
Pattern : D#L PW+ E28 TY6 ?
1st term : D (+5 positions) = P (+6 positions) = E (+7 positions) = T (+8 positions) = H
2nd term : # (+5 positions) = W (+6 positions) = 2 (+7 positions) = Y (+8 positions) = ^
3rd term : L (+5 positions) = + (+6 positions) = 8 (+7 positions) = 6 (+8 positions) = U
Thus, missing term = H^U
=> Ans - (A) | 259 | 654 | {"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} | 3.484375 | 3 | CC-MAIN-2024-38 | latest | en | 0.713055 |
https://la.mathworks.com/matlabcentral/answers/753834-searching-for-yellow-error-and-is-this-the-right-way-to-write-the-if-statement | 1,643,192,215,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304947.93/warc/CC-MAIN-20220126101419-20220126131419-00052.warc.gz | 402,227,780 | 23,690 | # Searching for Yellow Error, And is this the right way to write the 'if' Statement
1 view (last 30 days)
Zachary Steinwachs on 23 Feb 2021
Answered: Mahesh Taparia on 27 Feb 2021
Im trying to have it search for the color yellow on a black background and this code doesn't function how I thought it would. The print statement was just a test so I could see if it was finding a yellow pixel but it seems to print out the statment regardless. Eventually I want it to be able to pick up a yellow ball with a little more chaotic of a background tho.
% Red = [R(x,y)];
imshow(I)
R = A(:,:,1);
G = A(:,:,2);
B = A(:,:,3);
for x = 1:720
x = x+1;
for y = 1:720
y = y+1;
Red = [R(x,y)];
Gre = [G(x,y)];
Blu = [B(x,y)];
if Red > 150 && Gre > 150 && Blu < 150
fprintf("i")
else
end
end
end
Mahesh Taparia on 27 Feb 2021
Hi
I assume, you want to find the pixels which satisfy the condition mentioned in your code. You can change your code to the below code:
R = A(:,:,1);
G = A(:,:,2);
B = A(:,:,3);
finalImage = zeros(720,720);
for x = 1:720
for y = 1:720
Red = [R(x,y)];
Gre = [G(x,y)];
Blu = [B(x,y)];
finalImage(x,y) = (Red > 150)&&(Gre > 150)&&(Blu < 150);
end
end
Hope it will help! | 382 | 1,178 | {"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} | 2.5625 | 3 | CC-MAIN-2022-05 | latest | en | 0.875588 |
https://mathequalslove.net/panda-squares-puzzle/ | 1,726,638,449,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651836.76/warc/CC-MAIN-20240918032902-20240918062902-00420.warc.gz | 346,154,467 | 49,922 | # Panda Squares Puzzle
My first introduction to the Panda Squares Puzzle was from one of my favorite inspiration sources: Twitter!
I saw a tweet by Jenny Leake that sparked my curiosity.
This curiosity led me to do a google search. I was pleasantly surprised to find David Butler‘s blog at the top of the search results.
From his blog post, I learned that the puzzle was from a book titled Ivan Moscovich’s Super Games. David asked his daughter to rename the puzzle from “Bits.” She chose “Panda Squares.” When I told my students that the name of the puzzle was “Panda Squares,” some of my students assumed that the pieces would assemble to create a panda.
David kindly offers a free download of the puzzle pieces on his blog. I put out a new puzzle each week for my kids to work on during their free time, and I decided this would make the perfect puzzle.
To begin, I printed several sets of panda squares in different sizes and laminated them.
MATH = LOVE RECOMMENDS…
A laminator is a MUST-HAVE for me as a math teacher! I spent my first six years as a teacher at a school with a broken laminator, so I had to find a way to laminate things myself.
I’ve had several laminators over the years. I currently use a Scotch laminator at home and a Swingline laminator at school.
I highly recommend splurging a bit on the actual laminator and buying the cheapest laminating pouches you can find!
I used my largest set for the puzzle table, but I printed smaller, individual puzzles for students to use by themselves later in the year.
I didn’t want to have to keep explaining the rules of the puzzle, so I printed up the instructions and added a clipart panda for extra cuteness. I’ve added a free download of these instructions to the bottom of this post.
I did run into the problem of students misinterpreting the instructions a bit. They didn’t realize that they had to use ALL of the 16 pieces. Bailey Calloway tweeted about having the same issue.
So, to combat this misconception, I have reworded my instructions a bit for the future.
To spark student interest in the panda squares puzzle, I spread out the pieces across the puzzle table at the front of my room. It took a bit of time for students to get intrigued enough to try, but soon I would glance over during free minutes of class and see things like this:
In his blog post about the panda squares puzzle, David Butler mentioned having students “notice and wonder” based on their various solutions to the puzzle. For my high school students, finding a single solution was enough of a challenge.
Over the course of the week that this puzzle was out, I only had one pair of students find a solution.
When I took a picture of their solution, they insisted on being in it, too.
Many other students tried, but they would often get frustrated when the last piece didn’t fit in nicely. It made me sad to watch them scramble the puzzle pieces in frustration instead of persevering and trying to rearrange the puzzle pieces to make it work.
Now, it’s a new week with a new puzzle, and I’ve already had multiple students comment that they wanted another chance with the panda squares puzzle. Guys, this is the sign of a good puzzle!
This will probably be the first puzzle of the year to make a second appearance on our puzzle table!
## Similar Posts
1. Unknown says:
Could you post the smaller sized pieces as well? This is a great activity for a Math Mastery class that I teach. Thank you!
1. David K Butler says:
If you change your print settings when you print it so that you print 16 per page, it should be the right size. 🙂
2. Unknown says:
Thank you!!
2. Unknown says:
I love the idea of having a puzzle table in my room – do you have a list of the puzzles you have used? I know I'm motivated now, but a few weeks in I will struggle to find puzzles and probably quit. 🙁 If I can get them all ready now I'm WAY more likely to do this!
3. Anonymous says:
Hi Sarah,
I cannot seem to download any of the files you have uploaded to appbox. is there any other way of getting these documents? I would like a copy of the Panda puzzle, Colour Square and your Christmas tree puzzle that you have blogged about in regards to your puzzle table.
4. Unknown says:
<a href=" https://puzzlefry.com>how many seconds in a year </a>PuzzleFry is the hub for interview puzzles, brain teasers, logic puzzles, brain games, riddles, Logical Questions, Math and Number Puzzles and quizzes. | 982 | 4,451 | {"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-2024-38 | latest | en | 0.975573 |
https://sio2.mimuw.edu.pl/c/pa-2014-1/s/41572/source/ | 1,722,864,026,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640447331.19/warc/CC-MAIN-20240805114033-20240805144033-00603.warc.gz | 422,713,884 | 7,675 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 #include #include #include #include #include #include #include #define REP(i, n) for(int i = 0; i < n; i++) #define FWD(i, a, b) for(int i = a; i < b; i++) #define ALL(u) (u).begin(), (u).end() using namespace std; typedef pair PII; typedef long long LL; typedef uint uint; const int INF = 1000000000; struct interval { int first, last, h; interval(int _first, int _last, int _h) { assert(_first <= _last); first = _first; last = _last; h = _h; } int len() { return last - first + 1; } void print() { printf("(f:%d l:%d h:%d) ", first, last, h); } }; class Sol { int n; vector plow, phigh; vector teams; vector ways; public: void sol() { scanf("%d", &n); plow.resize(n); phigh.resize(n); teams.resize(n+1, -1); ways.resize(n+1, 0); teams.back() = 0; ways.back() = 1; REP(i, n) { scanf("%d %d", &plow[i], &phigh[i]); } const LL mod = 1000000007; for(int pid = n-1; pid >= 0; pid--) { int cur_low = plow[pid], cur_high = phigh[pid]; int best = -1; for(int end = pid+1; end <= n; end++) { cur_low = max(plow[end-1], cur_low); cur_high = min(phigh[end-1], cur_high); if (end - pid >= cur_low and end - pid <= cur_high) { best = max(best, teams[end]); } if (end - pid > cur_high) { break; } } if (best == -1) continue; teams[pid] = best + 1; LL w = 0; cur_low = plow[pid]; cur_high = phigh[pid]; for(int end = pid+1; end <= n; end++) { cur_low = max(plow[end-1], cur_low); cur_high = min(phigh[end-1], cur_high); if (end - pid >= cur_low and end - pid <= cur_high) { if (teams[end] == best) { w += ways[end]; w %= mod; } } if (end - pid > cur_high) { break; } } ways[pid] = w; } if (teams[0] == -1) { printf("NIE\n"); } else { printf("%d %lld\n", teams[0], ways[0]); } } }; int main() { Sol s; s.sol(); return 0; } | 817 | 2,025 | {"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} | 2.59375 | 3 | CC-MAIN-2024-33 | latest | en | 0.247296 |
https://www.mathworks.com/matlabcentral/answers/463209-divide-block-outputs-inf-for-devision-of-10-0-04?s_tid=prof_contriblnk | 1,580,020,546,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251687725.76/warc/CC-MAIN-20200126043644-20200126073644-00100.warc.gz | 964,913,778 | 19,623 | # Divide Block outputs inf for devision of 10/0.04
11 views (last 30 days)
Klaas Albers on 21 May 2019
Answered: Klaas Albers on 21 May 2019
Hello,
I build a Simulink Model to Simulation the behavior of a heating system for domestic hot water. I used the NTU-Method to describe the heat exchanger. I´m currently trubbleshooting the model and i already resolved many issues.
The divide block I´m talking about outputs the value R_2 = m_dot,2 / m_dot,1 where m_dot,1 is controlled based on a tempreture and m_dot,2 is defined by a lookup table which resembles a user opening the tap for hot water. At the point where m_dot,2 goes from 0 to 10 l/min the Simulation stops and the Problem occures. I saturated both m´s at the lower level to 0.04 to avoid division by zero so the division in this block should be 10 / 0.04 = 250 which definitly isnt infinite :D
I attached the model an two scripts for constants and the profile for the lookup table for m_dot,2
I hope somebody can help me!
Kind Regards,
Klaas
Klaas Albers on 21 May 2019
I investigated the Problem further and think found the cause for the problem. Within the NTU-Method there is a special case when R_1 = 1 (for my case this means R_1 = R_2 = 1, because i have water on both side which means the cp is equal on both sides), in this case phi_i is calculated through a different formula than normal.
I caculated phi 1 and 2 for m_dot,2 = const. = 5 l/min and m_dot,1 = 0.1...10 in 0.1 increments using an excel sheet. Furthermore i caculated phi_1 = phi_2 for m_dot,2 = m_dot,1 = 5 l/min. I put all of this into a graph to showcase the Problem.
I think the problem originates because of the jump from the normaly caculated phi to the phi caculated with the formula for the special case.
Could i just interpolate the values in between? What would be the best way to do this?
I really hope somebody can help me to solve this issue! | 510 | 1,891 | {"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-2020-05 | latest | en | 0.914737 |
https://www.robot-forum.com/robotforum/thread/30024-bin-picking-singularity-problem/?postID=169445 | 1,624,470,880,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488539764.83/warc/CC-MAIN-20210623165014-20210623195014-00358.warc.gz | 886,821,527 | 26,245 | # Bin picking - singularity problem
• Hi,
I have problems with singularity on Bin picking cell. The Vision system is giving me location of the part (FRAME type information) and after i get the info that part is ready for picking i have PTP move 200mm above the location. Then i have LIN move to the point of picking.
I know that is LIN move problem for singularity and i already have set \$CP_VEL_TYPE to #VAR_ALL. But is it possible that the robot chose another path that is not near singularity or what to use that resolve the problem?
CODE:
In the attach is picture where the robot is in singularity.
ROBOT: KR16 1610mm
KRC: KRC4 standart
KSS: v8.3.17
Best regards
## Files
• You're literally telling the robot to stick to this and only this, linear, direct path between two points by using a LIN move. That's why it will never move in a different direction unless you tell it to.
If you want it to avoid a singularity, use a PTP path, or rotate the axis manually to a position that doesn't cause a singularity before executing the LIN move.
• Yeah i stick to linear move because if i have PTP move it is possible for collision. For better understanding the paths of robot see attachment. This robot does never have the same path because the parts (elements) are always in different location inside bin.
## Files
Edited once, last by Knezo ().
• Vision system have primary and secondary system. Primary system sends me location of part (FRAME type). On secondary system i scan picked part (2D picture) and the system send me correction for fine placing. Correction is in X, Y and A coordinates (gripper magnet, known Z=0, B and C orientation). So the orientation of the part is important, because the location where i place the part i have limited movemend (limits for correction of X,Y and A).
So if i understand properly \$ORI_TYPE=#JOINT causes unknown rotation of TCP in A,B and C orientation. So if its this the case than this is not possible.
• Normally, in an application like this, I make my move to the pre-pickup point in PTP, and only use LIN for the final move to engage the part, and keep the LIN moves to low speed. This usually allows me to avoid the A4/A6 over-speed errors. It might be necessary to create another "over-bin" PTP move, offset from the pre-pick move, to minimize the collision potential for the PTP motion. Something like this:
Done correctly, the PTP moves will be similar enough to LINs that collision risks should be greatly reduced.
Another option would be to predict the singularities using the INVERSE function, checking the A5 value, and creating a program branch to avoid being stopped by the singularity. Options:
1. Reduce speed if singularity is predicted
2. Skip the part and ask the vision system for the next-best part to pick up (hopefully the "stirring" of the bin will shift the parts around
• each robot should have KUE_WEG.SRC somewhere on C:\KRC....
this tries to move robot to end point so that wrist moves as little as possible.
Not sure what the program name means.... maybe "kuerzeste weg"
2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly
• Sorry that i didn't end this conversation. Lot of work in robot field I solve the problem with calculating inverse kinematic and i tell to vision system that this part is not reachable for the robot
Thanks guys!
Create an account | 779 | 3,411 | {"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} | 2.703125 | 3 | CC-MAIN-2021-25 | latest | en | 0.913698 |
https://www.usefullinks.org/cat/Polytopes.html | 1,716,084,630,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057631.79/warc/CC-MAIN-20240519005014-20240519035014-00364.warc.gz | 951,927,012 | 10,687 | Category: Polytopes
Cyclohedron
In geometry, the cyclohedron is a -dimensional polytope where can be any non-negative integer. It was first introduced as a combinatorial object by Raoul Bott and Clifford Taubes and, for this reason,
Configuration (polytope)
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration. Other configurations in geometry are something different. These polytope configurations may be more accurately
Circumcenter of mass
In geometry, the circumcenter of mass is a center associated with a polygon which shares many of the properties of the center of mass. More generally, the circumcenter of mass may be defined for simpl
Integer points in convex polyhedra
The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear equations with nonnegative coefficients have" o
Polytope families
There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality. These are tabulated here with Petrie polygon projection graphs and Coxe
Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidosc
Simplicial polytope
In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions contains only triangular faces and corresponds via Steinitz's
Schlegel diagram
In geometry, a Schlegel diagram is a projection of a polytope from into through a point just outside one of its facets. The resulting entity is a of the facet in that, together with the original facet
Uniform k 21 polytope
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the En Coxeter group, and having only regular polytope facets. The family was named by their Coxeter symbol k21 b
Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself. More specifically: * In three-dimensional geome
Lists of uniform tilings on the sphere, plane, and hyperbolic plane
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, a
Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. A co
Isogonal figure
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex
Permutoassociahedron
In mathematics, the permutoassociahedron is an -dimensional polytope whose vertices correspond to the bracketings of the permutations of terms and whose edges connect two bracketings that can be obtai
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simple
Hessian polyhedron
In geometry, the Hessian polyhedron is a regular complex polyhedron 3{3}3{3}3, , in . It has 27 vertices, 72 3{} edges, and 27 3{3}3 faces. It is self-dual. Coxeter named it after Ludwig Otto Hesse fo
Chiral polytope
In mathematics, there are two competing definitions for a chiral polytope. One is that it is a polytope that is chiral (or "enantiomorphic"), meaning that it does not have mirror symmetry. By this def
Stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an origi
Expansion (geometry)
In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation
Region (model checking)
In model checking, a field of computer science, a region is a convex polytope in for some dimension , and more precisely a zone, satisfying some minimality property. The regions partition . The set of
Dissection problem
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this
Demihypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half
List of regular polytopes and compounds
This article lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an n-sphere, Euclidea
Polar sine
In geometry, the polar sine generalizes the sine function of angle to the vertex angle of a polytope. It is denoted by psin.
Order polynomial
The order polynomial is a polynomial studied in mathematics, in particular in algebraic graph theory and algebraic combinatorics. The order polynomial counts the number of order-preserving maps from a
Ehrhart polynomial
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The the
Hypersimplex
In polyhedral combinatorics, the hypersimplex is a convex polytope that generalizes the simplex. It is determined by two integers and , and is defined as the convex hull of the -dimensional vectors wh
Semiregular polytope
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-transitive and has all its facets being regular polytopes. E.L. Elte compiled a long
Cauchy's theorem (geometry)
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is,
Distributive polytope
In the geometry of convex polytopes, a distributive polytope is a convex polytope for which coordinatewise minima and maxima of pairs of points remain within the polytope. For example, this property i
Stacked polytope
In polyhedral combinatorics (a branch of mathematics), a stacked polytope is a polytope formed from a simplex by repeatedly gluing another simplex onto one of its facets.
Associahedron
In mathematics, an associahedron Kn is an (n – 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a string of n letters,
Vertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example, a square vertex arrangement is unders
Faceting
In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices. New edges of a faceted polyhedron may be create
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, wh
In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points.
List of polygons, polyhedra and polytopes
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polyto
Witting polytope
In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3{3}3{3}3{3}3, and Coxeter diagram . It has 240 vertices, 2160 3{} edges, 2160 3{3}3 faces, and 240 3{3
Hanner polytope
In geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after Olof Hanner, who introduced them in 1956.
Honeycomb (geometry)
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellat
Cyclotruncated simplectic honeycomb
In geometry, the cyclotruncated simplectic honeycomb (or cyclotruncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the affine Coxeter group. It is gi
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a
Permutohedron
In mathematics, the permutohedron of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates (labels) are the permutations of the first n natural numbers.
Racemic acid
Racemic acid is an old name for an optically inactive or racemic form of tartaric acid. It is an equal mixture of two mirror-image isomers (enantiomers), optically active in opposing directions. It oc
Apeirotope
In geometry, an apeirotope or infinite polytope is a generalized polytope which has infinitely many facets.
Minkowski problem for polytopes
In the geometry of convex polytopes, the Minkowski problem for polytopes concerns the specification of the shape of a polytope by the directions and measures of its facets. The theorem that every poly
Omnitruncated simplectic honeycomb
In geometry an omnitruncated simplectic honeycomb or omnitruncated n-simplex honeycomb is an n-dimensional uniform tessellation, based on the symmetry of the affine Coxeter group. Each is composed of
Möbius–Kantor polygon
In geometry, the Möbius–Kantor polygon is a regular complex polygon 3{3}3, , in . 3{3}3 has 8 vertices, and 8 edges. It is self-dual. Every vertex is shared by 3 triangular edges. Coxeter named it a M
Order polytope
In mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. The points of the order polytope are the monotonic functions from the given set to the u
Dual polyhedron
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to t
Quarter hypercubic honeycomb
In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q{4,3...3,4
Ludwig Schläfli
Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in develo
Matching polytope
In graph theory, the matching polytope of a given graph is a geometric object representing the possible matchings in the graph. It is a convex polytope each of whose corners corresponds to a matching.
Uniform 2 k1 polytope
In geometry, 2k1 polytope is a uniform polytope in n dimensions (n = k+4) constructed from the En Coxeter group. The family was named by their Coxeter symbol as 2k1 by its bifurcating Coxeter-Dynkin d
Simplectic honeycomb
In geometry, the simplectic honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the affine Coxeter group symmetry. It is represented by a Coxeter-Dynkin diagram
Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
Blind polytope
No description available.
Gosset–Elte figures
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all
Vertex (geometry)
In geometry, a vertex (in plural form: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an a
Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, CC, FRS, FRSC (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th cen
Kleetope
In geometry and polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope P is another polyhedron or polytope PK formed by replacing each facet of P with a shallow p
Pentagonal polytope
In geometry, a pentagonal polytope is a regular polytope in n dimensions constructed from the Hn Coxeter group. The family was named by H. S. M. Coxeter, because the two-dimensional pentagonal polytop
Hyperpyramid
A hyperpyramid is a generalisation of the normal pyramid to n dimensions. In the case of the pyramid one connects all vertices of the base, a polygon in a plane, to a point outside the plane, which is
Integral polytope
In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex hull of its
Difference bound matrix
In model checking, a field of computer science, a difference bound matrix (DBM) is a data structure used to represent some convex polytopes called zones. This structure can be used to efficiently impl
Uniform 1 k2 polytope
In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n = k+4) constructed from the En Coxeter group. The family was named by their Coxeter symbol 1k2 by its bifurcating Coxeter-Dynkin diag
Hypercubic honeycomb
In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group Rn (or
Petrie polygon
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one of the facets. The Petrie polygon of a regular p
Matroid polytope
In mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is a polytope constructed via the ba
Convex Polytopes
Convex Polytopes is a graduate-level mathematics textbook about convex polytopes, higher-dimensional generalizations of three-dimensional convex polyhedra. It was written by Branko Grünbaum, with cont
Hyperrectangle
In geometry, an orthotope (also called a hyperrectangle or a box) is the generalization of a rectangle to higher dimensions.A necessary and sufficient condition is that it is congruent to the Cartesia
Antiprism
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. The
Polytope
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in an
Hilbert cube
In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can
Schläfli orthoscheme
In geometry, a Schläfli orthoscheme is a type of simplex. The orthoscheme is the generalization of the right triangle to simplex figures of any number of dimensions. Orthoschemes are defined by a sequ
Normal polytope
In mathematics, specifically in combinatorial commutative algebra, a convex lattice polytope P is called normal if it has the following property: given any positive integer n, every lattice point of t
Runcination
In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges, and vertices, creating new facets in place of the original face, edge, and v
Computing the Continuous Discretely
Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra is an undergraduate-level textbook in geometry, on the interplay between the volume of convex polytopes and the number of la
Blaschke sum
In convex geometry and the geometry of convex polytopes, the Blaschke sum of two polytopes is a polytope that has a facet parallel to each facet of the two given polytopes, with the same measure. When
Regular complex polygon
In geometry, a regular complex polygon is a generalization of a regular polygon in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imagi
Abstract polytope
In mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely geometric properties such as points an
Regular polytope
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, whe
Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates from Kepler's names for the Archimedean solids
Wythoff symbol
In geometry, the Wythoff symbol is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It was first used by Coxeter, Longuet-Higgins and M
Eutactic star
In Euclidean geometry, a eutactic star is a geometrical figure in a Euclidean space. A star is a figure consisting of any number of opposing pairs of vectors (or arms) issuing from a central origin. A
Rectification (geometry)
In Euclidean geometry, rectification, also known as critical truncation or complete-truncation, is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its v
Cross-polytope
In geometry, a cross-polytope, hyperoctahedron, orthoplex, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space. A 2-dimensional cross-polytope is a square, a 3-dimensi
Bitruncation
In geometry, a bitruncation is an operation on regular polytopes. It represents a truncation beyond rectification. The original edges are lost completely and the original faces remain as smaller copie
Gram–Euler theorem
In geometry, the Gram–Euler theorem, Gram-Sommerville, Brianchon-Gram or Gram relation (named after Jørgen Pedersen Gram, Leonhard Euler, Duncan Sommerville and Charles Julien Brianchon) is a generali
Regular Polytopes (book)
Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter. It was originally published by Methuen in 1947 and by Pitman Publishing in 1948, with a second edit
Density (polytope)
In geometry, the density of a star polyhedron is a generalization of the concept of winding number from two dimensions to higher dimensions,representing the number of windings of the polyhedron around
Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is
Proprism
In geometry of 4 dimensions or higher, a proprism is a polytope resulting from the Cartesian product of two or more polytopes, each of two dimensions or higher. The term was coined by John Horton Conw
Uniform polytope
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. The uniform polytopes in two dimensions are the regular polygons (the definition
Alternated hypercubic honeycomb
In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation. It is given a S | 4,950 | 20,421 | {"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} | 3.390625 | 3 | CC-MAIN-2024-22 | latest | en | 0.946249 |
https://cheatography.com/lavanya-m22/cheat-sheets/numpy/ | 1,718,878,626,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861916.26/warc/CC-MAIN-20240620074431-20240620104431-00447.warc.gz | 143,802,839 | 20,841 | Show Menu
Cheatography
# NumPy Cheat Sheet by Lavanya-M22
NumPy cheatsheet by Lavanya and
### Why NumPy?
NumPy is an open-source numerical Python library used for working with arrays. It aims to provide an array object that is upto 50x faster than traditional python list takes significantly less amount of memory as compared to python lists.
### How to Install Numpy
``````pip install numpy or conda install numpy``````
### Importing Library
``import numpy as np``
### Attributes of ndarray
ndarray.shape Tuple of array shape ndarray.ndim Number of array dimensions as interger ndarray.size Number of elements in the array ndarray,dtype Data type of array’s elements ndarray.base To check if object has its own memory
### Slicing
arr[0] Returns the element at index 0 arr[1,2] Returns array element on index [1][2] arr[0:3] Returns the elements at indices on outer dimension arr[0:3,2] Returns the elements on rows 0,1,2 at column 2 arr
### Statistics
np.mean(arr,axis=0/1) Compute the arithmetic mean along the specified axis. arr.sum() Sum of array elements over a given axis arr.min() Return the minimum along a given axis arr.max() Return the maximum along a given axis np.var(arr) Compute the variance along the specified axis np.std(arr) Compute the standard deviation along the specified axis. arr.corrcoef() Return Pearson product-moment correlation coefficients
### Creating Arrays
np.array(object) Creates an array np.array([1,2,3]) 1D array np.array([(1,2,3),(4,5,6)]) 2D array np.zeros(shape) Return a new array of given shape and type, filled with zeros np.ones(shape) Return a new array of given shape and type, filled with ones np.eye(no. of rows) Return a 2-D array with ones on the diagonal and zeros elsewhere np.arange(start,stop,step) Return evenly spaced values within a given interval. np.random.rand(shape) Return array of random floats between 0–1 of fiven shape np.random.randint(low,high) Return random integers from low (inclusive) to high (exclusive) np.linspace(start, stop, n) Returns n evenly spaced numbers over a specified interval
### commonly used methods
np.sort(arr) Returns a sorted copy of the array np.argsort(arr) Returns the indices that would sort an array np.resize(a, new_shape) Return a new array with the specified shape np.dot(arr1, arr2) Dot product of two arrays arr.copy() Returns a copy of the array arr.view() New view of array with the same data arr.flatten() Return a copy of the array collapsed into 1D arr.reshape(new_shape) Returns an array containing the same data with a new shape
### Math operators
np.add(arr_1, arr_2) Add arguments element-wise np.subtract(arr_1, arr_2) Subtract arguments, element-wise np.multiply(arr_1, arr_2) Multiply arguments, element-wise np.divide(arr_1, arr_2) Divide arguments, element-wise np.power(arr_1, arr_2) First array elements raised to powers from second array, element-wise np.sqrt(arr) Return the non-negative square-root of an array, element-wise np.log(arr) Natural logarithm, element-wise np.ceil(arr) Rounds up to the nearest int , element-wise np.floor(arr) Rounds down to the nearest int ,element-wise np.abs(arr) Absolute value of each element in the array np.round(arr) Rounds to the nearest int
### Useful links
NumPy Official documenataion w3schools NumPy Tutorial NumPy Illustrated: The Visual Guide to NumPy NumPy: creating and manipulating numerical data
## Comments
No comments yet. Add yours below!
## Add a Comment
Your Comment
Please enter your name.
Please enter your email address
Please enter your Comment.
## Related Cheat Sheets
Python 1.1 Numpy Cheat Sheet | 987 | 3,687 | {"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-2024-26 | latest | en | 0.635461 |
https://7sage.com/lsat_explanations/lsat-15-section-3-question-15/ | 1,726,631,655,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651836.76/warc/CC-MAIN-20240918032902-20240918062902-00181.warc.gz | 57,473,970 | 38,243 | ### You need a full course to see this video. Enroll now and get started in less than a minute.
Target time: 0:52
This is question data from the 7Sage LSAT Scorer. You can score your LSATs, track your results, and analyze your performance with pretty charts and vital statistics - all with a ← sign up in less than 10 seconds
Question
QuickView
Choices
Curve Question
Difficulty
Psg/Game/S
Difficulty
Explanation
PT15 S3 Q15
+LR
Method of reasoning or descriptive +Method
A
3%
157
B
94%
164
C
0%
155
D
0%
161
E
2%
157
125
135
145
+Easier 147.322 +SubsectionMedium
We can identify this question as Method of Reasoning because of the question stem: “Dr. Nash responds to Dr. Godfrey’s argument by doing which of the following?”
When dealing with a Method of Reasoning question, we know we are looking for an answer choice that correctly describes the structure of our entire argument. Our correct answer is going to fit the argument exactly. Our wrong answer choices likely explain argument structures we are familiar with, but that simply don’t apply to the specific question we are looking at. Knowing what the right and wrong answers are going to do, we can jump into the stimulus.
This question presents us with two speakers. Right away, we should recognize that there are two conclusions and two reasons behind them. Our first speaker, Dr. Godfrey, points out a correlation. We learn that high school students who are now working over 15 hours per week receive lower grades than their peers. Dr. Godfrey concludes that because these overlap that the first (working) must be causing the second (lower grades). While that is one possible interpretation of a correlation, we know that just because two things happen at the same time does not mean they happen because of each other.
Dr. Nash points out the interpretation Dr. Godfrey has forgotten is just as likely. It does not have to be the case that having a job causes low grades. It could just as easily be the case that students receiving low grades turn to after school jobs to begin building careers or their self esteem. Using structural analysis we can identify the first speaker incorrectly concludes A because B. Meanwhile, Dr. Nash points out it is just as likely we have B because A.
Answer Choice (A) This answer choice does not match the structure of our argument. By telling us that the argument attempts to “downplay the seriousness of the problems,” the answer ascribes a position to Dr. Nash that cannot be supported. Dr. Nash makes no comment on how serious these problems are. They could be big, they could be small. The only information Dr. Nash responds with is the direction of causation the arrow could be pointing toward.
Correct Answer Choice (B) This is exactly what we are looking for. This answer choice correctly summarizes the structure of our entire argument by affirming that Dr. Nash points out a possible alternative outcome. This is the only answer choice that points out how Dr. Nash corrects Dr. Godfrey’s causation mistake.
Answer Choice (C) This answer choice does not line up with the structure of the stimulus. This answer choice claims Dr. Nash has a problem with the accuracy of Dr. Godfrey’s evidence. But a conclusion built on this argument would reference the validity of the numbers in some way shape or form. We know that accuracy of the evidence isn’t the problem in our argument - it’s the interpretation of that evidence. Dr. Godfrey forgets about one way we could interpret the facts rather than questioning whether the facts were good to begin with.
Answer Choice (D) This answer choice does not accurately summarize what is going on in our stimulus. This answer claims that the fault of the academic problems is what Dr. Nash is concerned about. But Dr. Nash does not come to the defense of the schools as this answer choice claims.
Answer Choice (E) This answer choice is not what we are looking for. Our second speaker simply suggests the causal relationship simply in the opposite direction. This does not align with what answer choice (E) suggests, which is that there is no relationship between these variables at all. | 884 | 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} | 3.453125 | 3 | CC-MAIN-2024-38 | latest | en | 0.950748 |
http://iocoach.com/calculate-percent/calculate-percentage-error-of.html | 1,516,317,999,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887660.30/warc/CC-MAIN-20180118230513-20180119010513-00283.warc.gz | 167,655,456 | 3,689 | # iocoach.com
Home > Calculate Percent > Calculate Percentage Error Of
# Calculate Percentage Error Of
## Contents
In many situations, the you agree to our cookie policy. Flag 20% Percentage Error is all about comparing a guess or estimate to an exact value. Nearly all of the graphics are a newsletter. Co-authors: 11 Updated: Views:248,982 68% of people http://iocoach.com/calculate-percent/calculate-percentage-error-in.html is 21 years.
question Flag as... This is also called the accepted, experimental or true value.Note due to percent error, deviation, and percent deviation. Updated September how. Create an account EXPLORE Community DashboardRandom ArticleAbout UsCategoriesRecent Changes HELP as...
## How To Calculate Percentage Error In Chemistry
Home About wikiHow Jobs Terms of Use RSS Site map Log duplicate Thanks! most of the images and PDF files found on sciencenotes.org. Flag question Flag as... US Write an ArticleRequest a New ArticleAnswer a RequestMore Ideas...
Reply ↓ Todd Helmenstine Post authorJanuary 28, 2016 your blog cannot share posts by email. Calculate Percentage Difference to know is the approximate and exact value and you'll be on your way. We can also use a theoretical value (when block of aluminum to be 2.68 g/cm3.
Solve for the measured or observed value.Note due to the How To Calculate Percentage Error In Matlab Ignore any US Write an ArticleRequest a New ArticleAnswer a RequestMore Ideas... Percent error or percentage error expresses as a percentage the difference 10 and the estimated value is 9.
## How To Calculate Percentage Error In Physics
http://iocoach.com/calculate-percent/calculate-percentage-error-chemistry.html as... Our Story Advertise With Us Site Map Help Write for About Careers at in the kinetic energy of a particle? And we can use Percentage Error Simply multiply the How To Calculate Percent Error Multiply the result by 100.
Yes No Not Helpful 2 Helpful 4 Unanswered Questions try again. The graph below is a as... Determine, for each measurement, the error, http://iocoach.com/calculate-percent/calculate-percentage-of-error.html wikiHow better. In this case, the real value is answer into percent form.
How To Calculate Percentage Error In Temperature Change time, he found his real height to be 5 feet. Thanks for Cookies make
## The difference between the actual and experimental value is always the absolute
In this example, the student has measured the percentage of calculated to be 19.71. Contact at room temperature and find it to be 2.70 g/cm3. How To Calculate Percentage Error In Calibration valid email address. WikiHow relies on ad money to vote Click a star to vote Thanks for voting!
What are the ages Flag to determine your grade in lab experiments, specifically percent error. Thanks for http://iocoach.com/calculate-percent/calculate-percentage-error-for.html most people will be satisfied with the percent error rounded to three significant digits. The theoretical has been corrected.
Simply divide -1, the result when 10 is physics formulas)is 0.64 seconds. Two standard deviations, or two sigmas, away from the mean (the red question Flag as... Becomean subtract the theoretical value from the experimental value if you are keeping negative signs. See percentage change, difference you agree to our cookie policy.
minus sign. Yes No Can answer into percent form. pendulum are 0.2% and 2% respectively ,the maximum % age error in LT2 is? Answer this displacement in a container of a known volume of water.
the Day Recipe of the Day Sign up There was an error. we're pretending!), so we have to do it the hard way. If you need to know positive or negative error, this is done by dropping the | 792 | 3,703 | {"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-2018-05 | latest | en | 0.832212 |
http://mathematica.stackexchange.com/questions/30788/parametricndsolve-and-constraint-satisfaction-problem | 1,469,801,101,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257830091.67/warc/CC-MAIN-20160723071030-00239-ip-10-185-27-174.ec2.internal.warc.gz | 162,611,907 | 18,843 | # ParametricNDSolve and Constraint satisfaction problem
I am trying to find the values of two parameters that allow for a specific result of my differential equations, under different initial conditions.
Given a system of equations:
TestSystem = {H'[t] == p - H[t] (k1 sh[t]), H[0] == H0,
sh'[t] == -k1 H[t] sh[t] + k2 ss[t], sh[0] == sh0,
st == sh[t] + ss[t]};
I use ParametricNDSolve to compute the values of the dependent variables, while leaving k1 and k2 unspecified:
TestSolver[H0e_, st0_] :=
ParametricNDSolve[
TestSystem /. p -> 0 /. {H0 -> H0e}
/. sh0 -> st0 /. st -> st0
/. k2 -> k2estim /. k1 -> k1estim, {h, sh, st}, {t, 0,
300}, {k1estim, k2estim}];
The conditions that I want to evaluate are then specified by m,d,hh, at t=300:
m = 100 sh[k1estim, k2estim][300]/st;
d = 100 ss[k1estim, k2estim][300]/st;
hh = h[k1estim, k2estim][300];
cond1a[k1estim_, k2estim_] :=
Evaluate[m /. st -> 5.*^-6 /. TestSolver[1.*^-5, 5.*^-6]]
cond1b[k1estim_, k2estim_] :=
Evaluate[d /. st -> 5.*^-6 /. TestSolver[1.*^-5, 5.*^-6]]
cond1c[k1estim_, k2estim_] :=
Evaluate[hh /. TestSolver[1.*^-5, 5.*^-6]]
cond2a[k1estim_, k2estim_] :=
Evaluate[m /. st -> 5.*^-6 /. TestSolver[5.*^-5, 5.*^-6]]
cond2b[k1estim_, k2estim_] :=
Evaluate[d /. st -> 5.*^-6 /. TestSolver[5.*^-5, 5.*^-6]]
cond2c[k1estim_, k2estim_] :=
Evaluate[hh /. TestSolver[5.*^-5, 5.*^-6]]
Now, say that I wanted to find the following
1 < cond1a < 100,
0 < cond1b < 1,
1.*^-8 < cond1c < 1*^-5,
1 < cond2a < 50,
50 < cond2b < 100,
1.*^-8 < cond2c < 1*^-5,
How could I find the values of k1 and k2 that would satisfy such a thing?
I was considering using NMinimize like this:
NMinimize[{1/cond1a+cond1b+cond1c+cond2a+1/cond2b+cond2c,cons},{k1,k2}]
(where cons would be the required constrains).
Yet, this does not seem like an efficient and plausible way to solve this problem. Does anyone have any ideas on how I could approach this problem? Given that this is a multi-objective optimization problem, how would you suggest that I could specify the objective function?
Thank you so much!
-
It appears to be a constraint satisfaction problem rather than optimization per se. You might thus use a simple objective, say (the constant function) 1, and pass the constraints in a way that they get evaluated for numeric values of the parameters k1,k2. – Daniel Lichtblau Aug 20 '13 at 21:07
@DanielLichtblau I see! You are suggesting considering any objective function of the above (e.g. minimize cond1b, since I want it to be close to 0), and apply all the constraints, correct? – Sosi Aug 21 '13 at 12:53
Yes, that's correct. – Daniel Lichtblau Aug 21 '13 at 14:46
Well, indeed that seems like a nice suggestion! Now my problem is having a very wide span for both parameters. Evaluating everything yields some NMinimize::incst: error. I'll try to work around this. Also, would you like to post your suggestion as answer? – Sosi Aug 21 '13 at 15:16
I had to make a number of corrections and adjustments to the code, but here is the idea.
TestSystem = {h'[t] == p - h[t] (k1 sh[t]), h[0] == H0,
sh'[t] == -k1 h[t] sh[t] + k2 ss[t], sh[0] == sh0,
st == sh[t] + ss[t]};
TestSolver[H0e_, st0_] :=
ParametricNDSolve[
TestSystem /. p -> 0 /. {H0 -> H0e} /. sh0 -> st0 /. st -> st0 /.
k2 -> k2estim /. k1 -> k1estim, {h, sh, ss}, {t, 0,
300}, {k1estim, k2estim}];
m[k1estim_?NumberQ, k2estim_?NumberQ] :=
100 sh[k1estim, k2estim][300]/st;
d[k1estim_?NumberQ, k2estim_?NumberQ] :=
100 ss[k1estim, k2estim][300]/st;
hh[k1estim_?NumberQ, k2estim_?NumberQ] := h[k1estim, k2estim][300];
tsres1 = TestSolver[1.*^-5, 5.*^-6];
tsres5 = TestSolver[5.*^-5, 5.*^-6];
cond1a[k1estim_?NumberQ, k2estim_?NumberQ] :=
m[k1estim, k2estim] /. st -> 5.*^-6 /. tsres1
cond1b[k1estim_?NumberQ, k2estim_?NumberQ] :=
d[k1estim, k2estim] /. st -> 5.*^-6 /. tsres1
cond1c[k1estim_?NumberQ, k2estim_?NumberQ] :=
hh[k1estim, k2estim] /. tsres1
cond2a[k1estim_?NumberQ, k2estim_?NumberQ] :=
m[k1estim, k2estim] /. st -> 5.*^-6 /. tsres5
cond2b[k1estim_?NumberQ, k2estim_?NumberQ] :=
d[k1estim, k2estim] /. st -> 5.*^-6 /. tsres5
cond2c[k1estim_?NumberQ, k2estim_?NumberQ] :=
hh[k1estim, k2estim] /. tsres5
constraints[k1_, k2_] = {1 <= cond1a[k1, k2] <= 100,
0 <= cond1b[k1, k2] <= 1, 1.*^-8 <= cond1c[k1, k2] <= 1*^-5,
1 <= cond2a[k1, k2] <= 50, 50 <= cond2b[k1, k2] <= 100,
1.*^-8 <= cond2c[k1, k2] <= 1*^-5};
Now can do e.g.
Timing[{min, vals} =
NMinimize[{1/cond1a[k1, k2]^2 + cond1b[k1, k2]^2 +
cond1c[k1, k2]^2 + 1/cond2a[k1, k2]^2 + 1/cond2b[k1, k2]^2 +
cond2c[k1, k2]^2,
constraints[k1, k2]}, {{k1, -100, 100}, {k2, -100, 100}}]]
I'm not sure how good a job it will do though. I played a bit more and got a possibly viable result by changing the initial ranges.
Timing[{min, vals} =
NMinimize[{1/cond1a[k1, k2]^2 + cond1b[k1, k2]^2 +
cond1c[k1, k2]^2 + 1/cond2a[k1, k2]^2 + 1/cond2b[k1, k2]^2 +
cond2c[k1, k2]^2,
constraints[k1, k2]}, {{k1, -1000, 1000}, {k2, -10, 10}}]]
[some warning messages omitted]
(* {17.440000, {0.235039300883, {k1 -> 5534.72060398,
k2 -> 0.0377418151532}}} *)
Now check for constraint satisfaction.
In[314]:= {cond1a[k1, k2], cond1b[k1, k2], cond1c[k1, k2],
cond2a[k1, k2], cond2b[k1, k2], cond2c[k1, k2]} /. vals
(* Out[314]= {99.5161215794, 0.483878420575,
1.0140995435*10^-8, 49.9885948839, 50.0114051161,
5.75765494239*10^-6} *)
In[315]:= constraints[k1, k2] /. vals
(* Out[315]= {True, True, True, True, True, True} *)
-
Sorry to bump this old thread, but some time ago when I was no longer working with this I thought about a different approach that possibly could give what I wanted. I was thinking that maybe using CountourPlot[] possibly would be more efficient, with the countours specifying which areas would satisfy the constraints? Anyways, this is just an idea. If I get some spare time I'll try it out just for fun – Sosi Oct 2 '14 at 13:14 | 2,217 | 5,852 | {"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} | 2.984375 | 3 | CC-MAIN-2016-30 | latest | en | 0.685811 |
https://keras.io/api/ops/fft/ | 1,716,052,582,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057440.7/warc/CC-MAIN-20240518152242-20240518182242-00290.warc.gz | 304,420,433 | 6,081 | # FFT ops
[source]
### `fft` function
``````keras.ops.fft(x)
``````
Computes the Fast Fourier Transform along last axis of input.
Arguments
• x: Tuple of the real and imaginary parts of the input tensor. Both tensors in the tuple should be of floating type.
Returns
A tuple containing two tensors - the real and imaginary parts of the output tensor.
Example
``````>>> x = (
... keras.ops.convert_to_tensor([1., 2.]),
... keras.ops.convert_to_tensor([0., 1.]),
... )
>>> fft(x)
(array([ 3., -1.], dtype=float32), array([ 1., -1.], dtype=float32))
``````
[source]
### `fft2` function
``````keras.ops.fft2(x)
``````
Computes the 2D Fast Fourier Transform along the last two axes of input.
Arguments
• x: Tuple of the real and imaginary parts of the input tensor. Both tensors in the tuple should be of floating type.
Returns
A tuple containing two tensors - the real and imaginary parts of the output.
Example
``````>>> x = (
... keras.ops.convert_to_tensor([[1., 2.], [2., 1.]]),
... keras.ops.convert_to_tensor([[0., 1.], [1., 0.]]),
... )
>>> fft2(x)
(array([[ 6., 0.],
[ 0., -2.]], dtype=float32), array([[ 2., 0.],
[ 0., -2.]], dtype=float32))
``````
[source]
### `rfft` function
``````keras.ops.rfft(x, fft_length=None)
``````
Real-valued Fast Fourier Transform along the last axis of the input.
Computes the 1D Discrete Fourier Transform of a real-valued signal over the inner-most dimension of input.
Since the Discrete Fourier Transform of a real-valued signal is Hermitian-symmetric, RFFT only returns the `fft_length / 2 + 1` unique components of the FFT: the zero-frequency term, followed by the `fft_length / 2` positive-frequency terms.
Along the axis RFFT is computed on, if `fft_length` is smaller than the corresponding dimension of the input, the dimension is cropped. If it is larger, the dimension is padded with zeros.
Arguments
• x: Input tensor.
• fft_length: An integer representing the number of the fft length. If not specified, it is inferred from the length of the last axis of `x`. Defaults to `None`.
Returns
A tuple containing two tensors - the real and imaginary parts of the output.
Examples
``````>>> x = keras.ops.convert_to_tensor([0.0, 1.0, 2.0, 3.0, 4.0])
>>> rfft(x)
(array([10.0, -2.5, -2.5]), array([0.0, 3.4409548, 0.81229924]))
``````
``````>>> rfft(x, 3)
(array([3.0, -1.5]), array([0.0, 0.8660254]))
``````
[source]
### `stft` function
``````keras.ops.stft(
x, sequence_length, sequence_stride, fft_length, window="hann", center=True
)
``````
Short-Time Fourier Transform along the last axis of the input.
The STFT computes the Fourier transform of short overlapping windows of the input. This giving frequency components of the signal as they change over time.
Arguments
• x: Input tensor.
• sequence_length: An integer representing the sequence length.
• sequence_stride: An integer representing the sequence hop size.
• fft_length: An integer representing the size of the FFT to apply. If not specified, uses the smallest power of 2 enclosing `sequence_length`.
• window: A string, a tensor of the window or `None`. If `window` is a string, available values are `"hann"` and `"hamming"`. If `window` is a tensor, it will be used directly as the window and its length must be `sequence_length`. If `window` is `None`, no windowing is used. Defaults to `"hann"`.
• center: Whether to pad `x` on both sides so that the t-th sequence is centered at time `t * sequence_stride`. Otherwise, the t-th sequence begins at time `t * sequence_stride`. Defaults to `True`.
Returns
A tuple containing two tensors - the real and imaginary parts of the STFT output.
Example
``````>>> x = keras.ops.convert_to_tensor([0.0, 1.0, 2.0, 3.0, 4.0])
>>> stft(x, 3, 2, 3)
(array([[0.75, -0.375],
[3.75, -1.875],
[5.25, -2.625]]), array([[0.0, 0.64951905],
[0.0, 0.64951905],
[0.0, -0.64951905]]))
``````
[source]
### `irfft` function
``````keras.ops.irfft(x, fft_length=None)
``````
Inverse real-valued Fast Fourier transform along the last axis.
Computes the inverse 1D Discrete Fourier Transform of a real-valued signal over the inner-most dimension of input.
The inner-most dimension of the input is assumed to be the result of RFFT: the `fft_length / 2 + 1` unique components of the DFT of a real-valued signal. If `fft_length` is not provided, it is computed from the size of the inner-most dimension of the input `(fft_length = 2 * (inner - 1))`. If the FFT length used to compute is odd, it should be provided since it cannot be inferred properly.
Along the axis IRFFT is computed on, if `fft_length / 2 + 1` is smaller than the corresponding dimension of the input, the dimension is cropped. If it is larger, the dimension is padded with zeros.
Arguments
• x: Tuple of the real and imaginary parts of the input tensor. Both tensors in the tuple should be of floating type.
• fft_length: An integer representing the number of the fft length. If not specified, it is inferred from the length of the last axis of `x`. Defaults to `None`.
Returns
A tensor containing the inverse real-valued Fast Fourier Transform along the last axis of `x`.
Examples
``````>>> real = keras.ops.convert_to_tensor([0.0, 1.0, 2.0, 3.0, 4.0])
>>> imag = keras.ops.convert_to_tensor([0.0, 1.0, 2.0, 3.0, 4.0])
>>> irfft((real, imag))
array([0.66666667, -0.9106836, 0.24401694])
``````
``````>>> irfft(rfft(real, 5), 5)
array([0.0, 1.0, 2.0, 3.0, 4.0])
``````
[source]
### `istft` function
``````keras.ops.istft(
x,
sequence_length,
sequence_stride,
fft_length,
length=None,
window="hann",
center=True,
)
``````
Inverse Short-Time Fourier Transform along the last axis of the input.
To reconstruct an original waveform, the parameters should be the same in `stft`.
Arguments
• x: Tuple of the real and imaginary parts of the input tensor. Both tensors in the tuple should be of floating type.
• sequence_length: An integer representing the sequence length.
• sequence_stride: An integer representing the sequence hop size.
• fft_length: An integer representing the size of the FFT that produced `stft`.
• length: An integer representing the output is clipped to exactly length. If not specified, no padding or clipping take place. Defaults to `None`.
• window: A string, a tensor of the window or `None`. If `window` is a string, available values are `"hann"` and `"hamming"`. If `window` is a tensor, it will be used directly as the window and its length must be `sequence_length`. If `window` is `None`, no windowing is used. Defaults to `"hann"`.
• center: Whether `x` was padded on both sides so that the t-th sequence is centered at time `t * sequence_stride`. Defaults to `True`.
Returns
A tensor containing the inverse Short-Time Fourier Transform along the last axis of `x`.
Example
``````>>> x = keras.ops.convert_to_tensor([0.0, 1.0, 2.0, 3.0, 4.0])
>>> istft(stft(x, 1, 1, 1), 1, 1, 1)
array([0.0, 1.0, 2.0, 3.0, 4.0])
`````` | 1,964 | 6,925 | {"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-2024-22 | latest | en | 0.641168 |
https://golangrepo.com/repo/thcyron-graphs-go-data-structures | 1,685,595,074,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647614.56/warc/CC-MAIN-20230601042457-20230601072457-00007.warc.gz | 328,209,332 | 10,581 | # Graph algorithms written in Go
### Related tags
Data Structures graphs
# Graph Algorithms in Go
This repository contains implementations of various graph algorithms written in Go. I’ve written them to learn about these algorithms.
## Implemented
• Data structues
• Graph and Digraph
• Flow network
• Set
• Sorting algorithms
• Spanning tree algorithms
• Shortest path algorithms
• Search algorithms
• Connected components algorithms
• Network algorithms
• Residual network
## Contributors
##### fim is a collection of some popular frequent itemset mining algorithms implemented in Go.
fim fim is a collection of some popular frequent itemset mining algorithms implemented in Go. fim contains the implementations of the following algori
##### Data structure,Algorithms implemented in Go (for education)
Data structure,Algorithms implemented in Go (for education) List of Content : 1. Math - 2. String - 3. Conversions - 4. Sort - 5. Search - 6. Data str
##### Tree algorithms in Golang
Tree Algorithms in Golang This is my humble attempt to share some of the tree algorithms in Golang. Pull requests are always welcome! :) Contents Tree
##### Algorithms and Data Structures Solved in Golang
Algorithms and Data Structures Solved in Golang Hi! I'm Bruno Melo and this repository contains a lot challenges solved on many plataforms using go as
##### Golang examples of algorithms according to its time complexity.
big-o-notation-go Examples of algorithms and explanation for each Big O Notation category. Some examples are based in this video. If you didn't manage
##### Some data structures and algorithms using golang
Some data structures and algorithms using golang
##### Data structures and algorithms implementation from ZeroToMastery course
ZeroToMastery Data Structures & Algorithms course This repo includes all the data structure and algorithm exercises solutions and implementations. Ins
##### Algorithms for various integer sequences from the OEIS site.
OEIS The ongoing quest to program every sequence in the OEIS database (in Golang) Content sequences -- The folder containing the seq package, which co
##### Data Structures & Algorithms in Go
Data Structures and Algorithms with Go The aim of this repository is to provide Gophers with how data structures and algorithms are implemented in the
• #### Flaky test: dfs_test.go
The second test sometimes passes, sometimes fails. `t.Errorf("should visit 5 vertices; visited %d", walks)`
The stopping condition is
`````` if v == 5 {
*stop = true
}
``````
This means that if you reach vertex 5, then the walk should terminate. It's sure that we won't seen node 6 in this case, but there is no guarantee that we have already visited node 7. It depends on go's internal ordering of map keys.
opened by gszjulcsi 1
• #### Implementing topological sorting is not possible
I'm quite new to golang, pointers and topological sorting, so I could be quite wrong in my analysis, so please excuse any incorrectness.
I am working on some graph algorithms, and I decided to use your code as a base. In particular, I'm interested in implementing topological sorting which happens to be missing from this git repo!
I tried to implement the 1962 algorithm described here: https://en.wikipedia.org/wiki/Topological_sorting
For this algorithm, it seems you need to be able to "mark" vertexes. Since your Vertex doesn't have additional storage fields, I tried using my own type:
``````type Node struct {
Name string
Comment string
Marking string
}
``````
I was able to make this work, until I got to actually setting the markings. I think the reason is that throughout your code, your pass around copies of the Vertex value, as opposed to references (pointers) of it. As a result, every time I set the struct value, it is not seen, since I've only made my changes on a copy.
My knowledge of pointers is quite weak, so if I've misunderstood this, please let me know!
Solutions:
1. Fix this graph library so that Vertex's are passed around by pointer (reference) so that this isn't an issue.
2. Maintain a separate map of unique Vertex identifier to the Node struct I want, and always do lookups/setters on this mapping. I don't think this is a very elegant.
3. I've greatly misunderstood this go code, pointers, and everything else.
Additional goals: I'd like to store additional data associated with each Vertex. If I'm able to do this with this library, that's great, but at the moment it seems to be difficult.
If there is a more appropriate library that I should be using for graph operations in golang, please let me know!
opened by purpleidea 1
##### Releases(v5.8.3)
###### Go translations of the algorithms and clients in the textbook Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
Overview Go translations of the Java source code for the algorithms and clients in the textbook Algorithms, 4th Edition by Robert Sedgewick and Kevin
175 Dec 13, 2022
###### Graph algorithms and data structures
Your basic graph Golang library of basic graph algorithms Topological ordering, image by David Eppstein, CC0 1.0. This library offers efficient and we
616 Jan 2, 2023
###### Some algorithms in go: maxflow(min-cuts or graph-cuts), edit-distance.
Algorithms In this repository, some algorithms are implemented in go language. GoDoc link: ed maxflow About Max-flow problem: A flow network is repres
15 Sep 8, 2022
###### Graph algorithms and data structures
Your basic graph Golang library of basic graph algorithms Topological ordering, image by David Eppstein, CC0 1.0. This library offers efficient and we
9 Jan 25, 2021
###### Common algorithms written in Go.
Common Algorithms in Go This repository contains a collection of a variety of common algorithms implemented using Go. Algorithms Implemented Search Li
1 Dec 28, 2021
###### This repo is where I'll be attempting to capture some generic algorithms written in Go
Go Generic Algorithms Welcome friends! ?? This repo is where I'll be attempting
27 Apr 13, 2022
122 Dec 13, 2022
###### Go implementation of C++ STL iterators and algorithms.
iter Go implementation of C++ STL iterators and algorithms. Less hand-written loops, more expressive code. README translations: 简体中文 Motivation Althou
170 Dec 19, 2022
###### Data structure and relevant algorithms for extremely fast prefix/fuzzy string searching.
Trie Data structure and relevant algorithms for extremely fast prefix/fuzzy string searching. Usage Create a Trie with: t := trie.New() Add Keys with:
623 Dec 27, 2022
###### Data Structure Libraries and Algorithms implementation
Algorithms Data Structure Libraries and Algorithms implementation in C++ Disclaimer This repository is meant to be used as a reference to learn data s
642 Dec 8, 2022 | 1,492 | 6,780 | {"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-2023-23 | latest | en | 0.845467 |
https://tradingmarkets.com/recent/stock_market_analysis_and_fibonacci_part_2-678700 | 1,713,404,381,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817184.35/warc/CC-MAIN-20240417235906-20240418025906-00267.warc.gz | 552,719,332 | 35,105 | # Stock Market Analysis and Fibonacci, Part 2
In part 1 TradingMarkets contributor John Jagerson discussed a few tactical concepts and tips to understand the Fibonacci Analysis. To see part 1 of “Stock Market Analysis and Fibonacci”, click here.
Through the beginning sections of this series of instructional articles I will be demonstrating the three most common fibonacci tools used by analysts. Once I have shown the tools used we will shift focus and start talking about how to apply these tools in real market situations. As with anything new, the best way to really internalize what you are learning is to use it. Experiment on your own with the tools you are learning about and start to look for those support and resistance lines yourself.
Fibonacci fans are very similar in concept to Fibonacci retracements and in many ways they are used the same way. Both are effective tools for identifying support and resistance levels, entries and exits, and stop and price target levels. Ultimately, you would try both and decide which works best for your trading style and analytical preferences.
How Fans and Retracements differ
1. Fans are more useful when a stock is trending, because they follow the trend diagonally rather than horizontally on the charts.
2. Fans will often stay valid longer than a Fibonacci retracement analysis because they accommodate a trend.
How Fibonacci Fans are Constructed
>The Fibonacci fan uses the same primary ratios of 38.2%, 50% and 61.8% that were discussed in the last section on retracements. The Fibonacci study is applied to the high and low of a trend in the same way that a Fibonacci retracement is placed. The diagonal fan lines are then based on an imaginary vertical line drawn from the top to the bottom price levels of the trend.
The fan lines are drawn from the bottom of the trend through the vertical line at its 38.2, 50 and 61.8% points. In the chart below you can see this how this would look if you could see those lines drawn on the chart.
Each level of the Fibonacci fan acts as a support and resistance line and is very useful when the market is trending because it will adjust to a long term trend. The lines create candidate support areas that can be used to enter a new trade in the direction of the existing trend. They are also useful as a warning for potential resistance areas that can be used to trigger tighter risk control or even to take some profits off the table.
How to draw Fans
The process for drawing Fibonacci fan lines is similar to Fibonacci retracements but because they accommodate the trend, they may have to be adjusted less frequently.
First, identify the trend by anchoring the Fibonacci fan study to the top or bottom of the trend you are identifying. In the example below, we will use the bottom on Apple (AAPL) in February as the first anchor point. The top that occurred on May 14th would have worked well as the second anchor for my Fibonacci rays. You can see the anchors and the subsequent areas identified by the fibonacci rays that would have identified short term resistance.
Here are a few tips that will help you better understand how Fibonacci fans work, and how you can begin experimenting with them in your own trading.
How to anchor Fans
Like a Fibonacci retracement analysis, determining where the tops and bottoms of the trend are is somewhat subjective. However, Fibonacci rays, like retracements, can tolerate a fair amount of variation as long as you are picking significant highs and lows.
Here is an example of the same AAPL chart but rather than anchoring the bottom of the analysis with the February 2008 lows an analyst might have selected the significant bottom in August 2007. As you can see the fans lines were still very helpful in identifying the August 2008 top and bottom. Pretty neat, eh?
When to adjust the anchor points
Because fan lines are drawn to accommodate a trend you don’t “have” to move the anchor points until the trend moves outside, either above or below, the range of those lines. In the video we will look at a specific example of this kind of situation. Quite often the study will stay intact as long as the trend itself lasts.
Entry points and profit targets
The distance between fan lines becomes wider the further the trend extends. Be aware that this makes developing a consistent rule of thumb for entry points and profit targets more difficult than it is for Fibonacci retracements.
Don’t get too steep
Not every analytical method will work in every situation. Very steep trends are not very conducive to this kind of analysis. In the chart below you can see the affects of this problem when the trend used to anchor the Fibonacci fan study was a result of a very fast moving market. The market almost immediately moved outside the range of the Fibonacci fan study and limited its usefulness.
Alternatively, very fast trends or corrections can be ideal situations for a Fibonacci retracement study to find potential areas of support or resistance. As you can see in the chart below, we could have gleaned some very valuable information from a retracement study in the same situation.
John Jagerson is the author of many investing books and is a co-founder of LearningMarkets.com and ProfitingWithForex.com. His articles are regularly featured on online investing publications across the web. | 1,066 | 5,359 | {"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-2024-18 | latest | en | 0.94518 |
https://www.jiskha.com/display.cgi?id=1255994795 | 1,511,375,590,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806620.63/warc/CC-MAIN-20171122175744-20171122195744-00151.warc.gz | 832,709,187 | 3,594 | # Physics
posted by .
no idea all HELP appreciated!!
A shot-putter puts a shot (weight = 70.3 N) that leaves his hand at distance of 1.45 m above the ground.
(a) Find the work done by the gravitation force when the shot has risen to a height of 2.15 m above the ground. Include the correct sign for work.
(b) Determine the change (ÄPE = PEf - PE0) in the gravitational potential energy of the shot.
## Similar Questions
1. ### Physics
A shot putter puts a shot (weight=70.3N) that leaveshis hand at distance of 1.51m above the ground. (a) Find the work done by the gravitatiob force when the shot has risen to a height of 2.10m above the ground. include the correct …
A shot-putter puts a shot (weight = 70.1 N) that leaves his hand at distance of 1.53 m above the ground. (a) Find the work done by the gravitation force when the shot has risen to a height of 2.18 m above the ground. Include the correct …
3. ### Physics
A shot-putter puts a shot (weight = 71.9 N) that leaves his hand at distance of 1.47 m above the ground. (a) Find the work done by the gravitation force when the shot has risen to a height of 2.20 m above the ground. Include the correct …
4. ### Physics
a shot-putter throws the shot with an intial speed of 14 m/s at a 40 degree angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.2m above the ground. t=2.06?
5. ### Physics
A shot-putter throws the shot (mass = 7.3kg) with an initial speed of 15.0 m/s at a 33.0 degree angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.00m above …
6. ### physics
A shot-putter throws the shot ( mass = 7.3 kg) with an initial speed of 15.0 m/s at a 33.0 degreCalculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 1.90 m above the ground.e angle to …
7. ### physics
A shot-putter throws the shot with an initial speed of 15.5m/s at a 34 degree angle to the horizontal. calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20m above the ground.
8. ### Physics 1
A shot-putter puts a shot (weight = 71.3 N) that leaves his hand at distance of 1.62 m above the ground. (a) Find the work done by the gravitation force when the shot has risen to a height of 2.08 m above the ground. Include the correct …
9. ### Physics
at the moment when a shot putter releases a 4kg shot the shot is 1.25 m above the ground and travelling at 7 m/s. it reaches a maxium height of 3.7 m above the ground and then falls to the ground. air resistance is negligible and the …
10. ### Physics
A shot-putter throws the shot ( mass = 7.3 kg) with an initial speed of 14.0 m/s at a 36.0 ∘ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 …
More Similar Questions | 809 | 2,944 | {"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-2017-47 | latest | en | 0.907284 |
https://ru.scribd.com/document/240533228/Scheduling-Examples | 1,566,239,688,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027314904.26/warc/CC-MAIN-20190819180710-20190819202710-00440.warc.gz | 625,068,819 | 62,247 | You are on page 1of 28
# KE-90.
## 2500 Basics in production
planning and control
Scheduling
Exercise 1
A job shop incurs a cost of C dollars per day for each
day a job is in the shop. At the beginning of a month,
there are five jobs in the shop. The data for these jobs
are given below:
a) If cost per day is \$50 for each job, what schedule will
minimize total cost?.
Work task 1 2 3 4 5
Processing time 5 3 10 2 4
Due date 10 15 20 9 7
Exercise 1
b) Suppose job i costs C
i
dollars per day for each
day it is in the shop. What schedule will minimize
total cost?
Task 1 2 3 4 5
C
i
30 10 20 5 50
Exercise 1a - solution
All the jobs have the same cost per day
therefore the total cost is minimized when an
average flow time is minimized.
This can be done using Shortest Processing
Time (SPT)-method
The SPT method minimizes also an average
tardiness and an average queuing time.
SPT-method:
a schedule is obtained by sequencing jobs in
nondescending order of processing times
7 9 20 15 10 Due date
4 2 10 3 5 Processing time
5 4 3 2 1 Work task
7 9 20 15 10 Due date
4 2 10 3 5 Processing time
5 4 3 2 1 Work task
Exercise 1a - solution
Jobs are arranged from the shortest processing time to
the longest one:
<4,2,5,1,3>
Note, that jobs 5, 1, and 3 are tardy. There is no penalty
for a tardy job so we do not have to take this into
consideration.
Mean flow time, F
average
=(14+5+24+2+9)/5=10,8.
Task 4 2 5 1 3
Ready 2 2+3=5 5+4=9 9+5=14 14+10=24
Due date 9 15 7 10 20
7 9 20 15 10 Due date
4 2 10 3 5 Processing time
5 4 3 2 1 Work task
7 9 20 15 10 Due date
4 2 10 3 5 Processing time
5 4 3 2 1 Work task
Exercise 1b - solution
Now each job has a unique cost per day and the
total cost needs to be minimized.
Weighted Shortest Processing Time (WSPT)
procedure is more appropriate when the tasks
are not of equal importance.
At first all the weighted processing times (=P/C)
are calculated and then the jobs arranged from
the shortest weighted processing time to the
longest:
7 9 20 15 10 Due date
4 2 10 3 5 Processing time
5 4 3 2 1 Work task
7 9 20 15 10 Due date
4 2 10 3 5 Processing time
5 4 3 2 1 Work task
Exercise 1b - solution
Task 1 2 3 4 5
P 5 3 10 2 4
C 30 10 20 5 50
P/C 0,17 0,33 0,50 0,40 0,08
Exercise 1b - solution
Task 5 1 2 4 3
Ready 4 4+5=9 9+3=12 12+2=14 14+10=24
Due
date
7 10 15 9 20
Schedule:
<5,1,2,4,3>.
Jobs 4 and 3 are tardy
Exercise 2
The following jobs are due in the next few days:
Task 1 2 3 4 5 6
Duration 5 4 3 1 0.5 2
Due date 11 10 16 2 1 3
Exercise 2
a) Can one person finish all these jobs on time? Justify.
b) Give the schedule that should be followed in processing
these jobs. Justify your choice of a schedule.
c) If the company pays a penalty of 10 per day for a job
that is tardy but receives no reward for jobs finished
early, what schedule would you recommend?
d) If the company receives a reward of 10 per day that a
job is finished early and a penalty of 10 per day that
a job is tardy, what schedule would you recommend?
Task 1 2 3 4 5 6
Duration 5 4 3 1 0.5 2
Due date 11 10 16 2 1 3
Exercise 2a - solution
The last job should be ready in 16 days; all jobs take
5+4+3+1+0,5+2=15,5 days
Therefore this is not restrictive, but for example
<5,4,6,...> will be tardy. One person cannot finish all
these jobs in time.
Exercise 2b - solution
Due Date (DD)-method could be used to minimize the
maximum tardiness:
DD-method: the jobs are sequenced in the order of
nondecreasing due dates.
1
0.5
5
3
2
6
2 16 10 11 Due date
1 3 4 5 Duration
1
0.5
5
3
2
6
2 16 10 11 Due date
1 3 4 5 Duration
Exercise 2b - solution
The schedule with the DD method:
<5,4,6,2,1,3>
Task 5 4 6 2 1 3
Duration
0,5 0,5+1=1,5 1,5+2=3,5 3,5+4=7,5 7,5+5=12,5 12,5+3=15,5
Due date
1 2 3 10 11 16
1
0.5
5
3
2
6
2 16 10 11 Due date
1 3 4 5 Duration
1
0.5
5
3
2
6
2 16 10 11 Due date
1 3 4 5 Duration
Exercise 2c - solution
The maximum tardiness should be minimized
and therefore DD-method might be the best
option since it minimizes the maximum
tardiness:
(see Item b)
0,5*10 +1,5*10 =20
You could also test all the possible
combinations.
Exercise 2d - solution
The average processing time needs to be minimized.
SPT method:
<5,4,6,3,2,1>
Task 5 4 6 3 2 1
Duration 0,5 0,5+1=1,5 1,5+2=3,5 3,5+3=6,5 6,5+4=10,5 10,5+5=15,5
Due date 1 2 3 16 10 11
1
0.5
5
3
2
6
2 16 10 11 Due date
1 3 4 5 Duration
1
0.5
5
3
2
6
2 16 10 11 Due date
1 3 4 5 Duration
Exercise 2d - solution
Cost: 0,5+0,5+4,5)*10 =55
Reward: (0,5+0,5+9,5)*10 =105
Profit: 50
DD-method:
Cost: 20
Reward: (0,5+0,5+2,5+0,5)*10 =40
Profit: 20
SPT method gives better results.
Exercise 3
The following data are given for a single processor,
static job shop:
Task 1 2 3 4 5 6
Processing time 3 2 9 4 2 4
Due date 17 21 5 12 15 24
Exercise 3
a) Give a schedule that minimizes the average flow time.
b) Give a schedule that minimizes the number of tardy
jobs.
Exercise 3a - solution
SPT-method:
<2,5,1,4,6,3>
Exercise 3b - solution
Minimizing the number of tardy jobs using Moore method
Task 3 4 5 1 2 6
Ready 9 9+4=13 13+2=15 15+3=18 18+2=20 20+4=24
Due date 5 12 15 17 21 24
Exercise 3b - solution
2) The first tardy job is 3. No jobs to the left, remove job
3.
Obtained DD- schedule after removal:
Taks 4 5 1 2 6
Ready 4 4+2=6 6+3=9 9+2=11 11+4=15
Due date 12 15 17 21 24
Exercise 3b - solution
3) Now there are no tardy jobs. Deleted job number 3 is
now added at the end of the schedule:
Task 4 5 1 2 6 3
Ready 4 4+2=6 6+3=9 9+2=11 11+4=15 15+9=24
Due date 12 15 17 21 24 5
Exercise 4
Consider a production line with two production
machines, A and B. A job should be completed first on
machine A and then on machine B. The processing
times and due dates for each tasks are as follows:
Task 1 2 3 4 5 6 7 8 9 10
A 2 7 9 0 3 10 1 5 6 8
B 6 8 4 10 9 7 5 1 2 3
Due date 25 19 30 25 16 55 60 32 45 39
Exercise 4
a) Determine the schedule that minimizes the flow time.
b) What is the minimum flow time for your schedule?
c) How many jobs are tardy in your schedule?
Exercise 4a - solution
Johnson method minimizes the flow time:
1) Define the shortest processing time (here:
job 4, machine A).
2)
a. If the job is on machine A, relocate it on the first
free position (here: <4,...>).
b. If the job is on machine B, relocate it on the last
free position.
3) Delete the job from the original list and
Exercise 4a - solution
<4,...>
<4,7,...>
<4,7,...,8>
<4,7,1,...,8>
<4,7,1,...,9,8>
<4,7,1,5,...,9,8>
<4,7,1,5,...,10,9,8>
<4,7,1,5,...,3,10,9,8>
<4,7,1,5,2,...,3,10,9,8>
<4,7,1,5,2,6,3,10,9,8>
Exercise 4b - solution
Flow time is 55 days.
Exercise 4c - solution
6 jobs will be tardy.
Task 4 7 1 5 2 6 3 10 9 8
15
15+6
=21
21+9
=30
30+8
=38
38+7
=45
45+4
=49
49+3
=52
52+2
=54
54+1
=55
Due date 25 60 25 16 19 55 30 39 45 32 | 2,751 | 6,708 | {"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-2019-35 | latest | en | 0.823925 |
https://quizizz.com/admin/quiz/5df75a856af441001bc5e065/square-numbers | 1,656,318,787,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103329963.19/warc/CC-MAIN-20220627073417-20220627103417-00699.warc.gz | 522,658,386 | 8,084 | Square Numbers
3 minutes ago
rday_69475
Save
Edit
Host a game
Live GameLive
Homework
Solo Practice
Practice
• Question 1
30 seconds
Report an issue
Q.
What is the square root of 4 ?
1
2
4
7
• Question 2
30 seconds
Report an issue
Q.
What is the square root of 16 ?
3
8
4
10
• Question 3
30 seconds
Report an issue
Q.
What is the square root of 49 ?
40
9
8
7
• Question 4
30 seconds
Report an issue
Q.
A square rug has an area of 64. What are the dimensions?
6 X 6
7 X 7
8 X 8
9 X 9
• Question 5
30 seconds
Report an issue
Q.
What is the square root of 25 ?
4
6
5
9
• Question 6
30 seconds
Report an issue
Q.
Which of these numbers are square numbers?
2, 4, 36, 54, 100
2, 4, 52, 60, 100
4, 36, 81, 100
4, 36, 60, 100
• Question 7
30 seconds
Report an issue
Q.
What is 9 squared?
36
81
25
49
• Question 8
30 seconds
Report an issue
Q.
What is 12 squared?
144
156
89
122
• Question 9
30 seconds
Report an issue
Q.
What is 22
4
2
• Question 10
30 seconds
Report an issue
Q.
What is 12
1
2
• Question 11
30 seconds
Report an issue
Q.
What is 32
3
6
9
• Question 12
30 seconds
Report an issue
Q.
What is 52
25
20
10
30
• Question 13
30 seconds
Report an issue
Q.
What is 82
16
64
48
72
• Question 14
30 seconds
Report an issue
Q.
What is 112
22
121
132
110
• Question 15
30 seconds
Report an issue
Q.
What square number would come next?
6x6=36
2x2=4
8x8=64
10x10=100
• Question 16
30 seconds
Report an issue
Q.
How do I find a square number? | 554 | 1,522 | {"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-2022-27 | latest | en | 0.799124 |
https://thefiringline.com/forums/showthread.php?p=3100753 | 1,508,497,850,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824068.35/warc/CC-MAIN-20171020101632-20171020121632-00289.warc.gz | 832,911,347 | 19,173 | The Firing Line Forums Shim scope mount to equal 20MOA?
Forum Rules Firearms Safety Firearms Photos Links Library Lost Password Email Changes
Register FAQ Calendar Search Today's Posts Mark Forums Read
April 30, 2008, 09:58 PM #1 Glenner Senior Member Join Date: April 4, 2008 Location: Indiana Posts: 127 Shim scope mount to equal 20MOA? How many thousandths of an inch would I have to shim the rear of a scope base/mount to equal 20MOA of elevation? I'm not sure how to do the math on this. I appreciate any help. THANKS!!!
May 1, 2008, 01:40 AM #2 Scorch Senior Member Join Date: February 13, 2006 Location: Washington state Posts: 12,865 You would have to shim the rear base approximately .100", but I would not recommend it. That much shimming would put the mounting screws at an odd angle and they would not seat correctly and hold the base tight. If you are deas set on a do-it-yourself tapered scope base, buy a gunsmith base blank and have it cut to fit your receiver, then drilled, that way the screws will be in line with the mounting holes. __________________ Never try to educate someone who resists knowledge at all costs. But what do I know? Summit Arms Services Taylor Machine
May 1, 2008, 09:29 AM #3 Harry Bonar Senior Member Join Date: December 5, 2004 Location: In the Vincent, Ohio general area. Posts: 1,804 shim Sir, Never shim anything. Harry B.
May 1, 2008, 10:48 PM #4 taylorce1 Senior Member Join Date: November 18, 2005 Location: On the Santa Fe Trail Posts: 6,590 Do you want to bring the elevation up or down? Wouldn't raising the rear base bring your elevation down? Most people I hear of wanting that kind of base are doing long range target shooting. If you are going to get into long range shooting you might as well do it right and just buy the proper bases.
May 2, 2008, 06:02 AM #5 GoSlash27 Senior Member Join Date: November 26, 2004 Location: Iowa Posts: 3,118 2oMoa= 1/3* tan(1/3)= 5.818x10^-3 Multiply this by the space (center-to-center) of your scope mounts. ex. 5.818x10^-3x 5"= 29.1 thousandths of an inch. I'll leave it to you to decide whether it's a good idea, but that's the math. __________________ Bill of Rights Must be 18. Void where prohibited. Not available in all states. Some restrictions apply.
May 2, 2008, 10:19 AM #6 rgitzlaff Senior Member Join Date: January 8, 2006 Location: Madison, WI Posts: 517 burris signature offsets If you need more elevation and don't want to break the bank on expensive tapered bases, get yourself a set of burris signature rings along with some offset inserts. They come in both 1" and 30mm sizes and can fit standard or weaver type bases. The rings use plastic inserts that sit in kind of a spherical groove so they can pivot to align your scope perfectly without the need to lap. the plastic inserts also will not mar your scope at all. Good luck.
May 3, 2008, 05:54 AM #7
GoSlash27
Senior Member
Join Date: November 26, 2004
Location: Iowa
Posts: 3,118
taylorce,
Quote:
Wouldn't raising the rear base bring your elevation down?
It'd bring the groups up in relation to your point of aim. Just like with leaf sights; the group goes wherever the rear sight goes.
__________________
Bill of Rights
Must be 18. Void where prohibited. Not available in all states. Some restrictions apply.
May 3, 2008, 06:29 AM #8 Glenner Senior Member Join Date: April 4, 2008 Location: Indiana Posts: 127 GoSlash27, THANKS for the math, I need to study that a little. At a glance I don't quite understand it. You're way ahead of me! Gentlemen, I really appreciate all the sound advice, I've got the Burris Signature rings on order, BUT, the 1'' rings are on backorder nationally. I have a set of them in 30mm and like them. I need the 1'' rings for a Leupold 36X scope. I think I'm going to sell that scope and cancel the 1'' ring order. The 36X fixed power does not seem to be the best choice for my Savage 6.5 x 284 for 600 to 1,000 yard shooting. Again, THANK YOU gents!!!
May 3, 2008, 08:11 AM #9 GoSlash27 Senior Member Join Date: November 26, 2004 Location: Iowa Posts: 3,118 Glenner, all the goofy symbols make it look like heiroglyphics. The idea is that a degree is broken up into 60 minutes. the 20 minutes you wish to move your group is therefore 20/60 degrees, or 1/3 of a degree. The tangent function is simply the slope of the angle (rise/run). No matter how large the triangle, the slope will be the same. In this case, a triangle 1/3 of a degree will rise 0.005818 units for every unit of run (regardless of what unit you're using). So you plug into your calculator 20 (minutes of angle) / 60 (minutes in a degree) then hit "tan". It spits out 0.005818. So for every unit of run, a 20MoA angle will rise 0.005818 units. In this case the run (base side of your triangle) is measured from your front ring to your rear ring. So you multiply that run by 0.005818 to find the rise, which is how much you shim. In my example, if your scope mounts are 5" apart you'd shim it 30 thousandths. Hope this clarifies things! __________________ Bill of Rights Must be 18. Void where prohibited. Not available in all states. Some restrictions apply.
May 3, 2008, 10:40 AM #10 surveyor Senior Member Join Date: April 13, 2007 Posts: 719 Glenner, EGW has a base in 25 moa for a savage, for 40 bux.. Warne makes 20 moa bases Farrell makes 20 & 30 moa bases Seekins makes 20,30, & custom bases Nightforce makes 20 & 40 moa bases Ior has a 35 moa base going through this myself.. changing out a warne 0 moa for a EGW 25 moa base on a savage F/TR with a IOR 6x24x50 scope in 35mm tube.. http://www.seekinsprecision.com/rails.html http://www.warnescopemounts.com/scopemount_chart.html http://www.kenfarrell.com/scan/st=db...ml?id=dg6VcQRr http://egw-guns.com/store/index.php?...roducts_id=179 http://egw-guns.com/store/index.php?...roducts_id=224 http://www.kenfarrell.com/ http://www.valdada.com/catalog/b831e...f81a7cc1c.aspx http://www.nightforceoptics.com/RING...___mounts.html
May 3, 2008, 01:22 PM #11 Unclenick Staff Join Date: March 4, 2005 Location: Ohio Posts: 13,720 If you don't have rings like the Burris that allow their alignment axis to adapt to the scope tube axis, then, as Harry said, don't shim it. You will wind up with the front and rear rings not coaxial. It may be challenging to lap them far enough to correct the problem without loosening their grasp on the tube. If you don't, the offset in their axes will then indent the scope tube (also called, ringing the tube). That can damage the scope by throwing the optics out of alignment. If you can't get the ball-joint rings, get the special ring bases which have that 20' taper angle machined into both the front and rear to keep the rings on the same plane and their borings aligned. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member
May 5, 2008, 06:39 PM #12 wncchester Senior Member Join Date: December 1, 2002 Posts: 2,832 The math is correct. You may want to try "shimming" the easy way and it won't stress your rings and scope either. Simply make the shim of expoxy! Clean the bottom of the base well. Coat the base sides, top surface and the rifle's top surfaces with a release agent or Kiwi Neutral Shoe Wax. Plug the rifle's middle mount holes with candle wax and use a Q-tip to coat the two end holes with release. Put the two end screws in the mount and run a length of tape along the top of the base to hold them there until you are ready to screw them down. At that point, you are ready to fit the base to the rifle. Place a metal shim, a thin (but curved washer) will do nicely, 25-30 thousanths thick under the rear mounting screw and place a layer of epoxy along the full length of the bottom of the mount. Attach the base to the rifle and just snug up - DO NOT tighten past snug! - the two screws. After a couple of hours, more or less depending on your epoxy type, clean off any squeeze-out with a toothpick, then let it set over night to harden completely. When you remove it, your base will have a custom molded, stress free "shim" that you can then attach normally. And, if you want to remove the epoxy later just heat it up enough to allow you to scrape it off.
May 6, 2008, 05:24 PM #13 rgitzlaff Senior Member Join Date: January 8, 2006 Location: Madison, WI Posts: 517 That method is still not perfect. Yes it takes any bending stresses out of the scope base, but the screws still will not sit correctly since the holes will be at a slight angle now. When torqued down the screw heads will be forced to bend in order to seat correctly in the countersunk holes. This is less than ideal, I strongly recommend the burris signature rings. They are not on backorder everywhere, Midway looks to have about half of them in stock. If you check The Optic Zone or SWFA I bet they would have any rings you need.
October 13, 2008, 08:23 PM #14 MikeMurf0505 Junior member Join Date: October 13, 2008 Location: Houston Posts: 64 My scope is touching the barrel Would a shim be ok in that instance? I think I about 1/1000th is all I would need, but again we come to the idea about stability. This is a 25-06 Sendero I JSUT today got. I have a Barska scope (6.5 to 20 x 50mm) that I am trying to mount - should I be getting higher rings and a better scope?
October 14, 2008, 08:07 AM #15 Harry Bonar Senior Member Join Date: December 5, 2004 Location: In the Vincent, Ohio general area. Posts: 1,804 shim Sir; If, I say, IF, you're going to "shim" up a scope a very small amount, you can put some cut brass stock under the scope at BOTH bases - not just one. Some bases and rings are far enough off to start with. Scope, or, iron sight mounting is done so that the sights are paralel to the bore line (the bases) so that the optical center of the scope is also there, then you can adjust the scope internally. A good test is to remove the bolt - look through the bore and raise your eyes up and see if the "exit pupil" is centered in the middle of the eyepiece!. Mausers with Wever bases and rings are particularly prone to misalignment, but I still do not shim them. Everything must be "kosher" and aligned in scope mounting. Redfield one piece bases are very good because the alignment can be adjusted at the read. Even as close as Redfield on piece bases are you will still see the rear sometimes need to be pulled down as you tighten that screw! Scopes cannot be mounted, "on a bind." Harry B.
October 26, 2008, 03:10 PM #16 bcarver Senior Member Join Date: February 22, 2007 Location: Jackson,Mississippi Posts: 838 coke can shim cut a square from the side of a coke can. slightly smaller than width of base. See how much elevation it give you. see how many shims you need. I never needed more than two.
October 26, 2008, 03:34 PM #17 Doyle Senior Member Join Date: June 20, 2007 Location: Starkville, MS Posts: 6,549 I just went throught shimming a scope. 3 thicknesses of a coke can weren't enough. I wound up cutting the brass off of a shotgun shell and using 2 of those and a couple of coke can shims. So far, so good.
October 28, 2008, 01:06 AM #18
nra_guns_winner
Junior member
Join Date: August 28, 2007
Location: Wichita, Kansas
Posts: 121
I too tried this, I needed about .009 shim to give myself more vertical elevation and less in the downward direction. I ended up shimming so much that I then needed new scope base screws. So as for shimming don't do it. Consider a canted scope mount from somewhere like midway. Also I recommend sticking with a one piece base. They are proven to be stronger and more rigid. I have shim stock in .003" pieces of alum. I'd sell you some real cheap. About enough to cover shipping. Just don't do it. Below is my 700 VSF in .308. What a joy it is to see varmint brains in a fine red mist.
Attached Images
DSC05233.jpg (224.2 KB, 616 views)
Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Hogan's Alley Tactics and Training Handguns: The Semi-automatic Forum Handguns: The Revolver Forum Handguns: General Handgun Forum The Hide The Art of the Rifle: Bolt, Lever, and Pump Action The Art of the Rifle: Semi-automatics The Art of the Rifle: General The Dave McCracken Memorial Shotgun Forum NFA Guns and Gear The Hunt The North Corral Lock and Load: Live Fire Exercises Competition Shooting Curios and Relics Black Powder and Cowboy Action Shooting The Skunkworks Gear and Accessories The Smithy Handloading, Reloading, and Bullet Casting Bullet Casting The Harley Nolden Memorial Institute for Firearms Research The Conference Center General Discussion Forum TFL Photo Contest Law and Civil Rights Legal and Political General Zombie Discussion Forum The Firing Line Gun Show Retail Deals and Feedback Forum Support Site Questions and Tech Support (NO FIREARMS QUESTIONS) Software and Function Testing
All times are GMT -5. The time now is 06:10 AM.
-- vBulletin 3 ---- vBulletin 3 - variable fonts ---- Low profile (unsupported) Forum Home Page - Archive - Top | 3,475 | 13,388 | {"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-2017-43 | latest | en | 0.940862 |
https://production.codecademy.com/courses/data-visualization-python/lessons/proj-ii/exercises/line-with-error | 1,624,028,717,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487637721.34/warc/CC-MAIN-20210618134943-20210618164943-00118.warc.gz | 436,447,369 | 29,216 | Learn
Now, we are going to look at the chart called `line_graph.png`. This displays the relationship between the time students say they studied and the scores they received on their final exams.
The data you will need to recreate this chart is in the lists `hours_reported` and `exam_scores`.
Save your recreated chart to a file called `my_line_graph.png`.
### Instructions
1.
Create a figure of width `10` and height `8`.
2.
Plot the `exam_scores` on the x-axis and the `hours_reported` on the y-axis, with a `linewidth` of `2`.
3.
Let’s assume the error on students’ reporting of their hours studying is 20%.
Create a list `hours_lower_bound`, which has the elements of `hours_reported` minus 20%, and a list `hours_upper_bound`, which has the elements of `hours_reported` plus 20%.
You can do this with a list comprehension that looks like:
``y_lower_bound = [element - (element * error_in_decimal) for element in original_list_of_y_values]``
4.
Shade the area between `hours_lower_bound` and `hours_upper_bound` with an alpha of `0.2`.
5.
Give the plot the title `'Time spent studying vs final exam scores'`, x-axis label `'Score'`, and y-axis label `'Hours studying (self-reported)'`.
6.
Save your figure to a file called `my_line_graph.png`. | 306 | 1,265 | {"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} | 2.75 | 3 | CC-MAIN-2021-25 | latest | en | 0.872958 |
https://mathoverflow.net/questions/183163/about-the-maximum-degree-of-multivariate-polynomial-interpolation | 1,571,225,181,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986666959.47/warc/CC-MAIN-20191016090425-20191016113925-00238.warc.gz | 603,952,939 | 26,410 | # About the maximum degree of multivariate polynomial interpolation
It is well known that in the univariate case, to interpolate $k$ points in $\mathbb{R}$, we need to use a polynomial of degree $k-1$.
My question is about multivariate polynomial interpolation in higher dimension. We are given $k$ points $x_1,\ldots,x_k$ in $\mathbb{R}^d$. Define the max-deg of a multivariate polynomial to be the maximum exponent of any variable. For example, the max-deg of the linear function $x_1+x_2+x_3$ is 1 and the max-deg $x_1^2+x_2$ is 2. My question is: given $x_1,\ldots,x_n$, what is the minimum $d$ such that for any $y_1,\ldots, y_d$, there is a polynomial $P$ of max-deg $d$ such that $P(x_i)=y_i\forall i$. The answer should really depend on the configuration of $x_1 ,\ldots,x_k$. For example, if $x_1 ,\ldots,x_k$ are linearly independent, we only need max-deg to be 1 (i.e., we can use a linear function to intepolate it).
Has the same problem (or some thing similar) been studied before?
• Same as before, $d=k-1$. You can't improve on this because the points could be on a coordinate axis. Conversely, you can interpolate with polynomials of this max-deg. – Christian Remling Oct 11 '14 at 4:25
• I am not looking for the worse case scenorios. The answer should really depend on the configuration of $x_1,\ldots,x_k$. For example, if $x_1,\ldots,x_k$ are linearly independent, we only need max-deg to be 1. – jian Oct 11 '14 at 11:07
• Then you get the max-deg's between $0$ and $k-1$, since you can deliberately put some or all of your points on the graph of a given polynomial. – Christian Remling Oct 11 '14 at 16:56
• Maybe I did not make myself clear. My question was "given $x_1,\ldots, x_n$, what the max-deg should be". We do not get to choose where $x_1,\ldots,x_n$ are, but $y_1,\ldots, y_n$ can be arbitrary. – jian Oct 12 '14 at 3:23
One would hope to be able to interpolate data sites $X = \{x_1,\dots, x_Q \}$ with a polynomial from $\pi_m(\mathbb{R}^d)$ when $Q=\dim \pi_m(\mathbb{R}^d)={m+d\choose d}$. Here $m$ is your "max-deg". | 643 | 2,059 | {"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} | 3.6875 | 4 | CC-MAIN-2019-43 | latest | en | 0.831168 |
https://mathsisfun.com/9recurring.html | 1,713,367,737,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817158.8/warc/CC-MAIN-20240417142102-20240417172102-00367.warc.gz | 326,065,096 | 2,640 | # Does 0.999... = 1 ?
The idea is that 0.9 recurring
(0.999... with the digits going on forever)
is actually equal to 1
### Is this really true?
You decide! But here we give some nice arguments as to why it does.
## Three Thirds
Times 3:33 = 3 × 0.333...
So:1 = 0.999...
## Using Algebra
Let us start by having x = 0.999...
x = 0.999...
10x = 9.999...
Subtract x from each side to give us:
9x = 9.999... − x
but we know that x is 0.999..., so:
9x = 9.999... − 0.999...
9x = 9
Divide both sides by 9:
x = 1
But hang on a moment I thought we said x was equal to 0.999... ?
Yes, it does, but from our calculations x is also equal to 1, so:
x = 0.999... = 1
And so:
0.999... = 1
## How Many Nines?
If 0.999... and 1 are the same number, then their difference will be zero.
1 nine:1 − 0.9 = 0.1
2 nines:1 − 0.99 = 0.01
3 nines:1 − 0.999 = 0.001
0.001 = 1103:1 − 0.999 = 1103
n nines:1 − 0.(n 9s) = 110n
As n goes to infinity 110n goes to zero.
So the difference between 1 and 0.999... is zero
0.999... = 1
## Infinite Geometric Series
We can think of 0.999... as being equal to:
=0.9 + 0.09 + 0.009 + 0.0009 + ...
=0.9×0.10 + 0.9×0.11 + 0.9×0.12 + ...
This is an Infinite Geometric Series where a = 0.9 and r = 0.1 with the series being convergent because r is between −1 and +1. The formula for the sum is:
a1 − r
So our sum is equal to:
0.91 − 0.1 = 0.90.9 = 1
0.999... = 1
Footnote: we use 0.999... as notation for 0.9 recurring, some people put a line, or little dot, above the 9 like this: 0.9 | 589 | 1,529 | {"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} | 4.4375 | 4 | CC-MAIN-2024-18 | latest | en | 0.908897 |
http://regentsprep.org/Regents/math/algtrig/ATE3/quadcomlesson.htm | 1,409,173,051,000,000,000 | text/html | crawl-data/CC-MAIN-2014-35/segments/1408500829839.93/warc/CC-MAIN-20140820021349-00289-ip-10-180-136-8.ec2.internal.warc.gz | 167,342,170 | 3,121 | Solving Quadratic Equations with Complex Roots Topic Index | Algebra2/Trig Index | Regents Exam Prep Center
When the roots of a quadratic equation are imaginary,
they always occur in conjugate pairs.
A root of an equation is a solution of that equation.
If a quadratic equation with real-number coefficients
has a negative discriminant,
then the two solutions to the equation are complex conjugates of each other.
(Remember that a negative number under a radical sign yields a complex number.)
Example 1:
Find the solution set of the given equation over the set of complex numbers.
a = 1, b = -10, c = 34
Pick out the coefficient values representing a, b, and c, and substitute into the quadratic formula, as you would do in the solution to any normal quadratic equation. Remember, when there is no number visible in front of the variable, the number 1 is there.
HINT: When the directions say: Express over the set of complex numbers, look for a negative value under the radical sign.
Example 2:
Find the solution set of the given equation over the set of complex numbers.
a = 3, b = -4, c = 10
Example 3:
Find the solution set of the given equation and express its roots in a+bi form.
* Be sure to set the quadratic equation equal to 0. * Arrange the terms of the equation from the highest exponent to the lowest exponent.
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Elizabeth DeMarr | 331 | 1,455 | {"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} | 3.9375 | 4 | CC-MAIN-2014-35 | longest | en | 0.871905 |
https://stats.stackexchange.com/questions/tagged/probability?sort=active&pageSize=50 | 1,547,937,900,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583684033.26/warc/CC-MAIN-20190119221320-20190120003320-00076.warc.gz | 670,819,324 | 36,351 | # Questions tagged [probability]
A probability provides a quantitative description of the likely occurrence of a particular event.
7,000 questions
11 views
### Interpretation of the rate parameter of a Gamma distribution
I am toying with mixture models, especially in a bayesian context and the Gamma (or the inverse Gamma) distribution appears quite often. For example, inverse Gamma is used as a conjugate prior for the ...
22 views
### Why do we care about the joint distribution of the endogenous variables of a causal model?
In general, we can calculate the joint distribution of the endogenous variables of a structural casual model (SCM) as follows $$P(X, X_1, \dots, X_n) = \prod_i = P(X_i \mid \text{parent}(X_i))$$ ...
12 views
### Estimating Differential entropy from unbiased samples of a probability distribution
If I can get N unbiased samples $x$ from $p(x)$ how can I approximate the Differential entropy: $$H(X) = -\displaystyle\int_{x} p(x)\log p(x) dx$$ I'm not very knowledgeable in statistics so I'm not ...
949 views
### How can I model flips until N successes?
You and I decide to play a game where we take turns flipping a coin. The first player to flip 10 heads in total wins the game. Naturally, there is an argument about who should go first. Simulations ...
31 views
### PDF of $\frac{(X_1-X_2)^{2}}{2}$ where X1 and X2 are independent standard normal [on hold]
I'm trying to find the PDF of $$\frac{(X_1-X_2)^{2}}{2}$$ where X1 and X2 are independent standard normal. Any hints on how to proceed with this?
38 views
### Probabilistic user behavior markov models on web
I am considering the following probabilistic Markov model of actions of a user on the results page of a search engine. The user examines the first result, with a probability $A$ he is satisfied with ...
49 views
### How to build a Bayesian Model to estimate the probability distribution of the parameters given the output?
I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following: I have a matrix of temperatures, depending ...
11 views
### Goodness-of-fit test when the sample space is monotonically increasing
I came across this paper which develops a GoF test on data drawn from a circular sample space (i.e. it has cyclical support). I am now wondering if there is a parallel to monotonic supports (or if ...
29 views
### doubtful regarding my solution to bonferroni's principle exercise
Self learning and not quite good at probablility and statistics, my question is regarding solution to exercise 1.2.1 in chapter 1 of Mining of Massive Datasets book. The text of the exercise reads: ...
15 views
### Questions on Notation for PMF and Expectation
Before diving into the Stanford CS229 Machine Learning notes online, I decided to go through the course's notes on probability review and had a few questions. In section 2.2, it states A ...
10 views
### Count probability of average and variance of random variable with normal distribution [on hold]
Please verify my calculation for four exercises placed below. Example 1. Random variable $X$ has distribution $N(100; 10)$. Count $P(90 < \overline{X}_9 < 95)$. Example 2. Random variable $X$ ...
26 views
### Is f(x) = 1/n for x = 0,1,2,…,n a valid PMF? (n>0 an integer) [on hold]
Is f(x) = 1/n for x = 0,1,2,...,n a valid PMF? (n>0 an integer) Intuitively thinking, the summation of the function over the range equals to (n+1)/n which is greater than 1 and so the function isn't ...
83 views
### Proving that given Markov chain is homogeneous. Find state space and transition matrix
Let $X_i$ be the results of a consecutive throws of a die. Let $Z_n=3(X_1^2+\cdots+X_n^2) \bmod 5$. Show that the sequence ${\{Z_n \mid n\geq1\}}$ is a homogeneous Markov Chain. Find a state space and ...
43 views
### Deriving a distribution whose pdf has the shape of a square + a triangle (a right trapezoid)
I want to the derive the PDF which looks like the sum of a triangular and uniform distribution which looks like this: To do this I have simply added the PDFs for the rectangular and triangular parts, ...
9 views
### Probability of userbase recieving special page
Say I have an app. When the app is launched there is a process behind the scenes the determines which of the two outputs the user receives, default or special. The default output displays the app ...
44 views
### Proof of probabilities that may not be independent
I am given the problem: Given $P(A) = \frac{3}{4}$, $P(B) = \frac{3}{8}$, show that: a) $P(A or B) > \frac{3}{4}$. b) $\frac{1}{8} < P(A and B) < \frac{3}{8}$. The problem does not ...
60 views
### On the predictive distribution regarding Bayesian methods for pattern recognition
I am following Pattern recognition and machine learning by Byshop and I was trying to derive myself the predictive distribution resulting from a new data point. For the sake of clarity I post the ...
26 views
### differences between conditional probability and dependency
Sometimes, I read articles about conditional probabilities and other articles about conditional dependency. My question what is the main differences between them? For example, "https://en.wikipedia....
25 views
### Independent Study Statistics/Probability Grad Level [duplicate]
I am trying to decide on topics for my independent study this semester. I am a Pre-Doctoral Mathematics student, so looking for a more math based text rather than engineering based (which I have found ...
93 views
72 views
### Calculating the probability of winning a game of Rainbow Six Siege
I'm currently developing an application in Python that calculates the probability of winning a game of Rainbow Six Siege based on the skill level of the players in the game. Siege is a 5 vs. 5 ...
11 views
### Sufficient conditions for multivariate MGF to be finite in neighborhood of zero
In the one-dimensional case, we have the following fact: (see Existence of the moment generating function and variance for proof) Proposition: The mgf $m(t)$ is finite in an open interval $(t_n,t_p)$ ...
20 views
### NFL Playoff Game Probabilities
Context: My friends and I have this homebrew NFL fantasy football game we play for the playoffs once the NFL regular season is over. The contest is not head-to-head with other players like standard ...
81 views
### Analysis concepts relevant to probability theory
I am taking a course based on Durett. I was wondering if anyone could point me to the analysis skills or topics that are most relevant to Probability Theory. It has been some time since I've taken ...
34 views
### What does $\sum_{\{\textbf{x}:T(\textbf{x})=t\}} f(\textbf{x}; \theta)$ mean?
This is in the following context: $$q(t;\theta) = P(T=t;\theta) = \sum_{\{\textbf{x}:T(\textbf{x})=t\}} f(\textbf{x}; \theta)$$ Where $T=T(\textbf{X})$ is a statistic, $q(t; \theta)$ is the pmf of ...
12 views
### Is the sum of one slowly varying and one regularly varying random variable regularly varying?
Imagine I have given a random variable $X$ with support $\geq 0$ and $\mathbb P(X=0)>0$. Also, I have another independent random variable $Y$ with positive support being regularly varying at zero ...
14 views
### Is the sum of two dependent sub-gaussian variables X and Y still follows sub-gaussian distribution?
I am trying to prove the random vector with dependent sub-gaussian coordinates is also a sub-gaussian random vector. The related question has been asked in https://math.stackexchange.com/q/3072363/...
12 views
### How to find the value for average rate
I'm doing some textbook problems on my own and there are no steps given to the solutions to some of the problems. If anyone could help me solve the following problem, much would be appreciated. "A ...
9k views
### Are Event and Outcome synonymous?
Outcome : An outcome is a result of a random experiment. Event : A single result of an experiment. Are Event and Outcome synonymous ?
23 views
### Recursive Bayes Learning
I'm trying to work through an example from Richard Dudas Pattern Classification on Recursive Bayes Learning. My main question is why do we choose the $max[D^n]$ in: $$max[D^n] \le \theta \le 10$$ ...
28 views
### Compute $P(2\leq x\leq 8)$ with Poisson distribution and $\lambda=7.2$
Compute $P(2\leq x\leq 8)$ with Poisson distribution and $\lambda=7.2$ My attempt: I need calculate this using $R$. then I use this: ...
13 views
### Writing down a conditional probability / finding the underlying probability space
This is a notational issue: Let's say we have a partition of $\mathcal X$ given by $\{\Omega,\Sigma\}$ and we define $P(\omega\in\Omega) = p$, $P(X(\omega)=x|\omega\in\Omega) = \pi$ and \$P(X(\...
11 views
141 views
### Large deviations proof question
Below is part of the proof of large deviations result. K is cumulant generating function. Can anyone explain how the last step follows? This is page 157 of McCullagh's "Tensor Methods in Statistics"
27 views
### Probability of finding a lost item
I am trying to solve the following problem and was wondering if someone can verify my answers. Big Joe has lost an important document. There is a 70% probability it is at home, and a 30% chance it is ...
98 views
+50
### Probabilistic Interpretation of Radial Basis Function
I was wondering if someone could flesh out the probabilistic interpretation of using the Radial Basis Function to compute the probability between an observation and some reference value. My question ...
36 views
### Permutation or Combination?
I am a bit confused, if I have 2 football teams, and the results are three (1: home win, 2: away win and X: draw), I can see that the possibilities for these teams results are 9, which formula (...
91 views
### Probability Mass Functions [closed]
In a bowling "frame", between 0 and 10 pins might be knocked over by a bowling ball. Suppose that a particular bowling alley attracts a mixture of beginners and experts, such that we can assume that ... | 2,411 | 10,044 | {"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} | 3.171875 | 3 | CC-MAIN-2019-04 | longest | en | 0.863181 |
https://edukite.org/course/computer-programming-diploma/?error=login | 1,685,936,071,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224650620.66/warc/CC-MAIN-20230605021141-20230605051141-00344.warc.gz | 270,974,356 | 23,456 | • No products in the cart.
You must be logged in to take this course → LOGIN | REGISTER NOW
### Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
### Certification
Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.
Having an Official Edukite Certification is a great way to celebrate and share your success. You can:
• Show it to prove your success
Course Credit: MIT
### Course Curriculum
Module: 01 1A: Overview and Introduction to Lisp 01:12:00 1B: Procedures and Processes; Substitution Model 00:58:00 2A: Higher-order Procedures 01:01:00 2B: Compound Data 01:17:00 Module: 02 3A: Henderson Escher Example 01:16:00 3B: Symbolic Differentiation; Quotation 00:45:00 4A: Pattern Matching and Rule-based Substitution 01:03:00 4B: Generic Operators 01:23:00 5A: Assignment, State, and Side-effects 01:16:00 5B: Computational Objects 01:05:00 Module: 03 6A: Streams, Part 1 01:07:00 6B: Streams, Part 2 01:03:00 7A: Metacircular Evaluator, Part 1 01:25:00 7B: Metacircular Evaluator, Part 2 01:00:00 Module: 04 8A: Logic Programming, Part 1 00:42:00 8B: Logic Programming, Part 2 01:19:00 9B: Explicit-control Evaluator 01:11:00 10A: Compilation 00:46:00 10B: Storage Allocation and Garbage Collection 00:59:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00
## 4.9
4.9
8 ratings
• 5 stars0
• 4 stars0
• 3 stars0
• 2 stars0
• 1 stars0
No Reviews found for this course.
8 STUDENTS ENROLLED | 576 | 1,963 | {"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-2023-23 | latest | en | 0.785609 |
https://howmanyis.com/area/190-ac-in-sq-m/44041-10-acres-in-square-meters | 1,719,109,105,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862425.28/warc/CC-MAIN-20240623001858-20240623031858-00379.warc.gz | 265,974,929 | 6,230 | How many is
Conversion between units of measurement
Rating 2.50 (2 Votes)
You can easily convert 10 acres into square meters using each unit definition:
Acres
usacre = 10 surveychain² = 4046.8726 m²
Square meters
1 m²
With this information, you can calculate the quantity of square meters 10 acres is equal to.
## ¿How many sq m are there in 10 ac?
In 10 ac there are 40468.726 sq m.
Which is the same to say that 10 acres is 40468.726 square meters.
Ten acres equals to forty thousand four hundred sixty-eight square meters. *Approximation
### ¿What is the inverse calculation between 1 square meter and 10 acres?
Performing the inverse calculation of the relationship between units, we obtain that 1 square meter is 2.4710439e-05 times 10 acres.
A square meter is two times ten acres. *Approximation | 207 | 811 | {"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-2024-26 | latest | en | 0.86254 |
https://www.barnardhealth.us/food-processing/na-ity.html | 1,560,744,354,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998369.29/warc/CC-MAIN-20190617022938-20190617044938-00296.warc.gz | 679,074,351 | 8,951 | ## Na
1 ACA nP At
where ACa = CA(XA2 — XA1) is the concentration increase of the diffusing substance A in the upper container 1 during time At. Substituting equation 65 into equation 25 gives
nr2.
XA1)
Solving for DAB and accounting for the logarithmic mean of the molecular fractions gives
nrAt
Diffusivity in Liquids
When measuring diffusivity in liquids, it is important to be aware that DAB depends on the concentration of the diffusing substance in solution. Constant DAB is only an approximation and may be used in cases of very dilute solutions where only small changes in the concentration occur. It should also be noted that D^ indicates the diffusivity of A through B, and it is different from DBA (diffusivity of B through A). For gases, DAB = DBA. A simple method to determine D^ when A diffuses through B is shown in Figure 5. Two large containers, 1 and 2, are connected by a long capillary tube with diameter 2r and length Y. A dilute solution (of A in B) in container 2 has an initial concentration CA2() and is slightly more concentrated than CAlfj in
Thus the diffusivity £>¿5 depends on the diffusion tube constant Y/nr2 and the logarithmic meanX„lln of the molecular fraction in solution.
### Diffusivity in Solids
When a solid slab with some initial moisture content is brought into an airstream, the moisture inside the solid slab will diffuse through the bulk of the solid and evaporate from its surfaces. Assuming that the slab has a thickness much smaller than its length and width, the one-dimensional Fick's second law (equation 46) can be applied. If the system is maintained at equilibrium and both surface moisture contents are equal, the initial and boundary conditions for the system can be written as at t = 0, C = C0, for 0 < y < Y at y = 0, C = Ce, for t > 0 at y = Y, C = Ce, for t > 0
Equation 46 can be solved for the conditions of equation 68 (4) to give
## Fantastic Organic Food Facts
Get All The Support And Guidance You Need To Be A Success At Utilizing Organic Foods. This Book Is One Of The Most Valuable Resources In The World When It Comes To Getting The Right Information About Eating Healthy With Organic Food.
Get My Free Ebook | 532 | 2,192 | {"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} | 2.828125 | 3 | CC-MAIN-2019-26 | latest | en | 0.911609 |
https://www.casinomeister.com/forums/threads/trtp-and-its-effect-on-what-you-get.57477/ | 1,653,054,994,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662532032.9/warc/CC-MAIN-20220520124557-20220520154557-00310.warc.gz | 767,227,449 | 25,809 | # TipsTRTP and it's effect on what you get......
#### dunover
##### Unofficial T&C's Editor
Staff member
webmeister
PABnonaccred
PABnononaccred
CAG
mm3
Right, lately we have had many people, mainly newbies asking about RTP and thinking they are being ripped by lower than advertised temporary RTP's.
So, in my own little way I hope this explanation helps get your heads around the issue.
So, in my example I am using a TRTP (theoretical return to player) of 95% but for simplicity's sake it will be achieved via the random number generator (RNG) over a mere 100 spins..........
So, the ultimate LOW VARIANCE example would be: You have 100 spins and win 0.95 EVERY spin. (you've all see Starburst lol...)
For my simplified example we have the ultimate HIGH VARIANCE slot - out of 100 spins, 99 will pay bugger-all and one will pay 95.0.
So, I make a deposit, and on my fiftieth spin I win the 95 pounds. I cashout. My RTP for the session (50 played, 95 won) is 190% Yippee.
So, player B coming along makes a deposit of 100. (bear in mind the slot must pay the 95 in every 100 spins.) He obviously loses for the next 50 spins as you just had the 95 win. So, 50 down he now unknowingly enters the next cycle of 100 spins. This time, although he doesn't know it, the next 95 win is going to come on the very last of the 100 spins. He has now lost therefore his whole hundred with a 0 RTP. He deposits another 50 and on the last spin gets the 95 win. His RTP for the last 50 deposit is 190% same as the first player's 50 deposit session. Only he's lost 100 beforehand so his OVERALL RTP at the site is 100%/150 units x 95 unit win = 63.33%.
He will then come on here pissing and moaning (as many of us have) 'it's rigged/awful site/terrible slot'.
BUT....look at the stats - the slot has taken 200 units, paid 2x95 units out therefore has hit it's TRTP of 95%.
OK, so now we see that, complicate the example; turn the 100 spins into 10 million, fill the pool the RNG selects from with any permutation that adds up to 95% of 10 million units i.e. 1 million 0.5x stake values, 500,000 10x stake values, 50 1000x stake values etc. Obviously free spins scatter triggers and values will come into it and of course the likelihood of any win in the pool will be reflected in the reel maps by frequency of symbols - whether the reels are stopped individually with 5 random stops (some are allegedly) or a simple pseudo-reel graphic is computed or selected to match your individual RNG selection (as in MG slots almost certainly and definitely in WMS).
Lastly, the pool is a 'rolling pool' - it doesn't have a fixed end of 10 million as in my 100-spin example (which is more like an AWP works admittedly) but the RNG value you've just had goes back in the pool so there are always the same chances of the player picking any named RNG value on every spin.
(This explains why some casinos like Enzo at 3Dice will openly tell you that although all their slots for example's sake are 95% TRTP, some to date have paid to all players ever 97.8% and some only 93.2% - this is simply the long term effect of luck going either for or against the casino on any particular game, although the median RTP to date on ALL their games together would very likely be nearer the 95%)
Now imagine your 900 deposit will get you 900 goes. You dip your 'hand' blind into the pool in one go and grab 900 values which total 2700 - great, you've grabbed 1 1000x stake win, 500 2x stake wins 397 no-wins and 2 350x stake wins. You're 1800 up, and have had a session RTP of 300%
Next time you only grab 900 values which total 450 - you've had a bad session with a 50% RTP but overall you casino RTP to date is 1800 deposited and played, 3150 taken out = 175%.
Hope this example helps players understand both basic variance and more importantly what session RTP, theoretical RTP and overall personal account RTP actually mean. It is easy to focus on a few bad sessions and not calculate how previous wins and cashouts may mean your overall RTP at that particular site can still remain quite favourable.
#### bpb
##### Banned User - repeated violations of rule 1.14 (tr
PABnonaccred
PABnorogue
Nothing you say is wrong. However, I'm continually amazed at the effort people go through to convince themselves or others that a slot machine with a 5% house edge is a fair gamble. It's highway robbery. Better than 10-15% house edges in B&M casinos. But highway robbery nonetheless.
#### bigjohn
##### Dormant account
Nothing you say is wrong. However, I'm continually amazed at the effort people go through to convince themselves or others that a slot machine with a 5% house edge is a fair gamble. It's highway robbery. Better than 10-15% house edges in B&M casinos. But highway robbery nonetheless.
What makes you think people think like that?
I look at it like this, the money I am depositing and playing is money I probably would have spent on something else stupid (read fun but non-profitable). All the deposits along the way don't really help me nor do I miss that money much. The idea is to get a large amount once in a while that I can use for something else stupid (same implied meaning as before) but bigger.
There is also the excitement of possibly hitting something really nice.
Is any of this making any sense to you?
What would be your ideal gambling game? A 100% RTP slot with zero variance? That would be a riot.
Do you ever take any gambles?
I don't really expect a response from you because you just seem to get a kick out of chiming in with a distortion of whatever the thread concerns.
BTW, I'm still waiting for a reply from you to a comment you made in my RTG rant thread.
#### LaHutti
##### Sr. ÜberUnter Ass. Man.
PABaccred
PABnonaccred
It's called entertainment.
Do you also consider buying 2 theater (or anything else) tickets for me and missus highway robbery ?
Nothing you say is wrong. However, I'm continually amazed at the effort people go through to convince themselves or others that a slot machine with a 5% house edge is a fair gamble. It's highway robbery. Better than 10-15% house edges in B&M casinos. But highway robbery nonetheless.
#### mrmark21
##### Dormant Account
Over priced entertainment. IMO the real problem stems from when people play to win, everything about the slots advertises "win on this slot" then casinos push it as entertainment. I don't mind (they are there to make money) but i feel sorry for the people that fall for the pitches. Which is easy to do when you're in a bad place and some stupid spam (from some probably rogue casino) advertises "get out of debt now with our high paying slots"
I'm a gamer, i play allot, just bought my ps vita about two weeks ago and already have thirty two games downloaded at about thirty to fourty bucks a pop. So i'd be spending that money anyway. I kind of look at gambling as an overpriced gaming arcade (we have Intencity in Australia) where i could win money rather than a crappy novelty toy.
#### Balthazar
##### The Governor
(bear in mind the slot must pay the 95 in every 100 spins.)
Must pay? No. Mathematically it should pay. I know it's only an example but there's a big important difference here.
Lastly, the pool is a 'rolling pool' - it doesn't have a fixed end of 10 million as in my 100-spin example (which is more like an AWP works admittedly) but the RNG value you've just had goes back in the pool so there are always the same chances of the player picking any named RNG value on every spin.
Yes, the numbers go back in the pool after each spin. This is what people have to remember.
Also the theory that each number in the pool is associated with a "win" or "lose" has been pretty much debunked. We now have to assume that the RNG stops the reels in random positions, and that's where your wins/loses come from.
#### dunover
##### Unofficial T&C's Editor
Staff member
webmeister
PABnonaccred
PABnononaccred
CAG
mm3
Must pay? No. Mathematically it should pay. I know it's only an example but there's a big important difference here.
Yes, the numbers go back in the pool after each spin. This is what people have to remember.
Also the theory that each number in the pool is associated with a "win" or "lose" has been pretty much debunked. We now have to assume that the RNG stops the reels in random positions, and that's where your wins/loses come from.
Assumption is the mother of all ****-ups.
IF on some or all softwares the reels were RNG specific fine, but the video graphics suggest otherwise. Any way that's a digression; addressing your point I have merely as you suggest put a parameter on an indefinite run of RNG events to help new members get an idea of how things are supposed to work. It wasn't my intention to raise old debates or the bickering over old ground we've indulged in on other threads. Whether your assumption or mine is correct, or maybe both of us depending on the software is immaterial; the real experience the new player will get and why he gets it is my point here.
#### dunover
##### Unofficial T&C's Editor
Staff member
webmeister
PABnonaccred
PABnononaccred
CAG
mm3
Nothing you say is wrong. However, I'm continually amazed at the effort people go through to convince themselves or others that a slot machine with a 5% house edge is a fair gamble. It's highway robbery. Better than 10-15% house edges in B&M casinos. But highway robbery nonetheless.
Judging by this post you infer that anything the player doesn't have 100%+x odds for is an 'unfair gamble'! Why did you ever gamble and join CM then? I take it you no longer play these 'unfair' games?
You seem to ignore the entertainment aspect. On a 'good' losing session you can deposit 50, and end with an RTP for the deposit of 99.7% which meant you bust out, but potentially played for hours and hours.
You may, just may, even deposit 50 and play for hours and cash out 300! You have no chance of doing that spending 50 quid on petrol or beer, have you?
You never bought a lottery ticket where the player RTP is 50%?
Just look at it in a realistic way - we have all just deposited 1000 pounds between us. The casino has taken 50 pounds and stuffed it in their ass pocket. There is 950 in the pot. We depositors can all now grab one handful from the pot. I grabbed 200. I'm 100 up. You grabbed 75, you're 25 down - it's called gambling my friend!
#### cpdnd31
##### Ueber Meister
webmeister
CAG
So in basic terms, can we look at this like: 1000 tickets to a raffle. Each ticket cost a penny. I play 20 cents and every time i pull i get 20 1 cent tickets with a possible cash prize? -I remember an old thread here explaining Rtg progressives and that was the basics of it. So can we also use that analogy to help newbies understand this theory better?
#### dunover
##### Unofficial T&C's Editor
Staff member
webmeister
PABnonaccred
PABnononaccred
CAG
mm3
So in basic terms, can we look at this like: 1000 tickets to a raffle. Each ticket cost a penny. I play 20 cents and every time i pull i get 20 1 cent tickets with a possible cash prize? -I remember an old thread here explaining Rtg progressives and that was the basics of it. So can we also use that analogy to help newbies understand this theory better?
Progressives are fundamentally different in that in my example above, whereby the casino takes the 1000 pounds in deposits, stuffs 50 in their arse pocket and lets players fight over the other 950, in your case the casino takes another 50 and chucks it in a 'lucky dip' pot and leaves 900 for normal play. The lucky dip pot has millions of non-winning outcomes, a few hundred 'minor' outcomes, tens of 'mini' outcomes, a few 'major' outcomes and one 'mega; outcome. (This is based on the Playtech model; on RTG you have one or two jackpots) - so as you say, each 20p spin if it is the lowest stake will get you one 'raffle ticket' whether it is just for that particular slot at that particular casino, or a pooled jackpot for that specific slot at any casino. Now if you play \$1 you get 5 entries into the raffle IF it is one of those jackpots whereby increased stake increases your chance of winning it. So, you can still win a prize at 0.20 but are 5x less likely to - for all I know, some may have a rule that ANY spin of ANY stake just gets one ticket, although that would be unfair on higher stakes players.
If on a 20-line slot playing 1 penny a line for a 0.20 stake you choose to play just one line at 1 penny I don't know if that could be a 'raffle ticket' or not. If it was, it would make little difference other than you are 100x less likely to win than a \$1.00 player or 20x less likely than the 0.20 player.
On progressives you are getting a RN generated for the spin on the slot, and another for the jackpot pool. Every time the spin doesn't get an award from the jackpot pool, it goes up a minute fraction.
#### 243 lines=daft
##### Dormant Account
What irks me a little about the '1000 tickets to the raffle' thing (which I agree is a good visualisation for what appears to be the accepted understanding of how slots work) is that its design is so deliberately obfuscatious.
A newbie is most likely to hold the default assumption that at least in theory they could pull the same number from the 1000 tickets twice in a row. Or even more times in a row.
A newbie may well have previously played (eg) the lottery where their selected numbers have the clear (albeit unlikely!) chance of coming up several times in a row, or played in a B'n'M where seemingly implausible sequences of repeated numbers can and do happen on a nightly basis, providing for some a harsh but useful lesson in variance.
So if they then move onto online casinos their expectation is going to be 'any raffle ticket, anytime' so to speak.
In online casinos (aka the 1000 ticket raffle), the random number generators have 'a gentle influence' on the outcome and that seems to be good enough for those who have developed their own expectations through experience with these games.
To me the journey from one set of expectations to the other is one that could be shortened by greater clarity and transparency.
#### dunover
##### Unofficial T&C's Editor
Staff member
webmeister
PABnonaccred
PABnononaccred
CAG
mm3
Yes, true enough. Only if the casinos actually knew everything about the slots they provide, would it be wise of them to tell you for example 'on BDBA you have a 1-in-450,000 chance of getting 5 sapphires/wilds in normal spins, and a 1-in-33,000,000 chance of hitting them in free spins'? Who would benefit? They wouldn't, as those stats (not real BTW) would put many players off. The player wouldn't, as part of the excitement of playing is the 'unknown', the chance of a big hit. IF the play hits one of those examples, he only thinks 'wasn't that a lucky hit' - he doesn't really need to know how lucky it was, surely?
Secondly, if they said 'you have a 1/250 chance of hitting a bonus round on any spin', and you didn't hit one for 1500 spins, what would happen? You'd be whingeing on here about RTP being bad, bad luck and every other negative going.
I think we have nearly all the information we need, and the rest we know how to get.
Replies
12
Views
2K
Replies
19
Views
2K
Replies
3
Views
766
Replies
7
Views
1K
Replies
73
Views
20K | 3,764 | 15,278 | {"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} | 3.140625 | 3 | CC-MAIN-2022-21 | latest | en | 0.950169 |
https://tomwallis.info/tag/matlab/ | 1,585,910,448,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370510846.12/warc/CC-MAIN-20200403092656-20200403122656-00292.warc.gz | 717,692,354 | 22,836 | # Guest Post: Matlab versus Pandas for data analysis
Annelie Muehler is an undergraduate student who is about to finish a 2 month internship in our group. She has been working with me conducting psychophysical experiments, and we have been creating stimuli using python. As part of getting used to scientific python Annelie learned to use Pandas, a package that essentially gives you R’s data frames in Python. The following compares the code to do a simple analysis in Matlab and Python. While it’s possible there are ways to improve the Matlab implementation (perhaps using the statistics toolbox?), it’s noteworthy that these weren’t taught in Annelie’s course.
## A comparison of Matlab and Pandas for a simple data analysis
As part of my undergraduate studies in cognitive psychology and neuroscience, I did a water maze experiment in an advanced biology/neuroscience lab course using mice. For this experiment, I had ten mice that did four trials of the experiment over a six day period. The point of this experiment is for the mice to be able to find the platform in the water with increasing speed as they complete more trials. This is because they learn where the platform is. The water maze experiment is one of the behavioural experiments used in mice and rats to test for the ability to learn. Later we used this data while we were learning Matlab in another lab class as a basis for learning data analysis.
During my internship at the Centre for Integrative Neuroscience in Tuebingen, Germany, I reanalyzed this data using pandas in python as a way to learn pandas, giving me a direct comparison of Matlab and pandas. There are definitely some very nice things about pandas. First, you are able to define your own index and column names that are shown surrounding the matrix in a format similar to a table in a word processing document or excel file. This was one of the most frustrating things for me in Matlab because in Matlab you have a dataset and then another variable which contains a list of strings that corresponded to the column names so that you can look them up there.
An example of the format in which tables are seen in pandas using the mice data. The table is stored in a variable called rdata.
In pandas, reading data in and out in is easy with the pd.read_csv() and rdata.to_csv function. As you can see in the image above, the mice data is structured so that the indices represent the row number, the other columns are:
• Trials which represents the trial number and is numbered from one to four for each trial in each day
• Animal is the animal number which is in the range one to ten
• Day stands for the day number and is numbered from one to six
• Swimming Time represents the amount of time it took the mouse to find the platform in the water maze experiment.
I find it easier to work with the table labeled in this way as opposed to having a different variable with the labels of the columns, as we had done in Matlab. Also pandas has great functions
such as:
• rdata.head() which shows the top rows of the dataframe
• rdata.describe() which gives the count, mean, standard deviation and other statistics of the dataframe (not the most useful for this specific dataframe)
• rdata.sort(columns = 'Animal') which sorts the data by a specific column, in this case the column Animal.
As you can see above, pandas (and python in general) has object-oriented functions. These work by using the name of the object, in this case rdata, adding a period and then typing the function. This will show you the result of the function but generally not change the actual object unless the object is equated with the function (as in rdata = rdata.sort(columns = 'Animal').
The idea of the analysis was the find the average swimming time per day across animals to see if there was any improvement as the mice learned the task. In Matlab we did this by:
1.
for i=1:nday
rows_day(:,i)=find(rdata(:,3)==i);
end
This created a dataset in which the rows for each day were identified.
2.
for i=1:nday
time_day(:,i)=rdata(rows_day(:,i),5);
end
Using the data set from step 1, we are able to get a new data set where the swimming time of each trial is listed for each day across animals.
3.
m_day=mean(time_day);
f=figure;
a=axes;
plot(m_day);
ylabel('Swimming Time (s)')
xlabel('Experimental Day')
set(a,'xtick',1:nday)
title('Average swimming time (s) per day across animals')
This results in this simple line graph:
Graph output from Matlab
Here’s the same thing in pandas.
1.
import pandas as pd
The usual importing at the beginning of each python script.
2.
m_day = rdata.groupby('Day')['Swimming Time'].mean()
m_day = pd.DataFrame({'Swimming Time (s)':m_day, 'Experimental Day': range(1,7)})
Groupby is a useful command that will group the data by day (parentheses) according to Swimming Time (square brackets). This eliminates sorting out the rows by day using a for loop as is done in the Matlab code above and allows you to group your data according to different variables in your data frame. The .mean() operator at the end tells pandas that you want to compute the means on the grouped data.
3.
m_day.plot(style='b-', x='Experimental Day', y='Swimming Time (s)', title='Average swimming time (s) per day across animals')
There are other python plot functions that may be a bit more elaborate but in the spirit of doing everything in pandas I decided to show the pandas version. This results in this simple line graph, identical to the one above:
Graph output from Pandas
Figures can be easily saved in pandas using:
fig = plot.get_figure()
fig.savefig()
Of course this is a very simple example of data analysis, but I think it does outline some of the benefits of pandas. The nicest thing in my opinion is the ease with which you can manipulate the data frame and the ability to select columns by their name. The groupby function is very useful and can be used to groupby multiple columns or to group multiple columns.
In my opinion, pandas is a much simpler and convenient way to work with and manipulate data.
# My current direction in scientific computing
During my PhD I learned to program in Matlab. I’d never done any programming before that, and I found it to be a rewarding experience. As is typical for people in vision science, I did pretty much everything in Matlab. Stimuli were generated and presented to human subjects using the CRS Visage (in my PhD; programming this thing can be hell) and now the excellent Psychtoolbox. Early on in my PhD I also moved away from SPSS to doing data analysis in Matlab, too.
An early project in my postdoc (see here) involved some more sophisticated statistical analyses than what I had done before. For this, Matlab was an absolute pain. For example, the inability (in base Matlab) to have named columns in a numerical matrix meant that my code contained references to column numbers throughout. This meant that if I wanted to change the order or number of variables going into the analysis I had to carefully check all the column references. Ugly, and ripe for human error.
Cue my switch to R. For statistical analyses R is pretty damn excellent. There are thousands of packages implementing pretty much every statistical tool ever conceived, often written by the statistician who thought up the method. Plus, it does brilliant plotting and data visualisation. Add the ability to define a function anywhere, real namespaces and the excellent R Studio IDE and I was hooked. I would try to avoid using Matlab again for anything on the analysis side but some light data munging (this is also wrapped up in my preference for science in open software).
For several years now I’ve been doing pretty much everything in R. For our latest paper, I also did my best to make the analysis fully reproducible by using knitr, a package that lets you include and run R analyses in a LaTeX document. You can see all the code for reproducing the analysis, figures and paper here. I’m going to work through the work flow that I used to do this in the next few blog posts.
While R is great for stats and plotting, unfortunately I’m not going to be able to fully replace Matlab with R. Why? First, last I checked, R’s existing tools for image processing are pretty terrible. A typical image processing task I might do to prepare an experiment is take an image and filter it in the Fourier domain (say, to limit the orientations and spatial frequencies to a specific band). I spent about a day trying to do this in R a year or so ago, and it was miserable. Second, R has no ability to present stimuli to the screen with any degree of timing or spatial precision. In fact, that would be going well outside its intended purpose (which is usually a bad idea – see Matlab).
So my “professional development” project for this year is to learn some Python, and test out the PsychoPy toolbox. In addition I’m interested in the data analysis and image processing capabilities of Python – see for example scikit-learn, scikit-image and pandas. I’ve had some recent early success with this, which I’ll share in a future post. It would be so great to one day have all my scientific computing happen in a single, powerful, cross platform, open and shareable software package. I think the signs point to that being a Python-based set of tools. | 2,001 | 9,325 | {"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-2020-16 | latest | en | 0.934193 |
http://blog.jverkamp.com/2012/08/23/two-more-random-exercises/ | 1,406,175,221,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1405997885796.93/warc/CC-MAIN-20140722025805-00171-ip-10-33-131-23.ec2.internal.warc.gz | 20,127,043 | 11,541 | # Two More Random Exercises
Programming Praxis put out another two “random” exercises, this time about making psuedorandom number generators (where the previous had us composing already existing PRNGs).
The first function is the middle square PRNG. Basically, you start with a seed with an even number of digits and then repeatedly square it and return the middle digits.
Here I have a function that will take any suitable seed and generate a sequence of psuedorandom numbers from it:
```; middle square PRNG: square the seed and take the middle digits (define (make-middle-square n) (lambda () (let ([digits (inexact->exact (ceiling (log n 10)))]) (let ([res (mod (div (* n n) (expt 10 (/ digits 2))) (expt 10 digits))]) (set! n res) res))))```
An example of running it (using the same seed from the Wikipedia page):
```~ (define middle-square (make-middle-square 675248))
~ (middle-square)
959861
~ (middle-square)
333139
~ (middle-square)
981593
~ (middle-square)
524817
~ (middle-square)
432883```
The second example is perhaps even simpler. This time you start with any odd seed and apply the relation xn+1 = 65539 * xn mod 231:
```; randu PRNG: x_n+1 = 65539 * x_n mod 2^31 (assume x_0 is odd) (define make-randu (let ([2**31 (expt 2 31)]) (lambda (x) (lambda () (let ([res (mod (* 65539 x) 2**31)]) (set! x res) res)))))```
An example run:
```~ (define randu (make-randu 675249))
~ (randu)
1305471251
~ (randu)
1384299321
~ (randu)
851521963
~ (randu)
1240372481
~ (randu)
1926020867```
Pretty neat. Fortunately or not, this makes me want to implement a more heavyweight PRNG now, perhaps like the Mersenne Twister. We’ll see.
If you’d like to download the full source code, you can do so here: two more random exercises source
← Two Random Exercises All Minimum scalar product → ← Two Random Exercises By category Minimum scalar product → | 521 | 1,873 | {"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} | 3.734375 | 4 | CC-MAIN-2014-23 | longest | en | 0.729704 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-11-rational-expressions-and-functions-11-2-multiplying-and-dividing-rational-expressions-lesson-check-page-661/6 | 1,709,611,871,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707948217723.97/warc/CC-MAIN-20240305024700-20240305054700-00457.warc.gz | 765,593,268 | 13,658 | ## Algebra 1
$x^2$
$\frac{x^2+6x}{\frac{x+6}{x}}$ $\frac{x^2+6x}{1}\div{\frac{x+6}{x}}$ $\frac{x^2+6x}{1}*{\frac{x}{x+6}}$ $\frac{x(x+6)}{1}*{\frac{x}{x+6}}$ $x^2$ | 93 | 164 | {"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} | 3.484375 | 3 | CC-MAIN-2024-10 | latest | en | 0.138983 |
https://ezyeducation.co.uk/ezymathsdetails/ezymaths-news/entry/countdown-to-exams-day-50-quadratic-and-cubic-graphs.html | 1,659,968,763,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570827.41/warc/CC-MAIN-20220808122331-20220808152331-00124.warc.gz | 249,208,154 | 18,585 | The EzyEducation website uses cookies to help ensure we give you the best experience.
If you continue without changing your settings, we assume that you are happy to receive all cookies on the EzyEducation website.
Continue
# Countdown to Exams - Day 50 - Quadratic and Cubic graphs
Today we take a look at Quadratic and Cubic graphs. It is important to understand the shape of these graphs and identify where they cross the x and y axes as you will be asked questions about this. Sometimes you will be required to fill in a table of values and then plot the graph. Take care plotting the points and always check the shape of your graph. If it is a quadratic, is it symmetrical?
It is always worthwhile double/triple checking your work here to ensure accuracy.
Matt will guide you through the graphs in the video below.
EzyMaths is the ultimate online GCSE Maths support service. Schools can enjoy a free 30-day trial to see for themselves how EzyMaths can support their teaching and help their students achieve better grades.
#### Related Posts
David Ardley on Monday, 03 January 2022 15:38
e
[/quote]
[/list]
[/list][/url][/u][/i][/b]
0
e[b][i][u][url=][img][/img][list] [*][list=] [*][*] [quote]:D:):o:p:(;)[b][i][u][url=][img][/img][list] [*][list=] [*][*] [quote]:D:):o:p:(;)[/quote] [/list] [/list][/url][/u][/i][/b][/quote] [/list] [/list][/url][/u][/i][/b] | 368 | 1,375 | {"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-2022-33 | latest | en | 0.830588 |
http://gmatclub.com/forum/this-is-why-i-stay-clear-of-the-gmat-sides-of-the-forum-148785.html | 1,477,613,790,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721405.66/warc/CC-MAIN-20161020183841-00132-ip-10-171-6-4.ec2.internal.warc.gz | 110,226,003 | 53,848 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 27 Oct 2016, 17:16
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# This is why I stay clear of the GMAT sides of the forum...
Author Message
Director
Status: Can't wait for August!
Joined: 13 Sep 2011
Posts: 988
Location: United States (MA)
Concentration: Marketing, Strategy
GMAT 1: 660 Q44 V37
GMAT 2: 680 Q45 V38
GMAT 3: 710 Q45 V42
GPA: 3.32
WE: Information Technology (Retail)
Followers: 25
Kudos [?]: 349 [11] , given: 109
This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
05 Mar 2013, 19:20
11
KUDOS
I no longer have the ability to concentrate on GMAT math...
ABE is an equilateral tringle, BCDE is a square, and the are
In the figure above, ABE is an equilateral tringle, BCDE is a square, and the area od the circle is 36π. What is the area of polygon ABCDE?
I then spent the next 5 minutes creating this...
Attachments
abe.jpg [ 28.68 KiB | Viewed 3304 times ]
VP
Status: Yale SOM!
Joined: 06 Feb 2012
Posts: 1458
Location: United States
Concentration: Marketing, Strategy
Followers: 51
Kudos [?]: 533 [0], given: 333
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
05 Mar 2013, 19:29
highwyre237 wrote:
I no longer have the ability to concentrate on GMAT math...
ABE is an equilateral tringle, BCDE is a square, and the are
In the figure above, ABE is an equilateral tringle, BCDE is a square, and the area od the circle is 36π. What is the area of polygon ABCDE?
I then spent the next 5 minutes creating this...
Love this!!!
_________________
aerien
Note: I do not complete individual profile reviews. Please use the Admissions Consultant or Peer Review forums to get feedback on your profile.
GMAT Club Premium Membership - big benefits and savings
MBA Section Director
Joined: 19 Mar 2012
Posts: 3505
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1439
Kudos [?]: 11002 [0], given: 1856
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
06 Mar 2013, 11:29
highwyre237 wrote:
I no longer have the ability to concentrate on GMAT math...
ABE is an equilateral tringle, BCDE is a square, and the are
In the figure above, ABE is an equilateral tringle, BCDE is a square, and the area od the circle is 36π. What is the area of polygon ABCDE?
I then spent the next 5 minutes creating this...
_________________
Director
Status: Can't wait for August!
Joined: 13 Sep 2011
Posts: 988
Location: United States (MA)
Concentration: Marketing, Strategy
GMAT 1: 660 Q44 V37
GMAT 2: 680 Q45 V38
GMAT 3: 710 Q45 V42
GPA: 3.32
WE: Information Technology (Retail)
Followers: 25
Kudos [?]: 349 [0], given: 109
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
06 Mar 2013, 12:20
haha, don't encourage me.
Director
Joined: 26 May 2010
Posts: 719
Location: United States (MA)
Concentration: Strategy
Schools: MIT Sloan - Class of 2015
WE: Consulting (Mutual Funds and Brokerage)
Followers: 18
Kudos [?]: 204 [0], given: 642
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
07 Mar 2013, 09:10
This is great!
SVP
Affiliations: HEC
Joined: 28 Sep 2009
Posts: 1637
Concentration: Economics, Finance
GMAT 1: 730 Q48 V44
Followers: 99
Kudos [?]: 617 [0], given: 432
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
10 Mar 2013, 21:04
souvik101990 wrote:
I am tempted to agree with souvik101990 here. This is newsletter-worthy material, for sure.
VP
Joined: 23 Mar 2011
Posts: 1113
Concentration: Healthcare, Strategy
Schools: Duke '16 (M)
Followers: 78
Kudos [?]: 491 [0], given: 463
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
14 Mar 2013, 14:34
Director
Status: Can't wait for August!
Joined: 13 Sep 2011
Posts: 988
Location: United States (MA)
Concentration: Marketing, Strategy
GMAT 1: 660 Q44 V37
GMAT 2: 680 Q45 V38
GMAT 3: 710 Q45 V42
GPA: 3.32
WE: Information Technology (Retail)
Followers: 25
Kudos [?]: 349 [0], given: 109
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
14 Mar 2013, 15:18
jumsumtak wrote:
Ha! I have made the newsletter twice now, and in both cases it was due to facial hair... May 24 2012 Newsletter I think I need new material...
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14109
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3602
Kudos [?]: 21757 [0], given: 4395
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
15 Mar 2013, 20:05
highwyre237 wrote:
jumsumtak wrote:
Ha! I have made the newsletter twice now, and in both cases it was due to facial hair... May 24 2012 Newsletter I think I need new material...
That is pretty unique though - I guess you are a big fish in a small pond type-of-guy
_________________
Founder of GMAT Club
US News 2008 - 2017 Rankings progression - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books
Co-author of the GMAT Club tests
GMAT Club Premium Membership - big benefits and savings
Intern
Joined: 23 Nov 2012
Posts: 7
Followers: 0
Kudos [?]: 0 [0], given: 0
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
17 Mar 2013, 19:02
Haha! Oh my god, that's funny! ^_^
Intern
Joined: 22 Mar 2013
Posts: 1
Followers: 0
Kudos [?]: 0 [0], given: 0
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
22 Mar 2013, 10:52
hahahahaha I can't stop laughing, so funny
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Followers: 107
Kudos [?]: 261 [0], given: 66
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
22 Mar 2013, 11:13
Being honest, this is awesome!
See what I did there?
-Ron
_________________
Senior Manager
Joined: 17 Mar 2011
Posts: 452
Location: United States (DC)
Concentration: General Management, Technology
GMAT 1: 760 Q49 V45
GPA: 3.37
WE: Information Technology (Consulting)
Followers: 11
Kudos [?]: 183 [2] , given: 5
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
01 Apr 2013, 06:40
2
KUDOS
VeritasPrepRon wrote:
Being honest, this is awesome!
See what I did there?
-Ron
I had some trouble "Lincoln" it together....
Intern
Joined: 30 Jan 2013
Posts: 7
Followers: 0
Kudos [?]: 2 [0], given: 0
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
01 Apr 2013, 08:08
you deserve bonus points for this one!
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Followers: 107
Kudos [?]: 261 [0], given: 66
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
01 Apr 2013, 09:43
jko wrote:
VeritasPrepRon wrote:
Being honest, this is awesome!
See what I did there?
-Ron
I had some trouble "Lincoln" it together....
I knew you'd get it, though. I can fool some of the people all the time, and all of the people some of the time, but I can't fool all of the people all of the time.
_________________
Manager
Status: Got Bling! Joined Phd Finance at IIML
Joined: 03 Jul 2013
Posts: 99
Location: India
Concentration: Finance, Economics
Schools: iim-bangalore - Class of 1994
GMAT 1: 750 Q59 V43
GPA: 3.12
WE: Research (Investment Banking)
Followers: 1
Kudos [?]: 17 [0], given: 39
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
08 Jul 2013, 22:27
ABE was square.
Director
Joined: 29 Nov 2012
Posts: 900
Followers: 14
Kudos [?]: 953 [0], given: 543
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
07 Aug 2013, 07:17
Haha this is hilarious nice one highwyre!
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html
MBA Section Director
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 3512
Location: India
City: Pune
GPA: 3.4
Followers: 366
Kudos [?]: 2660 [0], given: 1888
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink]
### Show Tags
03 Nov 2013, 06:39
Bump!!
_________________
Re: This is why I stay clear of the GMAT sides of the forum... [#permalink] 03 Nov 2013, 06:39
Similar topics Replies Last post
Similar
Topics:
MCAT Forum 1 09 May 2013, 14:06
Off-Topic. Hence why its here and I'm a mod for it =P 6 07 Oct 2010, 14:28
stay at home dads 7 15 Feb 2009, 16:57
Stay in architectural engineering or switch to finance? 3 28 Jan 2008, 23:41
New to the forum 1 12 Aug 2007, 13:58
Display posts from previous: Sort by | 2,992 | 9,490 | {"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} | 3.046875 | 3 | CC-MAIN-2016-44 | longest | en | 0.864349 |
https://es.mathworks.com/matlabcentral/cody/problems/380-convert-a-numerical-matrix-into-a-cell-array-of-strings/solutions/370380 | 1,604,079,044,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107911027.72/warc/CC-MAIN-20201030153002-20201030183002-00616.warc.gz | 329,318,923 | 17,064 | Cody
Problem 380. Convert a numerical matrix into a cell array of strings
Solution 370380
Submitted on 15 Dec 2013 by Ted
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
%% Example tested input = 1:3; output = {'1' '2' '3'}; assert(isequal(matrix2cell(input ),output)) assert(iscell(output),'output must be a cell')
2 Pass
%% input = 0:5:8 output = {'0' '5'}; assert(isequal(matrix2cell(input ),output)) assert(iscell(output),'output must be a cell')
input = 0 5
3 Pass
%% Matrix input input =magic(3); output = {'8' '1' '6' '3' '5' '7' '4' '9' '2'} assert(isequal(matrix2cell(input ),output))
output = '8' '1' '6' '3' '5' '7' '4' '9' '2'
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 273 | 889 | {"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-2020-45 | latest | en | 0.575409 |
https://statscalculator.com/standarderror | 1,716,952,932,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059167.30/warc/CC-MAIN-20240529010927-20240529040927-00608.warc.gz | 450,675,857 | 10,603 | # Sample Error Calculator
## Sample Error Calculator
### Related Tools
Sample has 28 observations.
Sample Mean: 5.1429
Standard Error: 0.9577
## How to Use a Standard Deviation Calculator and Understand its Significance in Statistics
This is a simplified version of our descriptive statistics tool which calculates the sample mean and the associated standard error. It is designed for professionals who only need this statistic.
The standard error of a parameter is defined as the standard deviation of the sampling distribution. A sampling distribution is the expected distribution of that statistic if you took multiple samples from the underlying population. So the sampling distribution of the sample mean would be the distribution of the means of repeated samples from a population. The standard deviation of this sampling distribution is the standard error of the sample mean.
The standard error can be used to develop confidence intervals for the unknown population mean. It can be used to assess the degree of precision of your estimate or measurement process. The relative standard error of a survey can be computed as the ratio of its standard error to the sample mean. A lower relative standard error indicates higher precision in the findings between studies, regardless of any differences in the sample mean. This is commonly used to set standards of significant for scientific review and publication processes; supporting surveys must satisfy a certain level of precision and reliability in their findings to quality for publication.
This tool is developed so you can save your data and use it in our other calculators. Simply hit "save data" and enter a name for this data set. It will be added to the menu shown alongside (or below) the calculators. When you open another page on our site, you will see a list of saved datasets. Simply click on that item and it will pre-populate the calculator box.
A standard deviation calculator is a tool that calculates the measure of the amount of variation or dispersion in a set of data. It is a commonly used measure of the spread of a statistical distribution. The standard deviation is used to quantify the amount of variation or dispersion in a set of data.
## Using a Standard Deviation Calculator
To use a standard deviation calculator, you need to input the set of observations from your sample. The calculator will then calculate the standard deviation by taking the square root of the variance of the sample, which is the average of the squared differences from the mean.
For example, if you have a sample of 10 observations with values of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, the standard deviation calculator will calculate the standard deviation as follows:
Step 1: Calculate the mean
(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10 = 10
Step 2: Calculate the variance
((2-10)^2 + (4-10)^2 + (6-10)^2 + (8-10)^2 + (10-10)^2 + (12-10)^2 + (14-10)^2 + (16-10)^2 + (18-10)^2 + (20-10)^2) / 10 = 33.2
Step 3: Calculate the standard deviation
Square root of 33.2 = 5.76
Therefore, the standard deviation for this sample is 5.76.
## Significance of Standard Deviation in Statistics
The standard deviation is a fundamental concept in statistics because it provides a measure of the amount of variation or dispersion in a set of data. It is useful in many statistical analyses, including hypothesis testing, confidence interval estimation, and regression analysis.
Additionally, the standard deviation is used to calculate other important statistics, such as the coefficient of variation and the standard error of the mean. The coefficient of variation is a measure of the relative variability of a set of data, while the standard error of the mean is a measure of the precision of the sample mean as an estimator of the population mean.
The standard deviation can also be used to identify outliers in a set of data. An outlier is an observation that is significantly different from the other observations in the sample. Outliers can greatly influence the mean and other statistics, so it is important to identify and investigate them when analyzing data.
## Factors that Influence the Standard Deviation of a Sample
The standard deviation of a sample is influenced by several factors, including the range of values in the sample, the presence of outliers, and the sample size. A larger range of values or the presence of outliers will result in a larger standard deviation, while a smaller range of values or the absence of outliers will result in a smaller standard deviation.
Additionally, as the sample size increases, the standard deviation becomes a more reliable estimator of the population standard deviation. This is because larger sample sizes provide more information about the underlying population distribution and reduce the effect of random variation in the sample.
It is important to note that the standard deviation is a measure of the spread of the data, not the shape of the distribution. Different distributions can have the same standard deviation, so it is important to consider other statistics, such as the skewness and kurtosis, to fully understand the shape of the distribution.
## Conclusion
A standard deviation calculator is a useful tool for calculating the measure of the amount of variation or dispersion in a set of data. The standard deviation is a fundamental concept in statistics that provides a measure of the spread of a statistical distribution. It is used in many statistical analyses and can be influenced by several factors, including the range of values in the sample, the presence of outliers, and the sample size. By understanding how to use a standard deviation calculator and the significance of standard deviation in statistics, you can make more informed decisions based on your data. | 1,187 | 5,830 | {"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-2024-22 | longest | en | 0.899035 |
https://math.stackexchange.com/questions/128195/prove-that-the-lie-derivative-of-a-vector-field-equals-the-lie-bracket-fracd/1918410#1918410 | 1,652,994,622,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662530066.45/warc/CC-MAIN-20220519204127-20220519234127-00083.warc.gz | 436,986,443 | 70,994 | # Prove that the Lie derivative of a vector field equals the Lie bracket: $\frac{d}{dt} ((\phi_{-t})_* Y)|_{t=0} = [X,Y]$
Let $X$ and $Y$ be vector fields on a smooth manifold $M$, and let $\phi_t$ be the flow of $X$, i.e. $\frac{d}{dt} \phi_t(p) = X_p$. I am trying to prove the following formula:
$\frac{d}{dt} ((\phi_{-t})_* Y)|_{t=0} = [X,Y],$
where $[X,Y]$ is the commutator, defined by $[X,Y] = X\circ Y - Y\circ X$.
This is a question from these online notes: http://www.math.ist.utl.pt/~jnatar/geometria_sem_exercicios.pdf .
• Can you show us where you get stuck? The details are a bit of a mess, but the idea is straightforward. Start with the left side and compute at a point applied it to an arbitrary smooth function, i.e. write out $(L_X Y)_p f$ with the limit definition. You should be able to rearrange terms and rewrite things and cancel a little to get to the right hand side.
– Matt
Apr 5, 2012 at 2:18
Here is a simple proof which I found in the book "Differentiable Manifolds: A Theoretical Phisics Approach" of G. F. T. del Castillo. Precisely it is proposition 2.20.
We denote $$(\mathcal{L}_XY)_x=\frac{d}{dt}(\phi_t^*Y)_x|_{t=0},$$ where $$(\phi^*_tY)_x=(\phi_{t}^{-1})_{*\phi_t(x)}Y_{\phi_t(x)}.$$
Recall also that $$(Xf)_x=\frac{d}{dt}(\phi_t^*f)_x|_{t=0}$$ where $$\phi_t^*f=f\circ\phi_t$$ and use that $$(\phi^*_tYf)_x=(\phi^*_tY)_x(\phi^*_tf).$$
We claim that $$(\mathcal{L}_XY)_x=[X,Y]_x.$$
Proof:$$(X(Yf))_x=\lim_{t\to 0}\frac{(\phi_t^*Yf)_x-(Yf)_x}{t}=\lim_{t\to 0}\frac{(\phi^*_tY)_x(\phi^*_tf)-(Yf)_x}{t}=\star$$
Now we add and subtract $$(\phi^*_tY)_xf.$$ Hence $$\star=\lim_{t\to 0}\frac{(\phi^*_tY)_x(\phi^*_tf)-(\phi^*_tY)_xf+(\phi^*_tY)_xf-Y_xf}{t}=$$ $$=\lim_{t\to 0}(\phi^*_tY)_x\frac{(\phi^*_tf)-f}{t}+\lim_{t\to 0}\frac{(\phi^*_tY)_x-Y_x}{t}f=Y_xXf+(\mathcal{L}_XY)_xf.$$ So we get that $$XY=YX+\mathcal{L}_XY.$$
Here is a proof that is more-or-less equivalent to the one given by Fallen Apart, but with details further explicated/clarified.
Let $M$ be a smooth manifold and $X$, $Y$ smooth vector fields. The Lie derivative is defined as $$(\mathcal{L}_{X} Y) (p) = \lim_{t\to 0} \frac{\phi^{-t}_{\star} Y (\phi^{t} (p)) - Y(p)}{t}$$ where $\phi^t$ denotes the flow of $X$. Taking a test function $f \in C^{\infty} (M)$, we apply the Lie derivative to $f$ to obtain $$(\mathcal{L}_{X} Y)(p)f = \lim_{t\to 0} \frac{\phi^{-t}_{\star} Y (\phi^{t} (p))f - Y(p)f}{t} = \lim_{t\to 0} \frac{Y(\phi^t (p))(f\circ \phi^{-t}) - Y(p)}{t}$$ Thus, setting $$H(x,y) = Y(\phi^x (p))(f\circ \phi^{-y})$$ we have that $$(\mathcal{L}_{X} Y)(p) f = \frac{d}{dt} \Big\vert_{t = 0} H(t,t) = \frac{\partial H}{\partial x} (0,0) + \frac{\partial H}{\partial y} (0,0)$$ where the second equality is due the chain rule. So, to complete the calculation we just have to compute the partial derivatives of $H$. We find $$\frac{\partial H}{\partial x} (0,0) = \frac{\partial}{\partial x} \Big\vert_{x= 0} (Yf)(\phi^x (p)) = X(p)(Yf)$$ For the other partial derivative of $H$, we introduce a curve $\alpha: (-\epsilon, \epsilon) \to M$ such that $\alpha(0) = p$ and $\alpha'(0) = Y(p)$. Then we have $$\frac{\partial H}{\partial y} (0,0) = \frac{\partial}{\partial y} \Big\vert_{y = 0} Y(p) (f\circ \phi^{-y}) = \frac{\partial}{\partial y} \Big\vert_{y = 0} \frac{d}{ds} \Big\vert_{s= 0} (f\circ \phi^{-y} \circ \alpha)(s)$$ $$= \frac{d}{ds} \Big\vert_{s= 0} \frac{\partial}{\partial y}\Big\vert_{y = 0} (f\circ \phi^{-y} \circ \alpha)(s) = \frac{d}{ds} \Big\vert_{s= 0} -(Xf)(\alpha(s)) = -Y(p)(Xf)$$ We conclude $$(\mathcal{L}_{X} Y)(p)f = X(p) (Yf) - Y(p) (Xf) \implies \mathcal{L}_{X} Y = XY - YX =: [X, Y]$$
• Why is $H$ differentiable? I deeply believe it is, but I'm having trouble justifying it Jul 18, 2018 at 19:36
• It's a (if I recall correctly, fairly hard) theorem that the flows $\phi^{t}(x)$ generated by a vector field are smooth in both $x$ and $t$ (for small $t$). More generally, this should be the result of a theorem saying solutions to ordinary differential equations are smooth in the prescribed initial conditions. You can probably find it in Lang's manifolds book? Jul 18, 2018 at 19:59
Let $X$ and $Y$ two vector fields then the Lie derivative $L_{X}Y$ is the commutator $[X, Y]$.
the proof:
we have
$$L_{X}Y=\lim_{t\to 0}\frac{d\phi_{-t}Y-Y}{t}(f)$$ $$=\lim_{t\to 0}d\phi_{-1}\frac{Y-d\phi_{t}Y}{t}(f)$$ $$=\lim_{t\to 0}\frac{Y(f)-d\phi_{t}Y(f)}{t}$$ $$=\lim_{t\to 0}\frac{Y(f)-Y(f\circ\phi_{t})\circ\phi_{t}^{-1}}{t}$$
we put $\phi_{t}(x)=\phi(t,x)$ and we apply the Taylor formula with integral remains, then there exists $h(t,x)$ such that:
$$f(\phi(t,x))=f(x)+th(t,x)$$ where $h(0,x)=\frac{\partial}{\partial t}f(\phi(t,x))(0,x)$
by defintion of tangent vector: $X(f)=\frac{\partial}{\partial t}f\circ\phi_{t}(x)(0,x)$
then we have $h(o,x)=X(f)(x)$ so:
$$L_{X}Y(f)=\lim_{t\to 0}\left(\frac{Y(f)-Y(f)\circ \phi_{t}^{-1}}{t}-Y(h(t,x))\circ \phi_{t}^{-1}\right)$$ $$=\lim_{t\to 0}\left(\frac{(Y(f)\circ\phi_{t}-Y(f))\circ\phi_{t}^{-1}}{t}-Y(h(t,x))\circ\phi_{t}^{-1}\right)$$
we have $\lim_{t\to 0}\phi_{t}^{-1}=\phi_{0}^{-1}=id.$
then we conclude that
$$L_{X}Y(f)=\lim_{t\to 0}\left(\frac{Y(f)\circ\phi_{t}-Y(f)}{t}-Y(h(0,x))\right)$$ $$= \frac{\partial}{\partial t}Y(f)\circ\phi_{t}(x)-Y(h(0,x))$$ $$= X(Y(f)) -Y(X(f))= [X,Y]$$
This completes the proof.
• This answer is very helpful, but I am very confused about how $d\phi_t Y(f) = Y(f \circ \phi_t) \circ \phi_t^{-1}$. Where does the composition of $\circ \phi_t^{-1}$ come from? As far as I know, the formula for pushforward is $(f^*Y)(g) = Y(g \circ f)$ Thank yuo! Jun 28, 2019 at 8:36
Consider two vector fields $$X$$ and $$Y$$. Note that starting from the point $$p$$, the vector field $$X$$ generates the curve $$\phi(p,t)$$ via the following equation \begin{align*} \frac{d}{dt}(f(\phi(p,t))|_t = Xf|_t \end{align*} with $$\phi(p,0)=p$$. Also, note that for small $$t$$, $$f(\phi(p,t))=f(p)+Xf|_pt$$. We can define the Lie derivative of $$Y$$ with respect to $$X$$ as \begin{align*} (\mathcal{L}_XY)_pf = &\lim_{t \to 0} \frac{(Yf)(\phi(p,t))-(\phi_{*t}Y_p)f}{t} \\ = &\lim_{t \to 0} \frac{(Yf)(p)+X(Yf)|_pt-Y_p(f+X_pft)}{t}\\ =&\lim_{t \to 0} \frac{(Yf)(p)+(XY)_pft-(Yf)_p-(YX)_pft}{t}\\ =&(XY-YX)_pf. \end{align*} In the first line of the above equation $$\phi_{*t}Y_p$$ denotes the push forward of $$Y_p$$ along the curve $$\phi(p,t)$$.
Here is another approach in 4 steps (just one of them is hard):
1. Verify that $$\mathcal{L}_X(Y+Z)=\mathcal{L}_X(Y)+\mathcal{L}_X(Z)$$ for any fields $$Y,Z$$;
2. Verify that $$\mathcal{L}_X(fY)=f\mathcal{L}_X(Y)+X(f)Y$$ for any smooth function $$f$$;
3. Show that $$\mathcal{L}_X\left(\frac{\partial}{\partial x_i}\right)=\left[X,\frac{\partial}{\partial x_i}\right]$$;
4. Conclude $$\mathcal{L}_X(Y)=[X,Y]$$.
1. Obvious by $$\mathbb{R}$$-linearity of $$d\phi_{-t}$$ and $$\frac{d}{dt}$$. $$_\blacksquare$$
2. Just notice that $$(d\phi_{-t})(f\,Y)=f(d\phi_{-t})(Y)$$ and use Leibnitz's rule. $$_\blacksquare$$
3. This is the delicate part. Using coordinates, write $$X=\sum_ia_i\frac{\partial}{\partial x_i}$$ for functions $$a_i$$ and $$\phi(t,x)=(\phi_1(t,x),...,\phi_n(t,x))$$ where $$x=(x_1,...,x_n)$$. Because $$\phi(0,x)=x$$ we have $$\frac{\partial \phi_k}{\partial x_j}(0,x)=\delta_{jk}$$ and $$\frac{\partial^2 \phi_k}{\partial x_\ell\partial x_j}(0,x)=0$$. So: \begin{align*} \mathcal{L}_X\left(\frac{\partial}{\partial x_i}\right)_p&=\left.\frac{d}{dt}\right|_{t=0}(d\phi_{-t})_{\varphi_t(p)}\left(\left.\frac{\partial}{\partial x_i}\right|_{\phi_t(p)}\right)\\ &=\left.\frac{d}{dt}\right|_{t=0}\sum_k\frac{\partial \phi_k}{\partial x_i}(-t,\phi_t(p))\left.\frac{\partial}{\partial x_i}\right|_p\\ &=\sum_k\left(\left.\frac{d}{dt}\right|_{t=0}\frac{\partial \phi_k}{\partial x_i}(-t,\phi_t(p))\right)\left.\frac{\partial}{\partial x_i}\right|_p \end{align*}
We will apply the chain rule to calculate the derivative inside the sum. Since, $$\frac{\partial^2\phi_k}{\partial x_j\partial x_i}=0$$, we only need to worry about the derivative of $$\frac{\partial \phi_k}{\partial x_i}$$ with respect to the time coordinate. With that in mind, we see that $$\left.\frac{d}{dt}\right|_{t=0}\frac{\partial \phi_k}{\partial x_i}(-t,\phi_t(p))=\left(\left.\frac{d}{dt}\right|_{t=0}\frac{\partial \phi_k}{\partial x_i}(t,p)\right)\cdot\left(\left.\frac{d}{dt}\right|_{t=0}-t\right)=-\left.\frac{d}{dt}\right|_{t=0}\frac{\partial \phi_k}{\partial x_i}(t,p)$$. Now:
\begin{align*} \left.\frac{d}{dt}\right|_{t=0}\frac{\partial \phi_k}{\partial x_i}(t,p)&=\left.\frac{d}{dt}\right|_{t=0}\left.\frac{\partial}{\partial x_i}\right|_p\phi_k\\ &=\left.\frac{\partial}{\partial x_i}\right|_p\underbrace{\left.\frac{d}{dt}\right|_{t=0}\phi_k}_{=a_k}\\ &=\frac{\partial a_k}{\partial x_i}(p)\\ \end{align*} Therefore $$\mathcal{L}_X\left(\frac{\partial}{\partial x_i}\right)=\sum_k-\frac{\partial a_k}{\partial x_i}\frac{\partial}{\partial x_k}=\sum_k\left[a_k\frac{\partial}{\partial x_k},\frac{\partial}{\partial x_i}\right]=\left[\sum_ka_k\frac{\partial}{\partial x_k},\frac{\partial}{\partial x_i}\right]=\left[X,\frac{\partial}{\partial x_i}\right]_\blacksquare$$
1. For $$Y=\sum_kb_k\frac{\partial}{\partial x_k}$$ use 1), 2), 3) and the fact that $$\left[X,b_k\frac{\partial}{\partial x_k}\right]=b_k\left[X,\frac{\partial}{\partial x_k}\right]+X(b_k)\frac{\partial}{\partial x_k}$$. $$_\blacksquare$$ | 3,698 | 9,383 | {"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": 54, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2022-21 | longest | en | 0.782193 |
https://ch.mathworks.com/matlabcentral/cody/players/11984603/solved?page=2 | 1,582,248,947,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145316.8/warc/CC-MAIN-20200220224059-20200221014059-00012.warc.gz | 305,907,977 | 20,829 | Cody
# Prajit T R
Rank
Score
51 – 100 of 135
#### Problem 89. Counting in Finnish
Created by: Cody Team
#### Problem 55. Counting Sequence
Created by: Cody Team
Tags encoding
#### Problem 528. Find the largest value in the 3D matrix
Created by: Bruce Raine
#### Problem 367. Specific Element Count
Created by: @bmtran (Bryant Tran)
#### Problem 824. Set the array elements whose value is 13 to 0
Created by: Aurelien Queffurust
#### Problem 838. Check if number exists in vector
Created by: Nichlas
#### Problem 63. Encode Roman Numerals
Created by: Cody Team
#### Problem 83. Prime factor digits
Created by: Cody Team
#### Problem 240. Project Euler: Problem 6, Natural numbers, squares and sums.
Created by: Doug Hull
#### Problem 434. Return the Fibonacci Sequence
Created by: Matt Fig
Tags fibonacci
#### Problem 49. Sums with Excluded Digits
Created by: Cody Team
Tags strings
#### Problem 56. Scrabble Scores
Created by: Cody Team
Created by: Tim
#### Problem 13. Remove all the consonants
Created by: Cody Team
Tags regexp, basics
#### Problem 729. Flag largest magnitude swings as they occur
Created by: Doug Hull
Tags asee
#### Problem 731. Given a window, how many subsets of a vector sum positive
Created by: Doug Hull
Tags asee, good
#### Problem 751. Implement simple rotation cypher
Created by: Doug Hull
#### Problem 60. The Goldbach Conjecture
Created by: Cody Team
Tags primes
#### Problem 105. How to find the position of an element in a vector without using the find function
Created by: Chelsea
Tags find, indexing
#### Problem 41. Cell joiner
Created by: Cody Team
Tags matlab, strings
#### Problem 2024. Triangle sequence
Created by: Tanya Morton
#### Problem 2020. Area of an Isoceles Triangle
Created by: Tanya Morton
#### Problem 2022. Find a Pythagorean triple
Created by: Tanya Morton
Tags pythagoras
#### Problem 2018. Side of a rhombus
Created by: Tanya Morton
#### Problem 2017. Side of an equilateral triangle
Created by: Tanya Morton
#### Problem 2023. Is this triangle right-angled?
Created by: Tanya Morton
Tags pythagoras
#### Problem 2019. Dimensions of a rectangle
Created by: Tanya Morton
#### Problem 2016. Area of an equilateral triangle
Created by: Tanya Morton
#### Problem 1974. Length of a short side
Created by: Tanya Morton
#### Problem 2021. Is this triangle right-angled?
Created by: Tanya Morton
#### Problem 29. Nearest Numbers
Created by: Cody Team
#### Problem 51. Find the two most distant points
Created by: Cody Team
Tags distance
#### Problem 2015. Length of the hypotenuse
Created by: Tanya Morton
#### Problem 73. Replace NaNs with the number that appears to its left in the row.
Created by: Cody Team
Tags matlab
#### Problem 23. Finding Perfect Squares
Created by: Cody Team
#### Problem 67. Find common elements in matrix rows
Created by: Cody Team
Tags matlab
#### Problem 16. Return the largest number that is adjacent to a zero
Created by: Cody Team
Tags vectors
#### Problem 24. Function Iterator
Created by: Cody Team
#### Problem 1774. Free passes for everyone!
Created by: Alfonso Nieto-Castanon
#### Problem 50. QWERTY coordinates
Created by: Cody Team
Tags indexing
#### Problem 39. Which values occur exactly three times?
Created by: Cody Team
Tags search
#### Problem 40. Reverse Run-Length Encoder
Created by: Cody Team
Tags encoding
#### Problem 37. Pascal's Triangle
Created by: Cody Team
#### Problem 80. Test for balanced parentheses
Created by: Cody Team
Tags parens, regexp
#### Problem 87. Indexed Probability Table
Created by: Cody Team
Tags matlab
#### Problem 34. Binary numbers
Created by: Cody Team
Tags matlab
#### Problem 15. Find the longest sequence of 1's in a binary sequence.
Created by: Cody Team
#### Problem 115. Distance walked 1D
Created by: AMITAVA BISWAS
#### Problem 62. Elapsed Time
Created by: Cody Team
Tags time
#### Problem 76. De-dupe
Created by: Cody Team
Tags matlab
51 – 100 of 135 | 1,037 | 4,015 | {"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-2020-10 | latest | en | 0.703542 |
http://mathhelpforum.com/algebra/54894-simple-re-arrangement-fo-formula.html | 1,527,496,552,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794872114.89/warc/CC-MAIN-20180528072218-20180528092218-00480.warc.gz | 187,607,769 | 10,879 | # Thread: Simple re-arrangement fo formula
1. ## Simple re-arrangement fo formula
Hello Folks,
I need to re-arrange this formula and im not sure if i am going about it the right way, can someone please help me.
My first thing to do would be to multiply both sides by 1000 and then multiply both sides by T.
Is this correct, do i treat the (4.302 x 10^-3) as a single entity?
so the result would be
T = 4.302 x 10^-3 x 1000
Thanks.
Edit: Is 4.302 x 10^-3 a single entity as it is standard form?
and should i work it out in my calculator like
1000 x (4.302 x 10^-3)??
Thanks again
2. Originally Posted by liam41
Hello Folks,
I need to re-arrange this formula and im not sure if i am going about it the right way, can someone please help me.
If you're solving for T, simply cross multiply (you have a proportion here)
$\displaystyle T=1000(4.302)(10^{-3})$
$\displaystyle T=10^3(10^{-3})(4.302)$
$\displaystyle T=10^0(4.302)$
$\displaystyle T=1(4.302)$
$\displaystyle T=4.302$
3. at the risk of sounding like a complete idiot, well theres no risk, i do. I dont understand your answer, a proportionate?
I'm sorry, I've not done maths in a long while and this has kinda been sprung on me.
Your solution seems a lot different to mine, could you explain it?
I was more wondering if i had A technique, even tho it may not necessarily be the best.
thank you.
4. Originally Posted by liam41
at the risk of sounding like a complete idiot, well theres no risk, i do. I dont understand your answer, a proportionate?
I'm sorry, I've not done maths in a long while and this has kinda been sprung on me.
Your solution seems a lot different to mine, could you explain it?
I was more wondering if i had A technique, even tho it may not necessarily be the best.
thank you.
You had exactly the same thing as I did. I just went after it a bit differently. A proportion is simply two fractions that are equivalent to each other.
If $\displaystyle \frac{a}{b}=\frac{c}{d}$, then $\displaystyle bc=ad$ | 548 | 2,008 | {"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} | 3.96875 | 4 | CC-MAIN-2018-22 | latest | en | 0.94446 |
andrewtop.com | 1,534,622,279,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221213737.64/warc/CC-MAIN-20180818193409-20180818213409-00455.warc.gz | 22,414,511 | 6,938 | ### Introduction
When I learned about iterated function systems, I became very interested in them what can be done with them. Despite not having gone over the subject of 3D iterated function systems explicitly, there was no reason why any of the subject matter learned in class could not be applied in 3D. It seemed like there would be non-trivial problems to solve in converting some of the classic 2D fractals to 3D, and hence I thought this would make a good topic for my final project.
This paper describes the nuisances of adapting a IFS rendering algorithm to 3D. A companion program was created called IFS3d which was made to accompany this paper and show some of the results. IFS3d's use is explained in the next section. We will explore the process of adapting many famous 2D iterated function systems (such as Sierpinski's Gasket) to their 3D counterparts.
### How to use IFS3d
IFS3d is a program created to accompany this paper, so that some of the elements of this paper may be tested and demonstrated. It is written in C++ and the source code is available. IFS3d uses SDL and OpenGL to setup and render to the graphic display.
IFS3d is executed from the command line. IFS3d take one parameter, the name of the input file to open and read the IFS to render from. For example you may type IFS3d Gasket3D.ifs to start IFS3d displaying a 3d version of Sierpinski's Gasket.
When IFS3d is opened, it will initialize with the camera looking at the center of the fractal. You can control the position of the camera in various ways through the mouse. When the left mouse button is pressed, mouse movements will result in rotations of the camera. If both the left and right mouse buttons are pressed, vertical mouse movements will be interpreted as zooming in and out of the fractal. Pressing the ESC key will quit the program.
When the number key 1 is pressed, the camera will be set to a perspective projection (default). The camera can be set to an orthographic projection by pressing 2. Orthographic mode may be helpful in examining the 2d appearance of a 3d fractal from some angle. Finally if 3 is pressed, the z values of the points will be interpreted as time values, and the remaining x and y coordinates are plotted as if we were rendering a 2d fractal. When in the mode resulting from hitting 3, z values will continuously move from 0 to 1 over 5 seconds, and then repeat.
One may notice 8 red dots on the display when moving the camera around. The dots highlight the corners of the unit box (0,0,0) - (1,1,1). They are displayed to give a sense of scale. Notice how fractals such as Sierpinski's Gasket always stay within the box.
### IFS File Format
The IFS file is simply a text file. It is parsed as follows:
Name of IFS
iterations IterationCount
functionCount NumberOfFunctions
VariationName Weight a b c d e f g h j k l m
... (NumberOfFunctions times)
All italics text in the above template mean user specified values. All non-italics text indicates a string literal that must be typed exactly that way.
Name of IFS is simply any string terminated by a new line character which will be used as the title of your IFS. IterationCount is the number of points that will be iterated (and plotted). The higher this number is, the denser (and more accurate) your IFS' fixed point will appear. NumberOfFunctions is the number of functions that are part of the system.
The next lines (and there will be NumberOfFunctions of them), define the functions that make up the IFS. VariationName can be either linear, sinusoidal or spherical. Choosing linear will give you a standard affine transformation. Choosing either sinusoidal or spherical will apply an extra mapping to the points after they have been multiplied by the affine matrix. This feature is an afterthought and not supported very well, so most examples provided simply use linear. Weight is the weight that will be given to the current function when the IFS plotting algorithm needs to choose a random function in the system. The number is relative to the total weights of all functions. The following numbers represent entries in a 4x4 affine matrix as follows:
a b c d
e f g h
j k l m
0 0 0 1
The best way to learn the IFS file format is of course to look at any of the provided examples.
### Difference between viewing fractals in 3D instead of 2D
Although most aspects of viewing fractals in 2D are unchanged when viewing them in 3D, there are still some subtle differences. In 2D your perspective is normally fixed, in that the resolution of the screen doesn't change, and so most algorithms simply snap every point produced to the closest pixel on the screen. This is not necessary (and even undesirable) in 3D, since the camera may zoom in or out or rotate, all of which would look bad if every point was snapped to a grid.
Points then, are instead stored exactly as they are generated. The points are generated once at the beginning of IFS3d execution and then they are simply re-rendered every frame, transformed by the camera transform. Since the points are drawn in their exact locations, it is possible to zoom in on one area of the fractal until you can see individual points, and then zoom in farther right in to one single point.
Although obvious, it's worth noting that no changes need to be made to the point generating algorithm, as it works for all dimensions.
### Adapting 2D Fractals to 3D
This section will analyze a number of different popular 2D fractals, and how one would go about importing them in to a 3D environment. It should be noted that all 2D fractals can be created within a 3D environment by simply j = k = l = m = c = g = 0, and treating the remaining values a, b, d, e, f, and h as you would in a standard 2D affine transformation.
Sierpinski's Gasket is the popular fractal of a triangle with a triangle cut out of it (creating 3 sub-triangles of which this step is applied recursively).
Sierpinski's Gasket can be created by using 3 affine functions:
0.5 0 0 0
0 0.5 0 0
0 0 0 0
0 0 0 1
0.5 0 0 0.5
0 0.5 0 0
0 0 0 0
0 0 0 1
0.5 0 0 0.25
0 0.5 0 0.5
0 0 0 0
0 0 0 1
Which maps the unit cube in to 3 unit squares (with z = 0, this is 2d) in a triangle formation.
One would imagine that a 3D version of Sierpinski's Gasket might have the form of a pyramid instead of a triangle (or an extruded triangle). Similar to how Sierpinski's Gasket was constructed in 2D, we may visualize 4 boxes lying on the ground, with 1 box sitting on the middle of all of these. One may visualize that if we subdivide these 5 boxes one more time, we will have the top pyramid using as a base the bottom 4 pyramids, and we realize that this solution may be feasible. We test our solution by entering following matrices in to IFS3d (one function for every box, positioned in each different location). Since we are dealing with 3 dimensions now, we must not project away the z values to 0. The matrices follow:
0.5 0 0 0
0 0.5 0 0
0 0 0.5 0
0 0 0 1
0.5 0 0 0
0 0.5 0 0
0 0 0.5 0.5
0 0 0 1
0.5 0 0 0.5
0 0.5 0 0
0 0 0.5 0.5
0 0 0 1
0.5 0 0 0
0 0.5 0 0
0 0 0.5 0.5
0 0 0 1
0.5 0 0 0.25
0 0.5 0 0.5
0 0 0.5 0.25
0 0 0 1
And indeed, this gives us a 3D version of Sierpinski's Gasket.
### The Cantor Set
One might define a 3D Cantor Set to be {x,y,z | x belongs to C, y belongs to C, z belongs to C}. Under this definition we can see that the set is contained within 8 cubes of side length 1/3, each in one corner of the unit cube. Under this reasoning we may proceed in the same fashion as we did for Sierpinski's Gasket (by shrinking the unit cube by 1/3 and then transforming it to a corner of the unit cube) to obtain an 8 function system which converges to the Cantor Set in 3D.
Figure 3: Cantor Set in 3D (Cantor3D.ifs)
### The Fern
The fern is a much trickier IFS to convert to 3D, partly because it's a trickier IFS than the previous systems even in 2D. The 2D fern can of course be displayed in a 3D environment, but one might expect to see the branches popping out in a true 3D version of it (so perhaps it will be more of a bush than a fern).
Figure 4: Fern in 2D (2DFern.ifs)
The fern is composed of four functions. One of them is the stem, and it projects all points on to the Y axis to form a straight line. Two functions are used to place leaves on the left and right. These are achieved by transforming up in the Y direction, scaling down and rotating around the Z axis by roughly 30 degrees. The last function represents the rest of the fern, and transforms it by shrinking it slightly, rotating it around the Z axis slightly, and transforming up in the Y direction a bit. The system can be examined by looking at the example Fern2D.ifs.
A first attempt at converting the fern to 3D might be to modify the function responsible for drawing the rest of the fern so that it includes a rotation around the Y axis (as well as its rotation around the Z axis). This may be accomplished by taking the original matrix, F, and obtaining the new matrix, F' as follows:
F' = F * RotY
where RotY is a matrix representing a rotation around the Y axis. A rotation around the Y axis can be described as:
cos(ANGLE) 0 sin(ANGLE) 0
0 1 0 0
-sin(ANGLE) 0 cos(ANGLE) 0
0 0 0 1
where ANGLE is the angle of the rotation. Entering this new system (Fern3D.ifs) we do indeed obtain a 3d fern, but it is very bushy and difficult to see what is happening.
Figure 5: Fern in 3D, first attempt (3DFern.ifs)
Certainly there must be a more visually concise system. Much of the incoherency of the above image is caused from the leaves also being bushy (and so the leaves of the leaves, and etc…). We need to find a way to keep the 3d rotations while restricting the rotations within the leaves. One way to accomplish this would be to, for each leaf, project our fern to the XY-plane, and THEN rotate it. This process is similar to how the stem is constructed, except instead of projecting to an axis, we are projecting to a plane. A matrix that projects to the XY-plane is given as:
1 0 0 0
0 1 0 0
0 0 0 0
0 0 0 1
And so, if we have the original transformations for the two leaves, T1 and T2, we can form T1' and T2' as follows:
T1' = T1 * Proj
T2' = T2 * Proj
Where Proj is the projection matrix defined above. Running the new system through IFS3d gives a much prettier and coherent 3D version of the fern (ReFlattened3DFern.ifs)
Figure 6: Fern in 3D with flattened leaves (ReFlattened3DFern.ifs)
Figure 7: Flattened leaf fern viewed from above
The top down view makes it obvious how flat the leaves really are though (even though this is not obvious from most other angles), but perhaps we can fix this as well by having the leaves make a slight rotation around their Y-axis after they have been projected. This can be accomplished by forming a rotation matrix around the Y-axis, RotY, and instead construct T1' and T2' as follows:
T1' = T1 * RotY * Proj
T2' = T2 * RotY * Proj
Since the projection is the last matrix in the matrix multiplication chain, it will be a plied before the rotation around the Y-axis, so the rotation will not be lost to the projection.
Figure 8: Fern with leaves rotated around Y (Final3DFern.ifs)
Figure 9: Final version of 3D fern viewed from above
The final fern IFS is given in Final3DFern.ifs.
### Conclusion
Although all of the concepts of iterated function systems remain the same, regardless of how many dimensions we're operating in, there are still some subtle practical considerations to take in to account when moving from 2D fractals to 3D fractals. The algorithm itself, for example, cannot assume anymore that we are operating on a grid, and so we must store all exact values for points.
Clearly the set of 3D fractals contains the set of 2D fractals (we can always project to 0 on the z-axis) and with examples like the 3D fern, we see that there are many more complicated iterated function systems that cannot be generated in 2D. Given the proper knowledge of how matrix transformations can be applied to functions in IFS to produce intended results, we can sculpt many different shapes in 3D simply by plotting points.
### References
Gulick, D., Encounters with Chaos, Pp. 1-320, ©McGraw-Hill Education, 1992. | 3,337 | 12,583 | {"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} | 2.65625 | 3 | CC-MAIN-2018-34 | longest | en | 0.950713 |
https://ru.coursera.org/learn/algorithms-divide-conquer/reviews?authMode=login&page=16 | 1,620,773,587,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243990419.12/warc/CC-MAIN-20210511214444-20210512004444-00174.warc.gz | 514,919,623 | 133,049 | Вернуться к Divide and Conquer, Sorting and Searching, and Randomized Algorithms
# Отзывы учащихся о курсе Divide and Conquer, Sorting and Searching, and Randomized Algorithms от партнера Стэнфордский университет
4.8
звезд
Оценки: 4,475
Рецензии: 867
## О курсе
The primary topics in this part of the specialization are: asymptotic ("Big-oh") notation, sorting and searching, divide and conquer (master method, integer and matrix multiplication, closest pair), and randomized algorithms (QuickSort, contraction algorithm for min cuts)....
## Лучшие рецензии
KS
13 сент. 2018 г.
Well researched. Topics covered well, with walkthrough for exam.le cases for each new introduced algorithm. Great experience, learned a lot of important algorithms and algorithmic thinking practices.
DT
26 мая 2020 г.
Thank you for teaching me this course. I learned a lot of new things, including Divide-and-Conquer, MergeSort, QuickSort, and Randomization Algorithms, along with proof for their asymptotic runtime
Фильтр по:
## 376–400 из 848 отзывов о курсе Divide and Conquer, Sorting and Searching, and Randomized Algorithms
автор: Inderpreet S
5 дек. 2019 г.
Great start in the specialisation of algorithm and data structures.
автор: Hemanth A
30 мар. 2017 г.
Well designed and good to refresh the basics on many top algorithms
автор: Raj K
5 сент. 2020 г.
Classes are just so inspirational!. I’m so, so thankful every day!
автор: Arka M
23 июля 2018 г.
Great Course. :D Thank you for letting me a part of this community
автор: Jamie J S
1 янв. 2017 г.
I'm so glad that I've taken this course. This is really fantastic.
автор: Michal K
5 дек. 2020 г.
Great mathematical background for D&C algorithms. Also quite fun!
автор: ndatimana g
12 июня 2020 г.
awesome material. by now I am able to understand algorithm deeply
автор: Jonathan H
19 мая 2018 г.
One of the best specializations on this site. Highly recommended!
автор: Subhajit S
27 мар. 2018 г.
The instructor was excellent. His way of teaching was really good
автор: Mingwei C
29 авг. 2020 г.
I am amazed how well this online course is designed! Thank you!
автор: Zilu T
28 дек. 2018 г.
Excellent course, a very good overview of fundamental concepts.
автор: Vikas D
16 дек. 2016 г.
Awesome,right now I know why algorithms are most important..!!
автор: Shubham C
11 окт. 2020 г.
One o the best course available in the market for algorithms.
автор: Mincan C
6 мар. 2020 г.
Very helpful. Got better understanding of divide and conquer.
автор: 黃正豪
31 авг. 2018 г.
Quizzes and assignments could be challenging but it worth it.
автор: Kishan P
30 июня 2018 г.
A perfectly balanced course... neither too fast nor too slow.
автор: Bryan Z
8 февр. 2019 г.
Great course. Love the clear instruction and lecture videos.
автор: Jianhui L
12 июня 2018 г.
Good course overall. Hope more algorithms can be introduced
автор: yashaswi
26 дек. 2017 г.
Great structure and the quiz questions are also pretty good
автор: Qingyang L
22 авг. 2017 г.
really good, it helps me learn deeper about the algorithms.
автор: MAHARSHI P
14 июня 2019 г.
such a good course which I had never learned from anywhere
автор: Arun M
17 янв. 2020 г.
loved this course.
I found this course pretty interesting.
автор: Simeon M
25 авг. 2018 г.
Very good and very engaging course, strongly recommended! | 918 | 3,380 | {"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} | 2.671875 | 3 | CC-MAIN-2021-21 | longest | en | 0.550451 |
http://www.studystack.com/flashcard-663313 | 1,477,165,863,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719041.14/warc/CC-MAIN-20161020183839-00239-ip-10-171-6-4.ec2.internal.warc.gz | 712,865,029 | 16,814 | Busy. Please wait.
or
Forgot Password?
Don't have an account? Sign up
or
taken
why
Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.
By signing up, I agree to StudyStack's Terms of Service and Privacy Policy.
Already a StudyStack user? Log In
Reset Password
Enter the email address associated with your account, and we'll email you a link to reset your password.
Remove ads
Don't know (0)
Know (0)
remaining cards (0)
Save
0:01
Flashcards Matching Hangman Crossword Type In Quiz Test StudyStack Study Table Bug Match Hungry Bug Unscramble Chopped Targets
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
# Factorials
### Factorials up to 10! (with division)
QuestionAnswer
1! 1
2! 2 x 1 = 2
3! 3 x 2 x 1 = 6
4! 4 x 3 x 2 x 1 = 24
5! 5 x 4 x 3 x 2 x 1 = 120
6! 6 x 5 x 4 x 3 x 2 x 1 = 720
3! / 2! (3 x 2 x 1) / (2 x 1) = 3
5! / 3! (5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 5 x 4 = 20
6! / 3! (6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 6 x 5 x 4 = 120
7! 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
8! 40320
9! 362,880
10! 3,628,800
Created by: mogomog | 477 | 1,256 | {"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-2016-44 | latest | en | 0.778586 |
http://en.wikipedia.org/wiki/Flow_Shop_Scheduling_Problem | 1,405,235,635,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1404776437410.51/warc/CC-MAIN-20140707234037-00085-ip-10-180-212-248.ec2.internal.warc.gz | 43,366,726 | 10,593 | # Flow shop scheduling
(Redirected from Flow Shop Scheduling Problem)
Flow shop scheduling problems, are a class of scheduling problems with a work shop or group shop in which the flow control shall enable an appropriate sequencing for each job and for processing on a set of machines or with other resources 1,2,...,m in compliance with given processing orders. Especially the maintaining of a continuous flow of processing tasks is desired with a minimum of idle time and a minimum of waiting time. Flow shop scheduling is a special case of job shop scheduling where there is strict order of all operations to be performed on all jobs. Flow shop scheduling may apply as well to production facilities as to computing designs.
A special type of flow shop scheduling problem is the permutation flow shop scheduling problem in which the processing order of the jobs on the resources is the same for each subsequent step of processing.
## Sequencing Performance Measurements (γ)
The sequencing problem can be stated as determining a sequence S such that one or several sequencing objectives are optimized.
1. (Average)Flow time, $\sum (w_i) F_i$
2. Makespan,Cmax
3. (Average) Tardiness, $\sum (w_i) T_i$
4. ....
detailed discussion of performance measurement can be found in Malakooti (2013).
## Complexity of flow shop scheduling
As presented by Garey et al. (1976), most of extensions of the flow shop scheduling problems are Np-Hard and few of them can be solved optimally in O(nlogn), for example F2|prmu|Cmax can be solved optimally by using Johnson's Rule (1954).
## Solution Methods
The proposed methods to solve flow shop scheduling problems can be classified to exact methods such as Branch and Bound and dynamic programming, Heuristic algorithms and metaheuristics.
### minimizing makespan,Cmax
F2|prmu|Cmax and F3|prmu|Cmax can be solved optimally by using Johnson's Rule (1954) but for general case there is no algorithm that grantee the optimality of the solution.
### Other objectives
So far, there is no algorithm which can grantee optimal solution.
the detailed discussion of the available solution methods are provided by Malakooti (2013).
## References
• Taillard, E. (January 1993). "Benchmarks for basic scheduling problems". European Journal of Operational Research 64 (2): 278–285. doi:10.1016/0377-2217(93)90182-M.
• Malakooti, B (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons. ISBN 978-1-118-58537-5.
• Garey, M. R., Johnson, D. S., & Sethi, R. (1976). The complexity of flowshop and jobshop scheduling. Mathematics of operations research, 1(2), 117-129.
• Johnson, S. M. (1954). Optimal two‐and three‐stage production schedules with setup times included. Naval research logistics quarterly, 1(1), 61-68. | 657 | 2,782 | {"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": 0, "img_math": 2, "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} | 2.5625 | 3 | CC-MAIN-2014-23 | longest | en | 0.915574 |
https://www.bgonline.org/forums/webbbs_config.pl?noframes;read=148492 | 1,723,183,126,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640759711.49/warc/CC-MAIN-20240809044241-20240809074241-00735.warc.gz | 535,335,638 | 4,319 | BGonline.org Forums
Solution - Auction the Byes in the first round!!!
Posted By: Bob Koca
Date: Tuesday, 29 October 2013, at 3:16 p.m.
In Response To: Solution - Auction the Byes in the first round!!! (Phil Simborg)
"Each player plays the other two say, a 7 point match, and if there is a clear winner, he is the winner, and if the other two tie..."
After each player has played the other two either all three are 1-1 or one player has won outright at 2 - 0 with one player at 1 -1 and another at 0 - 2 so your tiebreak for 2nd/3rd never happens.
Assuming equal opponents there is a 3/4 chance that the first round is decisive. On average 1 1/3 rounds of the tiebreak will be needed. However there is no upper limit. Compared to the 2 time slots that are needed if there had been 4 players left each round requires 3 time slots.
3/4 one round 3/16 two rounds 3/64 three rounds 1/64 four or more rounds.
As you suggest this means that the match lengths need to be shortened from the usual 11 pointers that would be occurring if there had been four players left. Is it desirable that the more important rounds are to fewer points? Also I am not sure even then that the timing is acceptable. On average it is good but the tails are heavy.
Agree it is completely fair and exciting.
Post Response
Subject:
Message: | 335 | 1,320 | {"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-2024-33 | latest | en | 0.974736 |
https://it.scribd.com/document/253703661/Sensors-2-Strain-Gauge | 1,585,497,871,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370494349.3/warc/CC-MAIN-20200329140021-20200329170021-00332.warc.gz | 538,966,191 | 82,256 | Sei sulla pagina 1di 11
Experimental Methods
Module code DME 811
Dr Riaz A Mufti
(B.Sc, M.Sc Eng (UK), PhD (UK), CEng (UK), MIMechE (UK), P.E (PEC))
Strain gauges
Strain Gauge
What is Strain?
Strain is the amount of deformation of a body due to an applied force. More specifically,
strain () is defined as the fractional change in length, as shown in Figure below.
## Strain can be positive (tensile) or negative (compressive). In practice, the magnitude of
measured strain is very small. Therefore, strain is often expressed as microstrain ().
## When a bar is strained with a uniaxial force, as in Figure, a phenomenon known as
Poisson Strain causes the width of the bar, D, to contract in the transverse, or
perpendicular, direction. The magnitude of this transverse contraction is a material
property indicated by its Poisson's Ratio. The Poisson's Ratio of a material is defined
as the negative ratio of the strain in the transverse direction (perpendicular to the force)
to the strain in the axial direction (parallel to the force), or = T/.
Dr Riaz A Mufti
## National Instruments Texas USA
NI Academy at SMME - NUST
Strain Gauge
While there are several methods of measuring strain,
the most common is with a strain gauge, a device
whose electrical resistance varies in proportion to the
amount of strain in the device.
The metallic strain gauge consists of a very fine wire or,
more commonly, metallic foil arranged in a grid pattern.
The grid pattern maximizes the amount of metallic wire
or foil subject to strain in the parallel direction (Figure).
The cross sectional area of the grid is minimized to
reduce the effect of shear strain and Poisson Strain.
The grid is bonded to a thin backing, called the carrier,
which is attached directly to the test specimen.
Therefore, the strain experienced by the test specimen
is transferred directly to the strain gauge, which
responds with a linear change in electrical resistance.
Dr Riaz A Mufti
National Instruments Texas USA
NI Academy at SMME - NUST
Strain Gauge
It is very important that the strain gauge be properly mounted onto the test specimen so that
the strain is accurately transferred from the test specimen, though the adhesive and strain
gauge backing, to the foil itself. Manufacturers of strain gauges are the best source of
information on proper mounting of strain gauges.
A fundamental parameter of the strain gauge is its sensitivity to strain, expressed
quantitatively as the gauge factor (GF). Gauge factor is defined as the ratio of fractional
change in electrical resistance to the fractional change in length (strain):
## The Gauge Factor for metallic strain gauges is typically around 2.
Ideally, we would like the resistance of the strain gauge to change only in response to applied
strain. However, strain gauge material, as well as the specimen material to which the gauge is
applied, will also respond to changes in temperature. Strain gauge manufacturers attempt to
minimize sensitivity to temperature by processing the gauge material to compensate for the
thermal expansion of the specimen material for which the gauge is intended. While
compensated gauges reduce the thermal sensitivity, they do not totally remove it.NationalNI LabVIEW
Dr Riaz A Mufti
Instruments Texas USA
## NI Academy at SMME - NUST
Strain Gauge
To measure such small changes in resistance, and compensate for the temperature
sensitivity discussed in the previous slide, strain gauges are almost always used in a bridge
configuration with a voltage or current excitation source. The general Wheatstone bridge,
illustrated below, consists of four resistive arms with an excitation voltage, VEX, that is
applied across the bridge.
The output voltage of the bridge, VO, will be equal to:
Dr Riaz A Mufti
National Instruments Texas USA
NI Academy at SMME - NUST
Strain Gauge
From this equation, it is apparent that when R1/R2 = R3/R4, the voltage output VO will be zero.
Under these conditions, the bridge is said to be balanced. Any change in resistance in any
arm of the bridge will result in a nonzero output voltage.
Therefore, if we replace R4 in Figure 3 with an active strain gauge, any changes in the strain
gauge resistance will unbalance the bridge and produce a nonzero output voltage. If the
nominal resistance of the strain gauge is designated as RG, then the strain-induced change
in resistance, R, can be expressed as R = RGGF. Assuming that R1 = R2 and R3 = RG,
the bridge equation above can be rewritten to express VO/ VEX as a function of strain (see
Figure 4). Note the presence of the 1/(1+GF/2) term that indicates the nonlinearity of the
quarter-bridge output with respect to strain.
Dr Riaz A Mufti
National Instruments Texas USA
NI Academy at SMME - NUST
Strain Gauge
By using two strain gauges in the bridge, the effect of temperature can be avoided. For
example, Figure 5 illustrates a strain gauge configuration where one gauge is active (RG +
R), and a second gauge is placed transverse to the applied strain. Therefore, the strain
has little effect on the second gauge, called the dummy gauge. However, any changes in
temperature will affect both gauges in the same way. Because the temperature changes are
identical in the two gauges, the ratio of their resistance does not change, the voltage VO
does not change, and the effects of the temperature change are minimized.
Dr Riaz A Mufti
National Instruments Texas USA
NI Academy at SMME - NUST
Strain Gauge
Alternatively, you can double the sensitivity of the bridge to strain by making both gauges
active, although in different directions. For example, Figure 6 illustrates a bending beam
application with one bridge mounted in tension (RG + R) and the other mounted in
compression (RG R). This half-bridge configuration, whose circuit diagram is also
illustrated in Figure 6, yields an output voltage that is linear and approximately doubles
the output of the quarter-bridge circuit.
Dr Riaz A Mufti
National Instruments Texas USA
NI Academy at SMME - NUST
Strain Gauge
You can further increase the sensitivity of the circuit by
making all four of the arms of the bridge active strain
gauges, and mounting two gauges in tension and two
gauges in compression. The full-bridge circuit is shown
in Figure 7 below.
The equations given here for the Wheatstone bridge
circuits assume an initially balanced bridge that
generates zero output when no strain is applied. In
practice however, resistance tolerances and strain
induced by gauge application will generate some initial
offset voltage. This initial offset voltage is typically
handled in two ways. First, you can use a special offsetnulling, or balancing, circuit to adjust the resistance in the
bridge to rebalance the bridge to zero output.
Alternatively, you can measure the initial unstrained
output of the circuit and compensate in software
Dr Riaz A Mufti
National Instruments Texas USA
NI Academy at SMME - NUST
Dr Riaz A Mufti | 1,568 | 6,955 | {"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-2020-16 | latest | en | 0.920179 |
https://ww2.mathworks.cn/matlabcentral/cody/problems/7-column-removal/solutions/2764594 | 1,611,126,581,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519923.26/warc/CC-MAIN-20210120054203-20210120084203-00492.warc.gz | 636,162,313 | 18,844 | Cody
Problem 7. Column Removal
Solution 2764594
Submitted on 31 Jul 2020
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 Fail
A = [1 2 3; 4 5 6]; n = 2; B_correct = [1 3; 4 6]; assert(isequal(column_removal(A,n),B_correct))
Error in solution: Line: 2 Column: 8 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.
2 Fail
A = magic(4); n = 3; B = [16 2 13; 5 11 8; 9 7 12; 4 14 1]; B_correct = B; assert(isequal(column_removal(A,n),B_correct))
Error in solution: Line: 2 Column: 8 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.
3 Fail
A = 1:10; n = 7; B_correct = [1 2 3 4 5 6 8 9 10]; assert(isequal(column_removal(A,n),B_correct))
Error in solution: Line: 2 Column: 8 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 357 | 1,202 | {"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} | 2.578125 | 3 | CC-MAIN-2021-04 | latest | en | 0.542605 |
https://rdrr.io/cran/LearningRlab/man/explain.absolute_acum_frecuency.html | 1,669,681,354,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710684.84/warc/CC-MAIN-20221128235805-20221129025805-00360.warc.gz | 531,661,276 | 7,812 | explain.absolute_acum_frecuency: Absolute Accumulated Frecuency Calculus Explained In LearningRlab: Statistical Learning Functions
explain.absolute_acum_frecuency R Documentation
Absolute Accumulated Frecuency Calculus Explained
Description
Step by step demonstration of the absolute accumulated frecuency calculus
Usage
```explain.absolute_acum_frecuency(v,x)
```
Arguments
`v` Should be a vector `x` Should be a number
Details
To calculate the absolute accumulated frecuency, the user should give a vector and a number. We can saw the absolute accumulated frecuency formule in the frecuency_acum_absolute help document.
Value
A demonstration of the calculus process
Note
A vector is created by c(), like c(1,2,3,4,5) creates a vector with the numbers: 1,2,3,4,5
Author(s)
Dennis Monheimius, dennis.monhemimius@edu.uah.es
Eduardo Benito, eduardo.benito@edu.uah.es
Universidad de Alcala de Henares
Examples
```{
#data creation
data <- c(1,2,2,5,10,4,2)
value = 2
#function execution
explain.absolute_acum_frecuency(data, value)
}
```
LearningRlab documentation built on June 18, 2022, 1:06 a.m. | 312 | 1,116 | {"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-2022-49 | latest | en | 0.494511 |
https://calculat.io/en/number/fraction-as-a-decimal/3--7--13 | 1,720,910,582,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514517.94/warc/CC-MAIN-20240713212202-20240714002202-00558.warc.gz | 135,355,831 | 25,878 | # Fraction 3 7/13 as a decimal
## What is 3 7/13 as a decimal?
Answer: Fraction 3 7/13 as a decimal is 3.538461538461... or 3.538461
3
7
/
13
=3.538461538461... = 3.538461
## Explanation of 3 7/13 Fraction to Decimal Conversion
To convert 3 7/13 to decimal you need simply divide numerator 7 by denominator 13. The result of the division is:
7 ÷ 13 = 3.538461538461...
and then add the whole part (3):
0.538 + 3 = 3.538461538461...
Another way to convert fraction 3 and 7/13 to decimal is to change this mixed fraction to an improper fraction. To do so we need first multiply the whole part (3) by the denominator (13):
3 × 13 = 39
then add the result to the numerator (7):
39 + 7 = 46
and finally divide the result by the denominator (13):
46
/
13
= 46 ÷ 13 =3.538461538461...
Since the remainder has a repeating pattern (538461) which repeats after every 6 digits, so we can write the repeating decimal as:
3.538461
where the vinculum (overline) or the parentheses indicate that the digit 538461 repeats infinitely
## Fraction to Decimal Conversion Table
FractionDecimal
5.3
4.16
3.7
3.63
3.583
3.538461
3.46
3.4117647058823529
3.38
3.368421052631578947
3 7/213.3
3 7/223.318
3 7/233.3043478260869565217391
3 7/243.2916
3 7/263.2692307
3 7/273.259
3 7/28
3 7/293.2413793103448275862068965517
3 7/303.23
## About "Fraction to Decimal Converter" Calculator
This online Fraction to Decimal converter is a useful tool designed to help you easily convert any fraction to its equivalent decimal form. For example, it can help you find out what is 3 7/13 as a decimal? (The answer is: 3.(538461)). Whether you are a student or a professional, this converter can save you time and effort in performing manual calculations.
To use this converter, simply enter the fraction you want to convert in the provided fields. You will need to enter the whole part (if any), numerator, and denominator of the fraction. For example, if you want to convert 3 7/13 to its decimal equivalent, you would enter '3' as the whole part, '7' as the numerator, and '13' as the denominator.
Once you have entered the fraction, hit the 'Convert' button to get the results. The converter will then display the decimal equivalent of the fraction, which in this case is 3.538461538461.... Additionally, it will provide a step-by-step explanation of the conversion process, so you can understand how the decimal equivalent was obtained. However, if the result is a repeating decimal, the converter will display the repeating pattern using parentheses or vinculum (overline) to indicate the repeating digits.
One of the key features of this converter is its ability to output repeating fractions. In mathematics, a repeating fraction is a decimal that has a repeating pattern of digits, such as 0.33333... or 0.142857142857... This is different from a terminating decimal, which is a decimal that ends after a certain number of digits, such as 0.5 or 0.75.
Using this online Fraction to Decimal converter is a quick and easy way to convert any fraction to its decimal equivalent. It can be especially helpful for those who struggle with manual calculations or who need to perform conversions frequently.
## FAQ
### What is 3 7/13 as a decimal?
Fraction 3 7/13 as a decimal is 3.538461538461... or 3.538461 | 900 | 3,297 | {"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-2024-30 | latest | en | 0.787435 |
http://www.propheti.ca/da633dzd/4768f3-left-inverse-is-right-inverse | 1,620,339,386,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00414.warc.gz | 85,408,825 | 12,657 | # left inverse is right inverse
Posted by on Jan 8, 2021 | No Comments
0 & \text{if } \sin(x) = 0, \end{cases} The same argument shows that any other left inverse bâ²b'bâ² must equal c,c,c, and hence b.b.b. Homework Statement Let A be a square matrix with right inverse B. By Lemma 1.11 we may conclude that these two inverses agree and are a two-sided inverse ⦠Dear Pedro, for the group inverse, yes. Let GGG be a group. g2â(x)={ln(x)0âif x>0if xâ¤0.â Information and translations of left inverse in the most comprehensive dictionary definitions resource on the web. f(x) has domain $-2\le x<1\text{or}x\ge 3$, or in interval notation, $\left[-2,1\right)\cup \left[3,\infty \right)$. Each of the toolkit functions has an inverse. just P has to be left invertible and Q right invertible, and of course rank A= rank A 2 (the condition of existence). If $f$ has an inverse mapping $f^{-1}$, then the equation $$f(x) = y \qquad (3)$$ has a unique solution for each $y \in f[M]$. No rank-deficient matrix has any (even one-sided) inverse. https://goo.gl/JQ8Nys If y is a Left or Right Inverse for x in a Group then y is the Inverse of x Proof. âabcdaaaaabcbdbcdcbcdabcd These theorems are useful, so having a list of them is convenient. For a function to have an inverse, it must be one-to-one (pass the horizontal line test). The transpose of the left inverse of is the right inverse . g1(x)={lnâ¡(â£xâ£)if xâ 00if x=0, g_1(x) = \begin{cases} \ln(|x|) &\text{if } x \ne 0 \\ It is shown that (1) a homomorphic image of S is a right inverse semigroup, (2) the ⦠The first step is to graph the function. each step follows from the facts already stated. Therefore it has a two-sided inverse. Find a function with more than one right inverse. Letâs recall the definitions real quick, Iâll try to explain each of them and then state how they are all related. A set of equivalent statements that characterize right inverse semigroups S are given. 0 & \text{if } x \le 0. Let S=RS= \mathbb RS=R with aâb=ab+a+b. denotes composition).. l is a left inverse of f if l . Meaning of left inverse. The (two-sided) identity is the identity function i(x)=x. Here are a collection of proofs of lemmas about the relationships between function inverses and in-/sur-/bijectivity. The identity element is 0,0,0, so the inverse of any element aaa is âa,-a,âa, as (âa)+a=a+(âa)=0. $f$ is said to be ⦠Which elements have left inverses? Homework Equations Some definitions. Thus gâ
ââ
fâ=âidA. Exercise 1. A matrix has a left inverse if and only if its rank equals its number of columns and the number of rows is more than the number of column . If an element a has both a left inverse L and a right inverse R, i.e., La = 1 and aR = 1, then L = R, a is invertible, R is its inverse. To prove A has a left inverse C and that B = C. Homework Equations Matrix multiplication is asociative (AB)C=A(BC). (âââ) Suppose f is injective. An element might have no left or right inverse, or it might have different left and right inverses, or it might have more than one of each. Then. Free functions inverse calculator - find functions inverse step-by-step This website uses cookies to ensure you get the best experience. \begin{array}{|c|cccc|}\hline *&a&b&c&d \\ \hline a&a&a&a&a \\ b&c&b&d&b \\ c&d&c&b&c \\ d&a&b&c&d \\ \hline \end{array} For T = a certain diagonal matrix, V*T*U' is the inverse or pseudo-inverse, including the left & right cases. Definition. If every other element has a multiplicative inverse, then RRR is called a division ring, and if RRR is also commutative, then it is called a field. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Proof: We must show that for any câââC, there exists some a in A with f(g(a))â=âc. 1. f is injective if and only if it has a left inverse 2. f is surjective if and only if it has a right inverse 3. f is bijective if and only if it has a two-sided inverse 4. if f has both a left- and a right- inverse, then they must be the same function (thus we are justified in talking about "the" inverse of f). A left unit that is also a right unit is simply called a unit. Notice that the restriction in the domain divides the absolute value function into two halves. From the table of Laplace transforms in Section 8.8,, This same quadratic function, as seen in Example 1, has a restriction on its domain which is x \ge 0.After plotting the function in xy-axis, I can see that the graph is a parabola cut in half for all x values equal to or greater ⦠The Inverse Square Law codifies the way the intensity of light falls off as we move away from the light source. Then every element of RRR has a two-sided additive inverse (R(R(R is a group under addition),),), but not every element of RRR has a multiplicative inverse. The only relatio⦠Left and right inverses; pseudoinverse Although pseudoinverses will not appear on the exam, this lecture will help us to prepare. This discussion of how and when matrices have inverses improves our understanding of the four fundamental subspaces and of many other key topics in the course. If only a right inverse $f_{R}^{-1}$ exists, then a solution of (3) exists, but its uniqueness is an open question. Solve the triangle in Figure 8 for ⦠By above, we know that f has a left inverse and a right inverse. Please Subscribe here, thank you!!! In other words, we wish to show that whenever f(x)â=âf(y), that xâ=ây. More explicitly, let SSS be a set, â*â a binary operation on S,S,S, and aâS.a\in S.aâS. If $f$ has an inverse mapping $f^{-1}$, then the equation $$f(x) = y \qquad (3)$$ has a unique solution for each $y \in f[M]$. Similarly, any other right inverse equals b, b, b, and hence c. c. c. So there is exactly one left inverse and exactly one right inverse, and they coincide, so there is exactly one two-sided inverse. We define g as follows: on a given input y, we know that there is at least one x with f(x)â=ây (since f is surjective). {eq}\eqalign{ & {\text{We have the function }}\,f\left( x \right) = {\left( {x + 6} \right)^2} - 3,{\text{ for }}x \geqslant - 6. Existence and Properties of Inverse Elements, https://brilliant.org/wiki/inverse-element/. In the following proofs, unless stated otherwise, f will denote a function from A to B and g will denote a function from B to A. I will also assume that A and B are non-empty; some of these claims are false when either A or B is empty (for example, a function from â
âB cannot have an inverse, because there are no functions from Bââ
). By using this website, you agree to our Cookie Policy. The calculator will find the inverse of the given function, with steps shown. No mumbo jumbo. Typically, the right and left inverses coincide on a suitable domain, and in this case we simply call the right and left inverse function the inverse function. Log in. There is a binary operation given by composition fâg=fâg, f*g = f \circ g,fâg=fâg, i.e. Log in here. We provide below a counterexample. Overall, we rate Inverse Left-Center biased for story selection and High for factual reporting due to proper sourcing. Here, he is abusing the naming a little, because the function combine does not take as input the pair of lists, but is curried into taking each separately.. f\colon {\mathbb R} \to {\mathbb R}.f:RâR. One also says that a left (or right) unit is an invertible element, i.e. Let SS S be the set of functions fââ£:RââRâ. By above, this implies that fâ
ââ
g is a surjection. an element that admits a right (or left) inverse with respect to the multiplication law. Hence it is bijective. âabcdâaacdaâbabcbâcadbcâdabcdââ (f*g)(x) = f\big(g(x)\big).(fâg)(x)=f(g(x)). Two sided inverse A 2-sided inverse of a matrix A is a matrix Aâ1 for which AAâ1 = I = Aâ1 A. If only a left inverse $f_{L}^{-1}$ exists, then any solution is unique, ⦠Subtract [b], and then multiply on the right by b^j; from ab=1 (and thus (1-ba)b = 0) we conclude 1 - ba = 0. f(x)={tanâ¡(x)if sinâ¡(x)â 00if sinâ¡(x)=0, A semigroup S (with zero) is called a right inverse semigroup if every (nonnull) principal left ideal of S has a unique idempotent generator. Proof (â): If it is bijective, it has a left inverse (since injective) and a right inverse (since surjective), which must be one and the same by the previous factoid Proof (â): If it has a two-sided inverse, it is both injective (since there is a left inverse) and surjective (since there is a right inverse). If $$AN= I_n$$, then $$N$$ is called a right inverseof $$A$$. Its inverse, if it exists, is the matrix that satisfies where is the identity matrix. the stated fact is true (in the context of the assumptions that have been made). Since ddd is the identity, and bâc=câa=dâd=d,b*c=c*a=d*d=d,bâc=câa=dâd=d, it follows that. Work through a few examples and try to find a common pattern. Similarly, any other right inverse equals b, b, b, and hence c. c. c. So there is exactly one left inverse and exactly one right inverse, and they coincide, so there is exactly one two-sided inverse. If The inverse (a left inverse, a right inverse) operator is given by (2.9). Then composition of functions is an associative binary operation on S,S,S, with two-sided identity given by the identity function. (âââ) Suppose f is surjective. Formal definitions In a unital magma. The reason why we have to define the left inverse and the right inverse is because matrix multiplication is not ⦠I claim that for any x, (gâ
ââ
f)(x)â=âx. F \circ g, we rate inverse Left-Center biased for story selection and High for factual reporting due to sourcing... This together, we wish to show that g ( y ) ) â=ây ( aâc =bâe=b. Each step is explained as much as is necessary to make it clear 3,4,5 ) } \to. The given function, with steps shown inverses and in-/sur-/bijectivity right ( or )... Inverse for x \ge 3, we rate inverse Left-Center biased for selection... Invalid proof ( âââ ): Suppose f is bijective if and if. Of an element against its right inverse ), then we let g ( a two-sided inverse and! Biased for story selection and High for factual reporting due to proper sourcing ) inverse with respect the. ( g ( a left inverse is epimorphic, like the left inverse bâ²b'bâ² equal! Having a list of them is convenient you move right, the of. Only if it has a right inverse ( g ( x ) =x invertible! Selection and High for factual reporting due to proper sourcing image that shows light off. Since f and g is a binary operation given by ( 2.9 ) weâve called left! That gâ ââ fâ=âidA parts are, especially when transitioning from one part to another that there no! That maps to y ) â=âx and vice versa } f\left ( x â=âx. Straightforward to check that this is what weâve called the inverse of an element against its right inverse help... Lemmas about the relationships between function inverses and in-/sur-/bijectivity for most binary.... F is injective but not injective inverse equals b, b, b * c=c * *! Information and translations of left inverse ) the transpose of the given function, with two-sided identity 0.0.0 *... No right inverses ; pseudoinverse Although pseudoinverses will not appear on the web that is... Multiplication law x \ge 3, we know that f has a inverse! They are all related ): Suppose f is injective but not,. Codifies the way the intensity of light drops inverse g. since g is injective we! Inverse that is both surjective and injective and hence b.b.b 31 '17 at 9:51 right and inverse... And Properties of inverse Elements, https: //brilliant.org/wiki/inverse-element/ vice versa ( A\ ) function is one-to-one, will. One two-sided inverse, a left inverseof \ ( MA = I_n\ ), that xâ=ây translations left... X \ge 3, we know there is a bijection g\left ( y ) â=âx âc=bâ ( aâc ).! Useful, so 5x is equivalent to 5 * `. Example of a matrix a is a bijection agree to our Cookie Policy ( pass the horizontal line test.... We may conclude that xâ=ây the zero transformation on. inverse equals b, bâc=câa=dâd=d! Left inverse in the most comprehensive dictionary definitions resource on the web two surjections f: and!, even if the proof requires multiple parts, the reader is reminded what the are... Inverse square law codifies the way the intensity of light drops reader is reminded what the parts,... A matrix a has full rank is exactly one left inverse in right! X.I ( x ) â=âx a bijection M\ ) is called a left inverseof \ ( A\ ) you skip. Operator is given by composition fâg=fâg, i.e hence c.c.c right, the reader is reminded what the parts,! Let [ math ] f \colon x \longrightarrow y [ /math ] be a right inverseof \ ( I_n\... Reporting due to proper sourcing common pattern surjective if and only if it both. We must prove the implication in both directions a set of functions an. Words, variables, symbols, and they coincide, so there is some bâââB with (... FâG=FâG, f must also be surjective proof requires multiple parts, the transpose of the assumptions that have made! Second example was surjective but not surjective, we have xâ=âg ( f ( ). Off from left to right if f square matrix with right inverse existence Properties. Of proofs of lemmas about the relationships left inverse is right inverse function inverses and in-/sur-/bijectivity \colon { R... | 3,834 | 13,432 | {"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": 3, "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} | 3.84375 | 4 | CC-MAIN-2021-21 | latest | en | 0.818105 |
https://encyclopediaofmath.org/index.php?title=Faber_polynomials&oldid=17377 | 1,596,919,645,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738351.71/warc/CC-MAIN-20200808194923-20200808224923-00510.warc.gz | 303,717,554 | 6,912 | # Faber polynomials
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
A classical basis system that serves to represent analytic functions in a complex domain. Suppose that the complement of a bounded continuum containing more than one point is a simply-connected domain of the extended complex plane , and that the function , , is the conformal univalent mapping of onto the domain under the conditions and . Then the Faber polynomials can be defined as the sums of the terms of non-negative degree in in the Laurent expansions of the functions in a neighbourhood of the point . The Faber polynomials for can also be defined as the coefficients in the expansion
(1)
where the function is the inverse of . If is the disc , then . In the case when is the segment , the Faber polynomials are the Chebyshev polynomials of the first kind. These polynomials were introduced by G. Faber [1].
If is the closure of a simply-connected domain bounded by a rectifiable Jordan curve , and the function is analytic in , continuous in the closed domain and has bounded variation on , then it can be expanded in in a Faber series
(2)
that converges uniformly inside , that is, on every closed subset of , where the coefficients in the expansion are defined by the formula
The Faber series (2) converges uniformly in the closed domain if, for example, has a continuously-turning tangent the angle of inclination to the real axis of which, as a function of the arc length, satisfies a Lipschitz condition. Under the same condition on , the Lebesgue inequality
holds for every function that is analytic in and continuous in , where the constant is independent of and , and is the best uniform approximation to in by polynomials of degree not exceeding .
One can introduce a weight function in the numerator of the left-hand side of (1), where is analytic in , is different from zero and . Then the coefficients of the expansion (1) are called generalized Faber polynomials.
#### References
[1] G. Faber, "Ueber polynomische Entwicklungen" Math. Ann. , 57 (1903) pp. 389–408 [2] P.K. Suetin, "Series in Faber polynomials and several generalizations" J. Soviet Math. , 5 (1976) pp. 502–551 Itogi Nauk. i Tekhn. Sovr. Probl. Mat. , 5 (1975) pp. 73–140 [3] P.K. Suetin, "Series in Faber polynomials" , Moscow (1984) (In Russian) | 556 | 2,346 | {"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} | 2.953125 | 3 | CC-MAIN-2020-34 | latest | en | 0.936709 |
https://www.autoweek.com/car-life/a2141386/autoweek-asks-how-much-space-do-you-keep-between-car-ahead-red-lights/ | 1,660,819,814,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00646.warc.gz | 578,825,739 | 48,006 | # Autoweek Asks: How much space do you keep between the car ahead at red lights?
There's following too closely, and then there's contributing to congestion. Which side do you fall on?
Autoweek
Most drivers remember the two-second rule as being the safe following distance; some drivers actually observe it. While that rule of thumb is generally a good idea (and remember that it's three seconds for vehicles with dozens of crazy bumper stickers on them), one thing we've started noticing lately that some drivers observe a two-vehicle distance from the car in front of them at traffic lights.
First of all, this is a topic that's kind of overlooked in most driving courses -- all attention is paid to keeping a safe following distance from the vehicle in front of you while you're in motion. But the question of distance at red lights has become something of an interesting pattern to observe in different cities, especially in urban areas where every extra inch counts. The only thing worse than "a close talker" at traffic lights is a phone talker who leaves two car spaces in front of them, preventing others from getting into the line behind them.
Think about it: In an urban area, if a traffic light can accommodate just five vehicles and the second car in line maintains a one- or two-vehicle empty spot in front of it, only two or three cars will get through an intersection in a green light cycle. If a traffic light holds a maximum of 10 vehicles due to space and the length of the light, and each car keeps a whole car-length spot in front of them, this can contribute to congestion because only about five cars will get through, even though there is space for nine or 10 vehicles if they were closer together. At least in theory.
So is crunching in the smartest thing to do if your goal is to maximize space for everyone, or do you give the car ahead as much room as possible?
A recent study by Virginia Tech College of Engineering suggests that packing in closer is offset by the space required to accelerate from the light.
"The study, published this month in the New Journal of Physics, used video cameras attached to drone helicopters to capture footage of cars accelerating through a traffic light on the Virginia Tech Transportation Institute's Smart Road," Science Daily writes. "By systematically controlling the packing density of the cars, the researchers discovered that any decrease in distance to the light was completely offset by the time it took for cars to regain a comfortable spacing before drivers could accelerate."
Some people say, "Well, leaving a huge distance ahead of you gives you time to honk your horn if the car ahead puts it into reverse." That can be true if that car overshot the light and had to back up and you're the second car in line. But one other argument we've heard for keeping a very minimal distance from the car ahead of you is to discourage pedestrians and bikers to fit through that gap while you're stationary at a red light, which is a tactic some drivers use in cities to prevent jaywalkers from creating dangerous situations.
If you think that state laws regulate this sort of thing, the answer is that in most states the statute simply penalizes "Following too closely," which is usually backed up by lazy and subjective language regarding keeping a "prudent" following distance. Those statutes are written wide enough to give police a pretextual excuse to pull someone over, but they're not frequently enforced at intersections while cars are stationary unless an officer really wants to pull someone over. For one thing, a police officer has to be able to see the distance in the first place, and that's hard to do unless they're to the left or the right on a multilane road, and they're actually interested in making a traffic stop just based on that.
Still, this is something that DMV test-takers can lose points for on a driving exam because the rule of thumb that testers often use is the ability to see the rear tires of the car in front of you. Whether anyone would be able to get to work on time in an urban area like New York or Boston if everyone actually observed the rear-tire rule of thumb is another matter entirely.
How much space do you usually leave between your front bumper and the car ahead of you at traffic lights?
Let us know in the comments below. | 878 | 4,348 | {"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} | 2.65625 | 3 | CC-MAIN-2022-33 | latest | en | 0.974259 |
https://www.coursehero.com/file/6173930/Quiz-4-Solutions/ | 1,521,506,850,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647244.44/warc/CC-MAIN-20180319234034-20180320014034-00003.warc.gz | 798,842,086 | 27,308 | {[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
Quiz 4 Solutions
# Quiz 4 Solutions - CHMB 333 Name(print Jada-hm Quiz 4...
This preview shows page 1. Sign up to view the full content.
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: CHMB 333 Name (print): Jada-hm Quiz 4 February 4, 2011 I have neither given nor received unauthorized aid for this assignment. (initials) 1. Consider steady state, one-dimensional heat conduction through a plane wall, a cylindrical shell, and a spherical shell of uniform thickness with constant thennophysical properties and no thermal energy generation. What geometry (or geometries) will have a linear variation of temperature in the direction of heat transfer? pm coal? (5;. 3,1) (53" 33) 2. Hot water flows through a PVC pipe (k—"~ 0.092 W/m-K) whose inner diameter 13 2 cm, and outer diameter 2 5 cm. The temperature of the interior surface of this pipe is 50° C, and the temperature of the exterior surface of the pipe is 20°C. Calculate the rate of heat loss per unit length of the pipe. [ISMM starts: (5'th lerkAT (3&3) 3. Harvested grains, like wheat, undergo an exothermic reaction while they are being stored. This heat generation causes these grains to spoil or even start fires if not controlled properly. Wheat (k = 0.5 me-K) is stored on the ground (effectively an adiabatic surface) 1n 5 m thick layers. Air at 22° C contacts the upper surface of this layer of wheat with h= 3 “Kim2 -K If the temperature of the upper surface 15 24°C, what 18 the temperature of the wheat next to the ground? “exact ‘lB-Flwi Cé'fi-m SW61 volume. ham l" oil. Conducil’lw) P? 43;. Mrfa-rm Wail-'5‘“ '5 , admhahn, sm‘faC-L (300% 53w?) '12 7W) fCt-f: Enact! T31) ...
View Full Document
{[ snackBarMessage ]}
Ask a homework question - tutors are online | 524 | 1,844 | {"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} | 3.125 | 3 | CC-MAIN-2018-13 | latest | en | 0.817494 |
https://studysoup.com/tsg/52382/thomas-calculus-early-transcendentals-13-edition-chapter-5-problem-79pe | 1,597,105,284,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738723.55/warc/CC-MAIN-20200810235513-20200811025513-00025.warc.gz | 500,811,740 | 11,523 | ×
×
# Evaluating Definite IntegralsEvaluate the | Ch 5 - 79PE
ISBN: 9780321884077 57
## Solution for problem 79PE Chapter 5
Thomas' Calculus: Early Transcendentals | 13th Edition
• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants
Thomas' Calculus: Early Transcendentals | 13th Edition
4 5 1 304 Reviews
17
2
Problem 79PE
Evaluating Definite Integrals
Evaluate the integrals
Step-by-Step Solution:
Step 1 of 2:
In this problem, we need to evaluate the integral.
Step 2 of 2
##### ISBN: 9780321884077
The answer to “Evaluating Definite IntegralsEvaluate the integrals” is broken down into a number of easy to follow steps, and 5 words. Since the solution to 79PE from 5 chapter was answered, more than 230 students have viewed the full step-by-step answer. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. This full solution covers the following key subjects: Integrals, evaluating, evaluate, Definite. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. The full step-by-step solution to problem: 79PE from chapter: 5 was answered by , our top Calculus solution expert on 08/01/17, 02:37PM. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13.
#### Related chapters
Unlock Textbook Solution | 380 | 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} | 2.5625 | 3 | CC-MAIN-2020-34 | latest | en | 0.837552 |
https://community.jmp.com/t5/Short-Videos/Selecting-Variables-Using-Effect-Summary/ta-p/271967 | 1,601,495,271,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402127397.84/warc/CC-MAIN-20200930172714-20200930202714-00522.warc.gz | 331,020,575 | 69,685 | Choose Language Hide Translation Bar
Community Manager
## Selecting Variables Using Effect Summary
Statistical Thinking for Industrial Problem Solving
In this video, we see how to use the Effect Summary table for variable selection using the Impurity data.
We’ll start by fitting a full model, with interactions, using Fit Model.
First, we’ll select Impurity as the Y.
Then, we’ll select Temp through Shift, and select Macros, and then Factorial to Degree. This adds all main effects and two-way interactions as model effects.
We’ll use the default personality and click Run.
The Effect Summary table shows the terms in the model, in ascending order of p-value.
We can use the Effect Summary table to slowly remove nonsignificant terms from the model, one at a time, starting from the bottom.
We can’t remove Reaction Time because it is involved in two-way interactions that are still in the model.
As we slowly remove terms, the p-values for the terms in the model all update, along with all the statistical output. We’ll use a p-value threshold of 0.05. Our final reduced model has all five main effects and three interactions.
Catalyst Conc and Temp are the most significant, followed by the interaction between Catalyst Conc and Reaction Time.
Reactor is significant, indicating that there is a difference in impurity between the three reactors. There is also a significant interaction between Reactor and Shift, indicating that the reactors perform differently, relative to Impurity, on the different shifts.
Let’s explore this model using the Prediction Profiler. Ignoring the other factors, lower values of Temp and Catalyst Conc have lower impurity. At these values, if we change Reaction Time, we don’t see much of a change in Impurity. And Shift 1 has the lowest value of Impurity on Reactor 2, and Shift 2 has the lowest value of Impurity on Reactor 1.
Article Labels
Article Tags
Contributors | 400 | 1,919 | {"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} | 2.578125 | 3 | CC-MAIN-2020-40 | latest | en | 0.882597 |
http://pmean.com/news/2008-12.html | 1,624,233,817,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488259200.84/warc/CC-MAIN-20210620235118-20210621025118-00629.warc.gz | 41,184,067 | 11,333 | You are viewing the webpage version of the Monthly Mean newsletter for December 2008. This newsletter was sent out on December 5, 2008.
The monthly mean for December is 16.0.
Welcome to the Monthly Mean newsletter for December 2008. If you are having trouble reading this newsletter in your email system, please go to www.pmean.com/news/2008-12.html. If you are not yet subscribed to this newsletter, you can sign on at www.pmean.com/news. If you no longer wish to receive this newsletter, there is a link to unsubscribe at the bottom of this email. Here's a list of topics.
1. Monthly Mean Quote.
"The statistics on sanity are that one out of every four Americans is suffering from some form of mental illness. Think of your three best friends. If they're okay, then it's you." Rita Mae Brown, as quoted at www.quotationspage.com/quote/1380.html.
2. Combining measures on different scales.
Someone was asking about meta-analysis and the process of combining outcomes measured on different scales. Some of the papers in the meta-analysis described their outcomes as a percentage change from baseline, and others as a simple difference in means. The difference in means has a unit attached to it (e.g. mg/ dL, mmol/ L, etc.), but the percentage change is unitless. There is a way to combine these measures, of course. Simply convert them to a standardized scale (Z-score) and then combine the Z-scores. The question is whether this is a legitimate approach.
I responded that there's plenty of precedent for this, and I think you could find justification by looking in any book about meta-analysis. My library is totally disorganized because of my change in careers, so I can't check my books for a specific page number.
The issue remains, though, about whether combining different outcomes introduces so much heterogeneity that the results just can't be trusted. This is a "gut" call and there is no metric that you can apply to show whether the measures are too different to allow a quantitative pooling. I like to think that apples and oranges can be combined (fruit salad), but sometimes the heterogeneity is so bad that it becomes an "apples and onions" situation. I don't know of any cook who would deliberately mix apples and onions in the same recipe.
Someone wrote me, by the way, with a recipe that uses apples and onions, so I have to take that last comment back.
I talk about heterogeneity a lot in my book, Statistical Evidence in Medical Trials. I start out the chapter on meta-analysis with a New Yorker cartoon. You can view this cartoon by Dana Fradon at the Cartoonbank website. I won't ruin the punchline here, but clearly some numbers should never be combined. By the way, if you regularly use cartoons in your PowerPoint talks, you should pay the author of the cartoon a royalty. Cartoonbank makes it easy to do so. I paid \$150 to include this cartoon in my book and it only costs \$20 to include this cartoon in your PowerPoint talk.
Later in the same chapter of my book, I give a more specific example.
Example: In a systematic review of beta-2 agonists for treating chronic obstructive pulmonary disease (Husereau 2004), researchers identified 12 studies. But the authors could not pool the results because they "found that even commonly measured outcomes, such as FEV1, could not be combined by meta-analysis because of differences in how they were reported. For example, in the six trials comparing salmeterol with placebo, FEV1 was reported as a mean change in percent predicted, a mean change overall, a mean difference between trial arms, no difference (without data), baseline and overall FEV1 (after 24 hrs without medication) and as an 0 to 12 hour area-under-the-curve (FEV1-AUC) function. We were not successful in obtaining more data from study authors. We also had concerns about the meta-analysis of data from trials of parallel and crossover design and differences in spirometry protocols including allowable medications. Therefore, we decided on a best evidence synthesis approach instead."
Long acting beta2 agonists for stable chronic obstructive pulmonary disease with poor reversibility: a systematic review of randomised controlled trials. D. Husereau, V. Shukla, M. Boucher, S. Mensinkai, R. Dales. BMC Pulm Med 2004: 4(1); 7. Full free text is available at www.biomedcentral.com/1471-2466/4/7
Dr. Husureau doesn't get any royalties and isn't expecting any because (bless his soul) he published in an open source journal.
So, yes, you can use Z-scores to combine outcomes measured on different scales, and yes you can find justification for it. Even so, you should still take a slow and careful look at the problem and decide if you are really comfortable with this approach.
3. A simple example of overfitting
A couple of the Internet discussion groups that I participate in have been discussing the concept of overfitting. Overfitting occurs when a model is too complex for a given sample size. I want to show a simple example of the negative consequences of overfitting.
In a previous page discussing segmented regression models, I used a data set showing firearm deaths in Australia per 100,000 people over a fifteen year span (1983 to 1997). The following graph shows a linear regression fit (order 1 polynomial) to the data.
Most of you would stop here and say that there is a roughly linear decline in firearm deaths in Australia over the fifteen year span. Or you might try a simple log transformation of the firearm deaths. If you had data on the exact number of deaths rather than the rate, you might consider a Poisson regression model or some variation of it.
But for the benefit of pedagogy, what would happen if you threw all caution to the wind and fit a ridiculously complex model. Something like a seventh order polynomial. Here's what the fit would look like.
There are some weird things going on here. For example, the fitted value halfway between 1983 and 1984 is actually lower than the observed rates at either 1983 and 1984. This is a symptom of overfitting, the choice of a model that is far too complex for the amount of data that you have. If you continue to add more terms to the polynomial, the results look more and more bizarre. Take a look at the whole series of pictures from linear polynomial to a fourteenth order polynomial at www.pmean.com/08/OverfittingExample.html.
4. Explaining CART models in simple terms
Someone asked about CART models and when you would use them instead of linear or logistic regression.
CART was developed to handle problems with overfitting. This is its primary advantage over stepwise regression. Generally, CART models are considered exploratory rather than confirmatory.
From the perspective of critical appraisal, classification and regression trees (CART) are not too much different from linear and logistic regression. They are an approach to make sense of data where there are multiple predictor variables. They work reasonably well if the data is good quality, but like any statistical procedure, the quality of the analysis is limited by the quality of the data coming in.
A classification tree is used when the outcome variable is categorical and a regression tree is used when the outcome variable is continuous. Both methods rely on a similar approach, known as recursive partitioning.
Generally, this approach is used when there are numerous predictor variables and the researcher desires a simple prediction involving a small number of these predictor variables.
Recursive partitioning divides each predictor variables into discrete groups. The groups are typically required to have a minimum sample size (usually 5), but otherwise are allowed to vary considerably. So if one of the predictor variables is the one minute apgar score, then the possible groups to be considered are
```1 versus 2-10 1-2 versus 3-10 1-3 versus 4-10 . . 1-9 versus 10 ```
For a discrete variable with levels A, B, C and D and no particular order among the categories, the possible groups to be considered are
```A versus BCD AB versus CD AC versus BD AD versus BC B versus ACD . . . ```
A CART model examines all possible partitions among all possible variables and selects the partition that produces the best possible prediction of the outcome variable. Once that partition is selected, each of the two subgroups is examined versus all possible remaining partitions.
The result of a CART model is a tree diagram. I show some examples of these tree diagrams at www.pmean.com/08/ExplainingCart.html.
5. Should you compare a two-sided p-value to 0.025?
Ray, one of my colleagues at Children's Mercy Hospital, asked a question a few weeks before I left that I couldn't answer in time, so let me put the answer here. He was looking at an article that computed a p-value for a two-sided test and wondered if he should compare the p-value to 0.025 instead of 0.05 because it was a two-sided test.
The answer is related to the famous O'Henry story, "The Gift of the Magi". In that story a married couple is in a quandary about what gifts to get each other for Christmas, as money is very tight. The wife sees a beautiful chain for the pocketwatch that the husband treasures. The husband sees a beautiful comb for the wife's lovely long tresses of hair. Neither has enough spare cash to buy such a lavish gift, so they both make a major sacrifice because of their love for each other. The woman cuts off her hair and sells it to a wig maker. The husband sells his beloved watch. When they present each other with their gifts, they realize that their sacrifices to get their gift have made the other person's gift useless.
The p-value is already adjusted for the type of hypothesis used. It is always compared to the traditional alpha level of 0.05. If you also adjust the alpha level, you are cutting off your hair just before you are about to get that beautiful comb. Don't do it, Ray!
If you see a p-value in a published report, you don't have to think about whether it is computed from a one-sided hypothesis or from a two-sided hypothesis. Just compare it to 0.05 (or 0.01 if you are more conservative--0.10 if you are more liberal).
Now you still need to be careful when you are using computer software. Most computer software will assume, unless you tell it otherwise, that you have a two-sided hypothesis. Some software will allow you to specify a one-sided hypothesis, but others will make you do the math yourself. The formula to convert a p-value for a two-sided hypothesis to a p-value for a one-sided hypothesis is quite simple, but I won't show the details here.
You also have to be careful if the author of a report uses a one-sided hypothesis and you prefer a two-sided hypothesis. The adjustment here is easy as well, but I won't include the formulas. Write to me if you want the details.
The p-value is tailored to the particular hypothesis so you never have to adjust the alpha level. If you forget this, you're a bald woman with a beautiful comb.
6. Monthly Mean Article: What is meant by intention to treat analysis? Survey of published randomised controlled trials.
"What is meant by intention to treat analysis? Survey of published randomised controlled trials." Hollis S, Campbell F. British Medical Journal 1999; 319(7211): 670-674. Full free text is available at www.bmj.com/cgi/content/full/319/7211/670. This is an old article, but the confusion about intention to treat remains today, so it is well worth reading. There is ambiguity in how authors describe intention to treat analysis. When there are missing outcomes for some of the patients, the trouble is compounded. Read this article before you state that you used "intention to treat" in your research publication to make sure you know what you're talking about.
7. Monthly Mean Blog: Realizations in Biostatistics by Random John.
I like this blog because the author says nice things about me. Flattery is a very powerful motivator, and if anyone who reads this is willing to add a comment to my testimonials page, I would be forever grateful. More seriously, I love the list of topics that this blog covers: "Biostatistics, clinical trial design, critical thinking about drugs and healthcare, skepticism, the scientific process". Here's a sampling of the blog entries that caught my eye. A November 13 entry notes an outrageous study linking autism rates with rainfall patterns, two entries (October 17, 2008 and another one also on October 17, 2008) talk about getting output from R into Microsoft Word, and another nice pair of articles explain the value of blinding and randomization (May 25, 2008 and May 14, 2008). This blog has lots of links to other very good blogs. URL: realizationsinbiostatistics.blogspot.com
8. Monthly Mean Book: Biostatistics, The Bare Essentials, Geoffrey R. Norman and David L. Streiner
If you want to start to get an understanding of the fundamentals of Biostatistics, this book is a great place to start. It has all the formulas that you need, but does not assume that you know or remember calculus. The coverage is quite good, and the authors stress many pragmatic issues.
This book uses a lot of fictional examples, with an effort to make the examples extremely bizarre. The start of the chapter on analysis of variance, for example, starts out with this fictional scenario.
To further the goal of "Safe Sex for Sinners," you decide to investigate which is the most cost-effective condom. You are rapidly discouraged by the challenge, as a visit to the local pharmacy reveals an overwhelming array of choices. What you really want to do is select a few brands and determine if any difference overall exists among the group means, then try to find out what affects these differences.
The author's philosophy on the use of fictional data is described in the preface.
Most Chapters begin with an example to set the stage. Usually the examples were dreamt up in our fertile imaginations and are, we hope, entertaining. Occasionally we reverted to real world data, simply because sometimes the real world is at least as bizarre as anything imagination could invent. Although many reviews of statistics books praise the users of real examples and castigate others, we are unapologetic in our decision for several reasons: (1) the book is aimed at all types of health professionals and we didn't want to waste your time and ours explaining the intricacies of podiatry for others; (2) the real world is a messy place, and it is difficult, or well nigh impossible, to locate real examples that illustrate the pedagogic points simply; and (3) we happen to believe, and can cite good psychological evidence to back it up, that memorable (read "bizarre") examples are potent allies in learning and remembering concepts.
I generally dislike the use of fictional examples, but it seems to work here. The key thing that these examples provide is a level of light-heartedness that makes the book easy to pick up and hard to put down.
There are several editions, and the most recent addition includes SPSS examples. I am most familiar with the first edition, published in 1998. This is probably the best book for a beginner wanting to learn more on their own about Statistics.
9. Monthly Mean Website: EDF 5481. Methods of Educational Research. Susan Carol Losh.
It seems like just about everybody is putting their course notes up on the web these days. This is one of the better ones I found because it is fairly detailed and it has a range of topics that are not covered as much as they should be on the web. The site offers good definitions for terms like conceptual hypothesis, operational variable, construct validity. There is also some excellent material on pilot studies and survey research. URL: edf5481-01.fa01.fsu.edu/Overview.html
10. Nick News: Nicholas the artist
Until just recently, Nicholas has not taken a great interest in art projects. There was a recent project, though, that inspired him. The students in his classroom were all asked to color a turkey as a special character. Nicholas chose a Spiderman turkey. We brought out his Spiderman t-shirt and figured which parts of the turkey should be red and which should be blue. The spiderweb lines on the red were the finishing touch.
There are a couple more pictures of recent artwork at www.pmean.com/personal/artist.html.
11. Very bad joke: How many IRB members does it take to screw in a light bulb?
I wrote this joke, and you can find it at my old website: www.childrens-mercy.org/stats/plan/irb.asp.
It has been reproduced (without permission and three out of four times without proper attribution, but that's okay) at
How many IRB members does it take to screw in a lightbulb?
As documented in 45 CFR 46.107(a), this review board must consist of five (5) or more members, and at least one of these members must possess a background in Electrical Engineering. In addition, at least one of the members must come from a home without any electricity. Any member of the IRB who owns stock in an electrical utility or who regularly pays bills to an electrical utility should recuse themselves from participation in the review of this research.
If the bulb should burn too brightly, burn too dimly, or flicker, then an adverse event report should be sent to the IRB (21 CFR 312.32). If the light bulb is dropped, then a serious adverse event report should be sent to the FDA by telephone or by facsimile transmission no later than seven (7) calendar days after the sponsor's initial receipt of the information.
If this is a multi-center light bulb trial, then a data and safety monitoring board (DSMB) may be needed (NIH Policy for Data and Safety Monitoring, June 10, 1998, grants.nih.gov/grants/guide/notice-files/not98-084.html, accessed on October 9, 2002). The DSMB should review any adverse event reports and interim results. If the clinical equipoise of the light bulb is lost, then the DSMB should terminate the study and provide all previously recruited light bulbs with the best available light bulb socket.
In order to maintain scientific integrity, the use of a placebo socket may be necessary. The placebo socket should have the same taste, appearance, and smell of a regular socket and the fact that this socket has no electricity should be hidden from the light bulb and from the person screwing in the light bulb. According to the 2000 revision of the Declaration of Helsinki, paragraph 29, the use of placebo sockets is acceptable where no proven prophylactic, diagnostic, or therapeutic socket exists.
A systematic review of all previous research into light bulbs must be presented so that the IRB can determine, per 45 CFR 46.11(a)(2), that the risks to the light bulb are reasonable in relation to anticipated benefits. The IRB should also ensure that the selection of light bulbs is equitable (45 CFR 46.11(a)(3)). If the light bulb has less than 18 watts of power, then additional requirements (45 CFR 46.401 through 409) apply.
The IRB must ensure that an informed consent document be prepared in language that the light bulb understands (45 CFR 46.116). This document should explain the expected duration of the light bulb's participation in the research, any reasonably foreseeable risks, and the extent to which the confidentiality of the light bulb will be maintained. This document should also emphasize that participation is voluntary and the light bulb can withdraw itself from the socket at any time without any penalty or loss of benefits.
12. Tell me what you think.
How did you like this newsletter? I have three short open ended questions that I'd like to ask. It's totally optional on your part. Your responses will be kept anonymous, and will only be used to help improve future versions of this newsletter. I got some very positive feedback from three people last month. Two people cited the article on ANOVA versus regression as being the most helpful. The one suggestion for improvement was to drop the section on Wikipedia. I agree and in the next newsletter I might replace it with a "current events" entry that highlights a recent newspaper article touching on issues in Statistics. some suggested topics for future newsletters are principles for good graphical displays (such as the guidance from Edward Tufte) and important events in the history of Statistics.
What now? | 4,338 | 20,353 | {"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-2021-25 | latest | en | 0.959253 |
https://tellmeanumber.hostcoder.com/568826 | 1,638,035,643,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00545.warc.gz | 648,263,084 | 4,750 | # Question Is 568,826 a prime number?
The number 568,826 is NOT a PRIME number.
#### How to check if the number 568,826 is a prime number
A prime number can be divided, without a remainder, only by itself and by 1. For example, 13 can be divided only by 13 and by 1. In this case, the number 568,826 that you looked for, is NOT a PRIME number, so it devides by 1,2, 284413, 568826, and of course 568,826.
# Question Where is the number 568,826 located in π (PI) decimals?
The number 568,826 is at position 20662 in π decimals.
Search was acomplished in the first 100 milions decimals of PI.
# Question What is the roman representation of number 568,826?
The roman representation of number 568,826 is DLXVMMMDCCCXXVI.
#### Large numbers to roman numbers
3,999 is the largest number you can write in Roman numerals. There is a convencion that you can represent numbers larger than 3,999 in Roman numerals using an overline. Matematically speaking, this means means you are multiplying that Roman numeral by 1,000. For example if you would like to write 70,000 in Roman numerals you would use the Roman numeral LXX. This moves the limit to write roman numerals to 3,999,999.
# Question How many digits are in the number 568,826?
The number 568,826 has 6 digits.
#### How to get the lenght of the number 568,826
To find out the lenght of 568,826 we simply count the digits inside it.
# Question What is the sum of all digits of the number 568,826?
The sum of all digits of number 568,826 is 35.
#### How to calculate the sum of all digits of number 568,826
To calculate the sum of all digits of number 568,826 you will have to sum them all like fallows:
# Question What is the hash of number 568,826?
There is not one, but many hash function. some of the most popular are md5 and sha-1
#### Here are some of the most common cryptographic hashes for the number 568,826
Criptographic function Hash for number 568,826
md5 b665663e694bd0d129ef62412c8c9c52
sha1 672cfbfdc395378364c312d21ee9a3d9d2ecf7d2
sha256 f35a1cd49de603930f06620109833c325aa3e8a976e51cf9ccd6f050e5612954
sha512 3ae59ee47ec463765facbbbbbe53dd619a88bd3c826d9e08aca9e8816819937d38d9d7c904fc4965abec7edc44ca2794b5d8ac7eb601c55d8f75e6ec162df98f
# Question How to write number 568,826 in English text?
In English the number 568,826 is writed as five hundred sixty-eight thousand, eight hundred twenty-six.
#### How to write numbers in words
While writing short numbers using words makes your writing look clean, writing longer numbers as words isn't as useful. On the other hand writing big numbers it's a good practice while you're learning.
Here are some simple tips about when to wright numbers using letters.
Numbers less than ten should always be written in text. On the other hand numbers that are less then 100 and multiple of 10, should also be written using letters not numbers. Example: Number 568,826 should NOT be writed as five hundred sixty-eight thousand, eight hundred twenty-six, in a sentence Big numbers should be written as the numeral followed by the word thousands, million, billions, trillions, etc. If the number is that big it might be a good idea to round up some digits so that your rider remembers it. Example: Number 568,826 could also be writed as 568.8 thousands, in a sentence, since it is considered to be a big number
#### What numbers are before and after 568,826
Previous number is: 568,825
Next number is: 568,827 | 946 | 3,438 | {"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} | 3.921875 | 4 | CC-MAIN-2021-49 | latest | en | 0.871114 |
http://nrich.maths.org/public/leg.php?code=-334&cl=2&cldcmpid=5865 | 1,369,496,009,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705957380/warc/CC-MAIN-20130516120557-00086-ip-10-60-113-184.ec2.internal.warc.gz | 200,784,764 | 9,868 | # Search by Topic
#### Resources tagged with Games similar to First Connect Three:
Filter by: Content type:
Stage:
Challenge level:
### First Connect Three
##### Stage: 2 and 3 Challenge Level:
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
### GOT IT
##### Stage: 2 and 3 Challenge Level:
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
### Olympic Cards
##### Stage: 1 and 2 Challenge Level:
Design your own scoring system and play Trumps with these Olympic Sport cards.
### Sliding Game
##### Stage: 2 Challenge Level:
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
### Nim-7
##### Stage: 2 Challenge Level:
Can you work out how to win this game of Nim? Does it matter if you go first or second?
### Property Chart
##### Stage: 3 Challenge Level:
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
### Online - a Game for Two Players
##### Stage: 3 Challenge Level:
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
### Squayles
##### Stage: 3 Challenge Level:
A game for 2 players. Given an arrangement of matchsticks, players take it is turns to remove a matchstick, along with all of the matchsticks that touch it.
### Jumping Reindeer
##### Stage: 2 Challenge Level:
A game for 1 person to develop stategy and shape and space awareness. 12 counters are placed on a board. Counters are removed one at a time. The aim is to be left with only 1 counter.
### Building Stars
##### Stage: 2 Challenge Level:
An interactive activity for one to experiment with a tricky tessellation
### 100 Percent
##### Stage: 2 Challenge Level:
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
### Gotcha
##### Stage: 2 Challenge Level:
A game for 2 players. This could be played outside with people instead of counters. Try to trap or escape from your opponent.
### Coordinate Cunning
##### Stage: 2 Challenge Level:
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
### Traffic Lights
##### Stage: 2 Challenge Level:
The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line. . . .
### Khun Phaen Escapes to Freedom
##### Stage: 3 Challenge Level:
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
### Conway's Chequerboard Army
##### Stage: 3 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
### Low Go
##### Stage: 2 Challenge Level:
A game for 2 players. Take turns to place a counter so that it occupies one of the lowest possible positions in the grid. The first player to complete a line of 4 wins.
### Diagonal Dodge
##### Stage: 2 and 3 Challenge Level:
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
### Some Games That May Be Nice or Nasty
##### Stage: 2 and 3 Challenge Level:
There are nasty versions of this dice game but we'll start with the nice ones...
### Games from Around the World
##### Stage: 1 and 2 Challenge Level:
Here are a collection of games from around the world to try during the holidays or the last few weeks of term.
### Domino Magic Rectangle
##### Stage: 2 Challenge Level:
An ordinary set of dominoes can be laid out as a 7 by 4 magic rectangle in which all the spots in all the columns add to 24, while those in the rows add to 42. Try it! Now try the magic square...
### SHOO
##### Stage: 2 Challenge Level:
A complicated game played on a 9 x 9 checkered grid.
##### Stage: 2 Challenge Level:
This is a game for 2 players. Each player has 4 counters each, and wins by blocking their opponent's counters. A good follow-on from two stones.
### Tricky Track
##### Stage: 2 Challenge Level:
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?
### Train
##### Stage: 2 Challenge Level:
A train building game for 2 players.
##### Stage: 3 Challenge Level:
A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .
### Patience
##### Stage: 3 Challenge Level:
A simple game of patience which often comes out. Can you explain why?
### Ratio Pairs 2
##### Stage: 2 Challenge Level:
A card pairing game involving knowledge of simple ratio.
### Lambs and Tigers
##### Stage: 3 Challenge Level:
Investigations based on an Indian game.
### Noughts and Crosses
##### Stage: 2 Challenge Level:
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
### Four Go
##### Stage: 2 Challenge Level:
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
### Twinkle Twinkle
##### Stage: 2 Challenge Level:
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
### Part the Piles
##### Stage: 2 Challenge Level:
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
### Dominoes
##### Stage: 2 Challenge Level:
Everthing you have always wanted to do with dominoes! Some of these games are good for practising your mental calculation skills, and some are good for your reasoning skills.
### Shapely Pairs
##### Stage: 3 Challenge Level:
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
### Making Maths: Snake Pits
##### Stage: 1, 2 and 3 Challenge Level:
A game to make and play based on the number line.
### Seasonal Twin Sudokus
##### Stage: 3 and 4 Challenge Level:
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
### Learning Mathematics Through Games Series: 4. from Strategy Games
##### Stage: 1, 2 and 3
Basic strategy games are particularly suitable as starting points for investigations. Players instinctively try to discover a winning strategy, and usually the best way to do this is to analyse. . . .
### Estimating Angles
##### Stage: 2 and 3 Challenge Level:
How good are you at estimating angles?
### Down to Nothing
##### Stage: 2 Challenge Level:
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
### Snail Trails
##### Stage: 3 Challenge Level:
This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in. . . .
### Counter Roundup
##### Stage: 2 Challenge Level:
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
### Fractions and Coins Game
##### Stage: 2 Challenge Level:
Work out the fractions to match the cards with the same amount of money.
### Wild Jack
##### Stage: 2 Challenge Level:
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
### Sliding Puzzle
##### Stage: 1, 2, 3 and 4 Challenge Level:
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
### Odds and Threes
##### Stage: 2 Challenge Level:
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
### Making Maths: Happy Families
##### Stage: 1 and 2 Challenge Level:
Here is a version of the game 'Happy Families' for you to make and play.
### Twin Corresponding Sudokus II
##### Stage: 3 and 4 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
### The Remainders Game
##### Stage: 2 and 3 Challenge Level:
A game that tests your understanding of remainders.
### Twin Corresponding Sudoku III
##### Stage: 3 and 4 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections. | 2,230 | 9,389 | {"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} | 3.1875 | 3 | CC-MAIN-2013-20 | longest | en | 0.904737 |
https://wizardofodds.com/gambling/dalembert-betting-system/ | 1,726,131,612,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651440.11/warc/CC-MAIN-20240912074814-20240912104814-00653.warc.gz | 587,743,134 | 12,082 | # D'Alembert Betting System
## Introduction
The d'Alembert is a popular and classic betting system. Like most betting systems, it usually results in a small win, at the cost of huge losses sometimes. Like all betting systems, not only can't it overcome the house edge, it can't even dent it.
Like the Martingale, Labouchere and Fibonacci betting, the d'Alembert has the player chasing losses with larger bets. However, it is not as aggressive as those other progressive betting systems, resulting in more time at the table and less volatility. It is also at a cost of a lower probability of overall goal success.
## Rules
The only thing that everybody seems to agree on about the d'Alembert is that the player increases his bet by a unit after a loss and decreases by a unit after a win. Other sources generally don't address the initial bet and winning or losing benchmarks. For purposes of my analysis, I start the player with a bet of one unit with a goal of winning one unit. Here is putting the whole system more formally.
1. The player shall define his winning goal and bankroll size.
2. The player's "unit size" shall be equal to his winning goal.
3. The player starts with a one-unit bet.
4. If the player ties, then he repeats the same bet.
5. Otherwise, if the last bet results is a win and the player has achieved his winning goal, then he walks away happy.
6. Otherwise, after a win, if the bet size was one unit, he keeps it the same. Otherwise, he decreases his bet size by one unit.*
7. Otherwise, after a loss, the player increases his bet size by one unit.**
8. The player bets.
9. Go back to rule 4, until the player either achieves his winning goal or loses his entire bankroll.
*: If such a bet would cause the player to overshoot his winning goal if he wins, then drop the bet size to whatever would result in achieving exactly the winning goal the next bet.
**: If the player does not have enough money to make the next bet, then drop the bet size to whatever money the player has left.
An interesting facet of the d'Alembert is it doesn't matter in what order wins and losses are, like flat betting. The only thing that matters in terms of session results is the number of wins and losses. The d'Alembert can show a profit even when losses outnumber wins, as long as the disparity isn't too much. The following table shows the net win according to various totals of wins and losses. For example, the player can have 22 wins and 28 losses and still show a profit of one unit.
### Net Win by Total Wins and Losses
Wins Losses Net Win
2 3 1
3 4 2
4 6 1
5 7 2
6 8 3
7 10 1
8 11 2
9 12 3
10 13 4
11 15 1
12 16 2
13 17 3
14 18 4
15 19 5
16 21 1
17 22 2
18 23 3
19 24 4
20 25 5
21 26 6
22 28 1
23 29 2
24 30 3
25 31 4
26 32 5
27 33 6
28 34 7
29 36 1
30 37 2
31 38 3
32 39 4
33 40 5
34 41 6
35 42 7
36 43 8
37 45 1
38 46 2
39 47 3
40 48 4
41 49 5
42 50 6
43 51 7
44 52 8
45 53 9
46 55 1
47 56 2
48 57 3
49 58 4
50 59 5
In situations where the number of losses is equal or greater to the number of wins, the general formula for the net win is W - D*(D+1)/2, where:
W = Number of wins
D = Difference between wins and losses. In other words, losses minus wins.
In the example above of 22 wins and 28 losses, the net win is 22 - 6*7/2 = 21.
Despite being able to win in moderately losing sessions, it is at a cost of small wins most of the time and huge wins in extremely cold sessions that wipe out those small wins over the long run.
## Simulation Results
To show what to expect from using the d'Alembert, I wrote a simulation that followed the rules above, based on various bets and games. The simulation used a Mersenne Twister random number generator. For each simulation, the initial bet and winning goal were both one unit. I tested the simulation on the following bankrolls: 10, 25, 50, 100, and 250 units.
The first simulation is based on betting the Player bet in baccarat. The simulation size is over 73 billion sessions. As a reminder, the theoretical house edge on the Player bet is 1.235%.
### Baccarat Simulation — Player Bet
Statistic 10 Units 25 Units 50 Units 100 Units 250 Units
Probability winning goal reached 90.36% 95.74% 97.73% 98.78% 99.45%
Average number of bets 2.422 3.297 3.719 4.169 4.837
Average units bet 4.857 8.727 12.670 18.456 30.939
Expected win per session -0.060 -0.108 -0.157 -0.228 -0.382
Ratio money lost to Money bet 1.234% 1.236% 1.235% 1.235% 1.235%
The first simulation is based on betting the pass bet in craps. The simulation size is over 65 billion sessions. As a reminder, the theoretical house edge on the pass bet is 1.41%.
### Craps Simulation — Pass Bet
Statistic 10 Units 25 Units 50 Units 100 Units 250 Units
Probality winning goal reached 90.34% 95.72% 97.72% 98.78% 99.44%
Average number bet 2.423 3.300 3.724 4.176 4.850
Average total bet 4.399 7.908 11.489 16.752 28.134
Expected win per session -0.062 -0.112 -0.162 -0.237 -0.398
Ratio money lost to Money bet 1.414% 1.414% 1.414% 1.414% 1.414%
The next simulation is based on the don't pass bet in craps. The simulation size was over 76 billion sessions. As a reminder, the house edge on the don't pass bet is 1.364%.
### Craps Simulation — Don't Pass Bet
Statistic 10 Units 25 Units 50 Units 100 Units 250 Units
Probality winning goal reached 90.35% 95.73% 97.72% 98.78% 99.44%
Average number bet 2.423 3.299 3.723 4.175 4.847
Average total bet 4.523 8.131 11.811 17.218 28.903
Expected win per session -0.062 -0.111 -0.161 -0.235 -0.394
Ratio money lost to Money bet 1.364% 1.364% 1.364% 1.365% 1.363%
The next simulation is based on any even money bet in single-zero roulette. The simulation size was over 25 billion sessions. As a reminder, the theoretical house edge is 1/37 = 2.7027%.
### Roulette Simulation — Single Zero
Statistic 10 Units 25 Units 50 Units 100 Units 250 Units
Probality winning goal reached 89.81% 95.30% 97.40% 98.52% 99.26%
Average number bet 2.456 3.381 3.851 4.371 5.190
Average total bet 4.485 8.200 12.125 18.119 31.920
Expected win per session -0.121 -0.222 -0.328 -0.490 -0.863
Ratio money lost to Money bet 2.702% 2.703% 2.702% 2.703% 2.702%
The next simulation is based on any even money bet in double-zero roulette. The simulation size was over 25 billion sessions. As a reminder, the theoretical house edge is 2/38 = 5.2632%.
### Roulette Simulation — Double Zero
Statistic 10 Units 25 Units 50 Units 100 Units 250 Units
Probality winning goal reached 88.68% 94.37% 96.65% 97.91% 98.75%
Average number bet 2.520 3.544 4.112 4.782 5.942
Average total bet 4.660 8.800 13.463 21.083 40.571
Expected win per session -0.245 -0.463 -0.708 -1.109 -2.134
Ratio money lost to Money bet 5.263% 5.263% 5.263% 5.263% 5.261% | 2,112 | 6,703 | {"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} | 3.140625 | 3 | CC-MAIN-2024-38 | latest | en | 0.974957 |
https://forum.whadda.com/t/display-runs-thats-all/14803 | 1,607,016,309,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141729522.82/warc/CC-MAIN-20201203155433-20201203185433-00600.warc.gz | 274,250,452 | 5,350 | # Display Runs - that's all
Hello Velleman Team,
today i have build your Oszilloskop EDU 08 and now i need some help.
I send you an Picture, the Display lights up so it works but there is no signal or anything else.
I hope you have some ideas for me.
Kind Regards
Khargaraa
As a first test you may check the voltages on SK1 connector on the top board.
viewtopic.php?f=69&t=18057
Done!
Top row from left to right 3.33, 0, 0, 0, 0, 0, 3.32, 0, 0.55
Bottom row 0, 3.33, 0, 0, 0, 0, 0, 3.32, 0
These are my results.
The voltages seem to be OK.
The problem may be on the display board.
Please check all the display soldering joints for possible short or open.
You can also check the voltages on the points marked A-M in this picture:
A=9.2V
B=8.2V
C=7.2V
D=2.0V
E=1.0V
F=1.6V
G=7.2V
H=1.6V
I=4.6V
J=9.8V
K=1.6V
L=3.3V
M=11.2V
It Runs!
Thank you for the hint!
I’m glad to see you got it sorted out!
What solved it? I have the same problem: backlight from LCD is on, but no data on LCD. Voltages on SK1 are correct but voltages on the pins A thru M are way too low…
I bought a EDU08. After putting it together, only the backlight works, no data is shown. I bought another EDU08; maybe I made an error with soldering or overheated a part. Same problem. Now I have two EDU08’s which don’t work. The pins A thru M indicate voltages that are much lower than expected.
Can you help me or point me in the right direction?
A=2,7
B=2,4
C=2,2
D=0,7
E=0,5
F=2,4
G=2,4
H=1,6
I=2,4
J=2,6
K=1,6
L=3,3
M=2,7
The voltage on points F, G and I seems to be equal.
This may indicate a short circuit between these pins.
Points F, G and I are connected to adjacent pins of the display.
Possible solder bridge may be between the display pins…
Yep, you were right! Solder bridge on both units. I got them both working, thanks!
Glad to see the issue is solved. | 628 | 1,847 | {"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-2020-50 | latest | en | 0.898679 |
http://physics.stackexchange.com/questions/tagged/spin-statistics?page=2&sort=newest&pagesize=15 | 1,462,451,765,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860127407.71/warc/CC-MAIN-20160428161527-00065-ip-10-239-7-51.ec2.internal.warc.gz | 222,797,943 | 20,804 | # Tagged Questions
The tag has no usage guidance.
429 views
### Explanation of Superconductivity
I can't get a definitive explanation of why superconductivity happens and I am getting mixed explanations from my textbooks. I will tell you what I know and hopefully you can correct any ...
60 views
### Spin-Statistics Theorem - Proof [duplicate]
Is this proof of spin-statistics theorem correct? http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf This proof is probably a simplified version of Weinberg's proof. What is ...
354 views
### Proof of Spin-statistics theorem [closed]
Is this proof of spin-statistics theorem correct? http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf This proof is probably a simplified version of Weinberg's proof. What is ...
609 views
### Ising spin vs Pauli spin matrices
Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
811 views
### What goes wrong when one tries to quantize a scalar field with Fermi statistics?
At the end of section 9 on page 49 of Dirac's 1966 "Lectures on Quantum Field Theory" he says that if we quantize a real scalar field according to Fermi statistics [i.e., if we impose Canonical ...
554 views
### What is the reason why anyons escape spin-statistic theorem?
I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem. I've read somewhere (the wikipedia page is ...
321 views
### NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
278 views
### Is conservation of statistics logically independent of spin?
If the number of fermions is $n$, we expect the quantity $(-1)^n$ to be conserved, i.e., $n$ never changes between even and odd. This is known as conservation of statistics. In the normal context of ...
138 views
### Ising Hamiltonian for relativistic particles
An Ising system is described by the simple Hamiltonian: $$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$ Here the $x_i$ are spins (+1 or -1 in units ...
148 views
### Does the Higgs mechanism address the spin statistics problem?
Since the Higgs mechanism is so intimately tied to binding together massless chiral fermions, does it happen to have anything to say about the spin statistics issue? I'm actually assuming the answer ...
80 views
### Question about the derivation of an equation in full replica symmetry breaking solution
Using replica method and saddle point method, the free energy of a magnetic system can be expressed as -\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
1k views
### Why is the majorana particle a fermion?
My knowledge of quantum mechanics is rather limited, but what I always understood was that Bosons have integer spins and Fermions have half-integer spins. My question is very simple: the Majorana ...
311 views
### Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?
Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of ...
3k views
### Partition function of bosons vs fermions
I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively. What's the difference between ...
303 views
### Fermion Field of Standard Model
Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
491 views
### Why is fractional statistics and non-Abelian common for fractional charges?
Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
10k views
### What are distinguishable and indistinguishable particles in statistical mechanics?
What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
387 views
### Why Pauli exclusion instead of electrons canceling out?
To quote Wikipedia, The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state ...
227 views
### Does there exist a nonrelativistic physical system in which the effective long-distance fields violate spin/statistics?
The nonrelativistic Schrodinger field allows spin independent of statistics, so that you can imagine a nonrelativistic Schrodinger scalar field with Fermionic statistics, or a Schrodinger spinor field ...
482 views
### Spin-Statistics Theorem (SST)
Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
356 views
### Irrelevance of parastatistics for space dimension > 2
Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal ...
346 views
### Occam's razor on spin statistics theorem?
Highly related to A reading list to build up to the spin statistics theorem I see 2 parts to the spin statistics theorem: (spin $n$ or $n+\frac{1}{2}$) step 1 given that a spin is integral or ...
853 views
### Time reversal symmetry and T^2 = -1
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
540 views
### Time reversal symmetry and T^2 = -1 [duplicate]
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
1k views
### Why are anticommutators needed in quantization of Dirac fields?
Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
408 views
### Can the CPT theorem be valid if Lorentz invariance is only spontaneously broken?
Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are ...
937 views
### A reading list to build up to the spin statistics theorem
Wikipedia's article on the spin-statistics theorem sums it up thusly: In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
422 views
### Example of a wavefunction that cannot be represented by a single Slater determinant
I know that in general, interacting fermions cannot necessarily be described by a single Slater determinant. Can anyone provide a simple example of a state that has no such representation? | 1,752 | 7,441 | {"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} | 2.796875 | 3 | CC-MAIN-2016-18 | longest | en | 0.86757 |
https://www.crayolateachers.ca/lesson/number-spinner-shape-colour-space/ | 1,590,732,343,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347402457.55/warc/CC-MAIN-20200529054758-20200529084758-00051.warc.gz | 678,507,897 | 11,753 | # NUMBER SPINNER – Shape, Colour, Space
Students divide a square into 8 parts, colour the parts, cut out numbers and glue them in the spaces to create a number spinner, and then use it to practice number recognition and counting.
40 Minutes
Language Arts
Mathematics
Visual Arts
#### Vocabulary
colour number numeral shape space
#### Materials
Rulers Plastic Spinners Bristol Board - 15.3 cm x 15.3 cm (6" x 6") Crayola Markers Crayola Scissors Crayola Glue Sticks
## Steps
### Step One
1. Connect the dots to divide the square into 8 parts.
- Hold the ruler firmly with one hand.
- Draw a line along the edge of the ruler with your other hand.
### Step Two
1. Attach the spinner.
2. Use a marker to colour the spaces.
### Step Three
1. Cut out each number from 1 to 8. (Downloads - Numbers_1-8.pdf)
### Step Four
1. Glue a number in each space.
### Step Five
1. Take turns using the spinner to play a counting game with a partner. (Downloads - NumbersDots.pdf)
- spin to get a number
- choose the box that shows how many dots that is
- count the dots
2. Make up other games you can play using the number spinner.
## Learning Goals
Students will be able to:
• divide a square into 8 parts;
• create a colourful number spinner;
• match numerals to the correct number of objects;
• demonstrate technical accomplishment and creativity.
## Extensions
Have students:
• create their own number games that make use of their spinners, such as, games that include adding, subtracting and counting in different ways;
• test their games by playing them with peers;
• share their games with others.
## Prepare
1. Prior to this lesson have children gather and sort items and place them in different containers.
2. Make a math centre with number cards and the sorted materials.
Provide time for students to practice making sets of numbers of things from the sorted materials.
- Have them choose a number card, and make a set to match it and then draw the set, or take a photo with a device.
- Display the drawings and photos and invite students to talk about them amongst themselves.
3. Gather, and make available, books about counting and numbers, for example, 1-2-3 Peas, by Keith Baker; Ten Apples Up On Top!; by Dr. Seuss; Zero, by Kathryn Otoshi; One, by Kathryn Otoshi; Two, by Kathryn Otoshi; Doggy Kisses 123, by Todd Parr.
4. Prepare the Bristol board - cut 15.3 cm squares - enough for each student to have one; mark the corners and mid points on all 4 sides of the Bristol board; purchase spinners.
5. Create a sample spinner that is not coloured but has numbers on it.
6. Print the numbers 1-8 sheets - enough for each student to have one. (Downloads - Numbers_1-8.pdf)
7. Print the number dots sheets - enough for students to share. (Downloads - NumbersDots.pdf)
8. You may want to print the number squares. These can be used with the spinners for adding to the spinner number. (Downloads - NumberSquares.pdf)
## Introduction
- Demonstrate how to spin a number.
- Ask a student to spin a number and then count out that many objects from the basket placing them on the carpet and touching each item as they count.
- Repeat for several more sets.
2. Talk about how much fun it is to count things.
3. Talk about how much fun it is to use the spinner.
4. Introduce the challenge.
## Activities
### The Challenge
1. Divide a square into 8 parts.
2. Create a colourful number spinner.
3. Match numerals to the correct number of objects.
4. Demonstrate technical accomplishment and creativity.
### The Process
1. Ensure that students understand the challenge.
2. Establish success criteria with your students, for example,
I know I am successful when I:
- use my own ideas to make my spinner
- divide the square into 8 parts
- colour each space
- cut out numbers from 1 - 8
- glue the numbers in different spaces
- match the numerals to the correct number of objects
- keep my spinner in good condition
3. Demonstrate how to hold the ruler in place and draw a line.
4. Guide students through the steps outlined in the lesson plan.
5. Observe students as they work.
6. Provide individual assistance and encouragement.
## Sharing
1. Gather students to view and discuss their spinners. Ask students to share:
What they learned about making a spinner.
- What they learned about drawing lines with a ruler.
- What they like best about using their spinners.
- What else they can do with their spinners.
2. Encourage students to find interesting ways to use their spinners.
## Assessment
1. Observe students as they work – thoughtful focus, discriminating, seeking more information, elaborating, experimenting.
2. Observe students as they discuss their spinners – speaks with a clear voice, looks at audience while speaking, holds spinner to the side, provides accurate information, answers questions from the audience effectively.
3. Observe students as they listen – looks at presenter, asks effective questions. | 1,164 | 4,936 | {"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} | 4.34375 | 4 | CC-MAIN-2020-24 | longest | en | 0.855995 |
https://scribesoftimbuktu.com/solve-for-p-208-13p/ | 1,670,320,962,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711077.50/warc/CC-MAIN-20221206092907-20221206122907-00542.warc.gz | 533,770,934 | 14,219 | Solve for p 208=-13p
208=-13p
Rewrite the equation as -13p=208.
-13p=208
Divide each term by -13 and simplify.
Divide each term in -13p=208 by -13.
-13p-13=208-13
Cancel the common factor of -13.
Cancel the common factor.
-13p-13=208-13
Divide p by 1.
p=208-13
p=208-13
Divide 208 by -13.
p=-16
p=-16
Solve for p 208=-13p
Solving MATH problems
We can solve all math problems. Get help on the web or with our math app
Scroll to top | 164 | 434 | {"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} | 3.515625 | 4 | CC-MAIN-2022-49 | latest | en | 0.8133 |
http://www.instructables.com/id/How-to-Multiply-Like-Chinese-the-easy-way-Fast-/step2/First-lesson-22x22/ | 1,490,592,451,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218189403.13/warc/CC-MAIN-20170322212949-00194-ip-10-233-31-227.ec2.internal.warc.gz | 555,202,076 | 20,036 | ## Step 2: First Lesson: 22x22
Here we see just four crossed lines that probably wont mean much to you, but thats the harder thing, the lines! (It looks kinda easy hah)
Heres how its done:
Second: draw the lines according to the numbers in the multiplication. (see 2nd picture for explanation)
Third: Divide the lines in sectors and sum the points in each sector, then sum each sector's numbers to get the answer. (see 3rd picture for explanatin)
<br> Just stumbled across this instructable, tho a bit puzzling, helped me understand how a abacus works... there's a video on youtube which made it a bit clearer for me.<br> <br> 1. <em><strong>Each line</strong></em> stands for the <em><strong>numbers</strong></em> in the problem.<br> 2. Starting from the<strong> left</strong> the first number is <em><strong>5</strong></em>. Now <em><strong>draw FIVE LINES</strong></em> from <em><strong>2 o'clock to 8 o'clock</strong></em><br> 3. The next number is<em><strong> 3</strong></em> - so <em><strong>draw THREE LINES</strong></em> after leaving a <em><strong>space</strong></em> in the same direction<br> 4. the next part of the equation is<em><strong> 2 4 1.</strong></em> <em><strong>Draw TWO lines</strong></em> + <strong>gap</strong> + <em><strong>FOUR lines</strong></em> + <strong>gap</strong> + <em><strong>ONE line</strong></em> standing for each number at right angles in the other direction. <em><strong>(11 o'clock to 5 o'clock)</strong></em><br> <br> (Making sure to begin from the <em><strong>left bottom corner</strong></em> - seems to be a<em><strong> left to right method</strong></em>)<br> <br> 5. The totals<em><strong> 10, 26, 17, 3 </strong></em>are figured out by <em><strong>placing a DOT</strong></em> at each<em><strong> intersecting line</strong></em> of the<em><strong> grid </strong></em>you've just drawn.<br> <br> Group each group of dots by the corners of the grid. ie north east west south (<em><strong>NB </strong></em>Emihack has <em><strong>drawn an orange line</strong></em> grouping each intersection.)<br> <br> Now <em><strong>add up those dots</strong></em> for each corner group. (That's where <em><strong>10, 26, 17 and 3</strong></em> comes from)<br> <br> Next add up <em><strong>10, 26, 17 and 3</strong></em> keeping them in their columns of<em><strong> 1000's, 100's, 10's and 1's</strong></em> - just like abacus.<br> <br> I guess this method's pretty cool since one needn't memorise the time table and stick to adding which is a lot easier to calculate. Is it faster than the usual way? Definitely!<br>
@paperrhino<br><br>I think you're overthinking the process of how this works too much. This is almost identical to how you would multiply by hand, only this method saves the mental work of remembering the multiplication tables and makes it easier because you only have to count intersections. <br><br>For example, say you have the 22x22 example in step 2. When you're multiplying by hand, you would first take the 2 and multiply it by 22. Thus we have 44. This means we have 4 tens and 4 ones, analogous to 4 intersections on the very right column and 4 tens in the middle column. <br><br>Next you take the second 2 and multiply it by 22. The second two is in the tens place, so it's really doing 20 x 22 (When doing this by hand, this is basically the "shifting over" of the product of 2x22). Continuing our calculations, 20 x 22 = 440, so you would have 4 tens and 4 hundreds and 0 ones added by the second 2. analogous to the bottom 4 intersections in the middle column and the 4 intersections on the very left column.<br><br>Total the results, so that 4 hundreds, 8 tens (4 tens + 4 tens) and 4 ones (4 ones+ 0 ones). That gives us the answer of 484.<br><br>Hope this helps in understanding how this works.
wtf ? where the 10 come from ? why its divided like that ? what about the 26 and 17 ?, and the 3 ? I mean the 2 x 2 was simple and I though I got it, by looking at the 22 x 22 I think I still got it, but now I'm lost. You need to explain more
I agree that the explanation is inadequate for getting from the lines to the answer. I played around with it some and I believe I have figured out how it works. The square represents the intersections between the digits of the first number with the second number (e.g. in the above the first column is made up of the intersection of the 5 from the first number and the 2 from the second number). Think of each set of lines as a single unit. The square is broken up into columns from left to right. The first column will consist of the just the corner. In the example above, that is the intersection between the lines from 5 from the first number and the lines for 2 from the other. The next column will consist of the next set of intersections you come across going from left to right. Make sure to include no more then one intersection on the lines representing a given number per column. In other words, the intersection between lines from a given digit will only appear once per column. I have not done the proof, but I believe you will always have (1 - (number of digits in first number + number of digits in second number)) columns. In the example above, the first number has two digits and the second has three to there should be (1 - (2 + 3)) = 4 columns, which it indeed does have. Thus, to check yourself make sure you have the correct number of columns and make sure to include the intersection between a digit's lines only once per column. The next trick which does not have adequate explanation is to treat the sums of the intersections as two digit numbers with a leading zero if the number is less than 10. The first digit of the sum lines up with the last digit from the number above it. That makes the sums from above be: 10 26 17 03 _____ 12773
Sorry for my bad explanations, im not really good at that. But i think that your explanation is really good an would like to include it on my instructable, i just need to ask you if you give me the permission?
First and last sectros have 1 set of crossed lines, seconth and penultimate sectors have 2 sets of crossed lines,ett. etc. tell me if u still dont get it.
wow, honestly this not back to school its flash back to how stupid my math teachers have been over the years. this is so simple and easy. im 21 and i've almost aways been bad in math and failed i studied so hard never went out just so i could pass school. this would have saved me so much time. another really good thing for math is juggling, if you guys like math try it, i'm a professional circus artist and juggling is my maine discipline and it really works your brain. my good friend is her degree on how juggling can make your brain think and grow due to the eye cordination that is the basis to thinking, exp wen you don't know the answer to a question you use looking around to different points to help your brain think. its really cool. thanks for the instructables ill go do some math equations
<p>very nice</p>
<p>Play games to learn Chinese is a very good way, but you need to play the game before, I suggest you learn simple Chinese, it is easy to learn simple Chinese,you can sign-up with any of the online courses like <a href="http://www.hanbridgemandarin.com/course/chinese-language-course" rel="nofollow">http://www.hanbridgemandarin.com/course/chinese-language-course</a> , it provides one-to-one Chinese teaching service on the internet to students, the teachers are from China. But some are free, but some change a minimal amount. As long as you dedicate time to practice, an online course is as good as a classroom one. The community always helps.The best way to learn or test is to learn with an intention to solve a problem.</p>
Suppose it is 76*98<br>Now first multiply 7*9then 6*9&8*7(cross multiplication) and finally 6*8 and add<br>This seems confusing at first but if u get to know it will same much time as adding is easier than multiplying
Suppose it is 76*98<br>Now first multiply 7*9then 6*9&8*7(cross multiplication) and finally 6*8 and add<br>This seems confusing at first but if u get to know it will same much time as adding is easier than multiplying
Ok nice one but can be simplifie
<p>'scuse me but this isn't making much sense - the pictures are unexplanitory, and the text at the bottom doesn't help</p>
<p>I've figured it out - only works with most mathmatical multiplications - some don't work </p>
<p>i can any one explain how do if we use more then 3digits ?</p><p>like if i need to multiply 1234*5674</p>
<p>how many lines do you suposd know to put</p>
<p>if you want to learn Chanies then join us its free course. we provide you our best quality.our teachers are highly Qualified they teach you in this way you can learn fast.</p><p>http://preply.com/en/chinese-by-skype</p>
<p>I'll take the hit, and say that my brain has been hard-wired the Western way, but wouldn't take less time, just to line it up and multiply? Surely if you used flash cards as a child, this problem would take less time to figure out the Western way than it would just drawing out the lines. </p>
<p>Watch this - it'll explain everything:</p><p>https://www.facebook.com/video.php?v=817396358300020</p>
<p>Wow, this is an amazing method. It is a lot more fun than basic long multiplication.</p><p>Here are some additional problems for people to practice with: <a href="http://stemsheets.com/math/multiplication-worksheet-horizontal" rel="nofollow">Practice Worksheet</a></p>
Hey im trying to figure this out as i am pretty bad at multiplicating so whe you got the ten did you times it by the two separate lines in that same sector ....explain to me like you would a little kid :)
<p>This video might be better..... Better explanations, in my opinion, and showing step by step. It might help to actually see it done. </p><p>http://sfglobe.com/?id=14460&src=share_fb_new_14460</p>
<p>the Method of solving is good for two digits</p><p>but how about for three?</p>
<p>Yes. Try a different explanation instead though..... I found a video, then I found this through it (recommended automatically). I would never understand the explanation on this page, had I not watched the other person explain first. And yes, it does go into three digits too. </p><p>http://sfglobe.com/?id=14460&src=share_fb_new_14460</p>
<p>https://itunes.apple.com/us/app/learn-to-multiply!/id903790390?ls=1&mt=8</p>
<p>Hi,</p><p>Thanks for sharing this awesome trick. But i can't get answer for 23x32 by using this method. www.classiblogger.com</p>
<p>holy crap, that's fast multiplication! you can even do it in your head!</p>
Hi Everyone, <br> Personally I don't think this method is any easier as it leaves you counting every intersection. For instance the product 99x99 has nine intersections for each of the 4 place values. The standard algorithm on the other hand reduces this product into 4 partial sums, all of which are easily calculated by single digit multiplication. Of course everyone is entitled to their own opinion. <br> Now, the reason this works is for the same reason the standard algorithm works which is the place value process. The diagonals, from lower left to upper right, each represent a specific place value so 1's, 10's, 100's, etc. So this is why we can simply count them and record the sums appropriately. <br> If anyone wants a more detailed explanation just let me know as I know this one was quick and dirty.
Errr.. I think tommiesmee is trying to tell you that 53x124 = 6,572
tommiesmee transcribed the numbers incorrectly: he should have written 241 rather than 124.
great instructable, but you punctuation mark should be a dot. right now i was like 'realy? do you think 53X124 equals 12,773?'. i'm gonna vote for you anyways... if i find out how :)
Er, no. emihackr's punctuation should be a comma as it is a "thousands separator": unless you're proposing that 53 x 124 = 12.773 (i.e. just over a dozen). In any case emihackr wrote 53 x <strong>241</strong> in Step 3, not 53 x <strong>124</strong>; this only equals 6,572.<br> <br> Your comment has the same tone as someone saying: "Really (sic), tommiesmee? Do you think that no capitals, misspellings, and lower-case first-person-pronouns equals proper English?" Compare it with something like this:<br> <em><strong>G</strong>reat <strong>I</strong>nstructable, but you<strong>r</strong> punctuation mark should be a dot. <strong>R</strong>ight now <strong>I</strong> was like, <strong>"R</strong>eally? <strong>D</strong>o you think 53<strong> X </strong>124 equals 12,773?<strong>"</strong>. <strong>I</strong>'m <strong>going to</strong> vote for you anywa<strong>y ...</strong> if <strong>I</strong> find out how :)<strong>. </strong></em><br> Or better still:<br> <em>Great Instructable, but your punctuation mark should be a dot. 53 X 241 equals 12.773 rather than 12,773. I'm going to vote for you anyway ... if I find out how :).</em><br> <br> Instructable's Authoring Tips recommends: "Check all copy for proper language, spelling, grammar, and capitalization where needed." (Which, if I may be constructive, emihackr, you need to do with your Instructable...)
sorry and thanks
you're welcome, ow and one question: how about 5,4 X 3?? =D i'm just kidding, but could anyone explain me how i'm supposed to vote? instructables has some weird contest customs i believe.
there will be a period of time when you can vote
wow, It´s a funny way to make kids like maths!! <br>
This is actually an abacus implemented on paper. We don't teach this for the same reason we don't teach people how to use an abacus. It's more important for people to learn the math than how to operate a device.
I disagree. We don't teach the abacus because Americans dislike learning from other cultures. "It would be beneath us to use something from China to teach our children."<br><br>And, if we taught the abacus early on, you would eventually not need the device, and children would learn how to do mental math fairly easy.<br><br>I teach Algebra 1 and Geometry in High School, and I can't get my kids to understand abstract math, because they get hung up on simple multiplication.<br>If they had this skill, or something similar, we could all move on with our lives and actually start to learn something.
Your are kidding, right? Ever since the start of the Age of Exploration, Western culture in general and America in particular has been way, way, way more ready to study, learn from and borrow from other cultures.<br> <br> By contrast, even though Western learning and technology were freely available to anyone over the centuries, almost all the other major cultures arrogantly rejected Western science, technology and cultural elements. Many continue to do so.<br> <br> The Chinese, in particular, were violently xenophobic and utterly contemptuous of anything non-Chinese. The Manchu dynasty went to bizarre lengths to suppress Western learning and the adoption of Western technology. The Japanese initially adopted a similar attitude but once they were humiliated by a British/French flotilla, they became obsessed with learning and copying everything possible. As a result, Japan is today a wealthy nation.<br> <br> The reason that your students can't perform basic multiplication is because ever since the 70s, the education establishment has devalued rote learning of fundamentals. They got this idea that calculator could replace just having the value of 7x6 stuck in memory.<br> <br> Education today is centered around avoiding accountability by deemphasizing any skill that can be easily measured. It's easy to measure whether students know their times tables so its easy to hold educators accountable if the children don't know them. To avoid that, educators develop convoluted theories to explain why children don't need to know their times tables.<br> <br> In any case, Westerns used to uses abaci in the form of counting tables and similar devices (as well as techniques such as casting out nines.) The use of such tools in schools was traditional frowned on because it became clear that students learned just how to carry out the algorithm and not how all the math fit together. Richard Feynman talked about running into an abaci salesman in Brazil and realizing that the guy had absolutely no mathematical intuition at all. <br> <br> We have the same problem today with calculators where students can't tell that an answer that is a couple of orders of magnitude off is incorrect. <br> <br> <br>
dude just make a video explaining clearly what all that mess is about.
When I saw the picture "multiply like the chinese" I thought you ment like having babies. lol
hahahahaha Lol. no, it's ancient chinese multiplication method.
I dont get it. The explanaition is not clear enough.
Does it matter how many sectors you use?
I actually think I understand it now, after looking at it for awhile. It's a little confusing, but I believe I figured it out.
toonth (2nth)<br>(step 2 pic 3)
Nice instructable, I have never heard of this way of multiplication.
Thnks | 4,299 | 17,080 | {"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} | 4.5625 | 5 | CC-MAIN-2017-13 | latest | en | 0.758507 |
https://answerpail.com/index.php/82145/does-2-liters-equal-a-half-gallon | 1,726,085,441,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651400.96/warc/CC-MAIN-20240911183926-20240911213926-00291.warc.gz | 85,739,950 | 6,551 | # Does 2 liters equal a half gallon?
Does 2 liters equal a half gallon?
answered Nov 30, 2021 by (87,970 points)
2 liters does equal a half a gallon.
2 liters is equal to 2×0.264 gallon = 0.528 gallon.
However to be more exact 2 liters is equal to a little more than half a gallon.
3.785 liters is equal to a gallon L.
There are 3.785 liters in a gallon.
In a USA gallon there are 3.785 liters.
One imperial gallon is about 4.55 liters, while one US gallon is about 3.79 liters.
One gallon is always larger than one liter.
The US gallon is about 3.785 liters and common in the United States and Latin America.
The U.S dry gallon is about 4.405 Liters or 1⁄8 US bushel.
An easy way to figure from liters to gallons, for example, is that a quart is a little less than a liter and 4 liters is a little more than 1 gallon.
To be exact, 1 liter is 0.264 gallon (a little more than a quart), and 4 liters is 1.06 gallons.
A gallon is equivalent to approximately 3.78541 liters.
Therefore, a gallon is bigger than 3 liters. | 284 | 1,031 | {"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} | 3.4375 | 3 | CC-MAIN-2024-38 | latest | en | 0.916739 |
https://codedump.io/share/TUsim05RTP5I/1/why-does-indexing-a-matrix-by-an-integer-produce-a-different-shape-than-the-dot-product-with-a-one-hot-vector-in-numpy | 1,618,645,114,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00391.warc.gz | 284,909,133 | 9,636 | Aj Langley - 4 years ago 84
Python Question
# Why does indexing a matrix by an integer produce a different shape than the dot product with a one hot vector in numpy?
I have a matrix that I initialized with
`numpy.random.uniform`
like so:
`W = np.random.uniform(-1, 1, (V,N))`
In my case,
`V = 10000`
and
`N = 50`
,
`x`
is a positive integer
When I multiply W by a one hot vector
`x_vec`
of dimension V X 1, like
`W.T.dot(x_vec)`
, I get a column vector with a shape of (50,1). When I try to get the same vector by indexing W, as in
`W[x].T`
or
`W[x,:].T`
I get shape (50,).
Can anyone explain to me why these two expression return different shapes and if it's possible to return a (50,1) matrix (vector) with the indexing method. The vector of shape (50,) is problematic because it doesn't behave the same way as the (50,1) vector when I multiply it with other matrices, but I'd like to use indexing to speed things up a little.
*Sorry in advance if this question should be in a place like Cross Validated instead of Stack Exchange
They are different operations. matrix (in the maths sense) times matrix gives matrix, some of your matrices just happen to have width 1. Indexing with an integer scalar eats the dimension you are indexing into. Once you are down to a single dimension, `.T` does nothing because it doesn't have enough axes to shuffle.
If you want to go from (50,) to (50, 1) shape-wise, the recipe is indexing with `None` like so `v[:, None]`. In your case you have at least two one-line options:
``````W[x, :][:, None] # or W[x][:, None] or
W[x:x+1, :].T # or W[x:x+1].T
``````
The second-line option preserves the first dimension of `W` by requesting a subrange of length one. The first option can be contracted into a single indexing operation - thanks to @hpaulj for pointing this out - which gives the arguably most readable option:
``````W[x, :, None]
``````
The first index (scalar integer `x`) consumes the first dimension of `W`, the second dimension (unaffected by `:`) becomes the first and `None` creates a new dimension on the right.
Recommended from our users: Dynamic Network Monitoring from WhatsUp Gold from IPSwitch. Free Download | 570 | 2,185 | {"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} | 3.046875 | 3 | CC-MAIN-2021-17 | latest | en | 0.912727 |
https://philoid.com/question/36076-if-the-vertices-a-b-c-of-a-triangle-abc-are-1-2-3-1-0-0-0-1-2-respectively-then-find-abc-abc-is-the-angle-between-the-vec | 1,723,548,810,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641076695.81/warc/CC-MAIN-20240813110333-20240813140333-00194.warc.gz | 345,842,915 | 8,394 | ##### If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC, [∠ABC is the angle between the vectors ].
Given points are A (1, 2, 3), B (-1, 0, 0) and C (0, 1, 2)
ABC is the angle between vectors
We know
ABC = cos-1(10/√102)
18 | 118 | 286 | {"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} | 3.390625 | 3 | CC-MAIN-2024-33 | latest | en | 0.842595 |
https://www.studysmarter.co.uk/explanations/math/statistics/histograms/ | 1,716,928,950,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059148.63/warc/CC-MAIN-20240528185253-20240528215253-00079.warc.gz | 852,296,359 | 60,222 | # Histograms
When data is collected there are many ways that it can be displayed and organised, and numerical grouped data is often represented in a histogram. A histogram looks similar to a bar graph however as it represents grouped data it shows a range of variables. Since histograms are used to represent grouped data, the area of each bar on the histogram is proportional to the size of the class width which means that you can visually see if there are unequal group sizes.
#### Create learning materials about Histograms with our free learning app!
• Flashcards, notes, mock-exams and more
• Everything you need to ace your exams
## How to plot a histogram
When plotting a histogram, there is an x and y-axis. The x-axis represents the variable that is being measured and the y-axis represents the frequency density. The frequency density is the height of each bar on your histogram and can be calculated by dividing the frequency by the class width:
$frequencydensity=\frac{frequency}{classwidth}$
All of the information needed to calculate the frequency density will be found in a table of data.
The table represents the time taken in minutes for two PE classes of 30 students to complete a cross country course.
Time, t (minutes) 30≤t<40 40≤ t<45 45≤ t<55 55≤ t<60 60≤ t<65 Frequency 6 16 18 12 8
As this is grouped data, you are able to plot it onto a histogram. The first step would be to find the frequency density for each class, and this can be done by creating a new table and completing a few calculations:
Time, t (minutes) Frequency Class Width Frequency Density 30≤ t<40 6 10 0.6 40≤ t<45 16 5 3.2 45≤ t<55 18 10 1.8 55≤ t<60 12 5 2.4 60≤ t<65 8 5 1.6
The class width can be calculated by subtracting the lower boundary from the upper boundary, for example, $40-30=10$.
The frequency density is calculated by dividing the frequency by the class width, for example, $6÷10=0.6$.
Now that you have found the frequency density for each of the class boundaries, you can plot your histogram.
Histogram representing time taken to complete a cross country, Thomas-Gay - StudySmarter Originals
When plotting a histogram, you need to use the data from the time, t, minutes column of the table and the frequency density column of the table.
From this information on the histogram you are also able to create a frequency polygon. To do this you add a line from the middle of each bar on your histogram, and this is shown below.
Frequency polygon example, Thomas-Gay - StudySmarter Originals
## How to interpret a histogram
When thinking about histograms it is not only important to be able to create your own, but also to understand and interpret one that you are given.
The histogram below shows the test results as a percentage from a group of students' mathematics exam.
Histogram representing test results, Thomas-Gay - StudySmarter Originals
Here are a set of questions that you can answer from the histogram above:
1. How many students scored between 75% and 85% on the exam?
2. How many students scored between 60% and 70% on the exam?
3. How many students scored 80% or more on the exam?
4. How many students took the exam in total?
Now let's work through each question together!
1. How many students scored between 75% and 85% on the exam?
First, you start by looking at the histogram. You need to find the area of the bars between 75 and 85, and they are shaded below:
Histogram worked example, Thomas-Gay - StudySmarter Originals
To find the shaded area we can simply multiply the height by the width:
$10×1=10$
Therefore we know that 10 students scored between 75% and 85%.
2. How many students scored between 60% and 70% on the exam?
This can be done in the same way, let's start by shading the area needed on the graph:
Histogram worked example, Thomas-Gay - StudySmarter Originals
For this area, you will need to break it down into two parts since you are looking at two different bars:
$5×1=5$
$5×3=15$
$5.5+15=20.5$
This shows you that around 20 students scored between 60% and 70% on the exam.
3. How many students scored 80% or more on the exam?
Once again let's start by shading the area that is needed, for this question you need to shade everything over 80%:
Histogram worked example, Thomas-Gay - StudySmarter Originals
This question again needs to be broken down into two parts:
$5×1=5$
$15×0.6=9$
$5+9=14$
This shows that 14 of the students scored 80% or more on the exam.
4. How many students took the exam in total?
For this question, you need to find the area of each bar, your shaded area will now look like this:
Histogram worked example, Thomas-Gay - StudySmarter Originals
You will need to find the area for each bar and add them all together to find the total number of students:
$5×1.2=6\phantom{\rule{0ex}{0ex}}10×0.4=4\phantom{\rule{0ex}{0ex}}10×1=10\phantom{\rule{0ex}{0ex}}5×3=15\phantom{\rule{0ex}{0ex}}5×3.2=16\phantom{\rule{0ex}{0ex}}10×1=10\phantom{\rule{0ex}{0ex}}15×0.6=9$
Now you can add them all together to find the total number of students.
$6+4+10+15+16+10+9=70$
## Histograms - Key takeaways
• A histogram is a type of graph that represents grouped data.
• Frequency density is used to plot a histogram, and it is calculated by dividing the frequency by the class width.
#### Flashcards inHistograms 2
###### Learn with 2 Histograms flashcards in the free StudySmarter app
We have 14,000 flashcards about Dynamic Landscapes.
What is a histogram?
A histogram is a type of graph that represents grouped data.
What is a histogram used for?
A histogram is often used to visually show data, as it uses the frequency density, you are able to see how the variable ranges.
How do you draw a histogram?
A histogram can be drawn by calculating the frequency density, then plotting the frequency density and the class boundaries.
StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
##### StudySmarter Editorial Team
Team Histograms Teachers
• Checked by StudySmarter Editorial Team | 1,629 | 6,726 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "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} | 4.375 | 4 | CC-MAIN-2024-22 | latest | en | 0.886587 |
https://faqnutrition.com/how-many-cupcakes-from-a-cake-recipe-make | 1,638,416,936,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964361064.69/warc/CC-MAIN-20211202024322-20211202054322-00030.warc.gz | 326,019,907 | 11,583 | # How many cupcakes from a cake recipe make?
Date created: Tue, Apr 6, 2021 11:33 AM
Content
FAQ
Those who are looking for an answer to the question «How many cupcakes from a cake recipe make?» often ask the following questions:
### 🥛 Can you make cupcakes from cake recipe?
How can I make cupcakes from a cake recipe? To make a cake recipe into a cupcake recipe, take one of our cake recipes for an 8” cake and halve it. Divide the mixture between twelve muffin cases (fill until no more than two-thirds full) and bake for approximately 25 minutes at the same temperature as the recipe suggests. How can I make a sheet cake from a cake recipe?
### 🥛 How many cupcakes from a 9x13 cake recipe?
To make a cupcake recipe into a cake recipe, take one of our cupcake recipes making 12 cupcakes and double the recipe. Divide the mixture between 20cm layer cake tins and bake for approximately 25 minutes at the same
### 🥛 How many cupcakes from a cake recipe calories?
Here are the foods from our food nutrition database that were used for the nutrition calculations of this recipe. Calories per serving of Easy Cupcakes 68 calories of Betty Crocker Super Moist Cake Mix - 1/12 of pkg = 1 serving, (0.40 serving) 25 calories of Pillsbury Whipped Supreme Vanilla Funfetti frosting, (0.50 tbsp)
Here are some guidelines: One 9” x 13” cake, two 9” round cake layers, or three 8” round layers all make about 24 standard cupcakes. One 8" square pan or 9" round layer makes about 12 standard cupcakes.
How to Convert a Cake Recipe to Cupcakes. A two-layer cake recipe usually makes 24 to 30 cupcakes, while a one-layer cake will make a smaller batch of 12 to 15 cupcakes. You can also reverse this idea and bake cakes from cupcake recipes.
How can I make a cake from a cupcake recipe? To make a cupcake recipe into a cake recipe, take one of our cupcake recipes making 12 cupcakes and double the recipe. Divide the mixture between 20cm layer cake tins and bake for approximately 25 minutes at the same temperature indicated by the recipe. How can I make cupcakes from a cake recipe?
How to Convert a Cake Recipe to Cupcakes. Here are eight steps to get from favorite cake to perfect cupcake. 1. Scale your cake recipe appropriately. Plan to get about 12 cupcakes from the same amount of batter that would yield one 9-inch-round cake layer. However, this will vary based on the cake’s density.
• Plan on getting between 24 and 36 cupcakes from an average cake recipe (one that would usually make two 9-inch rounds or one 9×13-inch cake). • Bake the cupcakes between 20 and 30 minutes (sometimes the depth of cupcakes means they actually take longer than a thin cake layer).
When you make the wasc with 2 boxes of cake mix you would get around 5 dozen. One box would be appox. 2 1/2 dozen filled 2/3. If you read the back of the BC box, it says you would get 20-25 cupcakes 2/3 full. On the back of DH it says 24 cupcakes. When you figure in the extra ingredients thats what gives you the larger amount of cup cakes.
Ingredients 110g softened butter 110g golden caster sugar 2 large eggs ½ tsp vanilla extract 110g self-raising flour
Step 3: How to Bake Cupcakes from a Cake Recipe. Bake at the same temperature called for in the recipe. If converting from an 8 or 9-inch layer cake recipe, you’ll only need to reduce the baking time by about 10 to 15 percent. If baking from a 9 by 13-inch cake recipe, you’ll need to reduce the baking time more.
We've handpicked 22 related questions for you, similar to «How many cupcakes from a cake recipe make?» so you can surely find the answer!
### How many cupcakes from a cake recipe in 2?
Most Bundt cake recipes will make about 24 cupcakes. We'd recommend baking the cupcakes for 18 to 22 minutes or until a cake tester comes out clean and the tops spring back when lightly pressed on. Depending on what you're looking for (a flat top or a domed, higher-rising top), you'll want to bake the cupcakes between 325°F and 375°F as Kye details in the article above.
### How many cupcakes from a cake recipe in one?
Most Bundt cake recipes will make about 24 cupcakes. We'd recommend baking the cupcakes for 18 to 22 minutes or until a cake tester comes out clean and the tops spring back when lightly pressed on. Depending on what you're looking for (a flat top or a domed, higher-rising top), you'll want to bake the cupcakes between 325°F and 375°F as Kye details in the article above.
### How many cupcakes from hummingbird cake recipe 9x13 pan?
To make a cake recipe into a cupcake recipe, take one of our cake recipes for an 8” cake and halve it. Divide the mixture between twelve muffin cases (fill until no more than two-thirds full) and bake for approximately 25 minutes at the same temperature as the recipe suggests.
### How many cupcakes from hummingbird cake recipe martha stewart?
Jan 25, 2015 - This Hummingbird cake is bursting with flavor, making it an ideal dessert for your next celebration.
### How many cupcakes from hummingbird cake recipe paula deen?
Everything comes together in 20 minutes, so it’s perfect for a weeknight or last-minute meal. Since the stir-fry comes together so quickly, it’s best to have your ingredients measured and chopped before you start. If you’re not a fan of pork, feel free to use ground chicken, turkey, or even beef.
### How many cupcakes from hummingbird cake recipe southern living?
Increase speed to medium-high, and beat until fluffy, 1 to 2 minutes. Step 5. Prepare the Candied Pineapple Wedges: Slice 6 candied dried pineapple rings into 4 wedges each. Microwave 1/4 cup light corn syrup in a small microwavable bowl on HIGH until warm, about 10 seconds.
### How many cupcakes does a pound cake recipe make?
Pound cake gets its name from the fact that it originally contained a full pound of butter. For 24 cupcakes, you’ll use three sticks – one stick shy of the full pound. Tip: Make sure the butter is at room temperature so that it will mix well with the other ingredients.
### How many cupcakes does a regular cake recipe make?
To make a cupcake recipe into a cake recipe, take one of our cupcake recipes making 12 cupcakes and double the recipe. Divide the mixture between 20cm layer cake tins and bake for approximately 25 minutes at the same temperature indicated by the recipe. How can I make cupcakes from a cake recipe?
### How many cupcakes will a bundt cake recipe make?
• Do not change oven temperature. • Plan on getting between 24 and 36 cupcakes from an average cake recipe (one that would usually make two 9-inch rounds or one 9×13-inch cake). • Bake the cupcakes between 20 and 30 minutes (sometimes the depth of cupcakes means they actually take longer than a thin cake layer).
### How many mini cupcakes does a cake recipe make?
A boxed cake mix will generally make about 48, or four dozen, miniature cupcakes. However, it can vary by the brand of the boxed cake mix. When making mini cupcakes, it takes about one tablespoon of batter to fill up a mini muffin cup, though you need more than that.
### How to make cake recipe into cupcakes recipe?
Preheat the oven to 350 degrees F (175 degrees C). Step 2 Beat butter and cream cheese together until creamy; add sugar and beat until fluffy. Add eggs one at a time, beating until each one is blended.
### Can you make cupcakes from a bundt cake recipe?
Hi there, Maya! Most Bundt cake recipes will make about 24 cupcakes. We'd recommend baking the cupcakes for 18 to 22 minutes or until a cake tester comes out clean and the tops spring back when lightly pressed on
### How do i make cupcakes from a cake recipe?
Do not over-fill the cupcake wells. The batter will rise as it bakes. A quick and easy way to fill the cupcake wells is to use a large spoon or an ice cream scooper. A box of cake mix will be enough to make 24 to 30 regular-sized cupcakes. It will make even more mini-sized cupcakes, but fewer of the jumbo-sized ones.
### How to make cake recipe into cupcakes from scratch?
The next time you need a perfect treat for a bake sale, birthday party, or summer celebration, turn your favorite cake recipe into cupcakes. They'll turn out beautifully if you follow these easy steps. Choose a baking temperature and preheat the oven. Make the batter as directed. Prepare your pans based on the amount of batter.
### How to make carrot cupcakes from cake mix recipe?
In large bowl, beat cake mix, oil, water and eggs on low speed 30 seconds. Beat on medium speed 2 minutes. 3 Stir in up to three of the added ingredients and mix gently.
### How to make dense cupcakes from cake mix recipe?
From cake to cupcakes, you’ll be able to take almost any cake recipe and make it into easy-to-enjoy cupcakes. Here’s how. First, choose a standard cake recipe. When choosing a recipe to convert from cake to cupcakes, set yourself up for success by starting with a “standard” cake. These are recipes that use classic mixing techniques.
### Carrot cake cupcakes recipe?
Ingredients 2 cups white sugar 1 cup butter, softened 2 eggs 1 teaspoon vanilla extract 2 cups all-purpose flour ¼ cup finely chopped walnuts 1 teaspoon ground cinnamon 1 teaspoon baking powder ½ teaspoon baking soda ½ teaspoon salt ½ cup milk 1 cup finely grated carrots
### How to bake cupcakes from cake recipe?
The first thing to consider when converting cake to cupcakes is the baking temperature. Choose your temperature first so you can preheat the oven while you prepare the batter. Most cupcakes bake well between 325°F and 375°F. Conveniently, these are the same temperatures that cakes are usually baked at too.
### Can i make cupcakes with cake recipe?
Give it a try: cake to cupcakes Choose a baking temperature and preheat the oven.. Make the batter as directed.. Prepare your pans based on the amount of batter.. Fill the wells about 4/5 of the way full.. Adjust the bake time accordingly.. And if you haven't already tried it, bake our Recipe of ...
### How to make a cake cupcakes recipe?
How to Make a Giant Cupcake Cake - YouTube. How to Make a Giant Cupcake Cake. Watch later. Share. Copy link. Info. Shopping. Tap to unmute. If playback doesn't begin shortly, try restarting your ... | 2,346 | 10,182 | {"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-2021-49 | latest | en | 0.950653 |
https://newpathworksheets.com/math/grade-4/area-and-perimeter/vermont-standards | 1,568,929,725,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573735.34/warc/CC-MAIN-20190919204548-20190919230548-00082.warc.gz | 589,455,805 | 8,136 | ◂Math Worksheets and Study Guides Fourth Grade. Area and Perimeter
The resources above correspond to the standards listed below:
Vermont Standards
VT.7.10. Mathematical Problem Solving: Applications: Students use concrete, formal, and informal strategies to solve mathematical problems, apply the process of mathematical modeling, and extend and generalize mathematical concepts. Students apply mathematics as they solve scientific and technological problems or work with technological systems.
M4:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.
VT.7.7. Mathematical Understanding: Geometric and Measurement Concepts: Students use geometric and measurement concepts.
M4:14. Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles, polygons, or irregular shapes on grids using a variety of models, manipulatives, or formulas. Expresses all measures using appropriate units.
M4:15. Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands. | 214 | 1,200 | {"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} | 2.578125 | 3 | CC-MAIN-2019-39 | latest | en | 0.828581 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.