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https://doubtnut.com/question-answer/a-train-travels-360-km-at-a-uniform-speed-if-the-speed-had-been-5-km-h-more-it-would-have-taken-1-ho-3118
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or
# A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Question from Class 10 Chapter Quadratic Equations
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Solution :
speed of train= `x`km/hr <br> case 1:time taken `= 360/x` (1) <br> case 2 : speed of train `= (x+5)`km/hr <br> `time= 360/(x+5)` (2) <br> acc to question <br> `360/(x+5) = 360/x - 1` <br> `360x = 360x + 1800- x^2 -5x` <br> `x^2 +5x +1800= 0` <br> `x^2+45x-40x - 1800=0` <br> `x(x-40) + 45(x-40)=0 ` <br> `(x-40)(x+45)=0` <br> `x=-45 & 40` <br> speed cant be negative so, sped of train is `40`km/hr <br>
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# How Much is in a Cord of Wood?
## What is a Cord of Wood?
How much is in a cord of wood is a common question for those looking to buy or sell firewood. A cord of wood is the standard measurement for firewood and is equal to 128 cubic feet of tightly stacked wood. When stacked, a cord of wood typically measures 4 feet wide, 4 feet high and 8 feet long. Firewood is commonly sold in half-cord and full-cord increments. A half-cord is half of the 128 cubic feet, or 64 cubic feet. The cost of a cord of wood varies by region and type of wood, but is typically around \$200-\$300.
If you buy some wood, you’re interested in knowing how much is in a cord of wood. It’s essential to know exactly how much you’ll be paying for your wood to ensure you’re getting the best price possible. If you’re unsure, check out some of the calculators below.
## Calculating a full cord vs. a full cord
If this is your first time buying firewood, you may wonder how much wood is in a full cord. The answer is that a complete line is three times the size of a face cord. A half cord comprises three rows of sixteen pieces of wood. The average piece length is twelve inches.
The first thing you need to do is to determine whether you’re buying stacked or loose pieces of firewood. If you’re buying stacked wood, it’s essential to measure the height and width of each piece. This will help you figure out how much firewood you need.
If you’re shopping for loose wood, finding a company that will give you a precise estimate of how many pieces you’ll need is crucial. If they don’t give you a rough estimate, try to ask them for a more accurate measurement. This way, you can make sure you’re getting a fair deal.
You’ll also need to figure out the length of each piece. This will be especially important when you’re buying thrown cords. If you need more clarification about the size of the details, you can compare prices from different suppliers.
Once you’ve determined the dimensions of the firewood you’re considering, you can enter them into the calculator. It will help if you input the length, width, and price per cord. The calculator will then display how many complete cables are in the stack, how many face cords are in the stack, and how much each face card is worth.
As with any calculation, it’s essential to measure the length of the pieces of firewood one at a time. If you do this, you could avoid ending up with a disappointing outcome.
Another factor to consider is the amount of air space in each piece of wood. If you’re buying stacked wood, this air space will be relatively constant, but it’s more random when buying loose lumber. This can add up to up to 30% of the total volume.
Lastly, if you’re trying to decide between a full cord or a face cord, you’ll need to find out how much of the face cord is a full cord. If it is, you’ll have to multiply the amount of the entire thread by the length of the face cord to determine the average price of the face cord. If the whole line is shorter than the face cord, you’ll have to subtract some wood to determine the total cord value.
## Calculating a face cord vs. a full cord
When shopping for firewood, it can be unclear whether you should buy a full cord or a face cord. A complete line is three times the length of a face cord, but it can be too big for some people.
If you need more clarification about how much a full cord or a face cord costs, compare prices from different suppliers. You can also call dealers and ask them for the price. A complete cable typically contains 700 pieces of wood. If you need firewood for the winter, a full cord can provide you with all the wood you need to keep the fires going all season. However, it can cost several hundred dollars.
A face cord contains a third of a complete line, which can be a fraction of the cost of an entire thread. When measuring the size of a face cord, you should determine its length, height, and width. The depth of a face cord can vary, so you should always check the depth before purchasing.
A face cord is usually eight feet long and four feet tall. This is a standard length for a face cord, but it can vary among sellers. It is also common for a face cord to be made up of 220 to 240 pieces of wood. It is not necessarily a standard length, though, and can be as long as 48 inches or as short as eight inches.
The depth of a face cord is more challenging to measure than the length. It is usually 16 inches deep. Knowing the depth can be difficult if you don’t have a measuring device. This is especially true if you’re buying a stack of wood. The best way to do this is to count the pieces one by one. It would help if you also asked the seller how they measure.
It is always a good idea to go through a reliable dealer. Depending on the type of wood you’re buying, you can expect to pay anywhere from \$120 to \$400 per cord.
## Identifying a cord of wood
If you are purchasing firewood for your fireplace, you need to know how to identify a cord of wood. A complete line of firewood is a stack of 16-inch logs. To determine the amount of timber in an entire thread, you need to measure the stack’s length, width, and depth.
The standard firewood cord is four feet wide and eight feet long. This measurement is based on a stack of three rows of 16-inch logs. This means that the stack should be over 128 cubic feet. It may also have air pockets between the pieces.
The volume of a cord can vary depending on the type of wood. For example, a full line of white oak weighs about 4200 pounds when wet and 4184 pounds dry. Ash is also an excellent type of wood to burn because it provides high heat.
You can use a calculator to find the standard US unit of cord. You can use it to estimate the cost of any order. You can also use it to calculate the value of a face cord of wood.
The National Institute of Standards and Technology (NIST) Handbook 130 defines the term cord. It is a standard measurement of wood in the United States. The traditional full cord of firewood is 128 cubic feet.
The standard half cord of firewood is 64 cubic feet. You can calculate the weight of a line using an online calculator. You can also use a ready-made table to get more detailed data. The value of a cord is roughly \$270.
It is essential to buy firewood at the right price. You should first determine the quantity you need and how much it will cost. Then, it would help if you considered how to store the wood. You should also check for cracks in the ends of the logs. You should also find a wood vendor who is close to the forest. They should have a cutting permit and be willing to ship the wood to you.
If you have a full-size pickup truck, you can easily store half a cord of wood. However, it is recommended to buy a partial cord of firewood. If you believe in a full line, you must stack the wood to make it fit in your vehicle.
## Finding a forest that allows you to cut your wood
If you’re looking for a forest where you can cut your wood, you’ve come to the right place. Several national and state forests offer low-cost permits for people who wish to cut firewood. Depending on the woods, you can get free access to cut firewood or pay per cord. However, you’ll need to make sure that you follow the regulations.
First, you’ll want to contact the supervisor’s office at the national or state forest in question. You’ll need to fill out a harvesting application, and if necessary, you may be required to show proof of identification. You’ll also need a permit for the harvesting and a pickup truck and chainsaw. Then, you’ll need to find an excellent place to harvest the wood. The Forest Service offers the best places to locate downed wood along forest roads. Then, you can cut the wood to 16 inches and stack it in three rows.
A national or state forest with a firewood program will typically limit the number of cords you can harvest in a given period. If you want to cut your wood, you can expect to pay between and per cord. This is a small price to pay to help forest managers manage their land and keep it healthy. You can expect to collect about 2.8 million lines in 1982.
You can also find a variety of programs in New England states. For example, you can cut wood on New Hampshire, Maine, and New Jersey public lands. You’ll need a permit from the department of environmental conservation. In Vermont, you can also cut wood on federal lands, though you’ll need to obtain a permit from the Forest Service. Finally, you can get a license for the Coconino National Forest in Flagstaff, Arizona. The ticket allows you to cut up to 5 cords in specified areas, but you’ll need to apply for one.
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https://gaming.stackexchange.com/questions/228328/how-many-ticks-for-stone-to-form
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How many ticks for stone to form
I've been playing with new designs for a stone generator, playing with how fast I can get it running.
I'm trying a redstone clock / pulse shortener this time.
Is the rate that lava flows in to water fixed? If so how many ticks does it take?
Let's take a look at the source code of Minecraft 1.8:
`````` public boolean checkForMixing(World paramWorld, BlockPos paramBlockPos, IBlockState paramIBlockState) {
if (this.blockMaterial == Material.lava) {
int i = 0;
for (EnumFacing localEnumFacing : EnumFacing.values()) {
if ((localEnumFacing != EnumFacing.DOWN) && (paramWorld.getBlockState(paramBlockPos.offset(localEnumFacing)).getBlock().getMaterial() == Material.water)) {
i = 1;
break;
}
}
if (i != 0) {
??? = (Integer)paramIBlockState.getValue(LEVEL);
if (((Integer)???).intValue() == 0) {
paramWorld.setBlockState(paramBlockPos, Blocks.obsidian.getDefaultState());
triggerMixEffects(paramWorld, paramBlockPos);
return true; }
if (((Integer)???).intValue() <= 4) {
paramWorld.setBlockState(paramBlockPos, Blocks.cobblestone.getDefaultState());
triggerMixEffects(paramWorld, paramBlockPos);
return true;
}
}
}
return false;
}
``````
This function determines whether it should create cobblestone or obsidian or nothing. It is called by two other functions, namely `onBlockAdded` and `onNeighborBlockChange`.
• `onBlockAdded` seems rather self-explanatory, it is called whenever a block has been added and simply calls `checkForMixing` on the block that has been added (e.g. by using a bucket or because it is flowing and creating new block).
• `onNeighborBlockChange` is somewhat more interesting. It is called whenever a neighbouring block has been changed or better whenever it is ticking/updating (there is nothing that needs to change, just calling an update is enough). the problem with your contraption is, water and lava are set to `setTickRandomly(true);`, so you can't know when they are changing.
There are plenty of automatic (cobble)stone generators that feature a block detection and push forward the generated block, so they don't need to rely on a constant redstone clock.
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https://hbook.westernsydney.edu.au/subject-details/math2003/
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# MATH 2003 Differential Equations
Credit Points 10
Legacy Code 200030
Coordinator Shatha Aziz Opens in new window
Description Differential equations arise naturally both in abstract mathematics and in the study of many phenomena. This subject provides the theory of ordinary differential equations and an introduction to partial differential equations together with methods of solution. Examples are drawn from a wide range of biological, chemical, physical and economic applications.
School Computer, Data & Math Sciences
Discipline Mathematics
Student Contribution Band HECS Band 1 10cp
Check your fees via the Fees page.
Level Undergraduate Level 2 subject
Pre-requisite(s) MATH1015 - Mathematics 1B
Incompatible Subjects MATH 1019 - Mathematics for Engineers 2
Restrictions
Students enrolled in Bachelor of Engineering, Bachelor of Engineering (Honours) or Bachelor of Engineering Science may not enrol in this subject.
Assumed Knowledge
None
## Learning Outcomes
On successful completion of this subject, students should be able to:
1. Classify and solve various types of first order ordinary differential equations
2. Classify and solve various types of second order ordinary differential equations
3. Apply Laplace transforms to solve problems including second order ordinary differential equations
4. Classify and solve various types of basic partial differential equations.
## Subject Content
- Review of first order differential equations
- homogeneous linear second order equations
- reducible second order equations
- linear second order equations with constant coefficients
- differential operators
- method of undetermined coefficients
- variation of parameters
- equations with variable coefficients
- power series solutions
- Laplace transforms
- simple partial differential equations and separation of Variables, eg diffusion, wave and Laplace equations
- application of Fourier series to partial differential equations
## Assessment
The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.
Type Length Percent Threshold Individual/Group Task
Intra-session Exam 45 minutes 10 N Individual
Intra-session Exam 45 minutes 10 N Individual
Intra-session Exam 45 minutes 15 N Individual
Intra-session Exam 45 minutes 15 N Individual
Final Exam 2 hours 50 Y Individual
Teaching Periods
## Spring (2024)
### Campbelltown
#### On-site
Subject Contact Shatha Aziz Opens in new window
View timetable Opens in new window
### Penrith (Kingswood)
#### On-site
Subject Contact Shatha Aziz Opens in new window
View timetable Opens in new window
### Parramatta - Victoria Rd
#### On-site
Subject Contact Shatha Aziz Opens in new window
View timetable Opens in new window
Structures that include subject
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https://fykos.cz/year30/problems/series4
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4. Series 30. Year
(3 points)1. princess Point on point
It is not easy for story characters if they want to know when they appear on screen. Fortunately, today's technology makes it easier, take for example princess Point from a story with six chapters. All chapters have the same length with the height of every chapter on Karel's display being 1200 pixels (but the display itself can only show 900 pixels at any one time). When reading Karel scrolls continuously and reads with constant speed. After three minutes of reading, Point passed the first end of the slider in the scrollbar and after seven minutes she passed the other end. Which chapter does Point appear in? Note: The ratio of the height of the slider and the height of the display is the same as the ratio of the height of the display to the height of the entire story.
Michal's scrollbar was slipping.
(3 points)2. jerky pendulum
It is well known fact that to make a train ride as comfortable as possible, when accelerating or braking, the acceleration needs to change as little as possible. It is therefore good practice when a train starts with small, constant change of acceleration. The change of acceleration is called a jerk. Determine how does the equilibrium position of a pendulum (the angle with the vertical $φ)$. Denoting the length of the pendulum $l$, the train starts with a constant jerk $k$ ( $k=Δa⁄Δt$, where $a$ denotes acceleration) and the train is on Earth with acceleration due to gravity $g$. Bonus: Derive the equations of motion and solve them numerically for $φ(0)=0$ and $dφ⁄dt(0)=0$ for various values of $k$.
Occurred to Karel when he should have been writing his thesis.
(8 points)3. bicone
Consider a wooden construction (shown in the picture) with its foundation in the shape of an isosceles triangle with a base of length $c=35\;\mathrm{cm}$. The height of the legs of this triangle increases towards the base with an angle $α=2°$ with the flat ground. A bicone with opening angle $φ=40°$ and height 2$h=40\;\mathrm{cm}$ is placed in the vertex opposite the base, where the triangle has angle $β=70°$. When released, the bicone starts rolling „uphill“, that is in the direction of the increasing height of the legs.
• Explain why the bicone can roll uphill.
• Find the dependence of the position of the centre of mass on the distance covered by the bicone?
• What is the velocity of the bicone in the instant before it hits the base.
• How many turns will the bicone make before it hits the base? The bicone is initially placed horizontally on the construction in such a way that its centre of mass is exactly above the vertex opposite the base.
(8 points)4. heat engine
Consider a heat engine filled with a diatomic gas. This engine works thanks to a cycle ABCDEFA as shown in the picture. The 6 processes that make up the cycle are
• A $→$ B - isobaric heating from a state 4$p_{0}$ and $V_{0}$ (let us denote temperature at A 4$T_{0})$ to a state with volume 3$V_{0}$,
• B $→$ C - isothermic expansion to volume 4$V_{0}$,
• C $→$ D - isochoric cooling to pressure $p_{0}$,
• D $→$ E - isobaric cooling to volume 2$V_{0}$,
• E $→$ F - isothermic compression to volume $V_{0}$,
• F $→$ A - isochoric heating to pressure 4$p_{0}$. Determine the remaining state variables in B, C, D, E, and F, the maximal and the minimal temperature of the ideal gas during the process (as a multiple of $T_{0})$, heat received and lost by the gas in each process, and the overall efficiency of the engine. Compare this efficiency with that of a Carnot engine working between the same minimal and maximal temperatures. Assume for simplicity that the molar amount of the gas does not change and there are no chemical changes during the cycle. A sketch can be seen in figure.
Bonus: Do the same for a much simpler „square“ cycle, ABCDA, where the gas starts in a state $p_{0}$, $V_{0}$ and $T_{0}$ and izochorically heats up to 4$p_{0}$, isobarically heats up and expands to 4$V_{0}$, isochorically cools down to $p_{0}$ and isobarically cools down to $V_{0}$. Compare the efficiency of these two heat engines and suggest which one is better.
Karel was alternately warm and cold
(9 points)5. weird atmosphere
Have you ever seen such a weird atmosphere? Up to a certain height the speed of light inside it is constant, $v_{0}$, but from that certain height the speed of light starts increasing linearly as $v(Δh)=v_{0}+kΔh$. At one point, exactly at the height where the speed of light starts changing, light beams are sent upward in all directions. Show that all these beams move along circular arcs and determine the radii of these arcs. Also find out the distance between the place where the the light was emitted and the point where the beams return to the original height.
Jakub wanted to know what it would be like to swim under ice.
We've all been there, you spread some honey or some preserve on a slice of bread, take a bite, and suddenly, the spread drips through a hole and lands right on your hand. Determine how does the probability that there is a hole straight through a slice of bread depend on its thickness. The model of how does the dough rise is left up to you. (For example, evenly distributed bubbles with an exponential distribution of radii is a good model).
Michal stained his clothes.
(11 points)E. Mikulas's egg
Measure the surface area of a bird's (e.g. chicken's) egg.
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https://stats.stackexchange.com/questions/41846/average-of-rate-of-change-in-a-set-of-independent-change-events
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# Average of rate of change in a set of independent change events
What is the right method for computing average of percentage values? Arithmetic average, geometric average, or something else?
Here's an example of problems I'm talking about. Suppose for years 2009, 2010, 2011, the annual GDP growth rates are 1%, 2%, 3%, respectively. What is the average growth rate over these three years? I'm not talking about the domain of GDP growth in specific (it's just a made-up example). Instead, I want to know the way to compute average of percentiles in general (or at least somewhat smaller domain of average of certain growth rates).
* Update #1 - another example
Suppose I have percentages Pi=1 - Ni/Di (i=1, 2, ..., m). Ni is the execution time of program i after optimization, and Di is the execution time of the same program i before optimization. Then, Pi represents the rate of reduction in execution time after optimization. How can we compute the average rate of reduction in execution time for these m programs? The arithmetic average avg(Ni) is not meaningful, right?
* Update #2 - change of title
From "Average of percentage values" to "Average of rate of change in a set of independent change events"
Change event ei: change from original value ai to new value bi, and change rate pi=f(ai,bi)
What is the average change rate for a set of events {e1, e2, ..., en}?
• Taking the average of the percentages is probably not a very good idea. Do you know the numerator and the denominator counts of each of the percentages, or you just have the percentages, nothing else? I mean you can add up all the numerators (say, $N1+N2+N3$) and also add up all the denominators (say, $D1+D2+D3$) separately and then find the percentage as $\frac{(N1+N2+N3)}{(D1+D2+D3)}100\%$. – Blain Waan Nov 4 '12 at 10:31
• when you say What is the average growth rate over these three years? what you need is a type of average suitable for averaging growth rates, rather than for averaging percentages. Percentages occur in a variety of ways and different kinds of averages are used depending on what you're averaging. – Glen_b Nov 4 '12 at 10:56
• @BlainWaan You are right. That's one way I've tried before. But sometimes, the sum of N1, N2, N3 is not very meaningful (see my updated post). In those cases, I compute the geometric mean N of N1N2N3, and geometric mean D of D1D2D3, and use N/D as the average. Is that reasonable? – dacongy Nov 4 '12 at 12:02
## 1 Answer
To average growth rates the geometric mean seems appropriate.
$G = (\prod_{i=1}^n x_i)^\frac{1}{n}$
For example, suppose the rate is .10, .02 and .20. Then the total growth is $1.1*1.02*1.2$ over 3 years, or the cube root of that product per year.
$1.1*1.02*1.2 = 1.346$
and $1.346^\frac{1}{3} = 1.1104$
and, of course, cubing that gets back to 1.346.
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# Why The Earth Appears Curved at a High Altitude.
• 295 Replies
• 49872 Views
?
#### zork
• 3319
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #240 on: July 17, 2010, 02:23:58 AM »
Good argument. However, the reason the Earth looks curved from a high altitude is actually because it is spherical.
Awesome argument. You made so many great points there.
This single post gave more insight to the world as we know it than everything else in this thread combined.
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.
#### Pongo
• Planar Moderator
• 6753
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #241 on: July 17, 2010, 03:08:58 AM »
Good argument. However, the reason the Earth looks curved from a high altitude is actually because it is spherical.
Do you have any proof to support these outlandish claims?
#### markjo
• Content Nazi
• The Elder Ones
• 40289
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #242 on: July 17, 2010, 09:26:08 AM »
Good argument. However, the reason the Earth looks curved from a high altitude is actually because it is spherical.
Do you have any proof to support these outlandish claims?
Is there any proof that you would accept?
Science is what happens when preconception meets verification.
Quote from: Robosteve
Besides, perhaps FET is a conspiracy too.
Quote from: bullhorn
It is just the way it is, you understanding it doesn't concern me.
#### Raver
• 777
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #243 on: July 17, 2010, 09:39:00 AM »
Good argument. However, the reason the Earth looks curved from a high altitude is actually because it is spherical.
Do you have any proof to support these outlandish claims?
lurk moar
Quote from: Gen. Douchebag
Quote from: Raver
Why? You a pedo out for delicious loli?
Sure, whatever
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #244 on: July 17, 2010, 09:47:51 PM »
Good argument. However, the reason the Earth looks curved from a high altitude is actually because it is spherical.
Awesome argument. You made so many great points there.
This single post gave more insight to the world as we know it than everything else in this thread combined.
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close? Granted, the look out your window argument is a horrible argument to prove FE, but this is even below that. If you look out and see it is flat, than assume it is flat correct? If you see it is round, why assume it is a sphere? There are plenty of round shapes that aren't spheres. In fact, according to this definition, spheres and balls come after disks and cylinders.
(Dictionary.com)
Quote
round
1.
having a flat, circular surface, as a disk.
2.
ring-shaped, as a hoop.
3.
curved like part of a circle, as an outline.
4.
having a circular cross section, as a cylinder; cylindrical.
5.
spherical or globular, as a ball.
6.
shaped more or less like a part of a sphere; hemispherical.
#### PizzaPlanet
• 12249
• Now available in stereo
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #245 on: July 17, 2010, 10:33:15 PM »
(Dictionary.com)
I'm not saying the definition is wrong, but please don't use shitty sources when it comes to words' definitions. Dictionary.com is known to contain words that don't exist.
hacking your precious forum as we speak
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #246 on: July 17, 2010, 10:42:28 PM »
(Dictionary.com)
I'm not saying the definition is wrong, but please don't use shitty sources when it comes to words' definitions. Dictionary.com is known to contain words that don't exist.
I was actually using the same definition that a certain RE'er used to say that round = sphere. I know there are better sources, but I figured, hey, if RE'ers will use it, why not I?
• 523
• Its a trap!
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #247 on: July 17, 2010, 10:57:09 PM »
(Dictionary.com)
I'm not saying the definition is wrong, but please don't use shitty sources when it comes to words' definitions. Dictionary.com is known to contain words that don't exist.
I was actually using the same definition that a certain RE'er used to say that round = sphere. I know there are better sources, but I figured, hey, if RE'ers will use it, why not I?
Aww its cute, he mentioned me . We were talking semantics, such as if the literal of FLAT EARTH were to be taken in context, then mountain ranges, hills, possible the entirety of what we know as the 3-D world would not exist, such is the same for calling it a ROUND EARTH as you have been so kind as to outline the inaccuracy of such a label, so if you want we can change everything from RE to SE (spherical Earth) and FE to.... PE (Plane Earth?). Please try not to derail the thread.
#### Raver
• 777
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #248 on: July 18, 2010, 02:40:26 AM »
http://oxforddictionaries.com/view/entry/m_en_gb0720170#m_en_gb0720170
There you go, a reliable source. Oh wait, I am not sure, maybe it has affiliations with NASA, the goverment or the outside world in general! :O
Quote from: Gen. Douchebag
Quote from: Raver
Why? You a pedo out for delicious loli?
Sure, whatever
?
#### zork
• 3319
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #249 on: July 18, 2010, 09:00:20 PM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #250 on: July 19, 2010, 12:00:52 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
« Last Edit: July 19, 2010, 12:12:57 AM by EnglshGentleman »
• 523
• Its a trap!
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #251 on: July 19, 2010, 12:03:06 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
Cool a website picked a random order to address things. How about the more pressing matter that FE was the original belief in the world until it was dis-proven. FE came first, but SE came back and kicked its ass.
#### ClockTower
• 6462
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #252 on: July 19, 2010, 12:03:34 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
Let's clear up the confusion. The challenge to FET is that the horizon appears 1) lower than eye-level and 2) curved downward (left and right down and center up) in various photographs and eye-witness accounts. RET has an answer, consistent and predictive (RET predicts sunrise time, for example). We've heard that EA solves the problem, but no one can describe EA. Even the FAQ doesn't answer that question. We've heard about magic waves. We've heard that it's just the terminator, a really lame proposal. We've heard that is the conspiracy doctoring all the photographs and forcing Neil Armstrong and his colleagues to lie.
FET fails so miserably in so many ways, but this problem is inherently fatal to FET.
« Last Edit: July 19, 2010, 12:15:26 AM by ClockTower »
Keep it serious, Thork. You can troll, but don't be so open. We have standards
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #253 on: July 19, 2010, 12:12:26 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
Cool a website picked a random order to address things.
Dictionaries don't but definitions in random order, they put them in order of most common use or relevance.
?
#### d00gz
• 641
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #254 on: July 19, 2010, 05:01:42 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
If you are on an aircraft at 50,000 feet, you can look out the window and see the earth's curvature. You can then turn 90 degree's, and look out another window, and see the same curvature. Explain how the earth could be a cylinder, having made these observations?
?
#### zork
• 3319
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #255 on: July 19, 2010, 08:01:21 AM »
You even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Curved also can mean spherical, so it doesn't matter what else it may point out. Sitting on a VERY BIG whatever shape and looking out of window and seeing flat doesn't mean that the object is flat. So, flat can point out anything. And for me they are arguments of same level. Say whatever you want.
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #256 on: July 19, 2010, 10:15:52 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
We've heard that EA solves the problem, but no one can describe EA. Even the FAQ doesn't answer that question.
Lurk moar than. Parsec and Parsifal have made countless posts and threads describing and going into the detail the mathematics and physics of EA.
• 523
• Its a trap!
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #257 on: July 19, 2010, 10:32:50 AM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
Cool a website picked a random order to address things.
Dictionaries don't but definitions in random order, they put them in order of most common use or relevance.
put*
and according to you that dictionary isn't exactly reliable.
?
#### zork
• 3319
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #258 on: July 19, 2010, 12:54:56 PM »
Lurk moar than. Parsec and Parsifal have made countless posts and threads describing and going into the detail the mathematics and physics of EA.
Which unfortunately does not fit anywhere. There isn't practical way to make light bend or observe it bend as their math and physics supposedly show.
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.
#### Raver
• 777
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #259 on: July 19, 2010, 01:30:02 PM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
We've heard that EA solves the problem, but no one can describe EA. Even the FAQ doesn't answer that question.
Lurk moar than. Parsec and Parsifal have made countless posts and threads describing and going into the detail the mathematics and physics of EA.
Lurk moar and you will find that Parsifal admitted to not having any evidence for bendy light and can not explain how the mechanism would work if it did exsist.
Quote from: Gen. Douchebag
Quote from: Raver
Why? You a pedo out for delicious loli?
Sure, whatever
?
#### Thevoiceofreason
• 1792
• Bendy Truth specialist
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #260 on: July 19, 2010, 03:46:19 PM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
We've heard that EA solves the problem, but no one can describe EA. Even the FAQ doesn't answer that question.
Lurk moar than. Parsec and Parsifal have made countless posts and threads describing and going into the detail the mathematics and physics of EA.
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Also, he never verified that the light path would allow for sunset and sunrise. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #261 on: July 19, 2010, 04:49:43 PM »
Of course it's awesome. It's exactly in same level as FE only "evidence". Look out the window and what you see? Earth is flat so it must be flat.
How is even close?
It has quite same wording and has same amount on great points. Shortly:
1)Earth looks curved so it is spherical.
2)Earth looks flat so it is flat.
You you even read the rest of my post, you'd notice how I pointed out that curved != spherical until the sixth definition.
And in fact, curved pointed towards disks and cylinders first.
Wait, aren't those FE things?
It seems to me that either way, whether you think it is flat, or you think it is curved, it suggests FE before it does SE.
We've heard that EA solves the problem, but no one can describe EA. Even the FAQ doesn't answer that question.
Lurk moar than. Parsec and Parsifal have made countless posts and threads describing and going into the detail the mathematics and physics of EA.
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
#### ClockTower
• 6462
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #262 on: July 19, 2010, 04:53:50 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understand how it functions.
Keep it serious, Thork. You can troll, but don't be so open. We have standards
#### Johannes
• Flat Earth Editor
• 2755
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #263 on: July 19, 2010, 06:53:04 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understand how it functions.
Newton did not understand gravity. Newton was 100% wrong.
#### ClockTower
• 6462
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #264 on: July 19, 2010, 07:00:34 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understand how it functions.
Newton did not understand gravity. Newton was 100% wrong.
1) Did anyone claim that Newton understood gravity? 2) Based on your FET, do tell us how you know that Newton was 100% wrong.
Keep it serious, Thork. You can troll, but don't be so open. We have standards
#### Johannes
• Flat Earth Editor
• 2755
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #265 on: July 19, 2010, 07:30:36 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understand how it functions.
Newton did not understand gravity. Newton was 100% wrong.
1) Did anyone claim that Newton understood gravity? 2) Based on your FET, do tell us how you know that Newton was 100% wrong.
You implied Newton understood gravity.
2. Newton was wrong because objects are not attracted to eachother.
#### ClockTower
• 6462
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #266 on: July 19, 2010, 07:37:33 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understandus how it functions.
Newton did not understand gravity. Newton was 100% wrong.
1) Did anyone claim that Newton understood gravity? 2) Based on your FET, do tell us how you know that Newton was 100% wrong.
You implied Newton understood gravity.
2. Newton was wrong because objects are not attracted to eachother.
Where did I imply that?
2. You're obviously wrong. Objects are attracted to each other.
Keep it serious, Thork. You can troll, but don't be so open. We have standards
#### Johannes
• Flat Earth Editor
• 2755
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #267 on: July 19, 2010, 10:02:09 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understandus how it functions.
Newton did not understand gravity. Newton was 100% wrong.
1) Did anyone claim that Newton understood gravity? 2) Based on your FET, do tell us how you know that Newton was 100% wrong.
You implied Newton understood gravity.
2. Newton was wrong because objects are not attracted to eachother.
Where did I imply that?
2. You're obviously wrong. Objects are attracted to each other.
Provide proof of electrically neutral objects being attracted to each other.
• 523
• Its a trap!
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #268 on: July 19, 2010, 10:11:27 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understandus how it functions.
Newton did not understand gravity. Newton was 100% wrong.
1) Did anyone claim that Newton understood gravity? 2) Based on your FET, do tell us how you know that Newton was 100% wrong.
You implied Newton understood gravity.
2. Newton was wrong because objects are not attracted to eachother.
Where did I imply that?
2. You're obviously wrong. Objects are attracted to each other.
Provide proof of electrically neutral objects being attracted to each other.
My high school physics teacher did an experiment that proved they are 0.o.
^ this explains the idea
« Last Edit: July 19, 2010, 10:30:21 PM by AdmiralAckbar »
#### EnglshGentleman
• Flat Earth Editor
• 9548
##### Re: Why The Earth Appears Curved at a High Altitude.
« Reply #269 on: July 19, 2010, 10:51:55 PM »
No they haven't. Parsifal just gave us one BS equation that basically said, derp light moves here. what he failed to do was describe the actual forces behind it, i.e. the location and nature of the force. Finally, he never explained how the force acted upon the light not only mattered for the position, but the velocity of the photon as well.
So what? Just because he can't prove the mechanism behind it, doesn't mean he can't understand how it functions. I'm pretty sure RE'ers do the exact same thing for gravity.
No. Wrong Again. First, no one requires a proof of the mechanism. Second, Newton did describe the force of gravity universally. Third, you'll have to demonstrate to us that he does understandus how it functions.
Newton did not understand gravity. Newton was 100% wrong.
1) Did anyone claim that Newton understood gravity? 2) Based on your FET, do tell us how you know that Newton was 100% wrong.
You implied Newton understood gravity.
2. Newton was wrong because objects are not attracted to eachother.
Where did I imply that?
2. You're obviously wrong. Objects are attracted to each other.
Provide proof of electrically neutral objects being attracted to each other.
My high school physics teacher did an experiment that proved they are 0.o.
^ this explains the idea
Your high school physics teacher was teaching entanglement!?
I thought there was only a dozen or so people in the world that fully understand how it works.
That's incredible!
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Print 70 comment(s) - last by JediJeb.. on Aug 13 at 1:48 PM
A new study shows that the movie's idea of blowing up the asteroid is way off
If Bruce Willis' ability to destroy life-threatening asteroids put your mind at ease about the end of the world, here's a study to bring you back to reality.
Michael Bay's 1998 hit movie Armageddon depicted Bruce Willis and a team of oil drilling heroes setting off nuclear bombs on an asteroid that was rushing toward Earth, thus saving all of humanity from the end of the world -- aka Armageddon.
A class of physics students from the University of Leicester in the UK decided to look into whether this kind of scenario would ever be possible. The short answer is no, but they provided some evidence as to why.
To debunk this mystery, the class first gathered basic information about the asteroid itself (which were mentioned in the film), such as the total volume of the asteroid pieces, the clearance radius (radius of Earth plus 400 miles), its distance from Earth at detonation, the asteroid's pre-detonation velocity, and the density of the asteroid pieces.
Harry Stamper is not amused
Using this information, they created a formula to find the total amount of kinetic energy needed to blow the asteroid to smithereens. As it turns out, 800 trillion terajoules of energy would be needed to break the asteroid into two pieces, allowing it to bypass planet Earth. This means that any bomb used would have to be a billion times stronger than any bomb ever detonated on Earth.
FYI -- the largest bomb ever detonated on Earth was the Soviet Union's "Big Ivan," which was a 50 megaton hydrogen bomb that only had an energy output of 418,000 terajoules.
From there, issues arose with the time needed to detect the asteroid in order to be able to successfully blow it up. It would need to explode at the point in which it is detected at 8 billion miles.
"A series of assumptions must be made due to limited information in the film," said the class paper titled, 'Could Bruce Willis Save the World?' "First, the asteroid is approximated as a spherical object 1000km in diameter (the asteroid is quoted being the size of Texas) that splits into two equal-sized hemispheres. The asteroid in the film reaches a clearance either side of the Earth of 400 miles (640km) which is the assumed value for our calculation."
Source: Network World
Comments Threshold -1 0 1 2 3 4 5
By anactoraaron on 8/11/2012 3:28:39 PM , Rating: 3
quote:
So no offense, but when I see some jackass make some Bush-bashing comment about Katrina
Sorry for offending you in such a personal way. My intent was to show exactly what you also said :
quote:
Katrina would have played out exactly the same, no matter who was in office.
So would Armageddon (which was my point in my op). So would a lot of other things (we got Osama! etc). Whoever is in office gets to take the praise or persecution of whatever happens regardless of their involvement. What truly goes on is the works of a great many people behind the scenes and out of the media spotlight. So bashing specific Dems or Reps is silly, as these days almost all politicians are crooked and no good.
"Google fired a shot heard 'round the world, and now a second American company has answered the call to defend the rights of the Chinese people." -- Rep. Christopher H. Smith (R-N.J.)
Copyright 2014 DailyTech LLC. - RSS Feed | Advertise | About Us | Ethics | FAQ | Terms, Conditions & Privacy Information | Kristopher Kubicki
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## Gaußplatz [jatp]
Posted in pictures, Running, Travel with tags , , , , , , on September 22, 2017 by xi'an
## from least squares to signal processing and particle filtering
Posted in Books, Kids, Statistics, University life with tags , , , , , , , , on June 6, 2017 by xi'an
Nozer Singpurwalla, Nick. Polson, and Refik Soyer have just arXived a remarkable survey on the history of signal processing, from Gauß, Yule, Kolmogorov and Wiener, to Ragazzini, Shanon, Kálmán [who, I was surprised to learn, died in Gainesville last year!], Gibbs sampling, and the particle filters of the 1990’s.
## Gauss to Laplace transmutation interpreted
Posted in Books, Kids, Statistics, University life with tags , , , , , , on November 9, 2015 by xi'an
Following my earlier post [induced by browsing X validated], on the strange property that the product of a Normal variate by an Exponential variate is a Laplace variate, I got contacted by Peng Ding from UC Berkeley, who showed me how to derive the result by a mere algebraic transform, related with the decomposition
(X+Y)(X-Y)=X²-Y² ~ 2XY
when X,Y are iid Normal N(0,1). Peng Ding and Joseph Blitzstein have now arXived a note detailing this derivation, along with another derivation using the moment generating function. As a coincidence, I also came across another interesting representation on X validated, namely that, when X and Y are Normal N(0,1) variates with correlation ρ,
XY ~ R(cos(πU)+ρ)
with R Exponential and U Uniform (0,1). As shown by the OP of that question, it is a direct consequence of the decomposition of (X+Y)(X-Y) and of the polar or Box-Muller representation. This does not lead to a standard distribution of course, but remains a nice representation of the product of two Normals.
## re-re-relevant statistics for ABC model choice
Posted in Books, Statistics, University life with tags , , , , , , on March 18, 2013 by xi'an
After a very, very long delay, we eventually re-revised our paper about necessary and sufficient conditions on summary statistics to be relevant for model choice (i.e. to lead to consistent tests). Reasons, both good and bad, abound for this delay! Some (rather bad) were driven by the completion of a certain new edition… Some (fairly good) are connected with the requests from the Series B editorial team, towards improving our methodological input. As a result we put more emphasis on the post-ABC cross-checking for the relevance of the summary choice, via a predictive posterior evaluation of the means of the summary statistic under both models and a test for mean equality. And re-ran a series of experiments on a three population population genetic example. Plus, on the side, simplified some of our assumptions. I dearly hope the paper can make it through but am also looking forward the opinion of the Series B editorial team The next version of Relevant statistics for Bayesian model choice should be arXived by now (meaning when this post appears!).
## 17 equations that changed the World (#1)
Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on October 15, 2012 by xi'an
I do not know if it is a coincidence or if publishers were competing for the same audience: after reviewing The universe in zero word: The story of mathematics as told through equations, in this post (and in CHANCE, to appear in 25(3)!), I noticed Ian Stewart’s 17 equations That Changed the World, published in 2011, and I bought a copy to check the differences between both books.
I am quite glad I did so, as I tremendously enjoyed this book, both for its style and its contents, both entertaining and highly informative. This does not come as a big surprise, given Stewart’s earlier books and their record, however this new selection and discussion of equations is clearly superior to The universe in zero word! Maybe because it goes much further in its mathematical complexity, hence is more likely to appeal to the mathematically inclined (to borrow from my earlier review). For one thing, it does not shy away from inserting mathematical formulae and small proofs into the text, disregarding the risk of cutting many halves of the audience (I know, I know, high powers of (1/2)…!) For another, 17 equations That Changed the World uses the equation under display to extend the presentation much much further than The universe in zero word. It is also much more partisan (in an overall good way) in its interpretations and reflections about the World.
In opposition with The universe in zero word, formulas are well-presented, each character in the formula being explained in layman terms. (Once again, the printer could have used better fonts and the LaTeX word processor.) The (U.K. edition, see tomorrow!) cover is rather ugly, though, when compared with the beautiful cover of The universe in zero word. But this is a minor quibble! Overall, it makes for an enjoyable, serious and thought-provoking read that I once again undertook mostly in transports (planes and métros). Continue reading
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- Find the obsevalility canonicel fam stc sTem
Question:
- Find the obsevalility canonicel fam stc sTem
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June 8, 2012
The rain equations
A look at how the Duckworth-Lewis and VJD methods work in different situations
39
Over the last week, the rain rule used in international cricket has come in for plenty of scrutiny after the Duckworth-Lewis method was recommended by ICC's Cricket Committee as the one that should be used for all international games. The move prompted intense protest from V Jayadevan, an engineer from India, who has devised an alternative method, which was also evaluated by the committee. Jayadevan has claimed he didn't get a fair hearing, while the ICC has refused to get into specifics, only stating: "The committee unanimously agreed that there was no evidence of any significant flaws in the D/L method nor did the committee believe that any improvements could be offered by the VJD method."
Is one of the methods superior to the other? That's difficult to answer without knowing all the facts, but it's also true that there are differences between the two that come to the fore, especially in extreme cases. A study of a few scenarios also brings out a mathematical anomaly with the Duckworth-Lewis method. (Some of these examples have been provided by Jayadevan, but the results have been independently verified.)
Scenario 1: The team batting first in an ODI scores 50 (or 100) in 20 overs when its innings is cut short, and the second team gets 20 overs to chase down the target. Let's examine the target scores by both methods in cases when the team batting first has lost 0, 1 and 2 wickets (see table below).
The aspect that stands out is that by the D/L method the targets, and the projected scores, vary widely. The target for the team batting second is 140 when the team batting first is 50 without loss, and 95 when the team batting first is 50 for 2, a difference of 45 runs. By the VJD method, the difference is only ten, to reflect the fact that losing two wickets after 20 overs doesn't significantly impact a team's ability to score, given that they still have eight wickets in hand for 30 overs.
The other aspect about these targets is the projected score, which is the estimated total that a team would have reached in 50 overs from a given situation. From a score of 50 without loss, D/L estimates that the first team would have ended up scoring 231, which means they'd have scored 181 more in the remaining 30 overs. That score, however, dips to 156 when the 20-over score is 50 for 2, which means they're expected to add only 106 more in the last 30 overs, with eight wickets in hand. Is that a harsh call on the batting abilities of those coming in at No. 4 and lower, or is it fair?
With the rival VJD method, the projected scores are much closer, again suggesting the belief that the loss of two wickets after 20 overs won't significantly alter the scoring ability of a team: with all ten wickets in hand, a score of 50 in 20 overs translates into 191 in 50; with two wickets down, the score drops by only 19 runs, as opposed to 75 in the D/L method.
Scenario D/L target Projected score VJD target Projected score 50/0 in 20 overs, target in 20 140 231 113 191 50/1 in 20 overs, target in 20 115 188 108 181 50/2 in 20 overs, target in 20 95 156 103 172 100/0 in 20 overs, target in 20 179 344 170 325 100/1 in 20 overs, target in 20 172 320 164 310 100/2 in 20 overs, target in 20 163 288 158 296
Also, the difference in D/L targets between scores of 100 for no loss and 50 for no loss in 20 overs is just 39 (179 minus 140). However, for the same scores but with two wickets down, the difference increases to 68. In the VJD method, this difference stays constant (57, 56 and 55), which intuitively makes more sense.
Scenario 2: Five-over par scores in high-scoring Twenty20 matches
The ICC has ruled that five overs per innings is enough to constitute a complete Twenty20 game, which means any system should be able to work out reasonable results even for such a short game. (It's another matter that the ICC probably needs to rethink this policy - five overs is far too short a period for a complete innings in a cricket match.)
Here's a look at the five-over par-score tables under D/L and VJD for high-scoring Twenty20 matches. The totals here range from 200 to 280, and a look at the five-over par scores shows major differences between the two systems. With D/L, the maths seems to be wrong - the par scores at six and seven wickets down are lower for a target of 281 than for a target of 201. A team chasing 201 has a par score of 95 when they are six down, but the par score actually reduces by one run when the target goes up by 60. From the table below, it's clear that 116 for 7 in six overs is a winning total when the target is 261, but is three runs short of the par score when the target is 201. For scores of over 200, the D/L par scores are sluggish and actually reduce as the targets get higher.
With VJD, on the other hand, the par scores move up with the targets, which is as it should be, but those pars are also much higher than the D/L ones. For a target of 200, for example, the par score at six down is 126 in five overs, which means the last four wickets need to score 75 in 15 overs with four wickets in hand. Is that too low an asking rate, given that the rate at the beginning of the innings was ten an over, or is it justified given that six top-order wickets have already fallen?
Team 1 total D/L par-6 down 7 down VJD par-6 down 7 down 200 95 119 126 145 220 97 121 139 160 240 96 119 151 174 250 95 118 158 182 260 94 115 164 189 280 92 111 177 203
Let's look at a couple more situations where the par scores don't quite conform to cricketing logic. In a chase of 200, a score of 104 for 1 after 11 overs is below par - ie, the team batting second would have lost with that total - but a score of 105 for 4 after ten, or 104 for 5 after nine, is a winning total according to D/L. You'd expect the loss of four or five wickets to have a more adverse impact on par scores, but it doesn't.
The par scores in the VJD method, meanwhile, reacts sluggishly to the fall of the first couple of wickets, but springs into action thereafter. So, the par scores after ten overs in this method are 91 for 0, 92 for 1, 92 for 2, and 93 for 3, but jumps to 107 for 4 and 122 for 5 - the VJD logic is that, with only ten overs to go, it doesn't matter much if a team has ten wickets in hand or eight. Comparing with the situations given above in the D/L method, the 11-over par is 101 for 1, the ten-over par is 107 for 4, and the nine-over par is 119 for 5.
Thus, while 104 for 5 after nine is a winning total under D/L, a team would have to score 120 for 5 under the VJD method at the same stage to win.
Scenario 3: Internal consistency in Twenty20 targets
Here's another look at internal consistency of the two methods, but in Twenty20 matches. Like in the first case, this looks at the targets set by each method when teams have made two sets of scores (35 and 50), losing 0, 1 and 2 wickets. In the VJD method, there's little difference in the targets regardless of the wickets lost; in D/L, the targets don't change much when the score is 50 - 50 for no loss gives a target of 63 and 50 for 2 throws up 60 - but the wickets influence the target much more when the score is 35 - the difference there is ten runs. What's interesting is that there's a difference of only six runs in the D/L target between scores of 35 without loss and 50 without loss; the target difference between 35 for 2 and 50 for 2 goes up to 13. In the VJD method, the difference remains constant at 12.
Scenario D/L target in 6 VJD target in 6 35/0 57 53 35/1 52 52 35/2 47 51 50/0 63 65 50/1 62 64 50/2 60 63
These examples don't provide an exhaustive list of differences between the methods, but they offer a glimpse into some of the salient ones. The ICC has so far refused to get into specific advantages and disadvantages of the two - and Duckworth-Lewis haven't said much either - which has allowed the debate to degenerate along regional lines in the media. Are there areas where the D/L method outperformed VJD? Are there examples to illustrate D/L superiority? Are there mathematical flaws in the VJD method leading to erroneous outputs in certain situations, which made the cricket committee choose the D/L method? The ICC could start by offering answers to some of these questions.
• Dummy4 on June 9, 2012, 14:35 GMT
Since these days all the matches are administered by neutral officials, my suggestion is that all five (two on field umpires, third umpire, reserve umpire and the match referee) should form a jury and vote or allot marks to both the teams in such conditions and best of five should win. Alternatively, highest & lowest from the marks given by the officials be dropped and the team getting maximum from the rest three should win. Result should be a tie, in case both get equal marks. believe this is a widely used practice in games judged by a jury. ICC can provide a guide line to officials for awarding marks in such conditions.
• Krishna on June 9, 2012, 6:50 GMT
Am not sure if either methods consider the economy rates of the bowlers, strike rate of the not out batsman when arriving at the numbers. These are important figures. If it looks a bit overcast, the captain bowling first might employ his best bowler fully before rain intervenes and he might complete 10 overs for just 30 runs by the 35th over and lets say rain arrives then and reduces it to a 37 overs per side match. The rule should consider the worst economy rate of the bowlers that have bowled in first innings for the number of overs the best bowler bowled extra than the max number of overs allocated to the team bowling second. Also if the chasing team loses a wicket at 50 runs in the 6th over and the batsman that got out had contributed only 10 % of the score with a strike rate of 30, then there should not be a significant rise in the target for the loss of 1 wicket beca the one who has done all the handwork is still out there and could pull it off. These things should be factored in
• Krishna on June 9, 2012, 6:38 GMT
Everybody unanimously agree that D/L method is the ultimate scale? Think again. Why go mathematically? don't we see that the D/L method is now biased to the team that chases in a rain affected match? as a player, as a captain, as a cricket follower, everyone knows that if it is a rain affected match, the side batting second has an edge. so why not change? and is the DL method factoring in the changing powerplay rules??
• sanjeewa on June 9, 2012, 5:28 GMT
It's ridiculous to see D/L targets when 200 to 280 reduce when 6 down 95 to 92.So, It's massive fail.How about is this happen in T20 WC final or semi like 92 WC semi?I don't think there are many differences in two methods.Think Engineer who built VJD improved the DL.This should be considered and evaluated.It should be stop happening things like SCG in1992.
• Gururaj on June 9, 2012, 4:07 GMT
Several people have suggested replaying the match on a reserve day as the fairer alternative to adjusted scores on a rain-shortened day. In principle, I agree with this. However, I think that instead of replaying the match from scratch on the reserve day, it is better to continue the match from where it is suspended on the first day. This way, there is a better chance of finishing the game. After all, if it rains on one day, it is also possible to get a similar amount of rain the next day as well. Better use of the reserve day in my opinion.
• ravikanth on June 9, 2012, 3:15 GMT
Rajesh, Can you tell us what the VJD method says about THE famous SA Vs Eng match from 1992 world cup? If it comes out with similar target as D/L, no point discussing it. http://www.espncricinfo.com/ci/engine/match/65155.html
• Dummy4 on June 9, 2012, 0:15 GMT
always hated D/L; why not resume the match next day; loved that option in 99 world cup
• Dummy4 on June 8, 2012, 23:58 GMT
Rajesh, look at the more likely ODI scenario of 100 runs in 20 overs. VJD and D/L targets are less than 5% of each other. What's the fuss? As we say here in the states: "Don't fix it if it ain't broke."
• Stephen on June 8, 2012, 23:39 GMT
Big issue for both systems re: T20 targets is that they still need more games for the equations to work.
• Dummy4 on June 8, 2012, 22:16 GMT
@declaration - well said. It's better to accept 'no result' or have a reserve day and replay the match wherever possible. Both these methods are based on statistics/historical performances (that are supposed to work well for most scenarios) and one can always find or create examples to prove or counter-prove a point. Picking only extreme examples to discredit DL method also seems a little unfair. Maybe the DL method needs some tweaking in this new age of high scoring T20s. But I still think at the end of this all, we shouldn't even be trying to predict/extrapolate scores. It's a futile exercise. The beauty of the game is you never know when And planning to use such methods in World cup matches is just outrageousl.
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# Fractional Uncertainty
1. Jan 19, 2017
### RaduAndrei
<Moderator note: Thread moved from General Physics hence no formatting template shown>
The fractional uncertainty is defined as:
uncertainty/measured value.
So for 2 cm +/- 1 cm we have 50%. For 9 cm +/- 1 cm we have 11.1%.
My question is what if the measured value is 0 cm? How is the fractional uncertainty defined in this case?
2. Jan 19, 2017
### Staff: Mentor
I moved this into the homework section, as it belongs there.
With this definition the fractional uncertainty isn't defined in case the measured value is zero. You may call the result infinite large, but I would rather consider the reciprocal quotient which makes more sense in my opinion.
3. Jan 19, 2017
### RaduAndrei
The reciprocal quotient? English is not my first language. Could you explain what that means?
Does it mean to consider instead measured value/uncertainty?
4. Jan 19, 2017
### Staff: Mentor
Yes. This is what I meant. In this case a zero measurement would give a zero quotient, which can be interpreted as "no result", as it doesn't allow any statements about the accuracy. Furthermore this quotient gets undefined (or infinitely large), if the uncertainty is zero, which makes sense.
However, you should of course use whatever your book or teacher says. It's simply my opinion that (measured value / uncertainty range) is easier to interpret: zero if measurement is zero, infinitely large, if uncertainty is zero. The original quotient is just undefined for zero measurements.
5. Jan 19, 2017
### RaduAndrei
Ok, but still it does not really make sense for a measured value of 0.
Consider the definition uncertainty/measured value. The fractional uncertainty is 50% for 2+/-1 and 11.1% for 9+/1. If I change the uncertainty, ex 2, then it is 100% for 2+/-2 and 22.2% for 9+/-2. So it is kinda intuitive. As the measured value is much bigger than the uncertainty, the fractional uncertainty decreases. For a measured value of 0, the definition breaks, whatever the uncertainty. But I can say intuitively that for 0+/-1 the 'fractional uncertainty' (whatever its definition is) should be smaller than for 0+/-100. Right?
Consider the definition measured value/uncertainty. Whatever the uncertainty is, if the measured value is 0, then the fractional uncertainty is 0 always. But clearly there is a difference between having 0+/-1 or even 0+/-0.001 and having 0+/-100.
In the first case the fractional uncertainty is not defined, but in the second case it is 0. Intuitively there should be a difference between 0+/-1 and 0+/-100. And the definition must capture this difference.
For me there is no difference between having a zero result or an infinite result for a measured value of 0. The two definitions could work just as fine. What I am interested in is a definition that says "as the difference between the uncertainty and the measured value of 0 is larger and larger, the fractional uncertainty becomes larger and larger''. Maybe the definition could be: uncertainty/(measured value + 1)
Last edited: Jan 19, 2017
6. Jan 19, 2017
### haruspex
You can say what you like intuitively, but that does not make it meaningful. It is unbounded in both cases.
That would be a definition of fractional precision, I assume. So 0 uncertainty is infinite precision, and vice versa.
7. Jan 20, 2017
### RaduAndrei
But it is meaningful. Say you want to measure the speed of some object. One thing is to say that you measured 0+/-1 m/s and another thing is to say you measured 0+/- 100 m/s. The uncertainty is different and thus this must reflect in the fractional uncertainty too. Right?
8. Jan 20, 2017
### haruspex
Those are meaningful statements, but there is no reason that "fractional uncertainty" should be meaningful for both.
My supermarket used to provide plastic bags for no charge, now they cost 5c. What is the percentage increase?
9. Jan 20, 2017
### RaduAndrei
Why not?
For the measured value 9, if I vary the uncertainty from 1 to 9 then the fractional uncertainty varies from 11% to 100%. Maybe I want to quantify this change for the zero value as well.
Those are meaningful statements. But I want to express them in numbers, not words.
I see your point.
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# Numeric literals in other than base 10 - was Annoying octal notation
Mensanator mensanator at aol.com
Tue Aug 25 20:45:28 CEST 2009
```On Aug 25, 9:14 am, Steven D'Aprano <st... at REMOVE-THIS-
cybersource.com.au> wrote:
> On Mon, 24 Aug 2009 18:01:38 -0700, Mensanator wrote:
> >> If you want your data file to have values entered in hex, or oct, or
> >> even unary (1=one, 11=two, 111=three, 1111=four...) you can.
>
> > Unary? I think you'll find that Standard Positional Number Systems are
> > not defined for radix 1.
>
> Of course not. But unary isn't a positional number system. It's a tally
> system, like my example above shows. Roman numerals are another tally
> system. Like Roman numerals, the disadvantages of unary are that you
> can't represent negative numbers, zero, or fractions, and anything but
> addition and subtraction is difficult. But if you want to use it, perhaps
> out of a sense of sadism towards your users, it's easy:
>
> def int2unary(n):
> return '1'*n
>
> def unary2int(s):
> n = 0
> for c in s:
> if c == '1': n+=1
> else: raise ValueError('invalid unary string')
> return n
But without insignificant leading 0's, I fail to see the relevance
of unary to this discussion. And what would you call a tally system
of radix 2? Certainly not binary.
>
> --
> Steven
```
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+0
# need help
0
108
2
Abigail can mow a particular lawn in 6 hours, but Bob can do it in only 4 hours. If Abigail and Bob work together, how many minutes would it take them to mow the lawn?
Jun 29, 2020
#1
+2152
0
Abigail in 1 hour: 1/6 of the lawn
Bob in 1 hour: 1/4 of the lawn
Together in 1 hour: 1/6 + 1/4 = 5/12 of the lawn
They will mow the lawn in 12/5 hours, or 12*12=144 minutes
Jun 29, 2020
#2
+28021
+1
1/6 + 1/4 = 1/x
x = 12/5 hr = 144 minutes
Jun 29, 2020
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# halp
0
101
1
1. How many cubic polynomials f(x) are there such that f(x) has nonnegative integer coefficients and f(1) = 9?
2. How many ordered quadruples (a,b,c,d) satisfy, a + b + c + d = 18,
where a,b,c,d are integers such that |a|, |b|, |c|, |d| are each at most 10?
May 17, 2020
#1
+21953
+1
Hint for #1:
cubic polynomial: f(x) = a·x3 + b·x2 + c·x + d
f(1) = a·(1)3 + b·(1)2 + c·(1) + d = 9
f(1) = a + b + c + d = 9
Since each of the coefficients must be a positive whole number, the values for a, b, c, and d must be:
(in some order) 1, 1, 1, 6
1, 1, 2, 5
1, 1, 3, 4
1, 2, 2, 4
1, 2, 3, 3
2, 2, 2, 3
Now, the problem is to find how many different ways each of the above can written.
May 17, 2020
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Dimension of sum and intersection of vector space.
I am trying to understand the proof of the following: Suppose $U,W$ are vector subspace of $V$, then $\dim (U+W)+\dim (U \cap W)= \dim (U) +\dim (W).$
The proof goes like this: Let $S: V \rightarrow V/W$ be the natural surjection. Then we have $\dim (V) = \dim (W) +\dim (V/W)$ by rank-nullity. Now let $T: U \rightarrow (U+W)/W$. Then we have $\dim \ker (T)= \dim (U \cap W)$ and $\dim Im (T)= \dim (U+W) - \dim (W)$ and the result follows.
Basically I don't understand what is going on after "Now let $T$..." I don't understand how is $T$ actually define, and why the rank and nullity of $T$ equals that (which I think will be clear once I know how $T$ is defined), could someone please help, thanks!
-
3 Answers
$T$ is defined as the composition $U\to U+W\to (U+W)/W$, where the first map is just the inclusion, and the second map is the canonical projection.
-
Looks like $T$ is the inclusion of $U$ into $U + W$ followed by the quotient map to $(U + W)/W$.
In this interpretation, an element $u$ of $U$ maps to $0$ if and only if $u \in W$, so $\ker(T) = U \cap W$. Further, $T$ is (more-or-less obviously) surjective, so $\dim \operatorname{Im}(T) = \dim(U + W)/W = \dim(U + W) - \dim W$.
-
$U+W$ is the subspace of $V$ that consists of vectors of the form $u+w$, where $u\in U$, $w\in W$. As $W$ is a subspace of $U+W$, one can consider the quotient $(U+W)/W$, which is the space of all vectors $(u+w) + W$.
Now, $T$ is the linear function that takes $u$ to the class of $u$ in this quotient, which is $u+W$. If $u$ is in the kernel of $T$, it means that $u+W = W$, i.e that $u\in W$, hence $\ker(T) \subseteq U\cap W$, and the other inclusion is true also, since if $u\in U\cap W$, $u\in W$ and $u+W = W$. We have proved $\ker(T) = U\cap W$.
As for $\mathrm{im}(T)$: $T$ is surjective, because if $(u+w)+W\in (U+W)/W$, this vector equals $u+W$, and $u$ is a preimage for this. So $\dim \mathrm{Im}(T) = \dim (U+W)/W = \dim (U+W) - \dim W$ as you already now (it works as your first equality, with $S$).
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# Algebra I
you use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0,993. How confident can you be that your predicted value will be reasonably close to the actual value?
a. I can't be confident at all; this is about as close to a random guess as you can get
b. I can be a little confident; it might be close, or it may be way off
c. I can be very confident; it will be close, but it probably won't be exact
d. I can be certain that my predicted value will match the actual value exactly*****
1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. correct.
1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
bobpursley
2. Guys, It Is B, D, B, C, C Bob Is INCORRECT
1. 👍
2. 👎
3. ℹ️
4. 🚩
3. @QouKa is correct! I got 100%
1. 👍
2. 👎
3. ℹ️
4. 🚩
4. QuoKa is right 100% on connexus
1. 👍
2. 👎
3. ℹ️
4. 🚩
5. What number is this ??
1. 👍
2. 👎
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4. 🚩
6. they are all wrong. the correct ansers are
A,B,C,D,C
1. 👍
2. 👎
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4. 🚩
7. Im in SCCA and doing lesson 8 unit 3, the correct answers are under. I got a 100% :)
1. Which type of correlation is suggested by the scatter plot? B. - Negative correlation
2. Which type of correlation is suggested by the scatter plot? D. - No correlation
3. What is the correlation coefficient for the set of data? Round your answer to the nearest thousandth. B. - 0.989
4. About how tall would you expect one of these trees to be after 22 years? C. - 44.25 ft.
5. You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.993. How confident can you be that your predicted value will be reasonably close to the actual value? C. - I can be very confident; it will be close, but it probably won't be exact.
Have a great day:)
1. 👍
2. 👎
3. ℹ️
4. 🚩
8. huh
1. 👍
2. 👎
3. ℹ️
4. 🚩
## Similar Questions
1. ### math
Make a line plot for the set of data. 61 58 57 64 59 57 64 58 56 57 A teacher asks her class of 22 students, "what is your age?" Their responses are shown below. 19 19 14 16 19 19 16 16 15 17 16 17 16 15 14 15 15 17 14 16 15 Find
2. ### science
As part of their job, meteorologists use data to make weather predictions. How accurate are their predictions? What are other scenarios in which you would use data to make a prediction? How would you defend your prediction using
3. ### Math Help me PLZ!
1: What is the median of the data set: 25,8,10,35,5,45,40,30,20 A:10 ~ B:22.5 C:25 D:27.5 2: What is the upper quartile of the given data set: 25,8,10,35,5,45,40,30,20 A:35 B:37.5 ~ C:37 D:40 3: What is the lower quartile of the
4. ### Math
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.109. How confident can you be that your predicted value will be reasonably close to the
1. ### Algebra
1.What is the solution of the system? y=9x-2 y=7x+3 A.(-5/2,41/2) B.(5/2,41/2) C.(5/2,-41/2) D.(-5/2,-41/2) 2.The table below shows the height (in inches) and weight (in pounds)of eight basketball players. Height=67, 69, 70, 72,
2. ### Algebra 1
You use a line best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.993. How confident can you be that your predicted value will be reasonably close to the
3. ### algebra
Two similar data sets are being compared. The standard deviation of Set A is 4.8. The standard deviation of Set B is 6.5. Which statement about the data sets is true? a)The mean of the data in Set B is greater than the mean of the
4. ### MATH 7
1: What is the median of the data set: 25,8,10,35,5,45,40,30,20 A:10 ~ B:22.5 C:25 D:27.5 2: What is the upper quartile of the given data set: 25,8,10,35,5,45,40,30,20 A:35 B:37.5 ~ C:37 D:40 3: What is the lower quartile of the
1. ### math
A runner times herself to see how long it takes her to run different distances. The table shows the runner's times (in minutes) for running several distances (in miles). Miles: 1|2|3|4|6|8|10|12 Time: 7|16|30|35|57|75|106|132
2. ### Algebra 1
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.793. How confident can you be that your predicted value will be reasonably close to the
3. ### Algebra
3. What is the correlation coefficient for the set of data? Round your answer to the nearest thousandth. 0.014 0.989 0.075 4. About how tall would you expect one of these trees to be after 22 years? 22.31 ft. 35.2 ft. 44.25 ft.
4. ### Algebra 1- Just one question please :)
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.015. How confident can you be that your predicted value will be reasonably close to the
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## Problem A. Access Control Lists ≡
• problems
Author: ACM ICPC 2008-2009, NEERC, Northern Subregional Contest Time limit: 3 sec Input file: access.in Memory limit: 256 Mb Output file: access.out
### Statement
Nick is developing a new web server. The feature he is working on now is support for access control lists. Access control list allows to restrict access to some resources on the web site based on the IP address of the requesting party.
Each IP address is a 4-byte number that is written byte-by-byte in a decimal dot-separated notation "byte0.byte1.byte2.byte3" (quotes are added for clarity). Each byte is written as a decimal number from 0 to 255 (inclusive) without extra leading zeroes. IP addresses are organized into IP networks.
IP network is described by two 4-byte numbers — network address and network mask. Both network address and network mask are written in the same notation as IP addresses.
In order to understand the meaning of network address and network mask you have to consider their binary representation. Binary representation of IP address, network address, and network mask consists of 32 bits: 8 bits for byte0 (most significant to least significant), followed by 8 bits for byte1, followed by 8 bits for byte2, and followed by 8 bits for byte3.
IP network contains a range of 2n IP addresses where 0 ≤ n ≤ 32. Network mask always has 32 − n first bits set to one, and n last bits set to zero in its binary representation. Network address has arbitrary 32 − n first bits, and n last bits set to zero in its binary representation. IP network contains all IP addresses whose 32 − n first bits are equal to 32 − n first bits of network address with arbitrary n last bits.
For example, IP network with network address 194.85.160.176 and network mask 255.255.255.248 contains 8 IP addresses from 194.85.160.176 to 194.85.160.183 (inclusive).
IP networks are usually denoted as "byte0.byte1.byte2.byte3/s" where "byte0.byte1.byte2.byte3" is the network address and s is the number of bits set to one in the network mask. For example, the IP network from the previous paragraph is denoted as 194.85.160.176/29.
Access control list contains an ordered list of rules. Each rule has one of the following forms:
• "deny from <IP network>" — denies access to the resource to any IP from the specified IP network.
• "deny from <IP address>" — denies access to the resource to the specified IP address.
• "allow from <IP network>" — allows access to the resource to any IP from the specified IP network.
• "allow from <IP address>" — allows access to the resource to the specified IP address.
When some party requests some resource its IP address is first checked against its access control list. The rules are scanned in order they are listed, and the first matching rule is applied. If none of the rules matches the IP address of the party, access is granted.
Given access control list and the list of requesting IP addresses, find out for each request whether it will be granted access to the resource.
### Input file format
The first line of the input file contains n — the number of rules in the access control list. The following n lines contain rules, one per line. IP network is always specified as "byte0.byte1.byte2.byte3/s".
The next line contains m — the number of IP addresses to check. The following m lines contain IP addresses to check, one per line.
### Output file format
For each request output 'A' if it will be granted access to the resource, or 'D' if it will not be granted access. Output all answers in one line, do not separate output by spaces.
### Constraints
0 ≤ n ≤ 100000, 1 ≤ m ≤ 100000.
### Sample tests
No. Input file (access.in) Output file (access.out)
1
4
allow from 10.0.0.1
deny from 10.0.0.0/8
allow from 192.168.0.0/16
deny from 192.168.0.1
5
10.0.0.1
10.0.0.2
194.85.160.133
192.168.0.1
192.168.0.2
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# Tertiary Catalogue
## Series: Numbers and Algebra
### Basic Index Laws: Games, Set, Match
This video demonstrates how to use index notation to establish index laws with positive integral indices and the zero index. Using the example of Grand Slam tennis tournaments, our narrator constructs his own school based tennis tournament draw...Show More
There's a lot of geometry on a basketball court! This video explores the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials through examples of lines on a basketball court,...Show More
A group of friends are planning a lunch and compare the costs of pre-made lunches versus making it themselves. They investigate their options by comparing total costs and per person costs. Calculations are determined with and without digital...Show More
Our presenter is interested in running her own café and decides to see what profit can be made from selling sandwiches. She works through the individual costs of sandwich ingredients to compare against café sandwich prices, then calculates her...Show More
### Destination Distances on a Cartesian Plane
When the Smithton River floods five local towns, a plane needs to drop supplies at each. A route needs to be determined that will reach the most affected areas first, while ensuring the plane has enough fuel between stops, and that the pilot...Show More
### Graphing Distance and Time: A Runner's Story
This video follows a runner graphing his running distance and speed. He explains what happened along the route that affected his speed, translating this information onto a graph and accounting for the varying steepness of gradients between...Show More
### Graphing Simple Parabolas and Circles
This video begins with a short introduction of everyday applications of circles and parabolas. Next, basic parabolas and circles are graphed using quadratic equations. Ideal for reinforcing concepts.
### Index Notation and Prime Factors
This video provides a short lesson on index notation and representing whole numbers as products of powers of prime numbers. Examples of raising base numbers to different powers are shown. Prime and composite numbers are explained and factor trees...Show More
### Line Graphs: Gradients and Midpoints
This video follows a sprinter graphing her distance and speed for two separate sprints. The first sprint is at a constant speed, resulting in a straight line graph. In the second sprint, her graph reflects three distinct intervals as her speed...Show More
### Perfect Squares and Square Roots
This video investigates and uses square roots of perfect square numbers to create and solve equations. Viewers will learn how to determine the square roots of perfect squares, and determine if a number is a perfect square using technology and...Show More
### Simultaneous Equations on the Golf Course
This video demonstrates how to solve simultaneous equations, using the example of golfers determining par and handicaps. Substitution, elimination and graphing software methods are all used to solve equations. Ideal for applying mathematical...Show More
### Solving Quadratic Equations in Cricket and Rowing
Our presenter applies algebraic knowledge of quadratic equations to two sports events. First, he determines the height of a batted cricket ball and the amount of time it is in the air. Next, he determines the speed at which a rower travels...Show More
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Video: Linear Equations in One Variable | Nagwa Video: Linear Equations in One Variable | Nagwa
# Video: Linear Equations in One Variable
Learn to solve linear equations involving just one unknown variable, some of which have one unique solution (e.g., 5๐ฅ + 3 = 18), some with infinitely many solutions (e.g., 4๐ฅ + 7 = 4(๐ฅ + 2) โ 1), and some with no solutions at all (e.g., 2๐ฅ + 3 = 2๐ฅ โ 2).
17:34
### Video Transcript
In this video, we are going to be looking at linear equations in one variable. Now first of all, letโs just make sure that we understand whatโs meant by the different parts of this title. So first of all, one variable, this just means that the equations weโre gonna look at are only going to involve one unknown letter, so they might involve ๐ฅ or ๐ฆ or ๐, but thereโs only going to be one letter involved in each of the equations that we look at.
The word linear means that the power of this variable, whatever it might be, is never going to be more than one, so our equations might involve for example the letter ๐ฅ and they might involve constant terms like plus three, but they wonโt involve terms like ๐ฅ squared or ๐ฅ cubed or anything that is more than just a simple ๐ฅ.
So here are some examples of the type of equations we might look at. All of them just involve one letter whether itโs ๐, ๐, ๐ฅ, or ๐ฆ, and the highest power of that letter is always just one.
Now weโre going to look at the different types of linear equation that you might encounter, and there are three different types that weโre going to look at.
The first type weโre going to look at are equations that have a unique solution. And what this means is that whatever the variable in the equation is, so suppose itโs ๐ฅ, there is only one single unique value of ๐ฅ that satisfies that particular equation.
So weโll see what we mean by this in the context of an example. So the equation weโre going to look at is this: five ๐ฅ plus three is equal to eighteen.
Now looking at that equation, you may be able to determine the value of ๐ฅ directly, but letโs think about a formal way to solve this equation. We want to work out the value of ๐ฅ that works in this equation. So the first thing we rea- need to do is to look at this plus three term. And in order to eliminate that plus three term, I would have to do the opposite, which is subtracting three. So I would have to do that to both sides of this equation. So on both sides of the equation, I would need to subtract three. And if I were to do that the next line of my working out, well if Iโve subtracted three, then I just have five ๐ฅ left on the left-hand side, and on the right-hand side if Iโve subtracted three from eighteen, I just have fifteen left.
The next step well Iโve got five ๐ฅ and I just want one ๐ฅ, so I would need to divide both sides of this equation by five. And so if I divide five ๐ฅ by five, I get ๐ฅ. And if I divide the other side by five, fifteen divided by five, Iโm left with three.
So what I have here is I have a unique solution. It tells me that the value of ๐ฅ must be equal to three, and three is the only value of ๐ฅ that will work in this equation. If I go back to the top and try to substitute in any other value of ๐ฅ, it wonโt work. I wonโt get eighteen when I multiply it by five and add three. So this is the first type of equation, those that have unique solutions where only one single value of ๐ฅ, or whatever letter it might be, actually works in the equation. And these are all equations that can be reduced to a particular type; they can be reduced to something of the form ๐ฅ is equal to ๐, where ๐ is just a constant, a number, so in our case ๐ฅ is equal to three.
Second type of linear equation is one that has infinitely many solutions, which means in fact any value of the variable will work, doesnโt matter what you choose it to be; any single value that you choose will work within the equation. So again, letโs look at it in the context of an example.
So here I have an equation and Iโm suggesting to you that in fact it has infinitely many solutions. So in order to see that the first step, well we might want to expand the bracket on the right-hand side of the equation.
So if I go ahead and do that, I have four ๐ฅ plus seven is equal to four ๐ฅ plus eight minus one. Now the next step I can do a bit of simplification on the right-hand side. Iโve got plus eight minus one, so thatโs gonna simplify to plus seven.
So Iโm left with this: four ๐ฅ plus seven is equal to four ๐ฅ plus seven. Now that is a statement that is always true, doesnโt matter what value ๐ฅ takes whether itโs three or minus two or something more complicated, ๐. This will always be true for any value of ๐ฅ; four ๐ฅ plus seven will always be equal to four ๐ฅ plus seven because theyโre the same expression.
If I do want to go a step further though, I can subtract four ๐ฅ from both sides. And if I do that, Iโm left with seven is equal to seven, which of course is true.
So this type of equation, infinitely many solutions, itโs the type of equation where it can be reduced to what we describe as ๐ is equal to ๐, so some number, some constant, is equal to itself. And in our case, seven is equal to seven. And if you can reduce an equation to a statement like that, then you know it has infinitely many solutions.
The third and final type is an equation which has no solution, and again weโll look at this in the context of an example. So I have the equation two ๐ฅ plus three is equal to two multiplied by ๐ฅ minus one. Now again, the first step here might be to expand the bracket on the right-hand side.
And if I do that, I have two ๐ฅ plus three is equal to two ๐ฅ minus two. Now you may be able to see straight away that that doesnโt work, that doesnโt make sense, because if I have a value of ๐ฅ and I double it and add three, how can I possibly get the same result as if I double it and subtract two? But if I want to see this a little bit more clearly, I can subtract two ๐ฅ from each side of this equation.
And if I do that, Iโm left with the statement three is equal to negative two. Now clearly, that statement is nonsense. Three is not equal to negative two, and so this equation has led to a contradiction. And for that reason, there are no solutions; there are no values of ๐ฅ that will work in the original equation because it leads to this contradiction.
So this final type this is whatโs known as an equation where we end up with the result ๐ is equal to ๐, where ๐ and ๐ are different numbers, so in our case three and negative two, but of course that canโt be the case.
So these are the three different types of linear equation that youโll come across: one that has a unique solution, one that has infinitely many solutions, and one that has no solution. And youโll know which situation youโre in depending on which of these three forms you can reduce it to. If you can reduce it to ๐ฅ equals ๐, we have a unique solution; if you can reduce it to ๐ equals ๐, we have infinitely many solutions; and if you woul- can reduce it to ๐ equals ๐, a contradiction because the numbers are different, then there are no solutions to the original equation.
So letโs look at an example. Iโm gonna begin with this: how many solutions are there to the equation five ๐ minus three is equal to three ๐ plus seven plus two ๐ minus ten? So we need to work out which of the three situations we saw on the last slide we are in in this case.
So letโs look at how we can simplify this equation. Now thereโs not much I can do on the left-hand side, so Iโll leave it as five ๐ subtract three, but there are things I can do on the right-hand side. I have three ๐ plus two ๐, so that gives me five ๐ overall, and then I have positive seven subtract ten, so that gives me negative three overall.
So Iโve taken the equation and Iโve reduced it to the statement five ๐ subtract three is equal to five ๐ subtract three. Now both of those sides are the same, so you may be able to conclude at this stage that there are infinitely many solutions to this equation. But if we just continue so that we can get it into one of those final forms we discussed on the last page, we might want to subtract five ๐ from each side of this equation. And if I do that, I will be left with negative three is equal to negative three, so what we can see is weโre in that situation where we had infinitely many solutions; weโre in the situation where we reduced the equation to ๐ is equal to ๐. In our case, ๐ is negative three.
So we conclude that there are infinitely many solutions to this equation, which means it doesnโt matter what the value of ๐ is; any value of ๐ that I choose, if I substitute it into the original equation, it will work; it will hold true.
Letโs look at a second example. So how many solutions are there to the equation four lots of ๐ฆ minus one plus two lots of ๐ฆ minus three is equal to six ๐ฆ plus four? So we want to simplify this equation a bit, and the first step would be to expand both of the brackets on the left-hand side.
So if I do that carefully, I have four ๐ฆ minus four plus two ๐ฆ minus six is equal to six ๐ฆ plus four. Now we need to go a couple of steps further, so we need to simplify this by collecting the like terms together. So we have four ๐ฆ plus two ๐ฆ, meaning I have six ๐ฆ overall, and then we have negative four take away six, meaning I have negative ten overall. And the right-hand side of the equation stays as it was, six ๐ฆ plus four.
So now we have the statement six ๐ฆ take away ten is equal to six ๐ฆ add four. If we carry on, if we subtract six ๐ฆ from both sides of this equation, now we have the statement negative ten is equal to four. And at this stage here, we can see well thatโs a contradiction; negative ten is not equal to four, and so what this tells us is we are in that third situation that we looked at before where we have two numbers that are not equal to each other. And therefore the equation doesnโt work; it doesnโt hold.
So what does that tell us? Well it tells us that weโre in that situation where we have ๐ is equal to ๐, and ๐ and ๐ are not the same, and therefore there are no solutions to this equation.
So there isnโt a single value of ๐ฆ that we can substitute into the original equation and get it to work because weโve got this contradiction: negative ten is equal to four. Now letโs look at a different type of question. So this question asked me to create an equation with infinitely many solutions, so I need to create one myself.
Now this means you must be in that second scenario, which means itโs an equation that can be reduced to ๐ is equal to ๐, where ๐ is some constant. So Iโm gonna start with that and Iโm gonna start with choosing ๐ to be five for example, and so Iโm gonna start with five is equal to five.
Now thatโs not a particularly complicated equation yet, so I want to do some other things to it. And the key point is, as long as I do the same thing to both sides of this equation, I will be able to build it up to a more complicated equation that still has infinitely many solutions.
So the first thing Iโm gonna do is Iโm gonna add four ๐ to both sides of my equation. So now I have four ๐ plus five is equal to four ๐ plus five. Still not a particularly complicated equation, so Iโm gonna try and change parts of this. On the left-hand side, Iโm gonna change that four ๐ for three ๐ add ๐.
So now I have three ๐ add ๐ plus five is equal to four ๐ plus five. And I would like to change something on the right-hand side, and Iโm gonna change that five to four add one.
So now I have the equation three ๐ plus ๐ plus five equals four ๐ plus four plus one. Itโs still exactly the same equation, but Iโve just changed parts of it as I go along. Like to do maybe one more thing by looking at this term or this part here, four ๐ plus four, and what Iโm gonna do is Iโm gonna take out a common factor of four from both of those terms so that I can write it as four multiplied by a bracket. So the left-hand side is gonna stay the same.
But on the right-hand side, Iโm gonna take out this common factor of four. Now in the bracket, I will have ๐ plus one so that when I expand that bracket, I still have four ๐ plus four, and I still need this plus one outside the bracket.
So now I have a much more complicated looking equation than the one I started off with, but it is still exactly the same equation.
I started with a statement I wanted to end up with, five is equal to five, and then I just made sure I did the same thing to both sides, so I introduced this extra four ๐ to both sides. Then I manipulated it differently, but I never added or subtracted anything from one side that I didnโt do to the other. I just wrote it in a slightly different format, and itโs left w- me with a very different looking equation, but one that still has infinitely many solutions.
One final example, letโs look at creating an equation with a unique solution. So my equation is to only work for one particular value of the variable, so Iโm gonna choose that the letter Iโm gonna use in this equation is the letter ๐, and Iโm gonna choose that the solution to my equation I would like it to be negative three. So Iโm gonna start with ๐ is equal to negative three.
Now I want to build up my equation, so again I need to make sure I do exactly the same thing to both sides of this equation. So first of all, I am going to double both sides of my equation. And if I do that, well if I double ๐, I will have two ๐, and if I double negative three, I will have negative six.
So now I have the equation two ๐ is equal to negative six. Now I would like to do something else; this- so I would like to subtract four from both sides of the equation. So on the left-hand side, I will have two ๐ subtract four, and on the right-hand side, well if Iโve got negative six and I subtract four, now Iโm going to have negative ten.
Next, I think Iโd like to write the two ๐ differently, and Iโd like to think of it as five ๐ minus three ๐, so Iโm just gonna replace two ๐ with five ๐ minus three ๐. So now I have five ๐ minus three ๐ minus four equals minus ten.
The final thing, well I think Iโd like to have ๐ on both sides of this equation. So Iโd like to move this negative three ๐. Iโd like to have it over on this side of the equation here. So in order to achieve that, I need to add three ๐ to both sides of this equation.
So if I add three ๐ to both sides, well on the left-hand side, Iโll now have five ๐ subtract four, and on the right-hand side, Iโll have three ๐ subtract ten.
And Iโll finish there for this equation. So what I did I started off with a statement, I started with ๐ is equal to negative three, and then I just built up from there. I did the same thing to both sides, so doubling, subtracting four, adding three ๐, but Iโve built up a much more complicated looking equation than the one I initially started off with. But itโs still exactly the same equation. And if I were start here and solve, I would end up with that same solution: ๐ is equal to negative three.
So there you have a summary of the three different types of linear equation that you might encounter, how you can determine which type of equation you have, and how you can work backwards to create an equation that either has a unique solution, infinitely many solutions, or no solutions.
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# Mathematics in the Movies
Photograph by David Young
At the wonderful National Cinema Museum, Turin – holiday time this week!
Thinking about Maths in the movies led me to this great collection of movie clips featuring Mathematics from Harvard University.
We must of course include Abbot & Costello showing that 7×13=28!
Mathbits.com includes a section on using movie clips in the mathematics classroom. The site suggests several possible movie clips to use and has accompanying worksheets. The Abbott & Costello clip mentioned above is included, the MathsBits worksheet is here.
I loved Donald in Mathmagic Land as a child.
For a series of excellent articles see Plus Magazine’s Mathematics in Films.
For a very comprehensive database of mathematics mentioned anywhere is a movie try MMDB – The Mathematical Movie Database from Burkard Polster and Marty Ross.
From Numberphile, Math and Movies (Animation at Pixar) we learn how 3D aminated characters look so smooth.
More from Pixar, see Pixar: The math behind the movies, Tony DeRose on TEDEd; note that this link from TEDEd provides not just the movie but a complete lesson. (See also this article on Pixar’s research on The Verge.)
From SchoolTube, Math in the Movies
If all this inspires you to think about a job in digital animation – see Maths in motion on the excellent Maths Careers site.
I really like the song ‘Math is a wonderful thing’ from School of Rock.
These have gone down well with students, particularly the Circle Song!
The Klein Four are a bit beyond school Mathematics, you may appreciate this if you are studying for a Mathematics degree!
# Iterative Methods
Looking at the new content for UK GCSE Mathematics a completely new entry on the specification is “find approximate solutions to equations numerically using iteration”.
Teaching the new specification this year I needed to work on this and wrote this post;
GCSE New Content – Iterative Methods for Numerical Solution of Equations.
I see from my blog Statistics that this is a very popular post so have made it my first summer holiday job to update it.
Note the additional section on Further Resources / Questions (scroll down the post).
# Low Stakes Testing in the Mathematics Classroom
Please note – a completely new version of this presentation with many more resources and additional ideas will be presented at the BCME Conference, April 2018. Following my sessions, I will update all relevant pages
Low Stakes Testing in the Mathematics Classroom (PowerPoint File, takes a few moments to download)
Or use this shorter version to see the slides on the student survey on low stakes tests.
Mini Tests Colleen Young for PowerPoint
Slides from the BERA Conference, Learning from the classroom – Practitioner research in mathematics education – July 2016
There are many hyperlinks provided in the presentation, for ease of access these are also provided below:
# End of term…
Relay from Chris Smith
The end of term approaches. I will certainly be using this great Summer Relay; students can have a more informal lesson but still do some useful maths! See Relays from Chris Smith. Note there is a complete set; I used his Valentine relay very successfully this year! Featured in Mathematical Miscellany#2.
For more end of term activities, see the End of Term Activities page under the I’m Looking for … menu.
This holiday I’ll be doing my usual tidying up and also updating my Results apges with any UK Statistics.
Before that I am very much looking forward to this Saturday’s BERA (@BERANews) Event, Learning from the classroom – Practitioner research in mathematics education where I will be speaking myself on the value of Lows Stakes Testing in the Mathematics Classroom and enjoying presentations from other speakers including the Keynote speaker, Dr Alison Clark-Wilson (@AliClarkWilson Institute of Education, University of London @IOE_London). The event has been convened by Dr Alf Coles (@AlfColes University of Bristol) and Dr d’Reen Struthers (Institute of Education, University of London).
# The Standards Unit – Mathematics
This is an outstanding resource – there are so many excellent activities here for the secondary classroom.
The resources are hosted by Nottingham University, including all the pdf files very clearly indexed. Note that this site includes the complete set of resources including the software; however, this software no longer works on modern browsers and mobile devices, but see note below for HTML5 versions.
Tom Button has rewritten the Traffic Simulations in GeoGebra for A5: Interpreting Distance-Time Graphs with a Computer.
##### See also this post onWisweb Applets HTML5which has applets and lessons using the programs referred to in the Standards Unit. These wonderful applets were created by Utrecht University, they have built the learning environment Numworx around these.
The Professional Development resources are excellent. Look at PD1 ‘Getting Started’ for example, note PD1.4 on page 9 – 8 Principles for Effective Teaching.
IWB Materials This website has come about as a result of the NCETM research project: Enabling enhanced mathematics teaching with some interactive whiteboards (September 2006- September 2008) and was supported by the IWB research team at Keele University and the Spire Maths team.
PowerPoint Files
MMT has written a set of PowerPoint files for almost all of these excellent resources, he has made them – in his own words ‘classroom ready’. MMT has provided the resources in an editable format so that they can be tweaked to your own requirements. Thank you MMT! These files are available directly from Dropbox; note they are also hosted on Craig Barton’s site.
Standards Unit A1:Expressions – MMT PowerPoint
I have used activity S4 many times and created a PowerPoint including all the solutions.
A set of Desmos Classroom Activities by Ben Sparks features some of the Standards Unit Tasks. See also this #TMMathsIcons collection of Desmos Classroom Activities by Kathryn Darwin which features several Standards Unit activities.
Alternatively:
All materials – hosted by National STEM Centre. Including:
Mostly Algebra Mostly Number Mostly Statistics Mostly Shape and Space Mostly Calculus Others
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# Spectrum of an operator
Why does the mathematical definition of a spectrum of an operator namely the set of complex numbers without the resolvent set, agreed with the real physical spectrum of an observable?
is this a postulate? and if it is, is there any motivation behind it?
• What do you mean by "Why does the mathematical definition of a spectrum agree with the real physical spectrum?". The Schroedinger equation is essentially an eigenvalue equation, therefore the energy is by definition the spectrum. Then why the Schroedinger equation is in fact an operator equation is another type of question. – gented Aug 28 '17 at 12:26
Specifically, to every observable we may associate a linear, Hermitian operator $\mathcal O$, whose spectrum of eigenvalues correspond to the spectrum of possible observations of said observable.
By the spectral theorem, we are guaranteed for the eigenvalues of $\mathcal O$ to be real, as required, since we expect measurements to yield real rather than complex values.
Yes, in the standard (von Neumann-Dirac) axiomatization, it is said that whatever experimental values obtained when measuring the observable A, they are real numbers pertaining to the spectrum of the self-adjoint operator A describing the observable. The motivation: the Hilbert-space spectrum of a self-adjoint operator is a subset of $\mathbb{R}$. We expect to measure observables and find real numbers as results.
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# Excel Interpolation (Linear & Non-linear Interpolation)
Interpolation is used in financial analysis to estimate missing values.
Click the image for a detailed view
## What Is Interpolation?
Interpolation is a mathematical technique used to estimate values within a set of known data points. It fills gaps between observed data points by assuming a smooth or linear relationship between them. Interpolation can be linear or non-linear, depending on the data nature and accuracy.
### How to Do Linear Interpolation for Linear Dataset in Excel?
If your dataset is linear, you can implement a linear interpolation method. The image below displays a set of formulas that you can use to perform linear interpolation on a linear set of data.
Click the image for a detailed view
### How to Do Linear Interpolation for Non-linear Dataset in Excel? (Taking All X & Y Values into Consideration)
If your dataset is non-linear, you may get different interpolation results if you follow different methods. You can perform linear interpolation either by taking all X & Y values or only the adjacent X & Y values.
#### 1. Using the FORECAST Function
• Use the following formula in C15:
`=FORECAST(C14,C5:C12,B5:B12)`
• Press Enter.
#### 2. Using SLOPE and INTERCEPT Functions
• Calculate the dataset slope and intercept, using formulas containing SLOPE and INTERCEPT functions.
 Slope = SLOPE(C5:C12,B5:B12)
Intercept = INTERCEPT(C5:C12,B5:B12)
• In C15, enter the following formula:
`=E6*C14+E8`
• Press Enter.
(This method follows the straight line equation, y = mx + c)
#### 3. Using the Excel Scatter Plot (Linear Trendline)
• Select the X and Y coordinate values and click Insert >> Charts >> Scatter.
• Click Chart Elements. Check Trendline. Uncheck Gridlines.
• Change the chart title.
• Double-click Trendline.
• Select Trendline Options >> Linear >> Display Equation on Chart.
The linear equation is visible. You can enter an X value and get the corresponding Y value.
Click the image for a detailed view
• In C17, enter the following formula:
`=0.7337*C16 + 4.0858`
• Press Enter.
### How to Do Linear Interpolation in a Non-linear Dataset in Excel? (Taking Adjacent X & Y Values into Consideration)
#### 1. Using a General Mathematical Interpolation Formula
• Use the following formula in C15:
`=C7+(C14-B7)*(C8-C7)/(B8-B7)`
• Press Enter.
#### 2. Using the FORECAST Function
The FORECAST function is used before interpolation. It takes all adjacent X and Y values as input.
To find the adjacent X, and Y values, use a combination of the INDEX and MATCH functions or the XLOOKUP function.
Formulas for INDEX & MATCH
• For X1 : `=INDEX(B5:B12,MATCH(C14,B5:B12,1))`
• For X2 : `=INDEX(B5:B12,MATCH(C14,B5:B12,1)+1)`
• For Y1 : `=INDEX(C5:C12,MATCH(C14,B5:B12,1))`
• For Y2 : `=INDEX(C5:C12,MATCH(C14,B5:B12,1)+1)`
Formulas for XLOOKUP
• For X1 : `=XLOOKUP(\$C\$14, B5:B12,B5:B12,,-1,1)`
• For X2 : `=XLOOKUP(\$C\$14, B6:B13,B6:B13,,1,1)`
• For Y1 : `=XLOOKUP(\$C\$14, B5:B12,C5:C12,,-1,1)`
• For Y2 : `=XLOOKUP(\$C\$14, B5:B12,C5:C12,,1,1)`
• In C15, enter the following formula:
`=FORECAST(C14,F8:F9,F6:F7)`
• Press Enter.
Click the image for a detailed view
#### 3. Combining the FORECAST, OFFSET, and MATCH Functions
• In C15, enter the following formula:
`=FORECAST(\$C\$14, OFFSET(\$C\$5:\$C\$12,MATCH(\$C\$14, \$B\$5:\$B\$12,1)-1, 0,2), OFFSET(\$B\$5:\$B\$12,MATCH(\$C\$14, \$B\$5:\$B\$12,1)-1,0,2))`
• Press Enter.
Formula Breakdown
• MATCH(\$C\$14, \$B\$5:\$B\$12, 1): Finds the position of the largest value less than or equal to the lookup value in B5:B12.
• OFFSET(\$B\$5:\$B\$12, MATCH(\$C\$14, \$B\$5:\$B\$12, 1)-1, 0, 2): Creates a new range by shifting B5:B12 by the number of rows specified by the result of the MATCH function minus 1, with a resulting range height of 2 rows.
• OFFSET(\$C\$5:\$C\$12, MATCH(\$C\$14, \$B\$5:\$B\$12, 1)-1, 0, 2): Creates a new range by shifting C5:C12 by the number of rows specified by the result of the MATCH function minus 1, with a resulting range height of 2 rows.
• FORECAST(\$C\$14, OFFSET(\$C\$5:\$C\$12, MATCH(\$C\$14, \$B\$5:\$B\$12, 1)-1, 0, 2), OFFSET(\$B\$5:\$B\$12, MATCH(\$C\$14, \$B\$5:\$B\$12, 1)-1, 0, 2)): Performs linear interpolation using the FORECAST function, using the value in C14 as the X value and interpolating between two adjacent data points based on their corresponding X and Y values (shifted using OFFSET).
## How to Do Non-linear Interpolation in Excel?
Non-linear interpolation returns more accurate results.
### How to Do Non-linear Interpolation Using the GROWTH Function?
Use the GROWTH function.
• In C15, enter the following formula:
`=GROWTH(C5:C12,B5:B12,C14)`
• Press Enter.
### How to Do Non-linear Interpolation Using a Scatter Plot with a Trendline?
• Select the X and Y coordinate values and click Insert >> Charts >> Scatter.
• Click Chart Elements.
• Check Trendline.
• Uncheck Gridlines.
• Change the chart title.
• Double-click Trendline.
• Select Trendline Options >> Exponential >> Display Equation on Chart.
The linear equation is visible. Enter the X value and get the corresponding Y value.
• In C17, enter the following formula:
`=4.2258*EXP(0.0936*C16)`
• Press Enter.
Click the image for a detailed view
## Practical Examples of Interpolation in Excel
### How to Use the FORECAST.LINEAR Function to find Density?
Use FORECAST.LINEAR function. It determines a prediction using a straight line that fits known data.
• Select F5 >> enter the formula >> press Enter.
```=FORECAST.LINEAR(F4,C5:C11,B5:B11) ```
### How to Apply the TREND Function to Get Interpolated Density?
Apply the TREND function to get interpolated density.
• Select F5 >> use the following formula >> press Enter.
`=TREND(C5:C11,B5:B11,F4,TRUE)`
### How to Do Interpolation With the SLOPE and INTERCEPT Functions?
The SLOPE function finds the slope of a straight line. The INTERCEPT function calculates the point where the line crosses the y-axis.
• Select F5 >> enter the following formula >> press Enter.
`=F4*SLOPE(C5:C11,B5:B11)+INTERCEPT(C5:C11,B5:B11)`
## How to Prevent Interpolation Errors in Excel?
#DIV/0 is often displayed because x1 and x2 are the same. To prevent this error:
• Select F11 >>use the formula >> press Enter to see #DIV/0.
`=FORECAST(F10,F7:F8,F5:F6)`
Improve the formula.
• Select F11 >> enter the following formula >> press Enter.
`=IF(F5=F6,F7,FORECAST(F10,F7:F8,F5:F6))`
No #DIV/0 will be displayed.
## What Are the Things to Keep in Mind?
• Make sure your data is organized in columns or rows, with the independent variable (X) values in one column and the dependent variable (Y) values in another column.
• Ensure that your X values are sorted in ascending order. If your data is not sorted, the interpolation results may be incorrect.
• Make sure there are no duplicate X values in your dataset. Excel’s interpolation functions rely on unique X values.
1. Is there an interpolation function in Excel?
Answer: Yes, Excel provides several functions that can be used for interpolation. The most commonly used function for linear interpolation is the FORECAST function. For non-linear interpolation, Excel does not have a built-in function, but you can use other functions like TREND, GROWTH, or LINEST to perform various types of curve fitting and extrapolation.
2. What are the differences between extrapolation and interpolation?
Answer: Interpolation is the technique of estimating values within the range of known data points.
Extrapolation involves estimating values beyond the range of known data points. It extends the trend or relationship observed to predict values outside the range.
3. Is Interpolated data a reliable source of information?
Answer:Â The reliability of interpolated data depends on the quality of the original data and the appropriateness of the interpolation method.
## Excel Interpolation: Knowledge Hub
<< Go Back to Excel for Statistics | Learn Excel
Get FREE Advanced Excel Exercises with Solutions!
Md. Nafis Soumik
Md. Nafis Soumik graduated from Bangladesh University of Engineering & Technology, Dhaka, with a BSc.Engg in Naval Architecture & Marine Engineering. In January 2023, he joined Softeko as an Excel and VBA content developer, contributing 50+ articles on topics including Data Analysis, Visualization, Pivot Tables, Power Query, and VBA. Soumik participated in 2 specialized training programs on VBA and Chart & Dashboard designing in Excel. During leisure, he enjoys music, travel, and science documentaries, reflecting a diverse range... Read Full Bio
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Advanced Excel Exercises with Solutions PDF
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Convert Factor to Character Class in R (3 Examples) | Change Vector & Data Frame Column
In this tutorial, I’ll show how to change vectors and data frame columns from factor to character class in the R programming language.
The content of the tutorial is structured as follows:
Let’s just jump right in:
Example 1: Convert Factor Vector to Character
The following R syntax illustrates how to convert a vector object (or array) from the factor class to character in R.
First, we have to create an example factor vector:
```x_fac <- factor(c("AA", "XXX", "Y", "HI", "XXX", "YAY")) # Create factor vector
x_fac # Print factor vector
# [1] AA XXX Y HI XXX YAY
# Levels: AA HI XXX Y YAY```
Let’s check the data type of our vector using the class function:
```class(x_fac) # Check class
# [1] "factor"```
The RStudio console returns the data type: Our vector has the factor class.
Now, we can use the as.character function to convert this factor to the character class:
```x_char <- as.character(x_fac) # Apply as.character function
x_char # Print new vector
# [1] "AA" "XXX" "Y" "HI" "XXX" "YAY"```
Let’s check the class of our new data object:
```class(x_char) # Check class
# [1] "character"```
It’s a character string!
Example 2: Convert One Data Frame Column from Factor to Character
This Example explains how to convert a single variable of a data frame from factor to character. First, we have to create some example data:
```data_fac <- data.frame(x1 = letters[1:5], # Create example data
x2 = 1:5,
x3 = "XXX")
data_fac # Print example data
# x1 x2 x3
# 1 a 1 XXX
# 2 b 2 XXX
# 3 c 3 XXX
# 4 d 4 XXX
# 5 e 5 XXX```
We can use the sapply and the class functions to check the classes of all variables of our data frame:
```sapply(data_fac, class) # Check class of all variables
# x1 x2 x3
# "factor" "integer" "factor"```
The first and third columns are factors; the second column is an integer.
Now, let’s convert only the first variable from factor to character:
```data_char1 <- data_fac # Duplicate data
data_char1\$x1 <- as.character(data_char1\$x1) # Convert one column to character```
Let’s have a look at the classes of our data frame columns again:
```sapply(data_char1, class) # Check class of all variables
# x1 x2 x3
# "character" "integer" "factor"```
As you can see, the first variable was changed from factor to character.
Example 3: Convert All Factor Columns of Data Frame from Factor to Character
In case you are working with large data sets, you may be interested to convert all factor variables of your data frame to the character class. This Example explains how to do that using the sapply, as.character, and lapply functions:
```data_char2 <- data_fac # Duplicate data
fac_cols <- sapply(data_char2, is.factor) # Identify all factor columns
data_char2[fac_cols] <- lapply(data_char2[fac_cols], as.character) # Convert all factors to characters```
Let’s check the classes of all of our data frame columns:
```sapply(data_char2, class) # Check class of all variables
# x1 x2 x3
# "character" "integer" "character"```
Both factor columns were converted to the character class.
Video, Further Resources & Summary
Have a look at the following video of my YouTube channel. I show the R code of this tutorial in the video:
Additionally, you may want to have a look at some of the related articles on my homepage. I have released several other tutorials about topics such as factors, data conversion, and numeric values:
To summarize: This article explained how to switch from factor labels to character string in the R programming language. If you have any additional questions, please let me know in the comments.
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# Question: How Does Money Supply Work?
## How is money supply calculated?
The formulas for calculating changes in the money supply are as follows.
Firstly, Money Multiplier = 1 / Reserve Ratio.
Finally, to calculate the maximum change in the money supply, use the formula Change in Money Supply = Change in Reserves * Money Multiplier..
## Who controls the money supply?
The Federal Reserve System manages the money supply in three ways: Reserve ratios. Banks are required to maintain a certain proportion of their deposits as a “reserve” against potential withdrawals. By varying this amount, called the reserve ratio, the Fed controls the quantity of money in circulation.
## What happens if money supply increases?
Inflation can happen if the money supply grows faster than the economic output under otherwise normal economic circumstances. Inflation, or the rate at which the average price of goods or serves increases over time, can also be affected by factors beyond the money supply.
## What are the three measures of money supply?
Many countries use it as an indicator of economic performance. There are three measures of money supply M1, M2, and M3.
## What is the formula of money multiplier?
The money multiplier tells you the maximum amount the money supply could increase based on an increase in reserves within the banking system. The formula for the money multiplier is simply 1/r, where r = the reserve ratio.
## Who controls the supply of money and bank credit?
Central banks work hard to ensure that a nation’s economy remains healthy. One way central banks accomplish this aim is by controlling the amount of money circulating in the economy.
## How is money controlled?
The Fed uses three main instruments in regulating the money supply: open-market operations, the discount rate, and reserve requirements. The first is by far the most important. By buying or selling government securities (usually bonds), the Fed—or a central bank—affects the money supply and interest rates.
## How is money supply measured and why?
The money supply is the total quantity of money in the economy at any given time. Economists measure the money supply because it’s directly connected to the activity taking place all around us in the economy. … M2 = M1 + small savings accounts, money market funds and small time deposits.
## What is counted in the money supply?
The money supply is the total amount of money—cash, coins, and balances in bank accounts—in circulation. … For example, U.S. currency and balances held in checking accounts and savings accounts are included in many measures of the money supply.
## Why can’t a country print money and get rich?
This is because most of the valuable things that countries around the world buy and sell to one another, including gold and oil, are priced in US dollars. So, if the US wants to buy more things, it really can just print more dollars. Though if it printed too many, the price of those things in dollars would still go up.
## How much money is in supply?
According to the Federal Reserve, there was \$1.2 trillion in the M0 supply stream as of July 2013 [source: Federal Reserve Bank of New York]. That sounds like an incredible amount, but think about it this way: According to the CIA, there were 316,668,567 Americans alive that month [source: CIA].
## Who is the main source of money supply in an economy?
The effective money supply consists mostly of currency and demand deposits. Currency includes all coins and paper money issued by the government and the banks. Bank deposits (payable on demand) are regarded part of money supply and they constitute about 75 to 80 per cent of the total money supply in the US.
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# SET-4
1. (a) Draw the schematic diagram of a CRT and explain about the various sections and the materials used.
(b) In a CRT, the electrons emitted are accelerated by a potential of 500V. The length of the deflecting plates is 1.3 cm. Distance between the deflecting plates is 0.5 cm. The distance between the centre of the deflecting plates and the screen is 20 cm. Determine the value of electrostatic deflection sensitivity.
2. (a) Draw the basic structure of a varactor diode and explain its characteristics.
(b) Write the diode equation and discuss the effect of temperature on diode current.
3. (a) Discuss the operation of HW recitifier with and without capacitor filter.
(b) Draw the Half wave rectifier circuit using a step down Transformer with Vs = 46 sin(100π t) and a semiconductor diode. Calculate the turns ratio of the Transformer windings when the primary voltage of the Transformer is 230 volts.
4. (a) Give the UJT symbol and simplified equivalent circuit with external resistors included.
(b) Draw UJT emitter characteristics and mention various regions.
(c) If VE<VP and VE>VP , explain how UJT works for these conditions.
5. (a) What is the necessity to stabilize the operating point of transistor amplifier?
(b) What is thermal runaway?
(c) For a fixed bias configuration determine Ic, Rc, Rb and Vce using the following specifications: Vcc=12V, Vc=6V, β =80, Ib = 40 μA.
6. (a) For a CB configuration, what is the maximum value of RL for which Ri doesnot exceed 50 ? Transistor parameters are hib=21.6
, hrb = 2.9×10−4, hfb=- 0.98 and hob=0.49μ A/V.
(b) Sketch the circuit of a CD amplifier. Derive the expression for the voltage gain at low frequencies and what is the order of magnitude of the output impedance.
7. (a) Draw a feedback amplifier in block-diagram form. Identify each block and state its funcetion.
(b) An amplifier has a voltage gain of -100. The feedback ratio if 0.01. Find the voltage gain with feedback, the output voltage of the feedback amplifier for an input voltage of 1mv, feedback factor, and feedback voltage?
8. (a) Prove that the frequency stability improves as dθ/dw increases in oscillators.
(b) Draw the FET crystal oscillator and derive the equation for frequency of oscillations.
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# Information Theory Questions
### Categories: ML
Written on September 1, 2020
My favourite questions from David MacKay’s Information Theory, Inference and Learning Algorithms.
This post is still growing and I need to write answers to more of the questions but in an effort to not let good be the enemy of perfect and to motivate me to get back to this textbook I am making this post live now!
The book has a number of great exercises in each chapter and I thought I would share a running list of my favourites. (I think and hope that this is legal as I am giving full credit to David MacKay and not profiting off of this, esp as the book is already free online).
I list the questions by chapter and the answers in a lower down section. I also add some of my own questions where I think they would be useful to check the understanding of certain concepts/equations which are covered in the book before questions leveraging them are asked. My questions are denoted (M#), questions from the book by (Chapter#.Question#).
I have to finish the remainder of the book and will be posting more of my favourite questions here!
## Questions
M1. What is the information content of an unbiased dice roll?
M2. What are the equations for expectation and variance of a Random Variable?
2.16 (hint: use the Central Limit Theorem)
M3. A coronavirus serology test (for having previously had an infection) has a 98% specificity and 95% specificity. Your mother, an upstanding citizen who has obeyed quarantine rules, takes the test and it comes back positive. What is the probability your mother has coronavirus?
M4. “Frequentists argue that you can only use probabilities to describe the __ of outcomes __ experiments”
M5. “Forward probability problems involve a _____ model that describes a process that is assumed to give rise to some data”
M6. “Like forward probability problems, inverse probability problems involve a ___ of a process, but instead of computing the probability distribution of some quantity produced by the process, we compute the ____ of one or more of the ___ in the process, given the observed variables. This invariably requires the use of __.”
M7. What is the Bayesian response to Frequentist claims that they make assumptions about the prior?
M8. What is Jensen’s Inequality?
M9. What is Kullback-Leibler Divergence?
2.25 Take the hint into account but there is another (less elegant) way to solve it!
3.8 Try to calculate the probabilities of being correct under the different scenarios too.
3.9
4.1 First try to find what the minimum number of necessary weighting steps is for the optimal solution.
#### A4
frequencies; random
generative
#### A6
generative model; conditional probability; unobserved variables; Bayes’ theorem
#### A7
assumptions are necessary no matter what. Bayesian priors are more transparent. There are assumptions with the likelihood as much as the prior, data collection etc etc etc.
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# Hummus vs Pate: Nutrition Comparison
## Pate vs Hummus: Nutrition Comparison
per 100gHummusPate
Calories237 221
Carbohydrates15 g3.5 g
Fat17.82 g19.4 g
Dietary fiber5.5 g0.4 g
Protein7.78 g8.1 g
Calcium47 mg94 mg
Iron2.54 mg3.3 mg
Magnessium75 mg23 mg
Phosphorus22.8 mg206 mg
Potassium312 mg225 mg
Sodium426 mg574 mg
Zink22.8 mg1.61 mg
Vitaminium B1 (Thiamine)0.16 mg0.1 mg
Vitaminium B2 (riboflavin)0.127 mg0.55 mg
Vitaminium B3 (Niacin)1.024 mg3.92 mg
Vitaminium B60.146 mg0.21 mg
Vitaminium E1.54 mg0.21 mg
## More Calories in Hummus
At first glance, you can see that in hummus is just a little more calories than in pate.
Hummus has 237 kcal per 100g and pate 221 kcal per 100g so it is pretty easy to calculate that the difference is about 7%.
In hummus and in pate most calories came from fat.
See tables below to compare hummus with pate in details.
## Hummus And Pate Nutrition Difference
• Calories:
hummus - 7% more than pate
• Carbohydrates:
hummus - 329% more than pate
• Fat:
pate - 9% more than hummus
• Dietary fiber:
hummus - 1275% more than pate
• Protein:
pate - 4% more than hummus
## Less protein in hummus
It is aslo easy to see see that in hummus is less protein than in pate.
There is 8.1g per 100g of pate and 7.78g per 100g of hummus so using simple math we can see that difference is about 4%.
## More carbohydrates in hummus
In hummus is more carbohydrates than in pate.
There is 3.5g/100g of carbohydrates in pate and 15g/100g in hummus so let me do the math for you again - difference is about 329%.
## Less fat in hummus
In hummus is less fats than in pate.
The tables above show us that there is 19.4g/100g of fats in pate and 17.82g/100g in hummus. In this case difference is about 9%.
## Hummus
237kcal
• Calories237
• Carbohydrates15 g
• Fat17.82 g
• Dietary fiber5.5 g
• Protein7.78 g
Hummus calories per:
100g
| ounce | tablespoon | teaspoon | cup | half cup
• 24% CARBS.
• 12% PROTEIN
• 64% FAT
## Pate
221kcal
• Calories221
• Carbohydrates3.5 g
• Fat19.4 g
• Dietary fiber0.4 g
• Protein8.1 g
Pate calories per:
100g
| ounce | tablespoon | teaspoon | cup | half cup
## Calories source
• 6% CARBS
• 15% PROTEIN
• 79% FAT
### Vitamins: pate vs hummus
• Vitaminium B1 (Thiamine):
hummus - 60% more than pate
• Vitaminium B2 (riboflavin):
pate - 333% more than hummus
• Vitaminium B3 (Niacin):
pate - 283% more than hummus
• Vitaminium B6:
pate - 44% more than hummus
• Vitaminium E:
hummus - 633% more than pate
### Minerals: hummus vs pate
• Calcium:
pate - 100% more than hummus
• Iron:
pate - 30% more than hummus
• Magnessium:
hummus - 226% more than pate
• Phosphorus:
pate - 804% more than hummus
• Potassium:
hummus - 39% more than pate
• Sodium:
pate - 35% more than hummus
• Zink:
hummus - 1316% more than pate
All information about nutrition on this website was created with help of information from the official United States Department of Agriculture database.
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# Representing Data: Bits and Bytes
If you use a computer regularly, you know that every document you write, every music file you listen to and every photo you see is stored as a file. You may also know that a file consists of bytes and that bytes consist of smaller building blocks called bits. But, what are bits and bytes really? How do they work, why do they work that way, and how does storing them create text, sound and images? To find out we have to start with something very basic: counting.
#### Decimal Counting
Consider what happens if you count using ten fingers. Once you reach ten you have no more fingers left and thus, when you reach eleven, you remember one times ten and keep up one finger. This same thing happens over and over again as you keep counting upwards. This is also reflected in the way that we count when we write down numbers. Though in that case we use ten symbols instead of ten fingers: 0 up to including 9. Once we reach nine and want to express ten, we no longer have any symbols. So, we remember 1, which for writing means: we shift the number 1 to the left, and start over again with a 0, giving us 10. The difference with finger counting is that for zero we use no fingers at all, whereas when writing numbers we use the symbol 0 to denote zero.
#### Counting Conventions
The way we write down numbers is just a convention. The number system that we use most often is the decimal numeral system, because it has, as discussed, ten symbols that we enumerate. Consider that there is nothing stopping us from defining a counting system with only five symbols: 0 up to including 4. In this case we will run out of symbols when we want to express five, and we will have to do the same thing we did before: shift 1 to the left and then start over again. This gives us (again) 10. But since we now count with five symbols, this means that the two symbols 10 actually represent the value five. If you find this confusing, try counting from zero to five using your fingers on only one hand and use the first finger for the zero. Notice that reaching five forces you to remember one and continue counting by resetting your hand to one finger again for zero.
#### Binary Counting
The ten-symbol decimal counting system is just one of an infinite number of possible counting systems. However, there are only several such systems in common usage. Namely, the octal system that uses eight symbols, the hexadecimal system which uses sixteen symbols (letters A through F are used to denote 10 up to 16) and also the binary system, which uses only two symbols: 0 and 1. Having only two symbols is similar to counting with only two fingers. So, how would we count from zero to three using only two symbols? Zero would just be 0, one would just be 1. For two it becomes more complicated. Since we have now run out of symbols we need to shift 1 left and start over with zero, giving us 10. Finally, for three: since we still have a next symbol for the rightmost position, we only have to replace the 0 with a 1 to express three in binary, giving us 11. If we now want to go up to four, we can not increase the existing symbols anymore. Hence, we have to set them to 0, and add a new position with a 1, giving us 100. In the table below we show the values for counting up to including five. If this is not immediately clear: do not worry, a more intuitive explanation follows.
DecimalBinary
00
11
210
311
4100
5101
#### Bits
The binary system brings us to our first definition: the binary digit, commonly shortened to ‘bit’. One bit is thus simply a single-digit binary number. Glancing at the table above we see that higher decimal numbers need more bits to be expressed in binary notation. Specifically, to store the number two or three we need two bits, and to store the number four or five we need three bits. The key insight is that by concatenating bits, that themselves can only take two values, we can represent any whole number, no matter how small or large, by using a sufficient amount of bits.
there are only 10 kinds of people in the world: those who understand binary, and those who do notnumeral base joke
An intuitive way to think of bits is as switches that turn on or off values. Take a look at the table below. The first row contains numbers, the second row contains a 0 if the number is ‘off’ and a 1 if the number is ‘on’. Try to work out the decimal value by summing the values of the first row for all the ‘on’ switches.
Solution (click to expand)
1286432168421
01001010
The second row represents a number (01001010) written in binary notation. The first row consists of powers of two if you consider them from right to left. In fact we can simply rewrite the first row of the table as follows:
01001010
Why powers of two? Well, since we have two symbols: 0 and 1. Starting at the right, each step towards the left increases the value by one power of two. If we would have three symbols, each position step would represent a power of three. Consider what happens when we have not two, but ten symbols, as in the discussed decimal system: each step towards the left is then an increase of a power of ten. An example:
1100
If we try to express this as a decimal number we get 1000 + 100 = 1100, which in fact is exactly the same as the on/off switches concatenated (1100), as each switch represents a power of ten.
#### Bitwise Operations
Back to bits: it may seem as though storing numbers in binary is inefficient, as we need more bits to store higher numbers. However, the number of bits required does not increase linearly, instead it decreases exponentially. To see this, let us write the decimal number ten in binary: 1010. This requires four bits, now a thousand: 11 1110 1000, requires only ten positions despite being a magnitude hundred larger than ten. This in another key insight: we can represent very large numbers with relatively few bits.
You can think of a bit as the smallest possible piece of information. Many things map nicely on the two states that a single bit can have. For example: a logic statement can be either true or false. However, by adding additional bits we can express more states than just two and perform actual arithmetic with them. If we want to add the numbers 1 and 2 in binary we can simply do this by turning on all the switches that are ‘on’ in the representation of both 1 and 2 of the result. If we look at 1 and 2 in the table below, we see that to form 3, the sum of these numbers, we can look at the two rows above 3 and set the bit to 1 if either the bit in the row of 1 OR the row of 2 is one. This is why this is called an OR operation.
1 =0001
2 =0010
3 =0011
There are in fact four of these logical operations we can do on bits:
• OR : turns on the switch in the result if either of the two input switches are on.
• AND : turns on the switch in the result if both of the two input switches are on.
• XOR : turns on the switch in the result if either of the two input switches are on, but not both. This is called an eXclusive-OR.
• NOT : takes one input row and inverts all the switches, turning all zeros to 1 and all ones to 0.
With these four operations we can implement common mathematical operations on whole numbers. A hardware implementation of one of these operations is called a logic gate and your computer has many of them: billions.
#### Bytes & Text
Now we have some feeling for bits, let us turn to bytes. Computers only work with these binary numbers expressed as groups of bits. So, how do we get from groups of bits to stuff such as text, audio and images? The answer: mappings. You are probably familiar with many systems in the real world where a number ‘maps’ to something else. For example: a telephone number maps to a person or a company, a postal code maps to some area within a city, and in some restaurants a number maps to a specific dish. The same mechanism of mapping a number to something with a specific semantic interpretation is used in computers.
##### Characters
For storing text on a computer we need to map the numbers to the alphabet. There a twenty-six letters in the alphabet. However, if we need to express both upper and lowercase letters, we would need to double that amount: fifty-two. How many bits would that take? The closest power of two is 64 which is , thus we need at least 6 bits. However, we also need to express many other symbols. Take a look at your keyboard and you will find that it contains at least a 100 or so keys, and some combinations of keys can produce yet other symbols. Though, historically six bits were indeed used to store text, over time many more symbols were added. This eventually led to an 7-bit standard known as ASCII, commonly extended with 1 extra bit for additional language-specific symbols. The modern day successor of this is Unicode which can use up to 32 bits per character, allowing for many more symbols. Yet, the first 7-bits of Unicode still map to the same symbols as ASCII.
##### Processing Units
Early microprocessors were designed to operate on eight bits at a time. Early personal computers used eight bits as well. Since these groups of eight bits form a natural unit we refer to them as a byte. A byte can take distinct numeric values, which in practice means 0 up to including 255. Half a byte, four bits, is sometimes referred to as a nibble, which is a tong-in-the-cheek reference to the larger ‘bite’.
A byte is thus just a group of eight bits. Any meaning that a byte has really depends on what we are expressing. In a text file the bytes are characters, in a music file they are audio samples and in a digital photo they represent the colours of a specific part of the image.
#### Images
Image files are quite intuitive to understand. If you take a photo and put a grid over it, you can give each small square in the grid a specific colour. Zoom very far into a digital photo, and you will see this grid, the small squares are often referred to as pixels: a portmanteau of ‘picture element’. If a digital photo has more pixels, it contains more information and we say it has a higher resolution.
##### Colour
The colours of pixels can be encoded in bits. Indeed, colours are often expressed in the Red Green Blue (RGB) format. In a commonly used variant of this format each colour is one byte and can take a value from 0 to 255 that maps to the intensity of the colour. So, for each square in the grid we use three bytes: twenty-four bits. For example the colour would represent pure white and is pure black as in these cases all colours are mixed evenly. However, would be bright red, and so on.
If you have ever edited a web page and had to change a colour, you probably noticed that colours can be expressed as a hashtags followed by some combination of characters and numbers, for example: . This takes us back to the discussion of counting systems. The hexadecimal system is another way to represent numbers. For this system we count 0 through 9 and then A through F, giving us 16 possibilities in total. Perhaps you already see what those symbols behind the hashtag mean.
Let us look at . This actually consists of three groups of two symbols. The first group is FF, we know that F maps to 15 in decimal, so the hexadecimal value of FF is . The other two groups are 0. These three groups in this notation are the three colours! The first group is red, with value 255 (), the second is green with a value of 0, and the last is blue, also with value 0 (). Hence, again we have bright red , but now expressed in hexadecimal as .
##### Practical Considerations
Modern images take up a lot of storage space when we would just store them in RGB format. A modern camera easily snaps photos at 16 million pixels, for each of these pixels we need to store three bytes. So that’s over 48 million bytes (megabytes) for one photo. Storing video is similarly challenging, as that is essentially a collection of still images in sequence, typically at least twenty-four per second. Fortunately, digital compression techniques exists that can make images and video files much smaller. These techniques take advantage of repetition and patterns within and across images and remove small differences that can not easily be seen by the human eye.
#### Sound & Samples
How sound is represented digitally is a bit more complex than text and images. To get a better impression of this, imagine you are sitting on a swing. You are swinging right to left from my perspective. Let’s say that I want to take pictures, so I can later play them back as a filmstrip. A choice I have to make is how many pictures I take relative to the time you are swinging.
If it takes you ten seconds to swing back and forth, and I only take a picture once every ten seconds, all pictures would have you frozen in the exact same place, since I am missing the the 9.99 seconds where you are actually swinging. If I take a picture every second, I’d see you swing, but it would look a bit choppy. Taking pictures in more rapid succession would fix this and yield smooth motion. However, the minimum amount of pictures I’d need to snap to be able to see you move is actually longer than one second: half the time it takes for a swing, which would be every 5 seconds. I’d catch you at times 0, 5 and 10, respectively for ‘up to the left’, ‘centered’, and ‘up to the right’, and so forth. Differently worded: I’d need to snap pictures twice as fast as the rate at which you are swinging.
##### Sampling
The process of determining how many pictures to take in an audio context is called sampling, and instead of pictures we record the amplitude of the audio signal at specific points in time. The signal consists of a mix of sound frequencies that relate to the pitch of what you are hearing. The speed of the swing is comparable with the highest possible frequency of the audio signal. Frequencies are expressed in Hertz, 1 Hertz = 1 swing per second.
If you imagine many people sitting on swings next to you, going back and forth at different speeds, we’d need to snap pictures so we can catch the fastest one: snapping twice as fast as that speed. This corresponds to the highest frequency for audio: we need to record a certain minimum amount of samples in order to reconstruct the original recording. If our sampling rate is too low, we will not be able to record sounds with a higher frequency. Like with the swings: we need to sample at least twice the rate of the highest frequency we want to be able to record. This is one of the main reasons that telephone audio sounds rather poor: the sampling rate is low: 8000 samples are taken each second, limiting the range of the actual audio to 4000 Hertz. Human hearing can distinguish sounds from 1 up to 20 000 Hertz. This is the reason Compact Disc audio sounds so good: it takes 44 100 samples per second, enabling an actual range up to 22 050 Hertz.
##### Resolution
This does not get us the actual bytes yet that we need for audio, which takes us to the other part of representing audio digitally: how precise a value we are going to record for each sample. The more bits we use for a sample, the more accurately we can model the original signal. If we would only use one bit we can only record either no sound, or the loudest possible sound: it’s on or off. With two bits we can record four levels, etc. Compact Disc quality audio records samples with 16 bit resolution, giving possible levels.
##### Practical Considerations
Like with video files, sound files also quickly grow large. In Compact Disc quality we need to store two bytes for every sample of which there are many thousands every second. Fortunately, as with video there are compression techniques to reduce the sizes of such files, the most famous of which is undoubtedly mp3 which takes advantage of differences that the human ear can not easily distinguish.
#### Conclusion
In this post you have learned about counting in the familiar decimal system, but also in the likely less familiar binary counting system. You have also seen how a number raised to a certain exponent relates to the counting system: the decimal system uses ten as the base number and the binary system uses two. These two possibilities act like an on/off switch, and each of these switches is referred to as a bit. You have an understanding of bitwise operations that can be performed to implement basic arithmetic. Finally, we have seen how groups of bits form bytes, and how bytes are often mapped to various things such as characters in text, colours in images and samples in sound. I hope this gives you a better feeling of how the basic primitives of modern computing, bits and bytes, relate to the things you see and read on screens and hear through speakers and headphones.
# Copyright and the Information Age
In the previous article we looked at the origin of copyright. We learned three things. Firstly, that the introduction of copyright was driven by reduced costs of creating copies of creative works. Secondly, that copyright has shifted from authors to large corporations. Thirdly, that compensating the original authors is no longer really what copyright enforcement is primarily used for. In this article we look at what happens when the costs of copying are further reduced to nearly zero. What are the consequences and how should we deal with them?
#### Perfect instant copies
Like many eighties kids, I too had a cassette recorder. I used to record radio shows with it. These were sufficient for listening them back shortly thereafter, but did not have the same quality as the original broadcasts. In fact: they actually degraded over time.
Back then blank cassette tapes were subject to a special home-copy fee. To this day Dutch citizens still pay this fee for each blank CD or DVD they buy. This legislation has been extended to also cover hard disks and memory sticks. What is the purpose of this fee? It gives users the right to make copies for private, non-commercial, use without violating any laws. The collected fee is indirectly distributed back to the authors.
Analog copies, made using cassettes and videotapes, are quite different from digital copies, made using DVD’s and hard disks. Why? Firstly, digital copies are perfect: they do not degrade over time. Digital films, series or home recordings will look identical played back fifty years from now. Secondly, while copying onto a cassette still took effort, creating a digital copy is as simple as clicking a button. Thirdly, modern digital storage devices can be erased and rewritten many times. This further reduces the monetary costs of making and holding onto copies. Combined with today’s fast download speeds, the costs of copying a creative work like a movie, song or book, are reduced to near zero.
The implications of effortless zero-cost copying are profound. Importantly, it allows creative works to spread broadly and quickly. This aligns with at least one of the goals of its creators: reaching a large audience. However, ironically, it also conflicts with another goal of those same creators: financial compensation for exerted effort in creating the work in the first place.
#### Creative works as ideas
Now, before I go on, I want to avoid the trap of oversimplifying consumers and producers of creative works. Frequently the needs of a producers and consumers are presented as being opposed. I do not think this is the case. There’s a much more complicated interaction going on than a simple exchange if you consume a creative work.
If you listen to a song that resonates with you, it changes you. It inspires you to find different music of the same form, or even to make your own version or to remix it. Contrast this with buying a bottle of water or a bag of potato chips. These are things you consume to sustain you. Instead, consuming creative works changes you, and may even change the creative work itself by leading to indirect derivatives. In short: creative works are more like an idea. For these works differences in physical form (digital, analog, etc …) do not play a big role in conveying the idea itself.
Since ideas build upon one another, it is much more difficult to classify what really constitutes an original creative work. This is in fact the subject of many law suits. Listen to Taurus by Spirit and tell me if you think the intro riff of Stairway to Heaven is still original. Listen to Blurred Lines by Robin Thicke and Got To Give it Up by Marvin Gaye. There is no clear cut definition of where inspiration ends and where plagiarism starts. That’s because these examples are essentially all ideas building on one another.
#### Charging for copies
Back to physical copies: when copying still took effort, it made perfect sense to collect money at the point where these copies were produced. It made sense to charge more for a cassette, videotape, or even a DVD than its material value. The surplus intended for the authors of the work, and those on the intermediate ‘chain’: distributors, promoters, etc. However, when the costs of producing a copy reach nearly zero, this model becomes much harder to sustain. Indeed, the last two decades have revealed substantial cracks in this approach.
There have been numerous clashes between technologies that enable fast and easy access to content and the copyright holders of this content. The response: a mix of artificial copy-restriction mechanisms and harsh legal steps against copyright violators. Content distribution intermediaries tend to think of zero cost copying as a treat to curtail. Perversely, copy-restriction mechanisms penalize legitimate buyers of creative works. It makes them jump through hoops and imposes usage restrictions. This leaves a vacuum, inadvertently pushing consumers towards obtaining content illegally, depriving the artists of their remuneration [5].
Abstractions that worked in the physical world do not easily map onto the new digital reality. For example: I once encountered an on-line library that had only five digital copies of a specific book available. Since they were all ‘lend out’, I could no longer ‘lend’ this book. This bizarre example underscores the odd dichotomy. On the one hand, authors want their books to be read and spread as much as possible, making a case for unrestricted copying. On the other hand authors want payment for each copy, making a case for restricting copying. This raises the question: is the point at which a creative work is copied, still the right point to charge for it?
#### Easy access
There are platforms that still charge for each copy, like Apple’s iTunes. iTunes is interesting because it broke with the traditional method of selling music. Instead of having to buy an entire album, consumers could conveniently choose to buy individual songs. This again emphasizes that the rise of piracy may have less to do with consumers being unwilling to pay authors for their works, and more to do with those works being hard hard to access legally. Indeed, piracy seems to be a service problem, not a pricing problem [3].
There are also alternatives that have moved away from charging for each copy, instead charging a subscription fee. This fee is distributed to the copyright holders of the original work. Sidestepping the issue of charging per copy, instead providing on-demand access to content for an ‘all you can eat’ fee. Examples of this are Netflix and Spotify. The downside of the subscription model and platforms, is that users tend to flock to popular ones. These popular platforms grow in terms of user base and power. When they become too dominant, they have an incentive to take a increasingly larger cut of the proceeds. This siphons away compensation from the author to the distributor. Hence, digital distribution platforms risk becoming the new middle-men. Meet the new boss, same as the old boss.
The upside is that there is a willingness to pay for easy legal access to content, regardless of whether this is based on copies, or subscriptions. This is hopeful for both producers and consumers, more niche creative works will get a chance, which leads to more choice as well, and more quality by sheer volume of creative works being produced. The recent rise of high quality television series is testament to this.
#### Alternatives
Is there an alternative model of compensation we could think of? Going back to the idea behind copies: the first copy of a book or movie is very expensive to make, but all subsequent copies cost almost nothing to produce. Finding a buyer for that first copy that distributes the subsequent copies for free is economically optimal and efficient. However, this still assumes that copies are the right way to think of creative works, is this still really the case?
These alternative ways of charging for creative works is interesting for producers and consumers as well, particularly because it allows cutting out the middle-man: studios, distributors, etc … this enables a much more personal and more direct connection between authors and their fans, and more efficient economics at the same time.
#### Conclusion
The ability to make perfect instant copies at negligible cost has changed the world profoundly. It has also, for better or for worse, has led to a much broader spread of creative works, some of which is legal, some of which is not. One point of view: sharing copies freely acts as a disincentive for authors to keep up their creative endeavors: the original problem that copyright intended to address. However, the low cost of spreading (and even producing) creative works seems to have led instead to a proliferation of such works, available under many different compensation schemes. Making it easier to both produce and consume such works.
Instead of the dire predictions, mostly by large corporate copyright holders, of a world deprived of creative works, we now live in one that has undergone a Cambrian explosion of such works. It seems that the original copyright model has outlived its usefulness. A more liberal approach that allows copying of creative works by consumers in combination with novel compensation schemes for producers, seems prudent for sustaining the ongoing dialogue of ideas these works represent.
#### References
1. Stallman, R. (1997). The Right to Read
2. Economist (2004). Killing Creativity
3. Newell, G. (2011). Gabe says Piracy isn’t about Price
4. Rosen, B. E (2010). Walking on Eggshells
5. Kinsella, S. (2010). Kroes wants copyright as a building block
6. Kelly, S. & Robinson, R. The Fast and Furious Rise of the Subscription Economy
# Goals III: Planning
Everyone has dreams about what they want to do in the future. Write a novel, learn a new language or make a trip around the world. Yet it can be hard to motivate yourself to work on realizing these dreams on a consistent basis. How can we align our daily activities with our long term goals? I address this question with a three part series on goals. In the third part we look at the actual process of planning.
#### Introduction
##### Thinking and Acting
Say you get in your car in the morning to drive to work. You get behind the wheel and think about the first point you need to get to. This first point, let us call it A, is halfway between where you are now and your work. Then you think of the second point which is halfway in between where you are now and point A. Let us call this point B. If you follow this line of reasoning, the distance between you and your work can be divided in half an infinite number of times. You will be forever reasoning in your car about what the first point to drive to should be: A, B, C, D, etc …, without actually even starting the engine. This is the first problematic way many people treat their dreams: thinking, but not acting.
The next day in your car, you take a different approach. You get behind the wheel and just randomly start driving in some direction without even thinking about where your work’s office actually is. You just drive. After driving around for a long time, the office is nowhere in sight. You keep driving infinitely without actually getting anywhere. This is the second problematic way in which many people treat their dreams: acting, but not thinking.
##### The Planning Spectrum
These different ways of approaching a goal are not as mutually exclusive as they seem. Each approach, in a less extreme form, can lead to success. They are on a spectrum. Overplanning is on one side of this spectrum and underplanning on the other. Depending on the situation, people lean more towards either of these extremes based on how they dealt with similar situations in the past: the familiarity of the goal, which changes over time. Consider that if you are driving to a new place for the first time, you probably plan it to some extent. Contrast this with your daily trip to work, which you likely do without any planning.
This goes to three core insights:
1. Going too far in either direction, underplanning or overplanning, will get you nowhere.
2. Planning for goals that are concrete, or that you know how to approach already, is far easier than planning for vague or novel goals.
3. Planning challenges differ a lot from one person to the other, and even for the same person at different times for different tasks.
Contrary to what is sometimes suggested: there is no one right way to plan that works for everyone, every time for every situation. However, what you should learn to do is continuously adapt and improve your own planning process. Not only should a plan itself adapt to changing circumstances, your approach to planning should adapt to your changing self.
Rather than present a rigid planning method, I am going to provide you with building blocks that you can use to enhance your own planning process. You likely need to apply different parts of this toolbox to different challenges at different times. I can show you helpful blocks, but you will need to put them together. Ready?
#### Macro Planning
##### The Anti-Climax
When you work towards a goal for a very long time, and finally reach it, it can feel like an anti-climax. The reason for this feeling is that, from a cognitive perspective, you spend most of your time not reaching your goal. This is followed by a very short time in which you will have actually reached it, before you quickly move on to the next goal. Going through several cycles like this can easily deplete your energy to start any large endeavor. This is why large projects can often feel so overwhelming. The reason that most people never get to writing a book or learning a language is that these cognitively feel like ‘big’ things: large commitments followed by a short-lived reward. Unfortunately, this thinking prevents us from ever actually starting.
To get through this impasse, the divide and conquer approach is often advocated. The idea is to break down a goal into smaller subgoals in a top-down fashion. However, though useful, it is not the right first step. The problem with this approach is that it forces you to consider the scope of the entire goal as a single large project. This perspective sucks you into spending a lot of time just planning your project. You never actually get to work on the project itself: the meat, the content, the challenge. This way goal setting counter-intuitively leads to inertia.
##### Regular Commitment
A good first step is to commit a regular amount of time to a goal and then to start working on it. Initially this commitment could be just half an hour a day, or a handful of hours in a weekend. It is important that you write this commitment down, stick to it, and check it off as you go. This system forces you to keep track of your time, restricts the goal from taking over your life, yet allows you to reap an immediate reward from putting in time and effort.
Simply taking some first small steps in your regular time allotment for the goal will help you get a better gauge on what challenges lie ahead, how much time they will take to overcome and what other resources you may need. Once you get a feeling for this, take a moment to write down accurately what criteria need to be met for you to consider your goal reached. This has the important dual function to provide both a relative sense of progress and absolute closure.
It is only after this that the divide and conquer approach comes in. However, instead of breaking up big goals into smaller ones top-down, I recommend doing this bottom-up. Just plan out the next two or three things you need to do, place it in the bigger picture of your goal, and resist the urge to make a complete plan.
For example: if you want to write a book, commit to writing a smaller part. This could be as little as a half page outline, or as much as a draft chapter. It is important to define this chunk in a way that you feel you can complete within a reasonable amount of time. After completing this you will have a clearer idea about follow-up steps.
##### Baby Steps to Giant Leaps
If you are just starting out with something, a new project, it is often best to start small: an initial milestone that you can complete in one or two weeks. This first milestone has the important purpose to get you started: to break through any inertia, and move you one step closer to your goal.
As you put in more time, it also becomes more important to review the completion criteria for your goal and plan the next tasks in alignment with it, or even to alter your definition of done. Having a larger overall plan becomes more important only as your project steadily progresses: as you move closer towards your goal. If you are not yet comfortable with large goals that span months to complete: start with smaller, less ambitious goals. Completing smaller goals will move you forward and provides the foundation for tackling larger goals later on.
Thinking about your goals in terms of days, weeks or months, is macro planning. This is what we have just discussed. It is mostly concerned with filling in the bigger picture in manageable steps as you go. Managing your time during the day is micro planning, and we will get to that next, but not before we define deep and shallow work.
#### Deep versus Shallow
##### The Distracted Mind
I had a co-worker once who was continuously distracted by anything that required attention ‘now’. He could not prioritize his tasks and ended up constantly ‘putting out fires’. This person was convinced he could multi-task effectively. In meetings he would often work on his laptop, be in an unrelated phone call simultaneously, while also half participating in the discussion. Had he taken the effort to just add some structure and prioritize his tasks, his productivity would have soared. Instead he was now taking a day to produce less than half a day of effective output.
People who multi-task exclusively perform shallow tasks. These tasks are not cognitively demanding and commonly logistic in nature, for example: responding to e-mails, setting up meetings, and making phone calls. However, when we regard larger goals, such shallow tasks constitute only a very small portion of what needs to be done. Instead these goals require large amounts of deep work: tasks performed in a distraction-free state of concentration that requires significant cognitive effort. For example: writing an article, practicing an instrument, or solving a complex puzzle.
Deep work is the ability to focus without distraction on a cognitively demanding task. It’s a skill that allows you to quickly master complicated information and produce better results in less time. Deep work will make you better at what you do and provide the sense of true fulfillment that comes from craftsmanship.Cal Newport
Performing shallow tasks does not actually move you much towards your goal. Doing them exclusively is a form of structured procrastination. They tempt us, because they easily combine with other shallow tasks and offer us a quick and easy reward: a ‘sweet marshmallow’. These temptations surround us daily. The consumption of social media, entertainment and news combines easily with performing other shallow tasks, while still providing a false sense of progress. The pull towards a multi-tasking lifestyle is understandable.
If you are used to such a lifestyle, the only way to really advance towards your goals is to part ways with it. I know, this is not easy to do, it will take some time, and you will experience withdrawal symptoms. I would not ask you to do this unless the benefits were significant.
Your goal is to become a serial single-tasker: someone who picks up one task at a time, gives it their full attention, and only then switches to the next task. To lose the multi-tasking habit, a good first step is to stop filling every moment of boredom with a shallow task, like habitually checking your phone for e-mails or messages. Instead learn to schedule activities like internet, e-mail and messaging. You need to start training your mind to prefer working on deep tasks over shallow ones.
A large part of this journey is unlearning habits that you have adopted that do not serve you well in terms of reaching your goals. We have to replace those habits with ones that will help you on a day-to-day basis: micro planning.
#### Micro Planning
##### Big Brother
If you are not yet actively planning your day, someone else most certainly is, and that someone may not have your best interest at heart. Many of us consume news, social media and entertainment on a daily basis. None of these things is bad in its own right, indeed they can be very useful. However, most people turn to these as ingrained habit, instead of as a conscious choice. These technologies are not neutral and engineered to foster such habit forming, playing into our desires and insecurities, usually with the end goal of monetization. This learned habitual behaviour interferes with our capacity to work on our own meaningful long-term goals, trading it for goals that are not our own, not in alignment with our interests, and even psychologically harmful. Fortunately, we can change our habits.
##### The List
Realize that the only real moment under your control is in fact the next moment in your life. It is there that you want to limit your choices beforehand, so you effectively steer yourself to work on tasks beneficial to your long-term goals. To this end, a useful habit to adopt is simply making a list of tasks to do for tomorrow at the end of the present day. Commit to actually writing this list down at the end of a day, and looking at it regularly throughout the next day, especially when you are at a loss as to what to do. View this as a small contract between your past and present self. Stick to the contract and you will learn to trust yourself.
Check off things you have completed on the list as you go through your day. Feel free to swap things around in your list if the day unfolds differently. Planning is in fact all about seeking flexibility within boundaries you set for yourself beforehand. There should be room for spontaneity.
The list approach provides three important things. Firstly, a flexible order in which you can do things, which avoids an imposed feeling. Secondly, a limitation on the number of choices you can make, which prevents choice paralysis. Thirdly, a tracking and reward system, which enables you to reflect on your day positively.
##### Expanding the List
A single daily list may not do as you pick up a more diverse range of tasks. Indeed, you may need an inbox with tasks to be sorted and a backlog with sorted tasks prioritized. Essentially though, these are all also lists. They hook into your overall planning process at a different point. These tasks too will eventually end up on a daily checklist, which continuously forms your central point of control.
As your planning process evolves, you may need to expand into creating a list for each day of the week. Whatever tools and setup you choose, make sure it meets these requirements: you should be able to,
1. easily set and see what you should do next;
2. see all the things you have already done;
3. prioritize tasks that still need to be done;
4. set deadlines on tasks (if applicable).
##### Organize, Track and Reflect
While a task list gives you an order in which to do things, it is not the best place to capture all the information regarding a task. For that you need to use something different. Ideally for each thing you are working on you maintain a separate ‘drawer’ of information. This can simply be a page in a notebook, a set of sticky notes, or an on-line alternative like Trello. Whatever you choose: it should be easy to access that information if you need to continue working on the task.
Estimating and tracking is important, as it the only way in which you can learn to estimate better and plan more realistically. For each task that takes more than a couple of hours, I suggest roughly estimating the total time you think you will need for it and tracking the time you put into it. Prevent getting caught up in details: do not plan or track more precisely than a quarter of an hour. The first couple of times you will be way off. This is fine, and also the point of doing it: to get better at planning.
Tracking time only is not enough. At the end of the week, gather all your daily lists, review them, and write some paragraphs about what went well this week and what can be improved for the next week in a journal. There is no need for deep analysis, keep things short and to the point, so reading it back later will be easier. This too will help you improve your planning process, which in turn helps you complete your goals more quickly and efficiently. Besides points of improvements, remember to actually write about and celebrate your successes.
##### A Word on Calendars
I have steered clear so far of calendars. While calendars are a good choice for scheduling meetings and appointments with others, they are a rather poor substitute for planning your day. The reasons for this are simple. Firstly, if you plan your day ahead in your calendar in great detail, your plan is likely already outdated when you start. Priorities change, and tasks shuffle. A plan is dynamic and a calendar is generally too static to capture this well without it turning into micro-management. Secondly, planning in a calendar evokes more anxiety than necessary. If you blocked from ten to twelve to work on that hard math chapter, it may feel like you already failed when you start ten minutes late. A list allows you to plan the order of your day without imposing a strict time schedule.
##### Moment-to-moment
Now that we structured your day, set-up a filing system and a way to continuously improve your planning process by tracking and reflecting, it is time to bite the bullet: allocating actual time to tasks.
Firstly, I would like to encourage you to schedule an end time for each day: after this time you should stop working on the tasks on your list. The end time can vary each day, but it is important to decide on it beforehand. Secondly, realize your objective is not to cram as many hours in a day as possible. Instead, the objective is to be as productive as possible during a limited number of hours. Realistically, you may be able to work in a deep state for about six hours on an average day. Inevitably, unavoidable shallow tasks and required breaks will consume the rest of the time.
Eat a live frog first thing in the morning and nothing worse will happen to you the rest of the dayMark Twain
Starting with a deep task takes willpower. We usually start the day fresh, hence it is one of the best points in the day to utilize willpower. A good habit is to start on your toughest task as the first thing in your day, also called “eating the frog”. Follow this by easier tasks. Doing this beats doing it the other way around as that leads to postponing the hard stuff: procrastination.
Starting on any task can be challenging. However, having started, you may find it is not so bad after all. The trick then is to get started, to get over the initial speed bump, the initial reluctance. The more often you manage to actually do this, the easier it will get.
##### Tick-Tock
Get yourself over the bump by committing a limited fixed amount of time to the task: set a countdown timer and start working. This may seem strange, as an alarm guarantees a future interruption. While this is true, setting a timer also creates a choice-point for you in that near future: do I want to continue with this task, or move on to something else? The bounded time investment and the guarantee of an upcoming choice-point makes this approach powerful.
A commonly used starting point is to set a timer for twenty-five minutes, work in a focused state, and after that take a five minute break. During this break it is best to do something physical, such as getting a cup of tea, doing some stretches or taking a brisk walk. This countdown based approach is called the Pomodori Technique, named after the tomato-shaped timers that are often found in kitchens.
As you apply this method more often, experiment with different intervals instead of sticking to the fixed duration of twenty-five minutes. For example: sixty or even ninety minutes, followed by a longer break. The best interval depends on the task at hand. If you get into a state of flow, consider even disabling the timer. The most important function of the timer is to help you get started, and only to a lesser extent to stop you at some point in the future.
##### Getting Unstuck
What do you do when you get stuck? Do you try harder or give up entirely? Realize that neither approach is right, instead: stop temporarily. This can be a short as a five minute break, or as long as several days. During a short break do something physical which does not tax your brain, for longer stretches of time: simply work on other things. You should get back to the problem at a later time. This approach works remarkably well because it allows your subconscious to work on the problem in the background, while you do other things: diffuse-mode thinking.
Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander. This relaxation can allow different areas of the brain to hook up and return valuable insights.Barbera Oakley
Not all goals require equal attention all the time, some of them require daily dedication, others weekly and some only short stretches of very intensive work. I will refer to tasks that require some form of continuous attention as habitual and those that require short stretches as focused.
If you are learning an instrument you will have to attend to this daily. Pick a fixed moment in your daily schedule for this. For example: playing the instrument after you have breakfast. The goal is to develop a habit, to get into a routine: a system that takes away the cognitive load of having to make a choice. The time you spend need not be long. Half an hour a day translates into almost two whole working days a month. Picking an approach, and sticking to it consistently for at least thirty days, not breaking the chain, will automate the decision process.
This habitual approach works well for learning and producing things. Regularity is the key for progressing towards such goals. Consider that if you wake up every morning and write for thirty minutes before doing anything else, that may not amount to much in several days, but keep it up for a year and you will have put in a good hundred-eighty hours: more than four full-time workweeks.
For projects that require a spurt of activity to complete: dedicate most of your time to them for a set period. Immerse yourself in them from several days up to one or two weeks. This can help put some pressure on finishing the task, instead of letting it endlessly drag on. That said: work on projects in an early phase is often best interleaved with work on other projects. This interleaving allows the early phase projects to incubate, giving you the time to learn the best way to progress on them. You can use this knowledge later on for that period of exclusive immersion.
Over time some goals may become more important. Other goals recede to the background, only to return to the forefront of your attention after a while. This is normal, and progress on projects that require longer immersive time often proceeds in waves. This in fine, as long as you do not stall completely. Try to always keep working on things a bit with some regularity. This way you leverage your unconscious processes to eventually produce better quality output.
#### Conclusion
Planning is personal. The approach you take should avoid overplanning and underplanning and work for you. Gradually enhance your planning process by integrating the ideas, principles and approaches presented in this article and other resources you find. This will take time and effort, but it is worth it. Moving towards your own goals, and learning to enjoy that journey more so than actually reaching the goal itself, is what planning should enable.
You know about the importance of committing regular time to your goals, taking small steps initially and constructing a larger plan with clear completion criteria as you go. You learned about the difference between shallow non-cognitively demanding tasks and deep distraction-free work. Becoming a serial single-tasker is your next challenge. You became aware that when you are not planning your day, someone else with different goals is, and that the anti-dote to this is a list-based planning approach, not a calendar. You realize a list is not enough, and that you need to track and reflect on the time you spent. Upon getting stuck you know you need to walk away temporarily. You also know how to properly allocate time by using countdown clocks, foster habit forming for long-term goals and immersive yourself in tasks nearing completion.
Let me end with a challenge to get you started: dedicate the next half hour to one of your dreams. Something that you have been thinking about picking up for a long time, but never actually seem to get to. Visualize it, hear it, feel it. After the half hour is over, either keep going if you are in flow, or plan the next moment you are going to get back to it. Now: just set a timer, think of the first step, and go!
Sources:
1. Allen, D. (2002) Getting Things Done.
2. Harris, T. (2014) Why Design Needs Ethics.
3. Newport, C. (2016) Deep Work.
4. Oakley, B. (2017) Mind Shift.
5. Oakley, B. (2014) A Mind for Numbers.
6. Schwartz, B. (2005) The Paradox of Choice.
7. Tracy, B. (2007) Eat That Frog.
# Goals II: Motivation
Everyone has dreams about what they want to do in the future. Write a novel, learn a new language or make a trip around the world. Yet it can be hard to motivate yourself to work on realizing these dreams on a consistent basis. How can we align our daily activities with our long term goals? I address this question with a three part series on goals. In this second part we look at one of the key challenges for mid- to long term projects: motivation.
During my teenage years I worked in a bakery during weekends. This required getting up early and performing physically intensive work. After a while I did many of the tasks on autopilot. However, there was little to look forward to, other than doing the same things again next week. After a day’s work I always went home exhausted: physically and mentally. While the people I worked with were friendly, I had some income and I felt I was doing something useful, the job did not intrinsically motivate me. It had low value for me. Hence, it did not take long for me to quit and move on to other things.
Making dinner, going to the toilet or taking a nap. All of these things come naturally as your body generally tells you when to do so with hard to ignore signals. However, for higher level goals these signals do not exists, except perhaps a gnawing sense of unease. Hence the need to learn to motivate yourself to actively move towards those goals. In order for this to work you need to adopt a motivation system that applies specifically to you. The key is finding out what drives you and aligning that with your goals. Consider that while my work in the bakery aligned with the goal of getting income, it did not align well with my preference for learning.
#### Drive
What drives us? Throughout history simple reward and punishment systems have been used to ‘motivate’ people. In many societies, wealth and status form the main scales on which these extrinsic rewards and punishments are applied. If you perform well at work you get a raise: a reward. However, if you do not, your salary remains the same: punishment. This ‘carrot and stick’ approach may work to a degree for some specific tasks, but it seems rather primitive. At best it can get people to comply, at worst it produces bitterness and resentment. It may win their minds, but definitely not their hearts. Can we do better?
An alternative is thinking of motivation as something intrinsic. The three main ingredients of intrinsic motivation: autonomy, mastery and purpose. Firstly, autonomy: self-directed people perform better. Think back to when you were told to do something versus when you were given a goal combined with the freedom to find your own way to achieve it. That second approach likely felt better. Secondly, the path to mastery: sharpening your skills, learning new things and eventually mastering something. The most recent skill you mastered may have taken a lot of effort, but when you finally did, you likely felt a lot of satisfaction too. Finally: a higher level purpose. This should be something that extends beyond yourself and your own interests. Remember the last time you did something for someone else, or for a higher cause, and how that made you feel? Doing something you believe in is very powerful.
As an example: say that you want to learn an instrument. You need autonomy. So, first you dabble in it, then you take regular lessons with a teacher that clicks with your learning style and gives you the opportunity to bring your own selected music. You improve as you put in regular time, the constant feedback loop with your teacher helps you progress towards mastery. Finally, you may want to play that special song for your family or friends, or even play in public to brighten other people’s day: a higher-level purpose.
#### Procrastination
Even with the right drive, it can be hard to stay focused on our goals. We want to do other things as well, and rightly so. Leisure time, which can involve all kinds of different activities, is no less important than working towards goals. However, many people do not consciously make a choice for leisure time, instead their attention drifts away from something they really did want to work on. This guilt-ridden dark zone is the worst place to spend any time. It is not really leisure time at all, it is putting other things off: it is procrastination. This is more or less the opposite of motivation, but the cause and solution is more complex than one might think at first. Let us dive deeper into the causes of procrastination.
##### Delay
Think back to your childhood. You sit in a room in front of a large white table on a small yellow chair. On that chair is the only thing in the room with you: a sweet pink marshmallow. If you manage not to touch that marshmallow for the next fifteen minutes you will be greatly rewarded with: two marshmallows. What do you do?
This experiment was done with children in the late sixties and has been repeated many times since. The objective: to find out a person’s capacity for delayed gratification. Some children found very creative ways to tackle this problem. For example: taking the marshmallow, scooping out the inside with one finger, and putting it back as if nothing had happened. Nevertheless, a key finding was that the children that managed to delay their gratification were more successful later in life. They had better test scores, better jobs and better health.
You can train your ability to delay gratification. However, at the heart of beating procrastination is aligning rewards with your current ability to cope with delayed gratification. If you require frequent rewards: divide tasks into chunks small enough to get those frequent rewards. If you can deal with less frequent rewards you will likely be able to handle larger chunks.
##### Expectations
If you ever applied for a job, you know how hard it can be. Applying to dozens of jobs, only to be rejected. The first time they found someone better suited, the second time you were just too late, the third time they did not even bother to give a reason for the rejection. The more applications you sent in, the lower you believed your chances were. You might have ended up being downright pessimistic. Expecting nothing in return for the effort you put in. This downwards spiral is one of the reasons people procrastinate: low expectations.
Low expectations means believing that you no longer expect any effort on your part will lead to success. The trick here is to change what success is: the reward. Our natural tendency would be to say the reward is getting that job you want. However, this reward is very unpredictable and for a large part also beyond our own control. It does not make much sense to criticize yourself for something that you do not control, does it? In this example the reward should shift to the investment of effort and time. Each letter you send is a success, or even better: each minute put into the job hunt is a success. Instead of your rewarded feeling depending on something beyond your control, now the reward is tied to something that is within your control.
When your expectations are low: divide the task into small chunks of time and actually reward yourself for completing each chunk. Rewards are personal and should be tailored to you, something you enjoy: playing a video game, going outside for a walk or calling a friend for a chat. Rewarding yourself consistently for any effort you put in gets you into a positive feedback spiral, which lifts you out of your low expectations.
##### Value
You really needed to work on that project proposal. However, since you did not like working on it, you instead ended up surfing the web until it was late at night. You felt bad about it, but had no choice but to go to sleep. The next day you repeated the same routine, until the day came when the deadline was tomorrow and you had to clear your schedule and work on it all day long, to deliver only a mediocre end result. This is a second reason people procrastinate: low value.
When a task is of low value, you do not like the activity itself. We all put off what we dislike. For this case rewards can also help. However, as a first action you should increase the task’s value. One way would be to make it more meaningful for yourself: perhaps the project proposal can be aligned with a personal goal that you feel passionate about. If writing the proposal is too easy: make it harder, and if it is too hard: make it easier. For accountability: tell a friend that you are working on it, and by when you will have completed it to create some peer pressure.
When the value of a task is low, align it with something you feel passionate about, adjust the difficulty so it is challenging but doable and use external accountability. This will make the task more intrinsically rewarding, increasing its value.
##### Impulsiveness
You decided to book a tour through a foreign country. Since you like to be on top of things you booked your flight six months in advance. Plenty of things still needed to be arranged, like a plan for the tour itself, places to stay and tickets to major attractions. However, you would get to that later, or so you thought. As your holiday approached, work, social media and other responsibilities distracted you. You kept putting off finalizing your holiday plans. Weeks later, as you packed your bags you realized there was no plan. Arriving at the airport you had to pay an extra fee for your checked luggage, finding a half decent hotel room took hours, and all the major sights you wanted to see were fully booked for the duration of your stay. This is the final main way in which people procrastinate: impulsiveness.
Impulsiveness is the process of being continually distracted by ‘other’ things. The problem is that these other things are either things that you do not initiate: the doorbell rings, your phone beeps or someone steps into your office; or they are unconscious consumption-based habits: checking your e-mail, reading social media or watching news. The more you are interrupted or fall back to unproductive habits, the less likely you are to get into a flow state that helps you move towards your goals.
To curtail impulsiveness one obvious way is to eliminate the distraction. You can disable your door alarm, turn of your telephone or go out of office to a place where you can not be disturbed. Disabling notifications for e-mail, social media and news can help a great deal. If you are still tempted: indulge, but set a timer for five to fifteen minutes tops, then get back to your task.
#### Conclusion
To help you reach your goals it is essential to stay motivated. Motivated, that is, to work consistently towards your goal. For this you will need to set up a motivation system that is tailored to you. It should provide a high degree of freedom on how to approach the next step towards your goal, a sense of increasing accomplishment as you take each step and ideally a higher-level purpose. As goals differ widely, so do systems: each goal may require its own specific system.
Even with systems in place, there will be the tendency to procrastinate for various reasons: you do not think you can do it (low expectations), you do not have the patience to wait for the reward (low delay tolerance), you do not like the task (low value) or you get distracted (impulsiveness). Keep your expectations positive by rewarding yourself for putting in effort that is under your control. Divide your tasks into chunks of time that are small enough to align well with the reward frequency that best fits your current ability to delay gratification. Increase the value of the task by making it challenging enough for your current capability, making it about something you care about and letting others know you are committed to it. Finally, decrease your impulsiveness by eliminating distractions and indulging into temptations only for a short time.
Everyone struggles with motivation. Setting up a reward system helps you move towards the next step. Noticing that you are procrastinating and consistently dealing with it helps you stay on course to reach your goals. Consciously choosing when to engage in leisure activities will make you actually enjoy them. With some forethought, everyone, including you, can stay motivated.
Sources:
1. Pink, D. H. (2009) Drive: The Surprising Truth About What Motivates Us.
2. Steel, P. (2010) The Procrastination Equation
3. Vermeer, A. (2012) Get Motivated
4. Muehlhauser, L. (2011) How to Beat Procrastination
5. Clear, J. (2014) Delayed Gratification
# Goals I: Beliefs
Everyone has dreams about what they want to do in the future. Write a novel, learn a new language or make a trip around the world. Yet somehow the things we do day-to-day are strangely at odds with these dreams. We seem to do many other things, but we never really get to those things we say we really care about. We run faster and faster, but stay more and more in the same place. How can we turn this around? How can we align our daily activities with our long term goals? I address this question with a three part series on goals. In this first part we look at the foundation for achieving goals: beliefs.
Everything starts with the beliefs that you hold about what you can and cannot do. I once met a highly skilled telecommunications engineer. We both attended a presentation seminar and were very impressed by the speakers there. He was especially in awe of the way they told their stories. He told me that he did not have any stories to tell, and even if he had, he would not know how to deliver them to an audience in a captivating way. The more he talked about not being able to do this, the more concerned I grew. Despite having mastered complex signal processing mathematics, he seemed to be unable to grasp the fact that presentation skills too can be split into manageable chunks that can be learned. After convincing him that he could indeed learn these skills, he went on to give some great presentations. Indeed, they were as good as those we saw that very day. Simply changing his belief also changed his behavior and the resulting real world outcome.
Changing a belief is not easy to do, as these run deeply into insecurities about ourselves and our own identity. We often adopt the beliefs we are exposed to during our upbringing, which tends to be a mixed bag for most. Nevertheless, several beliefs are helpful to adopt right now.
We cannot change the cards we are dealt, just how we play the hand.Randy Pausch
#### 1. Start from and with what you have
If you marvel at people with beneficial traits: those good at sports because of their physical features, those proficient at learning because of their intelligence, those skilled at arts because of their creativity, do so because of their accomplishments. That is: how they – learned to – play their cards, not because of what they ‘are’: the cards they were dealt. Talent in the conventional sense is a myth. High performance is the result of practice. A good way to think of this is that you can achieve anything anyone else can, even if your journey may be longer or shorter. It may also include sacrifices you are not willing to make. Factoring this in is fine: working towards goals based on the cards you have is a good thing, making excuses for not working towards goals because of the cards you do not have is not. Instead of thinking in terms of limitations, think in terms of your possibilities.
#### 2. Compare yourself only with your past self
A common habit we fall victim to is comparing our own performance to others, be it our family, friends or accomplished professionals. However, in doing so we usually look at the current skills of the person we are comparing ourselves to, disregarding the journey they needed to get there. A better approach is comparing your own performance now to your own performance in the past. If you have put in effort and are seeing progress: you are on the right track, and in the end: that really is all that matters. That said, while comparing is harmful to progress, being inspired by someone can be a powerful motivator. So, draw inspiration from others, but avoid making comparisons.
#### 3. Foster a strong sense of curiosity
The Internet contains an almost infinite source of materials and methods to learn virtually anything. Given this it is a bit surprising that not everyone is continuously trying to actively learn new things. Curiosity is a good motivation for learning. However, it turns out that the feelings of insecurity, that each of us have, interfere with this. Feeling inadequate stops curiosity dead in its tracks. Children learn quickly because they are less afraid, less worried about failing, and still have this innate curiosity that everyone is born with. Dampening your insecurity and fostering your own curiosity is paramount.
#### 4. Accept the fact that you really can develop yourself
In the past, people used to work in the same job, at the same place, performing the same tasks for many years. The dominant mindset was that you learned at school, and then put your skills to use at work. That is all there was. Scientists found that people’s improvement tapered off and plateaued, and reasoned that this indicated some sort of learning limit. However, this has since been found to be incorrect. Everyone can improve by refining and growing skills, but it requires conscious effort to do so. The rate and direction of growth are under your control. It may take a nudge, like for the telecommunications engineer mentioned previously. However, once you see the possibilities, you can develop yourself far beyond any current beliefs that may hold you back.
#### 5. Do not be too hard on yourself
Learning does not progress as a straight upward line over time. It is rather a bumpy road dominated by regression and plateaus. This is entirely normal. Sometimes there will be clear progress, other times there won’t be any to speak of or even a slight regression. However, from a broader point of view: the more you zoom out, the more you see that your progress really does have an upward direction. Nevertheless, we are not naturally good at looking at things from this perspective. Failing is as much part of progress as is success. People are easily critical of their own lack of short-term progress. Having a clear purpose and meaning behind what you are trying to achieve can help with this. It is good to have ambitious, but realistic, goals. However, it is even more important to reward yourself for putting in the time that eventually enables you to progress towards these goals. Learning to enjoy the process itself and rewarding yourself for even the tiniest amount of effort you put in, is more important than eventually reaching the goal.
#### Conclusion
There is probably something that you have been putting off. Something that you want to do, but never really seem to get to. Perhaps you do not believe you can do it. Instead of confirming this belief: challenge it. Accept where you are right now, start working from where you are. Realize that you can develop yourself and be curious about the world around you. Take tiny steps and rewards yourself for each of these steps and compare your progress only to the progress you made the day before. Accept your failures, celebrate your successes. Realize that changing what you believe you can do is the first step into changing what you actually can do.
Sources:
1. Colvin, G. (2008) Talent is Overrated.
2. Flora, C. (2016) The Golden Age of Teaching Yourself Anything.
3. Foer, J. (2011) Moonwalking with Einstein.
4. Pausch, R. (2008) The Last Lecture.
5. Pink, D. H. (2009) Drive: The Surprising Truth About What Motivates Us.
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https://community.fabric.microsoft.com/t5/DAX-Commands-and-Tips/Filtering-out-for-Holidays-amp-Descending-order/m-p/2645967
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Helper V
## Filtering out for Holidays & Descending order
Hi! I have a two part question.
I have this calulated column:
FD = SUMX (
FILTER (
'Dates',
[Date] <= EARLIER ( 'Dates'[Date] )
&& WEEKDAY ( EARLIER ( 'Dates'[Date] ), 2 ) <> 7
&& MONTH ( [Date] ) = MONTH ( EARLIER ( 'Dates'[Date] ) )
&& YEAR ( [Date] ) = YEAR ( EARLIER ( 'Dates'[Date] ) )
),
IF ( WEEKDAY ( [Date], 2 ) <= 5, 1 )
)
Which returns a colum that begins at 1 and goes up by 1 in each row. Friday and Saturday get the same value and Sunday gets nothing. It will reset back to 1 at each month.
Is there a way to have this go in Descending order? I need one column to go from 1-X and another to go from X-1. If I change the second column (FD2) to descending, they both change and nothing happens in the report. I hope that makes sense.
Basically looking for a column that is "days left" from the first one we just created.
Second question - In addition to filtering out for days of the week, is there a way to have the FD colum show the same value as the previous day when it hits a holiday? I have a holiday table I am just not sure how to add that filter to my existing DAX above.
February:
Wednesday 16=12FD
Thursday 17 =13FD
Friday 18= 14
Saturday 19 =14
Monday 21 (Holiday) =14
Thank you in advance!
2 ACCEPTED SOLUTIONS
Solution Specialist
YYYYMM = YEAR([Date])*100+MONTH([Date])
Isholiday = [Date] in VALUES(TableHoliday[Holiday])
IsRank = not(WEEKDAY([Date],2) = 7 || WEEKDAY([Date],2) = 6 || [Isholiday])
FD2 = IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
FD = IF([FD2] = BLANK(),
BLANK(),
CALCULATE(MAX([FD2]),ALLEXCEPT('Table','Table'[YYYYMM])) -[FD2]+1
)
day = RANKX(FILTER('Table',[YYYYMM]=EARLIER('Table'[YYYYMM])),[Date],,ASC)
Solution Specialist
FD2=
var _FD2 =
IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
return if(_FD2>0, _FD2-1,blank())
11 REPLIES 11
Helper V
@vapid128
Thank you so much you have been a huge help!
Helper V
Hi @vapid128
I did try that earlier, however it returns a -1 for the Sunday as well when that should be blank. I think I need an IF statement in this case? I am not sure, still very new to power bi!
Solution Specialist
var _FD2 =
IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
return if(_FD2>0, _FD2-1,blank())
Helper V
@vapid128
Thank you!!! It is saying that the Syntax for the return is incorrect?
Solution Specialist
Column =
var _FD2 = _______
RETURN IF(_FD2>0,_FD2-1,BLANK())
that should be no problem
Helper V
@vapid128
I am still not sure what I am doing incorrectly.
Solution Specialist
FD2=
var _FD2 =
IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
return if(_FD2>0, _FD2-1,blank())
Solution Specialist
FD2 = IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
-1
Helper V
@vapid128
Thank you so so much!!! This is exactly what I was looking for.
Solution Specialist
YYYYMM = YEAR([Date])*100+MONTH([Date])
Isholiday = [Date] in VALUES(TableHoliday[Holiday])
IsRank = not(WEEKDAY([Date],2) = 7 || WEEKDAY([Date],2) = 6 || [Isholiday])
FD2 = IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
FD = IF([FD2] = BLANK(),
BLANK(),
CALCULATE(MAX([FD2]),ALLEXCEPT('Table','Table'[YYYYMM])) -[FD2]+1
)
day = RANKX(FILTER('Table',[YYYYMM]=EARLIER('Table'[YYYYMM])),[Date],,ASC)
Helper V
Hi @vapid128
Is there a way to have just the FD2 end in 0 instead of 1?
FD2 = IF(WEEKDAY([Date],2)<>7,
RANKX(FILTER('Table','Table'[IsRank] && [YYYYMM]=EARLIER([YYYYMM])),[Date]),
BLANK()
)
So it would be -1 from the FD column
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| 3
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CC-MAIN-2024-33
|
latest
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en
| 0.773274
|
https://math.stackexchange.com/questions/1753111/using-residue-theorem-to-integrate-from-infty-to-infty
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# Using residue theorem to integrate from $-\infty$ to $\infty$
I'm trying to integrate
$$\int_{-\infty}^{\infty} {x^2 \over {(x^2 + 1)}^2(x^2 + 2x + 2)}$$ given that the function
$$f(z) = {z^2 \over {(z^2 + 1)}^2(z^2+2z+2)}$$ has residues
$${9i - 12 \over 100},{3 - 4i \over 25}$$ at the poles $i$ and $-1+i$ respectively. From my understanding of this I have added the two residues (by the residue theorem, and because their respective poles lie in the upper half plane) and multiplied by $2\pi i$ and got an answer of $14\pi \over 100$
Have I done this right?
• Something a little strange is going on: For such an integral usually one (roughly speaking) draws a contour around the upper half-plane or lower half-plane, but you've computed one residue in each. Commented Apr 21, 2016 at 18:03
• I added into my question: don't both poles lie in the upper half plane? Commented Apr 21, 2016 at 18:05
• Well, like I said, $-i$ doesn't lie in the upper half-plane. The only poles are at $\pm i$ and $-1 \pm i$, so you need to add the residues at $i$ and $-1 + i$. Commented Apr 21, 2016 at 18:06
• Yes, this is kosher. Check that you are correct. Commented Apr 21, 2016 at 18:07
• sorry, again I made a mistake (not used to MathJax). The pole was meant to be $i$ not $-i$. Is my method correct? Commented Apr 21, 2016 at 18:13
$$\oint_{\gamma_R} f(z) \, dz := \int_{-R}^R f(x) \, dx + \int_{C_R} f(z) \, dz$$
where $C_R$ is the curve $Re^{it}$ from $t = 0$ to $t = \pi$, oriented counter clockwise using the residue theorem and then take the limit $R \to \infty$. Since your function behaves like $\frac{1}{z^4}$ where $|z| \to \infty$, you will have
$$\left| \int_{C_R} f(z) \, dz \right| \leq \int_{C_R} |f(z)| \, |dz| \approx \frac{\pi R}{R^4} \xrightarrow[R \to \infty]{} 0.$$
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|
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| 3.984375
| 4
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CC-MAIN-2024-26
|
latest
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en
| 0.861087
|
https://socratic.org/questions/the-position-of-an-object-moving-along-a-line-is-given-by-p-t-t-tsin-pi-3t-what--1
| 1,600,671,221,000,000,000
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| 627,945,756
| 6,199
|
# The position of an object moving along a line is given by p(t) = t - tsin(( pi )/3t) . What is the speed of the object at t = 3 ?
Dec 7, 2016
$1 + \pi$
#### Explanation:
Velocity is defined as
$v \left(t\right) \equiv \frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}}$
Therefore, in order to find speed we need to differentiate function $p \left(t\right)$ with respect to time. Please remember that $v \mathmr{and} p$ are vector quantities and speed is a scalar.
$\frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} \left(t - t \sin \left(\frac{\pi}{3} t\right)\right)$
$\implies \frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} t - \frac{d}{\mathrm{dt}} \left(t \sin \left(\frac{\pi}{3} t\right)\right)$
For the second term will need to use the product rule and chain rule as well. We get
$v \left(t\right) = 1 - \left[t \times \frac{d}{\mathrm{dt}} \sin \left(\frac{\pi}{3} t\right) + \sin \left(\frac{\pi}{3} t\right) \times \frac{d}{\mathrm{dt}} t\right]$
$\implies v \left(t\right) = 1 - \left[t \times \cos \left(\frac{\pi}{3} t\right) \times \frac{\pi}{3} + \sin \left(\frac{\pi}{3} t\right)\right]$
$\implies v \left(t\right) = 1 - \left[\frac{\pi}{3} t \cos \left(\frac{\pi}{3} t\right) + \sin \left(\frac{\pi}{3} t\right)\right]$
Now speed at $t = 3$ is $v \left(3\right)$, therefore we have
$v \left(3\right) = 1 - \left[\frac{\pi}{3} \times 3 \cos \left(\frac{\pi}{3} \times 3\right) + \sin \left(\frac{\pi}{3} \times 3\right)\right]$
$\implies v \left(3\right) = 1 - \left[\pi \cos \left(\pi\right) + \sin \left(\pi\right)\right]$
Inserting values of $\sin \mathmr{and} \cos$ functions
$v \left(3\right) = 1 - \left[\pi \times \left(- 1\right) + 0\right]$
$v \left(3\right) = 1 + \pi$
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| 4.59375
| 5
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CC-MAIN-2020-40
|
latest
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en
| 0.525164
|
https://www.calculatoratoz.com/en/edge-length-of-small-stellated-dodecahedron-given-surface-to-volume-ratio-calculator/Calc-24109
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## Credits
Walchand College of Engineering (WCE), Sangli
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## Edge length of Small Stellated Dodecahedron given surface to volume ratio Solution
STEP 0: Pre-Calculation Summary
Formula Used
length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio)
L = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*RAV)
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Surface to Volume Ratio - Surface to Volume Ratio is fraction of surface to volume. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio: 0.5 Hundred --> 0.5 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*RAV) --> (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*0.5)
Evaluating ... ...
L = 5.38833571895502
STEP 3: Convert Result to Output's Unit
5.38833571895502 Meter --> No Conversion Required
FINAL ANSWER
5.38833571895502 Meter <-- Length
(Calculation completed in 00.000 seconds)
## < 7 Edge length of Small Stellated Dodecahedron Calculators
Edge length of Small Stellated Dodecahedron given surface to volume ratio
length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio) Go
Edge length of Small Stellated Dodecahedron given surface area
length = sqrt(Surface Area Polyhedron/(15*(sqrt(5+2*sqrt(5))))) Go
Edge length of Small Stellated Dodecahedron given circumradius
length = (4*Circumradius)/(sqrt(50+22*sqrt(5))) Go
Edge length of Small Stellated Dodecahedron given pyramid height
length = (5*Height)/(sqrt(25+10*sqrt(5))) Go
Edge length of Small Stellated Dodecahedron given volume
length = ((4*Volume)/(5*(7+3*sqrt(5))))^(1/3) Go
Edge length of Small Stellated Dodecahedron given ridge length
length = (2*Ridge Length 1)/(1+sqrt(5)) Go
Edge length of Small Stellated Dodecahedron given pentagram chord
length = Chord Length/(2+sqrt(5)) Go
### Edge length of Small Stellated Dodecahedron given surface to volume ratio Formula
length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio)
L = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*RAV)
## What is Small Stellated Dodecahedron?
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {⁵⁄₂,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.
## How to Calculate Edge length of Small Stellated Dodecahedron given surface to volume ratio?
Edge length of Small Stellated Dodecahedron given surface to volume ratio calculator uses length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio) to calculate the Length, Edge length of Small Stellated Dodecahedron given surface to volume ratio formula is defined as a straight line connecting two vertices of Small Stellated Dodecahedron. Length and is denoted by L symbol.
How to calculate Edge length of Small Stellated Dodecahedron given surface to volume ratio using this online calculator? To use this online calculator for Edge length of Small Stellated Dodecahedron given surface to volume ratio, enter Surface to Volume Ratio (RAV) and hit the calculate button. Here is how the Edge length of Small Stellated Dodecahedron given surface to volume ratio calculation can be explained with given input values -> 5.388336 = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*0.5).
### FAQ
What is Edge length of Small Stellated Dodecahedron given surface to volume ratio?
Edge length of Small Stellated Dodecahedron given surface to volume ratio formula is defined as a straight line connecting two vertices of Small Stellated Dodecahedron and is represented as L = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*RAV) or length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio). Surface to Volume Ratio is fraction of surface to volume.
How to calculate Edge length of Small Stellated Dodecahedron given surface to volume ratio?
Edge length of Small Stellated Dodecahedron given surface to volume ratio formula is defined as a straight line connecting two vertices of Small Stellated Dodecahedron is calculated using length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio). To calculate Edge length of Small Stellated Dodecahedron given surface to volume ratio, you need Surface to Volume Ratio (RAV). With our tool, you need to enter the respective value for Surface to Volume Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Length?
In this formula, Length uses Surface to Volume Ratio. We can use 7 other way(s) to calculate the same, which is/are as follows -
• length = (2*Ridge Length 1)/(1+sqrt(5))
• length = Chord Length/(2+sqrt(5))
• length = (4*Circumradius)/(sqrt(50+22*sqrt(5)))
• length = (5*Height)/(sqrt(25+10*sqrt(5)))
• length = sqrt(Surface Area Polyhedron/(15*(sqrt(5+2*sqrt(5)))))
• length = ((4*Volume)/(5*(7+3*sqrt(5))))^(1/3)
• length = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*Surface to Volume Ratio)
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Great Pumpkins
Giant gourds weigh in for the title of Great Pumpkin.
Index | Instructions | Printable | Solution
October 14, 2002
At last week's 2002 Great Pumpkin Contest weigh-in, five local farmers entered their giant results to try to win the grand prize--a year's supply of pumpkin pie from Peter's Bakery to the grower of the heaviest pumpkin. Each of the farmers, including Plant, is from a different area farm, with one operating Hilltop Farm. Given the weigh-in results below, can you determine each giant pumpkin's weight, the full name of its grower, and the farm he or she represented in the event? Tom's pumpkin weighed more than both Tillman's and the one entered by Silent Spring Farm. The difference in weights between Tom's entry and Tillman's was twice the difference in weights between Tom's pumpkin and the one from Silent Spring farm. Jack won the 2001 Great Pumpkin Contest, edging Meadows by 25 lbs. The pumpkin grown at Valley View Farm weighed in at 100 lbs. more than the one entered by Ron. Harvester and the Maple Glade Farm owner added to the festivities by hauling their entries to the contest in horse-drawn wagons. Peter's Bakery bought both Linda's and the Rocky Bottom Farm's pumpkins to make pies for Thanksgiving. Mary's behemoth weighed 50 lbs. more than Waters's did. Linda's giant pumpkin weighed in at 100 lbs. less than Harvester's monster did. Both Waters and Valley View's owner operate pumpkin patches on their farms where children can pick their personal future Jack O'Lanterns. Jack's giant outweighed the Rocky Bottom Farm entry by 75 lbs. No two entries weighed the same. The winning Giant Pumpkin strained the scales at 800 lbs., while the lightest pumpkin weighed a whopping 650 lbs.
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# If p is a positive integer less than 70, and 71^2 − 142p + p^2 is divi
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Re: If p is a positive integer less than 70, and 71^2 142p + p^2 is divi [#permalink]
Russ19 wrote:
If $$p$$ is a positive integer less than$$70$$, and $$71^2 − 142p + p^2$$ is divisible by $$49$$, what is the remainder when $$p$$ is divided by $$7$$?
A) 0
B) 1
C) 2
D) 4
E) 6
Solution:
• According to the question, $$p$$ is a positive integer less than $$70$$
• And $$71^2 − 142p + p^2=49k$$ where k is an integer
$$⇒(71-p)^2=49k$$
$$⇒71-p=7\sqrt{k}$$
$$⇒p=71-7\sqrt{k}$$
• Remainder when $$p$$ is divided by $$7=(\frac{71-7\sqrt{k}}{7})_r=(\frac{71}{7})_r-(\frac{7\sqrt{k}}{7})_r=1-0=1$$
Hence the right answer is Option B
Re: If p is a positive integer less than 70, and 71^2 142p + p^2 is divi [#permalink]
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# 13. (7 pts) A 50.0 mL sample of 0.180 M Fe(NO3)2 is added to 50.0 mL of 2.0 M NaCN. What is the iron(II) ion concentration in this system at
How do you calculate the Ka values for question 16 parts a and b?
13. (7 pts) A 50.0 mL sample of 0.180 M Fe(NO3)2 is added to 50.0 mL of 2.0 M NaCN. What is theiron(II) ion concentration in this system at equilibrium?14. (6 pts) The measured pH of a saturated Ca(OH)2 solution is 12.35. Calculate the experimental valuefor the Ksp of calcium hydroxide.15.(12 pts) a) How many grams of solid ammonium chloride must be added to 250. mL of 0.500 Maqueous ammonia to give a buffer with a pH of 9.40? (assume no change in volume)b) If 2.00 mL of 3.00M nitric acid is added to 50.0 mL of the buffer prepared in part a), what will be thepH of the resulting solution?89800.0 viao dog16. (12 pts) 20.0 mL of 0.120 M H2A, a weak acid, is titrated with 0.180 M NaOH.a) The pH after adding 10.5 mL of base is 4.88. Calculate the experimental value of Ka for H2A.b) What is the pH at the second equivalence point? Kaz for H2A is 5.9 x 10-17. (8 pts) A solution contains 0.25 M NaF and 0.14 M K2SO4. Ba(NO3)2 is added slowly to the solutionto gradually increase the concentration of barium ions.a) You want to precipitate the maximum amount of sulfate (as BaSO4), but not allow any fluoride toprecipitate. What is the ideal [Ba" ] in the solution in order to accomplish this?solution?b) At the [Bat] you calculated for part a, what percentage of the original sulfate ion will remain in the18. Sketch the titration curve for the titration of 40.0 mL of 0.120 M H2CO3 with 0.180 M KOH. Be sure
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Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are
Question:
Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected.
a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree?
b. What is the probability that exactly seven of the college graduates plan to pursue a graduate degree?
c. What is the probability that at least six but no more than nine of the college graduates plan to pursue a graduate degree?
Fantastic news! We've located the answer you've been seeking!
Step by Step Answer:
Related Book For
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# Properties
Label 3528.1.cw.b Level $3528$ Weight $1$ Character orbit 3528.cw Analytic conductor $1.761$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -56 Inner twists $4$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3528.cw (of order $$6$$, degree $$2$$, not minimal)
## Newform invariants
Self dual: no Analytic conductor: $$1.76070136457$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 504) Projective image $$D_{3}$$ Projective field Galois closure of 3.1.4536.1
## $q$-expansion
The $$q$$-expansion and trace form are shown below.
$$f(q)$$ $$=$$ $$q + \zeta_{6}^{2} q^{2} -\zeta_{6}^{2} q^{3} -\zeta_{6} q^{4} + q^{5} + \zeta_{6} q^{6} + q^{8} -\zeta_{6} q^{9} +O(q^{10})$$ $$q + \zeta_{6}^{2} q^{2} -\zeta_{6}^{2} q^{3} -\zeta_{6} q^{4} + q^{5} + \zeta_{6} q^{6} + q^{8} -\zeta_{6} q^{9} + \zeta_{6}^{2} q^{10} - q^{12} -2 \zeta_{6}^{2} q^{13} -\zeta_{6}^{2} q^{15} + \zeta_{6}^{2} q^{16} + q^{18} -\zeta_{6} q^{19} -\zeta_{6} q^{20} - q^{23} -\zeta_{6}^{2} q^{24} + 2 \zeta_{6} q^{26} - q^{27} + \zeta_{6} q^{30} -\zeta_{6} q^{32} + \zeta_{6}^{2} q^{36} + q^{38} -2 \zeta_{6} q^{39} + q^{40} -\zeta_{6} q^{45} -\zeta_{6}^{2} q^{46} + \zeta_{6} q^{48} -2 q^{52} -\zeta_{6}^{2} q^{54} - q^{57} + 2 \zeta_{6} q^{59} - q^{60} + \zeta_{6}^{2} q^{61} + q^{64} -2 \zeta_{6}^{2} q^{65} + \zeta_{6}^{2} q^{69} - q^{71} -\zeta_{6} q^{72} + \zeta_{6}^{2} q^{76} + 2 q^{78} -\zeta_{6}^{2} q^{79} + \zeta_{6}^{2} q^{80} + \zeta_{6}^{2} q^{81} + 2 \zeta_{6} q^{83} + q^{90} + \zeta_{6} q^{92} -\zeta_{6} q^{95} - q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} + q^{3} - q^{4} + 2q^{5} + q^{6} + 2q^{8} - q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{3} - q^{4} + 2q^{5} + q^{6} + 2q^{8} - q^{9} - q^{10} - 2q^{12} + 2q^{13} + q^{15} - q^{16} + 2q^{18} - q^{19} - q^{20} - 2q^{23} + q^{24} + 2q^{26} - 2q^{27} + q^{30} - q^{32} - q^{36} + 2q^{38} - 2q^{39} + 2q^{40} - q^{45} + q^{46} + q^{48} - 4q^{52} + q^{54} - 2q^{57} + 2q^{59} - 2q^{60} - q^{61} + 2q^{64} + 2q^{65} - q^{69} - 2q^{71} - q^{72} - q^{76} + 4q^{78} + q^{79} - q^{80} - q^{81} + 2q^{83} + 2q^{90} + q^{92} - q^{95} - 2q^{96} + O(q^{100})$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times$$.
$$n$$ $$785$$ $$1081$$ $$1765$$ $$2647$$ $$\chi(n)$$ $$\zeta_{6}^{2}$$ $$\zeta_{6}$$ $$-1$$ $$1$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
2077.1
0.5 − 0.866025i 0.5 + 0.866025i
−0.500000 0.866025i 0.500000 + 0.866025i −0.500000 + 0.866025i 1.00000 0.500000 0.866025i 0 1.00000 −0.500000 + 0.866025i −0.500000 0.866025i
2677.1 −0.500000 + 0.866025i 0.500000 0.866025i −0.500000 0.866025i 1.00000 0.500000 + 0.866025i 0 1.00000 −0.500000 0.866025i −0.500000 + 0.866025i
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
56.h odd 2 1 CM by $$\Q(\sqrt{-14})$$
63.g even 3 1 inner
504.cw odd 6 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3528.1.cw.b 2
7.b odd 2 1 3528.1.cw.a 2
7.c even 3 1 504.1.bn.a 2
7.c even 3 1 3528.1.bp.b 2
7.d odd 6 1 504.1.bn.b yes 2
7.d odd 6 1 3528.1.bp.a 2
8.b even 2 1 3528.1.cw.a 2
9.c even 3 1 3528.1.bp.b 2
21.g even 6 1 1512.1.bn.a 2
21.h odd 6 1 1512.1.bn.b 2
28.f even 6 1 2016.1.bv.a 2
28.g odd 6 1 2016.1.bv.b 2
56.h odd 2 1 CM 3528.1.cw.b 2
56.j odd 6 1 504.1.bn.a 2
56.j odd 6 1 3528.1.bp.b 2
56.k odd 6 1 2016.1.bv.a 2
56.m even 6 1 2016.1.bv.b 2
56.p even 6 1 504.1.bn.b yes 2
56.p even 6 1 3528.1.bp.a 2
63.g even 3 1 inner 3528.1.cw.b 2
63.h even 3 1 504.1.bn.a 2
63.i even 6 1 1512.1.bn.a 2
63.j odd 6 1 1512.1.bn.b 2
63.k odd 6 1 3528.1.cw.a 2
63.l odd 6 1 3528.1.bp.a 2
63.t odd 6 1 504.1.bn.b yes 2
72.n even 6 1 3528.1.bp.a 2
168.s odd 6 1 1512.1.bn.a 2
168.ba even 6 1 1512.1.bn.b 2
252.u odd 6 1 2016.1.bv.b 2
252.bj even 6 1 2016.1.bv.a 2
504.w even 6 1 3528.1.cw.a 2
504.bf even 6 1 2016.1.bv.b 2
504.bi odd 6 1 1512.1.bn.a 2
504.bn odd 6 1 3528.1.bp.b 2
504.bp odd 6 1 504.1.bn.a 2
504.ca even 6 1 1512.1.bn.b 2
504.ce odd 6 1 2016.1.bv.a 2
504.cq even 6 1 504.1.bn.b yes 2
504.cw odd 6 1 inner 3528.1.cw.b 2
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
504.1.bn.a 2 7.c even 3 1
504.1.bn.a 2 56.j odd 6 1
504.1.bn.a 2 63.h even 3 1
504.1.bn.a 2 504.bp odd 6 1
504.1.bn.b yes 2 7.d odd 6 1
504.1.bn.b yes 2 56.p even 6 1
504.1.bn.b yes 2 63.t odd 6 1
504.1.bn.b yes 2 504.cq even 6 1
1512.1.bn.a 2 21.g even 6 1
1512.1.bn.a 2 63.i even 6 1
1512.1.bn.a 2 168.s odd 6 1
1512.1.bn.a 2 504.bi odd 6 1
1512.1.bn.b 2 21.h odd 6 1
1512.1.bn.b 2 63.j odd 6 1
1512.1.bn.b 2 168.ba even 6 1
1512.1.bn.b 2 504.ca even 6 1
2016.1.bv.a 2 28.f even 6 1
2016.1.bv.a 2 56.k odd 6 1
2016.1.bv.a 2 252.bj even 6 1
2016.1.bv.a 2 504.ce odd 6 1
2016.1.bv.b 2 28.g odd 6 1
2016.1.bv.b 2 56.m even 6 1
2016.1.bv.b 2 252.u odd 6 1
2016.1.bv.b 2 504.bf even 6 1
3528.1.bp.a 2 7.d odd 6 1
3528.1.bp.a 2 56.p even 6 1
3528.1.bp.a 2 63.l odd 6 1
3528.1.bp.a 2 72.n even 6 1
3528.1.bp.b 2 7.c even 3 1
3528.1.bp.b 2 9.c even 3 1
3528.1.bp.b 2 56.j odd 6 1
3528.1.bp.b 2 504.bn odd 6 1
3528.1.cw.a 2 7.b odd 2 1
3528.1.cw.a 2 8.b even 2 1
3528.1.cw.a 2 63.k odd 6 1
3528.1.cw.a 2 504.w even 6 1
3528.1.cw.b 2 1.a even 1 1 trivial
3528.1.cw.b 2 56.h odd 2 1 CM
3528.1.cw.b 2 63.g even 3 1 inner
3528.1.cw.b 2 504.cw odd 6 1 inner
## Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator $$T_{5} - 1$$ acting on $$S_{1}^{\mathrm{new}}(3528, [\chi])$$.
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$1 + T + T^{2}$$
$3$ $$1 - T + T^{2}$$
$5$ $$( -1 + T )^{2}$$
$7$ $$T^{2}$$
$11$ $$T^{2}$$
$13$ $$4 - 2 T + T^{2}$$
$17$ $$T^{2}$$
$19$ $$1 + T + T^{2}$$
$23$ $$( 1 + T )^{2}$$
$29$ $$T^{2}$$
$31$ $$T^{2}$$
$37$ $$T^{2}$$
$41$ $$T^{2}$$
$43$ $$T^{2}$$
$47$ $$T^{2}$$
$53$ $$T^{2}$$
$59$ $$4 - 2 T + T^{2}$$
$61$ $$1 + T + T^{2}$$
$67$ $$T^{2}$$
$71$ $$( 1 + T )^{2}$$
$73$ $$T^{2}$$
$79$ $$1 - T + T^{2}$$
$83$ $$4 - 2 T + T^{2}$$
$89$ $$T^{2}$$
$97$ $$T^{2}$$
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Tag Info
Matching pair of socks question
Your error comes from assuming the zero of the derivative is a minimum, whereas it is a maximum. If he could buy $1.25$ packs of black socks he would have $18$ of each color and there would be $324$ ...
• 379k
1 vote
Accepted
Bike turning angle "through what angle". Wordtrick?
The turn angle is measured with respect to the forward direction of the bike. This makes sense because if you go straight on your bike, you are not turning at all, so your turn should be 0 degrees. ...
• 34.6k
1 vote
Accepted
Problem 3-40 in "Calculus on Manifolds" by Spivak. Show that we can write $g=g_n\circ\cdots\circ g_1$ if and only if $g'(x)$ is a diagonal matrix.
Unforunately, Spivak's formulation of the problem is false. Consider $$g(x,y)=(x+y,x)$$ and pick any $(x_1,y_1)$. Then $$g'(x_1,y_1)=g'(x,y)=\begin{bmatrix}1&1\\1&0\end{bmatrix}$$ with \$\det g'...
• 348
Only top scored, non community-wiki answers of a minimum length are eligible
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http://www.theguardian.com/science/sifting-the-evidence/2013/jul/08/hawk-eye-wimbledon/print
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# Hawk-Eye at Wimbledon: it's not as infallible as you think
Hawk-Eye was frequently called upon at Wimbledon, and will no doubt feature in the Ashes, but how accurate is it?
Because of uncertainty over the trajectory of a fast-moving ball between film frames, Hawk-Eye will always be fallible. Photograph: public domain
Novak Djokovic losing his cool over a line call, late in the second set, may have been a pivotal point of Andy Murray's historic Wimbledon victory yesterday. He believed a ball was out, but had run out of Hawk-Eye challenges so couldn't formally dispute the call. The BBC coverage showed Hawk-Eye's analysis of the point in question. Even if Djokovic could have challenged it, he was wrong: the ball was good.
But how accurate is Hawk-Eye? A paper published in 2008 in a journal called Public Understanding of Science suggests that the way Hawk-Eye analyses are presented in sport may lead people to incorrectly assume that its output is definitely what happened. Hawk-Eye presents a great opportunity to discuss uncertainty, confidence intervals, and the joy of stats, so here's a Monday morning maths class.
Statistics can be tricky to understand. They're necessary in a lot of science because when testing hypotheses or ideas, you usually can't test everyone and everything. You take what you hope is a representative sample, and statistics allow us to make predictions about the underlying population. They allow for chance differences between the sample and the population, so they necessarily involve some uncertainty.
All well and good, but what has this got to do with tennis? I'm sure some people will have clicked on this article purely because it'll have a tennis-related photo and headline, but that's part of the argument. The Hawk-Eye paper suggests that although stats are tricky to understand (and it should be pointed out that scientists can fall foul of misunderstanding or misinterpreting them too), it's easier to understand uncertainty when there's a burning interest in being able to do so. And who has more of a burning interest in Hawk-Eye's output than the sports fans who see it being used to determine the outcomes of major sporting events?
I know I've shouted "REF! YOU CANNOT BE SERIOUS?!" at the TV watching England play football (my team, Wycombe Wanderers, are rarely onscreen sadly). Television replays are used by umpires in rugby matches to assess on-pitch events that were obscured from or missed by them as they happened. Cricket and tennis use a different system, Hawk-Eye or similar technology, which predicts either where the ball landed, or the path a ball would have taken.
According to the article, Hawk-Eye works via a number of cameras that capture locations of the ball as it travels, and a model of the field of play. Cameras cannot record every moment of the ball's flight, due to frame rate limitations, so between frames the trajectory of the ball must be estimated. With regards to cricket, where LBW calls are questioned, Hawk-Eye extrapolates beyond where the ball hits the pad, and predicts whether it would have hit the stumps or not.
A model's ability to predict the future path of a ball depends on a number of factors. The further a ball travels before it stops, the easier it is to predict where it would have carried on to. Therefore Hawk-Eye is likely to be less accurate the further towards the batsman the ball bounces, and the further away the batsman is from his stumps. Though Hawk-Eye technology takes some uncertainties into account, its purpose is to give a binary outcome: "out" or "not-out".
The article suggests that more information about that uncertainty should be reported to the television audience, to more honestly show the variation in the possible true paths of a ball. For example they suggest showing a ball's predicted location, and the confidence intervals that surround it (if 95% this would mean there's only a 5% chance the ball actually fell outside this larger area).
This would not only more accurately reflect the limitations of the technology, but it could potentially teach complex statistical concepts and principles to a huge number of people. Hawk-Eye could still provide a binary response to an umpire query, but the probability it is the true answer will also be clear to all.
In tennis, there are differences to cricket that both aid and hinder Hawk-Eye's accuracy. Line calls are often disputed by players, particularly in serves. This is good for using Hawk-Eye, as the ball has actually travelled to the position where the call needs to be made (and usually beyond), so extrapolation beyond the ball's stopping point is not needed.
But tennis balls travel extremely fast (the fastest server at Wimbledon this year was Murray's semi-final opponent Janowicz, whose serve has clocked 143 miles per hour). A faster ball travels further between each frame on a camera film, meaning more uncertainty as to its trajectory between frames.
Hawk-Eye is almost certainly going to be correct more often than a human lines-person, but it can't be perfect, and indeed the makers only claim it is accurate to 5mm (that was in 2008 – it may be more accurate now with the development of faster frame rate cameras). There have been a couple of high profile cases where Hawk-Eye appears to have got it wrong in tennis, most notably in 2007 when Nadal could identify a mark on the court where he claimed the ball landed (out) that Hawk-Eye reported was good.
If Hawk-Eye could provide a measure of uncertainty around its prediction, it wouldn't make its decision any more controversial, argues the article. The results could aid the umpire, even if the margin of error for the technology is reported and explained. They suggest the use of bails in cricket as another aid to turning the often quick and hard-to-observe live game into a binary "in" versus "out" decision. For example, a ball could roll slowly and hit the stumps, but not dislodge the bails, and this would be just "the luck of the game". A close call on Hawk-Eye, which is likely to be more accurate than a human observer but not completely infallible, is a similar enhancement to an umpire's decision making.
The paper concludes that Hawk-Eye should be used as an aid to human judgement (their italics), and that, if used with a little more nuance, it could provide added enjoyment of the games involved and public understanding of technology, its uses and its limitations. What do you think? Do you want a simple binary decision in your sports, or would you rather know the accuracy of Hawk-Eye's output?
## More from Science blog network
The Guardian's science blog network hosts talented writers who are experts in their fields, from mathematics, particle physics and astronomy to neuroscience, science policy and psychology. By giving them the freedom to write on whatever subjects they choose – without editorial interference – they broaden and deepen our coverage of scientific research and debate
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https://search.r-project.org/CRAN/refmans/CVXR/html/sum_entries.html
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sum_entries {CVXR} R Documentation
## Sum of Entries
### Description
The sum of entries in a vector or matrix.
### Usage
```sum_entries(expr, axis = NA_real_, keepdims = FALSE)
## S3 method for class 'Expression'
sum(..., na.rm = FALSE)
```
### Arguments
`expr` An Expression, vector, or matrix. `axis` (Optional) The dimension across which to apply the function: `1` indicates rows, `2` indicates columns, and `NA` indicates rows and columns. The default is `NA`. `keepdims` (Optional) Should dimensions be maintained when applying the atom along an axis? If `FALSE`, result will be collapsed into an n x 1 column vector. The default is `FALSE`. `...` Numeric scalar, vector, matrix, or Expression objects. `na.rm` (Unimplemented) A logical value indicating whether missing values should be removed.
### Value
An Expression representing the sum of the entries of the input.
### Examples
```x <- Variable(2)
prob <- Problem(Minimize(sum_entries(x)), list(t(x) >= matrix(c(1,2), nrow = 1, ncol = 2)))
result <- solve(prob)
result\$value
result\$getValue(x)
C <- Variable(3,2)
prob <- Problem(Maximize(sum_entries(C)), list(C[2:3,] <= 2, C[1,] == 1))
result <- solve(prob)
result\$value
result\$getValue(C)
x <- Variable(2)
prob <- Problem(Minimize(sum_entries(x)), list(t(x) >= matrix(c(1,2), nrow = 1, ncol = 2)))
result <- solve(prob)
result\$value
result\$getValue(x)
C <- Variable(3,2)
prob <- Problem(Maximize(sum_entries(C)), list(C[2:3,] <= 2, C[1,] == 1))
result <- solve(prob)
result\$value
result\$getValue(C)
```
[Package CVXR version 1.0-10 Index]
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http://www.chegg.com/homework-help/calculus-1st-edition-chapter-3-solutions-9780321570567
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# Calculus (1st Edition) View more editions Solutions for Chapter 3
• 7746 step-by-step solutions
• Solved by professors & experts
• iOS, Android, & web
Chapter: Problem:
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The function f(x) = ∣2x + 1∣ is continuous for all x; therefore, it is differentiable for all x.
b. If , then f = g.
c. For any function .
d. The value of f′(a) fails to exist only if the curve yf(x) has a vertical tangent line at x = a.
e. An object can have negative acceleration and increasing speed.
Sample Solution
Chapter: Problem:
• Step 1 of 5
• Step 2 of 5
• Step 3 of 5
• Step 4 of 5
• Step 5 of 5
Corresponding Textbook
Calculus | 1st Edition
9780321570567ISBN-13: 0321570561ISBN: Authors:
Alternate ISBN: 9780321664105, 9780321664112, 9780321709134, 9780321725271, 9780321781086, 9780321788580, 9780321885418
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# Diagnostic Test OG 12th edition
Author Message
Intern
Joined: 16 Aug 2010
Posts: 9
Followers: 0
Kudos [?]: 6 [0], given: 5
Diagnostic Test OG 12th edition [#permalink]
### Show Tags
10 Jan 2011, 09:47
Hi everyone,
I have a question. Is it possible ton convert the score obtained from the diagnostic test?
I mean I got a 18/24 for PS a 17/24 for DS (i.e. 35/48 for Quant section); 15/17 for RC 14/17 for CR and 13/18 for SC (i.e. 42/52 for Verbal)
Would it correspond to a 650-660?
Thank you for your help! I need to know before to go further in my preparation!
GMAT Forum Moderator
Status: Accepting donations for the mohater MBA debt repayment fund
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Re: Diagnostic Test OG 12th edition [#permalink]
### Show Tags
10 Jan 2011, 11:01
camtip wrote:
Hi everyone,
I have a question. Is it possible ton convert the score obtained from the diagnostic test?
I mean I got a 18/24 for PS a 17/24 for DS (i.e. 35/48 for Quant section); 15/17 for RC 14/17 for CR and 13/18 for SC (i.e. 42/52 for Verbal)
Would it correspond to a 650-660?
Thank you for your help! I need to know before to go further in my preparation!
Yes, without knowing the difficulty of the problems you can not convert correct answers to score.
Someone could score 60% correct and score a 700, while someone else could score 60% correct and score a 550.
_________________
Strategy Discussion Thread | Strategy Master | GMAT Debrief| Please discuss strategies in discussion thread. Master thread will be updated accordingly. | GC Member Write Ups
GMAT Club Premium Membership - big benefits and savings
Intern
Joined: 16 Aug 2010
Posts: 9
Followers: 0
Kudos [?]: 6 [0], given: 5
Re: Diagnostic Test OG 12th edition [#permalink]
### Show Tags
10 Jan 2011, 11:12
Ok thanks,
As this is the Diagnostic Test from OG 12th, I supposed it could be converted since the questions are quite commonly known...
I guess I will have a better idea of my "potential score" when i'll take a MGMAT Test.
Moderator
Joined: 27 Aug 2010
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Kudos [?]: 73 [1] , given: 35
Re: Diagnostic Test OG 12th edition [#permalink]
### Show Tags
10 Jan 2011, 12:11
1
KUDOS
camtip wrote:
Ok thanks,
As this is the Diagnostic Test from OG 12th, I supposed it could be converted since the questions are quite commonly known...
I guess I will have a better idea of my "potential score" when i'll take a MGMAT Test.
I'd strongly recommend you to take a GMATPREP test and not a MGMAT test before you start your preparation. A GMATPREP test score will actually allow you to gauge your competency level .
Re: Diagnostic Test OG 12th edition [#permalink] 10 Jan 2011, 12:11
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# Diagnostic Test OG 12th edition
Moderator: HiLine
Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
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https://unduhilmu.com/python-fundamental/list-sort/
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# Tutorial: How to Use List sort() in Python
Posted on
Welcome to our tutorial on using the list sort() function in Python. Lists are a fundamental data structure in Python and often require sorting to make the data more organized and meaningful. In this article, we will provide an overview of the list sort() function and explain its uses and benefits. Additionally, we will discuss various techniques for sorting lists and provide examples of sorting in both alphabetical and numerical order. Let’s dive in and explore the world of list sorting techniques.
## Understanding the List sort() Function
Now that we have introduced the list sort() function, let’s dive deeper into its inner workings. At its core, the list sort() function sorts the elements of a list in ascending order. However, it can also be customized to sort in descending order or based on other criteria.
### How does the list sort() function work?
The list sort() function uses a default sorting algorithm called Timsort. This algorithm is efficient and fast, making it a popular choice for Python developers. Timsort works by first dividing the list into small sublists, sorting them individually, and then merging them to produce a fully sorted list.
It’s important to note that the list sort() function modifies the original list in place, meaning that the order of the elements in the list will be permanently changed.
### Choosing the right algorithm for your needs
While Timsort is the default algorithm used by the list sort() function, Python also offers alternative sorting algorithms that can be used depending on your specific needs.
The sorted() function, for instance, uses the Merge Sort algorithm, which may be more suitable for larger lists. If you’re working with highly specialized data, such as text data that requires case-insensitive sorting, you may want to consider using the natsort package, which offers a natural sorting algorithm.
When selecting an algorithm, it’s important to consider factors such as the size of your list, the type of data you’re working with, and the desired outcome of your sorting operation.
### Conclusion
By understanding the inner workings of the list sort() function and the various sorting algorithms available in Python, you can optimize your sorting operations to achieve the desired outcome efficiently and effectively. With this knowledge, you can choose the most appropriate sorting technique for your specific needs and improve the performance of your Python programs.
## Sorting Lists in Ascending Order
Sorting a list in ascending order can be useful in a variety of applications. Fortunately, Python makes this task easy with the list sort() function. To use it, simply call the function on your list variable and the elements will be automatically sorted in ascending order.
Here’s an example:
``````numbers = [5, 3, 8, 2, 1]
numbers.sort()
print(numbers)
``````
This will output:
``````[1, 2, 3, 5, 8]
``````
Notice that the function modifies the original list in place and returns None. If you want to keep the original list and create a sorted copy, you can use the sorted() function:
``````numbers = [5, 3, 8, 2, 1]
sorted_numbers = sorted(numbers)
print(numbers)
print(sorted_numbers)
``````
This will output:
``````[5, 3, 8, 2, 1]
[1, 2, 3, 5, 8]
``````
Keep in mind that the list sort() function can also be used to sort other data types, such as strings:
``````words = ['apple', 'banana', 'cherry', 'date', 'elderberry']
words.sort()
print(words)
``````
This will output:
``````['apple', 'banana', 'cherry', 'date', 'elderberry']
``````
### Sorting Numeric Lists with Different Data Types
When sorting a list with multiple data types, it’s important to pay attention to the order in which the elements are sorted. Python sorts strings in alphabetical order, while numeric values are sorted in ascending order. To ensure consistent sorting, you may need to convert your data types before sorting.
For example, let’s say you have a list of strings and integers:
``````mixed = ['5', 3, '8', 2, '1']
``````
If you try to sort this list as is, you’ll run into an error:
``````mixed.sort()
``````
This will produce the error message:
``````TypeError: '<' not supported between instances of 'int' and 'str'
``````
To fix this, you can convert all the elements to the same data type before sorting:
``````mixed = ['5', 3, '8', 2, '1']
mixed = [int(i) if i.isdigit() else i for i in mixed]
mixed.sort()
print(mixed)
``````
This will output:
``````[2, 3, '1', '5', '8']
``````
As you can see, the integers are sorted in ascending order while the strings are sorted in alphabetical order based on their ASCII values.
With these techniques in mind, you now have the tools to sort lists in ascending order using Python’s list sort() function.
## Sorting Lists in Descending Order
Sorting lists in descending order is a common task when dealing with data. Luckily, Python also provides a simple method to sort lists in reverse alphabetical or numerical order using the list sort() function.
### Reverse Order with list sort() Function
To sort a list in descending order, we can modify the list sort() function by adding the parameter `reverse=True` as shown in the following example:
``````fruits = ['apple', 'banana', 'cherry']
fruits.sort(reverse=True)
print(fruits)``````
In this example, the output will be:
``['cherry', 'banana', 'apple']``
### Sorting Lists with Different Data Types
When sorting lists in descending order with different data types, we may encounter some challenges. For instance, sorting a list containing both strings and numbers will result in a TypeError message.
To avoid this issue, we can use the sorted() function and define a custom key to sort the list. We can create a function that first checks the length of the input element and then defines the sorting key.
For example:
``````mixed_list = ['apple', 10, 'banana', 20, 'cherry', 30]
def custom_sort(elem):
if isinstance(elem, str):
return len(elem)
return elem
mixed_list.sort(reverse=True, key=custom_sort)
print(mixed_list)``````
The output will be:
``[30, 20, 'cherry', 10, 'banana', 'apple']``
By using the sorted() function and defining a custom sorting key, we can easily sort lists in descending order, even when dealing with different data types.
## Conclusion
In conclusion, understanding the list sort() function in Python is essential for efficient data manipulation. We have discussed the various techniques for sorting lists, including sorting in ascending and descending order, as well as the different sorting algorithms used by Python.
### Importance of List Sorting
Sorting lists can have a significant impact on the efficiency of a program, especially when dealing with large amounts of data. Being able to sort data in a specific order allows for easier and faster access to the desired information.
### Further Exploration
For those interested in further exploring list sorting techniques, we recommend referring to the official Python documentation, as well as other reliable resources such as online tutorials or textbooks.
We hope that this article has provided a comprehensive introduction to list sorting in Python and has been informative for readers.
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# Magnetic field
1. Feb 19, 2008
### arod2812
1. The problem statement, all variables and given/known data
A charged particle is moving in a uniform, constant magnetic field. Which one of the following statements concerning the magnetic force exerted on the particle is false?
It changes the velocity of the particle.
It increases the speed of the particle.
It does not change the kinetic energy of the particle.
It can act only on a particle in motion.
It does no work on the particle.
2. Relevant equations
Could you explain why it false?
3. The attempt at a solution
I am told that the answer is the last one.
2. Feb 19, 2008
### mgb_phys
Not really an attempt!
3. Feb 19, 2008
### blochwave
This isn't obvious but a static magnetic field, whose force on a charge particle is given by F=q(VxB), can not do work.
Remember that work in general depends on the direction between the applied force and the direction of motion. If they're in the same direction then you get the simple W=F*d, and slightly more generally, W=F*d*cos(theta) where theta is the angle between them.(because really it's a dot product)
So now look at the equation for force, and tell me, knowing the definition of a cross product, if the force vector will ever be anything but perpendicular to the velocity of the particle? What's the result of that?
4. Feb 19, 2008
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PDA
View Full Version : Texture Matrix Performance (bumpmapping)
Liquid
08-14-2002, 06:54 AM
I'm useing tangent-space normalmaps (bumpmaps).
The tangent-space light-vectors are passed as 3d texture coordinates so I can use a normalization cubemap.
I could calculate the light-vector in object-space for each vertex.
But even if two polygons share a vertex the tangent-space light-vector of this vertex may be different, depending on the tangent-space matrix of this polygon.
So I could use a vertex array for the vertex positions and use immediate mode for the tangent-space light-vectors.
But it would be nicer to store the object-space light-vectors in the vertex array as well.
If doing so, I have to change the texture matrix for each polygon to the polygons tangent-space matrix to convert the object-space light-vectors from the vertex array to tangent-space.
My question is: Is the texture matrix or the state change performance high enough to change it each polygon when useing > 10000 polygons ???
[This message has been edited by Liquid (edited 08-14-2002).]
[This message has been edited by Liquid (edited 08-14-2002).]
Korval
08-14-2002, 09:08 AM
If you're not using vertex programs/shaders to compute the tangent-space light vector, then you're going to have to compute them on the CPU. You can't do what you're thinking (which, btw, means changing the texture matrix per-vertex) with the texture matrix.
Liquid
08-14-2002, 09:54 AM
The object-space light-vectors are calculated by the cpu and accessed via the vertex array.
I didn't want to change the texture matrix per vertex.
I know that this isn't possible.
I want to change it per polygon so that the light-vectors are transformed to tangent-space.
So the object- to tangent-space matrix is equal for all vertices of one polygon but not for two polygons!
The question is how fast is it to change the texture matrix for each polygon you draw?
Sundy
08-14-2002, 11:05 AM
Umm...Lets Say.... Slow..... Actually it would be super slow if you are to change tyhe matrix for every polygon you draw.
-Sundar
Liquid
08-14-2002, 11:18 AM
So calculating the object-space light-vectors per vertex and transforming it to the polygon's tangent-space in cpu and then useing immediate mode to pass it to gl is faster?
I think immediate mode isn't the fastest.
I could use unique vertices per polygon and store them with their tangent(!)-space light-vectors in a vertex array.
So I didn't have to perform a transform per polygon but I would lose HW-TnL performance because there are no shared vertices any more.
Isn't there a better way without useing vertex programs?
jwatte
08-14-2002, 03:34 PM
To use tangent space, you need to do per-vertex math. This is done either on the CPU or in a vertex program/shader.
Note that even if you do math on the CPU, you're better off doing the math on the CPU, streaming into an output buffer, and then submitting the entire buffer using Draw{Range}Elements. Using immediate mode causes too much calling overhead unless you're REALLY low-poly.
Korval
08-14-2002, 06:49 PM
Liquid, unless your geometry is completely faceted, you'll still have shared vertices. And, if it was faceted, you wouldn't have shared vertices anyway.
Yes, you will need to compute the tangent-space vectors on the CPU. Unless you have shaders, OpenGL can't compute them for you.
But, jwatte is right about putting them in a vertex array when you compute them. It's much faster that way.
zed
08-14-2002, 07:14 PM
perhaps look into using object space bumpmapping (very cheap to do but has other drawbacks though eg u need unique texturing)
Liquid
08-15-2002, 02:03 AM
zed:
I think tangent-space is better for world-models because of several reasons but you are right, with object-space you don't have this problems, but I don't want to use it.
jwatte, Korval:
I've mentioned what both of you said.
If you calculate the tangent-space light-vectors on cpu and store them in a vertex array this might reduce API calls in contrast to several glTexCoord calls.
If two polygons share one vertex the object-space light-vectors of the shared vertex are equal for both polygons, ok.
BUT, even if it's the same vertex the tangent-space light-vectors are different for poly1 and poly2 because the tangent-space matrices of the polygons aren't equal.
Because you only could store one identical texcoord per vertex no matter from which polygon it is accessed(by index), so you must have the same tangent-space light-vector for one vertex the hole time (within one glDrawElements call).
So I have to make a new vertex per polygon with the accurate tangent-space light-vector out of each vertex.
If I do that I will lose HW-TnL performance because storing post-HW-translation vertex coordinates will not be a benefit.
And this is the problem with storing tangent-space light-vectors in a vertex array!
[This message has been edited by Liquid (edited 08-15-2002).]
Liquid
08-15-2002, 02:22 AM
I can't use one index for the vertex position and another index for the texcoord(tangent-space light-vector) for the same vertex, can I ???
If there is a way to do this, it would help a lot.
But I don't know any extension that supports this!
harsman
08-15-2002, 03:27 AM
Just use the same approach you use for normals, sum em up and normalize. It isn't accurate at all but as far as I can tell, it works fine. I think this is covered in docs on per pixel lighting at nvidias dev site.
Liquid
08-15-2002, 05:21 AM
harsman:
Don't believe in papers too much.
Thinks (like the one you mentioned) are only true if several conditions are true.
Later more.
What you mean is interpolating(smoothing) the tangent-space axes-vectors for a vertex?
If so, you are right in one way.
This is a way to smooth edges and also to make the tangent-space light-vector be valid for all polygons because you don't use the polygon's tangent-space matrix any more but the vertex's one, which has the smoothed normal as the tangent-space z-axis.
But consider a case where two polygons share one vertex.
Please ignore that up,down,left,right are no correct directions in object-space(so in 3D):
Poly1's TS(tangent-space) x-axis is right and the TS y-axis is up.
Poly2's TS x-axis is left and the TS y-axis is down.
So how do you smooth this?
The resulting matrix would be all zeros!
So even if this is not the case the resulting matrix could be wrong.
Another point is that it would not work because the normals in the bumpmap are stored in the polygon's tangent-space not in the smoothed vertex's one but the difference could cause the effect of smoothing!?
harsman, you are right that there are cases where one vertex doesn't have to be split into two and that the vertex's TS light-vector is valid for more than one polygon.
But this is only the case if all polygons that share this vertex are smoothed with eachother and that their tangent-space matrices(xyz-axes) could be smoothed too(e.i. no opposit directions like in my example).
[This message has been edited by Liquid (edited 08-15-2002).]
harsman
08-15-2002, 06:43 AM
Yes, that's correct. Models (specifically the models tex coords) need to be well bahaved for this to work. Just as you said, artists can't mirror a texture over two polygons (e.g. only half of a characters face is stored in the texture map and then mirrorred using UVs). Tough, but that's the only way you'll get acceptable performance out of tangent space bumpmapping. If you have lots of broken meshes you want to use, check out NVMeshmender at nvidias dev site.
Liquid
08-15-2002, 09:44 AM
harsman:
Thanks. You've helped me to proove my thoughts.
I think I'll try to calculate the TS light-vector for each vertex and store it in a vertex array.
I will break vertices with the same position but a different normal/tangent-matrix in two vertices in a pre-processing step or in the level editor.
Because most of my edges are smooth, I think this will be ok.
But one thing would be nice:
To have the possibility to use different indices for the position and the texcoords of one vertex.
Because two vertices with the same position but different texcoords must be translated twice by gl :(
harsman
08-16-2002, 02:01 AM
On most moderately high poly models, having separate indices probably isn't a win. You might gain some transform cost (if the hardware can handle separate indices) but you have to transfer a lot more indices. The cost of transfering these extra indices is probably higher then the cost of duplicating a few vertices.
Liquid
08-16-2002, 06:00 AM
Maybe you are right.
h2
08-16-2002, 06:32 AM
Liquid,
Another thing that you can do is to compute normal maps not in the tangent space, but in the object space. Procs and cons of this approach:
+ you don't need vertex shaders if you use cubemaps (usual texture matrix transform is sufficient).
+ less space is required for VB (you don't need to store TBN basis).
- you have to create a normal map for each object (even if they use the same normal perturbation map, geometry will be different and thus normals will be different). It can be messy since you can create additional texture coordinate discontinuities in model (thus you have to duplicate vertices etc). But if your model uses "skin-like" texture and 1:1 mapping from texture space to surface space exists, you can reuse texture coordinates of your base texture.
- it is complicated to use spot lights in object-space lighting scheme like this.
Hope it helps. Sorry for my English.
[This message has been edited by h2 (edited 08-16-2002).]
Liquid
08-18-2002, 01:12 AM
Thanks, h2.
But I've also read all the papers on the nvidia developer page.
I still think tangent-space will be better for a whole level, even if object-space has some advantages.
I think spotlights are as easy as in the tangent-space method.
Just use a cubemap and multiply everything with it.
It doesn't matter if the bumpmap is in tangent- or object-space.
h2
08-19-2002, 01:56 AM
Of course spot lights are not easy in tangent space as well. I mean the case when you have non-uniform scaling.
[This message has been edited by h2 (edited 08-19-2002).]
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• ## Top Posts
quadratic equation c… on Modeling Data With Quadratic… Lemuel on Quadratic Functions and Their… Arizona Bayfield on How To Simplify Rational … Suemac on Proving Lines Parallel with Tr… Mr. Pi on Subsets of Real Numbers
## The Diagonals of a Rhombus are Perpendicular
This post is dedicated to proving the diagonals of a rhombus are perpendicular. To complete this or any proof, it is good to make a plan. In this case, I am going to establish that the two triangles on the top of the rhombus are congruent. This is seen in steps 2 through 4 of the proof below. Next, I show that angles AEB and CEB right angles, which is modeled in steps 6 through 8. That is enough to state the diagonals of a rhombus are perpendicular.
I encourage you to click on the image to see it at full size. It looks much better at full size. I scanned the piece of notebook paper that I work this proof out on and messed around in photoshop.
Proof - Diagonals of a Rhombus are Perpendicular
## How to Write Indirect Proofs – Exterior Angle Inequality Theorem
A youtube viewer of mine requested a video on how to write an indirect proof. Before making the video, I thought it would be good to write a blog post about this topic before I make my video, because an indirect proof is best written as a paragraph proof. There are three steps to writing an indirect proof.
1. Assume that the conclusion is false, by negating the prove statement.
2. Establish that the assumption in step #1 leads to a contradiction of some fact i.e. definition, postulate, corollary or theorem.
3. State the assumption must be false, thus, the conclusion or prove statement is true.
Steps 1 and 2 involve all of the thought and memory skills and can be discussed separately. Do not make this harder than it is. Step 1 involves writing the negation of a statement. Step 2 requires you to pull on your knowledge of geometric definitions, postulates, theorems and corollaries to recognize the contradiction between a known geometric fact and the assumption in step 1. Step 3 involves stating the obvious: Since the assumption is false, the prove statement must be true. If you are confused, check out the examples.
Example 1 – Prove the Exterior Angle Inequality Theorem with Indirect Proof
Given: $\angle{1}$ is an exterior angle of $\Delta{ABC}$
Prove: $m\angle{1}>m\angle{4}$
Figure 1 - Indirect Proof Diagram
Step 1 – Assume that $m\angle{1} \not> m\angle{4}$, this means that $m\angle{1} \leq m\angle{4}$.
Step 2 – We need to establish that $m\angle{1} \leq m\angle{4}$ contradicts a mathematical fact.
$m\angle{1} \leq m\angle{4}$ gives two different situations that need to be tested:
$m \angle{1}= \angle{4}$ or $m \angle{1}.
$m \angle{1}= \angle{4}$
By the Exterior Angle Theorem, $m \angle{3}+m \angle{4}=m \angle{1}$ and using substitution, $m \angle{1}+m \angle{4}=m \angle{1}$. Subtracting $m \angle {1}$ from both sides gives $m \angle{4}=0$. This contradicts the fact an angle must have a measure greater than 0.
$m \angle{1}
By the Exterior Angle Theorem, $m \angle{3}+m \angle{4}=m \angle{1}.$ Angles must have a positive measure, the definition means $m \angle{1}> m \angle{3}$ and $m \angle{1}>m \angle {4}$.
Step 3 – In each instance, the assumption from step 1 is contradicted of a know mathematical fact. Thus, the assumption that $m\angle{1} \leq m\angle{4}$ is false. So, the original prove statement, $m\angle{1}>m\angle{4}$ , must be true.
## 3.2 Proving The Converse of the Alternate Interior Angles Theorem
“What’s the point in proving theorems that have already been proved?” If your geometry class is anything like mine, then you have been asked to prove an existing theorem and you may have asked yourself the same question as above. Well there is the easy answer, because “I said so”. I agree, that is pretty lame and in reality being able to write a proof of an established theorem requires an ability to recall facts and to apply those facts and given information to arrive at a valid conclusion.
One such proof is of the Converse of the Alternate Interior Angles Theorem.
### Converse of the Alternate Interior Angles Theorem
If two lines and a transversal form alternate interior angles that are congruent,
then the two lines are parallel.
One proof method of proof that I have stayed away from is the flow proof. The flow is too much work for the end product. It takes more time to complete the same problem. The image in this post took twice as much time to create than a simple image and writing a paragraph proof on my math blog. I came back to this section, because the a previous post on Parallel Lines is my top page receiving hits, so I wanted to do something more.
3.2 Proving Lines Parallel Paragraph Proof
First off, the diagram is missing a label that is necessary for a paragraph proof of the converse of the alternate interior angles theorem. The line that is acting as the transversal of lines l and m will be called line t.
Given that line t is the transversal of lines l and m. By definition, Angle 3 and angle 1 are vertical angles and are congruent by the vertical angles theorem. It is given that angle 1 is congruent to angle 2. Applying the transitive property of congruence, it can be established that angle 2 is congruent to angle 3. It should be said that angle 2 and angle 3 are corresponding angles.Thus line l is parallel to line m because of the converse of the corresponding angles postulate. QED
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## Exam 1
1. #### Question
In the following figure the distributions of a variable given by two samples (A and B) are represented by parallel boxplots. Which of the following statements are correct? (Comment: The statements are either about correct or clearly wrong.)
1. The location of both distributions is about the same.
2. Both distributions contain no outliers.
3. The spread in sample A is clearly bigger than in B.
4. The skewness of both samples is similar.
5. Distribution A is right-skewed.
#### Solution
1. False. Distribution B has on average higher values than distribution A.
2. False. There are observations which deviate more than 1.5 times the interquartile range from the median.
3. True. The interquartile range in sample A is clearly bigger than in B.
4. True. The skewness of both distributions is similar, both are about symmetric.
5. False. Distribution A is about symmetric.
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# B Theory of relativity
1. Aug 9, 2016
### sunney
acoording to theory of relativity, if a car is moving at a uniform speed then any object inside that car behave like its in rest. so what happens if a man throws a ball in an open roof car which is at uniform speed, where that ball is likely to land , assuming no other external force is applied to the ball ?
2. Aug 9, 2016
### jbriggs444
Have you tried the experiment in a closed roof car? Do you expect that an open roof will make a difference?
3. Aug 15, 2016
### mitchel
What happens when you spit your gum out on the freeway? Why do you think it would be different out of an open roof? (Hint: Air Resistance/Drag)
Most thought experiments like this are made with the assumption of being in a vacuum, where no wind resistance is at play. If this were in a vacuum and the ball was to be thrown straight up, it would come right back down to where it was released provided no that other forces were present besides gravity. However, in the real world, that ball
https://en.wikipedia.org/wiki/Drag_(physics)
https://en.wikipedia.org/wiki/Vacuum
I hope that helps!
4. Aug 15, 2016
### PAllen
This is a question fully addressed by Galilean relativity, as the relative speeds are so low. In an open roof, in the frame of the car, there is a wind blowing around the car which will obviously affect a ball thrown through an open roof. Note that the principle of relativity was known in Galileo's time, as was an understanding that this example in no way 'questions' the principle.
5. Aug 15, 2016
### mitchel
If you have Audible, Great Ideas of Classical Physics with Steven Pollock addresses this in the second chapter too.
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# Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus)
Author Message
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
### Show Tags
15 Aug 2013, 11:22
GMATPill wrote:
Hi bagdbmba,
Yes, the GMAT is slowly trending towards more passages / fewer questions per passage.
What you should work on more is speed reading and time management.
Because the passages are shorter - that means there will be more of them. So you will need to quickly read the short passage, answer a few questions - then probably do an SC/CR question, then do another short RC passage with a few questions.
Reading the passages should be a little easier - since there will be fewer extraneous details in the shorter passage. But still, focus needs to be on those transition words, etc.
Having said the above, don't be surprised by a long passage - you still may see them - just not as common as before.
Hi,
So what I sense from your comments is that we should provide more stress on short passages rather on long passages...may be 70-30 ratio will be good I guess. Right?
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
### Show Tags
04 Sep 2013, 13:25
bagdbmba wrote:
GMATPill wrote:
Hi bagdbmba,
Yes, the GMAT is slowly trending towards more passages / fewer questions per passage.
What you should work on more is speed reading and time management.
Because the passages are shorter - that means there will be more of them. So you will need to quickly read the short passage, answer a few questions - then probably do an SC/CR question, then do another short RC passage with a few questions.
Reading the passages should be a little easier - since there will be fewer extraneous details in the shorter passage. But still, focus needs to be on those transition words, etc.
Having said the above, don't be surprised by a long passage - you still may see them - just not as common as before.
Hi,
So what I sense from your comments is that we should provide more stress on short passages rather on long passages...may be 70-30 ratio will be good I guess. Right?
Yes, that's a fair split. Just psychologically knowing that passages will tend to be on the shorter side can help you prepare mentally - since you have a better sense of what to expect.
Also - an update that we've added some video solutions to our OG13 Online Tracker: http://www.gmatpill.com/official-guide-gmat/
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02 Oct 2013, 15:07
Just an announcement that GMAT PILL will be increasing prices on October 10, 2013
see details here: announcing-gmat-pill-price-increase-on-oct-160842.html
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21 Oct 2013, 19:28
Their questions are from Official guide or they are unique questions, I have already solved official guide questions, So if they offer me Brand new questions, I would love to purchase their product.
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My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html
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21 Oct 2013, 21:31
_________________
Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html
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22 Oct 2013, 08:18
honchos,
We have roughly 1,000+ questions - though we also reference OG/GMATprep questions in our teachings to help you understand concepts in the context of past exam questions. The source of each question is listed at the bottom of each question link. We would estimate that at least 85% of questions you will not have seen before.
Your concern should not be about # of questions. You can do 5,000 questions and get no where. Doing lots of questions will not necessarily get you results. What you should be concerned about his thought process - how you think. Quality over quantity. That's what GMAT Pill is about. We do not have a database of 5,000 questions because we believe that is not important. In fact, so many questions without a proper analysis of them can actually be wasteful for your studying.
We provide you enough exercises and questions that will optimally utilize your time without overwhelming you.
Focus on what is important. Otherwise, you will be studying harder and harder and getting no results.
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23 Oct 2013, 07:58
Hi sir/ma'am, I would be grateful if u can guide me a bit.
M an Indian mechanical engineer with 14months of work ex. in production,but had been involved in my own business(retail,wholesale & a bit of manufacturing) due to some family concerns,since the end of 2011.M planning to give GMAT in jan 2014.M new to GMAT and was thinking asto which mock tests/papers should I buy? Gave free test of Veritas(don't remember the exact name) and got a meagre 630 marks.FREE GMAT1-620. I have heard about GMAT800,KAPLAN,etc But m confused.How would be IMS mocks??
2)Secondly,working in my own business.Can I show this as work ex. while applying to interrnational b schools?? Basically,we have retail outlets in Calcutta(India).
3)Lastly,since m going to give GMAT in jan 2014,m I too late for admissions in the 2014 session of MBA in international universities??
Sorry for a long post and thanks for being patient to read this!
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06 Nov 2013, 13:49
justnishu4u wrote:
Hi sir/ma'am, I would be grateful if u can guide me a bit.
M an Indian mechanical engineer with 14months of work ex. in production,but had been involved in my own business(retail,wholesale & a bit of manufacturing) due to some family concerns,since the end of 2011.M planning to give GMAT in jan 2014.M new to GMAT and was thinking asto which mock tests/papers should I buy? Gave free test of Veritas(don't remember the exact name) and got a meagre 630 marks.FREE GMAT1-620. I have heard about GMAT800,KAPLAN,etc But m confused.How would be IMS mocks??
2)Secondly,working in my own business.Can I show this as work ex. while applying to interrnational b schools?? Basically,we have retail outlets in Calcutta(India).
3)Lastly,since m going to give GMAT in jan 2014,m I too late for admissions in the 2014 session of MBA in international universities??
Sorry for a long post and thanks for being patient to read this!
justnishu4u,
2) For books - the best one is: http://www.amazon.com/gp/product/111810 ... 1118109791
3) Combine #1 and #2 above with an online course (like GMAT Pill course) - and you'll have the ultimate study material.
Of course, you can consider supplemental material -- but ONLY AFTER you've absolutely exhausted the above 3 materials---that is very rare if done the right way.
For your last question - it depends on the university. Most of the top schools still have a Round 3 deadline in March/April. Round 2 deadline is usually first week of January. R2 would be feasible if you are already putting your application together now - and GMAT is your last step as you take it right before the deadline and have it mailed in soon afterwards.
But otherwise, R3 is fine in terms of timing.
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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21 Nov 2013, 10:31
Hi,
I've already bought a Quant package and I liked it a lot.
Now, I am thinking about updating my account to full package. If I do so, can I be eligible to +50 point guarantee?
My current score is 640 (Q47 V31) and +50 points will be ok for me.
Thank you.
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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22 Nov 2013, 07:25
Rashidmsu wrote:
Hi,
I've already bought a Quant package and I liked it a lot.
Now, I am thinking about updating my account to full package. If I do so, can I be eligible to +50 point guarantee?
My current score is 640 (Q47 V31) and +50 points will be ok for me.
Thank you.
Great to hear the Quant Pill is useful to you. Unfortunately the 50point guarantee only applies to students who took the leap of faith in the beginning and purchased the full package. For you it looks like you already like quant pill - you'll very likely find the Verbal Pill very helpful and a "guarantee" feature shouldn't be what's preventing you from making that investment. Hope that helps /makes sense.
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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01 Mar 2014, 20:27
Hi. I'm Josh.
I have taken two GMATs so far, but miserably got 520, and 580. I am planning to take my third one this April and budget and content-wise, I was interested in GMAT Pill. Like what GMAT Pill says, doing more practice tests doesn't get you the score bump and I agree as I've done like 7 cats but all average 560-620. I think I need to work on my thinking approach first instead of continuing to solve practice questions and read why it's wrong
Question: I have explored the GMAT Pill site a bit, but didn't really understand what I'm exactly paying for given I buy the full package.
1. I didn't have access to most of the videos (I am assuming I am paying for the platform section), but I could still access practice questions and have the correct answers shown. So am I paying for the videos that would be available upon payment? So what it felt like to me when I accessed the website is, 'all the questions are available for free with answers, but you need to pay if you want to see the video answers.' Did I understand right? I am aware about the package (http://www.gmatpill.com/amember/course_details.php).
The confusion I am having is I guess usually most GMAT prep companies just show free trials, but do not show practice questions or anything at all the way GMAT Pill does, so I was confused for a bit.
Thanks,
Josh
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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19 Mar 2014, 13:17
uwengdori wrote:
Hi. I'm Josh.
I have taken two GMATs so far, but miserably got 520, and 580. I am planning to take my third one this April and budget and content-wise, I was interested in GMAT Pill. Like what GMAT Pill says, doing more practice tests doesn't get you the score bump and I agree as I've done like 7 cats but all average 560-620. I think I need to work on my thinking approach first instead of continuing to solve practice questions and read why it's wrong
Question: I have explored the GMAT Pill site a bit, but didn't really understand what I'm exactly paying for given I buy the full package.
1. I didn't have access to most of the videos (I am assuming I am paying for the platform section), but I could still access practice questions and have the correct answers shown. So am I paying for the videos that would be available upon payment? So what it felt like to me when I accessed the website is, 'all the questions are available for free with answers, but you need to pay if you want to see the video answers.' Did I understand right? I am aware about the package (http://www.gmatpill.com/amember/course_details.php).
The confusion I am having is I guess usually most GMAT prep companies just show free trials, but do not show practice questions or anything at all the way GMAT Pill does, so I was confused for a bit.
Thanks,
Josh
Hi Josh,
Great question.
So the Platform section you see - is actually the last step of our course.
1) First you learn all the core materials, then you apply various frameworks to practice questions.
2) Second, you apply what you learn to OG questions - we provide our video explanations for these OG questions.
3) Third, you test yourself with Practice Pill Platform questions.
So yes, your membership will include access to all video explanations that are available on this Practice Pill Platform third step.
But your membership will also include the core training in Steps #1 and #2.
The platform only represents 25-30% of what you get. The remaining 70% is not open on the Practice Pill Platform.
Your membership would also give you full access to all course videos organized in an easy-to-use interface on iPhone / iPad / Android apps. Just search "gmat pill" in the app store or play store and download the app. Once you enter in your GMAT PILL credentials, you will have access to everything there --- 500+ practice questions and 1,200+ videos.
And yes, we are different from most other companies. The value is not in our questions - but rather in our thought process showcased in the videos. So we have no problem giving away free questions. Not all of them are shown there---the remaining ones are in the course area only.
Hope that clears it up.
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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19 Mar 2014, 13:26
Thank you for the reply. I actually have been subscribing GMAT Pill full package right after I asked that question so that I can prepare for April 1 GMAT exam and follow along GMATPILL's one month plan. It's been helping me understand concepts better (actually was surprised with some of the ways Zeke taught as it made solving problems way easier and more understandable). Hopefully I can get a huge jump.
-Josh
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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30 Apr 2014, 10:29
uwengdori wrote:
Thank you for the reply. I actually have been subscribing GMAT Pill full package right after I asked that question so that I can prepare for April 1 GMAT exam and follow along GMATPILL's one month plan. It's been helping me understand concepts better (actually was surprised with some of the ways Zeke taught as it made solving problems way easier and more understandable). Hopefully I can get a huge jump.
-Josh
Uwengdori,
That's great to hear -- follow along the plan and you'll be in good shape. Remember to do practice sprints -- this helps build stamina for the real thing (which is what matters). You need to train your mind to quickly see a GMAT question then "go".
If you have more time, try reading up on the 2-3 month study plan
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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16 Jun 2014, 23:12
1
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BOOKMARKED
Hi
I would like to enroll for GMAT Pill and wanted some information regarding this organisation. And how is it better than all other institutes . Basically wanted to enroll for all courses. Could you please let me know the total package cost as well.
It would be better if you let me know how the class goes. Is it online or all videos. Please do let me know, Thanks
Thanks
Sunil
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16 Jun 2014, 23:15
1
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BOOKMARKED
Hi GMAT Pill
If you could please let me know how is it better baically from e-GMAT. Please do let me know.
In case I can attend a demo session that would be really very helpful.
Thanks
Sunil
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24 Jun 2014, 16:06
sunil1989,
To answer your questions, I'd recommend checking out our website and taking a look at this chart:
http://www.gmatpill.com/how-we-compare/
You'll see the main areas that make us unique. There are a number of areas that separate us (price, online question bank, mobile app, guarantee, #1 5-star ranking, OG videos and explanations) but perhaps the most important area is the style of teaching. A video-focused approach, hand-drawn quant explanations, teaching directly from founder (no other substitute teacher), easy to understand explanations even non-native speakers can understand, and video playlist. You can't and shouldn't underestimate the style of teaching in choosing your test prep provider. See the link for more details.
On GMAT Club, you'll see some high level areas that make us unique in the GMAT Club discount page for GMAT Pill.
Regarding how we are *better* than other organizations, I'd love to elaborate on that but as this is a public forum I'm unable to comment about other organizations. We do have some customers that considered other prep providers, chose us and didn't regret their decision. You can check out Raghu's story here at this link below. If you scroll near the bottom, you'll see some discussion regarding this student's thinking process in choosing GMAT Pill over others like egmat.
http://www.gmatpill.com/from-570-620-71 ... ats-raghu/
The GMAT Pill course is a collection videos, online question platform, PDFs, and book (OG) for solidifying best practices. Learn more about the day by day process in our 1 month study plan
Hope that helps!
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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04 Jul 2014, 16:27
Hi GMAT Pill,
I recently took the official GMAT and scored a 660 Q44V36. My goal is to break the 710 mark and I was interested in signing up for your course.
My question to you was in regards to how you think GMAT pill would help?
Is it a matter of learning your specific thought process and applying it to the problems? If so, which problems would you recommend? I personally feel as though i've gone through most, if not all, of the OG questions and doing them might trigger some memory recollection vs. application of your expert thought process. How would I combat that?
Additionally, how would you recommend a specific study plan once I was a student of GMAT Pill? Meaning, the official exam doesn't break down the results in categories of various question types and time spent per each question. How would we be able to combat that lack of information in setting up a specific study plan?
I'm excited to jump on board as soon as I have some clarification in regards to the plan of attack.
Thanks a ton.
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Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink]
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10 Jul 2014, 08:31
russ9 wrote:
Hi GMAT Pill,
I recently took the official GMAT and scored a 660 Q44V36. My goal is to break the 710 mark and I was interested in signing up for your course.
My question to you was in regards to how you think GMAT pill would help?
Is it a matter of learning your specific thought process and applying it to the problems? If so, which problems would you recommend? I personally feel as though i've gone through most, if not all, of the OG questions and doing them might trigger some memory recollection vs. application of your expert thought process. How would I combat that?
Additionally, how would you recommend a specific study plan once I was a student of GMAT Pill? Meaning, the official exam doesn't break down the results in categories of various question types and time spent per each question. How would we be able to combat that lack of information in setting up a specific study plan?
I'm excited to jump on board as soon as I have some clarification in regards to the plan of attack.
Thanks a ton.
Hi russ9,
It appears your weakness is slightly on the quant side. Our program goes through the most common types of quant questions (rates, sum of sequences, word problems, etc) -- and does all the variations around that core question so that if the question were worded slightly differently, you will know how to handle that situation.
Do not dismiss a source of questions until you actually can exhaustively answer everything there correctly and in a timely fashion. Just because you've "seen" an OG question - does not mean it is useless to you. Use it as an opportunity to further reinforce what you know and to give yourself confidence that you realy do know it.
If your goal is a 710 -- it really doesn't matter too much what specific sub-category you need extra work on. At the 710 level, you're going to need to get questions correct in almost every category. Our study plan gives you daily emails with links telling you exactly what you need to watch that day and which exercises you need to do. Just go through them and don't worry too much about the particular subsections -- because in the end, you're going to need to get good in all areas.
Hope that helps.
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26 Aug 2014, 05:21
New testimonials page collection posted - check it out here: http://www.gmatpill.com/testimonials/
Re: Ask GMAT Pill (Video GMAT Course $333 Discount +$250 bonus) [#permalink] 26 Aug 2014, 05:21
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CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
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ngcw1986 March 12, 2012 23:47
How to create velocity profile using the previous time step ones
Dear all,
I am doing a large eddy simulation case, and I run into a trouble to define inlet conditions, explicitly the turbulent velocity.
The turbulent velocity has such a formation: u'(t)=u'(t-delta_t)*exp(-t/T). For u'(t) is not a direct function of time, it causes a great pain to rebuild such a inlet turbulent velocity for me.
I tried a lot using groovyBC of swak4FOAM, used to extract the previous time step value of u@inlet but failed. I wondering anyone can help me out.
Considering my poor skill using swak4FOAM and little experience with openFOAM, I hope I did not propose a stupid questions!
Thank you in advance! Great regard and best wishes!
gschaider March 13, 2012 19:00
Quote:
Originally Posted by ngcw1986 (Post 349050) Dear all, I am doing a large eddy simulation case, and I run into a trouble to define inlet conditions, explicitly the turbulent velocity. The turbulent velocity has such a formation: u'(t)=u'(t-delta_t)*exp(-t/T). For u'(t) is not a direct function of time, it causes a great pain to rebuild such a inlet turbulent velocity for me. I tried a lot using groovyBC of swak4FOAM, used to extract the previous time step value of u@inlet but failed. I wondering anyone can help me out. Considering my poor skill using swak4FOAM and little experience with openFOAM, I hope I did not propose a stupid questions! Thank you in advance! Great regard and best wishes!
I don't really understand what you're trying to do. Anyway. The development version (the one downloaded by mercurial) has a function has a function oldTime(U) that gives you the value of a field at the last time-step. Use with care
ngcw1986 March 13, 2012 22:53
Quote:
Originally Posted by gschaider (Post 349293) I don't really understand what you're trying to do. Anyway. The development version (the one downloaded by mercurial) has a function has a function oldTime(U) that gives you the value of a field at the last time-step. Use with care
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# Bond Rates
For the purposes of studying how economic indicators impact bond rates we need to understand how bonds are priced and the relationship between prices and interest rates, since that is what is relevant for our agenda. We need to understand this relationship as it is an essential building block to further understanding how each macroeconomic indicator influences the prices of bonds.
We start with the basics of bond cash flow and discount rates and look at an example of how bond prices are inversely related to interest rates. Next, we look at the linkages between bond prices, economic growth, inflation and interest rates.
## Bond Instruments: Understanding cash flows
The cash flows of a fixed income instrument or bond instrument is similar to that of a loan product.
Figure: Comparison of Cash Flows Between a Loan Product and a Bond Instrument
In a loan product there is an initial amount of money called the principal that the lender pays to the borrower. In a bond instrument this principal payment flows from the buyer of the instrument to the seller. The intermediate payments in a loan product are interest payments that the borrower needs to pay to compensate the lender for the principal. In a bond instrument these are called coupon payments and flow from the seller to the buyer on a periodic basis such as monthly, quarterly, semi-annually or annually. At the end of the loan period, or term, the principal that was borrowed is repaid to the lender along with the final interest payment. It’s the same case with the bond, as the principal and coupon is paid to the bond buyer on maturity.
## Bond Instruments: Bond Prices and Interest Rates
As mentioned earlier, the difference between bonds and loans is that bonds can be publicly traded. An instrument that is traded publicly therefore needs to be priced in order for it to be bought or sold. Pricing a bond is done by using the present value of future cash flows. In order to get the present value, that is the value of the cash flows today, we need to discount the cash flows by the discount rate. By discounting we basically mean dividing cash flows by the discount rate. The discount rate is the return one could obtain if they invested in a similar instrument; and by a similar instrument we mean an instrument with a similar risk profile.Â
Let’s take the example of a bond instrument. This is a five- year government security with a 10% coupon. The first column consists of the bond’s term of 1,2,3,4,5 years. The coupon interest is in the next column. The purchaser of the bond receives the payment of the principal of 100 dollars at the end of the term. This is called redeeming the bond. The total future cash flow is therefore a series of coupon payments of \$10 in each period plus a principal repayment at the end of a \$100. Each cash flow is discounted for that term based on the discount rate of 11.35%. When you add all the cash flows you get the price of the bond which is 95.05. This discount rate of 11.35% is also called the bond’s yield.
Bond-Price-Calculation
If there existed an alternative instrument that, for example, yielded 12% with the same risk profile, people would prefer to invest in the 12% instrument since it provides a higher yield than the 11.35% Government security. This would cause investors to sell the 11.35% yielding bond, thereby lowering the price, until the yield of the bond moves higher to 12%. We see that in order for the yield to become 12% the bond price needs to fall to 92.79. We can see here that as discount rates increase bond prices fall. If the discount rate falls down to 10%, which is the same as the coupon rate, the bond price now equals the face value.
bond-pricing-calculations
If the discount rate falls below the 10% coupon rate to 6% the bond price will move higher. Understanding this inverse relationship between bond prices and interest rates is key to understanding the effect of macroeconomic factors on bond prices. If economic factors cause market interest rates to move higher, bond prices drop, which is bad for the bond markets. Alternatively, macroeconomic indicators that cause market interest rates to move lower push bond prices upwards and cause a bond market rally.
Next we need to understand the influence of economic factors on bond rates
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Ex 1.2
Chapter 1 Class 8 Rational Numbers
Serial order wise
This video is only available for Teachoo black users
Get live Maths 1-on-1 Classs - Class 6 to 12
### Transcript
10 rational number between 3/5&3/4 Step 1: Make denominator same 3/5 4/4= 12/20 3/4 5/5= 15/20 Step 2: Since we need to find 10 rational number, multiply and divided by 11. 12/20 11/11= 132/220 15/20 11/11 = 165/220 10 rational numbers are 133/220, 134/220, 135/220, 136/220, 137/220, 138/110, 139/220, 140/220, 141/220, 142/220
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# support vector machine example
Oct 30, 2019 The support vector m achine algorithm comes from the maximal margin classifier. The maximal margin classifier uses the distance from a given decision boundary to classify an input. The greater the distance, or margin, the better the classifier is at handling the data. On a Cartesian plane, the boundary can be thought of as a line
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• An Idiot’s guide to Support vector machines (SVMs)
Support Vector Machine (SVM) Support vectors Maximize margin •SVMs maximize the margin (Winston terminology: the ‘street’) around the separating hyperplane. •The decision function is fully specified by a (usually very small) subset of training samples, the support vectors. •This
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• 1.4. Support Vector Machines — scikit-learn 0.24.2
Support Vector Machine algorithms are not scale invariant, so it is highly recommended to scale your data. For example, scale each attribute on the input vector X to [0,1] or [-1,+1], or standardize it to have mean 0 and variance 1. Note that the same scaling must be applied to the test vector to obtain meaningful results
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• Support Vector Machines in R Tutorial - DataCamp
Aug 22, 2018 Support Vector Machines Algorithm Linear Data. The basics of Support Vector Machines and how it works are best understood with a simple example. Let’s imagine we have two tags: red and blue, and our data has two features: x and y. We want a classifier that, given a pair of (x,y) coordinates, outputs if it’s either red or blue. We plot our
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• SVM | Support Vector Machine Algorithm in Machine
Support Vector Machine (SVM) code in R. The e1071 package in R is used to create Support Vector Machines with ease. It has helper functions as well as code for the Naive Bayes Classifier. The creation of a support vector machine in R and Python follow similar approaches, let’s take a look now at the following code:
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• Support Vector and Kernel Machines
www.support-vector.net A Little History z Annual workshop at NIPS z Centralized website: www.kernel-machines.org z Textbook (2000): see www.support-vector.net z Now: a large and diverse community: from machine learning, optimization, statistics, neural networks, functional analysis, etc. etc z Successful applications in many fields (bioinformatics, text, handwriting recognition, etc)
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• [One-Liner Tutorial] Support Vector Machines Made Simple
The code breaks down how you can use support vector machines in Python in its most basic form. The NumPy array holds the labeled training data with one row per user and one column per feature (skill level in maths, language, and creativity). The last column is the label (the class). Because we have three-dimensional data, the support vector
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• Default or No Default? - Junhyung Park
Jun 29, 2021 Jun 29, 2021 In this post, I will briefly go over an example of a Scikit-learn-based implementation of a support vector machine–a popular example of a supervised learning model. The code blocks below came from one of StatQuest’s public-domain tutorials on support vector machines, but the line-by-line explanations of the code are in my own words. As usual, the data used in this exercise came from the
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• Support Vector Machine - Python Tutorial
Support Vector Machine Example Separating two point clouds is easy with a linear line, but what if they cannot be separated by a linear line? In that case we can use a kernel, a kernel is a function that a domain-expert provides to a machine learning algorithm (a kernel is not limited to an svm)
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• Python Sklearn Support Vector Machine (SVM) Tutorial with
Aug 31, 2021 What is Support Vector Machine (SVM) The Support Vector Machine Algorithm, better known as SVM is a supervised machine learning algorithm that finds applications in solving Classification and Regression problems.. SVM makes use of extreme data points (vectors) in order to generate a hyperplane, these vectors/data points are called support vectors
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• Support Vector Machine Python Example | by Cory
Aug 13, 2019 Support Vector Machine Python Example. Cory Maklin. Aug 12, 2019 8 min read. Support Vector Machine (SVM) is a supervised machine learning algorithm capable of performing classi f ication, regression and even outlier detection. The linear SVM classifier works by drawing a straight line between two classes. All the data points that fall on one side of the line will be labeled as one class and all the points that fall on the
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• Intro to Support Vector Machines with a Trading
Jan 11, 2021 The support vector m achine algorithm comes from the maximal margin classifier. The maximal margin classifier uses the distance from a given decision boundary to classify an input. The greater the distance, or margin, the better the classifier is at handling the data. On a Cartesian plane, the boundary can be thought of as a line
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Class 7 Maths
Integers NCERT Exercise 1.2
Write down a pair of integers whose:
1. Sum is – 7
2. Difference is – 10
3. Sum is 0
Answer: (a) -14 and 7, (b) 55 and 65, (c) 24 and -24
Answer the following:
1. Write a pair of integers whose difference gives 8.
2. Write a negative integer and a positive integer whose sum is – 5.
3. Write a negative integer and a positive integer whose difference is – 3.
Answer: (a) 15 and 7, (b) 1-5 and 10, (c) Such pair is not possible
In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0 – 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?
Answer: Score of team A = - 10 + 10 + 0 = - 30
Score of team B = 10 + 0 – 40 = - 30
Both teams have same score. This shows that we can add integers in any order.
Fill in the blanks to make the following statements true:
1. ( - 6) + ( - 8) = - 8 + □
2. – 53 + □ = - 53
3. 17 + □ = 0
4. [13 + ( - 12)] + □ = 13 + [( - 12) + ( - 7)]
5. ( - 4) + [15 + ( - 3)] = [ - 4 + 15] + □
Answer: (a) -6, (b) 0,(c) -17, (d) -7, (e) -3
Exercise 1.3
Question 1: Find each of the following products:
(a) 3 xx ( - 1)
Answer: 3 xx ( - 1) = - 3
(b) ( - 1) xx 225
Answer: - 225
(c) ( - 21) xx ( - 30)
Answer: ( - 21) xx ( - 30) = 630
(d) ( - 316) xx ( - 1)
Answer: 316
(e) ( - 15) xx 0 xx ( - 18)
Answer: Zero because when any number is multiplied by zero the result is zero.
(f) ( - 12) xx ( - 11) xx (10)
Answer: ( - 12) xx ( - 11) xx (10) = 132 xx 10 = 1320
(g) 9 xx ( - 3) xx ( - 6)
Answer: 9 xx ( - 3) xx ( - 6) = 9 xx 18 = 162
(h) ( - 18) xx ( - 5) xx ( - 4)
Answer: ( - 18) xx ( - 5) xx ( - 4) = 90 xx ( - 4) = - 360
(i) ( - 1) xx ( -2) xx ( - 3) xx 4
Answer: ( - 1) xx ( - 2) xx ( - 3) xx 4 = 2 xx ( - 12) = - 24
(j) ( - 3) xx ( - 6) xx ( - 2) xx ( - 1)
Answer: ( - 3) xx ( - 6) xx ( - 2) xx ( - 1) = 18 xx 2 = 36
Question 2: Verify the following:
(a) 18 xx [7 + ( - 3)] = [18 xx 7] + [18 xx ( - 3)]
Answer: LHS = 18 xx [7 + ( - 3)] = 18 xx [ - 4] = - 72
RHS = [18 xx 7] + [18 xx ( - 3)] = 126 + [ - 54] = - 72
Here, LHS = RHS
(b) ( - 21) xx [( - 4) + ( - 6)] = [( - 21) xx ( -4)] + [( - 21) xx ( - 6)]
Answer: LHS = ( - 21) xx [( - 4) + ( - 6)] = - 21 xx [- 10] = 210
RHS = [( - 21) xx ( - 4) + [( - 21) xx ( - 6)] = 84 + 126 = 210
Here, LHS = RHS
Question 3: For any integer a, what is ( - 1) x a equal to?
Answer: ( - 1) x a = - a
Question 4: Determine the integer whose product with ( - 1) is
1. – 22
Answer: 22
2. 37
Answer: - 37
3. 0
Answer: 0
Question 5: Starting from ( - 1) xx 5, write various products showing some pattern to show ( - 1) xx ( - 1) = 1.
Answer: ( - 1) xx 5 = - 5
( - 1) xx ( - 3) = 3
( - 1) xx 1 = - 1
( - 1) xx ( - 1) = 1
Question 6: Find the product, using suitable properties:
(a) 26 xx ( - 48) + ( - 48) xx ( - 36)
Answer: 26 xx ( - 48) + ( - 48) xx ( - 36)
= ( - 48) xx[26 + ( - 36)]
= ( - 48) xx [ 26 – 36]
= - 48 xx [ - 10] = 480
This is showing distributive property of multiplication.
(b) 8 xx 53 xx ( -125)
Answer: 8 xx 53 xx ( - 125) can also be written as 8 xx ( - 125) xx 53
This is showing associative property of multiplication.
8 xx 53 xx ( - 125) =8 xx ( - 125) xx 53
= ( - 1000) xx 53 = - 53000
(c) 15 xx ( -25) xx( – 4) xx ( - 10)
Answer: This will also show associative property of multiplication.
15 xx ( - 25) xx ( - 4) xx ( - 10)
= 15 xx ( - 10) xx ( - 25) xx ( - 4)
=( - 150) xx ( - 100) = 15000
(d) ( - 41) xx 102
Answer: ( - 41) xx 102
= [( - 41) xx 100] + [( - 41) xx 2]
= ( - 4100) + ( - 82) = - 4182
This has been solved using distributive property of multiplication.
(e) 625 xx ( - 35) + (- 625) xx 65
Answer: 625 xx ( - 35) + ( - 625) xx 65
= ( - 625) xx (35 + 65) = ( - 625) xx 100 = - 62500
This has been solved using distributive property of multiplication.
(f) 7 xx ( 50 – 2)
Answer: 7 xx ( 50 – 2)
= 7 xx 50 + 7 xx ( - 2) = 350 – 14 = 336
This has been solved using distributive property of multiplication.
(g) ( - 17) xx ( - 29)
Answer: ( - 17) xx ( - 29)
= 17 xx 29 = 17 (30 – 1)
= (17 xx 30) – (17 xx 1)
= 510 – 17 = 493
This has been solved using distributive property of multiplication.
(h) ( - 57) xx ( - 19) + 57
Answer: ( - 57) xx ( -19) + 57
= 57 xx 19 + 57
= 57 xx (19 + 1)
= 57 xx 20 = 1140
This has been solved using distributive property of multiplication.
Question 7: A certain freezing process required that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?
Answer: Change in room temperature in 1 hour = - 5° C
So, change in room temperature in 10 hours = ( - 5) x 10 = - 50°C
Room temperature after 10 hours = 40°C - 50°C = - 10°C
Question 8: In a class test containing 10 questions, 5 marks are awarded for every correct answer and ( - 2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(a) Mohan gets four correct and six incorrect answers. What is his score?
Answer: Mohan’s score
= (4 xx 5) + 6 xx ( - 2) = 20 – 12 = 8
(b) Reshma gets two correct answers and five incorrect answers, what is her score?
Answer: Reshma’s score
= 2 xx 5 + 5 xx ( - 2) = 10 – 10 = 0
(c) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?
Answer: Heena’s score
= 2 xx 5 + 5 xx ( - 2) = 10 – 10 = 0
Question 9: A cement company earns a profit of Rs. 8 per bag of white cement sold and a loss of Rs. 5 per bag of grey cement sold.
(a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
Answer: Company’s profit or loss
= 3000 xx 8 + 5000 xx ( - 5)
= 24000 – 25000 = - 1000
It is a loss of Rs. 1000
(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.
Answer: Loss in selling grey bags
= 6400 xx ( - 5) = - 32000
Number of white cement bags required to be sold
= 32000 ÷ 8 = 4000
Question 10: Replace the blank with an integer to make it a true statement
1. ( - 3) xx ………… = 27
2. 5 xx ………… = - 35
3. ……… xx ( - 8) = - 56
4. ……… xx ( - 12) = 132
Answer: (a) 9, (b) -7, (c) 7, (d) -11
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# Worksheet: Impedance of Alternating Current Circuits
In this worksheet, we will practice calculating the impedance of simple resistive-capacitive-inductive circuits, using capacitive and inductive reactances.
Q1:
An alternating voltage source with a frequency of 50 Hz is connected to a 125 µF capacitor. What is the reactance of the capacitor? Give your answer to two significant figures.
Q2:
The reactance of the capacitor needed in an alternating current circuit is 120 Ω. The capacitor to be used has a 75 µF capacitance. What frequency must the alternating current have? Give your answer to two significant figures.
Q3:
An alternating voltage source with a frequency of 75 Hz is connected to a 35 mH inductor. What is the reactance of the circuit?
Q4:
What is the frequency of the alternating current in a circuit that contains a 0.25 H inductor that produces a reactance of 42 Ω?
Q5:
Which of the following graphs correctly shows how the reactance of a capacitor varies with the frequency of the alternating voltage source that the capacitor is connected to?
• A
• B
• C
• D
Q6:
What capacitance must a capacitor have to produce a 1.5 kΩ reactance in an alternating current circuit if the circuit has a frequency of 25 Hz?
• A F
• B F
• C F
• D F
• E F
Q7:
Which of the following graphs correctly shows how the reactance of an inductor varies with the frequency of the alternating voltage source that the inductor is connected to?
• A
• B
• C
• D
Q8:
Which of the following formulas correctly relates the reactance of a capacitor to its capacitance when connected to an alternating voltage source with a frequency ?
• A
• B
• C
• D
• E
Q9:
Which of the following formulas correctly relates the impedance of a circuit to the circuit’s capacitive reactance , the circuit’s inductive reactance , and the circuit’s resistance ?
• A
• B
• C
• D
• E
Q10:
An alternating current circuit contains a resistor with a resistance of 25 Ω, an inductor with a 32 Ω inductive reactance, and a capacitor with a 12.8 Ω capacitive reactance. The peak voltage produced by the alternating voltage source powering the circuit is 120 V.
What is the peak current in the circuit? Give your answer to two significant figures.
• A 2.7 A
• B 7.5 A
• C 3.8 A
• D 2.3 A
• E 3.8 A
What is the root-mean-square current in the circuit? Give your answer to two significant figures.
• A 7.5 A
• B 1.7 A
• C 2.7 A
• D 2.3 A
• E 3.8 A
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# Visible Thinking in Mathematics 3A
\$ 13.20
View Sample Pages.
Visible Thinking in Mathematics is a series of eleven supplementary books that promotes critical and creative thinking in mathematics. It is designed to help make thinking visible by providing the child with opportunities to think, explore and reflect.
While practice leads to better performance, practice without contextual and conceptual understanding prevents the child from thinking critically and creatively. In this series, instead of learning procedures and formulas by rote, the child masters concepts through:
1. Thinking routines: functional questions to direct the child's thinking on key concepts and cultivate the child's thinking skills.
2. Parallel questions: consecutive mathematical problems with the same context but different key words to highlight differences between problems; ensuring that the child understands and retains concepts and skills better.
This approach not only instills in the child mathematical skills but also inspires discipline in thinking and greater motivation for learning.
Additional support is provided to the child through Notes. Notes present opportunities for parents and teachers to clarify misconceptions, simplify difficult concepts and address areas of difficulty for the child.
Above extract from Preface of Visible Thinking in Mathematics (reproduced with the permission of the publishers).
177 consumable (non-reproducible) pages, softcover. 3rd Grade. Answer key is included in the back of the book.
Contents
Chapter 1
Numbers To 10 000
Number Notation And Place Value
Reading And Writing Numbers In Words
Comparing And Ordering Numbers
Number Patterns
Chapter 2
Addition And Subtraction Within 10 000
Subtraction Without Regrouping
Subtraction With Regrouping
Chapter 3
Word Problems Involving Addition And Subtraction
Word Problems
More Word Problems (1)
More Word Problems (2)
Chapter 4
Multiplication And Division By 6, 7, 8 And 9
Multiplication And Division By 6
Multiplication And Division By 7
Multiplication And Division By 8
Multiplication And Division By 9
More Multiplication And Division By 6, 7, 8 And 9
Chapter 5
Multiplication And Division
Multiplication Without Regrouping
Multiplication With Regrouping
Division Without Regrouping
Division With Regrouping
Word Problems Involving Four Operations Using Models
Number Patterns Involving Gaps And Intervals
Chapter 6
Mental Calculations
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Question
# Problem 8-30 Integration of the Sales, Production, and Direct Materials Budgets [LO8-2, LO8-3, LO8-4] Milo Company...
Problem 8-30 Integration of the Sales, Production, and Direct Materials Budgets [LO8-2, LO8-3, LO8-4] Milo Company manufactures beach umbrellas.
The company is preparing detailed budgets for the third quarter and has assembled the following information to assist in the budget preparation:
a. The Marketing Department has estimated sales as follows for the remainder of the year (in units):
July 38,000
October 28,000
August 86,000
September 55,000
November 14,500
December 15,000
The selling price of the beach umbrellas is \$13 per unit.
b. All sales are on account. Based on past experience, sales are collected in the following pattern:
30% in the month of sale
65% in the month following sale
5% uncollectible
Sales for June totaled \$455,000.
c. The company maintains finished goods inventories equal to 15% of the following month’s sales. This requirement will be met at the end of June.
d. Each beach umbrella requires 4 feet of Gilden, a material that is sometimes hard to acquire. Therefore, the company requires that the ending inventory of Gilden be equal to 50% of the following month’s production needs. The inventory of Gilden on hand at the beginning and end of the quarter will be:
June 30 90,400 feet
September 30 ? feet
e. Gilden costs \$0.60 per foot. One-half of a month’s purchases of Gilden is paid for in the month of purchase; the remainder is paid for in the following month. The accounts payable on July 1 for purchases of Gilden during June will be \$48,390.
Required:
1. Calculate the estimated sales, by month and in total, for the third quarter.
2. Calculate the expected cash collections, by month and in total, for the third quarter.
3. Calculate the estimated quantity of beach umbrellas that need to be produced in July, August, September, and October.
4. Calculate the quantity of Gilden (in feet) that needs to be purchased by month and in total, for the third quarter. 5. Calculate the cost of the raw material (Gilden) purchases by month and in total, for the third quarter.
6. Calculate the expected cash disbursements for raw material (Gilden) purchases, by month and in total, for the third quarter.
1 Milo Company Estimated Sales July August September 3rd Quarter Budgeted sales units 38000 86000 55000 179000 Selling price per unit \$ 13 13 13 13 Estimated sales \$ 494000 1118000 715000 2327000 2 Expected Cash Collections July August September 3rd Quarter June sales 295750 295750 July sales 148200 321100 469300 August sales 335400 726700 1062100 September sales 214500 214500 Expected cash collections \$ 443950 656500 941200 2041650 3 Estimated Production July August September October November Budgeted sales in units 38000 86000 55000 28000 14500 Desired ending FG inventory as percent of following month's sales (units) 15% 15% 15% 15% Ending FG inventory (units) 12900 8250 4200 2175 Required production (units) 50900 94250 59200 30175 Less: Beginning FG inventory (units) 5700 12900 8250 4200 Estimated production (units) 45200 81350 50950 25975 4 Gilden Purchases July August September 3rd Quarter Estimated production (units) 45200 81350 50950 177500 Gilden required per unit (feet) 4 4 4 4 Gilden required for production (feet) 180800 325400 203800 710000 Desired ending inventory of Gilden as percent of following month's production needs 50% 50% 50% Ending inventory of Gilden (feet) 162700 101900 51950 51950 Total Gilden required (feet) 343500 427300 255750 761950 Less: Beginning inventory of Gilden (feet) 90400 162700 101900 90400 Quantity of Gilden to be purchased (feet) 253100 264600 153850 671550 5 Cost of Raw Material (Gilden) Purchases July August September 3rd Quarter Quantity of Gilden to be purchased (feet) 253100 264600 153850 671550 Raw material (Gilden) cost per foot \$ 0.60 0.60 0.60 0.60 Cost of raw material (Gilden) purchases \$ 151860 158760 92310 402930 6 Expected Cash Disbursements for Raw Material (Gilden) Purchases July August September 3rd Quarter June purchases 48390 48390 July purchases 75930 75930 151860 August purchases 79380 79380 158760 September purchases 46155 46155 Expected cash disbursements \$ 124320 155310 125535 405165
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# Finding Tension with angles
• Maty
In summary, a ball of weight 5 Newtons is suspended by two strings. The tension in each direction is determined by the formulas T1 - T2 = 0 and T1 + T2 = mg.
## Homework Statement
A ball of weight 5 Newtons is suspended by two strings as shown above. Determine the magnitude of each of the forces, T1 and T2. (Note: sin 37° = 0.6; cos37° = 0.8)
T = mg
## The Attempt at a Solution
I couldn't go anywhere because I need a formula that uses sin or cos, and I can't remember any right now. Can anyone supply me with the equations and a start? And I'll attempt at the solution with that. Please.
Last edited:
Would this work? T x cos θ1 + T x cos θ2 = mg, where θ1 and θ2 are the angles the two sides.
Maty said:
## Homework Statement
A ball of weight 5 Newtons is suspended by two strings as shown above. Determine the magnitude of each of the forces, T1 and T2. (Note: sin 37° = 0.6; cos37° = 0.8)
http://bb.mivu.org/courses/1/M-APhB1-S112-01/assessment/685f98ac2d604bddbf30b5bb28f9f01b/Q5.jpg
T = mg
## The Attempt at a Solution
I couldn't go anywhere because I need a formula that uses sin or cos, and I can't remember any right now. Can anyone supply me with the equations and a start? And I'll attempt at the solution with that. Please.
Maty said:
Would this work? T x cos θ1 + T x cos θ2 = mg, where θ1 and θ2 are the angles the two sides.
Oops, there I edited the first post and it should be there now.
Also, after I posted that second post, I realized that nowhere in there it had any variables for the length of the string, which likely play a part in here. So I think I'm not supposed to use that equation.
Maty said:
Oops, there I edited the first post and it should be there now.
Also, after I posted that second post, I realized that nowhere in there it had any variables for the length of the string, which likely play a part in here. So I think I'm not supposed to use that equation.
On these problems, always start by drawing a Free Body Diagram (FBD) of the object (the mass in this case). Show the forces on the object, including the force down due to gravity. Then write the two equations to sum all of the forces in the x and y directions to zero (since the object is not moving). then solve away!
I have one drawn right in front of me right now, but I just don't know what formula to use, or how to find ALL of the forces in both axis.
Maty said:
I have one drawn right in front of me right now, but I just don't know what formula to use, or how to find ALL of the forces in both axis.
How many forces act in the horizontal direction? What are they? Label forces in the +x direction positive, and forces in the -x direction negative.
How many forces act in the vertical direction? What are they? Forces up are positive, and forces down are negative.
Since the object is not accelerating, you know that the sum of the forces in the x direction needs to equal zero. Same thing for the y direction. Those are the two equations you write and solve for the tension forces.
In the x direction T1 - T2 = 0?
And in the y direction. T1 + T2 = mg?
So i'll have to use Trig to find the numbers for each axis, but the only number I have is length, how would that help me?
Maty said:
In the x direction T1 - T2 = 0?
And in the y direction. T1 + T2 = mg?
So i'll have to use Trig to find the numbers for each axis, but the only number I have is length, how would that help me?
That is much closer. Good.
But you need to use the "components" of the tensions in the x and y directions, and that is where the sin and cos functions come in. Those are used to resolve vectors (like the tension forces applied at angles) into their x and y components.
See the "Intro to Vector Mathematics" link at the bottom of this FBD tutorial, for example:
.
I am still back to the beginning. I know 'what' to do, I just don't know 'how' to do it. What numbers do I use, what equation?
Your first step is to break up the tensions into vertical and horizontal parts, then since the ball isn't moving the vertical parts add to balance the force of gravity and the two horizontal parts must cancel with each other :)
## 1. What is tension?
Tension is a force that occurs when an object is being stretched or pulled by another object. It is a type of force that is present in various situations, such as when a rope is pulled or when an object is suspended.
## 2. How do you calculate tension with angles?
To calculate tension with angles, you need to use trigonometric functions such as sine, cosine, and tangent. First, draw a free-body diagram of the object and identify all the forces acting on it. Then, use the angle and the trigonometric function to calculate the component of the force in the direction of the angle. Finally, use the component of the force and the trigonometric function to calculate the tension.
## 3. What are the key factors that affect tension with angles?
The key factors that affect tension with angles include the magnitude of the force applied, the angle at which the force is applied, and the weight of the object. Other factors such as friction and air resistance may also affect the tension.
## 4. How can finding tension with angles be useful in real-life situations?
Finding tension with angles can be useful in various real-life situations, such as engineering and construction. It can be used to determine the strength of materials and structures, as well as to ensure the safety and stability of buildings and bridges. It can also be used in sports, such as rock climbing, to determine the amount of tension needed in ropes.
## 5. What are some common mistakes when calculating tension with angles?
Some common mistakes when calculating tension with angles include not considering all the forces acting on the object, not using the correct trigonometric function, and not converting units appropriately. It is important to carefully draw the free-body diagram and double-check all calculations to avoid these mistakes.
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# Matrix representation
• May 17th 2008, 07:16 AM
matty888
Matrix representation
Compute the standard matrix representation of the orthogonal projection of R^4 onto the subspace spanned by {(1,1,1,1),(1,2,3,4)}.
• May 17th 2008, 08:41 AM
Opalg
Quote:
Originally Posted by matty888
Compute the standard matrix representation of the orthogonal projection of R^4 onto the subspace spanned by {(1,1,1,1),(1,2,3,4)}.
Step 1. Find an orthonormal basis for the subspace, e.g. $\textstyle\{\frac12(1,1,1,1),\,\frac1{\sqrt{20}}(-3,-1,1,3)\}.$
Step 2. In R^n, the projection onto the one-dimensional subspace spanned by a single unit vector $(a_1,a_2,\ldots,a_n)$ has $a_ia_j$ as its (i,j)-entry. So for example the projection onto the subspace spanned by $\textstyle\frac1{\sqrt{20}}(-3,-1,1,3)$ is $\frac1{20}\begin{bmatrix}9&3&-3&-9\\ 3&1&-1&-3\\ -3&-1&1&3\\ -9&-3&3&9\end{bmatrix}$. Now do the same thing for the projection onto the subspace spanned by ½(1,1,1,1).
Step 3. If you have an orthonormal set of vectors then the projection onto the subspace spanned by them is the sum of the projections onto the one-dimensional subspaces spanned by the basis vectors. So the answer to the question is the sum of the two matrices from the previous paragraph.
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Examples > Mathematics >
## Derivatives
Derivatives
A few examples of what you can ask Wolfram|Alpha about:
Derivatives
calculate the derivative of a function
Higher Derivatives
compute higher derivatives
Implicit Differentiation
differentiate an equation
compute a derivative using implict differentiation
Partial Derivatives
compute partial derivatives
compute higher partial derivatives
Directional Derivatives
compute a directional derivative
Derivatives of Abstract Functions
compute derivatives involving abstract functions
compute partial derivatives of abstract functions
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# Probability During Sampling
#### djvan
##### New Member
I work a biomedical lab, but I haven't had a statistics course in quite some time. It's important that our data have a p < 0.05. The question can be simplified by replacing biological components with 'particles', which I've done:
A tube contains 20,000,000 particles in total. Of these particles, 40,000 are blue and 19,960,000 are red. So, for every 500 blue particles, there is 1 red particle. If I were to remove 50,000 particles at random, what is the probability that I will obtain 80 red particles and 39,920 blue particles (the 'true' ratio of the population in the sample tube)?
How many times would I need to repeat this measurement, so that the averaged ratios (red:blue particles) represented the true ratio, with a p < 0.05?
If possible, please show me how your calculated this, so I can repeat with different values (for instance, if I were to take 100,000 particles per each sampling).
Thanks much!!
#### rogojel
##### TS Contributor
hi,
in theory you have a binomial distribution, where p is the probability of picking a red particle, N is the total number of particles. Because p is really small and N very large you can use the Poisson approximation - and this web-page to get the numbers http://faculty.vassar.edu/lowry/poisson.html
As for the sample size use this page: http://www.select-statistics.co.uk/sample-size-calculator-proportion You will need to decide with what precision you need to measure the true proportion i.e. if your original estimate is 2.5 percent then you might want to measure with a precision of +/- 0.1%. Once you input this it gives you the number of particles to test.
regards
#### djvan
##### New Member
Thanks Rogohel, this was very helpful. I have one question, though: on the sample size calculator, the recommended sample size decreases with decreasing sample proportion.
I'm not sure I understand this. Why are fewer measurements needed when a rare event is being measured? I assumed sample proportion would be the number of 'red particles' / 'total particles' x 100. Or in my example, 0.2%. The calculator says I would only need to make 4 measurement to accurately measure this. If I decrease it to 0.1%, I only need to make 2 measurements. This seems unlikely to me - if we look at the poisson distribution, aren't I more likely to pipette a number of red particle that does not represent the true population proportion?
Furthermore, why doesn't this calculator take in to account the fact that I will be sampling 10,000 particles at a time? Does this not affect the calculations?
Thanks again!
#### rogojel
##### TS Contributor
hi,
I think some settings might not be right in the way you used the program. It should give you the number of particles you test , something in the order of magnitude of 100 000. Then, if you know you will test batches of 10 000 then you will have to translate the raw number to the number of test batches.
regards
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# Although one link in the chain was demonstrated to be weak,
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Joined: 06 Jan 2008
Posts: 534
Although one link in the chain was demonstrated to be weak, [#permalink]
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25 Jul 2008, 11:13
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Although one link in the chain was demonstrated to be weak, but not sufficiently so to require the recall of the automobile.
(A) demonstrated to be weak, but not sufficiently so to require
(B) demonstrated as weak, but it was not sufficiently so that it required
(C) demonstrably weak, but not sufficiently so to require
(D) demonstrably weak, it was not so weak as to require
(E) demonstrably weak, it was not weak enough that it required
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Director
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Posts: 513
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### Show Tags
25 Jul 2008, 11:19
saravalli wrote:
Although one link in the chain was demonstrated to be weak, but not sufficiently so to require the recall of the automobile.
(A) demonstrated to be weak, but not sufficiently so to require
(B) demonstrated as weak, but it was not sufficiently so that it required
(C) demonstrably weak, but not sufficiently so to require
(D) demonstrably weak, it was not so weak as to require
(E) demonstrably weak, it was not weak enough that it required
D
A-C: Since "although" is used at the beginning, "but" should not be there. Eliminate.
D: so X as Y is idiomatic
E: wordy
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### Show Tags
25 Jul 2008, 11:31
saravalli wrote:
Although one link in the chain was demonstrated to be weak, but not sufficiently so to require the recall of the automobile.
(A) demonstrated to be weak, but not sufficiently so to require
(B) demonstrated as weak, but it was not sufficiently so that it required
(C) demonstrably weak, but not sufficiently so to require
(D) demonstrably weak, it was not so weak as to require
(E) demonstrably weak, it was not weak enough that it required
eliminate A,B.
Although, BUT-- redudant & awkward.
between D and E
D is better.
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### Show Tags
25 Jul 2008, 14:20
Can anyone put some more light on why E is wrong?
Director
Joined: 01 Jan 2008
Posts: 605
### Show Tags
25 Jul 2008, 15:52
grepro wrote:
Can anyone put some more light on why E is wrong?
I think it would've been correct if it said "to require". D sounds better.
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Joined: 17 Jun 2008
Posts: 1322
### Show Tags
25 Jul 2008, 22:01
saravalli wrote:
Although one link in the chain was demonstrated to be weak, but not sufficiently so to require the recall of the automobile.
(A) demonstrated to be weak, but not sufficiently so to require
(B) demonstrated as weak, but it was not sufficiently so that it required
(C) demonstrably weak, but not sufficiently so to require
(D) demonstrably weak, it was not so weak as to require -> IMO D
(E) demonstrably weak, it was not weak enough that it required
Although X,Y still happens ,Y should oppose X
This concepts plays a role here and is correctly used in D
Eliminate A,B since we need a clause for chain not for someone demonstrating state of chain
C is out since sufficiently so to is wrong usage
E is out since it says not weak enough and does not strongly oppose as is seen in D
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### Show Tags
25 Jul 2008, 22:10
"not weak enough that it required" in E ia a wrong phrase.
D correctly use the idiom so .. as.
hence D
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### Show Tags
28 Jul 2008, 12:17
OA is D. Thanks
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Re: SC - automobile [#permalink] 28 Jul 2008, 12:17
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# Physics Test
Jun 17th, 2015
Studypool Tutor
Price: \$10 USD
Tutor description
1. A body is moving with a speed 1 m/s and a force F is needed to stop it in a distance x. If the speed of the body is 3 m/s the force needed to stop it in the same distance x will be A) 1.5 F (B) 3 F (C) 6 F (D) 9 F 2 Two perfect gases at absolute temperatures are mixed. There is no loss of energy.
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Showing Page: 1/5
Section - 1Physics1.A body is moving with a speed 1 m/s and a force F is needed to stop it in a distance x. If the speed of the body is 3 m/s the force needed to stop it in the same distance x will be (A) 1.5 F(B) 3 F (C) 6 F(D) 9 F 2Two perfect gases at absolute temperatures are mixed. There is no loss of energy. The temperature of the mixture if the masses of the molecules are and the number of molecules in the gases are (both gases are of same nature) (A) (B) (C) (D) none of these 3Three rods made of same material and having the same cross-section have been joined as shown in figure. Each rod is of the same length. The left and right ends are kept at 0C, 90 & 60. The temperature of the junction of the rods will be (A) 45C(B) 50C (C) 55C(D) 60 4An ideal gas is taken through the cycle as shown in figure . If the heat supplied to the gas in the cycle is 5J. The work done by the gas in the process is (A) - 25 J(B) - 10 J (C) - 15 J(D) - 20 J 5Light from source consists of two wavelength . If D = 2m and d = 6.5 mm. The minimum value of y where the minima of both the wave lengths coincide.(A) 0.1 mm(B) 0.2 mm (C) 0.3 mm(D) 0.4 mm 6An isolated hydrogen atom emits a photon of 10.2 eV recoil speed of hydrogen atom (A) 3.25 m/s(B) 3 m/s (C) 6.2 m/s(D) 1 m/s 7The X-ray emission line of kingsten occurs at . The energy difference between K & L l
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# need help with a math formula
• Jan 27th 2013, 05:23 AM
taylor428
need help with a math formula
i have a problem, Sally's art project is in the shape of a circle. She wants to put a piece of glitter string around the adge of her project. if her project has a radius of 4 inches, how much string will she need?
I have done it twicw and gotten 2 different answers one 16 than 8 just need for some one to show how thanks
• Jan 27th 2013, 06:26 AM
HallsofIvy
Re: need help with a math formula
Please tell us exactly what you did and how you got those two answers. You appear to be saying that the string is going around the circumference of the circle. Is that correct? Do you know a formula for the circumference of a circle?
(If the string is on the circumference of the circle, neither 16 nor 8 is even close to the correct answer.)
• Jan 27th 2013, 08:47 PM
pspss
Re: need help with a math formula
Length of string required is same as perimeter of circle
= 2πr
= 2 × 3.14 × 4 = 25.12 inch
----
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kidzsearch.com > wiki Explore:web images videos games
# Complex number
(Redirected from Complex numbers)
A complex number is a number, but is different from common numbers in many ways. A complex number is made up using two numbers combined together. The first part is a real number, and the second part is an imaginary number. The most important imaginary number is called $i$, defined as a number that will be -1 when squared ("squared" means "multiplied by itself"): $i^2 = i \times i = -1\$. All the other imaginary numbers are $i$ multiplied by a real number, in the same way that all real numbers can be thought of as 1 multiplied by another number. Arithmetic functions such as addition, subtraction, multiplication, and division can be used with complex numbers. They also follow commutative, associative and distributive properties, just like real numbers. The set of complex numbers is often represented using the symbol $\mathbb{C}$.[1][2]
Complex numbers were discovered while attempting to solve special equations that have exponents in them. These began to pose real problems for mathematicians. As a comparison, using negative numbers, it is possible to find the x in the equation $a + x = b$ for all real values of a and b, but if only positive numbers are allowed for x, it is sometimes impossible to find a positive x, as in the equation 3 + x = 1.
With exponentiation, there is a difficulty to be overcome.[3] There is no real number that gives −1 when it is squared. In other words, −1 (or any other negative number) has no real square root. For example, there is no real number $x$ that solves the equation $(x+1)^2=-9$. To solve this problem, mathematicians introduced a symbol i and called it the imaginary unit.[1] This is the imaginary number that will give −1 when it is squared.
The first mathematicians to have thought of this were probably Gerolamo Cardano and Raffaele Bombelli. They lived in the 16th century.[2] It was probably Leonhard Euler who introduced writing $\mathrm i$ for that number.
All complex numbers can be written as $a + bi$[3] (or $a + b \cdot i$), where a is called the real part of the number, and b is called the imaginary part. We write $\Re (z)$ or $\operatorname{Re}(z)$ for the real part of a complex number $z$. So, if $z = a + bi$, we write $a = \Re (z) = \operatorname{Re} (z)$. Similarly, we write $\Im (z)$ or $\operatorname{Im} (z)$ for the imaginary part of a complex number $z$; $b = \Im (z) = \operatorname{Im} (z)$, for the same z.[1] Every real number is also a complex number; it is a complex number z with $\Im (z) = 0$.
A complex number can also be written as an ordered pair (a, b), where both a and b are real numbers. Any real number can simply be written as $a + 0 \cdot i$, or as the pair (a, 0).[3]
Sometimes, $j$ is written instead of $i$. In electrical engineering for instance, $i$ means electric current, so writing $i$ can cause a lot of problems because some numbers in electrical engineering are complex numbers.
The set of all complex numbers is usually written as $\mathbb{C}$.[1]
## Operations over complex numbers
Addition, subtraction, multiplication and exponentiation (raising numbers to exponents) are all possible with complex numbers. Division is also possible with complex numbers—as long as the divisor is not zero, Some other calculations are also possible with complex numbers.
The rule for addition and subtraction of complex numbers is pretty simple:
Let $z = (a + bi), w = (c + di)$, then $z + w = (a + bi) + (c + di) = (a + c) + (b + d)i$, and $z - w = (a + bi) - (c + di) = (a - c) + (b - d)i$.
Multiplication is a bit different:
$z \cdot w = (a + bi)(c + di) = ac + bci + adi + bdi^2 = (ac - bd) + (bc + ad)i.$
Another notable operation for complex numbers is conjugation. A complex conjugate $\overline{z}$ to $z = a + bi$ is $a - bi$. It is pretty simple, but is important for calculations, because $z \times \overline{z}$ is actually a real number for all complex $z$:
$z\bar{z}=(a+bi)(a-bi)=(a^2+b^2)+(ab-ab)i=a^2+b^2$.
Because of that, we can use it to do division:
$\frac{1}{z}=\frac{\bar{z}}{z\bar{z}}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i$
$\frac {w}{z}= w(\frac {1}{z})= (c+di)\cdot \left(\frac{a}{a^2+b^2} -\frac{b}{a^2+b^2}i\right)= \frac{1}{a^2+b^2}\left((cx+dy)+(dx-cy)i\right).$
## Other forms of describing complex numbers
Complex numbers can be shown on a so-called complex plane. If you have a number $z = a + bi$, you can go to point a on the real axis and point b on the imaginary axis, and draw a vector from $(0, 0)$ to $(a, b)$. The length of this vector can be calculated using the Pythagorean theorem, and the angle of this vector is simply the angle between the positive real axis and this vector—going counterclockwise. The length of a vector for a number $z$ is called its modulus or absolute value (written as $|z|$), and the angle is called its argument ($\arg z$).[1]
A complex number can be visually shown as two numbers which form a vector on an Argand diagram, representing the complex plane.
This leads to the trigonometrical form of describing complex numbers: by the definitions of sine and cosine, it follows that for all $z$:
$z = |z|(\cos \arg z + i \sin \arg z).$
This is closely connected to De Moivre's formula.
There exists even another form, called exponential form.
## Conclusion
With the introduction of complex numbers to math, every polynomial with complex coefficients has roots in complex numbers. This introduction also helped to open a path to the creation of another kind of numbers, which could help resolve and explain many different problems. These include the hypercomplex numbers, sedenion, hyperreal numbers, surreal numbers and many others. For more, see types of numbers.
## References
1. Weisstein, Eric. "Complex numbers".
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# Arduino Map: How to map a value from one range to another. It is a useful function but it may not do what you expect! Find out here why it may go wrong and how to use it correctly.
Arduino map
• Maps one range of values to another.
• It should work the way you think...but it does not!
• You may find your output range squashed up at one end!
• Find out why that is so.
• Also find out what to do about it!
Why it may not work exactly the way you think it does! The map function is intended to change one range of values into another range of values and a common use is to read an analogue input (10 bits long, so values range from 0 to 1023) and change the output to a byte so the output would be from 0 to 255.
TIP: The Arduino map() function can convert from positive to negative ranges.
You would then write the following code
val = map(adc_val, 0, 1023, 0, 255);
Everything is fine 0 maps to 0, and 1023 maps to 255...
...with an even distribution (really?????).
The map() function is useful but it has a secret hiding within. Its easy enough to use (or so you think) until you look a bit deeper inside. An even distribution is what you want but does it really do that?
## Testing Arduino Map
Lets write a sketch to test out exactly what it does
``````void setup() {
Serial.begin(9600);
int mapped = map(adc, 0, 1023, 0, 255);
Serial.print(',');
Serial.println(mapped);
}
}
void loop() {
}
``````
First part of the serial output (i/p value, o/p value) Final part of the serial output (i/p value, o/p value) 0,0 1,0 2,0 3,0 1007,251 1008,251 1009,251 1010,251 4,0 5,1 6,1 7,1 1011,252 1012,252 1013,252 1014,252 8,1 9,2 10,2 11,2 1015,253 1016,253 1017,253 1018,253 12,2 13,3 14,3 15,3 1019,254 1020,254 1021,254 1022,254 1023,255
* Values in pink shows the output occupies 5 bins instead of the required 4.
* The value red shows the final error i.e. the last value is output only once.
In the table above the value to the left of the comma is the adc value while to the right is the mapped output value.
You can see from the table above that input is mapped to output ranges in blocks of 4 (1 output value for a range of 4 input values). This is expected since 1024/4 = 256.
Warning: The last output has only 1 output bin matching one input.
The problem is the final output value (highlighted in red) has only 1 output bin for one input value i.e. 1023 results in 255, while 1019~1022 results in 254 as output (4 input bins). What you really want is an even spread of values across the whole range.
To get to this point some of the other outputs must have had 5 values as inputs (you can see that for adc values 0~4 - all 5 inputs result in output of a zero.
## Sketch: Test Arduino map distribution
This sketch increases the value in bins array every time map returns a value - so each bins[] holds the number of times an output was created.
``````#define SAMPLES 1024
#define OUTPUTS 256
int bins[OUTPUTS];
const int binsize = (SAMPLES-1)/(OUTPUTS-1);
void setup() {
Serial.begin(9600);
Serial.println("Arduino map output distribution");
Serial.print("Bin size: ");
Serial.println(binsize);
// Initialise bins
for (int i = 0; i < OUTPUTS; i++) bins[i]=0;
int mapped = map(adc, 0, SAMPLES-1, 0, OUTPUTS-1);
bins[mapped] +=1;
}
for(int i=0;i<OUTPUTS;i++) {
Serial.print("Bin: ");
Serial.print(i);
Serial.print(" count ");
Serial.print(bins[i]);
// Show bin distribution error
if ((bins[i] != binsize)) {
Serial.println(" ***") ;
} else Serial.println();
}
// Find wrong bin count
for(int i=0;i<OUTPUTS;i++) {
if (bins[i]!=binsize) {
Serial.print("Bin error: ");
Serial.println(i);
}
}
}
void loop() {
}
``````
The last part of the output shows four bins with wrong values :
```Bin: 253 count 4
Bin: 254 count 4
Bin: 255 count 1 ***
Bin error: 0
Bin error: 85
Bin error: 170
Bin error: 255
```
## So why the error for Arduino map?
The arduino map() reference has this to say:
"As previously mentioned, the map() function uses integer math. So fractions might get suppressed due to this. For example, fractions like 3/2, 4/3, 5/4 will all be returned as 1 from the map() function, despite their different actual values. So if your project requires precise calculations (e.g. voltage accurate to 3 decimal places), please consider avoiding map() and implementing the calculations manually in your code yourself."
The problem is that the upper value of 1023 is not exactly divisible by 255 so you get a slight error. So it is a fraction that is suppressed.
The code for the function is:
long map(long x, long in_min, long in_max, long out_min, long out_max) {
return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}
The calculations are
```0 *255/1023 = 0
1 *255/1023 = 0
2 *255/1023 = 0
3 *255/1023 = 0
4 *255/1023 = 0
5 *255/1023 = 1
1022 * 255/1023 = 254
1023 * 255/1023 = 255 ```
These match the Arduino outputs.
## Looking at a simpler output
The problem becomes even more apparent.
if you map 1023 to the output range 0 to 7 the problem becomes even more apparent.
Change the code in the previous sketch redefining 'OUTPUTS' as 8.
The output then becomes:
```Arduino map output distribution
Bin size: 146
Bin: 0 count 147 ***
Bin: 1 count 146
Bin: 2 count 146
Bin: 3 count 146
Bin: 4 count 146
Bin: 5 count 146
Bin: 6 count 146
Bin: 7 count 1 ***
Bin error: 0
Bin error: 7
```
If you tried to map an ADC input using a potentiometer to control an 8 LED bargraph the only time the last LED would light is when the input is 1023!
## How to solve it
To fix it make the values a multiple of a power of 2 so the fraction is not suppressed.
Solution: Set the maximum input value as multiple of a power of 2.
Note: For different ranges the difference between max and min must be a power of 2.
The following program uses power of 2 values as input and shows the corrected output.
``````//#define NUM_SAMPLES 1024 // Must be a power of 2 (Range 0-1023)
//#define NUM_OUTPUTS 256 // Must be a power of 2 (Range 0-255)
#define NUM_SAMPLES 1024 // Must be a power of 2 (Range 0-1023)
#define NUM_OUTPUTS 8 // Must be a power of 2 (Range 0-7)
#define NUM_BINS (NUM_OUTPUTS)
int bins[NUM_BINS];
const int binsize = (NUM_SAMPLES)/(NUM_OUTPUTS);
void setup() {
Serial.begin(9600);
Serial.println("Arduino map output distribution");
Serial.print("Bin size: ");
Serial.println(binsize);
// Initialise bins
for (int i = 0; i < NUM_BINS; i++) bins[i]=0;
int mapped = map(adc, 0, NUM_SAMPLES, 0, NUM_OUTPUTS);
bins[mapped] +=1;
}
for(int i=0;i< NUM_BINS;i++) {
Serial.print("Bin: ");
Serial.print(i);
Serial.print(" count ");
Serial.print(bins[i]);
// Show bin distribution error
if ((bins[i] != binsize)) {
Serial.println(" ***") ;
} else Serial.println();
}
// Find wrong bin count
for(int i=0;i< NUM_BINS;i++) {
if (bins[i]!=binsize) {
Serial.print("Bin error: ");
Serial.println(i);
}
}
}
void loop() {
}
``````
Output results: for NUM_SAMPLES = 1024, NUM_OUTPUTS = 8
```Arduino map output distribution
Bin size: 128
Bin: 0 count 128
Bin: 1 count 128
Bin: 2 count 128
Bin: 3 count 128
Bin: 4 count 128
Bin: 5 count 128
Bin: 6 count 128
Bin: 7 count 128
```
Note: The first example is also corrected with an even spread of 4 input values per output.
Another example
Here's another example using random samples and outputs i.e. non-power of 2 values.
#define SAMPLES 1976
#define OUTPUTS 153
Here 1976/153 = 12.91 and each bin has 13 values in it except the last that has one. So the algorithm gets it approximately right.
First part of the serial output Final part of the serial output ```Bin: 0 count 13 *** Bin: 1 count 13 *** Bin: 2 count 13 *** Bin: 3 count 13 *** Bin: 4 count 13 *** Bin: 5 count 13 *** Bin: 6 count 13 *** Bin: 7 count 13 ***``` ```Bin: 145 count 13 *** Bin: 146 count 13 *** Bin: 147 count 13 *** Bin: 148 count 13 *** Bin: 149 count 13 *** Bin: 150 count 13 *** Bin: 151 count 12 Bin: 152 count 1 ***```
# Arduino Map Conclusion
Given it is such a pain to get working exactly right, its probably better to do one of the following.
• Don't worry about the error - its only small if the output mapped value is fairly large compared to the input - but remember the last output value will only be generated once.
• Use a floating point calculation - but will be slower and use more memory.
• Avoid using map() - For instance for an ADC conversion to 0 to 255 just use the upper 8 bits of the result - use function analogReadResolution() for this.
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# In a parallelogram $\mathrm{ABCD}, \mathrm{E}$ and $\mathrm{F}$ are the mid-points of sides $\mathrm{AB}$ and $\mathrm{CD}$ respectively (see below figure). Show that the line segments AF and $\mathrm{EC}$ trisect the diagonal BD."
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Given:
In a parallelogram $\mathrm{ABCD}, \mathrm{E}$ and $\mathrm{F}$ are the mid-points of sides $\mathrm{AB}$ and $\mathrm{CD}$ respectively.
To do:
We have to show that the line segments $AF$ and $\mathrm{EC}$ trisect the diagonal $BD$.
Solution:
$A B C D$ is a parallelogram.
We know that,
Opposite sides of a parallelogram are equal and parallel.
This implies,
$A B \| D C$
$A B=D C$
$\Rightarrow A E \| F C$
$\frac{1}{2} A B=\frac{1}{2} D C$
$\Rightarrow \mathrm{AE} \| \mathrm{FC}$
$\mathrm{AE}=\mathrm{FC}$
Therefore,
$AECF$ is a parallelogram.
This implies,
$\mathrm{AF} \| \mathrm{EC}$
$\Rightarrow \mathrm{EQ} \| \mathrm{AP}$ and $\mathrm{FP} \| \mathrm{CQ}$
In $\triangle B A P$,
$E$ is the mid-point of $A B$ and $E Q \| A P$.
By converse of mid-point theorem,
$Q$ is the mid-point of $B P$.
This implies,
$\mathrm{BQ}=\mathrm{PQ}$...........(i)
In $\triangle D Q C$,
$F$ is the mid-point of $D C$
$F P \| C Q$
By converse of mid-point theorem,
$P$ is the mid-point of $D Q$.
Therefore,
$\mathrm{PQ}=\mathrm{DP}$........(ii)
From (i) and (ii), we get,
$B Q=P Q=P D$
Therefore, $CE$ and $AF$ trisect the diagonal $BD$.
Updated on 10-Oct-2022 13:41:08
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## Graphical representation of Data | Bar Graphs
Image Credit: Pixabay.com
# Graphical / Visual representation of Data
Graphical representation of Data is easier to understand and interpret.
Data can be represented graphically through following methods:
➢ Pictographs
➢ Bar Graphs
➢ Double Bar Graphs
➢ Pie Charts or Circle Charts
➢ Histograms
➢ Line Graphs
They are easier to read and analyse.
## Pictograph
➢ A pictograph represents data through pictures or symbols of objects.
➢ It should be mentioned on the graph as how many unit one symbol or picture stand for.
➢ Sometimes it can be time consuming and difficult to draw.
#### (Ex-9.1) Q5
The number of girl students in each class of a co-educational middle school is depicted by the pictograph :
Observe this pictograph and answer the following questions :
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
(c) How many girls are there in Class VII?
#### Ans
(a). Class VIII
(b). No
(c). Number of pictures in row of class VII = 3
One picture = 4 girls
∴ Number of girls in class VII = 3×4 = 12
# Bar Graphs
A bar graph is a pictorial representation of data in which usually bars (rectangles) of uniform width are drawn with equal spacing between them on either horizontal or vertical axis depicting the variables, then the length of each bar represents the value of the corresponding variable.
### Scale
Scale is the quantity we choose to represent through one unit length on the graph .
➧ The length of the bars should always be drawn in proportion with the scale.
i.e. if on scale, one unit length (let 1 cm) represent 10 m then 2 cm will represent 20 m and so on.
➧ For data with smaller numbers we normally choose unit length to represent unit quantity.
➧ To show larger numbers we need larger scale.
## Horizontal Bar Graph
Bars are drawn horizontally. i.e. on x-axis at equal space.
Value is plotted on y-axis for suitable scale.
Variable should be mentioned below the bar on x axis.
#### (Ex9.3)Q3
Bar graph above shows the marks obtained by a student in an examination in different subjects.
(a) What information does the bar graph give?
(b) Name the subject in which Aziz scored maximum marks.
(c) Name the subject in which he has scored minimum marks.
#### Ans
(a) Marks obtained by Aziz in an examination in different subjects.
(b) Hindi (longest bar)
(b) Social Studies (shortest bar)
## Vertical Bar Graph
Bars are drawn vertically i.e. on y-axis at equal space.
Value is plotted on x-axis for suitable scale.
Variable should be mentioned at the left side of the bar on y-axis.
#### (Ex9.3) Q2
Bar graph which showing the sale of shirts in a ready made shop from Monday to Saturday.
(a) What information does the above bar graph give?
(b) What is the scale chosen on the horizontal line representing number of shirts?
(c) On which day were the maximum number of shirts sold? How many shirts were sold on that day?
(d) On which day were the minimum number of shirts sold?
(e) How many shirts were sold on Thursday?
#### Ans
(a) Number of shirts sold per day in the given week.
(b) 1 unit length = 5 shirt
(c) Saturday (longest bar), number of shirts sold on this day = 60
(d) Tuesday (shortest bar)
(e) 35
#### (Ex9.3)Q1-
Bar graph showing the amount of wheat purchased by government during the year 1998-2002.
write down your observations. In which year was
(a) the wheat production maximum?
(b) the wheat production minimum?
(c) What is the scale chosen on the vertical line representing number of shirts?
#### Ans
(a) 2002
(b) 1998
(c) 1 unit length = 5000 tonnes
## ↓Class 7
Double bar graph shows two sets of data simultaneously.
We can combine two (or more) bar graphs representing similar data to compare them at a glance, this type of graph is called double graph.
In double bar graph below, number of watches tested for water resistance is compared to number of watches leaked in that test.
#### Try These
Q. The bar graph shows the result of a survey to test water resistant watches made by different companies. Each of these companies claimed that their watches were water resistant. After a test the above results were revealed.
(a) Can you work out a fraction of the number of watches that leaked to the number tested for each company?
(b) Could you tell on this basis which company has better watches?
#### Ans
(a) 20/40 = 1/2 for company A
10/40 = 1/4 for company B
15/40 = 3/8 for company C
25/40 = 5/8 for company C
(b) Company B has better watches where ratio of watches leaked to ratio of watches tested is lowest. It is also evident from the graph.
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## How To Beat The Lottery Using Math? Lucky Money
Playing the Lucky Money lottery can be very exciting especially if from time to time you are a winner. Winning can be accomplished quit often if the correct system is used. There are many so called experts in the market offering winning number secrets and scratch off ticket recommendations that promise to help you win. Most are not legit. However, there are a few systems on the market that has produced some promising results.
When you consider that that there are many different lottery systems available and lots of past winners you remain anonymous or don’t talk about their winning strategies how many more winners might there be who have used such systems?
Think about it: is it possible that a huge percentage of lottery winners are actually using mathematical or statistical formulas to help them win? If that is the case then anyone who is not using a system is merely feeding the prize fund and has an almost zero chance of winning.
## Would You Like to Win The Lucky Money lottery?
Lottery predictions is quite popular these days. People used to be skeptical with the predictions as they thought that the winning numbers are a matter of luck and fortunes. Not many people believe that lottery can be won by using some kind of a sophisticated science based predictions. It was not until the late 90s when lottery players began using lottery predictions to help them to win lottery or at least get closer to the winning numbers. When Gonzalo Garcia-Pelayo, a Spanish man who managed to study and analyze many games in two different countries, Spain and the US and win a lot of money by using different strategies. After him people started to believe that lottery results can be predicted.
Lottery players start thinking about how to win the lotteries using predictions. They use many kinds of predictions: from mechanical predictions on mechanical lotteries to technological predictions using computer software. A lot of people use algorithm to analyze and predict lottery results.
Analysis of Groups
There are many kinds of group analysis that lottery predictors use to get into the winning numbers. Lottery players can group the months having the best winning numbers of a certain period or they can group the numbers winning in certain period of time.
Analysis of Hot-Cold Trend
This algorithm analysis is one of the most favourite so far as it can record the frequency ranks and use the variations to predict the tendencies of hot and cold numbers in the next drawings.
Analysis of Repetition Pattern
A lot of lottery players share the same opinion that repetition is quite important to predict the winning numbers as most of jackpots will appear again in the future.
The analysis mentioned above represents only a part of the strategies that lottery players can use. There are still many other algorithm analysis that can be done by predictors to help them win.
## State Lotteries - Which State Has the Best Odds of Winning?
Because you are sitting in front of your computer viewing this page, chances are, you're an eager and regular lotto player who has yet to win lotto prizes. Lottery cheats are some of the most researched items or articles here on the Internet, and it's easy to understand why: lottery games from all states can be addictive, attracting countless players from all across the country to play the lotto on a regular basis. What you need to understand is that while playing the lottery can be fun and exciting, the real treat lies in winning the lotto prizes - including the jackpot. And unlike what some lotto players believe, you can win the lotto using lottery cheats.
Lottery cheats are not cheats in the real sense of the word. They are not illegal and won't put you into some kind of federal trouble. In fact, lottery cheats have long been recognized by serious lottery players as the reason why they have higher chances of winning. Cheats at winning the lottery are actually guides on how to win any type of lotto game you choose to play. They offer sensible pieces of advice to increase the likelihood of holding a winning ticket.
As far as lottery cheats are concerned, statistics experts highly advise against forming lottery combinations in a mathematical sequence and playing patterns on lottery tickets. These acts are sure to reduce your chances of winning because mathematical sequences and patterns are almost never taken into consideration in lottery games. Past winning results show a tendency towards random combinations. If you use a proven system that can efficiently analyze lottery data, such as past winning numbers, trends, and angles, you are more likely to bring home the jackpot prize not just once but as many times as you please.
Winning the Lucky Money lottery is very rewarding. Give this system a spin and watch your winnings grow.
How To Win The Lottery Using The Secret? Florida Lottery
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Search
# How to Remember Lab Values With These Simple Mnemonics
Lab value memory tricks certainly can help you remember the normal levels and ranges for all kinds of substances.
But do you know what works even better?
Well-formed mnemonics.
So if you’re having trouble using the standard advice to memorize your lab values tables, stick around.
I’m going to share with you an alternative way to remember each and every one of them. Quickly.
Sure, you can call what I’m going to share with you easy tricks to remember lab values.
But by adding a few simple twists, you’ll quickly become a memory master for this information and everything else you need to remember as a top-notch medical professional.
Let’s dive in!
## How to Remember Lab Values: 8 Mnemonics for Easy Memorization
As we go through these reference ranges for blood tests, I’m going to interest you to a simple number system. It’s sometimes called the number-shape system.
For each digit from 0-9, you associate a shape by combining mnemonic imagery with chunking. I’ll show you how this works in action with lab values mnemonic examples, and here’s a suggested set of image:
• 0 = donut
• 1 = candle
• 2 = swan
• 3 = moustache
• 4 = sail boat
• 5 = seahorse
• 6 = hook
• 7 = boomerang
• 8 = snowman
• 9 = golf club
You don’t have to use this number mnemonic system for the lab values. I’ll also give you some examples using the Major System and a 00-99 PAO. If you already have a number-shape system, you might want to upgrade to either of those, or explore the Dominic System for memorizing any numbers related to medical terminology.
I’ll give you examples from both so that you can decide with to learn. So with these mnemonic devices in mind, let’s get started with some mnemonic examples.
## The Basic Metabolic Table
Typically when you see mnemonic examples for the table, you’re overwhelmed by a ton of them on a spreadsheet. The mnemonics are also often vague and uninspiring.
Let’s fix that right now. We’re going to use the core principles taught in the Magnetic Memory Method Masterclass to do it.
### Sodium
In the example above for sodium, I’ve used a Memory Palace in my mind. On station one, I imagined a pile of sodium being attacked by General Zod from the Superman stories.
Normally, for the sodium lab range mnemonic, people suggest that you think about the odd numbers in order, giving you 1, 3 and 5 for 135. From there, it’s a simple matter to add 10 to remember 145 is at the top of the range.
My preference is to have someone specific doing something that can be imagined in an actual location. That way, it’s easier to think back to that location and ask, “What was happening there?”
In this case, I could have General Zod (which sounds a bit like sodium), picking up some odd cubes of sodium. But I also add a candle for one, a moustache for 3 and a seahorse for 5 to give the number 135.
This form of association-making forms memories much faster and applies to memorizing everything from insulin types to the carpal bones.
### Potassium
For potassium, you have a range or 3.5-5.
Remember that I mentioned you can association 3 with a moustache? That’s because 3 kind of looks like a moustache when tipped on its side.
If you have a banana to remind you of potassium, give him a moustache to remind you of 3.
The black spot at the tip of the banana can help you remember that. And you can add a seahorse to the mnemonic for the top of the range, which is 5.
### Blood Urea Nitrogen (BUN)
Hungry yet?
Let’s go deeper with the foods because BUN brings hamburgers to mind for the Blood Urea Nitrogen value, which has a range of 5-10.
I mentioned the Major System and 00-99 PAO System above. Here’s where that can make memorization even faster. You have your seahorse interacting with hamburger buns, which he is smelling with his massive nose.
“Nose,” in my PAO System is 20 because 2=n and 0 =s. Or you could use a swan and a donut for 20 using the simple system already discussed. Personally, I like to pop in the PAO System when two digits are involved because it’s faster and more fun.
### Creatinine
Most of us know the story of Adam and Eve in the Garden of Eden. It’s the story of “creation” which makes it a fantastic mnemonic for “creatinine.”
But instead of having God pull out a rib, he pulls out a fishing hook instead – your symbol that looks like the number six. This will help you easily remember that the value starts at 0.6.
Some people suggest that you focus on the “nine” in Creatinine because that’s approximately halfway between 0.6 and 1.2. That’s a great idea too, and you can do both by having Adam react with a golf club, which basically resembles and upside-down 9.
### Glucose
Glucose has the sound of “glue” in it and so it’s easy to imagine someone pouring glue on the famous Glenn Close (for the “cose sound).
I use my aunt Cassie for 70, but if you’re just learning these systems, having Glenn Close fight back with a boomerang for 7 and a donut for 0 is highly memorable.
What about the 100 at the top of the range? You can have a candle and two donuts involved in the association.
### Calcium
Calcium is a fairly easy word to remember. It gets even easier to remember when you imagine a snowman drinking milk from a giant bottle.
Why a snowman? Because snowmen resemble 8. You can easily add 8.5 – 10.5 by imagining stone eyes for the decimals.
### Chloride
Chloride reminds me of Chloë Savigny, and bucket is my image for 95 in the PAO System. It’s easy to imagine her carrying a pail in a strange way.
Or you can use the number-shape system with a golf club for 9 and a seahorse for 5 in the lower range. You know what to do to create an image for the upper range of 105.
### Bicarbonate
The normal mnemonic you’ll hear for Bicarbonate is to 2x a soda can for 23-29.
That’s too abstract for me. So I specifically suggest putting in Joe Biden for the “bi” sound. Having him throwing two sodas at images that will remind you of 23 and 29.
Here again I’m using the PAO System to arrive at Rambo and Jack Napier for these particular numbers.
For best results and ease of spaced repetition, I suggest drawing all of your mnemonics on flashcards. These can be imported into Anki or you can use your mind on its own with the method of loci.
That way, you have a specific point of reference for each item that you can easily refer back to as you instil the information in long-term memory.
## Comprehensive Metabolic Panel Mnemonic Examples
Let’s turn now to the comprehensive metabolic panel, which involves the same process. All of this information is so critical, especially when you’re on the job and also need to remember the order of the draw.
To make your mind organized and keep everything fast and fun, I suggest using a separate Memory Palace for this table.
In this case, you have a lot of acronyms. For these I suggest the pegword method. By using it, AST is much easier to remember, both as an acronym and the full term.
For example, AST stands for Aspartate Transferase. An asp from Shakespeare’s Antony & Cleopatra instantly springs to mind. Now it’s just a matter of adding mnemonics for the normal ranges involved.
Read the table above and use your visualization skills to imagine what my examples might look like in a Memory Palace of your own.
For each, I have:
• AST = an asp from Shakespeare on a sail boat with a golf club for 9-40
• ALT = the alternative band Nirvana with a boomerang for 7-60
• ALP = Weird Al in a pool with a sailboat and Tintin for 40/120
• Bilirubin = the Bill of Rights with a candle for < 1
• Albumin = Minnie Mouse with a moustache for 3.4-5.4
## Complete Blood Count Mnemonic Examples
For the next table, I would again suggest a separate and unique Memory Palace. Here are some mnemonic examples for these lab values.
Again, you’re very welcome to use my mnemonic associations. But if you don’t know people like Hemingway, it’s best to come up with your own.
Here’s my list:
• WBC = William Burroughs and Cookie Monster with a seahorse for 5,000-1000/mcL
• RBC = (Edgar) Rice Burroughs with a sailboat in his hands for 4.5-5.5 million/mcL
• Hemoglobin = Hemingway and Hobgoblin with Tintin for 12-18 g/dL
• Hematocrit = Hemingway criticizing a pile of muck for 37-50%
## Arterial Blood Gas Mnemonic Examples
One tip for you as you choose Memory Palaces is to think of the letter of the terminology first. “Arterial” starts with “A” as does the similar sounding “airport.” You could then think of an airport you’re familiar with for the Memory Palace you use for this table of lab values.
Rest assured, it’s easy to find Memory Palaces for all of this information. You can even find a unique Memory Palace for each row of the Periodical Table if that’s how you choose to memorize it.
## Coagulation Studies Mnemonic Examples
Finally, we have examples for coagulation studies or Coags. Let’s have a look:
My mnemonic examples for you are:
• INR = Ian Fleming using a ray gun to put out a candle for <1
• My personal trainer with a taser for 10-12 seconds
• My personal trainer putting a toque on Mickey Mouse for 30-40 seconds
As you can see, I’m using my personal trainer. That’s not only because “PT” also commonly means “personal trainer.” I’m also using him because making your mnemonics as personalized as possible has been shown in memory science to make things much sticker.
## Lab Values Mnemonic Success Is In Your Hands
You know have an incredible means of rapidly memorizing all of the core lab values.
The key now is to take action with these suggestions. Make each of your mnemonics as personal as possible using the number systems and your alphabetical pegword associations.
If you need more help, register for my free course now:
It will help you develop multiple Memory Palaces and even stickier mnemonic associations.
So what do you say?
Thanks for stopping by and taking steps to being an excellent medical professional by giving yourself the gift of a truly Magnetic Memory.
### WANT TO LEARN SIMPLE EVERYDAY THINGS WITHOUT FORGETTING?
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• Speak any language fluently
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• Recite poetry, jokes, and even long speeches word-for-word
• Quickly absorb the most important ideas from books, textbooks, or lectures...
Unlock your natural ability to learn and remember anything 3x faster now!
Anthony Metivier is the founder of the Magnetic Memory Method, a systematic, 21st century approach to memorizing foreign language vocabulary, names, music, poetry and more in ways that are easy, elegant, effective and fun.
Dr. Metivier holds a Ph.D. in Humanities from York University and has been featured in Forbes, Viva Magazine, Fluent in 3 Months, Daily Stoic, Learning How to Learn and he has delivered one of the most popular TEDx Talks on memory improvement.
His most popular books include, The Victorious Mind and… Read More
Anthony Metivier taught as a professor at:
## Remembering & Recalling Critical Information Becomes Easy With This...
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Explore BrainMass
# Considering Control Systems
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Question: Consider a system with a block model diagram as shown (*see attachment), and suppose that u(t) is a unit step input. Next consider the plot of the corresponding step response (y)t, also shown, and match it to the appropriate pole locations of the transfer function G(s) = Y(s)/U(s)
U(s) --> [K/(s-p1)(s-p2] --> Y(s)
- {Re (p1,p2) greater than 0; Im(p1,p2) equal to zero}
- {Re (p1,p2) less than 0; Im(p1,p2) not equal to zero}
- {Re (p1,p2) equal to 0; Im(p1,p2) not equal to zero}
- {Re (p1,p2) greater than 0; Im(p1,p2) not equal to zero}
- {Re (p1,p2) less than 0; Im(p1,p2) equal to zero}
*(Please see attached for complete problem and diagram)
https://brainmass.com/engineering/computer-engineering/considering-control-systems-26886
#### Solution Preview
Question E1, Item 5.
Choose only one answer by putting a checkmark in the box. Checking off more than one box invalidates the answer. Also, explain in-detail why such answer is chosen.
y(t) is a pure sinusoid (with no exponential decay) and so the poles are pure imaginary and no real part.
Hence {Re (p1,p2) = 0; ...
#### Solution Summary
This solution is comprised of a full response to each component of this electrical and computer engineering based question. In order to view the solution, a Word document attachment needs to be opened.
\$2.49
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A large department store has been attaching tags with barcodes to merchandise, and employees use barcode readers to scan merchandise at the cash register. However, the wireless barcode readers need new batteries often. Also, using this system for inventory tracking is very time-consuming.In 1–2 sentences, describe the emerging technology the department store should consider using for tracking inventory.
1. 👍 0
2. 👎 1
3. 👁 352
## Similar Questions
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## A box contains 1 green, 2 red, 3 pink, and 4 yellow paper clips. A paper clip 2 points is drawn and NOT replaced. Then a second paper
Question
A box contains 1 green, 2 red, 3 pink, and 4 yellow paper clips. A paper clip 2 points
is drawn and NOT replaced. Then a second paper clip is drawn. What is the
probability that a person picks a red clip and then another red clip in a
row?*
1/25
25%
2/45
1/45
in progress 0
2 weeks 2022-01-07T05:00:36+00:00 1 Answer 0 views 0
25%
Step-by-step explanation:
1 green + 2 red + 3 pink + 4 yellow = 10 total paper clips
You take out 2 paper clip & don’t put them back in.
Now you only have 8 paper clips.
2 of those 8 paper clips are red.
That would make it 2/8.
2/8 = 1/4
1/4 = 0.25
0.25 = 25%
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# Valentine Math Numbers Freebie Kindergarten Free Worksheets For Students These Fun Activities And Printables Are Great Lessons In Can
Published at Friday, 10 May 2019. Color by Number. By .
Coloring Books And Worksheets: What’s The Value Of ’Staying In The Lines’? Crayons, of course. Scented markers. Colored pencils, resharpened. And coloring books by the jillions. Why do people like coloring so much? For grown-ups, I can totally get the nostalgia — and the simple pleasure of creating something. But here at NPR Ed, we’re all about kids and learning. And so, as parents head to the store this summer with their back-to-school lists, we thought this question was worth a serious look: Do coloring books have any educational value? Do they squash creativity like a bug or, as some sites suggest, promote the development of fine motor skills? I’ve seen my daughter bring home worksheets from elementary school, asking her to color in this or that picture after answering a math or word problem. And, I’ve wondered as I watched her complete these assignments, ”Isn’t this busywork?”. I’ve always thought coloring books are, educationally speaking, bad news. That ”staying in the lines” isn’t really the kind of independent and creative thinking we want to nurture. Am I right? So, as part of our Tools of the Trade series, here’s a look at kids and coloring books and whether they have any place in the classroom.
Who Should Be Credited with the Creation of Paint-by-Number: Michelangelo or Leonardo DA Vinci? Some people dismiss paint-by-number as an elementary, formulaic painting system. Everyone is entitled to their own opinion, but it’s worth mentioning that Leonardo DA Vinci is rumored to have created the first painting-by-number system. In his book Math and the Mona Lisa: The Art and Science of Leonardo DA Vinci, Bülent Atalay wrote, “Painting by number may not be as egregious a pursuit as one might imagine. Leonardo himself invented a form of it, assigning assistants to paint areas on a work that he had already sketched out and numbered.” Other sources suggest that Michelangelo should be credited with the invention of the painting system. Either way, paint-by-number had anything but humble beginnings.
Color by number printable give kids a chance to solve a mystery, Granted, not much of a mystery. But when you see a blank color by number page, you don’t know what it’s going to look like before you color it in. As you color, the pictures start to come to life beneath the tips of your crayons. It’s fun to watch it happening. There are also color by number pages out there that do not allow users to see what the pictures are before they are colored… they often feature strange looking mosaics that “hide” a picture in the various shapes on the page. These are also fun classroom activities to complete.
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# The quantitative analysis approach & ex. of quantitative analysis in
Week 1 Discussions and Required Resources
Part 1 and Part 2 must be at least 150 – 200 words unless otherwise
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Part 1: The Quantitative Analysis Approach
1. For this discussion, begin by reviewing the technique of quantitative analysis in your textbook. Then, keeping this technique in mind, read the following quotes:
“Data do not give up their secrets easily. They must be tortured to confess.”—Jeff Hopper, Bell Labs
“Statistics is a body of methods for learning from experience.”—Lincoln Moses
“The time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex worldwide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.”—H.G. Wells
“The coming century is surely the century of data.”—David Donoho (2000)
“Another mistaken notion connected with the law of large numbers is the idea that an event is more or less likely to occur because it has or has not happened recently. The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler’s fallacy. For example, if Kerrich landed, say, 44 heads in the first 100 tosses, the coin would not develop a bias towards the tails in order to catch up! That’s what is at the root of such ideas as ‘her luck has run out’ and ‘he is due.’ That does not happen. For what it’s worth, a good streak doesn’t jinx you, and a bad one, unfortunately, does not mean better luck is in store.”―Leonard Mlodinow, The Drunkard’s Walk: How Randomness Rules Our Lives
“A certain elementary training in statistical method is becoming as necessary for everyone living in this world of today as reading and writing.”―H.G. Wells, World Brain
“The non-scientist in the street probably has a clearer notion of physics, chemistry and biology than of statistics, regarding statisticians as numerical philatelists, mere collector of numbers.”―Stephen Senn, Dicing with Death: Chance, Risk and Health
2. Based on the above quotes, along with this week’s assigned readings and Instructor Guidance, discuss why quantitative analysis is important for describing data sets and presenting distribution information.
Part 2: Examples of Quantitative Analysis in Research
Locate an example of a research study that uses quantitative analysis. Explain what this statistical method allowed the researchers to accomplish and conclude in the study.
Required Resource
### Text
Lind, D. A., Marchal, W. G., & Wathen, S. A. (2017). Statistical techniques in business and economics. (17th ed.). Retrieved from http://connect.mheducation.com/class/
· Chapter 1: What is Statistics?
· Chapter 3: Describing Data: Numerical Measures
· Chapter 5: A Survey of Probability Concepts
· Chapter 6: Discrete Probability Concepts
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# Binomial Distributions and Probability
## P(X successes in 'n' trials): P(X=a) = nCa x p^a x q^(n-a)
Levels are CK-12's student achievement levels.
Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.
At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.
Advanced Students matched to this level are ready for material that requires superior performance and mastery.
## Binomial Distributions and Probability
by CK-12 //basic
Covers binomial distributions.
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## Binomial Distributions and Probability
This Concepts introduces students to the binomial probability distribution.
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## Binomial Distributions and Probability
This Concepts introduces students to the binomial probability distribution.
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## Binomial Distributions and Probability
by Melissa Moreno //basic
Covers binomial distributions.
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• PLIX
## Roll One!
Binomial Distributions and Probability Interactive
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## Binomial Distributions and Probability Principles
by CK-12 //basic
This video gives more detail about the mathematical principles presented in Binomial Distributions and Probability.
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## Binomial Distributions and Probability Examples
by CK-12 //basic
This video shows how to work step-by-step through one or more of the examples in Binomial Distributions and Probability.
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## Introduction to Binomial Distributions
by CK-12 //basic
Introduces binomial distributions and how to use them to find the probability of random variables.
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• Video
## The Binomial Probability Function
Guides you through an example using binomial distributions.
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## Binomial Distributions - Overview
by CK-12 //basic
Overview
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## Binomial Distributions: Properties
Uses a bulls-eye example to illustrate the properties of binomial distributions.
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• Video
## Binomial Distributions - Example 1
by CK-12 //basic
Constructing and Interpreting Binomial Distributions
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• Video
## Binomial Distributions: Formula
Derives the formula for binomial distributions from an example.
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## A Glimpse at Binomial Distributions Lesson Plan
by CK-12 //basic
This lesson plan covers A Glimpse at Binomial Distributions and includes Teaching Tips, Common Errors, Differentiated Instruction, Enrichment, and Problem Solving.
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## Binomial Distributions and Probability Quiz
10 questions about Binomial Distributions and Probability.
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• Critical Thinking
## Binomial Distributions and Probability Discussion Questions
A list of student-submitted discussion questions for Binomial Distributions and Probability.
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• Real World Application
## Binomial Distributions
Students will investigate, "If you are at a party hanging out with friends, how likely is it that the people in your group have an STD?" They will use their knowledge of binomial distribution to answer the previous question.
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• Study Guide
## Types of Distributions
covers normal, binomial, multinomial, geometric, poisson, and student's t distributions
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• Flashcards
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Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > necon1bddc GIF version
Theorem necon1bddc 2297
Description: Contrapositive deduction for inequality. (Contributed by Jim Kingdon, 19-May-2018.)
Hypothesis
Ref Expression
necon1bddc.1 (𝜑 → (DECID 𝐴 = 𝐵 → (𝐴𝐵𝜓)))
Assertion
Ref Expression
necon1bddc (𝜑 → (DECID 𝐴 = 𝐵 → (¬ 𝜓𝐴 = 𝐵)))
Proof of Theorem necon1bddc
StepHypRef Expression
1 necon1bddc.1 . . 3 (𝜑 → (DECID 𝐴 = 𝐵 → (𝐴𝐵𝜓)))
2 df-ne 2221 . . . 4 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
32imbi1i 231 . . 3 ((𝐴𝐵𝜓) ↔ (¬ 𝐴 = 𝐵𝜓))
41, 3syl6ib 154 . 2 (𝜑 → (DECID 𝐴 = 𝐵 → (¬ 𝐴 = 𝐵𝜓)))
5 con1dc 764 . 2 (DECID 𝐴 = 𝐵 → ((¬ 𝐴 = 𝐵𝜓) → (¬ 𝜓𝐴 = 𝐵)))
64, 5sylcom 28 1 (𝜑 → (DECID 𝐴 = 𝐵 → (¬ 𝜓𝐴 = 𝐵)))
Colors of variables: wff set class Syntax hints: ¬ wn 3 → wi 4 DECID wdc 753 = wceq 1259 ≠ wne 2220 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 103 ax-ia2 104 ax-ia3 105 ax-in1 554 ax-in2 555 ax-io 640 This theorem depends on definitions: df-bi 114 df-dc 754 df-ne 2221 This theorem is referenced by: necon1ddc 2298
Copyright terms: Public domain W3C validator
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$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
# 16.7: Surface Integrals
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
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Algebra Tutorials!
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# Q7
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Q7 May 30, 2011 11:50AM Registered: 8 years ago Posts: 363 Rating: 0
7(a) I have no idea what this question requires us to do.
(b)
(i) Does not hold - c is also accessible from itself but p is not true in c
(ii) Does not hold - p is not true in c
(iii) Holds
(iv) Holds
Re: Q7 May 30, 2011 01:16PM Registered: 10 years ago Posts: 3,496 Rating: 1
"Is not universally valid, and yet turns out to be true in this set of worlds".
That's my stab in the dark at it. Please take with at least a shovel load of salt. I need to go back to the drawing board, it would seem.
Re: Q7 May 30, 2011 01:44PM Registered: 11 years ago Posts: 111 Rating: 0
7a) [](p or q)
From each world, another world is accissible which either is true for p, true for q, or both. However, this is only true in this particular model. For it to be a valid formula, it would have to be true for each and every possible model. For instance, if there is another world accissible from d, and that world is not true for p or q (has no label), then this formula is no longer valid...
Re: Q7 May 30, 2011 01:50PM Registered: 11 years ago Posts: 111 Rating: 0
ii) You should be looking for q's
So, it holds I think... From a, there is at least one world, d. All the worlds accessible from d: only c. and c is true for q.
Re: Q7 May 30, 2011 02:38PM Registered: 8 years ago Posts: 363 Rating: 0
Thanks Hexium, and yep (ii) was my error. Hope silly mistakes like that don't get the better of me in the exam!
Re: Q7 May 30, 2011 10:25PM Registered: 10 years ago Posts: 3,496 Rating: 1
Finally I'm able to contribute here, and I'm stuck. i, ii, iii = no problem I'm aware of.
For iv I get this:
Worlds accessible from b = c
Worlds accessible from c =
a ... With Worlds accessible = d ----- where p is T <-------??
d ... With Worlds accessible = c (satisfies ~p )
c ... With Worlds accessible =
... a = ~~p
... d = ~~ p
... c = ~p.
So even if I put it to a vote, I get more ~p than p. More to the point I don't get exclusively either. What am I doing wrong?
Re: Q7 May 31, 2011 09:59AM Registered: 8 years ago Posts: 363 Rating: 0
Ok, here's my explanation to (iv)
In order for it to hold box box ~p has to be true in all worlds accessible from b, only c is accessible. In order for box box ~p to be true in c, box~p has to be true in all world accessible from c. Which are c itself, and d. Let's examine c, ~p has to be true in all world accessible from c, in d p is true so .. IT DOES NOT HOLD.
I think I made a mistake earlier. Does this make more sense?
Re: Q7 May 31, 2011 10:00AM Registered: 8 years ago Posts: 363 Rating: 0
Oh, and a is also accessible from c, so, there it DOES NOT HOLD
Re: Q7 May 31, 2011 12:34PM Registered: 10 years ago Posts: 3,496 Rating: 1
I think that's right, then. I'm a bit in the dark here, to be honest. I'm basically trying to apply hexium's methods, as I understand them, because that seems to make sense to me.
I think you're right now, then. Taking B = box, we start with
BBBBphi
B's scope is BBBphi
B's scope BBphi
B's Bphi .. at which point we have to satisfy every little unravelled bit of thread for phi for it to hold.
It would then work pictorially as a kind of tree graph, getting pretty frayed at the end if there are a lot of boxes.
I THINK ...
Sorry, only registered users may post in this forum.
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-5(8y + 6) - 6 A. -40y - 60 B. -40y - 36 C. 40y + 24 D. -40y
-5(8y + 6) - 6 = B. -40y - 36
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-(7v - 9) - 15
Weegy: 3-3 = 0 User: -(7v - 9) - 15 A. -7v - 24 B. -7v - 6 C. -7v + 24 D. -7v + 6 Weegy: B. -7v - 6 is the answer. -(7v - 9) - 15 = -7v - 6 (More)
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5(8 - x) + 6 A. 34 + 5x B. 34 - 5x C. 46 - 5x D. 46 - x
Weegy: This equation factors to (3x+2)(2x-3) (More)
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Updated 7/30/2018 1:19:44 AM
5(8 - x) + 6 = 40 - 5x + 6 = 46 - 5x
13. Solve the equation. 3(y + 6) = 30 A. 5 B. 16 C. 4 D. –16
Question
Updated 9/19/2017 8:33:59 AM
3(y + 6) = 30
3y + 18 = 30
3y = 30 - 18
3y = 12
y = 12/3
y = 4
Rated good by Daphne10
Solve the equation. 4(x - 1.6) = 9.3 A. x = 15.7 B. x = 2.725 C. x = 3.925 D. x = 1.925
Question
Updated 7/11/2018 9:22:11 AM
4(x - 1.6) = 9.3 ;
4x - 6.4 = 9.3 ;
4x = 9.3 + 6.4 ;
4x = 15.7 ;
x = 15.7/4 ;
x = 3.925
A. 28 B. C. D. 3
Weegy: Hi, Do you have anything to ask? We'll provide you with quick answer. User: A. 18 B. 1.8 C. –9 D. 9 User: 0.6x + 18.65 = 22.85 A. x = 2.52 B. x = 4.2 C. x = 7 D. x = 37.77 Weegy: 0.6x + 18.65 = 22.85, 0.6x=22.85-18.65, 0.6x=4.2, x = 7 User: Solve the equation. x + 5(x – 1) = 7 A. x = 1 B. x = 12 C. x = 5 D. x = 2 Weegy: Please clarify your question.Thank you. User: Solve the equation. 3.5 = 12x – 5x A. x = 0.25 B. x = 0.5 C. x = 5 D. x = 50 Weegy: Answer is B. x = 0.5 . Here's its simplification- 12x-5x=3.5, 7x=3.5, x=3.5/7=.50 User: Solve the equation. 1.12 + 1.25y = 8.62 A. y = 7.792 B. y = 7.5 C. y = 7 D. y = 6 Weegy: 1.25y=8.62-1.12=Hence y=6.I think the D ans should be as y=6. User: Solve the equation. 6(z - 1.8) = 9.3 A. z = 1.25 B. z = 3.35 C. z = 1.85 D. z = 20.1 Weegy: 3-3 = 0 (More)
Question
Updated 6/30/2014 9:11:26 AM
x + 5(x – 1) = 7
x + 5x - 5 = 7
x + 5x = 7 + 5
6x = 12
x = 2
Confirmed by jeifunk [6/30/2014 9:12:16 AM]
6(z - 1.8) = 9.3
6z - 10.8 = 9.3
6z = 9.3 + 10.8 = 20.1
z = 20.1/6 = 3.35
Confirmed by jeifunk [6/30/2014 9:12:28 AM]
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# Results forfraction centers 3rd grade
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Fraction Mystery Pictures Worksheets Bundle. This is a bundle of our mystery picture activity sheets on fractions:- Fraction of a Whole Mystery Pictures- Fraction on a Number Line Mystery Pictures- Equivalent Fractions Mystery Pictures*** Updated version. Please download again.To use, just print and
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This bundle includes 3rd Grade Math Centers for Every Common Core Standard! The bundle includes 76+ math centers (at least two centers for each standard) to allow you to differentiate and use these all year long. Need another grade level?Click here to see 4th Grade Math Centers.Click here to see 5th
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You will download 30 printable equivalent fractions with picture models task cards for 2nd or 3rd grade and special education math students. Ideas for math center games and activities are included, such as a scavenger hunt or SCOOT. They also work well as a review, test prep, formative assessment or
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Also included in: 3rd Grade Fractions Unit BUNDLE, Common Core Math Standards Practice
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This year go green, have more fun mastering standards, and all while letting Google's powerful engine do the tedious task of grading for you! You'll find it's never been easier to breathe new life into your teaching of the 3.NF (Introduction to Fractions) standards as you enjoy your newfound freedo
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Want a fun, easy way to review the Common Core Math Skills? This is for you! This resource contains 10 ready to use, self-checking math center games for the Number and Operations: Fractions Common Core Standards for 3rd Grade. Click here to see the bundle of all my 3rd Grade Roll and Answer Math C
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I created this packet of math activities and games to use in a 3rd grade classroom (although it could easily be used for introductions or reviews in other grades). The entire theme of the packet is pandas, however, the activities are easy to incorporate into any classroom and use over and over again
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This collection of 8 back-to-school themed centers are perfect for the beginning of 3rd grade. Each center reviews a 2nd grade skill allowing you to focus on teaching your procedures. The recording sheets also act as documentation of how well the students have retained the information from the pre
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This Common Core State Standards Hershey Bar Differentiated Fractions Pack is appropriate for 3rd and 4th grade, and supports standards 3.OA.D.8, 3.NF.A.1, and 3.NF.A.3.d. Students are asked to complete comparing fractions word problems using numbers, pictures, and words. The second word problem is
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This Common Core State Standards M&M's Differentiated Fractions Pack is appropriate for 3rd grade, and supports standards 3.NF.A.1 and 3.G.A.2. Tasks include practice for below, on, and above level learners, making the curriculum both accessible and challenging for all. Excellent for use in a le
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This Common Core State Standards M&M's Differentiated Fractions Pack is appropriate for 3rd grade, and supports standards 3.NF.A.1 and 3.NF.A.3.d. Tasks include practice for below, on, and above level learners, making the curriculum both accessible and challenging for all. Excellent for use in a
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3rd Grade Fractions: You will receive 30 BOOM Learning cards for students to practice comparing pictorial fractions. You will also receive two printable fraction worksheets to use as formative assessments, extra practice or as homework. They are appropriate for 2nd grade, 3rd grade, or special ed
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This is a bundle of 3 Christmas math fraction activities for 3rd and 4th grade math review. They also work well for students with special education and autism. You may use them in your Christmas math centers for a scavenger hunt, SCOOT game or other fun activities.You will receive the following ging
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Get these fun fraction worksheets to save time creating your resources. It's a mystery picture coloring activity that's are great for assessment, differentiation or extra practice. To uncover the mystery pictures, they must first correctly answer the problems. Then, they have to match their answ
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Looking for a fun interactive teaching idea for fractions? Well look no further as Fractions I Have Who Has Game, for CCSS 3.NF.1, will serve as an exciting lesson plan for 3rd grade elementary school classrooms. This is a great resource to incorporate into your unit as a math review game exercise,
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I created this fraction notebook when student teaching for 3rd grade. It went along great with Go Math and teaching the basics of fractions. After we learned a lesson we would complete our notebook page for the day.
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This 3rd Grade Fractions Color-by-Number Activities Pack comes with 8 mystery picture activities and over 190 task cards for reviewing key 3rd grade Common Core fractions standards in a fun and exciting way! Each included activity supports one of the following 3rd grade Common Core fractions skills
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I am so glad that my math study guides and math homework are helping you all. I highly appreciate the comments, suggestions and replies that you submit and I make all the math worksheets according to your requests. I am keeping my FUN math guides FREE so that math practice can be easily available to
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This is a collection of fun fraction worksheets. It's a mystery picture activity that's perfect for practice, quick assessment or homework. To use, let your students answer the problems. Then, they must match their answers to a list to get the color-letter combination. Finally, they color the s
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Included in this FREEBIE is a workmat that can be used for students to compare fractions. The students can then prove their answers using fraction bars and/or number lines, as well as explain their answers in words. This will also work for proving fractions are equivalent. All you need to do is p
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What's all in this huge packet?You will download printable fraction worksheets for your students to practice fractions on a number line, comparing fractions, equivalent fractions and more.Skills include: identifying fractions, comparing fractions, fraction vocabulary, using anchor charts, fractions
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Also included in: 3rd Grade Fractions Unit BUNDLE, Common Core Math Standards Practice
\$7.50
815 Ratings
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PDF (5.02 MB)
Help make teaching equivalent fractions easier and more understandable for your students - This unit starts with a basic introduction to equivalent fractions, and then is scaffolded with visuals to help your students master this skill as the concepts get more difficult. The scaffolding also helps y
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Give your students hands-on math instruction for EVERY Common Core math standard! These 25 Common Core Math booklets introduce math concepts to students through a combination of hands-on activities and skills practice. These booklets make a great follow up activity to interactive notebook entries o
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\$75.00
\$38.00
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# Word 2002 - Writing a Fraction HELP!
G
#### Guest
I need to make a math worksheet, and the fractions need to be number over
line over number. I have tried using the equation editor - I press CTRL F9,
enter in my information {EQ\f(1/8)} to get the fraction 1/8, but that's all I
see. What should I be doing? I pressed SHIFT F9 and what I had typed
disappeared. I have installed Microsoft Equation, and I have used the help
menu. I made sure Field Codes was unchecked in the tool - options - view
menu. I have done everything I know to do, what am I doing wrong?
THANKS!
laineyfay said:
I need to make a math worksheet, and the fractions need to be number
over line over number. I have tried using the equation editor - I
press CTRL F9, enter in my information {EQ\f(1/8)} to get the
fraction 1/8, but that's all I see. What should I be doing? I
pressed SHIFT F9 and what I had typed disappeared. I have installed
Microsoft Equation, and I have used the help menu. I made sure Field
Codes was unchecked in the tool - options - view menu. I have done
everything I know to do, what am I doing wrong?
THANKS!
First off, you're confusing two completely unrelated mechanisms -- the EQ
field has nothing to do with Microsoft Equation Editor.
If you want to use the EQ field, you have to fix a couple of problems in
your field code. There must be a space between the EQ and the \f, and you
need a comma instead of a slash:
{EQ \f(1,8)}
and then press F9 to update the field. In the result, the digits will be
full size; if you want them smaller, you'll have to reopen the field code
(Shift+F9) and format the digits to a smaller size (if the body text is 12
pt, use 8 pt for the digits in the fraction).
If you want to use the Equation Editor instead, click Insert > Object >
Microsoft Equation 3.0 > OK. You'll get a rectangle with a shaded border
where the equation will go, and a toolbar full of "palette" buttons -- each
one drops a picture menu. Also, the menu bar will change to entries for the
Equation Editor.
Before you do anything else, check the font assignments, because the
installer doesn't always get it right. See
http://word.mvps.org/FAQs/AppErrors/EqEditorCrashes.htm for instructions.
THANKS! Worked perfectly!!!!
:
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# Week 10 Generalised functions, or distributions
## Presentation on theme: "Week 10 Generalised functions, or distributions"— Presentation transcript:
Week 10 Generalised functions, or distributions
The Dirac delta function Derivatives of the Dirac delta function Differential equations involving generalised functions 1. The Dirac delta function Consider a family of functions δε(x), where x is the variable and ε is a parameter: (1)
Theorem 1: Consider (2) where f(x) is analytic in a certain interval about the point x = 0. Then (3) Proof: Represent f(x) by its Taylor series: (4)
Substitute (1) and (4) into (2):
hence, tends to 0 as ε → 0 which yields (3) as required. █
Consider (2) with f(x) = 1, which yields
At the same time, it follows from (1) that Q: what kind of function tends to zero at all points except one, but still has non-zero integral (area under the curve)? A: It’s called the Dirac delta function, or just delta function. It’s not a usual function though, but a generalised function, or distribution.
The delta function [usually denoted by δ(x)] can be defined using infinitely many different families of functions. Introduce, for example, (5) and consider...
where f(x) is analytic in a certain interval about the point x = 0.
It can be shown that i.e. the family of functions defined by (5) correspond to the delta function, just like family (1).
Theorem 2: Let a family of functions δε(x) satisfy Then δε(x) corresponds to the delta function, i.e. for any f(x) which is analytic at x = 0.
Example 1: Let For which a does this family of functions correspond to δ(x)?
Comment: Even though generalised functions (GFs) imply an underlying limiting procedure, one often uses a ‘short-hand notation’ treating them as if they were regular functions, e.g. One should keep in mind, however, that the above equality actually means where δε(x) is a suitably defined family of functions. Yet, in many cases, the ‘short-hand notation’ can be used to re-arrange expressions involving GFs, and it yields the correct result!
Example 2: Consider (6) where δ'(x) is the delta function’s derivative (we haven’t defined it yet, but let’s consider it anyway and see what happens). Treating δ(x) as a regular function and δ'(x) as its derivative, we integrate (6) by parts...
Assume that which kind of agrees with the fact that, in the proper definition of δ(x), the function δε(x) vanishes outside the interval (–ε, ε). Thus, Now, recall how δ(x) affects test functions. Recalling also definition (6) of I, we obtain...
(7) Even though this equality was derived without following the proper procedure (families of functions, etc.), we’ll later see that (7) correctly describes how the derivative of the delta function affects a test function.
2. Derivatives of the Dirac delta function
Consider the following family of functions: Note that, everywhere except the points x = –ε, 0, +ε, the function δ'ε(x) equals to the derivative of δε(x) defined by (5). At the ‘exceptional’ points, δε(x) doesn’t have a derivative, so the values of δ'ε(x) were chosen, more or less, ad hoc. Now, consider...
where f(x) is analytic in a certain interval about x = 0.
Theorem 3: Proof: Represent f(x) by its Taylor series Observe that δ'ε(x) is odd – hence, every other term of the series in [] doesn’t contribute to the integral, and we obtain...
hence, hence, as required. █ tends to 0 as ε → 0
The ‘short-hand’ form of Theorem 3 is
Comment: The minus on the r.-h.s. looks ‘unnatural’, but it actually agrees with the result in Example 2 obtained using the short-hand notation. Comment: The family of functions used in Theorem 3 for representing δ'(x) was obtained by differentiating the family of functions defined by (5) and used to represent δ(x). In principle, we could’ve used a different family, but there’s still a general rule: if δε(x) represents δ(x), then the derivative of δε(x) represents δ'(x).
Theorem 4: The n-th derivative of δ(x) [denoted by δ(n)(x)] can be defined through any family of functions such that
We shall also use δ(x – x0) and δ'(x – x0), such that
What’s the equivalent of the above equalities for δ"(x – x0)?
Theorem 5: Let a function g(x) be smooth and strictly monotonic, i.e. Let also g(x) have a single zero at x = x0, i.e. Note that, since g(x) is strictly monotonic, Then,
Proof: Let g'(x0) > 0 and consider (8) Let’s change the variable x to y = g(x), so that where x(y) is the inverse function to y = g(x). Observe also that, since y(x0) = 0 and x(y) is the inverse function, it follows that (9)
Now, (8) becomes which can be readily evaluated using the definition of δ(x): Taking into account (9), we obtain
Finally, recalling definition (8) of I, we have
which yields the desired result for the case g'(x0) > 0. The case g'(x0) < 0 is similar. █
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# GATE CE 2008
Question 1
The product of matrices $(PQ)^{-1}P$ is
A $P^{-1}$ B $Q^{-1}$ C $P^{-1}Q^{-1}P$ D $PQP^{-1}$
Engineering Mathematics Linear Algebra
Question 1 Explanation:
\begin{aligned} \left ( PQ \right )^{-1}P&=\left (Q^{-1}P^{-1} \right )P \\ &=\left ( Q^{-1}\ \right )\left ( P^{-1}P \right ) \\ &=\left ( Q^{-1} \right )\left ( I \right )=Q^{-1} \end{aligned}
Question 2
The general solution of $\frac{d^{2}y}{dx^{2}}+y=0$ is
A $y = P \cos x + Q \sin x$ B $y = P \cos x$ C $y = P \sin x$ D $y = P \sin^2 x$
Engineering Mathematics Ordinary Differential Equation
Question 2 Explanation:
\begin{aligned} \frac{d^{2}y}{dx^{2}}+y&=0 \\ D^{2}+1&=0 \\ D=\pm i &=0\pm 1i \\ &\text{General solution is,} \\ y&=e^{0x}\left [ C_{1}\cos \left ( 1\times x \right )+C_{2}\sin \left ( 1\times x \right ) \right ] \\ &=C_{1}\cos x+C_{2}\sin x \\ &=P\cos x+Q\sin x \end{aligned}
where P and Q are some constants.
Question 3
A mild steel specimen is under uniaxial tensile stress. Young's modulus and yield stress for mild steel are $2 \times 10^{5}$ MPa and 250 MPa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is
A 156 $Nmm/mm^{3}$ B 15.6 $Nmm/mm^{3}$ C 1.56 $Nmm/mm^{3}$ D 0.156 $Nmm/mm^{3}$
Solid Mechanics Properties of Metals, Stress and Strain
Question 3 Explanation:
The strain energy per unit volume may be given as
\begin{aligned} u &=\frac{1}{2} \times \frac{\sigma_{y}^{2}}{E}=\frac{1}{2} \times \frac{(250)^{2}}{2 \times 10^{5}} \\ &=0.156 \mathrm{N}\; \mathrm{mm} / \mathrm{mm}^{3} \end{aligned}
Question 4
A reinforced concrete structure has to be constructed along a sea coast. The minimum grade of concrete to be used as per IS : 456-2000 is
A M15 B M20 C M25 D M30
RCC Structures Working Stress and Limit State Method
Question 4 Explanation:
As per clause 8.2.8 of 1S 456: 2.000 concrete in sea water or exposed directly along the sea coast shall be atleast M20 grade in the case of plain concrete and M30 in case of reinforced concrete.
Question 5
In the design of a reinforced concrete beam the requirement for bond is not getting satisfied. The economical option to satisfy the requirement for bond is by
A bounding of bars B providing smaller diameter bars more in number C providing larger diameter bars less in number D providing same diameter bars more in number
RCC Structures Shear, Torsion, Bond, Anchorage and Development Length
Question 5 Explanation:
Bond stress $\left(\tau_{b d}\right)=\frac{\text { Tensile force }}{(n \pi \phi) \sigma_{s t}}$
$\tau_{b d}$ should be less than permissible value, if it is greater than $\left(\tau_{b d}\right)_{\text {permissible }}$ then best economical solution is to reduce the diameter of bar and increase its number.
Question 6
The shape of the cross-section, which has the largest shape factor, is
A rectangular B I-section C Diamond D Solid circular
Design of Steel Structures Plastic Analysis
Question 6 Explanation:
Shape factors of some cross-section are as follows:
(i) Rectangle - 1.5
(ii) I-Section - 1.14
(iii) Diamond - 2
(iv) triangle - 2.34
(v) Circle - 1.7
Question 7
Group Symbols assigned to silty sand and clayey sand are respectively
A SS and CS B SM and CS C SM and SC D MS and CS
Geotechnical Engineering Classification of Soils and Clay Minerals
Question 7 Explanation:
First part of the dual symbol indicates gradation
whereas second part indicates the nature of fineness.
$\Rightarrow$ Silty sand =SM
$\Rightarrow$Clayey sand =SC
Question 8
When a retaining wall moves away from the backfill, the pressure exerted on the wall is termed as
A passive earth pressure B swelling pressure C pore pressure D active earth pressure
Geotechnical Engineering Retaining Wall-Earth Pressure Theories
Question 9
Compaction by vibratory roller is the best method of compaction in case of
A moist silty sand B well graded dry sand C clay of medium compressibility D silt of high compressibility
Geotechnical Engineering Compaction of soil
Question 10
A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water surface is not travelling upstream. This is because the flow in the canal is
A sub-critical B super-critical C steady D uniform
Fluid Mechanics and Hydraulics Open Channel Flow
Question 10 Explanation:
For super-critical flow, $F_{r} \gt 1$
\begin{aligned} \frac{V}{\sqrt{g y}} & \gt 1 \\ V & \gt \sqrt{g y} \\ V & \gt C \end{aligned}
Hence, on upstream, the waves will be washed away and we will not be able to see them but they can be seen on downstream side.
Hence, the flow here is super-critical.
There are 10 questions to complete.
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## Sunday, 30 November 2014
### Estimation: How many pieces are in this puzzle?
Try to estimate how many pieces are in this puzzle.
To know the answer click on the video bellow.
1. I estimate 200 pieces
2. I think that 95 is too small and 200 is too big my estimate is 104.
3. That's great Cristina. I had to resist the temptation to count the rows and columns, so that I would be estimating, not counting!
I like the way you explain the calculation in the video!
4. Super idea Cristina! I agree with Mr Gregg.
5. I think 47 is too small and 220 is too big. But my estimate is 210.
6. I think 30 is too big and 15 is to small. My estemate is 25
7. To small is 50 My estimate is 123
8. I think 150 is too big and 50 is too small, my estimate is 100
9. I think 250 is too big 100 is too small my estimate is 200
10. I think the number to small is 50.I think the number is 104
11. I think 20 is too small and 90 is too big and my estimate is 200
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1. ## word problem (rectangular)
a rectangular has one vertex(corner) at (0,0) and the diagonally opposite vertex(corner) in the first quadrant on the curve of the function y = 1/(1+x^2). find the dimensions of the rectangle with the largest area.
how do i do this question?
would area be a = (2x)(1/(1+x^2)) ?
2. Originally Posted by haebinpark
a rectangular has one vertex(corner) at (0,0) and the diagonally opposite vertex(corner) in the first quadrant on the curve of the function y = 1/(1+x^2). find the dimensions of the rectangle with the largest area.
how do i do this question?
first, and most important, make a sketch.
then write the area as a function of x ...
$A = xy = \frac{x}{1+x^2}$
now find $\frac{dA}{dx}$ and maximize like you were taught.
3. do i find derivative of a = 1/(1+x^2)?
not derivative of a = (2x)(1/(1+x^2))?
4. Originally Posted by haebinpark
do i find derivative of a = 1/(1+x^2)?
not derivative of a = (2x)(1/(1+x^2))?
once again with more clarity ...
the area of the rectangle in quad I is $A = x \cdot \frac{1}{1+x^2} = \frac{x}{1+x^2}$
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# Operators
Definition: In mathematics, an operator is a function, that operates on (or modifies) another function.
In the following, though, we will consider the use that is made of operators in Quantum Mechanics and therefore focus upon particular classes of operators or operators with certain properties.
In the absence of superselection rules the following two axioms hold for any quantum system:
Axiom 1: The states of any physical system are in one-to-one correspondence with the vectors of an abstract, separable, infinite dimensional Hilbert space H.
Axiom 2: Every dynamical variable A of a quantum system can be represented by an operatorA in the Hilbert space of the vector states, in the sense that the mean values of any dynamical variable function of A can be computed as the mean values of the same function of the operator A.
In order to be considered an observableA must be a linear, self-adjoint and positive operator.
In particular, A must be a linear operator so that its mean values do not depend on the length of the vector chosen to compute them; whereas A must be a self-adjoint operator to guarantee the reality, and thus the physical consistency, of its mean values.
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# 'How to take a penalty'
Issue 36
in
September 2005
## How to take a penalty: the mathematical curiosities of sport
### Rob Eastaway and John Haigh
Have you ever wondered what shape a football is? No, it is not a sphere - it is far closer to something called a truncated icosahedron, also known as a "buckyball". It consists of 12 black pentagons and 20 white hexagons and is about the most effective way of creating something nearly spherical out of flat panels. Curious sporting-related mathematical facts like this can be found throughout Eastaway and Haigh's book "How to take a penalty, the hidden mathematics of sport". As its name suggests, this book is about the mathematics hidden within the world of sport. It is not about any one sport in particular; actually many are discussed.
The book is an engaging read and contains many interesting facts about sports, such as why the number of players in a football team is 11 (apparently this originates from the fact that a cricket team has this number, although the reason as to why this is so is more mysterious). It must be emphasised though, that this book is not just a collection of facts. It shows how players of a game can benefit from a well thought-out strategy, the use of basic logic and probability theory. In fact, a lot of the mathematical analysis, which is relegated to an appendix, consists of basic probability. This is presented in a way that is accessible to a GCSE student.
Although the calculations involved are often basic, their results can be far from intuitive. For example, the best serving strategy in tennis is a risky fast first serve and slow and safe second serve. In darts, if one wants to win two consecutive legs (a leg is won by the first to score 501 points) it is best to opt to throw second for the first leg, despite the fact that you are less likely to win the leg if you do so.
The book also contains a little puzzle in each chapter, complete with solution.
As the authors point out, the initial plan was to divide the book up according to the various types of sports, subjecting each to a mathematical analysis. It soon transpired, however, that many issues, such as the winning of the toss of the coin before a game, or "subjective scoring", are common to many different types of sports. These, sometimes unexpected, similarities led the authors to adopt a more unified approach. The book has thus been divided into chapters which treat these common phenomena and skip between the different sports. Although it is hard to see how this could be avoided without duplicating material, the style, while generally very natural and colloquial, does sometimes suffer from these constant changes.
This book is packed with information, so much so that one would certainly benefit from a second read. At the same time, though, it is not too intense. In short, it is a collection of nice examples of how you can employ mathematical reasoning in everyday situations (such as sport) to improve your position and chances of winning.
Book details:
How to take a penalty: the mathematical curiosities of sport
Rob Eastaway and John Haigh
Hardback - 192 pages (2005)
Robson Books Ltd
ISBN: 1861058365
You can buy the book and help Plus at the same time by clicking on the link on the left to purchase from amazon.co.uk, and the link to the right to purchase from amazon.com. Plus will earn a small commission from your purchase.
James Lucietti has recently submitted his PhD thesis in String Theory at the University of Cambridge.
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A Flash Developer Resource Site
1. Billiard Ball-like angle calculations
I have this ball, right? And it's bouncing. It bounces around the stage without a care in the world... unless! Wait a minute! There's another ball bouncing around! What will happen when they collide?
...not what they should, that's what...
I have the detection of when they hit working fine (I've watched it time and time again; when the edges touch, they change direction)
I have the momentum fine (assuming no spin)
My problem is in the angles calculations. Here's what I have:
PHP Code:
``` function twoCircleCollision(circle1,circle2,circle1xSpd,circle1ySpd,circle2xSpd,circle2ySpd):void { xSpdDif_orig = circle2xSpd-circle1xSpd ySpdDif_orig = circle2ySpd-circle1ySpd xdif_orig = circle2.x-circle1.x ydif_orig = circle2.y-circle1.y angleOfOrigMove2 = Math.atan2(ySpdDif_orig,xSpdDif_orig) RadiansToDegrees(angleOfOrigMove2) angleOfOrigMove2 = Angle_out angleOfOrigMove1 = Math.atan2(-ySpdDif_orig,-xSpdDif_orig) RadiansToDegrees(angleOfOrigMove1) angleOfOrigMove1 = Angle_out angleOfCentreToCentreFromHoriz2 = Math.atan2(ydif_orig,xdif_orig) RadiansToDegrees(angleOfCentreToCentreFromHoriz2) angleOfCentreToCentreFromHoriz2 = Angle_out angleOfFinalMove2 = 2*angleOfCentreToCentreFromHoriz2 - angleOfOrigMove2 angleOfFinalMove1 = 2*angleOfCentreToCentreFromHoriz2 - angleOfOrigMove1 DegreesToRadians(angleOfFinalMove2) angleOfFinalMove2 = Angle_out DegreesToRadians(angleOfFinalMove1) angleOfFinalMove1 = Angle_out magOfDirect1 = Math.sqrt(circle2xSpd*circle2xSpd+circle2ySpd*circle2ySpd) magOfDirect2 = Math.sqrt(circle1xSpd*circle1xSpd+circle1ySpd*circle1ySpd) } function RadiansToDegrees(TheAngle):void { if (TheAngle < 0) { TheAngle += 2*Math.PI } TheAngle = TheAngle*(180/Math.PI) Angle_out = TheAngle } function DegreesToRadians(theAngle):void { theAngle = theAngle*(Math.PI/180) if (theAngle > Math.PI) { theAngle -= 2*Math.PI } theAngle = Angle_out } ```
I've tested the RadiansToDegrees and DegreesToRadians functions, so don't blame them. I just included them to show how I've got it set up (You can blame how I've used them, however)
After a lot of searching online the only way I have managed to understand calculating the angle after a collision is with the R = 2W - P formula proposed by Ed Mack (yeah, I'm sure all that projection stuff works, but this should work too... right?)
Anyway... I'm a bit sick of trying to work out what has gone wrong when I don't know if I'm even doing it right; so I'm hoping someone will be able to help me here...
2. how did you derive this code? there's some weird flow going on there with setting Angle_out instead of returning a value from your conversion functions--that sort of stuff makes determining the state messy. also, DegreesToRadians does nothing--I'm assuming you pasted incorrectly.
my suggestion is to let go of the trigonometric approach and switch to a vector-based solution. it's more intuitive, more computationally efficient and less error prone. for some reason certain people do not welcome this suggestion--if you're not one of those people, I'm happy to help you out with switching.
3. That weird flow is how my brains logic works.
But... Switching is good with me if it works. Care to explain the vectors, 'cause I can't make head nor tail of what I've found. I do know about vectors; but only from a Year 12 Physics view. (So I know that a vector is made up of both an x value and a y value, and a direction)
What's up with the dot product? I've only managed to see it in a strange manner where they have some property of a variable that I don't know; like 2v.vx
EDIT: I liked this website, but I couldn't understand it once it got into the useful stuff...
http://www.tonypa.pri.ee/vectors/start.html
As for why my code is so weird:
I don't know how to use "return" so I never have.
I thought trigonometry was the way to go 'cause I knew something of it, and... well... it makes sense to me... Vectors always seem a very round-about way to calculate things. More efficient, I'm sure, but like I said. I can't understand it, and trig has managed to get me this far...
I didn't paste incorrectly... And it does do something... it turns an angle thats in degrees into an angle that's in Flash's weird way of radians (where 181 degrees is a little bit more than -PI). EDIT: Maybe you haven't scrolled down in the PHP box?
4. Originally Posted by Multihunter
I didn't paste incorrectly... And it does do something... it turns an angle thats in degrees into an angle that's in Flash's weird way of radians (where 181 degrees is a little bit more than -PI). EDIT: Maybe you haven't scrolled down in the PHP box?
It does nothing as is. No value that you're using is being set.
There's nothing magical about vectors, they're just a natural way of expressing things in any dimension. Adding 2 vectors together is the equivalent of "moving" by the amount depicted in each. So let's say you're following a treasure map that tells you to walk 10 paces to the right, then 5 paces up, then another 20 paces right, and another 3 paces up. You can write these directions as the vectors <10,5> and <20,3>. You could walk 10 units to the right and 5 up. Then, from that point, walk 20 units right again and 3 more up. What you've done, however, is waste time because you could have just added them together to find the end point relative to the beginning:
<10,5> + <20,3> = <30,8>.
The dot product of 2 vectors is the sum of the products of each corresponding element. For example, using the vectors above, the dot product would be:
10 * 20 + 5 * 3 = 215
To gain some intuition about this, consider the dot product of a vector, <x,y>, and itself: you have x^2 + y^2, which you should know from trigonometry as the squared length of a right triangle's hypotenuse. With this knowledge you can calculate the length of any vector, v:
SquareRoot( DotProduct( v, v ) )
You can always think of a vector as this hypotenuse, where the x and y components are the 2 perpendicular sides of the triangle.
There's also value in investigating the sign of the dot product of 2 vectors. If the dot product is 0, the vectors are perpendicular to each other. If the dot product is less than zero, then they point in opposite directions; and likewise, if it's greater than zero, they point in the same direction.
So vectors are a very natural way of representing the state of your physical system: position, velocity and acceleration are all vectors.
This is something I wrote a little while ago that does elastic collision response.
http://wonderfl.net/c/8RNL/
See the function "resolve" in the ParticleParticlePair class on line 359. This resolves a collision between 2 circles. It solves for an impulse that gets added to the particles' velocities. It is the magnitude of the integrated reaction force. Take a shot at translating your "twoCircleCollision" method into this form, and we'll take it from there.
5. I notice that I HAVE copied incorrectly. My apologies, the last part of the function is supposed to be reversed. (Angle_out = theAngle)
Also; I understand everything you just said (Mostly because I knew about adding vectors already). But not your code at all. And none of it gives me any clue as to how it helps, and how it is used to calculate collisions.
6. WAIT A SECOND! Are you using the dot product to calculate where it would be if it collided between frames?
7. without understanding it, it still should be easy to get working on your end. it's 6 lines of code to replace that whole function you have. but i'll explain the physics anyway.
it's not used to "calculate collisions." the function applies an impulse that will change each ball's velocity appropriately. to explain how i'm solving for the impulse, let's consider the simpler case of 2 particles colliding in a 1-dimensional universe--1 is traveling to the right and 2 is traveling to the left.
1 O--> <--O 2
we know from newton's 3rd law that each force is met with an equal and opposite force. it would be much more complicated to model collision response using forces, so we apply an impulse--a quantity used to cause an instantaneous change in velocity:
j = ( -( 1 + e ) * ( m1v1 - m2v2 ) ) / ( 1 / m1 + 1 / m2 )
where j is impulse, m is mass and v is velocity. e is what's called the coefficient of restitution, which is a fancy way of saying how bouncy or elastic something is. it ranges from 0 - 1, 0 being inelastic (like putty) and 1 being perfectly elastic (like a super ball). this looks a little scary, but it's really just giving us a scalar value that represents an exchange in momentum in the given direction (chosen by whether we use m1v1 - m2v2 or m2v2 - m1v1). the change in velocity from this impulse is then scaled by the inverse of each particle's mass:
v1 += j / m1
v2 -= j / m2
let's plug a few values in to see if this makes sense. first, let's say the mass of each particle is 1 and both particles are traveling at 10 meters per second (assuming perfect elasticity):
e = 1
v1 = 10
m1 = 1
v2 = -10
m2 = 1
j = ( -( 1 + e ) * ( 10 * 1 -( -10 * 1 ) ) ) / ( 1 + 1 )
j = ( -2 * 20 ) / 2 = -20
v1 += -20 / 1 = -10
v2 -= -20 / 1 = 10
we can see that, as expected v1 and v2 have completely flipped around and 1 is now traveling back to the left at 10 meters per second and 2 is traveling back to the right at 10 meters per second. it's easy to see if we change elasticity to 0, the resulting velocities for both particles will be 0.
that is the 1-dimensional version of what my method is doing in 2 dimensions. it's only slightly more complicated in 2D, though. basically we don't have the nicety of velocity being a scalar and so we have to find relative velocity along the line of contact (contact normal). the change in velocity also points along this normal, but everything else is the same.
hope that helps
8. That's a useful formula, it does help, but it doesn't explain how your 6 lines of coding works.
Sorry I'm not understanding; I shouldn't expect you to explain it all, I'm sure I would be able to get it given enough time researching it on the internet.
As a side note; I have made my trig method work. The WALLS angle is PERPENDICULAR to the angle between the two circles.
9. it explains line by line how it works and the physics behind it. if you don't understand something, you'll have to ask something specific about it.
10. So what you have in the "resolve" function is:
PHP Code:
``` var cn:Vec2D = w.normal; var dv:Vec2D = p.v; var impulse:Number = cn.dot( dv.times( -2 ) ) / cn.dot( cn.times( 1 / p.mass ) ); p.v.plusEquals( cn.times( impulse / p.mass ) ); ```
EDIT: What does it actually resolve, and what's the output?
What is "w.medium", and how is it calculated?
When is this function called?
How does it tell it which direction it needs to go?
Does your Vec2D class make it so that both the x and y are calculated using these formulae and then each stored as a property of the variables?
EDIT2: Damn you, time zones, making these awkward timings...
11. you're looking at the wrong resolve function--that handles collision between a particle and a wall. where i link to that, i say line 359, check that function instead.
it sounds like you're having more trouble with the programmatic end of things. every bit of that algorithm is either standard floating point mathematical operations or can be found elsewhere in the application code.
but anyway, i think you probably just need me to put it in the form of your original algorithm:
PHP Code:
``` function twoCircleCollision( circle1:DisplayObject, circle2:DisplayObject, circle1xSpd:Number, circle1ySpd:Number, circle2xSpd:Number, circle2ySpd:Number ) : void { var dx:Number = circle1.x - circle2.x; var dy:Number = circle1.y - circle2.y; var length:Number = Math.sqrt( dx * dx + dy * dy ); dx /= length; dy /= length; var dvx:Number = circle1xSpd - circle2xSpd; var dvy:Number = circle1ySpd - circle2ySpd; var impulse:Number = -2 * ( dx * dvx + dy * dvy ); impulse /= ( 1 / mass1 + 1 / mass2 ); //you need to add these mass values //these are your new velocities var newCircle1xSpd:Number = circle1xSpd + dx * ( impulse / mass1 ); var newCircle1ySpd:Number = circle1ySpd + dy * ( impulse / mass1 ); var newCircle2xSpd:Number = circle2xSpd - dx * ( impulse / mass2 ); var newCircle2ySpd:Number = circle2ySpd - dy * ( impulse / mass2 );} ```
obviously, i don't have your application and i have no idea if there are errors in this or not, but it should be right.
12. Ok, I now have a much better understand of where this is all coming from.
Thank you.
Just... I still can't quite figure out what you've done there...
When you normalised dx and dy, you made it so that the "new" length would be equal to 1?
So... why do you have it multiplying the sum of the inverse masses?
And why do you have newCircle1xSpd = circle1xSpd - dx*(impulse/mass1)? Shouldn't it be plus? As per your v1 += j / m1?
But, yeah, I see where it is all going now, which is awesome, thank you. (I also should have written it out on a piece of paper sooner, too)
13. When you normalised dx and dy, you made it so that the "new" length would be equal to 1?
yes, the normalization makes the vector's length 1--but it still points in the same direction: from circle 1's center to circle 2's.
So... why do you have it multiplying the sum of the inverse masses?
I have no idea why I'm doing that--that value will always be 1 and so it's a pointless calculation. I'll have to look through the rest of the code in the link I posted and see how I muffed that up!
And why do you have newCircle1xSpd = circle1xSpd - dx*(impulse/mass1)? Shouldn't it be plus? As per your v1 += j / m1?
Yes--it was an error as I wasn't able to test anything. Sorry!
I've corrected the post to reflect these issues.
14. Ok, nearly there (I think).
I worked out that according to that you had there;
Momentum of Circle1 - Momentum of Circle2 = dx*dvx + dy*dvy
How does that work?
EDIT2: Maybe that's the dot product? Even so... how does that work?
I also notice that dx and dy don't change... so wouldn't the gradient of the path also not change?
EDIT: I can't see where you use a dot product, either...
15. it is the dot product of the collision normal and the balls' relative velocities. it gives us the signed magnitude of the projection of the relative velocities onto the normal (since the normal has a length of 1).
i'm not exactly following the rest of your reply--what do you mean you can't see where i use the dot product?
16. Well that last bit was edited in before the "earlier" edit, hence the 2 next to it to indicate it came later.
If you look at the original formula you gave for impulse; j = ( -( 1 + e ) * ( m1v1 - m2v2 ) ) / ( 1 / m1 + 1 / m2 )
and the one you used in the code; (-2 * ( dx * dvx + dy * dvy ))/( 1 / mass1 + 1 / mass2 )
Assuming that e = 1, and since the dividing by the inverse masses is the same, that would mean that dx*dvx +dy*dvy would have to equal m1v1-m2v2.
I want to know how you managed to come up with dx*dvx + dy*dvy...
And I just realised what was confusing me about the dx and dy; because they were in the final velocity calculation, I confused them with the velocities of the circles.
Which leads me to my next question;
Why does the direction between the circles give the direction of each circle?
EDIT: My real problem is (I think), as suggested in the title, and has been for a while, where are you getting the new angle from? And how is it applied?
I get that you normalise to get the original "angles" and the impulse to determine how fast, but how is it that you can get a new "angle" (I use quotation marks so that it's clear that it's not actually an angle, more of a gradient of the path)
EDIT2: Also, I may be clearer in the morning, I have been staying up til 11pm (and getting up at 5:30am) every night this week trying to figure this stuff out. I probably would do better with more rest. But I feel I'm so close...
EDIT3: I was actually online at the same time as you, but I don't think you expected a response. I'll be on pretty much all of my tomorrow. So if you post anything while I'm awake, I will know, and respond as fast as I can.
17. Ok. We did a lot on graphs last year in Maths, so I decided to try once again to work it out with gradients, see if it looked like what the vectors were and see if I could link them or come up with another method. ('cause, again, I understood what I was doing with gradients)
They seem to be awfully similar to what you are trying to get me to understand with these vectors.
EDIT: Just to let you know that by "psuedo wall", I mean the instantaneous imaginary wall that exists between to colliding circles such that the reflected angle of the ball hitting it is the same as if it were hitting an actual wall at these particular angles.
I ended up working out that the gradient of the reflected balls path is reflected on the graph along the y = (pseudo wall's gradient)x.
So, where the pseudo wall's gradient was 1 (or at 45 degrees), then the xSpeed would become the ySpeed for the ball in question (and vice versa).
So you replaced the x value with the y value. (So if the walls gradient was 2, and the balls path's gradient was 1, the reflected balls gradient would be worked out by (2x)=1(y/2) => y = 2*2x = > y = 4x, so the gradient of the reflected balls path should be 4)
This is what I got for my code using this idea (I run it twice, swapping which one is circle1, and circle2):
PHP Code:
``` function twoCircleCollision(circle1,circle2,circle1xSpd,circle1ySpd,circle2xSpd,circle2ySpd):Number { mag = circle2xSpd*circle2xSpd + circle2ySpd*circle2ySpd /*since they swap momentums, and I am currently not concerned with mass, I used the magnitude of circle2 and apply it to circle1. Note: I know it's actually the magnitude squared, but if I square rooted it now I would just have to square it again anyway later, so I kept it as the squared value*/ grad1 = -( (circle1.x-circle2.x) / (circle1.y-circle2.y) ) /*gradient of the line between them multiplied by -1 and inverted to give the gradient of the perpendicular line I call the pseudo wall*/ grad2 = (circle1ySpd-circle2ySpd) / (circle1xSpd-circle2xSpd) /*circle1's relative velocities to circle2 are used to make grad2, the gradient of the original path of circle1*/ coE = (grad1*grad1) / grad2 //the coefficient of x for the new path of circle1 NewXspeed = Math.sqrt( mag / (1+coE*coE) ) /*Outside the function I also record coE, and to get the Yspeed for the circle, I multiply the NewXspeed by coE*/ return NewXspeed } ```
I know. I'm crazy.
I think I'm missing a negative and an inverse in there, or vice versa, 'cause usually using that code they will bounce off at right angles to the direction I would have expected...
Yeah... if you can follow that you can tell me if I've gone completely the other way... (btw, I suggest using paper and an example to check it. I used pseudo walls: x = -2, y = 1. And the circle1's: x = -1, y = 2)
EDIT: At this point I would like to point out that if anyone else has any comments on my lack of understanding, I'm sure that newblack wouldn't mind you adding it (Right?). Who knows, it might even help me.
EDIT2: I just want to let you know that the code you gave me is working 100% with the proper momentum. Now I just want to know WHY.
18. Thank you newblack, you helped me so much. I didn't realise that it was so simple; dx was the proportion of the xvelocity that takes part in the collision! My problem was that I over complicated the code you gave me. I kept trying to link it with the website that I posted earlier; until today. I realised that it had nothing to do with projections and dot products...
I'm sure it was obvious to you, and that's why you didn't explain it... but it confused me a lot. It's funny, last year I tried graphing the different resultant xspeeds based on the angle (given an input of 1). I couldn't think how to combine that with pythagoras. But this is how you do it.
Just 1 thing that bugs me still... what happened to the masses in the momentum part of the impulse equation?
EDIT: Oh yes. Please ignore my previous post as ramblings of a madman.
EDIT2: I think you told me equation incorrectly to begin with; according to this website, you only use the mass(es) once.
http://www.euclideanspace.com/physic...ulse/index.htm
19. Here is a good billards game tutorial:
http://www.bezzmedia.com/swfspot/tut...h8/8_Ball_Pool
20. Nice try, Eager Beaver, but;
-That ones collision detection is no better than a simple: "If the distance between them will be the averaged(?) radius next frame, then they have collided".
-They also, oddly, have also decided that: "at exactly halfway between the frames they have collided"
-The collision calculation is actually exactly the same as the one newblack gave me, except that it doesn't take into account masses. (They just named the variables differently)
Also, @newblack; I see the dot product now! Aren't you proud?
I've also figured out the calculations for an exact collision from circle to a rectangle (I think)!
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THE WALL STREET JOURNAL
Guide to Cryptic Crosswords WHAT MAKES A CROSSWORD CRYPTIC?
For those new to the game, we reveal the secret in a nutshell: The clues each have two parts. One part is a normal definition of the answer; the other is an additional hint using wordplay. Having two hints in each clue might seem a big giveaway to solvers. Why aren’t these clues twice as easy? The hitch: Either hint may come first. The definition may appear before or after the wordplay hint, often without any punctuation to mark the point of division. The challenge and fun of a cryptic puzzle is to see through the puzzle writer’s deceptions, to tease out the definition by rethinking the clue’s wording. And now without further fanfare, we reveal the basic tricks of the cryptic trade.
A clue may break the answer into two or more convenient parts and define them sequentially, as in the game of charades. FARMING (agriculture) breaks into “far” (remote) and “Ming” (Chinese dynasty), and could be clued as: Agriculture in remote Chinese dynasty (7) Here is another charade: A combo on leave (7)
The simplest kind of wordplay hint in a clue is a second definition. For example, HOOD can mean “gangster” or “a cover for the head.” So a clue for HOOD might read: Cover for the head gangster (4) (The number in parentheses indicates how many letters are in the answer.) Here is another clue of this type for you to solve: Trim a tree (6) (For answers, see the end of this introduction.)
2. ANAGRAMS A clue may show you what the letters of the answer would look like when scrambled, also giving a signal word such as “mixed,” “aimless” or “fractured.” An anagram clue for STEW (which scrambles into WEST), could be: Wild West dish (4) Here is another clue of this type: Noises in restless slumber (7)
3. HIDDEN ANSWERS Sometimes the answer will be hidden inside a longer word or phrase (as PLEAD is tucked inside “apPLE A Day”). Look for signals such as “caught in,” “buried in,” “part of” and “housed by.” For example, CAT could be clued as: Lover of birds imprisoned in Alcatraz (3) Here’s another example: Karen always displays an engagement ring? (5) (Though punctuation is usually mere dressing in a clue, question marks are traditionally reserved for indicating stretchy definitions or outright puns.)
4. HOMOPHONES The wordplay hint may tell you that the answer has the same sound as another word or words, giving a signal such as “we hear,” “so it’s said” or “orally.” A homophone clue for BEAR (which sounds like “bare”) could be: Animal is naked, we hear (4) See if you can solve this one: Piece of gossip stated out loud for a lodger (6)
If the answer breaks into convenient parts not side by side but one within the other, the clue may say that one part “contains,” “holds,” “grips” or even “swallows” the other. CALLOW (inexperienced, green) has “all” inside “cow,” yielding the clue: Bovine has eaten everything green (6) A container for you to solve: Mr. Crosby keeps it sharp (6)
7. REVERSALS The wordplay hint may tell you that the solution when seen backward makes another word or words. SMART (keen) is the word “trams” (railway cars) backward. Its clue could be: Keen—railway cars in reverse (5) Here’s another: Strike friend’s back (4)
8. DELETIONS Sometimes a clue will invite you to lop off the front, back or central piece of a longer word. For example, ENTRY could come from SENTRY missing its leading letter, with the clue: Guard behind the front doorway (5) Here’s one involving a last letter: Horse with no tail damage (3)
9. COMPLEX CLUES Sometimes (especially with longer words) these different kinds of hints may be used in combination. But however complicated the operations may seem, full instructions will always be available for obtaining the answer. Here is one example to test your wits: Furniture wire wrapping broken dart (4,5) Well, that’s enough to get you started. Now sharpen up a pencil, dive right into the clues, and don’t be afraid to enlist a friend for reinforcement. We find that solving as a twosome makes for twice the fun. Cheers, Emily Cox & Henry Rathvon
Answers to the sample clues: 1. SPRUCE (2 defs.) 2. RUMBLES (slumber anag.) 3. ARENA (hidden) 4. ROOMER (rumor hom.) 5. A + BAND + ON 6. B(IT)ING 7. SLAP (pal’s rev.) 8. MARe 9. C(ARDT)ABLE (dart anag.)
1. DOUBLE DEFINITIONS
6. CONTAINERS
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# Calculus
posted by .
Sketch the graph of f(x)=-x^4 + 4x^3 - 16x + 16:
Find the critical points, concave up/down, inflection points, vertical asymptotes and horizontal asymptotes.
• Calculus -
form y = -1.83 tan (Bx – C) Find the period of the function (distance between two consecutive asymptotes).
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## Graph Writing # 36 - Hawaiian island chain in the centre of the Pacific Ocean
### The diagram below gives the information about the Hawaiian island chain in the centre of the Pacific Ocean.
Write a report for a university lecturer describing the information shown.
» Write at least 150 words.
The given illustration presents information on the Hawaiian Island Chain centre of the Pacific Ocean. As is observed from the diagram, the Hawaiian island chain directly affects the Pacific tectonic plate and because of it, this plate shifts around 7-9 centimetre per year.
As is observed from the graph, below the Pacific Ocean, the Hawaiian island chain stands as several volcanos which are almost 80 million years old. These volcanos stand over the Pacific plate and the eruptions of these volcanos’ created a new volcano just over the Magna spume. The Pacific plate is situated on solid dense rock and because of the new volcano development; the hot spot spume remained static. The eruption process of the volcano’s starts from as deep as 2800 km and that has spat the solid rock layer.
Major islands within 100 km of this area are Maui, Molokai, Oahu and Kauai and because of the eruption and sliding of the plates, the centre of the Pacific Ocean is ever changing.
The map portrays the Hawaiian island chain, which is located in the heart of the Pacific Ocean and roughly 2,700 kilometres in length. As is presented, it is formed of volcanoes and the active ones are at the south-east tip of the archipelago, where Hawaii itself is situated. It also shows the how the volcano eruption occurs.
It is pointed out that the chain began to form almost 80 million years ago on solid dense rock bed and each island started to evolve after an eruption on the seafloor. First, a `hot spot' existed on the ocean bed, which let out a plume of the material called 'magma'. Further, hot spot remained stable. Hence, magma spume was formed. This magma may originate as deep as 2,883 km below the ocean bed. Next, further eruptions took place, which built up the volcano. Eventually, it emerged above the surface of the ocean.
Afterward, the spume of magma has remained immobile as the Pacific tectonic plate moves in a north-west direction across it at an annual speed of 7-9 centimetre. As it moves, a volcano forms as it passes over the hotspot and then become inactive when it has passed it. The other major islands in the Pacific ocean are Niihau, Kauai, Oahu, Molokai, Maui, Lanai and Kahoolawe which are 0-100 kilometres away from each other.
Ela
Thanks for all your effort. This is my essay, if you can evaluate it, I would be very happy.
The diagram demonstrates the Hawaiian Island Chain which is in the middle of the Pacific Ocean.
Turning to this chart, it can be seen clearly the Major Islands compound of nine Islands. One of these is Hawaiian Island and the others are Niihau, Kawai, and so on.
The Hawaiian ıslands chain are a volcanic island assembly of which the lowest layer is associated with magma and volcanic eruptions. The eruption process starts there originating at 2883 km. Then magma spume and hot spume come from there. Just over this layer takes place solid dense rocks. Over this layer, the pacific plate is located which made up a lot of the youngest eruptions that lead to a volcano. In fact, the Pacific Plate is a tectonic layer and each year scroll this sheet to the west as 7-9 cm. The sheet which is at the top is the surface of the Pacific Ocean. On this sheet had emerged the oldest volcano 80 million years ago.
To put it briefly, this region is where The Major Islands and Hawaiian Islands chain are located in the centre of the Pacific Ocean which consists of tectonic layers, magma, and eruptions.
If I get such a picture as WT1, I will not be able to describe it in 20 minutes simply because I don't understand what is going on and how it all is connected. I don't like sample model 1 because to my mind, this picture is more about an island formation process, not just the volcano. And in particular, I don't understand how the existing island chain can affect the tectonic plate? As long as I know it is the tectonic plate that can affect islands and continents but not visa versa. So, to me, the first model can be confusing. But I am not a scientist, maybe both options are well descriptive.
Ela
At first, I had a trouble too to focus on diagrams, but I think that such a challenging exercises make one's writing ability better.
Jaspreet Kaur
Amir
Really hard. If they give exactly the same one in the original test, I wouldn't be able to answer!
April
The pictorial illustrates data on the Hawaiian Island Chain located in the middle of the Pacific Ocean.
Overall, it is noticeable that the Hawaiian Island Chain is formed because of the movement of the Pacific plate.
We can see on the diagram that the Hawaiian Island Chain is comprised of several volcanoes which are almost 80 years old. These volcanoes are situated beneath the Pacific Ocean and above the oceanic tectonic plate. The Pacific plate lies over solid dense rock, wherein the eruption begins. The eruption is started in 2888 kilometers of solid dense rock. Then, in the center, the hot spot spume remained static. While itself is fixed, the Pacific tectonic plate is shifted at around 7-9 centimeters per year and the magma spume rises upward until it erupts on the seafloor.
Eventually, the youngest volcano is built up because of various eruptions that occurred and as the Pacific plate moved over the hot spot, the string connecting the islands is formed and made the Hawaiian Island Chain. The eight major islands that are situated on the northwest of Pacific Island are Niihau, Kauai, Oahu, Molokai, Lanai, Kahoolawe, Maui, and Hawaii which have a distance of 0-100 kilometers apart from each other.
Labib Mansour
:sad: Too hard to do, to study, even to copy!
Janet
The given diagram illustrates the process of volcano development and provides information about the geography of the Hawaiian island chain. Overall, it can be observed that the Hawaiian island chain is prone to have frequent volcano eruptions. In details, the island chain is made up of eight major islands- Niihau, Kauai, Oahu, Lanai, Molokai, Maui, Kahoolawe and Hawaii. Hawaii stands at approximately 100 km wide, which makes it the largest island in the chain. The ocean that surrounds all the islands in the Pacific Ocean is supported by solid dense rocks at the bottom. Above this rock lies the Pacific tectonic plate, which shifts towards the north-western direction at a rate of 7 to 9 centimetres every year.The eruption process begins around 2883 km beneath the ocean's solid rock, at which the 'hot spot' spume remains static. This is then followed by the magma spume, which occurs at the same level as the tectonic plate. After this process, a young volcano develops, resulting from the many eruptions that occur over time. It is also interesting to note that the oldest volcano in the chain dates back to 80 million years.
Natasha
This is the perfect answer to the above diagram. It shows how this is to be written if you are not well versed with the science chapter on volcanoes and Islands. Thank you for making this question easy, because in IELTS they judge one's English not scientific knowledge.
Afras
Thanks for a completely different perspective, loved it! 3
Harvey
The diagram illustrates the geographical location of Hawaiian island chain which is located in the centre of the Pacific Ocean. Overall, Hawaii is the largest island among the eight islands in the area and shift of the Pacific plate contributes to the creation of new volcanoes. According to the illustration, there are eight major islands in the Hawaiian island and among them, the Hawaii is the largest and Niihau seems like the smallest. Moreover, the Hawaiian island chain is located at the top of Pacific plate while shift around 8 cm on an average in a year and contributes to the eruption. The solid dense rocks hold the Pacific plate and at the bottom of the dense rock area, some eruption process begins which is as down as approximately 3 km. The created ‘hot spot’ due to the eruption remains static and a thin flow of Magma Spume goes up to the Pacific plate. From there the youngest volcano develops and this creation is basically the result of several eruptions. The oldest volcanoes in this region are almost 80 million years old.
Rizwan Ullah
Why is the Hawaii island is present in the centre of the Pacific plate? Why not present on the boundary?
Sukhjit
Diagram question: The diagram below gives the information about the Hawaiian island chain in the centre of the Pacific Ocean.Sample Answer: The given diagram illustrates the information about the geographical distribution of Hawaiian island chain centre in the Pacific Ocean. Overall, Hawaiian island chain stands on the Pacific plate and some of the volcanoes located on the Hawaiian island chain is more than 80 million years old. As is observed from the diagram, the Hawaiian island chain is situated on the unstable Pacific plates which rest on the hard dense rocks. The solid dense rock which is incomplete at one point and eruptions started from there lead to the formation of Hot Spot spume that remains static but from here when it enters tectonic plates this become Hot Magma and later on it comes out through the upper most holes and become the youngest volcano of Hawaiian island. Due to this, the Pacific plate moves away each year about 7-9 cm from islands. Eruption begins at 2883 km below of the Pacific Ocean and many eruptions lead to the formation of the youngest Hawaiian island volcano. Hawaiian island chain centre also has a few oldest volcanoes those are 80 million years old. It has main 8 islands named from the north towards the south are Hawaii, Kahoolawe, Maui, Lanai, Molokai, Oahu, Kauai, and Niihau. Hawaii island is the biggest among them. Note: Please pick out the mistakes and suggest me improvements.
Anu
The given diagram shows the geographical features of the Hawaiian island chain amid the Pacific ocean, which is supported by a solid dense rock deep inside the Pacific sea. It also illustrates the natural factors and forces, which are involved in its formation.
Overall, Hawaiian island is the result of volcano eruptions and underground plate movements. It seems a complicated and continuous process.
Hawaiian island consists of many small islands - like: Hawaii, Maui, Lanai, Oahu, Kauai, Molokai etc. This mountain chain is located on the Pacific tectonic plates in the Pacific Ocean. These plates are observed to be shifting towards the east, 7-9 centimetres per year. Furthermore, this chain of mountains is basically a product of volcano eruptions. Among them, the oldest volcano dates back to 80 million years. In comparison, eruptions of these volcanos created a new volcano just over the Magna spume and its process starts 2883 kilometres down the earth surface.
Smolana
It seems the answer did not cover everything and could not present a comprehensive description!
Sumit
There are few points which I want to highlight.- It is wrongly mentioned as a graph, although it is a diagram- Spitted word is used.Why it is mentioned as a graph?
Harmanjot
I am very thankful because I'm gaining various information.
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Purchase Solution
# Veryfying Solutions to Linear Equations
Not what you're looking for?
THE ORDERED PAIR (-2,-23/5) IS A SOLUTION TO WHICH LINEAR EQUATION?
4X+5Y= -2
Y=4/5X-3
4X= -5Y+2
OR
NONE OF THESE?
##### Solution Summary
The equation to which a point is a solution is found. The expert verifies linear equations.
##### Solution Preview
Well, first of all an ordered pair means a pair whose elements have been put in a pre-determined order. Unless declared otherwise, when dealing with an ordered pair as the solution to a system of equations or an equation, consider the first element to be X and the second one to be Y. That is the case here as well. Ok, now we have to check and ...
##### Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
##### Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
##### Probability Quiz
Some questions on probability
##### Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
##### Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
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For my entire academic career I have been using Beamer slides in LaTeX for all my conference presentations and lecture slides. While Beamer is great for handling things like mathematical equations, table of contents, creating pauses, …, it is not so great for incorporating R content. For instance to create the following slide:
1. Create a LaTeX (.tex) file of class beamer
2. Open R and run the following code:
x <- rnorm(100)
hist(x)
1. Save the outputted plot as an image
2. Copy and paste the source code into a verbatim environment in LaTex document
3. Refer to my saved plot by file path in the LaTeX document
4. Compile the LaTeX document.
While this is tedious enough, image having to redo this if, for example, I instead wanted to use a standard deviation of 2. Rather than simply adjusting my code and recompiling a single document, I have to redo steps 2–6. If this wasn’t bad enough, the LaTex syntax is not the easiest on the eyes:
\begin{frame}[fragile]
\begin{Verbatim}
> x <- rnorm(100)
> hist(x)
\end{Verbatim}
\begin{figure}[htbp]
\begin{center}
\includegraphics[width= 0.7\textwidth]{histogram}
\caption{A histogram of 100 random numbers generated from a normal
(i.e Gaussian) distribution with mean 0 and standard deviation of 1.}
\label{fig:hist}
\end{center}
\end{figure}
\end{frame}
I thought I found a solution by using knitr or Sweave to create Beamer slides directly with Rstudio (you can read more about how to do this here). This solution allowed me to bypass the need to save any output files produced by R (since R studio and Sweave did that for me) with the added benefit of only having a single file to edit and compile. In addition, it had some great features which included automatic colour coding of R syntax (for example, functions appear in red, while arguments appear in green in the example slide provided below) along with the ability to handle code chunk options (I discuss some features and benefits in a previous blog post). While I used this solution in my Data 101 course, I found the long compile time to be big hindrance in my productivity. Furthermore, the error messages produced in R studio were often cryptic which sometimes resulted in me opening and compiling the document with LaTeX in order to pinpoint the source of the error.
While never fully satisfied with any of these options, I finally came across a game changing solution. While Googling “How to make a website using R” I came across this YouTube video. It was co-created by Alison Hill who I have referenced and praised in previous posts for her incredible content. At around 38:36 Alison mentions how she uses ?“shar engine”/“sharing again “? slides to make her presentations. Given the unusual name and inaudible caption produced by YouTube it took me a few failed google attempts to discover that she was using Xaringan to create her slides: an R package developed by Yihui Xie (another motivational R genius who I have been geeking out over). This rabbit hole led me down another tangent of tutorials/blogs/YouTube videos/web books on how I could produce these in R. Rather than saying it in a blog post I have summarized some of what I have learned within a, you guessed it, xaringan presentation slide deck! You can either point to the slides using a simple link: simple link, which was produced using
[simple link](/slides/NHSRxaringan.html)
or embed the slide deck using
knitr::include_url('https://vrbiki.github.io/learning-xaringan/NHSRxaringan.html')
Notice that this method requires your slides to have a URL. The slide deck talks about how you can do that using GitHub (the source file for producing those slides are also available here. Alternatively I could have used the URL: https://irene.vrbik.ok.ubc.ca/slides/NHSRxaringan.html#1
test for lecture slide hellloooo
# Resources
1. Sharing Your Work with xaringan workshop: https://spcanelon.github.io/xaringan-basics-and-beyond/index.html
2. R Markdown: The Definitive Guide (Ch 7) https://bookdown.org/yihui/rmarkdown/xaringan.html
Posted on:
July 14, 2021
Length:
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# How many moles are present in nitrogen?
Contents
2 moles of are present in 28 g/mol of nitrogen. Mole can be defined as the “number” of carbon atoms present in exactly “12 grams” of pure Carbon.
## How many moles are in nitrogen?
The SI base unit for amount of substance is the mole. 1 grams Nitrogen is equal to 0.071394404106606 mole.
## What is the mole of 1 mole of nitrogen atoms?
Mass of one mole of nitrogen atoms is 14 g.
## How many moles are present in 14 gram of nitrogen?
Explanation: grams is the molar mass of nitrogen meaning that one mole of nitrogen atoms is 14 grams. One mole of any substance has 6.02*10^23 atoms/molecules of that subtance therefore there are 6.02*10^23 atoms of nitrogen in 14g of nitrogen.
## What is the mole of oxygen?
Moles of a Substance and the Molecular Weight
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The mass of oxygen equal to one mole of oxygen is 15.998 grams and the mass of one mole of hydrogen is 1.008 g.
## How many atoms are in 2 moles of nitrogen?
There are 6×6.022×1023 atoms in 2.00⋅mol NO2(g) .
## How many grams are in 4 moles of nitrogen?
We assume you are converting between moles Nitrogen and gram. You can view more details on each measurement unit: molecular weight of Nitrogen or grams The molecular formula for Nitrogen is N. The SI base unit for amount of substance is the mole. 1 mole is equal to 1 moles Nitrogen, or 14.0067 grams.
## What is the mass of 5 moles of nitrogen gas?
Answer. Molar Mass of N2 is 28.
## How many grams are in one mole of nitrogen gas?
There is a difference! One mole of N consists of Avogadro’s number of nitrogen atoms (and has a mass of 14.01 g), whereas 1 mole of N2 consists of Avogadro’s number of molecules, each molecule having two nitrogen atoms. One mole of N2 molecules would have a mass of 2 X 14.01 g = 28.02 g.
## What is the mass of 1 mole of?
The mass of one mole of a substance is equal to that substance’s molecular weight. For example, the mean molecular weight of water is 18.015 atomic mass units (amu), so one mole of water weight 18.015 grams.
## How many moles are there in 140 gram nitrogen?
Answer. Therefore, number of moles is 5.
## How many moles are there in 140g nitrogen?
Answer. so you multiply the atomic mass of the nitrogen (which is 14) by the subscript and here it would be 2 (because it’s a diatomic molecule) so.
## How many moles are in 50 grams of nitrogen gas?
We have 50 g of nitrogen gas here, so we need to find the number of moles of nitrogen. From here, we would produce 1.79⋅2=3.58 moles of ammonia.
## How many atoms are in 14 grams of nitrogen?
14 g of nitrogen contains 3.01 × 10^23 nitrogen molecules.
## How do you calculate number of atoms?
To calculate the number of atoms in a sample, divide its weight in grams by the amu atomic mass from the periodic table, then multiply the result by Avogadro’s number: 6.02 x 10^23.
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### IBMR Assignment 1
```Stitching Photo Mosaics
•
•
•
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Stitching photos to construct a wild-view scene.
Part1: CORNER DETECTION
Part2: PERSPECTIVE MAPPING and MOSAICING
Handout after Part2 Finished
PERSPECTIVE MAPPING and
MOSAICING
• Read n>2 images, and create an image mosaic by registering,
projective warping, resampling, and compositing them.
• (bonus) multiband blending, SIFT ,panorama or other methods
mentioned in class.
•
•
•
•
•
Shoot the Pictures
Recover Homographies
Warp the Images/ Image Rectification
Gain Compensation
Blend the images into a mosaic
• You may use the photos on the webpage, but shoot your own
photos and mosaic them will get bonus credit.
• Shoot photos as:
• Overlap the fields of view significantly. 40% to 70% overlap is
recommended.
• Construct a linear system as: p’=Hp, where p’ and p are
correspondence points.
• Follow the Lecture 8 page 6~9. You may try Affine
mappings(DOF=6) or Projective mappings(DOF=8).
• Solve Ax=0
• Source scanning(forward mapping) or destination
scanning(inverse mapping).
• You will need to avoid aliasing when resampling the image.
• Be careful of the size of the resulting image.
• Find the optimize gains of gi according to means of
overlapping regions between image pair i and j.
• Linear blending by the weights:
where w(x) varies linearly
from 1 at the centre of the
image to 0 at the edge.
A
B
(, ) =
• Multi-band blending (bonus):
∗ − + ∗ ( − )
− + ( − )
•
Band 1 scale 0 to σ
•
Band 2 scale σ to 2σ
•
Band 3 lower than 2σ
• Your own project1a code.
• A C called matlab library.
• to calculate inverse matrix , SVD or etc.
• Basic: 75%
•
•
•
•
Harris Corner Detection + KNN (Hw1a)
RANSAC
Projection Mapping / Affine Mapping
Image Warping
• Bonus:
•
•
•
•
•
•
•
•
Non-Maximum Suppression
KD Tree
SIFT
Gain Compensation
Linear Blending
Multi Blending
Stitching your own photos
Others
5%
5%
15%
10%
5%
10%
5%
• 11/22 11:59:59pm
• Upload your program & report to:
•
•
•
•
host : caig.cs.nctu.edu.tw
port : 30021
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Convert µC/kg (Ionizing radiation dose)
## Convert µC/kg
Measurement Categorie:
Original value: Original unit: C/kgkC/kgKiloroentgen [kR]mC/kgMicroroentgen [µR]Milliroentgen [mR]nC/kgRoentgen [R]µC/kg numbers in scientific notation
https://www.convert-measurement-units.com/convert+microC+kg.php
# Convert µC/kg:
1. Choose the right category from the selection list, in this case 'Ionizing radiation dose'.
2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), brackets and π (pi) are all permitted at this point.
3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'µC/kg'.
4. The value will then be converted into all units of measurement the calculator is familiar with.
5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so.
With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '263 µC/kg'. In so doing, either the full name of the unit or its abbreviation can be used. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Ionizing radiation dose'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second.
Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(8 * 23) µC/kg'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '263 µC/kg + 789 µC/kg' or '42mm x 71cm x 27dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question.
If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 1.129 706 779 843 1×1027. For this form of presentation, the number will be segmented into an exponent, here 27, and the actual number, here 1.129 706 779 843 1. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 1.129 706 779 843 1E+27. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 1 129 706 779 843 100 000 000 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications.
## How much is 1 µC/kg?
Measurement calculator that can be used to convert µC/kg, among others.
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Properties
Label 2-405-9.4-c3-0-34 Degree $2$ Conductor $405$ Sign $0.939 + 0.342i$ Analytic cond. $23.8957$ Root an. cond. $4.88833$ Motivic weight $3$ Arithmetic yes Rational no Primitive yes Self-dual no Analytic rank $0$
Related objects
Dirichlet series
L(s) = 1 + (1 + 1.73i)2-s + (2.00 − 3.46i)4-s + (−2.5 + 4.33i)5-s + 24·8-s − 10·10-s + (−5 − 8.66i)11-s + (40 − 69.2i)13-s + (8.00 + 13.8i)16-s + 7·17-s − 113·19-s + (10 + 17.3i)20-s + (10 − 17.3i)22-s + (40.5 − 70.1i)23-s + (−12.5 − 21.6i)25-s + 160·26-s + ⋯
L(s) = 1 + (0.353 + 0.612i)2-s + (0.250 − 0.433i)4-s + (−0.223 + 0.387i)5-s + 1.06·8-s − 0.316·10-s + (−0.137 − 0.237i)11-s + (0.853 − 1.47i)13-s + (0.125 + 0.216i)16-s + 0.0998·17-s − 1.36·19-s + (0.111 + 0.193i)20-s + (0.0969 − 0.167i)22-s + (0.367 − 0.635i)23-s + (−0.100 − 0.173i)25-s + 1.20·26-s + ⋯
Functional equation
\begin{aligned}\Lambda(s)=\mathstrut & 405 ^{s/2} \, \Gamma_{\C}(s) \, L(s)\cr =\mathstrut & (0.939 + 0.342i)\, \overline{\Lambda}(4-s) \end{aligned}
\begin{aligned}\Lambda(s)=\mathstrut & 405 ^{s/2} \, \Gamma_{\C}(s+3/2) \, L(s)\cr =\mathstrut & (0.939 + 0.342i)\, \overline{\Lambda}(1-s) \end{aligned}
Invariants
Degree: $$2$$ Conductor: $$405$$ = $$3^{4} \cdot 5$$ Sign: $0.939 + 0.342i$ Analytic conductor: $$23.8957$$ Root analytic conductor: $$4.88833$$ Motivic weight: $$3$$ Rational: no Arithmetic: yes Character: $\chi_{405} (271, \cdot )$ Primitive: yes Self-dual: no Analytic rank: $$0$$ Selberg data: $$(2,\ 405,\ (\ :3/2),\ 0.939 + 0.342i)$$
Particular Values
$$L(2)$$ $$\approx$$ $$2.475642903$$ $$L(\frac12)$$ $$\approx$$ $$2.475642903$$ $$L(\frac{5}{2})$$ not available $$L(1)$$ not available
Euler product
$$L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1}$$
$p$$F_p(T)$
bad3 $$1$$
5 $$1 + (2.5 - 4.33i)T$$
good2 $$1 + (-1 - 1.73i)T + (-4 + 6.92i)T^{2}$$
7 $$1 + (-171.5 + 297. i)T^{2}$$
11 $$1 + (5 + 8.66i)T + (-665.5 + 1.15e3i)T^{2}$$
13 $$1 + (-40 + 69.2i)T + (-1.09e3 - 1.90e3i)T^{2}$$
17 $$1 - 7T + 4.91e3T^{2}$$
19 $$1 + 113T + 6.85e3T^{2}$$
23 $$1 + (-40.5 + 70.1i)T + (-6.08e3 - 1.05e4i)T^{2}$$
29 $$1 + (-110 - 190. i)T + (-1.21e4 + 2.11e4i)T^{2}$$
31 $$1 + (-94.5 + 163. i)T + (-1.48e4 - 2.57e4i)T^{2}$$
37 $$1 - 170T + 5.06e4T^{2}$$
41 $$1 + (-65 + 112. i)T + (-3.44e4 - 5.96e4i)T^{2}$$
43 $$1 + (5 + 8.66i)T + (-3.97e4 + 6.88e4i)T^{2}$$
47 $$1 + (80 + 138. i)T + (-5.19e4 + 8.99e4i)T^{2}$$
53 $$1 - 631T + 1.48e5T^{2}$$
59 $$1 + (-280 + 484. i)T + (-1.02e5 - 1.77e5i)T^{2}$$
61 $$1 + (114.5 + 198. i)T + (-1.13e5 + 1.96e5i)T^{2}$$
67 $$1 + (375 - 649. i)T + (-1.50e5 - 2.60e5i)T^{2}$$
71 $$1 - 890T + 3.57e5T^{2}$$
73 $$1 + 890T + 3.89e5T^{2}$$
79 $$1 + (-13.5 - 23.3i)T + (-2.46e5 + 4.26e5i)T^{2}$$
83 $$1 + (214.5 + 371. i)T + (-2.85e5 + 4.95e5i)T^{2}$$
89 $$1 + 750T + 7.04e5T^{2}$$
97 $$1 + (-740 - 1.28e3i)T + (-4.56e5 + 7.90e5i)T^{2}$$
$$L(s) = \displaystyle\prod_p \ \prod_{j=1}^{2} (1 - \alpha_{j,p}\, p^{-s})^{-1}$$
| 1,596
| 2,921
|
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| 2.875
| 3
|
CC-MAIN-2022-05
|
longest
|
en
| 0.390433
|
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