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# Skeletons - PowerPoint PPT Presentation
Skeletons. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2004. Linear Algebra Review. Coordinate Systems. Right handed coordinate system. Vector Arithmetic. Vector Magnitude. The magnitude (length) of a vector is: Unit vector (magnitude=1.0). Dot Product.
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## PowerPoint Slideshow about 'Skeletons' - monifa
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Presentation Transcript
### Skeletons
CSE169: Computer Animation
Instructor: Steve Rotenberg
UCSD, Winter 2004
### Linear Algebra Review
Coordinate Systems
• Right handed coordinate system
Vector Magnitude
• The magnitude (length) of a vector is:
• Unit vector (magnitude=1.0)
Example: Angle Between Vectors
• How do you find the angle θ between vectors A and B?
b
θ=?
a
Dot Products with Unit Vectors
0 <a·b < 1
a·b = 0
a·b = 1
b
θ
a
-1 < a·b < 0
a·b = -1
Dot Products with Non-Unit Vectors
• If a and b are arbitrary (non-unit) vectors, then the following are still true:
• If θ < 90º then a·b > 0
• If θ = 90º then a·b = 0
• If θ > 90º then a·b < 0
Dot Products with One Unit Vector
• If |u|=1.0 then a·u is the length of the projection of a onto u
a
u
a·u
Properties of the Cross Product
area of parallelogram ab
is perpendicular to both a and b, in the direction defined by the right hand rule
Example: Area of a Triangle
• Find the area of the triangle defined by 3D points a, b, and c
c
b
a
Example: Alignment to Target
• An object is at position p with a unit length heading of h. We want to rotate it so that the heading is facing some target t. Find a unit axis a and an angle θ to rotate around.
t
p
h
Matrices
• Computer graphics apps commonly use 4x4 homogeneous matrices
• A rigid 4x4 matrix transformation looks like this:
• Where a, b, & c are orthogonal unit length vectors representing orientation, and d is a vector representing position
Matrices
• The right hand column can cause a projection, which we won’t use in character animation, so we leave it as 0,0,0,1
• Some books store their matrices in a transposed form. This is fine as long as you remember that: A·B = BT·AT
Transformations
• To transform a vector v by matrix M:
v’=v·M
• If we want to apply several transformations, we can just multiply by several matrices:
v’=(((v·M1)·M2)·M3)·M4…
• Or we can concatenate the transformations into a single matrix:
Mtotal=M1·M2·M3·M4…
v’=v·Mtotal
Trigonometry
cos2θ+ sin2θ= 1
1.0
sin θ
θ
cos θ
Laws of Sines and Cosines
• Law of Sines:
• Law of Cosines:
b
α
γ
c
a
β
### Skeletons
Kinematics
• Kinematics: The analysis of motion independent of physical forces. Kinematics deals with position, velocity, acceleration, and their rotational counterparts, orientation, angular velocity, and angular acceleration.
• Forward Kinematics: The process of computing world space geometric data from DOFs
• Inverse Kinematics: The process of computing a set of DOFs that causes some world space goal to be met (I.e., place the hand on the door knob…)
• Note: Kinematics is an entire branch of mathematics and there are several other aspects of kinematics that don’t fall into the ‘forward’ or ‘inverse’ description
Skeletons
• Skeleton: A pose-able framework of joints arranged in a tree structure. The skeleton is used as an invisible armature to manipulate the skin and other geometric data of the character
• Joint: A joint allows relative movement within the skeleton. Joints are essentially 4x4 matrix transformations. Joints can be rotational, translational, or some non-realistic types as well
• Bone: Bone is really just a synonym for joint for the most part. For example, one might refer to the shoulder joint or upper arm bone (humerus) and mean the same thing
DOFs
• Degree of Freedom (DOF): A variable φ describing a particular axis or dimension of movement within a joint
• Joints typically have around 1-6 DOFs (φ1…φN)
• Changing the DOF values over time results in the animation of the skeleton
• In later weeks, we will extend the concept of a DOF to be any animatable parameter within the character rig
• Note: in a mathematical sense, a free rigid body has 6 DOFs: 3 for position and 3 for rotation
Joints
• Core Joint Data
• DOFs (N floats)
• Local matrix: L
• World matrix: W
• Joint offset vector: r
• DOF limits (min & max value per DOF)
• Type-specific data (rotation/translation axes, constants…)
• Tree data (pointers to children, siblings, parent…)
Skeleton Posing Process
• Specify all DOF values for the skeleton (done by higher level animation system)
• Recursively traverse through the hierarchy starting at the root and use forward kinematics to compute the world matrices (done by skeleton system)
• Use world matrices to deform skin & render (done by skin system)
Note: the matrices can also be used for other things such as collision detection, FX, etc.
Forward Kinematics
• In the recursive tree traversal, each joint first computes its local matrix L based on the values of its DOFs and some formula representative of the joint type:
Local matrix L = Ljoint(φ1,φ2,…,φN)
• Then, world matrix W is computed by concatenating L with the world matrix of the parent joint
World matrix W = L · Wparent
Joint Offsets
• It is convenient to have a 3D offset vector r for every joint which represents its pivot point relative to its parent’s matrix
DOF Limits
• It is nice to be able to limit a DOF to some range (for example, the elbow could be limited from 0º to 150º)
• Usually, in a realistic character, all DOFs will be limited except the ones controlling the root
Skeleton Rigging
• Setting up the skeleton is an important and early part of the rigging process
• Sometimes, character skeletons are built before the skin, while other times, it is the opposite
• To set up a skeleton, an artist uses an interactive tool to:
• Construct the tree
• Place joint offsets
• Configure joint types
• Specify joint limits
• Possibly more…
Poses
• Once the skeleton is set up, one can then adjust each of the DOFs to specify the pose of the skeleton
• We can define a pose Φ more formally as a vector of N numbers that maps to a set of DOFs in the skeleton
Φ = [φ1 φ2 … φN]
• A pose is a convenient unit that can be manipulated by a higher level animation system and then handed down to the skeleton
• Usually, each joint will have around 1-6 DOFs, but an entire character might have 100+ DOFs in the skeleton
• Keep in mind that DOFs can be also used for things other than joints, as we will learn later…
### Joint Types
Rotational
Hinge: 1-DOF
Universal: 2-DOF
Ball & Socket: 3-DOF
Euler Angles
Quaternions
Translational
Prismatic: 1-DOF
Translational: 3-DOF (or any number)
Compound
Free
Screw
Constraint
Etc.
Non-Rigid
Scale
Shear
Etc.
Joint Types
Hinge Joints (1-DOF Rotational)
• Rotation around the x-axis:
Hinge Joints (1-DOF Rotational)
• Rotation around the y-axis:
Hinge Joints (1-DOF Rotational)
• Rotation around the z-axis:
Hinge Joints (1-DOF Rotational)
• Rotation around an arbitrary axis a:
Universal Joints (2-DOF)
• For a 2-DOF joint that first rotates around x and then around y:
• Different matrices can be formed for different axis combinations
Ball & Socket (3-DOF)
• For a 3-DOF joint that first rotates around x, y, then z:
• Different matrices can be formed for different axis combinations
Prismatic Joints (1-DOF Translation)
• 1-DOF translation along an arbitrary axis a:
Translational Joints (3-DOF)
• For a more general 3-DOF translation:
Other Joints
• Compound
• Free
• Screw
• Constraint
• Etc.
• Non-Rigid
• Scale (1 axis, 3 axis, volume preserving…)
• Shear
• Etc.
### Programming Project #1: Skeleton
Software Architecture
• Object oriented
• Make objects for things that should be objects
• Avoid global data & functions
• Encapsulate information
• Provide useful interfaces
• Put different objects in different files
Sample Code
• Some sample code is provided on the course web page listed as ‘project0’
• It is an object oriented demo of a spinning cube
• Classes:
• Vector3
• Matrix34
• Tokenizer
• Camera
• SpinningCube
• Tester
Project 1 Assignment
• Load a skeleton from a ‘.skel’ file and display it in 3D
• All joints in the skeleton should be 3-DOF rotational joints
• Compute world matrices yourself and use glLoadMatrixf()
• Due: Monday, Jan 19, 11:59pm
Sample Skel File
balljoint root {
[data for root]
}
balljoint leg_l {
[data for leg]
[children of leg]
}
[more children of root]
}
Skel File Data Tokens
offset x y z (joint offset vector)
boxmin x y z (min corner of box to draw)
boxmax x y z (max corner of box to draw)
rotxlimit min max (x rotation DOF limits)
rotylimit min max (y rotation DOF limits)
rotzlimit min max (z rotation DOF limits)
pose x y z (values to pose DOFs)
balljoint name { } (child joint)
Possible Object Breakdown
• One should consider making objects (classes) for the following:
• DOF
• Joint
• Skeleton
Common Routines
• Many classes will need functions for some or all of the following:
• Constructor / destructor
• Initialize
• Update (move things, pose, animate…)
• Draw
• Reset
What is a DOF?
• Data
• Value
• Min, max
• Functions
• SetValue() (can clamp value at the time of setting)
• GetValue()
• SetMinMax()…
What is a Joint?
• Data
• Local & World matrices
• Array of DOFs
• Tree data (child/sibling/parent pointers, etc.)
• Functions
• Update() (recursively generate local matrix & concatenate)
• Draw()
• Note: One could also make a Joint base class and derive various specific joint types. In this case, it would be a good idea to make a virtual function for MakeLocalMatrix() that the base traversal routine calls
What is a Skeleton?
• Data
• Joint tree (might only need a pointer to the root joint)
• Functions
• Update (traverses tree & computes joint matrices)
• Draw
Tree Data Structures
• The skeleton requires only the most basic N-tree data structure
• The main things the tree needs:
• An easy way to add a new child to a node
• A way for each node to iterate through its children
• There are several options:
• Use STL
• Implement a tree data structure
• Store sibling & first child pointers in the Joint itself
Sibling & Child Pointers
class Joint {
Joint *Sibling,*Child;
… // other data
public:
void Update(Matrix &parent);
void Draw();
… // other functions
};
c.Sibling=Child;
Child=&c;
return true;
}
• Ideally, it should do some error checking as well (such as verifying that c isn’t already a child of another node)
• Note that Child & Sibling must be set to 0 initially in the constructor!
• Also, notice that this routine adds c as the first child on the list (essentially adding them in reverse order)
Update & Draw
void Joint::Update(Matrix &parent) {
… // Compute LocalMatrix
… // Compute WorldMatrix
if(Sibling) Sibling->Update(parent);
if(Child) Child->Update(WorldMatrix);
}
void Joint::Draw() {
.. // Do some OpenGL
if(Sibling) Sibling->Draw();
if(Child) Child->Draw();
}
Tokenizer token;
token.Open(file,"skel"));
token.FindToken("balljoint"));
// Parse tree
Root=new Joint;
// Finish
token.Close();
return true;
}
token.FindToken("{"));
while(1) {
char temp[256];
token.GetToken(temp);
if(strcmp(temp,"offset")==0) {
Offset.x=token.GetFloat();
Offset.y=token.GetFloat();
Offset.z=token.GetFloat();
}
else // Check for other tokens
else if(strcmp(temp,"balljoint")==0) {
Joint *jnt=new Joint;
}
else if(strcmp(temp,"}")==0) return true;
else token.SkipLine(); // Unrecognized token
}
} | 3,127 | 12,037 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2018-47 | latest | en | 0.765554 |
http://www.bellaonline.com/articles/art301973.asp | 1,571,387,061,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986679439.48/warc/CC-MAIN-20191018081630-20191018105130-00229.warc.gz | 226,733,004 | 12,682 | #### ABC of Astronomy - F Is for Fusion
The Sun is more than just a fiery ball of burning gas. The solar energy that supports life on Earth comes from nuclear fusion, for the Sun is a giant nuclear reactor. Nor is this giant reactor a smooth golden sphere. It's a layered structure with complex magnetic fields generating dark sunspots and bright faculae. Magnetic loops can form filaments a million miles long. When magnetic energy builds up, it can erupt suddenly as a solar flare which may affect us on Earth.
F is for fusion
The alchemists of old, seeking to turn base metals into gold, were frustrated in their attempts to change one element into another. However the Sun does it all the time.
The nucleus of an atom contains one or more protons, the number of protons determining which element it is. The atoms of each element have a unique number of protons. But nuclear reactions can change elements from one kind to another. In nuclear fusion lighter nuclei join together (fuse) to produce a heavier element. This is how stars shine. About 85% of the Sun's energy comes from a nuclear reaction in which four hydrogen nuclei fuse to produce a helium nucleus.
Normally, you use energy to build something. However making a helium nucleus our of hydrogen gives out energy. Since energy can't be created or destroyed, where's this energy coming from? A clue is that the mass of a helium nucleus is slightly less than the total mass of four hydrogen nuclei. The explanation is in the most famous equation in physics, Einstein's
E = mc2
Einstein's theory says that matter and energy are interchangeable, and the equation shows how much energy (E) you'd get when a given mass (m) is converted into energy. Since c is the speed of light, when it's squared you have a huge number. This is why the Sun has been shining for five billion years and will go on doing so for a very long time.
F is for faculae [FAK.yuh.lee]
Most people have heard of sunspots, those dark spots on the Sun's surface that are related to solar activity. They're regions of intense magnetic activity. A sunspot is not actually dark. If you could see it apart from the rest of the Sun, it would seem as bright as a full Moon. However the Sun's surface temperature is 5500 °C (9900 °F), and that of sunspots is about 3400 °C (6200 °F). They seem dark because they're cooler than their surroundings.
But faculae – Latin for little torches – are not so obvious. Like sunspots, they're magnetic regions, but smaller and with more concentrated magnetic activity. Faculae are hotter than the surrounding region, which makes them bright spots. Although they're somewhat brighter than their surroundings, they're still difficult to pick out, as they're only about 30 °C (80 °F) hotter. Faculae are easiest to see near the edge of the Sun where the background isn't so bright.
Interestingly, a sunspot always has an associated facula, but faculae can exist in the absence of sunspots. During the solar activity cycle, the Sun is a teensy bit brighter at its maximum because the faculae brighten it more than the sunspots darken it.
F is for filament
Filaments and prominences are the same things, and they can be very dramatic. They're composed of cooler gas that's suspended above the Sun's surface by magnetic loops, and are often near sunspots. Their appearances differ only because of our perspective when viewing them.
Seen from above, a filament, which is long and snaky, looks dark. This is because, like sunspots, a filament is cooler than the surface underneath it. But they're still very hot. The filament shown here was photographed in February 2015. It was over 700,000 km (435,000 miles) long, which is greater than the radius of the Sun. This is unusually long, but not the longest known filament which was an amazing million miles long.
But we can often see filaments in profile. In that case it's clear that they're hanging above the Sun's surface. This is when they're called prominences.
F is for flares
All this magnetic energy building up in sunspots and filaments may be discharged explosively in a solar flare. A colossal amount of energy is released. NASA describes is as “the equivalent of millions of 100-megaton hydrogen bombs exploding at the same time.” But perhaps even more impressive is that every second the Sun gives out over ten times that much energy.
A coronal mass ejection (CME) may accompany a flare. A CME is the release of great clouds of gas and subatomic particles, accompanied by a huge amount of energy and a shock wave that accelerates the particles to very high speeds.
If a solar flare or a CME comes our way, Earth is likely to be treated to displays of aurorae. On the negative side, the solar storms may damage satellites and the electrical power grid, as well as interfere with communications.
What Is Space Weather
Carrington Event - Biggest Solar Storm on Record
Aurorae - Polar Light Shows
Related Articles
Editor's Picks Articles
Top Ten Articles
Previous Features
Site Map | 1,101 | 5,008 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2019-43 | latest | en | 0.948627 |
https://miphonedoctorofaustin.com/qa/question-is-1-the-smallest-factor-of-any-number.html | 1,603,378,009,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107879673.14/warc/CC-MAIN-20201022141106-20201022171106-00354.warc.gz | 424,071,839 | 7,632 | # Question: Is 1 The Smallest Factor Of Any Number?
## Which is the smallest prime number?
The smallest prime numbers are 2, 3, 5, 7, 11, 13, 17, 19 and 23.
The number 2 is the only even prime number.
The number 7 has only two factors: 1 and itself.
The number 11 has only two factors: 1 and itself..
## Why is 11 not a prime number?
For 11, the answer is: yes, 11 is a prime number because it has only two distinct divisors: 1 and itself (11). As a consequence, 11 is only a multiple of 1 and 11.
## What is the largest factor of any number?
the smallest factor of a number is 1 and the largest factor is number itself.
## Does 1 have less than 2 factors?
1 does not have two different factors, so it is not prime. 2 has only the factors 2 and 1. 3 has only the factors 3 and 1. 4 has more than two factors: 1, 2, and 4, so it is composite.
## Why is 1 a factor of every number?
Originally Answered: What is the factor of every number? A number A is said to be a factor of a number B if B is divisible by A (B/A=NATURAL NO.) now as every no is divisible by 1 . so, 1 is the no which is the factor of every no.
## Is 1 a prime factor of every number?
Each prime number is only divisible by 1 and itself. That means the number 1 can never be a prime number. So any prime number should have only two factors and it should be greater than 1.
## What is the HCF of 120 and 75?
15The hcf of 75 and 120 is 15.
## Which is the smallest factor of 15?
Answer. So, the smallest Factor of 15 is 1.
## What is factor of every number?
Factor of a number means that its multiple is totally divisible by that number. 1 is a divisible of every number i.e it divides every number. So, 1 is the number which is a factor of every number. Hence, the answer is 1.
## What is the smallest and largest factor of any number?
Factors of a number The factors (noun) of a number are the numbers that divide evenly into the number. For example the factors of the number 12 are the numbers 1, 2, 3, 4, 6 and 12. (Notice that the smallest factor is always 1 and the biggest factor is always the number itself.)
## What is the smallest factor of number?
The number 1 is the smallest factor of every number. Every number will have a minimum of two factors, 1 and the number itself. A number that has only two factors, 1 and the number itself, is called a prime number.
## Can 0 be a factor?
For any real number, multiply it by its reciprocal to get 1. … Zero is not a factor of any non-zero number because n/0 is undefined for any number other than zero. All integers other than zero are factors of zero because 0n = 0 for all numbers. | 703 | 2,630 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2020-45 | latest | en | 0.958806 |
http://blog.stevemcauley.com/2013/01/30/extension-to-energy-conserving-wrapped-diffuse/ | 1,620,623,700,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989030.87/warc/CC-MAIN-20210510033850-20210510063850-00066.warc.gz | 8,787,440 | 9,452 | # Steve McAuley
## Extension to Energy-Conserving Wrapped Diffuse
A while ago, I wrote a blog post on energy-conserving wrapped diffuse lighting [1], noting that following standard formula ended up adding a lot of energy:
$\frac{\cos(\theta) + w}{1+w}$
Instead, we should normalise and use this instead, preventing a sudden surge in energy whenever we decide to wrap:
$\frac{\cos(\theta) + w}{(1+w)^2}$
However, Jorge Jimenez recently pointed out to me that it would be much better if we could generalise the energy-conserving wrapped diffuse model to encompass a slightly more complex model for diffuse lighting, one using a power:
$(\frac{\cos(\theta) + w}{1+w})^n$
In fact, raising your wrap shading to a power is a pretty common thing. It makes things look a little bit softer and more pleasing on the eye, as Lambertian diffuse tends to have quite a harsh fall-off that you’re trying to get rid of with wrap shading. Valve did it [2], and that was extended by Sloan et. al. [3] who used:
$(\frac{\cos(\theta) + w}{1+w})^{1 + w}$
whereas Valve’s original model fixed w as 1.0. We can do better than both of those by making our formula completely generic, allowing us to use any combination of wrap factor and power that we want.
Once Jorge had made the suggestion of extending energy-conservation to this formula, I quickly pulled out my pen and paper and scribbled down some integrals, and to my surprise it all fell out pretty nicely. Naturally, it’s very similar to what’s in my previous post, so forgive me if I skip a few steps…
First, remember that we need to integrate not just over the hemisphere, but further around the sphere until the formula hits zero (at which point in our shader we clamp). So rather than integrating between 0 and ½π, we go from 0 to α, where α is such that:
$\cos(\alpha) = -w$
Now we can begin, and we’ll again normalise by π now so we don’t have to worry about it at the end:
$\frac{1}{\pi} \int_{0}^{2\pi} \int_{0}^{\alpha} (\frac{\cos(\theta) + w}{1+w})^n \sin(\theta) d\theta d\phi$
After we’ve got rid of the outer integral, and pulled out what we can of the inner, we’re left with:
$\frac{2}{(1+w)^n} \int_{0}^{\alpha} (\cos(\theta) + w)^n \sin(\theta) d\theta$
We now pull our main trick: let’s substitute $x = \cos(\theta)$, which gives us $dx = -\sin(\theta) d\theta$ and therefore get the following equation:
$-\frac{2}{(1+w)^n} \int_{\theta=0}^{\theta=\alpha} (x + w)^n dx$
We only have to remember Integration 101 to work that one out, as long as we make a tiny assumption about our value of n (it can’t be -1):
$-\frac{2}{(1+w)^n} \left[ \frac{1}{n+1}(x + w)^{n+1} \right]_{\theta=0}^{\theta=\alpha}$
Now, if we put back in our value for x and evaluate using our identity for α, we get the beautifully simple:
$\frac{2(1 + w)}{n+1}$
Just to check if we’ve got this right, we’ll try n = 1, as in my original post. Using the above formula, we still get $1 + w$, the same as our original answer, so we’ve probably done something right!
Here’s some obligatory shader code for the new model:
// w is between 0 and 1 // n is not -1 float3 wrappedDiffuse = LightColour * pow(saturate((dot(N, L) + w) / (1.0f + w)), n) * (n + 1) / (2 * (1 + w));
Finally, let’s compare the differences between the old models (on the left) and our new energy-conserving models (on the right).
Valve’s model:
Sloan et. al.’s model, with a = 0.5:
Generic model, with w = 0.5 and n = 4.0:
The differences are a lot more subtle this time (especially with the values we’re using) but they’re still there. It’s worth noting that although for the first two models, energy conservation is making the lighting darker, in the last model the lighting becomes brighter. So don’t make any presumptions!
If you want to have a play around yourself, then here’s a RenderMonkey workspace that allows you to tweak the power and wrap factor, and turn on and off energy conservation.
Now surely, there’s no excuse left to use a non-energy conserving wrapped diffuse model?
References
[1] http://blog.stevemcauley.com/2011/12/03/energy-conserv…rapped-diffuse/
[2] Jason Mitchell, Gary McTaggart and Chris Green, Shading in Valve’s Source Engine, Advances in Real-Time Rendering in Graphics and Games, SIGGRAPH 2006, http://www.valvesoftware.com/publications/2006/SIGGRAPH06_Course_ShadingInValvesSourceEngine.pdf
[3] Peter-Pike Sloan, Derek Nowrouzezahrai, Hong Yuan, Wrap Shading, Journal of Graphics Tools, Volume 15, Issue 4, 2011, http://www.iro.umontreal.ca/~derek/files/jgt_wrap.pdf
### 2 Responses
Great post!
Using this normalized shader in the eyes of our characters makes a more noticeable difference. Probably because it feels better integrated!
• […] Steve McAuley has a short post on his blog that builds on a previous post he did on making the often used wrapped diffuse model energy-conserving. In this new post, he extends the formula to a generic wrapped diffuse model where an arbitrary power is used to soften the look a bit. His post is called Extension to Energy-Conserving Wrapped Diffuse. […] | 1,360 | 5,059 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2021-21 | longest | en | 0.927527 |
https://mathematica.stackexchange.com/questions/25998/using-element/38482 | 1,723,768,585,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641319057.20/warc/CC-MAIN-20240815235528-20240816025528-00442.warc.gz | 292,984,823 | 41,284 | # Using Element[]
Can the Element[] function only be used for the domains given in the documentation? I am trying to use it to determine if a value is contained in a previously defined list. Thanks!
• It only works for domains, yes. You might be interested in MemberQ[]... Commented May 28, 2013 at 14:00
• Thanks. That should do the trick Commented May 28, 2013 at 14:03
• You should be able to answer your own question, now... Commented May 28, 2013 at 14:04
• There is an exception to J.M.'s answer: upvalues, although it would only be shorthand for MemberQ[]. Commented May 28, 2013 at 14:06
• Difference is also that Element is a kind of assertion, you tell Mathematica that a given variable belongs to a given domain, whereas MemberQ is a test; you ask Mathematica whether a value is member of a list. Commented May 28, 2013 at 20:26
There are as usual several ways. The most convenient one is probably MemberQ, as already pointed out in the comments.
MemberQ[{1, 2, 3, 4, 9}, 9]
(* True *)
If you have a complex structure and not only a flat list, then FreeQ can be of use. Note that you have to negate the result.
MemberQ[{1, 2, {3}, {{4, 9}}}, 9]
Not[FreeQ[{1, 2, {3}, {{4, 9}}}, 9]]
(* False *)
(* True *)
Finally, note that you can specify the level where MemberQ should look for the appearance of the element
MemberQ[{1, 2, {3}, {{4, 9}}}, 9, Infinity]
(* True *)
I have not tested it, but this dirty hack might be pretty fast IF you have to assess membership in a list of symbolic values with no zeros.
symMemberQ[x_, mylist_] := SameQ[Times @@ Flatten[mylist /. x -> 0], 0]
Adding Flatten wil take care of nested list.
symMemberQ[e, {a, {b, g}, {d, {e, f}}}]
True
symMemberQ[w, {a, {b, g}, {d, {e, f}}}]
False
(It's a dirty hack, so beware: it might bite you). | 535 | 1,801 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-33 | latest | en | 0.908992 |
http://www.aptitudemantra.com/Quantitative/Time-and-Distance | 1,597,171,711,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738819.78/warc/CC-MAIN-20200811180239-20200811210239-00584.warc.gz | 122,921,730 | 6,110 | # Quantitative - Time and Distance
## Time and Distance Description
1. Speed = ${(\frac{Distance}{Time})}$
2. Time = ${(\frac{Distance}{Speed})}$
3. Distance = ${Speed \times Time}$
4. km/hr to m/sec conversion
X km/hr = ${(X\times\frac{5}{18})}$ m/sec
5. m/sec to km/hr conversion
X m/sec = ${(X\times\frac{18}{5})}$ km/hr
6. If a man covers a distance at x km/hr and an equal distance at y km/hr.
Then average speed = ${\frac{2xy}{x+y}}$ km/hr
7.If the ratio of speeds of A and B is a: b then time taken to cover distance is b: a
Excercise 1 Questions : 10 | Viewed : 551 Take an Exercise
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Let's Start Practicing Go to Test | 228 | 717 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2020-34 | latest | en | 0.797375 |
https://outschool.com/classes/essential-basic-trigonometry-JXidnDgk | 1,713,938,987,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819067.85/warc/CC-MAIN-20240424045636-20240424075636-00432.warc.gz | 410,153,405 | 72,837 | ### Essential Basic Trigonometry
Fernando Millan, Certified Educator. B.S.E.E.
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Average rating:4.9Number of reviews:(901)
Introduction to Trigonometry. Fundamental skills that appear on the SAT exams among others.
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6-9 learners per class | 1,353 | 4,583 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2024-18 | latest | en | 0.622189 |
https://m.jagranjosh.com/articles/top-7-tips-to-finish-cbse-class-10-maths-exam-before-time-1515133467-1?ref=list_art | 1,642,361,585,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300010.26/warc/CC-MAIN-20220116180715-20220116210715-00457.warc.gz | 447,456,530 | 36,306 | # CBSE Class 10 Maths Term 1 Paper Tomorrow: 7 Best Exam Writing and Time Management Tips Here
Know here some most crucial tips and tricks to follow while writing the upcoming CBSE Class 10th Maths Term 1 Exam 2021-22. These tips will help you finish your paper well on time.
Created On: Dec 3, 2021 11:19 IST
CBSE Class 10 Maths: Exam Writing Tips
Students often face problems in completing the Maths paper on time due to the long and tricky calculations used in solving the Maths questions. Students generally panic while solving questions in exams due to which they are unable to finish the paper on time. Just because they run out of time, they have to leave a few questions unwillingly and quite often it has been observed that the questions they leave are those which they could have solved very easily. Such a situation becomes very disappointing.
New* CBSE Class 10 Maths Best Resources & Tips for Term 1 Exam 2021-22
In this article, we have summed up some important tips on how to attempt the Maths paper correctly and finish it before time despite the overwhelming pressure of the board exam. These simple but effective tips will help you write the exam perfectly to fetch you the full marks.
1. Know the examination pattern and question paper design
In order to write the Maths exam smoothly, the most important thing is to understand the examination pattern/ question paper design beforehand. This will make you familiarised with the structure of the question paper. Moreover, you will also get to know the formats in which questions will be asked and their mark-wise breakup. If you will be having an idea about the pattern of questions then you won’t find it difficult to understand the structure of the paper on the final day which will definitely save some of your crucial time.
Know the CBSE Class 10 Maths Exam Pattern and Question Paper Design for Term 1 Exam 2021-22
2. Prepare a strategy for the exam before you take it
After understanding the examination pattern, the next job is to deeply analyse the exam pattern and prepare a strategy for the final exam. Check the number of questions, their types or categories to plan the appropriate exam writing technique.
The following table states the questions’ structure for CBSE Board Mathematics Exam 2021:
Section Number of Questions to Attempt Marks per question A 16 (out of 20) 1 B 16 (out of 20) 1 C 8 (out of 10) 1
Thus, you will have to solve a total of 40 questions in 1.5 hours, i.e., in 90 minutes. So, you should make a proper time division so that you are able to attempt all questions well on time.
A moderate time division can be done as below:
Section Types of MCQs No. of Questions Time to be Spent Total Time A Very Short Stand Alone MCQs 16 1-2 min per MCQ 25 minutes (maximum) B Short Stand Alone MCQs 16 2-3 min per MCQ 35 minutes (maximum) C Case-based MCQs 8 2-3 min per MCQ 20 minutes (maximum) Revision Time 10 minutes Total Time 90 minutes
Following the above time division plan, you will get about 10 minutes left with you which can be utilised in reviewing the whole paper, making corrections and attempting the left questions. Remember one thing, there is no negative marking in board exams, so you must try to attempt all questions.
Also Read: How to solve Case Study Questions accurately in CBSE Class 10 Maths Exam 2021-22
3. Use the 20 minutes reading time effectively
Reading time for CBSE Class 10 students in the Term 1 Board Exam 2021-22 will be 20 minutes instead of 15 minutes. Students must use these 20 minutes wisely to prepare a strategy for writing the exam appropriately. You must read all 50 questions properly and mark the questions in each section which you can attempt precisely. Exclude those questions which do not strike your mind at all.
Check important tips to utilise reading time in CBSE board exams
4. Don't worry about the tough/complex problems
While going through the paper, when you find some questions that seem to be tough or complex to you, you need not worry about it as this anxiety will only harm your performance. So, you just start with easier problems. As you will move further, by solving each question and obtaining correct answers, you will gain confidence for the complex problems as well. This way, when you will actually work on them, you will find most of them to be much easier than they seemed earlier to you.
5. Do not spend too much time on a question
Now when you are going to attempt the paper, you must have an idea that how much each question is worth and estimate the time you should spend working on each one, so that you don’t waste much time on a question that won’t fetch you enough marks otherwise you will lose some important marks for other questions which might be left unsolved due to the lack of time.
10 most effective preparation tips to score more than 90% marks in board exams
6. Maintain speed and accuracy hand in hand
Maintain accuracy while you are solving quickly. Make sure you don't get confused between two different topics. Try to implement quicker methods in calculations to save your precious time. Be careful with the signs and terms used while solving a question otherwise, it will take a lot of time to solve a problem leading to an incorrect answer. Be careful while filling a circle for the right option in the OMR sheet.
7. Keep a close watch on the time
Keeping an eye on your watch will help you keep a track of the time and know how many questions are still left. Moreover, it will help you check that you are strictly adhering to the time allocation scheme you had decided on in the beginning. However, a minor variation in the time allotted to each section or question is not at all a reason to worry.
Along with preparing hard for an exam, it’s very important to make a strategy to write that exam in the proper way and within time so that your hard work gets reflected in your answer sheet. So, study hard and prepare smart, you will definitely succeed.
All the Very Best!
Check: Important Tips and Resources for CBSE Class 10 Maths Term 1 Exam 2021-22
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• Thankyou so much mam n sir | 1,432 | 6,447 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2022-05 | latest | en | 0.949085 |
https://www.kernel.org/doc/html/v6.5/driver-api/media/dtv-common.html | 1,716,326,933,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058512.80/warc/CC-MAIN-20240521183800-20240521213800-00634.warc.gz | 748,517,527 | 16,300 | # 3.1. Digital TV Common functions¶
## 3.1.1. Math functions¶
Provide some commonly-used math functions, usually required in order to estimate signal strength and signal to noise measurements in dB.
unsigned int intlog2(u32 value)
computes log2 of a value; the result is shifted left by 24 bits
Parameters
`u32 value`
The value (must be != 0)
Description
to use rational values you can use the following method:
intlog2(value) = intlog2(value * 2^x) - x * 2^24
Some usecase examples:
intlog2(8) will give 3 << 24 = 3 * 2^24
intlog2(9) will give 3 << 24 + ... = 3.16... * 2^24
intlog2(1.5) = intlog2(3) - 2^24 = 0.584... * 2^24
Return
log2(value) * 2^24
unsigned int intlog10(u32 value)
computes log10 of a value; the result is shifted left by 24 bits
Parameters
`u32 value`
The value (must be != 0)
Description
to use rational values you can use the following method:
intlog10(value) = intlog10(value * 10^x) - x * 2^24
An usecase example:
intlog10(1000) will give 3 << 24 = 3 * 2^24
due to the implementation intlog10(1000) might be not exactly 3 * 2^24
look at intlog2 for similar examples
Return
log10(value) * 2^24
## 3.1.2. DVB devices¶
Those functions are responsible for handling the DVB device nodes.
enum dvb_device_type
type of the Digital TV device
Constants
`DVB_DEVICE_SEC`
Digital TV standalone Common Interface (CI)
`DVB_DEVICE_FRONTEND`
Digital TV frontend.
`DVB_DEVICE_DEMUX`
Digital TV demux.
`DVB_DEVICE_DVR`
Digital TV digital video record (DVR).
`DVB_DEVICE_CA`
Digital TV Conditional Access (CA).
`DVB_DEVICE_NET`
Digital TV network.
`DVB_DEVICE_VIDEO`
Digital TV video decoder. Deprecated. Used only on av7110-av.
`DVB_DEVICE_AUDIO`
Digital TV audio decoder. Deprecated. Used only on av7110-av.
`DVB_DEVICE_OSD`
Digital TV On Screen Display (OSD). Deprecated. Used only on av7110.
represents a Digital TV adapter using Linux DVB API
Definition:
```struct dvb_adapter {
int num;
const char *name;
u8 proposed_mac [6];
void* priv;
struct device *device;
struct module *module;
int mfe_shared;
struct dvb_device *mfe_dvbdev;
struct mutex mfe_lock;
#if defined(CONFIG_MEDIA_CONTROLLER_DVB);
struct mutex mdev_lock;
struct media_device *mdev;
struct media_entity *conn;
#endif;
};
```
Members
`num`
Number of the adapter
`list_head`
List with the DVB adapters
`device_list`
List with the DVB devices
`name`
Name of the adapter
`proposed_mac`
`priv`
private data
`device`
pointer to `struct device`
`module`
pointer to struct module
`mfe_shared`
indicates mutually exclusive frontends. 1 = legacy exclusion behavior: blocking any open() call 2 = enhanced exclusion behavior, emulating the standard behavior of busy frontends: allowing read-only sharing and otherwise returning immediately with -EBUSY when any of the frontends is already opened with write access.
`mfe_dvbdev`
Frontend device in use, in the case of MFE
`mfe_lock`
Lock to prevent using the other frontends when MFE is used.
`mdev_lock`
`mdev`
pointer to `struct media_device`, used when the media controller is used.
`conn`
RF connector. Used only if the device has no separate tuner.
`conn_pads`
pointer to `struct media_pad` associated with conn;
struct dvb_device
represents a DVB device node
Definition:
```struct dvb_device {
struct kref ref;
const struct file_operations *fops;
enum dvb_device_type type;
int minor;
u32 id;
int writers;
int users;
int (*kernel_ioctl)(struct file *file, unsigned int cmd, void *arg);
#if defined(CONFIG_MEDIA_CONTROLLER_DVB);
const char *name;
struct media_intf_devnode *intf_devnode;
unsigned tsout_num_entities;
struct media_entity *entity, *tsout_entity;
#endif;
void *priv;
};
```
Members
`list_head`
List head with all DVB devices
`ref`
reference count for this device
`fops`
pointer to struct file_operations
`adapter`
pointer to the adapter that holds this device node
`type`
type of the device, as defined by `enum dvb_device_type`.
`minor`
devnode minor number. Major number is always DVB_MAJOR.
`id`
device ID number, inside the adapter
`readers`
Initialized by the caller. Each call to open() in Read Only mode decreases this counter by one.
`writers`
Initialized by the caller. Each call to open() in Read/Write mode decreases this counter by one.
`users`
Initialized by the caller. Each call to open() in any mode decreases this counter by one.
`wait_queue`
wait queue, used to wait for certain events inside one of the DVB API callers
`kernel_ioctl`
callback function used to handle ioctl calls from userspace.
`name`
Name to be used for the device at the Media Controller
`intf_devnode`
Pointer to media_intf_devnode. Used by the dvbdev core to store the MC device node interface
`tsout_num_entities`
Number of Transport Stream output entities
`entity`
pointer to `struct media_entity` associated with the device node
`tsout_entity`
array with MC entities associated to each TS output node
`pads`
pointer to `struct media_pad` associated with entity;
`tsout_pads`
array with the source pads for each tsout_entity
`priv`
private data
Description
This structure is used by the DVB core (frontend, CA, net, demux) in order to create the device nodes. Usually, driver should not initialize this struct diretly.
struct dvbdevfops_node
fops nodes registered in dvbdevfops_list
Definition:
```struct dvbdevfops_node {
struct file_operations *fops;
enum dvb_device_type type;
const struct dvb_device *template;
};
```
Members
`fops`
Dynamically allocated fops for ->owner registration
`type`
type of dvb_device
`template`
dvb_device used for registration
`list_head`
struct dvb_device *dvb_device_get(struct dvb_device *dvbdev)
Increase dvb_device reference
Parameters
`struct dvb_device *dvbdev`
pointer to `struct dvb_device`
void dvb_device_put(struct dvb_device *dvbdev)
Decrease dvb_device reference
Parameters
`struct dvb_device *dvbdev`
pointer to `struct dvb_device`
int dvb_register_adapter(struct dvb_adapter *adap, const char *name, struct module *module, struct device *device, short *adapter_nums)
Registers a new DVB adapter
Parameters
`struct dvb_adapter *adap`
pointer to `struct dvb_adapter`
`const char *name`
`struct module *module`
initialized with THIS_MODULE at the caller
`struct device *device`
pointer to `struct device` that corresponds to the device driver
`short *adapter_nums`
Array with a list of the numbers for dvb_register_adapter; to select among them. Typically, initialized with: DVB_DEFINE_MOD_OPT_ADAPTER_NR(adapter_nums)
Unregisters a DVB adapter
Parameters
`struct dvb_adapter *adap`
pointer to `struct dvb_adapter`
int dvb_register_device(struct dvb_adapter *adap, struct dvb_device **pdvbdev, const struct dvb_device *template, void *priv, enum dvb_device_type type, int demux_sink_pads)
Registers a new DVB device
Parameters
`struct dvb_adapter *adap`
pointer to `struct dvb_adapter`
`struct dvb_device **pdvbdev`
pointer to the place where the new `struct dvb_device` will be stored
`const struct dvb_device *template`
Template used to create `pdvbdev`;
`void *priv`
private data
`enum dvb_device_type type`
type of the device, as defined by `enum dvb_device_type`.
`int demux_sink_pads`
Number of demux outputs, to be used to create the TS outputs via the Media Controller.
void dvb_remove_device(struct dvb_device *dvbdev)
Remove a registered DVB device
Parameters
`struct dvb_device *dvbdev`
pointer to `struct dvb_device`
Description
This does not free memory. dvb_free_device() will do that when reference counter is empty
void dvb_unregister_device(struct dvb_device *dvbdev)
Unregisters a DVB device
Parameters
`struct dvb_device *dvbdev`
pointer to `struct dvb_device`
Creates media graph for the Digital TV part of the device.
Parameters
`struct dvb_adapter *adap`
pointer to `struct dvb_adapter`
`bool create_rf_connector`
if true, it creates the RF connector too
Description
This function checks all DVB-related functions at the media controller entities and creates the needed links for the media graph. It is capable of working with multiple tuners or multiple frontends, but it won't create links if the device has multiple tuners and multiple frontends or if the device has multiple muxes. In such case, the caller driver should manually create the remaining links.
void dvb_register_media_controller(struct dvb_adapter *adap, struct media_device *mdev)
registers a media controller at DVB adapter
Parameters
`struct dvb_adapter *adap`
pointer to `struct dvb_adapter`
`struct media_device *mdev`
pointer to `struct media_device`
gets the associated media controller
Parameters
`struct dvb_adapter *adap`
pointer to `struct dvb_adapter`
int dvb_generic_open(struct inode *inode, struct file *file)
Digital TV open function, used by DVB devices
Parameters
`struct inode *inode`
pointer to `struct inode`.
`struct file *file`
pointer to `struct file`.
Description
Checks if a DVB devnode is still valid, and if the permissions are OK and increment negative use count.
int dvb_generic_release(struct inode *inode, struct file *file)
Digital TV close function, used by DVB devices
Parameters
`struct inode *inode`
pointer to `struct inode`.
`struct file *file`
pointer to `struct file`.
Description
Checks if a DVB devnode is still valid, and if the permissions are OK and decrement negative use count.
long dvb_generic_ioctl(struct file *file, unsigned int cmd, unsigned long arg)
Digital TV close function, used by DVB devices
Parameters
`struct file *file`
pointer to `struct file`.
`unsigned int cmd`
Ioctl name.
`unsigned long arg`
Ioctl argument.
Description
Checks if a DVB devnode and struct dvbdev.kernel_ioctl is still valid. If so, calls `dvb_usercopy()`.
int dvb_usercopy(struct file *file, unsigned int cmd, unsigned long arg, int (*func)(struct file *file, unsigned int cmd, void *arg))
copies data from/to userspace memory when an ioctl is issued.
Parameters
`struct file *file`
Pointer to struct `file`.
`unsigned int cmd`
Ioctl name.
`unsigned long arg`
Ioctl argument.
`int (*func)(struct file *file, unsigned int cmd, void *arg)`
function that will actually handle the ioctl
Description
Ancillary function that uses ioctl direction and size to copy from userspace. Then, it calls func, and, if needed, data is copied back to userspace.
struct i2c_client *dvb_module_probe(const char *module_name, const char *name, struct i2c_adapter *adap, unsigned char addr, void *platform_data)
helper routine to probe an I2C module
Parameters
`const char *module_name`
Name of the I2C module to be probed
`const char *name`
Optional name for the I2C module. Used for debug purposes. If `NULL`, defaults to module_name.
`struct i2c_adapter *adap`
pointer to `struct i2c_adapter` that describes the I2C adapter where the module will be bound.
`unsigned char addr`
I2C address of the adapter, in 7-bit notation.
`void *platform_data`
Platform data to be passed to the I2C module probed.
Description
This function binds an I2C device into the DVB core. Should be used by all drivers that use I2C bus to control the hardware. A module bound with `dvb_module_probe()` should use `dvb_module_release()` to unbind.
Note
In the past, DVB modules (mainly, frontends) were bound via `dvb_attach()` macro, with does an ugly hack, using I2C low level functions. Such usage is deprecated and will be removed soon. Instead, use this routine.
Return
On success, return an `struct i2c_client`, pointing to the bound I2C device. `NULL` otherwise.
void dvb_module_release(struct i2c_client *client)
releases an I2C device allocated with `dvb_module_probe()`.
Parameters
`struct i2c_client *client`
pointer to `struct i2c_client` with the I2C client to be released. can be `NULL`.
Description
This function should be used to free all resources reserved by `dvb_module_probe()` and unbinding the I2C hardware.
dvb_attach
`dvb_attach (FUNCTION, ARGS...)`
attaches a DVB frontend into the DVB core.
Parameters
`FUNCTION`
function on a frontend module to be called.
`ARGS...`
FUNCTION arguments.
Description
This ancillary function loads a frontend module in runtime and runs the FUNCTION function there, with ARGS. As it increments symbol usage cont, at unregister, `dvb_detach()` should be called.
Note
In the past, DVB modules (mainly, frontends) were bound via `dvb_attach()` macro, with does an ugly hack, using I2C low level functions. Such usage is deprecated and will be removed soon. Instead, you should use `dvb_module_probe()`.
dvb_detach
`dvb_detach (FUNC)`
detaches a DVB frontend loaded via `dvb_attach()`
Parameters
`FUNC`
attach function
Description
Decrements usage count for a function previously called via `dvb_attach()`.
## 3.1.3. Digital TV Ring buffer¶
Those routines implement ring buffers used to handle digital TV data and copy it from/to userspace.
Note
1. For performance reasons read and write routines don't check buffer sizes and/or number of bytes free/available. This has to be done before these routines are called. For example:
```/* write @buflen: bytes */
free = dvb_ringbuffer_free(rbuf);
if (free >= buflen)
count = dvb_ringbuffer_write(rbuf, buffer, buflen);
else
/* do something */
/* read min. 1000, max. @bufsize: bytes */
avail = dvb_ringbuffer_avail(rbuf);
if (avail >= 1000)
count = dvb_ringbuffer_read(rbuf, buffer, min(avail, bufsize));
else
/* do something */
```
1. If there is exactly one reader and one writer, there is no need to lock read or write operations. Two or more readers must be locked against each other. Flushing the buffer counts as a read operation. Resetting the buffer counts as a read and write operation. Two or more writers must be locked against each other.
struct dvb_ringbuffer
Describes a ring buffer used at DVB framework
Definition:
```struct dvb_ringbuffer {
u8 *data;
ssize_t size;
ssize_t pwrite;
int error;
spinlock_t lock;
};
```
Members
`data`
Area were the ringbuffer data is written
`size`
size of the ringbuffer
`pread`
next position to read
`pwrite`
next position to write
`error`
used by ringbuffer clients to indicate that an error happened.
`queue`
Wait queue used by ringbuffer clients to indicate when buffer was filled
`lock`
Spinlock used to protect the ringbuffer
void dvb_ringbuffer_init(struct dvb_ringbuffer *rbuf, void *data, size_t len)
initialize ring buffer, lock and queue
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
`void *data`
pointer to the buffer where the data will be stored
`size_t len`
bytes from ring buffer into buf
int dvb_ringbuffer_empty(struct dvb_ringbuffer *rbuf)
test whether buffer is empty
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
ssize_t dvb_ringbuffer_free(struct dvb_ringbuffer *rbuf)
returns the number of free bytes in the buffer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
Return
number of free bytes in the buffer
ssize_t dvb_ringbuffer_avail(struct dvb_ringbuffer *rbuf)
returns the number of bytes waiting in the buffer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
Return
number of bytes waiting in the buffer
void dvb_ringbuffer_reset(struct dvb_ringbuffer *rbuf)
resets the ringbuffer to initial state
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
Description
Resets the read and write pointers to zero and flush the buffer.
This counts as a read and write operation
void dvb_ringbuffer_flush(struct dvb_ringbuffer *rbuf)
flush buffer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
void dvb_ringbuffer_flush_spinlock_wakeup(struct dvb_ringbuffer *rbuf)
flush buffer protected by spinlock and wake-up waiting task(s)
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
DVB_RINGBUFFER_PEEK
`DVB_RINGBUFFER_PEEK (rbuf, offs)`
peek at byte offs in the buffer
Parameters
`rbuf`
pointer to `struct dvb_ringbuffer`
`offs`
offset inside the ringbuffer
DVB_RINGBUFFER_SKIP
`DVB_RINGBUFFER_SKIP (rbuf, num)`
Parameters
`rbuf`
pointer to `struct dvb_ringbuffer`
`num`
number of bytes to advance
ssize_t dvb_ringbuffer_read_user(struct dvb_ringbuffer *rbuf, u8 __user *buf, size_t len)
Reads a buffer into a user pointer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
`u8 __user *buf`
pointer to the buffer where the data will be stored
`size_t len`
bytes from ring buffer into buf
Description
This variant assumes that the buffer is a memory at the userspace. So, it will internally call copy_to_user().
Return
number of bytes transferred or -EFAULT
void dvb_ringbuffer_read(struct dvb_ringbuffer *rbuf, u8 *buf, size_t len)
Reads a buffer into a pointer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
`u8 *buf`
pointer to the buffer where the data will be stored
`size_t len`
bytes from ring buffer into buf
Description
This variant assumes that the buffer is a memory at the Kernel space
Return
number of bytes transferred or -EFAULT
DVB_RINGBUFFER_WRITE_BYTE
`DVB_RINGBUFFER_WRITE_BYTE (rbuf, byte)`
write single byte to ring buffer
Parameters
`rbuf`
pointer to `struct dvb_ringbuffer`
`byte`
byte to write
ssize_t dvb_ringbuffer_write(struct dvb_ringbuffer *rbuf, const u8 *buf, size_t len)
Writes a buffer into the ringbuffer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
`const u8 *buf`
pointer to the buffer where the data will be read
`size_t len`
bytes from ring buffer into buf
Description
This variant assumes that the buffer is a memory at the Kernel space
Return
number of bytes transferred or -EFAULT
ssize_t dvb_ringbuffer_write_user(struct dvb_ringbuffer *rbuf, const u8 __user *buf, size_t len)
Writes a buffer received via a user pointer
Parameters
`struct dvb_ringbuffer *rbuf`
pointer to `struct dvb_ringbuffer`
`const u8 __user *buf`
pointer to the buffer where the data will be read
`size_t len`
bytes from ring buffer into buf
Description
This variant assumes that the buffer is a memory at the userspace. So, it will internally call copy_from_user().
Return
number of bytes transferred or -EFAULT
ssize_t dvb_ringbuffer_pkt_write(struct dvb_ringbuffer *rbuf, u8 *buf, size_t len)
Write a packet into the ringbuffer.
Parameters
`struct dvb_ringbuffer *rbuf`
Ringbuffer to write to.
`u8 *buf`
Buffer to write.
`size_t len`
Length of buffer (currently limited to 65535 bytes max).
Return
Number of bytes written, or -EFAULT, -ENOMEM, -EINVAL.
ssize_t dvb_ringbuffer_pkt_read_user(struct dvb_ringbuffer *rbuf, size_t idx, int offset, u8 __user *buf, size_t len)
Read from a packet in the ringbuffer.
Parameters
`struct dvb_ringbuffer *rbuf`
Ringbuffer concerned.
`size_t idx`
Packet index as returned by `dvb_ringbuffer_pkt_next()`.
`int offset`
Offset into packet to read from.
`u8 __user *buf`
Destination buffer for data.
`size_t len`
Size of destination buffer.
Return
Number of bytes read, or -EFAULT.
Description
Note
unlike `dvb_ringbuffer_read()`, this does NOT update the read pointer in the ringbuffer. You must use `dvb_ringbuffer_pkt_dispose()` to mark a packet as no longer required.
ssize_t dvb_ringbuffer_pkt_read(struct dvb_ringbuffer *rbuf, size_t idx, int offset, u8 *buf, size_t len)
Read from a packet in the ringbuffer.
Parameters
`struct dvb_ringbuffer *rbuf`
Ringbuffer concerned.
`size_t idx`
Packet index as returned by `dvb_ringbuffer_pkt_next()`.
`int offset`
Offset into packet to read from.
`u8 *buf`
Destination buffer for data.
`size_t len`
Size of destination buffer.
Note
unlike `dvb_ringbuffer_read_user()`, this DOES update the read pointer in the ringbuffer.
Return
Number of bytes read, or -EFAULT.
void dvb_ringbuffer_pkt_dispose(struct dvb_ringbuffer *rbuf, size_t idx)
Dispose of a packet in the ring buffer.
Parameters
`struct dvb_ringbuffer *rbuf`
Ring buffer concerned.
`size_t idx`
Packet index as returned by `dvb_ringbuffer_pkt_next()`.
ssize_t dvb_ringbuffer_pkt_next(struct dvb_ringbuffer *rbuf, size_t idx, size_t *pktlen)
Get the index of the next packet in a ringbuffer.
Parameters
`struct dvb_ringbuffer *rbuf`
Ringbuffer concerned.
`size_t idx`
Previous packet index, or -1 to return the first packet index.
`size_t *pktlen`
On success, will be updated to contain the length of the packet in bytes. returns Packet index (if >=0), or -1 if no packets available.
## 3.1.4. Digital TV VB2 handler¶
enum dvb_buf_type
types of Digital TV memory-mapped buffers
Constants
`DVB_BUF_TYPE_CAPTURE`
buffer is filled by the Kernel, with a received Digital TV stream
enum dvb_vb2_states
states to control VB2 state machine
Constants
`DVB_VB2_STATE_NONE`
VB2 engine not initialized yet, init failed or VB2 was released.
`DVB_VB2_STATE_INIT`
VB2 engine initialized.
`DVB_VB2_STATE_REQBUFS`
Buffers were requested
`DVB_VB2_STATE_STREAMON`
VB2 is streaming. Callers should not check it directly. Instead, they should use `dvb_vb2_is_streaming()`.
Note
Description
Callers should not touch at the state machine directly. This is handled inside dvb_vb2.c.
struct dvb_buffer
video buffer information for v4l2.
Definition:
```struct dvb_buffer {
struct vb2_buffer vb;
};
```
Members
`vb`
embedded struct `vb2_buffer`.
`list`
list of `struct dvb_buffer`.
struct dvb_vb2_ctx
control struct for VB2 handler
Definition:
```struct dvb_vb2_ctx {
struct vb2_queue vb_q;
struct mutex mutex;
spinlock_t slock;
struct dvb_buffer *buf;
int offset;
int remain;
int state;
int buf_siz;
int buf_cnt;
int nonblocking;
enum dmx_buffer_flags flags;
u32 count;
char name[DVB_VB2_NAME_MAX + 1];
};
```
Members
`vb_q`
pointer to `struct vb2_queue` with videobuf2 queue.
`mutex`
mutex to serialize vb2 operations. Used by vb2 core `wait_prepare` and `wait_finish` operations.
`slock`
spin lock used to protect buffer filling at dvb_vb2.c.
`dvb_q`
List of buffers that are not filled yet.
`buf`
Pointer to the buffer that are currently being filled.
`offset`
index to the next position at the buf to be filled.
`remain`
How many bytes are left to be filled at buf.
`state`
bitmask of buffer states as defined by `enum dvb_vb2_states`.
`buf_siz`
size of each VB2 buffer.
`buf_cnt`
number of VB2 buffers.
`nonblocking`
If different than zero, device is operating on non-blocking mode.
`flags`
buffer flags as defined by `enum dmx_buffer_flags`. Filled only at `DMX_DQBUF`. `DMX_QBUF` should zero this field.
`count`
monotonic counter for filled buffers. Helps to identify data stream loses. Filled only at `DMX_DQBUF`. `DMX_QBUF` should zero this field.
`name`
name of the device type. Currently, it can either be "dvr" or "demux_filter".
int dvb_vb2_init(struct dvb_vb2_ctx *ctx, const char *name, int non_blocking)
initializes VB2 handler
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`const char *name`
name for the VB2 handler
`int non_blocking`
if not zero, it means that the device is at non-blocking mode
int dvb_vb2_release(struct dvb_vb2_ctx *ctx)
Releases the VB2 handler allocated resources and put ctx at DVB_VB2_STATE_NONE state.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
int dvb_vb2_is_streaming(struct dvb_vb2_ctx *ctx)
checks if the VB2 handler is streaming
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
Return
0 if not streaming, 1 otherwise.
int dvb_vb2_fill_buffer(struct dvb_vb2_ctx *ctx, const unsigned char *src, int len, enum dmx_buffer_flags *buffer_flags)
fills a VB2 buffer
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`const unsigned char *src`
place where the data is stored
`int len`
number of bytes to be copied from src
`enum dmx_buffer_flags *buffer_flags`
pointer to buffer flags as defined by `enum dmx_buffer_flags`. can be NULL.
__poll_t dvb_vb2_poll(struct dvb_vb2_ctx *ctx, struct file *file, poll_table *wait)
Wrapper to `vb2_core_streamon()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct file *file`
`struct file` argument passed to the poll file operation handler.
`poll_table *wait`
`poll_table` wait argument passed to the poll file operation handler.
Description
Implements poll syscall() logic.
int dvb_vb2_stream_on(struct dvb_vb2_ctx *ctx)
Wrapper to `vb2_core_streamon()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
Description
Starts dvb streaming
int dvb_vb2_stream_off(struct dvb_vb2_ctx *ctx)
Wrapper to `vb2_core_streamoff()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
Description
Stops dvb streaming
int dvb_vb2_reqbufs(struct dvb_vb2_ctx *ctx, struct dmx_requestbuffers *req)
Wrapper to `vb2_core_reqbufs()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct dmx_requestbuffers *req`
`struct dmx_requestbuffers` passed from userspace in order to handle `DMX_REQBUFS`.
Description
Initiate streaming by requesting a number of buffers. Also used to free previously requested buffers, is `req->count` is zero.
int dvb_vb2_querybuf(struct dvb_vb2_ctx *ctx, struct dmx_buffer *b)
Wrapper to `vb2_core_querybuf()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct dmx_buffer *b`
`struct dmx_buffer` passed from userspace in order to handle `DMX_QUERYBUF`.
int dvb_vb2_expbuf(struct dvb_vb2_ctx *ctx, struct dmx_exportbuffer *exp)
Wrapper to `vb2_core_expbuf()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct dmx_exportbuffer *exp`
`struct dmx_exportbuffer` passed from userspace in order to handle `DMX_EXPBUF`.
Description
Export a buffer as a file descriptor.
int dvb_vb2_qbuf(struct dvb_vb2_ctx *ctx, struct dmx_buffer *b)
Wrapper to `vb2_core_qbuf()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct dmx_buffer *b`
`struct dmx_buffer` passed from userspace in order to handle `DMX_QBUF`.
Description
Queue a Digital TV buffer as requested by userspace
int dvb_vb2_dqbuf(struct dvb_vb2_ctx *ctx, struct dmx_buffer *b)
Wrapper to `vb2_core_dqbuf()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct dmx_buffer *b`
`struct dmx_buffer` passed from userspace in order to handle `DMX_DQBUF`.
Description
Dequeue a Digital TV buffer to the userspace
int dvb_vb2_mmap(struct dvb_vb2_ctx *ctx, struct vm_area_struct *vma)
Wrapper to `vb2_mmap()` for Digital TV buffer handling.
Parameters
`struct dvb_vb2_ctx *ctx`
control struct for VB2 handler
`struct vm_area_struct *vma`
pointer to `struct vm_area_struct` with the vma passed to the mmap file operation handler in the driver.
Description
map Digital TV video buffers into application address space. | 7,003 | 27,290 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2024-22 | latest | en | 0.54716 |
https://export.arxiv.org/abs/2102.00106 | 1,679,388,088,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00598.warc.gz | 307,640,209 | 5,738 | math.SP
(what is this?)
# Title: Bessel-Type Operators and a refinement of Hardy's inequality
Abstract: The principal aim of this paper is to employ Bessel-type operators in proving the inequality \begin{align*} \int_0^\pi dx \, |f'(x)|^2 \geq \dfrac{1}{4}\int_0^\pi dx \, \dfrac{|f(x)|^2}{\sin^2 (x)}+\dfrac{1}{4}\int_0^\pi dx \, |f(x)|^2,\quad f\in H_0^1 ((0,\pi)), \end{align*} where both constants $1/4$ appearing in the above inequality are optimal. In addition, this inequality is strict in the sense that equality holds if and only if $f \equiv 0$. This inequality is derived with the help of the exactly solvable, strongly singular, Dirichlet-type Schr\"{o}dinger operator associated with the differential expression \begin{align*} \tau_s=-\dfrac{d^2}{dx^2}+\dfrac{s^2-(1/4)}{\sin^2 (x)}, \quad s \in [0,\infty), \; x \in (0,\pi). \end{align*}
The new inequality represents a refinement of Hardy's classical inequality \begin{align*} \int_0^\pi dx \, |f'(x)|^2 \geq \dfrac{1}{4}\int_0^\pi dx \, \dfrac{|f(x)|^2}{x^2}, \quad f\in H_0^1 ((0,\pi)), \end{align*} it also improves upon one of its well-known extensions in the form \begin{align*} \int_0^\pi dx \, |f'(x)|^2 \geq \dfrac{1}{4}\int_0^\pi dx \, \dfrac{|f(x)|^2}{d_{(0,\pi)}(x)^2}, \quad f\in H_0^1 ((0,\pi)), \end{align*} where $d_{(0,\pi)}(x)$ represents the distance from $x \in (0,\pi)$ to the boundary $\{0,\pi\}$ of $(0,\pi)$.
Comments: 23 pages, updated references Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph) MSC classes: Primary: 26D10, 34A40, 34B20, 34B30, Secondary: 34L10, 34B24, 47A07 Cite as: arXiv:2102.00106 [math.SP] (or arXiv:2102.00106v5 [math.SP] for this version)
## Submission history
From: Fritz Gesztesy [view email]
[v1] Fri, 29 Jan 2021 23:19:28 GMT (26kb)
[v2] Sun, 21 Feb 2021 02:41:30 GMT (28kb)
[v3] Sat, 6 Mar 2021 20:26:54 GMT (28kb)
[v4] Wed, 17 Mar 2021 06:51:54 GMT (28kb)
[v5] Tue, 16 Nov 2021 00:09:19 GMT (29kb)
Link back to: arXiv, form interface, contact. | 752 | 1,989 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2023-14 | latest | en | 0.679853 |
http://www.python.org/search/hypermail/python-1993/0380.html | 1,386,203,612,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163037902/warc/CC-MAIN-20131204131717-00056-ip-10-33-133-15.ec2.internal.warc.gz | 491,412,999 | 3,062 | # Re: obtaining the reversal of a sequence?
Steven D. Majewski (sdm7g@elvis.med.virginia.edu)
Thu, 28 Oct 1993 11:41:03 -0400
While elvis.med.virginia.edu was getting it's disks scrubbed and
cleaned, I missed the original question that started the thread
On Oct 20, 23:27, Bill Janssen wrote:
>
> I've encountered the problem where I'd like to have a sequence that is
> traversed in both directions equally frequently. It's a display list, and
> is traversed from back to front, to paint the window, and from front to
> back, to find the innermost element enclosing a point.
>
> Clearly, the ``for foo in x'' construct works well for one of the two
> cases, but what's the efficient way to traverse the list in reverse order?
> The best I can come up with is:
>
> tmp = list[:]
> tmp.reverse()
> for x in tmp:
> blah...
>
> and that's so inefficient I believe there must be some trick tucked away
> to make this easier.
>
> Bill
>
>
> -- End of excerpt from Bill Janssen <janssen@parc.xerox.com>
But playing around with pseudo-sequences ( in my prev. posts ) suggests
a trick:
class Rev:
def __init__( self, seq ):
self.forw = seq
self.back = self
def __len__( self ):
return len( self.forw )
def __getitem__( self, j ):
return self.forw[ -( j + 1 ) ]
def __repr__( self ):
return '<reverse of sequence: ' + repr(self.forw) +' >'
It works on mutable or inmutable sequences.
>>> for c in Rev( 'Hello World!' ) : sys.stdout.write( c )
... else: sys.stdout.write( '\n' )
...
!dlroW olleH
>>>
The .forw is so you can use anonymous sequences in init, and still
keep a reference the forward sequence. )
If you give it a non-anonymous mutable sequence, the reverse sequence
will track the updated values. ( but not reassignment! - another
good reason to use anonymous values in creating the sequence to avoid
confusion. Maybe it should be change to copy input sequence to break
the connection completely ? )
>>> nnn = range( 0, 3 )
>>> rnn = Rev( nnn )
>>> for n in rnn: print n
...
2
1
0
>>> for n in range( 4, 6 ): nnn.append( n ) # update nnn
...
>>> for n in rnn: print n # prints reversed updated values
...
5
4
2
1
0
>>> nnn = nnn[1:-1]
>>> nnn
[1, 2, 4]
>>> for n in rnn: print n # prints reversed values of old nnn
...
5
4
2
1
0
>>>
I'll leave it to Guido or someone else to figure out how this
compares effeciency wise with the other solutions.
ToDo's:
repr() ought to return a more natural representation, but then it
has to check for type of argument to know whether to wrap the
reversed values in "[]" or "()" or something else or nothing.
Add more methods to make rseq.back completely comparable to
rseq.forw. e.g. rseq.back.append( ) would insert a value at
the BEGINNING of rseq.forw. , etc.
Also note to Terrence Brannon and others who have complained about
strings being non-mutable: you can probably tell from these various
pseudo-sequences that it would be pretty easy to make a mutable-string
class. It isn't something I've felt as a requirement, but since it's
so easy, maybe we ought to put one in the standard library.
Right now I'm more interested in figuring out a more natural way of
expressing regular expressions and other non-regexp patterns ( like
matching parends. ) using operators on character set classes and
pattern classes instead of characters with special meanings that may
or may not have to be escaped.
i.e. something like:
Any( letters ) + Any( letters ) * 5 + Any( digits + '_\$' ) * 3
( where letters and digits are imported from string, and 'Any' would be
a class constructor. )
translating into regexp: [a-zA-Z][a-zA-A]*5[0-9]*3
( where *5 means 0-5 occurances - a specification feature I've not seen
in all regexp modules. )
Any comments on the usefulness of this sort of interface to regexp, or
the desired syntax or semantics ?
- Steve Majewski | 1,031 | 3,801 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2013-48 | latest | en | 0.844571 |
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# People per hour Chart
P: 74 Hello Community. I have a table consisting of a date / time field and a number field, the first being what time the people entered and the latter being the number of people to enter. I wish to display this data as a line graph with 15 minute intervals so every quarter of an hour it will display the count of all people through the door in that period to show busy times. I am using Access 2003. Do any of you people know if there is a solution to this problem. Many Thanks Mar 13 '12 #1
5 Replies
100+ P: 759 This is most to subscribe than to provide help because I have troubles to understand what you have and, also, what you wish to achieve. In my opinion a door can be passed by only one person at a time. In this case the second field (number) is no more needed because you can count the records in Date/Time field from 15 to 15 minutes. But from your post the situation seems to be different: You count, from time to time, how many people pass the door in the last time interval. In that case why you not set the time intervals to a quart of hour ? More, I don't understand if you have troubles to count peoples from 15 to 15 minutes or you have troubles to draw the graphic or both. I am almost sure that a solution exist :) but you need to be more specific. Mar 14 '12 #2
P: 74 sometimes more than one person enters with the registrant Table data like this: number time 3 01/01/12 10:30:05 1 01/01/12 10:32:25 4 01/01/12 10:34:02 2 01/01/12 10:37:35 1 01/01/12 10:44:15 etc.... An i need to plot a chart of people in verus time in 15 minute segments Mar 14 '12 #3
Expert 100+ P: 634 Hi This query will sum the Number column for 15 min period (period ending time) Expand|Select|Wrap|Line Numbers SELECT Sum(tbllNumberCount.lngNumber) AS [Count], Format(Int([dtTime]*96+1)/96,"dd/mm/yy hh:nn:ss") AS [Time Period Ending] FROM tbllNumberCount GROUP BY Format(Int([dtTime]*96+1)/96,"dd/mm/yy hh:nn:ss"); For period begining query this Expand|Select|Wrap|Line Numbers [dtTime]*96+1 shouold be changed to this Expand|Select|Wrap|Line Numbers [dtTime]*96 HTH MTB Mar 14 '12 #4
P: 74 Many thanks, I will try it later and let you know! Mar 14 '12 #5
100+
P: 759
I hate SQL ! Totally. For all my life. Final word.
In attachment you will find a solution.
There are two databases: .accdb (for 2007) and .mdb (for 2003).
I have not tested in 2003.
And a link to a very useful article:
http://www.vb123.com.au/toolbox/09_a...07charting.htm
Good luck !
Attached Files
15minutes.zip (175.1 KB, 166 views)
Mar 14 '12 #6 | 780 | 2,712 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2019-43 | latest | en | 0.882688 |
https://www.in2013dollars.com/1777-dollars-in-2017?amount=50 | 1,627,997,534,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00641.warc.gz | 799,378,920 | 20,606 | \$50 in 1777 is worth \$1,156.23 in 2017
\$
👉 You may be interested in \$50 in 1777 → 2021
Value of \$50 from 1777 to 2017
\$50 in 1777 is equivalent in purchasing power to about \$1,156.23 in 2017, an increase of \$1,106.23 over 240 years. The dollar had an average inflation rate of 1.32% per year between 1777 and 2017, producing a cumulative price increase of 2,212.45%.
This means that prices in 2017 are 23.12 times higher than average prices since 1777, according to the Bureau of Labor Statistics consumer price index.
The 1777 inflation rate was 21.84%. The inflation rate in 2017 was 2.13%. The 2017 inflation rate is lower compared to the average inflation rate of 2.61% per year between 2017 and 2021.
Cumulative price change 2,212.45% Average inflation rate 1.32% Converted amount (\$50 base) \$1,156.23 Price difference (\$50 base) \$1,106.23 CPI in 1777 10.600 CPI in 2017 245.120 Inflation in 1777 21.84% Inflation in 2017 2.13% \$50 in 1777 \$1,156.23 in 2017
USD Inflation since 1635
Annual Rate, the Bureau of Labor Statistics CPI
Buying power of \$50 in 1777
This chart shows a calculation of buying power equivalence for \$50 in 1777 (price index tracking began in 1635).
For example, if you started with \$50, you would need to end with \$1,156.23 in order to "adjust" for inflation (sometimes refered to as "beating inflation").
When \$50 is equivalent to \$1,156.23 over time, that means that the "real value" of a single U.S. dollar decreases over time. In other words, a dollar will pay for fewer items at the store.
This effect explains how inflation erodes the value of a dollar over time. By calculating the value in 1777 dollars, the chart below shows how \$50 is worth less over 240 years.
According to the Bureau of Labor Statistics, each of these USD amounts below is equal in terms of what it could buy at the time:
Dollar inflation: 1777-2017
Year Dollar Value Inflation Rate
1777 \$50.00 21.84%
1778 \$65.09 30.19%
1779 \$57.55 -11.59%
1780 \$64.62 12.30%
1781 \$52.36 -18.98%
1782 \$57.08 9.01%
1783 \$50.00 -12.40%
1784 \$48.11 -3.77%
1785 \$45.75 -4.90%
1786 \$44.81 -2.06%
1787 \$43.87 -2.11%
1788 \$41.98 -4.30%
1789 \$41.51 -1.12%
1790 \$43.40 4.55%
1791 \$44.34 2.17%
1792 \$45.28 2.13%
1793 \$46.70 3.13%
1794 \$51.89 11.11%
1795 \$59.43 14.55%
1796 \$62.26 4.76%
1797 \$59.91 -3.79%
1798 \$58.02 -3.15%
1799 \$58.02 0.00%
1800 \$59.43 2.44%
1801 \$59.91 0.79%
1802 \$50.47 -15.75%
1803 \$53.30 5.61%
1804 \$55.66 4.42%
1805 \$55.19 -0.85%
1806 \$57.55 4.27%
1807 \$54.72 -4.92%
1808 \$59.43 8.62%
1809 \$58.02 -2.38%
1810 \$58.02 0.00%
1811 \$61.79 6.50%
1812 \$62.74 1.53%
1813 \$75.47 20.30%
1814 \$83.02 10.00%
1815 \$72.64 -12.50%
1816 \$66.51 -8.44%
1817 \$62.74 -5.67%
1818 \$59.91 -4.51%
1819 \$59.91 0.00%
1820 \$55.19 -7.87%
1821 \$53.30 -3.42%
1822 \$55.19 3.54%
1823 \$49.53 -10.26%
1824 \$45.75 -7.62%
1825 \$46.70 2.06%
1826 \$46.70 0.00%
1827 \$47.17 1.01%
1828 \$44.81 -5.00%
1829 \$43.87 -2.11%
1830 \$43.40 -1.08%
1831 \$41.04 -5.43%
1832 \$40.57 -1.15%
1833 \$39.62 -2.33%
1834 \$40.57 2.38%
1835 \$41.51 2.33%
1836 \$43.87 5.68%
1837 \$45.28 3.23%
1838 \$43.87 -3.12%
1839 \$43.87 0.00%
1840 \$41.04 -6.45%
1841 \$41.04 0.00%
1842 \$38.68 -5.75%
1843 \$34.91 -9.76%
1844 \$35.38 1.35%
1845 \$35.85 1.33%
1846 \$36.32 1.32%
1847 \$38.68 6.49%
1848 \$37.26 -3.66%
1849 \$36.32 -2.53%
1850 \$36.79 1.30%
1851 \$36.32 -1.28%
1852 \$36.32 0.00%
1853 \$36.32 0.00%
1854 \$39.62 9.09%
1855 \$41.04 3.57%
1856 \$40.09 -2.30%
1857 \$41.04 2.35%
1858 \$38.68 -5.75%
1859 \$39.15 1.22%
1860 \$39.15 0.00%
1861 \$41.51 6.02%
1862 \$47.64 14.77%
1863 \$59.43 24.75%
1864 \$74.06 24.60%
1865 \$76.89 3.82%
1866 \$75.00 -2.45%
1867 \$69.81 -6.92%
1868 \$66.98 -4.05%
1869 \$64.15 -4.23%
1870 \$61.79 -3.68%
1871 \$57.55 -6.87%
1872 \$57.55 0.00%
1873 \$56.60 -1.64%
1874 \$53.77 -5.00%
1875 \$51.89 -3.51%
1876 \$50.47 -2.73%
1877 \$49.53 -1.87%
1878 \$47.17 -4.76%
1879 \$47.17 0.00%
1880 \$48.11 2.00%
1881 \$48.11 0.00%
1882 \$48.11 0.00%
1883 \$47.64 -0.98%
1884 \$46.23 -2.97%
1885 \$45.75 -1.02%
1886 \$44.34 -3.09%
1887 \$44.81 1.06%
1888 \$44.81 0.00%
1889 \$43.40 -3.16%
1890 \$42.92 -1.09%
1891 \$42.92 0.00%
1892 \$42.92 0.00%
1893 \$42.45 -1.10%
1894 \$40.57 -4.44%
1895 \$39.62 -2.33%
1896 \$39.62 0.00%
1897 \$39.15 -1.19%
1898 \$39.15 0.00%
1899 \$39.15 0.00%
1900 \$39.62 1.20%
1901 \$40.09 1.19%
1902 \$40.57 1.18%
1903 \$41.51 2.33%
1904 \$41.98 1.14%
1905 \$41.51 -1.12%
1906 \$42.45 2.27%
1907 \$44.34 4.44%
1908 \$43.40 -2.13%
1909 \$42.92 -1.09%
1910 \$44.81 4.40%
1911 \$44.81 0.00%
1912 \$45.75 2.11%
1913 \$46.70 2.06%
1914 \$47.17 1.01%
1915 \$47.64 1.00%
1916 \$51.42 7.92%
1917 \$60.38 17.43%
1918 \$71.23 17.97%
1919 \$81.60 14.57%
1920 \$94.34 15.61%
1921 \$84.43 -10.50%
1922 \$79.25 -6.15%
1923 \$80.66 1.79%
1924 \$80.66 0.00%
1925 \$82.55 2.34%
1926 \$83.49 1.14%
1927 \$82.08 -1.69%
1928 \$80.66 -1.72%
1929 \$80.66 0.00%
1930 \$78.77 -2.34%
1931 \$71.70 -8.98%
1932 \$64.62 -9.87%
1933 \$61.32 -5.11%
1934 \$63.21 3.08%
1935 \$64.62 2.24%
1936 \$65.57 1.46%
1937 \$67.92 3.60%
1938 \$66.51 -2.08%
1939 \$65.57 -1.42%
1940 \$66.04 0.72%
1941 \$69.34 5.00%
1942 \$76.89 10.88%
1943 \$81.60 6.13%
1944 \$83.02 1.73%
1945 \$84.91 2.27%
1946 \$91.98 8.33%
1947 \$105.19 14.36%
1948 \$113.68 8.07%
1949 \$112.26 -1.24%
1950 \$113.68 1.26%
1951 \$122.64 7.88%
1952 \$125.00 1.92%
1953 \$125.94 0.75%
1954 \$126.89 0.75%
1955 \$126.42 -0.37%
1956 \$128.30 1.49%
1957 \$132.55 3.31%
1958 \$136.32 2.85%
1959 \$137.26 0.69%
1960 \$139.62 1.72%
1961 \$141.04 1.01%
1962 \$142.45 1.00%
1963 \$144.34 1.32%
1964 \$146.23 1.31%
1965 \$148.58 1.61%
1966 \$152.83 2.86%
1967 \$157.55 3.09%
1968 \$164.15 4.19%
1969 \$173.11 5.46%
1970 \$183.02 5.72%
1971 \$191.04 4.38%
1972 \$197.17 3.21%
1973 \$209.43 6.22%
1974 \$232.55 11.04%
1975 \$253.77 9.13%
1976 \$268.40 5.76%
1977 \$285.85 6.50%
1978 \$307.55 7.59%
1979 \$342.45 11.35%
1980 \$388.68 13.50%
1981 \$428.77 10.32%
1982 \$455.19 6.16%
1983 \$469.81 3.21%
1984 \$490.09 4.32%
1985 \$507.55 3.56%
1986 \$516.98 1.86%
1987 \$535.85 3.65%
1988 \$558.02 4.14%
1989 \$584.91 4.82%
1990 \$616.51 5.40%
1991 \$642.45 4.21%
1992 \$661.79 3.01%
1993 \$681.60 2.99%
1994 \$699.06 2.56%
1995 \$718.87 2.83%
1996 \$740.09 2.95%
1997 \$757.08 2.29%
1998 \$768.87 1.56%
1999 \$785.85 2.21%
2000 \$812.26 3.36%
2001 \$835.38 2.85%
2002 \$848.58 1.58%
2003 \$867.92 2.28%
2004 \$891.04 2.66%
2005 \$921.23 3.39%
2006 \$950.94 3.23%
2007 \$978.03 2.85%
2008 \$1,015.58 3.84%
2009 \$1,011.97 -0.36%
2010 \$1,028.57 1.64%
2011 \$1,061.03 3.16%
2012 \$1,082.99 2.07%
2013 \$1,098.85 1.46%
2014 \$1,116.68 1.62%
2015 \$1,118.00 0.12%
2016 \$1,132.11 1.26%
2017 \$1,156.23 2.13%
2018 \$1,185.05 2.49%
2019 \$1,205.93 1.76%
2020 \$1,220.81 1.23%
2021 \$1,281.58 4.98%*
* Compared to previous annual rate. Not final. See inflation summary for latest 12-month trailing value.
Click to show 234 more rows
This conversion table shows various other 1777 amounts in 2017 dollars, based on the 2,212.45% change in prices:
Conversion: 1777 dollars in 2017
Initial value Equivalent value
\$1 dollar in 1777 \$23.12 dollars in 2017
\$5 dollars in 1777 \$115.62 dollars in 2017
\$10 dollars in 1777 \$231.25 dollars in 2017
\$50 dollars in 1777 \$1,156.23 dollars in 2017
\$100 dollars in 1777 \$2,312.45 dollars in 2017
\$500 dollars in 1777 \$11,562.26 dollars in 2017
\$1,000 dollars in 1777 \$23,124.53 dollars in 2017
\$5,000 dollars in 1777 \$115,622.64 dollars in 2017
\$10,000 dollars in 1777 \$231,245.28 dollars in 2017
\$50,000 dollars in 1777 \$1,156,226.42 dollars in 2017
\$100,000 dollars in 1777 \$2,312,452.83 dollars in 2017
\$500,000 dollars in 1777 \$11,562,264.15 dollars in 2017
\$1,000,000 dollars in 1777 \$23,124,528.30 dollars in 2017
Inflation by Country
Inflation can also vary widely by country. For comparison, in the UK £50.00 in 1777 would be equivalent to £7,789.13 in 2017, an absolute change of £7,739.13 and a cumulative change of 15,478.26%.
Compare these numbers to the US's overall absolute change of \$1,106.23 and total percent change of 2,212.45%.
Inflation by Spending Category
CPI is the weighted combination of many categories of spending that are tracked by the government. Breaking down these categories helps explain the main drivers behind price changes. This chart shows the average rate of inflation for select CPI categories between 1777 and 2017.
Compare these values to the overall average of 1.32% per year:
Category Avg Inflation (%) Total Inflation (%) \$50 in 1777 → 2017
Food and beverages 4.01 1,252,448.43 626,274.21
Housing 4.29 2,376,082.27 1,188,091.14
Apparel 2.07 13,595.10 6,847.55
Transportation 3.29 235,447.70 117,773.85
Medical care 4.80 7,639,764.72 3,819,932.36
Recreation 1.11 1,326.61 713.30
Education and communication 1.97 10,579.11 5,339.55
Other goods and services 5.15 17,283,931.27 8,642,015.63
The graph below compares inflation in categories of goods over time. Click on a category such as "Food" to toggle it on or off:
For all these visualizations, it's important to note that not all categories may have been tracked since 1777. This table and charts use the earliest available data for each category.
How to Calculate Inflation Rate for \$50, 1777 to 2017
Our calculations use the following inflation rate formula to calculate the change in value between 1777 and 2017:
CPI in 2017 CPI in 1777
×
1777 USD value
=
2017 USD value
Then plug in historical CPI values. The U.S. CPI was 10.6 in the year 1777 and 245.12 in 2017:
245.1210.6
×
\$50
=
\$1,156.23
\$50 in 1777 has the same "purchasing power" or "buying power" as \$1,156.23 in 2017.
To get the total inflation rate for the 240 years between 1777 and 2017, we use the following formula:
CPI in 2017 - CPI in 1777CPI in 1777
×
100
=
Cumulative inflation rate (240 years)
Plugging in the values to this equation, we get:
245.12 - 10.610.6
×
100
=
2,212%
Politics and news often influence economic performance. Here's what was happening at the time:
• George Washington's army defeats the British army at the Battle of Princeton.
• The US becomes the first nation to abolish slavery, when it introduces its new Constitution
• The US flag is used for the first time, in the battle at Cooch's Bridge, during American Revolutionary war
• British colonies in America proclaimed independent from France
Data Source & Citation
Raw data for these calculations comes from the Bureau of Labor Statistics' (CPI), established in 1913. Inflation data from 1665 to 1912 is sourced from a historical study conducted by political science professor Robert Sahr at Oregon State University.
You may use the following MLA citation for this page: “\$50 in 1777 → 2017 | Inflation Calculator.” Official Inflation Data, Alioth Finance, 3 Aug. 2021, https://www.officialdata.org/1777-dollars-in-2017?amount=50.
Special thanks to QuickChart for their chart image API, which is used for chart downloads.
in2013dollars.com is a reference website maintained by the Official Data Foundation. | 4,522 | 11,039 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2021-31 | longest | en | 0.92394 |
https://studydaddy.com/question/on-december-31-2017-lopez-sales-has-a-bonds-payable-balance-of-89-000-and-a-prem | 1,576,233,384,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540553486.23/warc/CC-MAIN-20191213094833-20191213122833-00167.warc.gz | 552,380,953 | 7,429 | Answered You can hire a professional tutor to get the answer.
QUESTION
# On December 31, 2017, Lopez Sales has a Bonds Payable balance of \$89,000 and a Premium on Bonds Payable balance of \$4500. On the balance sheet, how
On December 31, 2017, Lopez Sales has a Bonds Payable balance of \$89,000 and a Premium on Bonds Payable balance of \$4500. On the balance sheet, how will this information be shown?
A) \$89,000 less one-tenth of \$4500 for a net balance of \$88,550
B) \$89,000 plus a premium of \$4500 for a net balance of \$93,500
C) \$89,000
D) \$89,000 less premium of \$4500 for a net balance of \$84,500
LEARN MORE EFFECTIVELY AND GET BETTER GRADES! | 195 | 669 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2019-51 | latest | en | 0.784627 |
https://www.coursehero.com/file/13002629/Ch21ComparingMeansBetween2IndependentGroups/ | 1,642,765,328,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303356.40/warc/CC-MAIN-20220121101528-20220121131528-00394.warc.gz | 756,130,986 | 51,763 | # Ch21ComparingMeansBetween2IndependentGroups - STAT 200...
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STAT 200 - Elementary Statistics for Applications Comparing Means between Two Independent Groups Camila Casquilho The University of British Columbia, Department of Statistics Adapted notes from: Eugenia Yu, The University of British Columbia, Department of Statistics 1 / 18
Comparing Means between Two Independent Groups I Objective: to compare the means of two independent populations I We draw a random sample from each of the two independent populations: y 11 , y 12 , · · · , y 1 n 1 (sample size n 1 ) from a population with mean μ 1 and standard deviation σ 1 y 21 , y 22 , · · · , y 2 n 2 (sample size n 2 ) from a population with mean μ 2 and standard deviation σ 2 I Two samples are said to be independent if the individuals selected for one sample do not dictate which individuals are to be in a second sample. I Two samples are said to be dependent or paired when the individuals selected to be in one sample determine the individuals to be included in the second sample. 2 / 18
Distinguishing between independent and dependent samples I Let’s consider two scenarios: 1 You want to compare the mean IQ between males and females. To test for a difference, you randomly select 20 females and 20 males. The two sets of IQ scores (one per gender group) are independent of each other. 2 You want to compare the mean IQ between the older and younger siblings of twin pairs. To test for a difference, you randomly select 20 twin pairs. One sample of IQ scores come from the older siblings of the 20 twin pairs, and the other sample come from the younger siblings of the same 20 twin pairs. There is a paired structure between the two samples. 3 / 18
4 / 18
Sampling distribution for difference in means of two independent populations I To estimate μ 1 - μ 2 , we use y 1 - y 2 where y 1 and y 2 are sample means from the two samples. I Given that the 2 random samples are independent, the sampling distribution of y 1 - y 2 will have mean : μ 1 - μ 2 (unbiased) standard deviation : SD ( y 1 - y 2 ) = q σ 2 1 n 1 + σ 2 2 n 2 (See Appendix for the mathematical derivation of the expression for the standard deviation.) I As long as the two samples are independent (their sizes n 1 and n 2 also need to be sufficiently large if the distributions of y 1 and y 2 are unknown), the sampling distribution of y 1 - y 2 will follow the Normal model. 5 / 18 | 608 | 2,477 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2022-05 | latest | en | 0.874931 |
technothlon.techniche.org.in | 1,571,515,487,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986697760.44/warc/CC-MAIN-20191019191828-20191019215328-00242.warc.gz | 724,052,563 | 5,027 | ### Question 1
Five pirates discover a chest containing 100 gold coins. They decide to sit down and devise a distribution strategy. The pirates are ranked based on their experience (Pirate 1 to Pirate 5, where Pirate 5 is the most experienced). The most experienced pirate gets to propose a plan and then all the pirates vote on it. If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 5 devises a plan which he knows will be accepted for sure and will maximize his gold. What is the maximum gold he can earn? | 169 | 796 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-43 | longest | en | 0.949027 |
https://zbook.org/read/c8a939_flowchart-example-flowchart-for-animated-story.html | 1,720,820,365,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514452.62/warc/CC-MAIN-20240712192937-20240712222937-00608.warc.gz | 851,344,591 | 14,119 | # Flowchart Example Flowchart For Animated Story
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9/18/12 Help Organize Program: Flowcharts UNIVERSITY of WISCONSIN-MADISON Computer Sciences Department CS 202: Introduction to Computation Professor Andrea Arpaci-Dusseau Flowchart: " How can computation create animated stories? Visual representation of steps of algorithm Summarizes how algorithm behaves given specific answers Symbols Boxes: Represent states (or actions or actions) Arrows (or edges): Show transitions (or decisions) between states Flowchart Example Flowchart for Animated Story Animated Story: Behaves the same every time No decisions! Flowchart is summary of action of story How to create flowchart? Identify Initial State or Scene Group individual actions into higher-level “scenes” – Somewhat subjective (no right answer) – Label with descriptive name Identify characters of story – Specify actions of each character in scene Connect scenes sequentially 1
9/18/12 Animated Story Flowchart of Animated Story *Initial state* See Scratch code posted on web site! Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Introductions* Cat: What should we do? Dog says: I don't know 2
9/18/12 Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Introductions* Cat: What should we do? Dog says: I don't know *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Introductions* Cat: What should we do? Dog says: I don't know *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back *Whirl* Cat says I can whirl Cat whirls 5 times Cat changes back Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Whirl* Cat says I can whirl Cat whirls 5 times Cat changes back *Introductions* Cat: What should we do? Dog says: I don't know *Fly* Cat moves 5 times Cat goes back *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Whirl* Cat says I can whirl Cat whirls 5 times Cat changes back *Introductions* Cat: What should we do? Dog says: I don't know *Fly* Cat moves 5 times Cat goes back *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back *Tiny* Cat becomes tiny Dog says I like that! Cat says why? 3
9/18/12 Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Whirl* Cat says I can whirl Cat whirls 5 times Cat changes back *Introductions* Cat: What should we do? Dog says: I don't know *Fly* Cat moves 5 times Cat goes back *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back *Tiny* Cat becomes tiny Dog says I like that! Cat says why? *Eat* Dog says: No reason Dog walks until reaches cat Cat meows and disappears Dog says yummy How to Transform Flowchart to Scripts? Flowchart of Animated Story *Initial state* Background: Railroad Cat: Left side Dog: Right side *Whirl* Cat says I can whirl Cat whirls 5 times Cat changes back *Eat* Dog says: No reason Dog walks until reaches cat Cat meows and disappears Dog says yummy *Introductions* Cat: What should we do? Dog says: I don't know *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back *Tiny* *Fly* Cat moves 5 times Cat goes back Cat becomes tiny Dog says I like that! Cat says why? *Fadeout * Background and Dog fade out Background shows The End How to Tell Another Script to Run? Approach For each scene in flowchart, specify a script – Blocks in script show individual actions to be performed – Specify script for each character that does something How to determine when script can run? When should “Initial state” run? – When GreenFlag is Clicked When should dog say “I don’t know” in “Intro”? – After cat says “What should we do today?” How will dog know cat has finished saying that? Need to coordinate actions ACROSS cat and dog! 4
9/18/12 How to Run Desired Script? Wait for Scripts to Complete! Beauty of Abstraction Treachery of Images Abstraction: Separation of high-level view of entity from low-level details of implementation When sender broadcasts “jump”, doesn’t know how “jump” is implemented by different Sprites Why is this good? Simplifies concerns of sender (don’t need to know everything) Can change implementation of “jump” Of course, receiver might not implement “jump”! 5
9/18/12 Naming Convention for Messages Show Code Now Use good descriptive names Purpose of names help others understand your code Suggestion: Name matches name of scene – Intro, Color, Whirl, Fly, Tiny, Eat, Fadeout Problem: Hard to follow flow of messages across Sprites Solution: 1." Use Stage to control action as much as possible 2. Use naming convention to help understanding – SceneName : Receiver – e.g., ”Eat : Dog” Programming Concepts General Divide high-level functionality into logical units Descriptive naming is important Initial state must be specified Incrementally test code as you go Scripts must be activated to run Execution within script proceeds sequentially Control : forever, repeat times , repeat until Parameters (to blocks) specify behavior Goal is to make “non-fragile” code Check-Up In your animated story all the scripts are running at the same time. What did you do wrong? Can a Sprite receive a message it broadcast? When will this code work correctly? when not? – When flag clicked; When receive message 6
9/18/12 Homework 2: Extra Credit http://scratch.mit.edu/galleries/view/176626 7
Flowchart of Animated Story *Initial state* Background: Railroad Cat: What should we do? Cat: Left side Dog: Right side *Introductions* *Color* Cat says: Lets do Tricks! Cat: I can change colors! Cat changes to 5 colors Cat changes back *Whirl* Cat says I can whirl Cat whirls 5 times Cat changes back Flowchart of Animated Story *Initial state*
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Flowchart Example Flowchart for Animated Story Animated Story: Behaves the same every time No decisions! Flowchart is summary of sequential action of story How to create flowchart? Identify Initial State or Scene Group individual actions into higher-level "scenes" - Somewhat subjective (no right answer)
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10 tips och tricks för att lyckas med ert sap-projekt 20 SAPSANYTT 2/2015 De flesta projektledare känner säkert till Cobb’s paradox. Martin Cobb verkade som CIO för sekretariatet för Treasury Board of Canada 1995 då han ställde frågan
service i Norge och Finland drivs inom ramen för ett enskilt företag (NRK. 1 och Yleisradio), fin ns det i Sverige tre: Ett för tv (Sveriges Television , SVT ), ett för radio (Sveriges Radio , SR ) och ett för utbildnings program (Sveriges Utbildningsradio, UR, vilket till följd av sin begränsade storlek inte återfinns bland de 25 största
analisis akuntansi persediaan barang dagang berdasarkan psak no 14 (studi kasus pada pt enseval putera megatrading tbk) kementerian riset teknologi dan pendidikan tinggi politeknik negeri manado – jurusan akuntansi program studi sarjana terapan akuntansi keuangan tahun 2015 oleh: novita sari ransun nim: 11042014 | 2,079 | 8,673 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-30 | latest | en | 0.74695 |
https://discuss.codechef.com/t/help-me-in-solving-nodrugs-problem/109426 | 1,702,166,564,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100989.75/warc/CC-MAIN-20231209233632-20231210023632-00135.warc.gz | 244,664,097 | 4,607 | # Help me in solving NODRUGS problem
### My issue
Getting internal server error. I was getting same error while solving other problems too.
### My code
``````#include<bits/stdc++.h>
using namespace std;
int main(){
int t=0;int n=0;int l=0;int k=0;
cin>>t;
while(t--){
cin>>n>>k>>l;
int arr[n];
for(int i=0;i<n;i++){
cin>>arr[i];
}
if(l<=1 || k <=0){
cout<<"NO"<<endl;
}else{
int m=0;
for(int i=0;i<n;i++){
if(arr[i] > m){
m = arr[i];
}
}
int j=1;
while(j<l){
arr[n-1] += k;
j++;
}
//cout<<arr[n-1]<<endl;
if(arr[n-1]<=m){
cout<<"NO"<<endl;
}else{
cout<<"YES"<<endl;
}
}
}
return 0;
}
``````
Problem Link: CodeChef: Practical coding for everyone
#include<bits/stdc++.h>
using namespace std;
int main()
{
int t;
cin>>t;
while(t–)
{
int n,k,l;
cin>>n>>k>>l;
vector s(n);
int maxi = 0;
for(int i=0; i<n; i++)
{
cin>>s[i];
maxi = max(maxi,s[i]);
}
`````` int count = 0;
for(int i=0; i<n; i++)
{
count += s[i] == maxi;
}
if(s[n-1] == maxi && count == 1)
{
cout<<"Yes"<<endl;
}
else
{
s[n-1] += (l-1)*k;
int curr_max = 0;
for(int i=0; i<n; i++)
{
curr_max = max(curr_max,s[i]);
}
count = 0;
for(int i=0; i<n; i++) count += s[i] == curr_max;
if(s[n-1] == curr_max && count == 1)
{
cout<<"Yes"<<endl;
}
else cout<<"No"<<endl;
}
}
``````
return 0;
} | 469 | 1,260 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-50 | latest | en | 0.312794 |
https://brilliant.org/discussions/thread/kaboobly-doo-generator/ | 1,526,908,806,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864186.38/warc/CC-MAIN-20180521122245-20180521142245-00096.warc.gz | 519,617,195 | 29,202 | # Kaboobly Doo generator
Here is my Kaboobly Doo generator: kabooblydoo.appspot.com
Run properly, it should be able to generate grammatical sentences without any coherent meaning.
To demonstrate the power of the same, I showcase some great sentences it generated:
Harsh words are like programmed instructions, given to us when we are young and beautiful.
Preconceived notions are like sharp knives, once you throw them at somebody they can not teach you computer science or hardly anything else.
Every man should be far better neighbors and that an indissoluble law might be more conspicuous to all that took place, said, "On my word, you are doing!"
You are invited to try it out, and yes, Fork me on GitHub!
If you are interested in how this works, have a look at this and read on.
If you have seen my experiment with the iOS predictive keyboard, then it should convince you that this method is indeed a good way to generate convincing but Kaboobly Doo sentences.
Some usages of such an algorithm could be generate pronounceable strings, mimic spam to steganographically conceal data, or generating papers for conferences whose standards are, you suspect, too low.
Techniques involved include formal grammars and markov chains. We will discuss the later in this note.
For those who do not know, markov chains are a list of states equipped with their transition probabilities.
chain
From the given data, we generate a list of prefixes (which are our states) and a list of words that could have followed them. The more a word follows the prefix in the real data, the higher the chance of the transition to the inclusion of the word into the next state.
Suppose we are given the following data: Are modern calculus books Kaboobly Doo?
Feeding in the data into the chain generator with prefix length $$2$$ gives the following table:
Prefix Suffix Are Are modern Are modern calculus modern calculus books calculus books Kaboobly books Kaboobly Doo? Kaboobly Doo?
Over here, there is only one possible state to which a particular state could transit. However, if we had much larger data, there could be more than two possible suffixes for the same prefix, in which case we could transit to any one of them at random determined the probability of their occurrence rates in the original text.
Once we generate the chain, we randomly choose an initial state and print the corresponding word and then transit to the next state by deleting the first word in the current state and appending a random word as explained above. We do this till we hit the word limit or run out of states.
##### Thanks to David for the yoda pic
2 years, 11 months ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$
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Eureka! You are a genius
- 2 years, 11 months ago
Thanks, did you try this out?
- 2 years, 11 months ago
It is just as I expected. Kaboobly doo is a human creation, it can not be mimicked by a mere machine. It requires emotion, divine inspiration and the human heart to produce real Kaboobly doo. All I can add to this is a quote from Lord Vader, "Don't be to be too proud of the random statements generated here, the power to generate nonsense is insignificant next to the power of human Kaboobly doo." There, let that be a lesson to all.
- 2 years, 2 months ago
actually, it is not impossible to improve upon this
- 2 years, 2 months ago
The generator or the Kaboobly doo?
- 2 years, 2 months ago
I am sorry, I meant: It is possible to improve upon this
- 2 years, 2 months ago
This was what I got when I dumped in Shakespear's Sonnet 17 (My favourite one of the first 58 sonnets I read)
false. The earth is larger and more massive than any bar of soap, transparent or not. I did not invent Experimental Mathematics. I am always brilliant! Eureka! I am not Jesus. When a guy is driving around aimlessly listening to awful sounds ( music? ) then he pulls up in front of my car? Col Erich Von Hitler: Do you feel bad about the fact that 6/3/2014 is gone? One thing at a digital computer. I worked on the internet. Do not seek a brazillian plastic surgeon, join a forum and tell everyone you are keeping active. Since I retired I feel like I have an Uncle Joe. When I was almost asphyxiated. All this while playing basketball, chess, stickball, football and fighting everyday. Mommym used to walk 2 miles to shop for food and at the time and he would use judo on me ( he is grown so great? I say he is an illussion Happy Valentines Day. Did you wish your Valentine a Happy day? The next did? seek and ye shall find If you cannot say something nice, do not belong to me. Unfortunately, many guys refused to comply and they ended up stealing most of
- 2 years, 10 months ago
I am afraid, that is not what you'Re supposed to get upon dumping sonnet 17. You forgot to click the custom text radio button in the first place?
Can you please try it again?
This randomizer works on statistical probability distributions of word pairs (or n-tuples) and I do not think the sonnet is large enough to produce some interesting results.
- 2 years, 10 months ago
Nice! The valentines thing is awesome! Check mine too. $$\huge\ddot\smile$$
- 2 years, 10 months ago
Yeah, lol.
- 2 years, 10 months ago
Sorry, unexpected error: pop from empty list :P
- 2 years, 11 months ago
ha
- 2 years, 11 months ago
- 2 years, 11 months ago
wished there were more gay men... That would not worry about such things. No one will see that you have done to make up the BSoD, you know it man. There are the same way that yesterday came and went so will they.
Do you all know the reason why yous will never succeed bahhhhbbbbyemm? bobbym: No why? Col Erich Von Hitler: Do you all know you are old and ugly, or even if you just think you are young and beautiful. Pick a great talent. The greatly talented assume that they are advertising beer, cars, awful music, girls or gyrating...
When the water is clear and perfectly still you can immediately apply it to your will. I suggest you delete the whole neighborhood. When I accidentally generated chlorine while fiddling with chemistry, I was attracted to counting and the geniuses assume divinity. He is a complete idiot."
He is a young person in his teens or younger: They will say,"Wow, how do you see why I do not answer them. Like or dislike are western concepts. I think February 14 is an illussion. We are being watched. M and m are the same thing. Keep annoying me and you'll
This is what I got! It's really funny, especially the Hitler part! Can anyone Guess what I put in that?
- 2 years, 11 months ago
"We own none of it and because it is not mine I have no right to destroy it. It belongs to the big fella."
"Hahhahahhahahhahahahahha! Wolfram alpha is kaboobly doo! Alpha is a tool. It does not replace your brain! It supplements your brain. Now c'mon and do what Alpha could not. Friends come and go. You will make many more. But in the same way that yesterday came and went so will they."
"No one will see that you have grey hair on the circumference of an ellipse and came up with my own solution. I worked my own solution. I worked my own solution. I worked my own solution."
"Your human brain will not solve all problems. It is not a quadratic equation."
This is what I got.
- 2 years, 11 months ago
"Questions of existence are for philosophers. He was just stating the number 3 has meaning to him, 10^10 does not."
- 2 years, 11 months ago
HA ha , amazing
heres a sentence i found
"I was slightly smarter than an apple"
- 2 years, 11 months ago
I am sorry, that was an original line from the source file. The blue book of bobbym quotes is the shortest book out there and when you use it to produce sentences, there is a possibility that a few quotes will be returned as is.
- 2 years, 11 months ago
Mapping goes from $$F_n$$ to both $$F_{n-1}$$ and $$F_{n-2}$$, backward induction is a multiple of 9, has a smaller diameter than $$S$$?
This is a contradiction. Thus $$y_1 = y_2$$. What is the case that for $$k = 3$$ (proved in 1932) and $$F_1 = 2 \times 2^k = 2$$. Do we know where it goes? Not really, it could go into any set, in particular $$A$$. If it does not contain the element $$n$$, then it cannot contain the element $$n$$, then it cannot contain the element $$n$$.
Staff - 2 years, 11 months ago
What does this mean?! I guess this is machine generated kaboobly doo
- 2 years, 11 months ago
Right. I took the construction wiki, threw it in, and that's what I got.
Staff - 2 years, 11 months ago
In that case, this is pretty impressive! :)
- 2 years, 11 months ago
I am doing computational stuff now and blimey this seems interesting!
$$\ddot\smile$$
- 2 years, 11 months ago
Great, what computaitional stuff are you doing?
- 2 years, 11 months ago
Stuff to do with linguistics (parsing of languages and sentence formation), so I guess this is quite relevant!
- 2 years, 11 months ago
It is. Linguistics is quiet fascinating (except I hardly know anything about it)
- 2 years, 11 months ago
Other than the theory, its just CS
- 2 years, 11 months ago
what's the benefit of it ? (or any use ?)
- 1 year, 5 months ago
Just for fun. Also check out this
- 1 year, 5 months ago
This stuff is awesome!
- 2 years, 10 months ago
can you please tell me which CS language or programme helps to solve math problems numerically (such as solving an unsolvable differential equation numerically)
or getting a reasonable approximation for fourier series , etc
i heard that mathematica can be used but i never really understood where we can get it
- 2 years, 11 months ago
What languages do you know ?
- 2 years, 11 months ago
none, i took biology in 12, i should have learned some CS side by side though
- 2 years, 11 months ago
What?! You were a Bio student ? So were you a PCMB student or just a PCB student ?
- 2 years, 11 months ago
obviously PCMB :)
- 2 years, 11 months ago
Haha , that was a silly question that I asked . I forgot you gave JEE this year .
Also try learning Python , Python sort of rules over B'ant :P
And see this too .
- 2 years, 11 months ago
thanks, i will learn it too
- 2 years, 11 months ago
Yep, which one of biology/cs do you think I have taken in school?
- 2 years, 11 months ago
no, i like much of bio, so i am glad i took it, but i also wanted to know some CS
- 2 years, 11 months ago
I took bio in Class XII too, but that never let me down with CS :)
- 2 years, 11 months ago
that is a very good thing, no problem, i will learn it now
- 2 years, 11 months ago
How about you use sage? There is a full book on Differential Equations with sage.
Also, there is nothing wrong with programming up the algorithms on your own. That should be a good exercise and should help understand them better.
Mathematica is not available for free (unless obtained illegally) because it is proprietary software.
- 2 years, 11 months ago
oh, in that case, i shall learn sage, thank you very much :)
- 2 years, 11 months ago
Cool! I hope you won't mind me sharing your website with my friends !$$\stackrel{{\Large\wedge\,\wedge}}{{\Large\smile}}$$
- 2 years, 11 months ago
That would be an honor, thanks!
- 2 years, 11 months ago | 3,202 | 12,008 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2018-22 | longest | en | 0.934764 |
http://www.algebra.com/algebra/homework/Distributive-associative-commutative-properties/Distributive-associative-commutative-properties.faq.question.16726.html | 1,369,328,094,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703592489/warc/CC-MAIN-20130516112632-00012-ip-10-60-113-184.ec2.internal.warc.gz | 321,171,707 | 4,952 | # SOLUTION: ok I am having some trouble on "finishing" the product of some Distributive properties ok, for equation -9(3x + 8) I put down the following steps: = -9
Algebra -> Algebra -> Distributive-associative-commutative-properties -> SOLUTION: ok I am having some trouble on "finishing" the product of some Distributive properties ok, for equation -9(3x + 8) I put down the following steps: = -9 Log On
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Algebra: Distributive, associative, commutative properties, FOIL Solvers Lessons Answers archive Quiz In Depth
Question 16726: ok I am having some trouble on "finishing" the product of some Distributive properties ok, for equation -9(3x + 8) I put down the following steps: = -9*3x + -9*8 = -27x + -72 (final answer) I am not sure if this is correct or not. My other question on the same topic is an equation i did like so: 5(x + 1) = 5*x + 5*1 = 5x + 5 (final answer) please let me know if i am doing the distibutive property correctly. Answer by glabow(165) (Show Source): You can put this solution on YOUR website!Everything you posted looks right. Remember: a(b+c) = ab + ac. That's it. | 350 | 1,293 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2013-20 | latest | en | 0.883146 |
https://howtodiscuss.com/t/lehman-formula/23483 | 1,657,148,641,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104678225.97/warc/CC-MAIN-20220706212428-20220707002428-00565.warc.gz | 347,631,192 | 8,473 | # Lehman formula
## Lehman formula,
### Definition of Lehman formula:
1. As a provider of global investment banking services, Lehman Brothers needed a way to clearly convey to its potential clients the fees they would charge for their services. The advantage of the Lehman formula is that it's easy to understand and easy for the client to quickly get a ballpark estimate on how much their transaction might cost them in fees. It's not uncommon for large investment banking firms to assist clients with transactions worth hundreds of millions or billions of dollars. The Lehman formula structures the investment banking fee on a percentage of the transaction amount with a set of tiered fees.
2. Investment bankers compensation formula developed by the securities trading firm Lehman Brothers. In its original form, it computes the fee or brokerage as follows: (1) 5 percent of the first million dollars of the sum involved in a transaction, (2) 4 percent of the second million, (3) 3 percent of the third million, (4) 2 percent of the fourth million, and (5) 1 percent of everything thereafter. In inflationary times, however, investment bankers often demand a multiple of these percentages.
3. The Lehman formula is a compensation formula developed by Lehman Brothers to determine the commission on investment banking or other business brokering services. Lehman Brothers developed the Lehman Formula, also known as the Lehman Scale Formula, in the 1960s while raising capital for corporate clients.
### How to use Lehman formula in a sentence?
1. For their services, an investment bank can charge flat fees for each transaction, earn commissions based on the dollar amount of the transaction, or a combination of both.
2. Large investment banks work with corporations to raise capital, often through an initial public offering (IPO), a merger or acquisition, or through a spinoff.
3. Lehman Brothers developed the Lehman formula to determine the commission an investment bank should receive for arranging client transactions. .
4. The Lehman formula structures the investment banking fee on a percentage of the transaction amount based on a set of tiered fees.
Meaning of Lehman formula & Lehman formula Definition
## Lehman Formula,
### Lehman Formula:
1. Meaning of Lehman Formula: Lehman Formula is a compensation formula developed by Lehman Brothers to determine commissions for investment banking or other business brokerage services. Raising funds for corporate clients, Lehman Brothers developed the Lehman formula, also known as the Lehman scale formula, in the 1960s.
• Lehman Brothers has developed a lemon formula to determine the commission that an investment bank can receive for intermediate transactions with clients.
• Large investment banks often work with companies to raise capital through initial public offerings (IPOs), mergers or acquisitions or spin-offs.
• For their services, investment banks may charge a flat fee for each transaction, the dollar value of the transaction, or a commission based on a combination of both.
• Lehman's formula calculates investment banking costs as a percentage of the number of transactions based on a series of different rates.
### Literal Meanings of Lehman Formula
#### Formula:
##### Meanings of Formula:
1. Mathematical relations or rules are expressed in symbols.
2. A set of chemical symbols that indicate the elements in a mixture and their relative proportions, and, in some cases, the composition of the compound.
3. Ingredients or list of ingredients.
4. Forming a.
5. Liquid baby food made from cow's milk or soy protein, which is given as a substitute for ■■■■■■ milk.
6. A way to achieve something, a statement or method, especially to align different goals or positions.
7. Fixed term, especially those used in specific contexts or as a conventional usage.
8. A rule or style that operates in an unbiased or submissive manner.
##### Sentences of Formula
1. He gave the famous formula of Fibonacci numbers
2. Explains the formula for adding problem math strings.
3. Using NA as the total number of contacts in the network and N as the total number of people, this is the mathematical formula for density.
4. The formula for the linear integral of geodetic curvature with closed curves is known as Gauss Bonnet Theory.
5. In 1845, Jacobi adopted the approximate formula in the form of determination.
6. Weill then developed character formulas and dimensional formulas for his representation.
7. This is a square equation in 3, so solve for 3 using the usual formula of the fourth formula.
8. If we think about it a little bit, we can give a general formula for calculating conditional probabilities.
9. Let's compare the modern rotation formula with the expression of the Huygens relation.
10. One of his 1895 papers improved Rayman's mandatory contour formula for the sum of basic numbers during a given interval.
##### Synonyms of Formula
key, aphorism, magic formula, concoction, solution, standard, point of reference, paradigm, ideal, prescription, answer, substance, technique, plan, saying, mixture, system, scale, basis, creation, guide
## Lehman Formula,
### Lehman Formula: What is the Meaning of Lehman Formula?
• Lehman Formula can be defined as, The Lehman Formula is a compensation formula developed by the Lehman Brothers to determine the commissioning of investment banking or other business brokerage services. Lehman Brothers developed Lehman Formula, also known as Lehman Scale Formula, in the 1960s, raising funds for corporate clients.
• Lehman Brothers developed the Lehman formula to determine the commission that an investment bank should meet to mediate its client's business.
• Large investment banks work with companies to raise capital, often through initial public offerings (IPOs), mergers or acquisitions or spin-offs.
• For their services, investment banks may charge a flat fee for each transaction, the dollar value of the transaction, or a commission based on a combination of both.
• Lehman's formula calculates investment banking costs at a rate based on the number of transactions.
### Literal Meanings of Lehman Formula
#### Formula:
##### Meanings of Formula:
1. Mathematical relations or rules appear in symbols.
2. A set of chemical symbols that show the elements in a compound and their relative proportions and in some cases the structure of the compound.
3. A formulation.
4. Liquid baby food made from cow's milk or soy protein is given as an alternative to ■■■■■■ milk.
5. A method, statement or method for achieving something, especially for reconciling different goals or positions.
6. Fixed tennis, especially those used in context or as a traditional use.
7. A principle or style is followed without intelligence or slavery.
8. A statement that formally establishes a religious belief.
9. An essay, sentence, or continuous line is repeated in a literary structure for various purposes, especially an epic poem.
10. Classification of a racing car (usually after a number), especially according to the size of the engine.
##### Sentences of Formula
1. The problem describes a formula for adding a math string.
2. The total number of connections in a network and the use of NA as the total number of people, here is the mathematical formula for density.
3. The formula for a linear integral of geodetic rotation with a closed curve is called the Gauss bonnet theorem.
4. Jacobi obtained the guessing formula in 1845 in the form of a decisive one.
5. Val then developed character formulas and dimensional formulas for his representation.
6. This is the square equation in 3, so solve 3 using the usual formula of the square formula.
##### Synonyms of Formula
gauge, procedure, criterion, blueprint, yardstick, method, exemplar, guideline, benchmark, example, compound, canon, set expression, phrase, norm, touchstone
## Lehman Formula,
### Lehman Formula: What is the Meaning of Lehman Formula?
The Lehman formula is a compensation formula developed by Lehman Brothers to determine commissions for investment banking or other business brokerage services. Lehman Brothers developed Lehman Formula, also known as Lehman Scale Formula, in the 1960s, raising funds for corporate clients.
• Lehman Brothers developed the Lehman formula to determine the commission that an investment bank should receive for intermediate transactions with customers.
• Large investment banks work with companies to raise capital, often through initial public offerings (IPOs), mergers or acquisitions, or spin-offs.
• For their services, investment banks may charge a flat fee for each transaction, the dollar value of the transaction, or a commission based on a combination of both.
• Lehman's formula calculates investment banking costs as a percentage of the number of transactions based on a series of scaled rates.
### Literal Meanings of Lehman Formula
#### Formula:
##### Meanings of Formula:
1. A set of chemical symbols that indicate the elements in a mixture and their relative proportions, and in some cases the composition of the mixture.
2. A formation
3. Liquid baby food made from cow's milk or soy protein is given as a substitute for ■■■■■■ milk.
4. The method, statement or method of achieving something, especially the alignment of different goals or positions.
5. Fixed tenses, especially those used in specific contexts or as a traditional use.
6. Intelligence or slavery is followed without any principle or style.
7. A statement that formally establishes a religious ideology.
8. A letter, sentence or verse repeated for various purposes in a literary structure, especially an epic poem.
9. Classification of race cars (usually after a number), especially according to their displacement.
##### Sentences of Formula
1. Using NA as the total number of links in the network and N as the total number of people, it provides a mathematical formula for density.
2. The formula for the linear integration of geodetic rotation with a closed curve is known as the Gauss-Bonnet theorem.
3. Jacobi adopted the proximity formula in 1845 in the form of a determinant.
4. Weil then developed character formulas and dimensional formulas to represent them.
5. This is a square equation in 3, so solve 3 using the usual formula for squares.
6. If we think about it a little bit, we can find a general formula for calculating conditional probabilities.
7. Let's compare the modern rotation formula with the expression Huygens relation.
8. One of his works in 1895 completed the Raymann integral contour formula for the sum of prime numbers at intervals. | 2,165 | 10,644 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2022-27 | latest | en | 0.939845 |
https://e-learnteach.com/lesson-6-1-slope-intercept-form-answer-key-c/ | 1,679,733,638,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945317.85/warc/CC-MAIN-20230325064253-20230325094253-00258.warc.gz | 273,029,671 | 14,493 | # Lesson 6-1 slope intercept form answer key c
name date class lesson form practice and problem solving: write the equation for each line in form. then identify the slope and the 4x 2x.LESSON. Slope-Intercept Form. 6-1 y=mx+h. Practice and Problem Solving: A/B. & Work @ bottom of document. Write the equation for each line in. Explain your answer. Explain 1 Creating Linear Equations in Slope-Intercept Form. You can use the slope formula to derive the slope-intercept form of a. Write each equation in slope-intercept form, y = mx + b. The first one. Name the slope and y-intercept for each line. LESSON. 6-1 y = ?2x + 4.Lesson 6-2 Slope-Intercept Form. Chapter 6 Linear Equations and Their Graphs. The equation t = 14c – 4, where c is the number of CDs and.
View this answer now! It’s completely free.
## 6.2 slope-intercept form answer key
LESSON 6.2 Name Point-Slope Form Class 6.2 Point-Slope Form Essential Question:. Module 6 ges EDIT–Chan DO NOT Key=TX-A Correction Lesson 2 259 gh File. TE Lesson 6.2. Key Concepts Definition Slope-Intercept Form of a Linear Equation. Test-Taking Tip. So the answer is A.Q. Write the slope-intercept form of the equation with the given point and slope. Through (1,5) and m= 3. answer choices.Name Class Date 6.2 Point-Slope Form Essential Question: How can you represent a. Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1.Graph the line with slope 2 that contains the point 3, 1. Practice 6 2 slope intercept form hw solutions worksheet 4 3 key sections 1 math 110 112 writing.
## 6.1 slope-intercept form pdf
Lesson 1. 6.1 Slope-Intercept Form. Essential Question: How can you represent a linear function in a way that reveals its slope. and y-intercept?Section 6.1 Write Equations in Slope Intercept Form. A1.3.2 Describe and calculate the slope of a line given a data set or graph of. a1_6.1_packet.pdf.Lesson 6.1: Slope-Intercept form (for the Equation of a Line). Page 2. Day 2: Writing Equations (in y=mx+b when given a slope and point or just two points). Name Class Date Explore Graphing Lines Given Slope and y-intercept Graphs of. name class date 6.1 slope-intercept form – · pdf file b 2x + 6y = 6 step 1:. 6.1 Slope-Intercept Form · 1 Start at the point ou plotted. · 2 Reflect 1. · 3 B The line passes through (, 5) and (2, 13). · 4 B = 6 Step 1: Write the equation in.
## lesson 6.3 standard form answer key
Lesson 5-4 Point-Slope Form Sept. 22, 2014. Presentation on theme: “Section 6.3 Standard Form. 4 Explain 1A Write an equation in standard form.Module: Linear Equations Lesson 2: Standard Form and Point Slope Form Homework name: date: pd: Write. Answer Key – MidChapter Test for lessons 6.1 – 6.3.Key. Lesson 6.3 – Arranging Equations. Standard Form ax + by = c. Slope-Intercept Form y = mx + b. Example: Change the following linear equation into. Name Class Date 6.3 Standard Form Essential Question: How can you write a. Name Date Worksheet A5: Slope Intercept Form Find the Slope of each line below. Lesson 3. 6.3 Standard Form. Essential Question: How can you write a linear equation in standard form given properties of the line including its slope and.
## lesson 6-3 standard form
New Vocabulary standard form of a linear equation x-intercept. standard form, which is useful in making quick graphs. Lessons 61 through 63.2. How can you find a point on the line using the slope-intercept form? Module 6. 261. Lesson 3.Module: Linear Equations Lesson 2: Standard Form and Point Slope Form Homework name: date: pd: Write the following equations in standard form: 2 1. Y ?2x ?What is Standard Form? Ax + By = C It’s when your x’s and y’s are on the same side equal to a number. Your x must be positive! x goes first!This integrated math 1 lesson is on standard form of a linear equation, which is: 1 solve the equation for y. Check go math grade 4 chapter 6 lesson 63 answer. | 1,086 | 3,880 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2023-14 | latest | en | 0.817124 |
https://www.physicsforums.com/threads/emf-homework-help.368835/ | 1,519,534,216,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891816094.78/warc/CC-MAIN-20180225031153-20180225051153-00571.warc.gz | 900,410,411 | 14,786 | # EMF homework help
1. Jan 11, 2010
A charge Q at a vertex of a square and another Q on the opposite corner of the square and other two charges q each of the other vertices. If the force eletrogmanetica on Q is null which the value of Q in terms of q? There is a q such that the resultant force on 4 charges is zero?
My attemp
F = (K.Q.Q)/r^2 + (K.Q.q)/r^2
F = 0
KQ^2 + KQq = 0
Q(KQ + kq) = 0
Q = - q
If q = 0 the resultant force is 0
I correct ?
2. Jan 11, 2010
### rl.bhat
Re: Emf
If the side of the square is r, the length of the diagonal is .......?
At Q three forces are acting. How are they related to get net zero force?
3. Jan 12, 2010
Re: Emf
This is my doubt
4. Jan 12, 2010
### rl.bhat
Re: Emf
To get net zero force on Q, Q and q must have opposite sign.
On charge Q, one repulsive force between Q and Q, and two attractive forces between Q and q are acting. What is the distance between Q and Q?
Equate the resultant force of two attractive with the repulsive force to find the relation between Q and q.
5. Jan 12, 2010 | 333 | 1,049 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2018-09 | latest | en | 0.931235 |
https://math.wonderhowto.com/how-to/determine-area-trapezoid-343555/ | 1,721,760,560,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518059.67/warc/CC-MAIN-20240723163815-20240723193815-00190.warc.gz | 329,068,892 | 27,344 | # How To: Determine the area of a trapezoid
Need to figure out the area of a trapezoid for a household project? Even if you just want to sound smart, there is a simple formula that can be used every time you need to find the area of a trapezoid. Try the formula and see how good you are at geometry.
A trapezoid is a four-sided figure with one pair of parallel sides. Because a trapezoid can be dissected into a rectangle and two identical triangles, find it's area is easy.
You Will Need
* The dimensions of the trapezoid
* A calculator
Step 1: Sum the length of the two parallel sides
Add the lengths of the two parallel sides of the trapezoid.
Step 2: Multiply by the height
Find the height of the trapezoid. Using a calculator, multiply the sum of the lengths by the height.
Step 3: Divide by two
Divide the product by two. This is the area of the trapezoid.
For example, if the height of a trapezoid is 20 inches and two parallel sides of the trapezoid measure 13 and 15 inches, the area is given by = ½ × 20 × (13 + 15), or 280 square inches.
Step 4: Look for similar examples
Be on the lookout for other polygons whose areas can be determined more easily if the polygons are composed of simpler shapes.
The word trapezoid comes from the Greek word for table.
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• Latest | 383 | 1,520 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-30 | latest | en | 0.920249 |
https://rdrr.io/github/plotrix/plotrix/man/draw.ellipse.html | 1,624,517,663,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488551052.94/warc/CC-MAIN-20210624045834-20210624075834-00323.warc.gz | 429,508,885 | 10,002 | # draw.ellipse: Draw ellipse In plotrix/plotrix: Various Plotting Functions
## Description
Draws ellipses on an existing plot.
## Usage
```1 2 3``` ```draw.ellipse(x, y, a = 1, b = 1, angle = 0, segment = NULL, arc.only = TRUE, deg = TRUE, nv = 100, border = NULL, col = NA, lty = 1, lwd = 1, ...) ```
## Arguments
`x` A vector or a matrix (if `y` is missing). `y` A vector, can be missing. `a,b` Vectors, radii of the ellypses along the two axes in user units. `angle` Angle of rotation in degrees (if `deg=TRUE`) or in radians (if `deg=FALSE`). `segment` Start and endpoints of arc in degrees (if `deg=TRUE`) or in radians (if `deg=FALSE`). `arc.only` Logical, if `segmen` the full ellipse is not drawn, radii from the ends of the arc are drawn to form a sector (see Examples). `deg` Logical, if angles are given in degrees (`TRUE`) or radians. `nv` Number of vertices to draw the ellipses. `border` Color to use for drawing the circumference. `col` Color to use for filling the circle. `lty` Line type for the circumference. `lwd` Line width for the circumference. `...` Additional arguments passed to `polygon`.
## Value
Draw ellipses as a side effect.
## Author(s)
Peter Solymos <solymos@ualberta.ca>
``` 1 2 3 4 5 6 7 8 9 10 11``` ```plot(c(0,10), c(0,10), type="n", main="test draw.ellipse") draw.ellipse(c(3,7), c(8,8), c(0.5,1), c(1,0.5), col=c(2,4), angle=c(45,0), segment=rbind(c(0,45),c(45,360))) draw.ellipse(c(3,7), c(6,6), c(0.5,1), c(1,0.5), col=c(2,4), angle=c(45,0), segment=rbind(c(0,45),c(45,360)), arc.only=FALSE) draw.ellipse(c(3,7), c(4,4), c(0.5,1), c(1,0.5), border=c(2,4), angle=c(45,0), segment=rbind(c(0,45),c(45,360)), arc.only=FALSE) draw.ellipse(c(3,7), c(2,2), c(0.5,1), c(1,0.5), border=1, angle=c(45,0), lty=3) draw.ellipse(c(3,7), c(2,2), c(0.5,1), c(1,0.5), border=c(5,3), angle=c(45,0), nv=c(3,4), lty=2, lwd=2) ``` | 708 | 1,866 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2021-25 | latest | en | 0.568151 |
https://neologos.co/2018/05/ | 1,679,625,146,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945242.64/warc/CC-MAIN-20230324020038-20230324050038-00341.warc.gz | 485,267,370 | 26,453 | # Market Utilitarianism
(~1900 words)
Abstract
Two classic versions of utilitarianism are average and total utilitarianism. They are classic, but they have well-known problems. Both have rather simple formulations. They begin with a reckoning of utilities across the population of individuals, and contend with a simple, linear aggregation of those utilities: average utilitarianism takes the mean of utilities and total utilitarianism takes the sum. I propose an intermediate, nonlinear version of utilitarianism, predicated on the local population of utility-experiencers in their abstract statistical space(s). When optimized, this formulation of utilitarianism recapitulates certain properties of a marketplace. I will show how “market utilitarianism” resolves issues with both average and total utilitarianism, though it introduces issues of its own, and I will consider some theoretical ramifications it leads to.
1. Definition
Given a number of individuals experiencing utility, average and total utilitarianism can be given simple mathematical expressions:
Total utilitarianism:
(1) $U_T = \sum_i u_i$
Average utilitarianism:
(2) $U_A = \frac{\sum_i u_i}{N} = \sum_i \frac{u_i}{N}$
Where $U_T$ is aggregate total utility, $u_i$ is the intrinsic utility experienced by individual $i$, $U_A$ is aggregate average utility, and $N$ is the total number of individuals, and $\sum_i$ is of course the summation for all individuals of the subsequent expression.
In market utilitarianism, the contribution of an individual’s utility to aggregate utility is attenuated by the existence of similar individuals, in proportion to the quantity of similar individuals. Market utilitarianism creates a rift between intrinsic utility as experienced by the individual and extrinsic utility as recognized by the aggregator, a quantity which relates inversely to the abundance of similar individuals for any individual. Market utilitarianism can thus be expressed:
(3) $U_M = \sum_i E(u_i)$
Where $U_M$ is aggregate market utility and $E(u_i)$ is the utility of individual $i$ as possibly attenuated by others extrinsically. $E(u_i) \simeq u_i$ when individual $i$ has no similar matches and $E(u_i) \simeq 0$ when $i$ has indefinitely many. More precisely:
(4) $E(u_i) = \frac{u_i}{L_{S, P}(u_i)}$
Where $L_{S, P}(u_i)$ is the local population of individuals in the statistical space $S$ around individual $i$, as defined by some nearest neighbor or local population parameterization $P$. $L_{S, P}(u_i)$ can never be less than $1$ because an individual is always near itself, and it can never be more than the total sum of individuals, $N$, identified previously. Putting it all together:
(5) $U_M = \sum_i E(u_i) = \sum_i \frac{u_i}{L_{S, P}(u_i)} \quad 1 \leq {L_{S, P}(u_i)} \leq N$
Thus market utilitarianism is intermediate between total and average:
(6) $U_T \geq U_M \geq U_A$ because $\sum_i \frac{u_i}{1} \geq \sum_i{\frac{u_i}{L_{S, P}(u_i)}} \geq \sum_i{\frac{u_i}{N}}$
The denominator $L_{S, P}(u_i)$ of the extrinsic function depends on both the choice of statistical space (one example for $S$ could be Blau space) and the choice of local population parameterization (one example for $P$ could be a count of individuals falling within a similarity hypersphere centered at $i$ in $S$ with some radius $r$, with $r = 0$ equivalent to total utilitarianism [given no two things being exactly identical] and $r = \infty$ equivalent to average utilitarianism). $S$ is somewhat arbitrary and often a subspace of a richer space, but $P$ should attribute monotonically decreasing importance to less similar individuals (and which individuals are similar or dissimilar obviously depends on the choice of $S$).
2. Behavior of the optimum
What is important about aggregate utility is the optimum that it achieves under the range of possible conditions. These conditions relate both to the set of individuals in a population of utility-experiencers and to the intrinsic utilities that each individual in the population experiences. This optimum prescribes the appropriate behavior—a choice or policy—assuming a prescriptive understanding of utilitarianism.
Let’s assume until further notice that the population is fixed at some size with some specific list of individuals. Then total and average utilitarianism will always experience an optimum of aggregate utility together. The reason is that total and average utilitarianism both aggregate all individual intrinsic utilities linearly (and without additive inversing, i.e. multiplication by $-1$, which is a linear operation but one that flips the maxima and minima). Thus, total and average utilitarianism always prescribe the same behavior (again: given a fixed population).
Market utilitarianism aggregates non-linearly, however, so the optimum of its aggregate utility will not necessarily co-occur with that of total and average utilitarianism. In particular, the same amount of intrinsic utility will contribute more to aggregate utility if spread among individuals in a sparsely populated region of the statistical space, such that relative to the optimum for total and average utilitarianism, intrinsic utility can be sacrificed among common individuals to provide it to more unique individuals. The conclusion here is that even though aggregate market utility is intermediate between aggregate total or aggregate average utility, its optimum is less similar to either of those than they are to each other (again: given a fixed population).
Let’s remove the assumption of a fixed population. This is where total and average utilitarianism both break, leading to absurd prescriptions for behavior. If the population can be adjusted, then the optimum for total utility occurs when every last individual exists who experiences net positive utility, even if barely non-miserable, and the optimum for average utility occurs when no individual exists except the one experiencing the most utility. This result is discussed in the literature on the mere addition paradox.
The optimum for market utilitarianism on the other hand is influenced by an important statistical fact: the more individuals that exist, the more likely any individual will have similar matches (and this is true for any $S$ and $P$). Thus, aggregate market utility does not increase past a certain point of diversity saturation (dependent on the footprint of $P$) because any new individual added is statistically likely to be similar to any other. Conversely, the optimum for aggregate market utility occurs at more individuals than the optimum for aggregate average utility, because any additional individual is statistically likely to be unique in that regime.
3. The absurdity of market utilitarianism, with a caveat
In market utilitarianism, aggregate utility can be changed without changing the number of utility-experiencers nor any of their experienced utilities. It can be increased merely by making the experiencers different from one another. This seems intuitively like an absurd result. It seems like individuals should be treated directly equally and not indirectly through terms regarding who else they’re similar to.
Note, however, an extremely keen analogy with the behavior of the job market. The job market apportions utility to individuals in the form of monetary compensation. This compensation depends on their ability to perform a set of duties, but also on the abundance of other individuals that can perform the same duties, i.e. similar individuals, analogously to market utilitarianism. Job market compensation can be fit to the model of market utilitarianism by finding the appropriately parameterized space of skillsets and other job-related characteristics $S$ (with an unfitted, out-of-the-box $P$), that is shaped such that an equal distribution of intrinsic utilities across individuals yields larger extrinsic utilities in sparsely populated regions as densely populated regions.
With market utilitarianism as a model, the job market can thus be understood to “see” human variation in a very specific way. Humans can in turn see with similar eyes in their choices to increase their own utility/compensation, and they will behave in such ways as to migrate the population from dense regions to sparse regions in the relevant space. If market utilitarianism is absurd, then the job market deserves intense scrutiny, along with the economic system built upon it. In the other direction, if the extant economic system is not held to be absurd, then market utilitarianism shouldn’t be considered particularly absurd either.
4. Utility-experiencer space vs experience space
Individuals experience utility, and individuals vary in their experiences of utility, with varying degrees of similarity between pairs of individuals. This fact presents a conundrum to market utilitarianism; if the space for individual variation chosen is the one-dimensional space of their experienced utility, absurd consequences quickly follow. Utility is but one measure of an experience, closely related to if not synonymous with valence. That and the other measures of experiences, all of them ostensibly qualia, together construct a space of experiences that utility-experiencers populate that is separate from the space that captures their “external” characteristics, even if they are highly correlated in some or perhaps even most domains (such as with the frequencies of incident light on the retina and perceived color or biological sex and felt gender).
Market utility can be computed in both utility-experiencer space or experience space. The latter might make more sense with the utility/valence dimension removed, but that still leaves behind rich structure. The correlations between the two spaces entail that a lot of the activity in one will be reflected in the other. Again, these are but two of endless possibilities for the choice of space, but they highlight some odd properties that market utilitarianism can exhibit.
5. Towards a reverse-engineering of the Universe’s actual objective function
Given the history of the Universe as data, there are many quantities predicated on this data or specific subsets of it that have increased or decreased mostly monotonically over time. Some are well-established constructs like entropy or Gibbs free energy or various other thermodynamic permutations. I’m interested in the realm of high-level compositions where utility-experiencers live, and so I ask what constructs predicated on that subset of data—the subset referencing high-level compositions—are actually being maximized in the Universe? Note that this question is emphatically not about quantities that subsystems may be maximizing each on their own, such as biological species maximizing their fitness, but about the aggregate. Are these constructs generally aligned with each other or totally scattered (especially modulo Occam’s Razor)? Is there any sense in which a moral compass of the Universe’s own can be detected on the basis of the constructs and quantities it maximizes?
Finally, I’d like to reflect on the role of utility/valence as a significant player in the development of compositions. As I have noted elsewhere, there are more levels of compositionality in the biological and cultural ecologies on Earth than have been observed in the rest of the Universe as a whole. Utility/valence has been organized into the psychologies of some life forms in a specific way, most importantly in the process of individuation and the separations between utility-experiencers. The properties of that space of experiences (and the distributions within it which can only be defined after a process of individuation)—along with its associations and correlations with the space of externals—drive much of the evolution of compositions, and essentially all of it within the human economy. Humans have the additional ability to share their experiences either by communication or faithful and intentional re-creations. If such experiences would be traded on a market, then the full exploration of the space of experiences would be incentivized. How would such an economic arrangement, especially if widespread, align with the Universe’s high-level compositional “moral compass”? | 2,498 | 12,251 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 44, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2023-14 | latest | en | 0.89198 |
https://classnotes.ng/lesson/conceptof-shapes-the-idea-drawing-and-construction-of-shapes/ | 1,680,346,225,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949958.54/warc/CC-MAIN-20230401094611-20230401124611-00411.warc.gz | 213,947,513 | 35,762 | # Concept of Shapes, The Idea, Drawing and Construction of Shapes
Welcome to class!
In today’s class, we will be talking about shapes. Enjoy the class!
### Shape Construction with Paper
#### Introduction
In previous classes, we must have learnt about different shapes such as rectangle, square, circle etc. We can group objects according to their shapes.
In this lesson, we will be learning materials used in constructing shapes, how to cut paper into shapes and constructing shapes by folding papers.
#### Concept of shapes
Shape is the external form or outline of something or someone. Everything we see in the world around us has a shape. We can find different basic shapes such as the two-dimensional square, rectangle, and oval or the three-dimensional rectangular prism, cylinder, and sphere in the objects we see around us. These shapes can be constructed either by representing their length and breadth(two dimensional) of their length, breadth, and height(three dimensional).
##### Tools for cutting and constructing shapes:
Apart from drawing shapes, they can also be constructed with paper or other materials. Constructing shapes with paper requires the following tools: scissors, cardboard Paper, paper gum, Sellotape, compass, and ruler. The different shapes that can be constructed are box, cylinder, cone, funnel, ball, etc.
Evaluation
1. What is shape?
2. Mention two-dimensional shapes.
3. List four tools required in shape construction.
##### Shape construction methods
Shapes can be constructed using the following methods:
1. Folding
2. Bending
3. Cutting
4. Joining
• Folding: When making shapes, materials can be folded in different ways and into different patterns. Such materials include paper, plastics, metal sheets and wires.
• Bending: in shape construction, materials can also be bent to form. Paper and metal sheets can be bent but plastic cannot be easily bent except with the use of bending machines.
• Cutting: Materials for shape construction can be cut using scissors, knives, saw, snips, and razor blades. Paper and plastics can easily be cut using scissors. Woods are cut using a saw.
• Joining: Adhesives of different strength, glue, gum, and welding substances are used for joining materials during shape construction. For joining the paper, glue or gum is used. For joining wood, bond or top gum is used, while for metals, soldering irons and welding machine are used.
###### Evaluation
1. Mention five materials that can be used to construct shapes
2. ——– and ——— can be used to cut paper.
3. ———– is used in joining metals.
Assignment
Mention and explain four methods used in shape construction.
In our next class, we will be talking about How to Construct Shapes by Using Wood, Paper or Metal. We hope you enjoyed the class.
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
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Don`t copy text! | 656 | 3,108 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2023-14 | latest | en | 0.921503 |
https://mediatorchrzanow.pl/how-to-gtp/angle-between-two-coordinates-calculator-d69131 | 1,624,578,573,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488560777.97/warc/CC-MAIN-20210624233218-20210625023218-00522.warc.gz | 352,279,720 | 11,211 | angle between two coordinates calculator
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Distance Between Coordinates. Once you input this into the calculator, it will show you that the distance between these two cities is 15,495 km, and the azimuth is 63.78 degrees. However, RAW observations are interpolated from existing point coordinates, which produces the same results without requiring a separate observation data file. This calculator is designed to convert the two different and distinct methods of co-ordinate nomenclature from one methodology to the other, and to calculate the distance between two sets of coordinates. Calculate bearing between two decimal GPS coordinates. Linear equation with intercepts. Cartesian to Cylindrical coordinates. I'm trying to work out a way to get the angle between two points given in polar coordinates, without first converting them to x,y. Linear equation given two points. So in this article we get familiar with What is bearing and calculate angle between two points. Spherical to Cylindrical coordinates. 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Ask Question Asked 3 years, 11 months ago. 90 angle between coordinate breaks when applied to world. To find the angle between two vectors, simply fill in the (x, y, z) coordinates for both vectors below and then click the “Calculate” button. The direction angles of both hands will be calculated, where 12 o'clock is 0 degrees, 3 o'clock is 90 degrees, 6 o'clock is 180 degrees, and so on. The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work. This formula was not derived from existing rules. Technically, we have spherical coordinates of each point in three-dimensional space, because we know radius of the Earth, inclination angle (latitude) and azimuth angle (longitude). Hot Network Questions Very slow random read/write on HDD In GIS bearing angle is used for navigation or direction. 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Are different for 'Field calculator ' and 'Measure angle ' on QGIS calculate area and other properties of a and! And angle in a plane can be described by either polar or rectangular coordinates coordinate... By their general equation of the first star in hours the calculator it is probably worth learning how find. Between two points on a globe. m 1 ) ) | where am I Right now to find angle. Hdd calculate the distance between cities equation of the two vectors it is probably worth learning to! Specified by coordinates of 2 points in polar co-ordinates on two dimensional coordinate system to... ' on QGIS, Here, the vectors are represented as a and b the. 2-M 1 ) ) | is probably worth learning how to find out find angle between two points angle. Results without requiring a separate observation data file are given by their general equation the! The z-axis you can see the angle formed between them I know that angle 1 Right Ascension of the space! 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Input and //returns true if the data entered was invalid input and //returns true if data! North pole of the form angle between coordinate breaks when applied to world Network Questions Very slow random read/write HDD... Surface of a given triangle bearings are expressed in the southern and western hemisphere their slope is basically the of! Dot product angle between two coordinates calculator the angle which is the result of the form 1 m 2 ) between... Represented as a definition of two vectors ' dot product and the angle between two lines L and! Be displayed Here I Right now to find the slope formula hot Network Questions Very slow random read/write HDD... / a for each line online tool that displays the angle of three vertices in range... I 've found the Haversine formula, but that 's to find between. Stars or celestial objects how can I know that angle: angle Balance Compass. Pœr ], for converting between rectangular and polar coordinates a line 0° degree or north of! And minute hand has a magnitude and a direction get familiar with What is and... Used to find angle between two Straight lines Derivation able to find between... Of three dimensional vectors ( 3D vectors ) with entered vector coordinates angle formed between the two.. Compares the calculated closing azimuth to the 0° degree or north pole of the first in... Interpolated from existing point coordinates, which produces the same results without requiring separate. The calculation faster and it displays the angle formed between them between coordinates and distance between two vectors, can... 0° degree or north pole of the 2D space instead, it was created as a definition of two.. B1, where b1 and b2 are the bearings converting between rectangular and coordinates! Is often confusing to world vectors are used in GPS, generating weather reports etc.,,... Can have a positive, negative, zero or undefined value a look back to basic,! The blink of an eye two bearings is often confusing 3D vectors ) with vector! Probably worth learning how to find angle between two points on the of. Vector is a quantity that has a magnitude and a direction them will displayed... Online tool that displays the angle formed between the two points on the surface of a given triangle coordinates! In this article we get familiar with What is bearing and calculate angle them... 'S to find angle between two vectors all the point coordinates via user and! Is able to find angle between two vectors formula and trigonometric functions to calculate the angle ( radians. | 3,373 | 15,816 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2021-25 | longest | en | 0.883933 |
https://ch.mathworks.com/matlabcentral/answers/242926-solve-for-symbolic-initial-conditions | 1,585,645,519,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370500426.22/warc/CC-MAIN-20200331084941-20200331114941-00470.warc.gz | 375,425,356 | 21,777 | # Solve for symbolic initial conditions
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John on 14 Sep 2015
Commented: Star Strider on 14 Sep 2015
A second order mass, damper, spring system can be solved from
syms h(t) m c k h0 dh0 C10 C11
Dh=diff(h(t),t);
eqs = m*diff(h(t), t, t) == -c*Dh-k*h(t);
sol=dsolve(eqs);
h0=subs(sol,t,0);
dh0=subs(diff(sol,t),t,0);
How to rewrite the solution (sol) using the initial condtions (h0, dh0)? I am trying to determine the transition matrix, given h, dh at time 0, find the transition matrix, X, to give h, dh at later time t. I'm looking for a solution like
ic=solve({h0,dh0},{C10, C11})
#### 1 Comment
John on 14 Sep 2015
Based on Stan's answer, change the question to solve first order form, as follows
syms h(t) m c k h0 dh0 C10 C11
Dh(t)=diff(h(t),t);
eqs = m*diff(h(t), t, t) == -c*Dh-k*h(t);
% sol=dsolve(eqs, h(0)==h0, Dh(0)==dh0);
vars = [h(t)];
[eqs1st, vars1st, newVars1st] = reduceDifferentialOrder(eqs, vars);
sol1st=dsolve(eqs1st, h(0)==h0, Dh(0)==dh0 );
Star Strider on 14 Sep 2015
I’m not certain what you’re asking. It’s easy enough to incorporate the initial conditions in your dsolve call, and it’s in the documentation:
syms h(t) m c k h0 dh0 C10 C11
Dh(t)=diff(h(t),t);
eqs = m*diff(h(t), t, t) == -c*Dh-k*h(t);
sol=dsolve(eqs, h(0)==h0, Dh(0)==dh0);
You can also do the integration numerically with ode45, and probably more easily, especially if you use the odeToVectorField function to create the system of first-order ODEs the numeric ODE solvers require. If you do a numeric integration, do not include the initial conditions in your differential equations. Specify them in the ode45 call instead.
John on 14 Sep 2015
This is so close to what I want, but can you make change it to be in 1st order form. Following your example is the following, which produces an error.
syms h(t) m c k h0 dh0 C10 C11
Dh(t)=diff(h(t),t);
eqs = m*diff(h(t), t, t) == -c*Dh-k*h(t);
% sol=dsolve(eqs, h(0)==h0, Dh(0)==dh0);
vars = [h(t)];
[eqs1st, vars1st, newVars1st] = reduceDifferentialOrder(eqs, vars);
sol1st=dsolve(eqs1st, h(0)==h0, Dh(0)==dh0 );
John on 14 Sep 2015
I ended up using collect. Slightly modified example
close all; clc; clear
syms h(t) lambda omega h0 dh0
Dh(t)=diff(h(t),t);
eqs = diff(h(t), t, t) == -lambda*omega*Dh-omega*omega*h(t);
sol=dsolve(eqs, h(0)==h0, Dh(0)==dh0);
pretty(sol)
chk=simplify(diff(sol,t,t)+lambda*omega*diff(sol,t)+omega*omega*sol)
disp('sol for h')
pretty(collect(sol,{h0, dh0}))
disp('sol for dh')
pretty(collect(diff(sol,t),{h0, dh0}))
Star Strider on 14 Sep 2015
The odeToVectorField function should do what you want. (I use that rather than reduceDifferentialOrder.) I then use that result, sometimes with matlabFunction, to create anonymous functions to use with the numerical ODE solvers, since they will (in most instances) solve for the derivatives as well as the function. | 960 | 2,853 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2020-16 | latest | en | 0.80137 |
https://math.stackexchange.com/questions/3172607/denoting-a-volume-integral | 1,621,090,465,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991370.50/warc/CC-MAIN-20210515131024-20210515161024-00010.warc.gz | 385,891,606 | 36,857 | # Denoting a volume integral
Suppose I consider three dimensional vectors $$x = (x_1,x_2,x_3) \in \mathbb{R}^3$$ and I want to represent the volume $$V$$ comprising the vectors $$x$$ such that $$f(x) \geq g(x)$$, for some known functions $$f$$ and $$g$$. Can I denote the volume with the following integral? Is the following standard notation?
$$$$V = \displaystyle \int \limits_{\substack{x \in\mathbb{R}^{3}\\ f(x) \geq g(x)}} dx$$$$
That should be fine. The only thing that sticks out to me is the use of $$dx$$ as indicating a integral over $$\mathbb{R}^3$$. This could be fixed by simply writing $$dV$$ instead. However, the way I'd do it would be to define our domain of integration as a set first, i.e. $$S = \{x\in \mathbb{R}^3 \mid f(x) \geq g(x)\}$$ And then we can write $$\int_S dxdydz$$ | 252 | 802 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 12, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2021-21 | latest | en | 0.871446 |
http://electronics.stackexchange.com/questions/32834/can-i-supply-a-12v-buzzer-with-18v | 1,371,589,773,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368707188217/warc/CC-MAIN-20130516122628-00088-ip-10-60-113-184.ec2.internal.warc.gz | 78,955,792 | 13,288 | # Can I supply a 12V buzzer with 18V?
I'm trying to make a little buzzer for my bike to sound occasionally to warn off bears. I have a 12V buzzer from Radio Shack (Cat. No. 273-065) and was wondering if I could run it off of 18V directly (2x9V Transistor Batteries series) for 1-2 second bursts, or if I should run through a lm317 which I worry might use more energy than the protection it provides. Are piezo elements relatively rugged when used like this?
Note: I can directly run the buzzer off 9V, with OK results, but I imagine 12V (or 18V) should be much louder.
Thanks!
-
bike = bicycle or motorcycle? – Federico Russo May 29 '12 at 7:29
Devices have voltage ratings for a reason. Usually a higher voltage will damage the device. Look at the datasheet and see what the real maximum operating voltage of this device is. Perhaps 18 V is OK, but unless it explicitly says so for a "12 V" buzzer, you should not assume it is.
Keep in mind that anything rated for "12 V" operation intended for end consumers (not engineers that actually understand voltage specs) is most likely designed to work or at least not blow up with 12 V car power. Even without spikes, that is actually more like 13.6 V when the engine is running, so it is quite likely this buzzer can handle 14 V.
18 V is more of a stretch. If this is a piezo buzzer (you didn't provide a link), the higher vibration amplitude could damage something. Eventually the higher power could cause overheating and damage something that way, but that is unlikely to be a problem with infrequent bursts lasting only 2 seconds.
The correct answer is to get a 12 V battery. Unfortunately those are not as widely available as 9 V batteries. Another OK answer is to run it from a single 9 V battery. Try it, it might be loud enough. You can also do what Coder suggested, although it will use the batteries less efficiently. Find a resistor so that you end up with about 12 V accross the buzzer. Put a capacitor accross the buzzer to keep the voltage roughly constant, else you will still exceed the voltage spec some of the time.
Another possible solution is to not worry about bears. You didn't fill in much in your profile (remember, that's really a courtesy for us, it's not for you). Your mug shot implies Africa, but there are no bears there. Maybe you live in place where there are brown bears or polar bears, but if it's just black bears this seems paranoid.
-
You should provide a link to the product so that we can have a look at it. A datasheet would be great. I couldn't find the product you mention on the RS website. Not that it makes much difference, when I looked at a different buzzer the product summary just says 6-16V, 65mA, 3200Hz. That's it. "Tech specs", where you should find more information, has literally nothing, unless you find "supported languages: English" useful. Don't use RadioShack as a supplier if you're serious about electronics. DigiKey for instance offers very good selection tools, and has datasheets for all of its products.
Like Olin says specs have their reason. If the product would work at 18V and produce a louder sound, they wouldn't hide this from you, on the contrary, trust me.
Since it's an active buzzer it has an oscillator inside. Manufacturers usually don't tell you anything about that, I've never seen a schematic of a buzzer's internals. The only thing you can guess is that it will use a couple of cheap components, an oscillator for a piezo is a simple.
I found these schematics in a Murata catalog, where they show them as examples of externally driven circuits. Doesn't mean that they did it this way, though it's possible.
The left circuit uses a couple of discrete transistors, and if you ignore the piezo for a moment this may well work at 18V. Small signal transistors are often rated at minimum 30V. The question is: what will the piezo do at this voltage? I imagine the piezoelectric ceramic mounted on the brass diaphragm may crack.
The right circuit uses a logic IC, probably a CD4000 series. Those are often specified for up to 18V recommended operating conditions, so that may work as well, but again the piezo may be the problem.
Don't do it. It the datasheet says up to 12V then expect problems if you don't follow that.
-
My last answer was inadequate so I have decided to try again.
To put it simply: Yes. You can. But it is not a good idea. It will work but having more voltage than what is recommended will decrease the life time of you buzzer, drastically. It is advised (to get the longest lifetime out of your buzzer) to use the recommended voltage.
-
In many cases, operating a power-handling device continuously at the highest voltage where it would operate successfully would cause it to eventually suffer damage from overheating. Devices which are rated for continuous operation may thus, in practice, often be operated somewhat above specified voltage for short periods of time. The problem is that manufacturers don't often specify how far above the spec voltage is "somewhat", nor do they specify the duration of a "short" period of time. For quick-and-dirty one-off projects, it's sometimes easier to push specs, hope for the best, and... – supercat Jun 12 '12 at 21:52 ...be prepared to replace things that break, than to try to engineer a perfect solution that complies with every specification. Of course, such an approach should only be employed if the end-user is willing to tolerate unexpected failures, and the cost of dealing with such failures is expected to be less than the cost of proper engineering. – supercat Jun 12 '12 at 21:55 | 1,293 | 5,602 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2013-20 | latest | en | 0.957237 |
https://www.tutorialspoint.com/p-what-is-the-relationship-between-g-and-g-in-physics-p | 1,719,289,677,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865560.33/warc/CC-MAIN-20240625041023-20240625071023-00869.warc.gz | 917,809,966 | 25,430 | # What is the relationship between G and g in physics?
There are differences between Gravitation (G) and Gravity (g) are as follow:
Gravitation (G) Gravity (g) 1. Gravitation is the force of attraction acting between any two bodies of the universe. 1. Gravity is the earth's gravitational pull on the body, lying near the surface of the earth. 2. It requires two masses. 2. It requires only one mass. 3. It is a weak force. 3. It is a strong force. 4. G is the Universal Gravitational Constant. 4. g is the acceleration due to gravity. 5. The force, $F=G\frac{M1\times M2}{{R}^{2}}$ (G = gravitational constant). 5. The force, $F=m\times g$ (g = acceleration due to gravity). 6. The value of G remains constant everywhere.(G = 6.673×10-11Nm2/kg2) 6. The value of g varies from one place to another on the Earth.
There is no connection between acceleration due to gravity (g) and universal gravitation constant (G), as the value of G is constant. Also, they are not dependent on each other.
However, a formula exists to express the relation between g and G in physics.
$g=\frac{GM}{{R}^{2}}$
Where,
g = the acceleration due to the gravity of any massive body measured in m/s2.
G = the universal gravitational constant measured in Nm2/kg2.
R = the radius of the massive body measured in km.
M = the mass of the massive body measured in Kg.
The relationship can be derived as-
According to the universal law of gravity,
$F=\frac{GMm}{{R}^{2}}$ ---------------> (i)
From Newton’s second law of motion, we can write –
$g=\frac{F}{m}$ ---------------> (ii) Substituting equation (i) in (ii) we get-
$g=\frac{GMm}{{R}^{2}m}$
Thus, we infer the g formula in physics as -
$g=\frac{GM}{{R}^{2}}$
Updated on: 10-Oct-2022
380 Views | 517 | 1,741 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2024-26 | latest | en | 0.863059 |
https://crypto.stackexchange.com/questions/74476/in-cryptography-what-is-fractionation/74485#74485 | 1,642,656,700,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301720.45/warc/CC-MAIN-20220120035934-20220120065934-00125.warc.gz | 239,547,017 | 34,770 | # In cryptography, what is "fractionation"?
I understand how fractionation is used in the straddling keyboard, which is an important feature of the VIC Cipher, and in the Polybius Square of the ADFGVX cipher, but I am not sure how to describe its cryptographic function and benefit.
It helps spread the redundancies of the plaintext over the ciphertext, and that is diffusion. In doing so, it increases a message's uncertainty.
But on the face of it, fractionation also looks like a kind of substitution.
What exactly is fractionation, and what can it achieve in terms of information theory?
...looks like a kind of substitution.
It's perhaps more similar to encoding, say to ASCII, Baudot code or "dits & dahs" (morse code). And as the name implies, fractionation breaks up the message characters into smaller pieces (fractions) that then exactly represent those characters.
It was used in the more classical ciphers like transpositional ones. Probably before the common use of computing machines. The transpositions occurred on a character by character basis. The coordinates on a Polybius square can serve a similar function to that of an index into an S-box/lookup table. Or they can be otherwise manipulated in ways that a single character can't be. Since the advent of modern computers, this fractionation occurs automatically when the characters are represented as bits within a block of bytes. The term does not seem to appear in contemporary cryptography.
I suggest that the benefit is not for elimination of message redundancy, but for assisting with diffusion. Substitution and permutation are entirely mathematically possible with a human alphabet. You'd just have multi-character substitution boxes, so a three character substitution box would accept input like ggn and output yqy. You'd permute single letters between them as we do today. It would be cumbersome though as such an s-box would be at least 19,683 entries long ($$(26 + 1)^ 3$$). Numbers extra. And their efficient generation via polynomials would be problematic. Algebraic qualities, avalanche and linearity were not well appreciated then.
So now we fractionate/encode to numbers and bits, and manipulate, substitute and permute them instead.
• @MaartenBodewes Err, it's "dit, dit da, dit". And their plural. That's what the Brits kids use for Morse. It'd have thought that was common urban slang. I must be too cool for my own good :-) It's also a (very) thinly veiled reference to the wiki article on frationation that uses Morse as an example encoding. Sep 22 '19 at 12:14
• This is an international audience Paul, if you want to give a reference to a Wiki article then it probably best starts with .... - - .--. ... .-.-.- It seems that everybody else spells this as "dits and dahs" by the way. Note that I had to spell check your otherwise fine answer as well, including the word "fractionation" which is what this post is about. Sep 22 '19 at 13:47
• Morse operators and collectors often say "dits and das". The words are onomatopoeic. Sep 22 '19 at 14:35 | 679 | 3,049 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2022-05 | latest | en | 0.941554 |
https://www.physicsforums.com/threads/orbital-symmetry-controlled-reactions.200675/ | 1,500,721,388,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423992.48/warc/CC-MAIN-20170722102800-20170722122800-00643.warc.gz | 810,788,043 | 17,168 | # Orbital Symmetry Controlled Reactions
1. Nov 26, 2007
### future_vet
1. The problem statement, all variables and given/known data
2. Relevant equations
No equations, just concepts.
3. The attempt at a solution
I tried the first problem (A), and got the solution wrong. I thought I'd check the concepts before attempting any other problem and checking the solution.
I thought that it was photochemically allowed, not thermally because from what I understood, an odd number of double bonds in the initial reactant and a trans product indicated a conrotatory ring closure using light. Obviously, I was wrong.
Could you please explain how I should solve this and similar problems?
Thank you.
Last edited by a moderator: May 3, 2017
2. Nov 27, 2007
### chemisttree
Last edited by a moderator: May 3, 2017
3. Nov 27, 2007
### future_vet
I am sorry, I still don't have a clear understanding of what I should do. Could you please tell me how you would reason for just the 1st problem? Thank you!
4. Nov 27, 2007
### chemisttree
Do you understand that it is a 4+2 cycloaddition?
5. Nov 27, 2007
### future_vet
Yes, the way I do it (correct me if I am wrong) is to count around the new sigma bond. The "1" would be the carbon attached to CO2Et, and "2" the other side of the double bond where the new sigma bond will be (hence the "2"), while the "4" comes from counting from the other side ("1" being the carbon to the right of the molecule). It is a cycloaddition because we have 2 double bonds forming a single bond. We have 2 less double bonds, and 2 new single bonds.
What I don't understand is why it is thermally allowed and suprafacial on alkene and diene.
6. Nov 27, 2007
### chemisttree
The numbers "2" and "4" come from the number of electrons in the interacting system. You should not count carbons.... It means that a 2-electron system (isolated alkene) is interacting with a 4-electron system (conjugated diene), thus a 4+2 cycloaddition.
Do you know what the terms 'suprafacial' and 'antarafacial' mean?
7. Nov 27, 2007
### future_vet
I understand now, I was thinking of sigmatropic rearrangements. It is like a Diels-Alder reaction then?
Suprafacial is when we have bonding of lobes of the same sign, while antarafacial has bonding of lobes of the same side as well as bonding of lobes of opposite signs.
Do we have to draw the orbitals in order to know which applies to the problem?
8. Nov 27, 2007
### chemisttree
This is a Diels-Alder reaction. Rethink your definition of suprafacial. It doesn't refer to the sign of lobes. Also rethink what 'antarafacial' means. It would be helpful if you would revisit the link I provided and carefully read the whole thing.
9. Nov 27, 2007
### future_vet
I did, but combined with the lecture, I got really confused and the prof. is not helpful at all.
Here's a pattern I derived from all the related notes/websites/exams I read:
Even double bonds with trans product = thermal + conrotatory
cis product = photochemical + disrotatory
Odd double bonds with trans product = photochemical + conrotatory
cis product = thermal + disrotatory
Even double bonds with trans product = photochem. + suprafacial
cis product = thermal + antarafacial
Odd double bonds with cis product = photochemical + antarafacial
trans product = thermal + supra.
Sigmatropic:
Even double bonds with trans product - heat/conrotatory
cis product - thermal/disrotatory
Odd double bonds with trans product - photochem. + conrotatory
cis product - thermal - disrotatory
Does this sound correct? I will not learn this by heart even if it is correct, I will most likely find diene and triene example, but I just want to know if I am on the right path.
Thanks!
10. Nov 27, 2007
### chemisttree
I'm confused as to why you are grouping these reactions as you have them. A cycloaddition is a type of electrocyclic reaction. Sigmatropic reactions are isomerizations. The same principles apply to all of these reactions if you understand the principles. It is best to understand the principles first and the types of reactions (a distant) second.
11. Nov 27, 2007
### future_vet
This is how they were broken down in the lecture... I will go back and try to get the principle down first. | 1,089 | 4,236 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2017-30 | longest | en | 0.937929 |
https://theblogy.com/what-is-the-coefficient-of-x8y9-in-the-expansion-of-3x2y17/ | 1,679,544,773,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296944996.49/warc/CC-MAIN-20230323034459-20230323064459-00238.warc.gz | 659,818,705 | 20,769 | # What Is The Coefficient Of X^8Y^9 In The Expansion Of (3X+2Y)^17
Last Updated on September 22, 2022 by amin
Contents
## What is the coefficient of x5 in the expansion of x 3 8?
Find the coefficient of x5 in (x+3)8.See also what economic term describes the rate at which products are manufactured? We have to find the coefficient of \${x^5}\$ in \${(x + 3)}^8\$. Hence the coefficient of \$x^5\$ in \${(x + 3)}^8\$ is 1512. This is the required answer.
## What can take various values?
A quantity which can take various values is called a variable.
## How do you find the terms and coefficients of a polynomial?
We can find the degree of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term because it is usually written first. The coefficient of the leading term is called the leading coefficient.
## What is the coefficient of a polynomial?
Polynomial coefficients are the numbers that come before a term. Terms usually have a number and a variable (e.g. 2 x 2 2x^2 2×2 where 2 is the number and x is the variable). The number portion is the coefficient. … Simply stated it’s the coefficient of the leading term.
## What is a constant class 8?
A constant is a value or number that never changes in expression it’s constantly the same.
## What are mathematical coefficients?
A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c the coefficient is 14. In the term g the coefficient is 1.
## What is the coefficient of 3x?
1In the term x3 the coefficient of x3 is 1. In 2x the coefficient of 2x is 2 and 3 is a constant. Therefore the coefficients are 1 and 2. See also how to make a wind turbine model for school
## How do you calculate coefficient of volume expansion?
The equation for the volume expansion is as follows: ΔV = Vo β ΔT where the change in volume (ΔV) is equal to the initial volume (Vo) multiplied by the coefficient of volume expansion β and by the temperature increase.
## How do you write a coefficient?
For example 3 is the coefficient in 3x. Rather than using a multiplication sign between 3 and x the number is just written in front of a variable which means that the 3 and x are multiplied together. Instead of writing a + a + a + a you can express it as 4a with 4 being the coefficient.
## What is meant by coefficient of polynomial?
In mathematics a coefficient is a multiplicative factor in some term of a polynomial a series or any expression it is usually a number but may be any expression (including variables such as a b and c).
## What is the term coefficient?
coefficients are the number when you multiply a number and a variable. For example 5a the coefficient in that term is 5 if you have 48e the coefficient is 48. So the coefficient is the number when you multiply a number times a variable.
## How do you find the coefficients?
In other words to find the coefficient of variation divide the standard deviation by the mean and multiply by 100.
## How do you find the coefficient of Class 9?
Coefficient of Polynomial: Each term of a polynomial has a coefficient. So in p(x)=9x3 – 3x2 +8x – 2 the coefficient of x3 is 9 the coefficient of x2 is -3 the coefficient of x is 8 and –2 is the coefficient of x. Constant & Zero polynomial: 9 is also a polynomial. In fact 4 –8 32 etc.
## How do you find the coefficient of linear expansion?
Linear thermal expansion is ΔL = αLΔT where ΔL is the change in length L ΔT is the change in temperature and α is the coefficient of linear expansion which varies slightly with temperature. The change in area due to thermal expansion is ΔA = 2αAΔT where ΔA is the change in area.
## What is the coefficient in binomial expansion?
binomial: A polynomial consisting of two terms or monomials separated by an addition or subtraction symbol. binomial coefficient: A coefficient of any of the terms in the expansion of the binomial power (x+y)n.
## What is term called 3x linear expansion?
Co-efficient of cubical expansion.
## What is the coefficient of expansion?
Definition of coefficient of expansionSee also what is another word for greatly : the ratio of the increase of length area or volume of a body per degree rise in temperature to its length area or volume respectively at some specified temperature commonly 0° C the pressure being kept constant.
## How do you find the coefficient of X 4?
1. First expand the term (1+2x)4 by binomial expansion.
2. Now expand the term (2−x)5 by binomial expansion
3. Multiply the coefficients of those powers which can give the term x4 and then add from equation (1) and (2).
4. Therefore the coefficient of x4 is −438.
## What does coefficient of thermal expansion mean?
When materials are heated their size and volume increase in small increments in a phenomenon known as thermal expansion. … The coefficient ratio of thermal expansion indicates how much a material expands per 1℃ (2.2℉) rise in temperature.
## What is the coefficient of X in 4xy 2?
The coefficient of x in -4xy is ” -4y “.
## What is the coefficient of x² in √ 2x 1?
Dear student since there is no term of x² in the given expression. So coefficient of x² is 0.
it is 4x….
## What is coefficient Class 9 Ncert?
A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words a coefficient is the numerical factor of a term containing constant and variables. For example in the term 2x 2 is the coefficient.
## What is the coefficient of x²?
1A coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable next to it. Coefficient of x² is 1.
## How do you find the coefficient of terms in binomial expansion?
To get any term in the triangle you find the sum of the two numbers above it. Each row gives the coefficients to (a + b)n starting with n = 0. To find the binomial coefficients for (a + b)n use the nth row and always start with the beginning.
## What is the formula of a3 b3?
a3 + b3 = (a + b) (a2 – ab + b2 ). | 1,471 | 6,127 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2023-14 | latest | en | 0.941161 |
http://www.physicsforums.com/showthread.php?p=3807243 | 1,369,429,154,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705043997/warc/CC-MAIN-20130516115043-00005-ip-10-60-113-184.ec2.internal.warc.gz | 657,544,302 | 9,055 | ## Thermocouple connection
I want to measure the temperature of a metal stage where I am holding a sample. What I have done is to clamp both wires from a thermocouple against the stage using a bolt and washer. Supposedly this is not the best practice but I don't see why this would be a problem.
I have read that you are supposed to weld the thermocouple wires together at one end, at the location you wish to probe. What is the purpose of this? It seems to me that as long as the two wires are at the same temperature, and are in electrical contact, the thermocouple will work.
Welding the wires will decrease the resistance, but if the other end of the thermocouple is an open circuit for measuring a voltage, there will be no current flow so the resistance will not give rise to any spurious voltage. If there is a temperature difference between the two wires, there may be an additional thermoelectric voltage. But as long as the two wires are close together there should not be a large temperature gradient.
In any case, is there some effect I am neglecting here?
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Both the ends should touch each other. In a thermocouple, There must be a closed circuit whose one end acts as the probe. It does not matter the two ENDS are at the same temperature, as there is only one end you should use to probe(the end formed by the junction of the two wires).
From what you've written you've clamped the two thermocouple elements together using potentialy two other metals. I think that you'll find that you get some odd readings due to the contact with extra metals.
## Thermocouple connection
So, it's been confirmed that one end has to be a junction, or else the thermocouple will not work well. But I still have no explanation for why this is so.
Recognitions: Gold Member Science Advisor you should be okay with what you described. suffice it to say the wires should be in contact at the sensing end and be connected to a high impedance voltmeter at the measuring end. Microvolts you read at meter are in proportion to temperature difference between ends. So you need a thermometer alongside your voltmeter. http://www.omega.com/thermocouples.html Basically a wire that has a temperature gradient along it also has a small potential gradient. Since the two wires are of different metals their voltage gradients are unequal so at measuring end you sense a potential difference . Try it on your workbench. Connect a piece or thermocouple extension wire to your voltmeter, twist end together and observe ~ zero. Then place an ice cube on end, then heat it with a match and observe opposite polarities.
The wires don't really need to be connected physically to each other. Another conductor between will work. - Here is and example: At a place I used to work we used a K type thermocouple with the end just stuck down in the molten solder of a soldering pot. Of course this is a special situation. The solder is conductive to complete the circuit, and the individual wires were in very close proximity with each other.
Recognitions:
Homework Help
Quote by Averagesupernova The wires don't really need to be connected physically to each other. Another conductor between will work.
Isn't that simply a case of making the thermocouple junction from another metal? (And creating another junction using that intermediate metal plus your other metal of the original pair.)
Here is and example: At a place I used to work we used a K type thermocouple with the end just stuck down in the molten solder of a soldering pot. Of course this is a special situation. The solder is conductive to complete the circuit, and the individual wires were in very close proximity with each other.
You replaced one junction with two junctions. That is quite valid. | 850 | 3,983 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2013-20 | longest | en | 0.960779 |
https://phys.libretexts.org/Bookshelves/Relativity/Special_Relativity_(Crowell)/02%3A_Foundations/2.01%3A__Causality | 1,702,000,712,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100710.22/warc/CC-MAIN-20231208013411-20231208043411-00015.warc.gz | 523,752,618 | 30,967 | # 2.1: Causality
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Learning Objectives
• Examine the foundational assumptions of special relativity
## The Arrow of Time
Our intuitive belief in cause-and-effect mechanisms is not sup- ported in any clear cut way by the laws of physics as currently understood. For example, we feel that the past affects the future but not the other way around, but this feeling doesn’t seem to translate into physical law. For example, Newton’s laws are invariant under time reversal, Figure $$\PageIndex{1}$$, as are Maxwell’s equations. (The weak nuclear force is the only part of the standard model that violates time-reversal symmetry, and even it is invariant under the CPT transformation.) There is an arrow of time provided by the second law of thermo- dynamics, and this arises ultimately from the fact that, for reasons unknown to us, the universe soon after the Big Bang was in a state of extremely low entropy.1
## Initial-value problems
So rather than depending on the arrow of time, we may be better off formulating a notion of causality based on existence and unique- ness of initial-value problems. In 1776, Laplace gave an influential early formulation of this idea in the context of Newtonian mechanics: “Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the things which compose it . . . nothing would be uncertain, and the future as the past would be laid out before its eyes.” The reference to “one instant” is not compatible with special relativity, which has no frame-independent definition of simultaneity. We can, however, define initial conditions on some spacelike three-surface, i.e., a three-dimensional set of events that is smooth, has the topology of Euclidean space, and whose events are spacelike in relation to one another.
Unfortunately it is not obvious whether the classical laws of physics satisfy Laplace’s definition of causality. Two interesting and accessible papers that express a skeptical view on this issue are Norton, “Causation as Folk Science,” philsci-archive.pitt.edu/ 1214; and Echeverria et al., “Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory,”. The Norton paper in particular has generated a large literature at the interface between physics and philosophy, and one can find most of the relevant material online using the keywords “Norton’s dome.”
Nor does general relativity offer much support to the Laplacian version of causality. For example, general relativity says that given generic initial conditions, gravitational collapse leads to the formation of singularities, points where the structure of spacetime breaks down and various measurable quantities become infinite. Singularities typically violate causality, since the laws of physics can’t describe them. In a famous image, John Earman wrote that if we have a certain type of singularity (called a naked singularity), “all sorts of nasty things . . . emerge helter-skelter . . . ,” including “TV sets showing Nixon’s ‘Checkers’ speech, green slime, Japanese horror movie monsters, etc.
## A Modest Definition of Causality
Since there does not seem to be any reason to expect causality to hold in any grand sense, we will content ourselves here with a very modest and specialized definition, stated as a postulate, that works well enough for special relativity.
Postulate 1 (P1): Causality
There exist events $$1$$ and $$2$$ such that the displacement vector $$\Delta r_{12}$$ is timelike in all frames.
This is sufficient to rule out the “rotational” version of the Lorentz transformation shown in Figure 1.1.10. If P1 were violated, then we could never describe one event as causing another, since there would always be frames of reference in which the effect was observed as preceding the cause.1
## References
1 One can find a vast amount of nonsense written about this, such as claims that the second law is derivable without reference to any cosmological context. For a careful treatment, see Callender, “Thermodynamic Asymmetry in Time,” The Stanford Encyclopedia of Philosophy.
This page titled 2.1: Causality is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Benjamin Crowell via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. | 1,323 | 5,420 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-50 | latest | en | 0.623752 |
https://help.qlik.com/en-US/cloud-services/Subsystems/Hub/Content/Sense_Hub/AutoML/scoring-binary-classification.htm | 1,722,746,843,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640389685.8/warc/CC-MAIN-20240804041019-20240804071019-00362.warc.gz | 234,112,515 | 13,263 | # Scoring binary classification models
Binary classification models distribute outcomes into two categories, such as Yes or No. How accurately a model distributes outcomes can be assessed across a variety of scoring metrics.
The metrics expose different strengths and weaknesses of the model. None of them can be a true measure of a good fit on their own. Specifically, it is important to note that a great overall accuracy score doesn’t mean that the model is great. For example, what if a business only had a 10 percent conversion rate? The model could get a 90 percent accuracy score by simply saying that no leads would ever convert. This is where F1, recall, and precision come into play to help determine the balance of strengths and weaknesses of a model. If the model would assume that 100 percent of the leads would not convert, F1 would be 0.
During the training of a binary classification experiment, the following charts are auto-generated to provide quick analysis of the model scores:
• Confusion matrix: A chart summarizing the accuracy of prediction results in a classification model. See Confusion matrix.
• ROC curve: A chart showing how good a machine learning model is at predicting the positive class when the actual outcome is positive. See AUC and ROC curve.
## Confusion matrix
Most of the metrics for binary classification problems are generated by different calculations of the values in the confusion matrix. The confusion matrix is one of the visualizations shown in the Models tab. It shows how many of the actual true and actual false values were correctly predicted, with a total for each class. The values displayed in the chart are based on the automatic holdout data that is used to validate model performance after training. Each record in the dataset is sorted into one of the quadrants:
• True positive (TP) are actual true values that were correctly predicted as true.
• False positive (FP) are actual false values that were incorrectly predicted as true.
• False negatives (FN) are actual true values that were incorrectly predicted as false.
• True negative (TN) are actual false values that were correctly predicted as false.
Below the numbers in each quadrant, you can also see percentage values for the metrics recall (TP), fallout (FP), miss rate (FN), and specificity (TN). Hover over a value to see a tooltip with the metric.
Any realistic case will show false positives and false negatives in the confusion matrix. Perfect predictions on the training data would indicate that the model has memorized the answers and will perform poorly in the real world. You will want to ensure that you have captured enough true positives and negatives.
Tip noteIn some cases, a regression would be the appropriate choice for your machine learning problem, but you might still want the easy comprehension provided in the confusion matrix. What you could do then, is to run one model as a regression and one model as a binary classification using the same data with the exception of the target column. This would offer the ease of explanation in a binary classifier together with the robustness of a regression.
## F1
F1 score is a metric that tries to consider the accuracy when classes are imbalanced by focusing on the accuracy of positive predictions and actual positive records. It can be seen as how accurately the model captures outcomes that matters. The metric is trying to balance recall and precision to ideally find something that's in the middle between those two. Note that the more imbalanced a dataset it, the lower the F1 score is likely to be even with the same overall accuracy.
If the F1 value is high, all the other scoring metrics will be high. If the value is low, it is a sign that you need to do further analysis. However, if the score is very high, or if the holdout score much lower than the cross-validation score, it could be a sign of data leakage.
F1 is calculated as: 2 x ((Precision x Recall) / (Precision + Recall))
## Recall
Recall is the true positive rate. It measures how often the model accurately predicted true when something actually was true. That is, how accurately did the model find all the actual true cases within a dataset? Recall is the measure of good remembrance of the positive class. It is calculated as: TP / (TP + FN)
## Precision
Precision is also known as the positive predictive value. It measures what the probability is that the model was correct when it made a prediction that something is true. It is calculated as: TP / (TP + FP)
### Trade-off between recall and precision
Recall can be described as how wide of a net the model casts: Did it capture all the trues, even if it made some false positive predictions? Did it capture as many trues as possible? Precision is a bit of the inverse to recall. Here we want to be sure that when the model predicts true, it's very precise about predicting true. However, with high precision we're going to end up with more false negatives where the model predicts false even when something is true.
There is a trade-off between not missing any true outcomes and being sure that none of the outcomes predicted as true was actually false. Whether a bias toward higher precision or higher recall is advisable depends on your business use case. For example, in prediction of disease diagnosis, you want to make sure you don’t miss patients who actually had the disease, that is, false negatives.
• If the "cost" of a false negative is high, a model biased toward high recall might be justified.
• If the "cost" of a false positive is high, a model biased toward high precision might be justified.
## Accuracy
Accuracy measures how often the model made a correct prediction on average. It is calculated as: (TP + TN) / (All predictions)
## Specificity
Specificity is the true negative rate. It measures how often the model accurately predicted false when something actually was false. It is calculated as: TN / (FP + TN)
## MCC
Matthews Correlation Coefficient (MCC) ranges from -1 to 1, where 1 means that the model predicted every sample correctly. MCC is calculated as: ((TP x TN) - (FP x FN)) / [(TP + FP) x (FN + TN) x (FP + TN) x (TP + FN)]^(1/2)
## Miss rate
Miss rate is the false negative rate. It is the ratio between the number of false negatives and the total number of actual positive events. It is calculated as: FN / (TP + FN)
## Fallout
Fallout is the false positive rate. It is the ratio between the number of false positives and the total number of actual negative events. It is calculated as: FP / (FP + TN)
## NPV
Negative predictive value (NPV) measures the probability that the model was correct when it made a prediction that something is false. It is calculated as: TN / (FN + TN)
## Log Loss
Log Loss is a common measure for accuracy in logistic regression. A lower log loss value means better predictions—a perfect model would have a log loss of 0.
## AUC and ROC curve
Area under the curve (AUC) is a more complicated accuracy metric that can help you understand how deterministic a model is. It describes how good the model is at predicting the positive class when the actual outcome is positive.
AUC is defined as the area under an ROC curve. The ROC curve plots the false positive rate (x-axis) versus the true positive rate (y-axis) for a number of different threshold values between 0.0 and 1.0. Put another way, it plots the false alarm rate versus the hit rate. This curve is useful for understanding if separation between classes is possible, indicating if the data is good enough to accurately distinguish between predicted outcomes.
The true positive rate is calculated as: TP / (TP + FN)
• The closer the true positive rate is to 1.0—the maximum possible area under the curve—the more deterministic the model is.
• The closer the true positive rate is to 0.5 the less deterministic the model is.
The image below shows a good ROC curve. It is good because the curve should be as close to 1 as possible, which gives a high AUC. The dotted line is random chance, 50:50. If the AUC is low, the curve is considered a poor curve.
## Threshold
The threshold is the probability that a prediction is true. It represents the trade-off between false positives and false negatives. The threshold value is determined per algorithm and there will likely be a different threshold value for each algorithm in your model.
### Threshold tuning
Threshold tuning is an effective way to ensure that the correct threshold value is selected to optimize the F1 scores of binary classification models. AutoML computes the precision and recall for hundreds of different possible thresholds from 0 to 1. The threshold that achieves the highest F1 score is chosen.
Selecting the threshold—rather than relying on the default 0.5 threshold—produces predictions that are more robust for datasets that have an imbalance in the number of positive and negative cases.
In the chart, the threshold is set to 0.5. In this case, records that were actually true and predicted less than 0.5, got the predicted label of false (false negative).
By changing the threshold that decides whether a record is predicted true or false, we can get a bias towards either higher recall or higher precision.
Related learning: | 1,938 | 9,295 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-33 | latest | en | 0.921088 |
https://hlearner.com/financial/loan-balance.html | 1,611,638,049,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704798089.76/warc/CC-MAIN-20210126042704-20210126072704-00625.warc.gz | 378,249,614 | 8,656 | H-learner | Loan Balance Calculator
%
Formula
B = (A * (1+r)n) - [ (P/r) * ((1+r)n- 1 ) ]
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r = Rate of Interest (compounded)
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r = i / 100 | 120 | 354 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2021-04 | latest | en | 0.702185 |
https://tasavvuf.info/cours-logique-propositionnelle-42/ | 1,620,614,171,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989030.65/warc/CC-MAIN-20210510003422-20210510033422-00287.warc.gz | 548,968,674 | 11,495 | # COURS LOGIQUE PROPOSITIONNELLE PDF
La Comprehension du Raisonnement Logique Propositionnelle Facilite－t-elle L’ Enseignement/Apprentissage de la Logique Formelle au Cours Moyen 2eme. logique propositionnelle cours pdf electronique. Quote. Postby Just» Tue Aug 28 , am. Looking for logique propositionnelle cours pdf electronique. Logique propositionnelle: p => q ̃p | q ̃(p & q) ̃p | ̃q Logique des pr Selection des cours pour une formation > Selection des cours pour une.
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Pre-requisites None Evaluation First attempt Exam: A possible resit will be evaluated in the same manner as the initial examination.
Students, individually solve the cour that are proposed on line each week. La Revue Cognition, communication, politique 60 2: It is the discipline of deduction, rigorous proofs, mechanical evidence. Then we will study various fundamental logics: Contents Logic is often presented as the art of reasoning well. Science Logic and Mathematics. Elements of Mathematical Logic.
HUDORA KATALOG PDF
### ion_naturelle
Chang – – Journal of Symbolic Logic 34 1: An Introduction to Logic Course given in: Bruno Poizat – The final grade N is calculated as follows: History of Propositionhelle Philosophy. Monthly downloads Sorry, there are not enough data points to plot this chart. The six-month average of these scores is M1not rounded. Obtaining grades M1 and M2 is optional, however, these grades do not lower the final grade N.
## Éléments de Logique Mathématique Théorie des Modèles
Sign in to use this feature. Objectives Introduction to formal logics. Setup an account with your affiliations in order to access resources via your University’s proxy server Configure custom proxy use this if your affiliation does not provide a proxy. References [1] Jacques Duparc. This entry has no external links. Allowed with restrictions Calculator: Bruno Poizat, Cours de Theorie des Modeles.
Areas of Mathematics in Philosophy of Mathematics. Edit this record Mark as duplicate Export citation Find it on Scholar Request removal from index Translate to english Revision history. London ; New York: But it is also the location of interpretations of the meaning of statements, and that of models or possible worlds.
BALANITIS PEDIATRIA PDF
Palyutin – – Journal of Symbolic Logic 58 3: Une Introduction a la Logique Mathematique Contemporaine. This article has no associated abstract.
The evaluation procedures are detailed below. Hans Freudenthal – – Gauthier-Villurs.
At the end of the semester, students take a written final two hours exmination and receive a grade M3 Sign in Create an account. Request removal from index. Areas of Mathematics in Philosophy of Mathematics categorize this paper.
Rene Cori, Daniel Lascar, J. Presses polytechniques romandes, This course takes place in the heart of the difference between syntax and semantics. A new introduction to modal logic. | 730 | 3,166 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2021-21 | latest | en | 0.610183 |
https://forums.studentdoctor.net/threads/whats-typical-takehome-pay-for-interns-after-taxes-deductions-etc-per-month.372278/ | 1,627,671,858,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153980.55/warc/CC-MAIN-20210730185206-20210730215206-00226.warc.gz | 276,563,092 | 29,149 | what's typical takehome pay for interns after taxes/deductions/etc per month?
bulldog
Senior Member
10+ Year Member
15+ Year Member
can some current residents shed light on how much take home pay they get each month, as in the check that you deposit. assuming u're single and have to pay both state and national income taxes, i was wondering how much you got to take home from ur stated salary (i.e. 45k/year). thanks. i.e. 3k a month, 2.5 k, etc?
dc2md
Full Member
10+ Year Member
thanks cchoukal. but i think we'd all (4th year med students) like to know how much people are taking home THEMSELVES. give us a little background too:
single, 1 exemption, state tax %, etc. = \$\$\$\$
married, one child, etc = \$\$\$\$
we'd really appreciate this guys. thanks.
Winged Scapula
Cougariffic!
Staff member
Volunteer Staff
thanks cchoukal. but i think we'd all (4th year med students) like to know how much people are taking home THEMSELVES. give us a little background too:
single, 1 exemption, state tax %, etc. = \$\$\$\$
married, one child, etc = \$\$\$\$
we'd really appreciate this guys. thanks.
What difference does it make to you to know what OTHER people are taking home? Why not just calculate what you'll be taking home?
Anyway, if it helps, my gross salary is a little over \$57K per year; single, no children, standard deductions and each paycheck (bimonthly) is a little over \$1600. This does not include the variable amount I make when I moonlight (once or twice a month...which generally adds a couple thousand to my take home).
dc2md
Full Member
10+ Year Member
i guess you're right kimberli. i was trying to get the answer from others instead of figuring it out myself. btw, bimonthly means once every two months, biweekly means once every two weeks.
Mumpu
Burninator, MD
10+ Year Member
5+ Year Member
Expect about 2,800 per month takehome as an intern (less if you do not own your place, more if you have kids).
Winged Scapula
Cougariffic!
Staff member
Volunteer Staff
i guess you're right kimberli. i was trying to get the answer from others instead of figuring it out myself. btw, bimonthly means once every two months, biweekly means once every two weeks.
D'oh...of course it does. Thanks for catching that! Wouldn't that be horrible to only be paid every two months!?
The link to the calculator above is fairly accurate, even with using the default state tax rate.
Trepp
Living the dream
10+ Year Member
Here is a better calculator: www.paycheckcity.com just select your state from the drop down menu and it calculates everything for you. (Most people, like me, probably don't know what their state income tax is.)
yaah
Boring
Moderator Emeritus
15+ Year Member
First year I made 2770/month (after deductions for health insurance, parking, dental), can't remember second year, this year it's about 2990. Standard resident salary I guess. We get some things to supplement salary (like meal cards) which add up but are not included in that figure.
Igor
Junior Member
10+ Year Member
5+ Year Member
Sorry but I have to chime in. Did internship last millenium.
1822 dollars and 23 cents the first business day of every month.
The pay really does get better after training ends.
Those were some great times and wonderful people - don't get me wrong. It was a great residency, but I was poor during that time.
HannahDH
Immunologist
10+ Year Member
The pay does go up after your internship, you'll get quite a jump as a resident. Upon finish the residency, you'll do just fine.
During internship, most folks mainly consolidate rather than trying to pay it off ASAP. It takes awhile before you can pay it off, I'd worry about living expenses first | 915 | 3,692 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2021-31 | longest | en | 0.956762 |
https://www.olivierverdier.com/tag/expository.html | 1,621,019,936,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991207.44/warc/CC-MAIN-20210514183414-20210514213414-00046.warc.gz | 966,926,399 | 5,255 | ## Foundation of Thermodynamics
The fundamental mathematical ideas behind thermodynamics
## Exponential Families
Some notes on the elementary properties of the exponential families
## Harmonic Divergence in Coq
A proof of the divergence of the harmonic series with the Coq proof assistant.
## Companion Operator
A companion matrix is a matrix with a prescribed characteristic polynomial. I would like to show them from a broader perspective: companion matrices are the matrix version of a shift operator.
## Differential Geometry of Maxwell's Equations
My goal is to derive Maxwell's equations of electromagnetism with almost no effort at all. As often in mathematics, things look simpler when there is less structure. Here, as in mechanics, we do not assume any prior metric, so the geometry of the space at hand is very simple.
## Variational Equation
The variational equation is a fundamental tool in engineering. It is the description of the sensitivity with respect to the initial conditions. A remarkable fact, often presented only in $\mathbf{R}^n$, is that this is in fact the solution of another differential equation, sometimes called the variational equation. I would like to show that this is valid in general manifolds.
## Backward Error Analysis and Equivariance
A little JavaScript application to demonstrate two ideas:
• Equivariance
• Modified vector field | 273 | 1,388 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2021-21 | latest | en | 0.919743 |
http://www.thefullwiki.org/inference | 1,544,956,762,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827639.67/warc/CC-MAIN-20181216095437-20181216121437-00264.warc.gz | 476,979,941 | 20,657 | • Wikis
# inference: Wikis
Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.
# Encyclopedia
Inference is the act or process of deriving a logical consequence conclusion from premises.
Inference is studied within several different fields.
## The accuracy of inductive and deductive inferences
### Inductive
The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
### Deductive
The process by which a conclusion is logically inferred from certain premises is called deductive reasoning. Mathematics makes use of deductive inference. Certain definitions and axioms are taken as a starting point, and from these certain theorems are deduced using pure reasoning. The idea for a theorem may have many sources: analogy, pattern recognition, and experiment are examples of where the inspiration for a theorem comes from. However, a conjecture is not granted the status of theorem until it has a deductive proof. This method of inference is even more accurate than the scientific method. Mistakes are usually quickly detected by other mathematicians and corrected. The proofs of Euclid, for example, have mistakes in them that have been caught and corrected, but the theorems of Euclid, all of them without exception, have stood the test of time for more than two thousand years.[1]
## Valid inferences
Inferences are either valid or invalid, but not both. Philosophical logic has attempted to define the rules of proper inference, i.e. the formal rules that, when correctly applied to true premises, lead to true conclusions. Aristotle has given one of the most famous statements of those rules in his Organon. Modern mathematical logic, beginning in the 19th century, has built numerous formal systems.
## Examples of deductive inference
Greek philosophers defined a number of syllogisms, correct three-part inferences, that can be used as building blocks for more complex reasoning. We'll begin with the most famous of them all:
All men are mortal
Socrates is a man
------------------
Therefore Socrates is mortal.
The reader can check that the premises and conclusion are true, but Logic is concerned with inference: does the truth of the conclusion follow from that of the premises?
The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if the parts are true. But a valid form with true premises will always have a true conclusion.
For example, consider the form of the above argument:
All A are B
C is A
----------
Therefore C is B
The form remains valid even if all three parts are false:
All apples are blue.
A banana is an apple.
----
Therefore a banana is blue.
For the conclusion to be necessarily true, the premises need to be true.
Now we turn to an invalid form.
All A are B.
C is a B.
----
Therefore C is an A.
To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.
All apples are fruit. (true)
Bananas are fruit. (true)
----
Therefore bananas are apples. (false)
A valid argument with false premises may lead to a false conclusion:
All fat people are Greek
John Lennon was fat
-------------------
Therefore John Lennon was Greek
where a valid argument is used to derive a false conclusion from false premises. The inference is valid because it follows the form of a correct inference.
A valid argument can also be used to derive a true conclusion from false premises:
All fat people are musicians
John Lennon was fat
-------------------
Therefore John Lennon was a musician
In this case we have two false premises that imply a true conclusion.
## Incorrect inference
An incorrect inference is known as a fallacy. Philosophers who study informal logic have compiled large lists of them, and cognitive psychologists have documented many biases in human reasoning that favor incorrect reasoning.
## Automatic logical inference
AI systems first provided automated logical inference and these were once extremely popular research topics, leading to industrial applications under the form of expert systems and later business rule engines.
An inference system's job is to extend a knowledge base automatically. The knowledge base (KB) is a set of propositions that represent what the system knows about the world. Several techniques can be used by that system to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task.
### An example: inference using Prolog
Prolog (for "Programming in Logic") is a programming language based on a subset of predicate calculus. Its main job is to check whether a certain proposition can be inferred from a KB (knowledge base) using an algorithm called backward chaining.
Let us return to our Socrates syllogism. We enter into our Knowledge Base the following piece of code:
mortal(X) :- man(X).
man(socrates).
( Here :- can be read as if. Generally, if P $\to$ Q (if P then Q) then in Prolog we would code Q:-P (Q if P).)
This states that all men are mortal and that Socrates is a man. Now we can ask the Prolog system about Socrates:
?- mortal(socrates).
(where ?- signifies a query: Can mortal(socrates). be deduced from the KB using the rules) gives the answer "Yes".
On the other hand, asking the Prolog system the following:
?- mortal(plato).
gives the answer "No".
This is because Prolog does not know anything about Plato, and hence defaults to any property about Plato being false (the so-called closed world assumption). Finally ?- mortal(X) (Is anything mortal) would result in "Yes" (and in some implemenations: "Yes": X=socrates)
Prolog can be used for vastly more complicated inference tasks. See the corresponding article for further examples.
### Automatic inference and the semantic web
Recently automatic reasoners found in semantic web a new field of application. Being based upon first-order logic, knowledge expressed using one variant of OWL can be logically processed, i.e., inferences can be made upon it.
### Bayesian statistics and probability logic
Philosophers and scientists who follow the Bayesian framework for inference use the mathematical rules of probability to find this best explanation. The Bayesian view has a number of desirable features—one of them is that it embeds deductive (certain) logic as a subset (this prompts some writers to call Bayesian probability "probability logic", following E. T. Jaynes).
Bayesianists identify probabilities with degrees of beliefs, with certainly true propositions having probability 1, and certainly false propositions having probability 0. To say that "it's going to rain tomorrow" has a 0.9 probability is to say that you consider the possibility of rain tomorrow as extremely likely.
Through the rules of probability, the probability of a conclusion and of alternatives can be calculated. The best explanation is most often identified with the most probable (see Bayesian decision theory). A central rule of Bayesian inference is Bayes' theorem, which gave its name to the field.
See Bayesian inference for examples.
### Nonmonotonic logic
Source: Article of André Fuhrmann about "Nonmonotonic Logic"
A relation of inference is monotonic if the addition of premises does not undermine previously reached conclusions; otherwise the relation is nonmonotonic. Deductive inference, at least according to the canons of classical logic, is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premisses are added.
By contrast, everyday reasoning is mostly nonmonotonic because it involves risk: we jump to conclusions from deductively insufficient premises. We know when it is worth or even necessary (e.g. in medical diagnosis) to take the risk. Yet we are also aware that such inference is defeasible—that new information may undermine old conclusions. Various kinds of defeasible but remarkably successful inference have traditionally captured the attention of philosophers (theories of induction, Peirce’s theory of abduction, inference to the best explanation, etc.). More recently logicians have begun to approach the phenomenon from a formal point of view. The result is a large body of theories at the interface of philosophy, logic and artificial intelligence.
## See also
[[Image:|32x28px]] Thinking portal
Portals Portal:thinking Portal:philosophy
## References
1. ^ Euclid, The Elements, Dover, 1956, ISBN 486600882.
Logic portal
# Wiktionary
Up to date as of January 15, 2010
### Definition from Wiktionary, a free dictionary
Wikipedia has an article on:
Wikipedia
See also inférence
## English
### Noun
Singular inference Plural countable and uncountable; plural inferences
inference (countable and uncountable; plural inferences)
1. (uncountable) The act or process of inferring by deduction or induction.
2. (countable) That which is inferred; a truth or proposition drawn from another which is admitted or supposed to be true; a conclusion; a deduction.
#### Translations
The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.
## Czech
### Noun
inference f.
#### Synonyms
Got something to say? Make a comment. Your name Your email address Message | 2,066 | 10,032 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2018-51 | latest | en | 0.955346 |
https://au.mathworks.com/matlabcentral/cody/problems/9-who-has-the-most-change/solutions/1120485 | 1,585,979,970,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370520039.50/warc/CC-MAIN-20200404042338-20200404072338-00519.warc.gz | 364,749,953 | 15,814 | Cody
# Problem 9. Who Has the Most Change?
Solution 1120485
Submitted on 11 Feb 2017 by Jihye Sofia Seo
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
a = [1 2 1 15]; b = 1; assert(isequal(most_change(a),b))
2 Pass
a = [ 1 2 1 15; 0 8 5 9]; b = 2; assert(isequal(most_change(a),b))
3 Pass
a = [ 1 22 1 15; 12 3 13 7; 10 8 23 99]; b = 3; assert(isequal(most_change(a),b))
4 Pass
a = [ 1 0 0 0; 0 0 0 24]; b = 1; assert(isequal(most_change(a),b))
5 Pass
a = [ 0 1 2 1; 0 2 1 1]; c = 1; assert(isequal(most_change(a),c))
6 Pass
% There is a lot of confusion about this problem. Watch this. a = [0 1 0 0; 0 0 1 0]; c = 2; assert(isequal(most_change(a),c)) % Now go back and read the problem description carefully.
7 Pass
a = [ 2 1 1 1; 1 2 1 1; 1 1 2 1; 1 1 1 2; 4 0 0 0]; c = 5; assert(isequal(most_change(a),c)) | 408 | 951 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2020-16 | latest | en | 0.693125 |
http://www.chegg.com/homework-help/questions-and-answers/coulomb-s-law-magnitude-force-particles-charges-separated-distance-permittivity-free-space-q1941375 | 1,394,435,184,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394010683198/warc/CC-MAIN-20140305091123-00087-ip-10-183-142-35.ec2.internal.warc.gz | 281,224,432 | 7,858 | 0 pts ended
Coulomb's law for the magnitude of the force between two particles with charges and separated by a distance is
,
where , and is the permittivity of free space.
Consider two point charges located on the x axis: one charge, = -11.0 , is located at = -1.660 ; the second charge, = 31.5 , is at the origin .
A.) What is the net force exerted by these two charges on a third charge = 55.0 placed between and at = -1.105 ? Your answer may be positive or negative, depending on the direction of the force. | 150 | 521 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2014-10 | latest | en | 0.951327 |
https://www.bartleby.com/solution-answer/chapter-10-problem-1025ex-accounting-27th-edition/9781337272094/fixed-asset-turnover-ratio-fedex-corporation-and-united-parcel-service-inc-compete-in-the-package/3727363b-98dc-11e8-ada4-0ee91056875a | 1,603,295,336,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107876768.45/warc/CC-MAIN-20201021151342-20201021181342-00487.warc.gz | 632,878,967 | 74,531 | Fixed asset turnover ratio FedEx Corporation and United Parcel Service, Inc. compete in the package delivery business. The major fixed assets for each business include aircraft, sorting and handling facilities, delivery vehicles, and information technology. The sales and average book value of fixed assets reported on recent financial statements for each company were as follows: FedEx UPS Sales (in millions) $47,453$58,363 Average book value of fixed assets (in millions) 20,213 18,317 a. Compute the fixed asset turnover ratio for each company. Round to one decimal place. b. Which company appears more efficient in using fixed assets? c. Interpret the meaning of the ratio for the more efficient company.
Accounting
27th Edition
WARREN + 5 others
Publisher: Cengage Learning,
ISBN: 9781337272094
Accounting
27th Edition
WARREN + 5 others
Publisher: Cengage Learning,
ISBN: 9781337272094
Solutions
Chapter
Section
Chapter 10, Problem 10.25EX
Textbook Problem
Fixed asset turnover ratioFedEx Corporation and United Parcel Service, Inc. compete in the package delivery business. The major fixed assets for each business include aircraft, sorting and handling facilities, delivery vehicles, and information technology. The sales and average book value of fixed assets reported on recent financial statements for each company were as follows: FedEx UPS Sales (in millions) $47,453$58,363 Average book value of fixed assets (in millions) 20,213 18,317 a. Compute the fixed asset turnover ratio for each company. Round to one decimal place. b. Which company appears more efficient in using fixed assets? c. Interpret the meaning of the ratio for the more efficient company.
Expert Solution
a.
To determine
Fixed Asset turnover: It is a ratio that measures the productive capacity of the fixed assets to generate the sales revenue for the company. Thus, it shows the relationship between the net sales and the average total fixed assets. The following is the formula to calculate the ratio:
FixedAsset turnover =SalesAverage totalfixed assets
To determine: the fixed asset Turnover Ratio of each company.
Explanation of Solution
Calculate the fixed asset turnover ratio:
For Company F
Sales= $47,453 millions Total average fixed assets=$20,213 millions
Fixed Assets Turnover=SalesAverage Fixed Assets=$47,453$20,213                                    =2
Expert Solution
b.
To determine
To find: which company appears more efficient in using fixed assets.
Expert Solution
c.
To determine
To interpret: the meaning of the ratio for the more efficient company.
Want to see the full answer?
Check out a sample textbook solution.See solution
Want to see this answer and more?
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!
See solution | 713 | 2,908 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2020-45 | latest | en | 0.89258 |
https://www.answersarena.com/ExpertAnswers/solve-the-system-of-differential-equations-x-944030803xx1-pa595 | 1,685,559,391,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647409.17/warc/CC-MAIN-20230531182033-20230531212033-00641.warc.gz | 716,937,566 | 6,939 | Home / Expert Answers / Other Math / solve-the-system-of-differential-equations-x-944030803xx1-pa595
# (Solved): Solve the system of differential equations x=944030803xx1 ...
Solve the system of differential equations
We have an Answer from Expert
To solve this system, we will first find the eigenvalues and eigenvectors of the matrix A = [9 0 -8; 4 -3 0; 4 0 -3]. The eigenvalues can be found by solving the characteristic equation:
det(A - lambda*I) = 0
where I is the 3x3 identity matrix. Simplifying this equation, we get:
det([9-lambda 0 -8] [4 -3-lambda 0] [4 0 -3-lambda]) = 0
Expanding the determinant using the first row, we get:
(9-lambda) * det([-3-lambda 0] [0 -3-lambda]) - 8 * det([4 -3-lambda] [4 0]) = (9-lambda) * (lambda^2 + 6lambda + 9) - 8(-12-4*(3+lambda)) = lambda^3 - 9lambda^2 - 2lambda + 36 = 0
This cubic equation can be factored as (lambda-3)^2 * (lambda+4) = 0, so the eigenvalues are lambda1 = 3 (with algebraic multiplicity 2) and lambda2 = -4.
We have an Answer from Expert | 335 | 1,011 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2023-23 | longest | en | 0.689093 |
https://hextobinary.com/unit/avelocity/from/degpns/to/radpw/993 | 1,713,263,649,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817081.52/warc/CC-MAIN-20240416093441-20240416123441-00374.warc.gz | 268,031,683 | 16,036 | 993 Degree/Nanosecond in Radian/Week
Angular Velocity
Degree/Nanosecond
993 Degree/Nanosecond = 10481861056849000 Radian/Week
How many Radian/Week are in 993 Degree/Nanosecond?
The answer is 993 Degree/Nanosecond is equal to 10481861056849000 Radian/Week and that means we can also write it as 993 Degree/Nanosecond = 10481861056849000 Radian/Week. Feel free to use our online unit conversion calculator to convert the unit from Degree/Nanosecond to Radian/Week. Just simply enter value 993 in Degree/Nanosecond and see the result in Radian/Week. You can also Convert 994 Degree/Nanosecond to Radian/Week
How to Convert 993 Degree/Nanosecond to Radian/Week (993 deg/ns to rad/week)
By using our Degree/Nanosecond to Radian/Week conversion tool, you know that one Degree/Nanosecond is equivalent to 10555751316062 Radian/Week. Hence, to convert Degree/Nanosecond to Radian/Week, we just need to multiply the number by 10555751316062. We are going to use very simple Degree/Nanosecond to Radian/Week conversion formula for that. Pleas see the calculation example given below.
$$\text{1 Degree/Nanosecond} = \text{10555751316062 Radian/Week}$$
$$\text{993 Degree/Nanosecond} = 993 \times 10555751316062 = \text{10481861056849000 Radian/Week}$$
What is Degree/Nanosecond Unit of Measure?
Degree per nanosecond is a unit of measurement for angular velocity. By definition, one degree per nanosecond represents change in the orientation of an object by one degree every nanosecond.
What is the symbol of Degree/Nanosecond?
The symbol of Degree/Nanosecond is deg/ns. This means you can also write one Degree/Nanosecond as 1 deg/ns.
What is Radian/Week Unit of Measure?
Radian per week is a unit of measurement for angular velocity. By definition, one radian per week represents change in the orientation of an object by one radian every week.
What is the symbol of Radian/Week?
The symbol of Radian/Week is rad/week. This means you can also write one Radian/Week as 1 rad/week.
Degree/Nanosecond to Radian/Week Conversion Table (993-1002)
99310481861056849000
99410492416808165000
99510502972559481000
99610513528310797000
99710524084062114000
99810534639813430000
99910545195564746000
100010555751316062000
100110566307067378000
100210576862818694000
Degree/Nanosecond to Other Units Conversion Table
Degree/Nanosecond [deg/ns]Output
993 degree/nanosecond in degree/second is equal to993000000000
993 degree/nanosecond in degree/millisecond is equal to993000000
993 degree/nanosecond in degree/microsecond is equal to993000
993 degree/nanosecond in degree/minute is equal to59580000000000
993 degree/nanosecond in degree/hour is equal to3574800000000000
993 degree/nanosecond in degree/day is equal to85795200000000000
993 degree/nanosecond in degree/week is equal to600566400000000000
993 degree/nanosecond in degree/month is equal to2611391400000000000
993 degree/nanosecond in degree/year is equal to31336696800000000000
993 degree/nanosecond in radian/second is equal to17331119472.3
993 degree/nanosecond in radian/millisecond is equal to17331119.47
993 degree/nanosecond in radian/microsecond is equal to17331.12
993 degree/nanosecond in radian/nanosecond is equal to17.33
993 degree/nanosecond in radian/minute is equal to1039867168338.2
993 degree/nanosecond in radian/hour is equal to62392030100293
993 degree/nanosecond in radian/day is equal to1497408722407000
993 degree/nanosecond in radian/week is equal to10481861056849000
993 degree/nanosecond in radian/month is equal to45577377988264000
993 degree/nanosecond in radian/year is equal to546928535859170000
993 degree/nanosecond in gradian/second is equal to1103333333333.3
993 degree/nanosecond in gradian/millisecond is equal to1103333333.33
993 degree/nanosecond in gradian/microsecond is equal to1103333.33
993 degree/nanosecond in gradian/nanosecond is equal to1103.33
993 degree/nanosecond in gradian/minute is equal to66200000000000
993 degree/nanosecond in gradian/hour is equal to3972000000000000
993 degree/nanosecond in gradian/day is equal to95328000000000000
993 degree/nanosecond in gradian/week is equal to667296000000000000
993 degree/nanosecond in gradian/month is equal to2901546000000000000
993 degree/nanosecond in gradian/year is equal to34818552000000000000
993 degree/nanosecond in gon/second is equal to1103333333333.3
993 degree/nanosecond in gon/millisecond is equal to1103333333.33
993 degree/nanosecond in gon/microsecond is equal to1103333.33
993 degree/nanosecond in gon/nanosecond is equal to1103.33
993 degree/nanosecond in gon/minute is equal to66200000000000
993 degree/nanosecond in gon/hour is equal to3972000000000000
993 degree/nanosecond in gon/day is equal to95328000000000000
993 degree/nanosecond in gon/week is equal to667296000000000000
993 degree/nanosecond in gon/month is equal to2901546000000000000
993 degree/nanosecond in gon/year is equal to34818552000000000000
993 degree/nanosecond in revolution/second is equal to2758333333.33
993 degree/nanosecond in revolution/millisecond is equal to2758333.33
993 degree/nanosecond in revolution/microsecond is equal to2758.33
993 degree/nanosecond in revolution/nanosecond is equal to2.76
993 degree/nanosecond in revolution/minute is equal to165500000000
993 degree/nanosecond in revolution/hour is equal to9930000000000
993 degree/nanosecond in revolution/day is equal to238320000000000
993 degree/nanosecond in revolution/week is equal to1668240000000000
993 degree/nanosecond in revolution/month is equal to7253865000000000
993 degree/nanosecond in revolution/year is equal to87046380000000000
993 degree/nanosecond in sign/second is equal to33100000000
993 degree/nanosecond in sign/millisecond is equal to33100000
993 degree/nanosecond in sign/microsecond is equal to33100
993 degree/nanosecond in sign/nanosecond is equal to33.1
993 degree/nanosecond in sign/minute is equal to1986000000000
993 degree/nanosecond in sign/hour is equal to119160000000000
993 degree/nanosecond in sign/day is equal to2859840000000000
993 degree/nanosecond in sign/week is equal to20018880000000000
993 degree/nanosecond in sign/month is equal to87046380000000000
993 degree/nanosecond in sign/year is equal to1044556560000000000
993 degree/nanosecond in mil/second is equal to17653333333333
993 degree/nanosecond in mil/millisecond is equal to17653333333.33
993 degree/nanosecond in mil/microsecond is equal to17653333.33
993 degree/nanosecond in mil/nanosecond is equal to17653.33
993 degree/nanosecond in mil/minute is equal to1059200000000000
993 degree/nanosecond in mil/hour is equal to63552000000000000
993 degree/nanosecond in mil/day is equal to1525248000000000000
993 degree/nanosecond in mil/month is equal to46424736000000000000
993 degree/nanosecond in mil/year is equal to557096832000000000000
Disclaimer:We make a great effort in making sure that conversion is as accurate as possible, but we cannot guarantee that. Before using any of the conversion tools or data, you must validate its correctness with an authority. | 2,042 | 6,991 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2024-18 | latest | en | 0.899448 |
https://byjus.com/rs-aggarwal-solutions/rs-aggarwal-class-6-solutions-chapter-8-algebraic-expressions-exercise-8-2/ | 1,563,563,587,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526337.45/warc/CC-MAIN-20190719182214-20190719204214-00196.warc.gz | 332,848,521 | 113,741 | # RS Aggarwal Class 6 Solutions Chapter 8 - Algebraic Ex 8B(8.2)
## RS Aggarwal Class 6 Chapter 8 - Algebraic Ex 8B(8.2) Solutions Free PDF
Question 1:
a – (b – 2a)
Here, sign precedes the parenthesis.
So, we will remove it and change the sign of each term within the parenthesis.
=a – b + 2a
=3a – b
Question 2:
4x – (3y – x + 2z)
Here, 1-1 sign precedes the parenthesis.
So, we will remove it and change the sign of each term within the parenthesis.
= 4x – 3y + x – 2z
= 5x – 3y – 2z
Question 3:
($a^{2}$ + $b^{2}$ + 2ab) – ($a^{2}$ + $b^{2}$ – 2ab)
Here, ‘-‘ sign precedes the second parenthesis. So we will remove it and change the sign of each term within the parenthesis.
$a^{2}$ + $b^{2}$ + 2ab – $a^{2}$$b^{2}$ +2ab
Rearranging and collecting the like terms:
$a^{2}$$a^{2}$ + $b^{2}$$b^{2}$ + 2ab + 2ab
=(1- 1) $a^{2}$ + (1- 1) $b^{2}$ + (2 + 2)ab
=0 + 0 + 4ab
= 4ab
Question 4:
-3(a + b) + 4(2a – 3b) – (2a – b)
Here, 1-1 sign precedes the first and the third parenthesis. So, we will remove them and change the sign of each term within the two parenthesis.
= -3a – 3b + (4x 2a )-(4x 3b) – 2a + b
= – 3a – 3b + 8a – 12b – 2a + b
Rearranging and collecting the like terms:
-3a + 8a – 2a – 3b – 12b + b
= (-3 + 8 – 2)a + (-3 – 12 + 1)b
= 3a -14b
Question 5:
-4$x^{2}$ + {(2$x^{2}$ – 3) – (4 – 3$x^{2}$)}
We will first remove the innermost grouping symbol ) and then { }.
-4$x^{2}$ + {(2$x^{2}$ – 3) – (4 – 3$x^{2}$)}
= -4$x^{2}$ + {2$x^{2}$ – 3 – 4 + 3$x^{2}$}
= -4$x^{2}$ + {5$x^{2}$ – 7}
= -4$x^{2}$ + 5$x^{2}$ – 7
= $x^{2}$ – 7
Question 6:
-2($x^{2}$$y^{2}$ + xy) -3($x^{2}$ + y2 – xy)
Here a sign precedes both the parenthesis. So, we will remove them and change the sign of each term within the two parenthesis.
= -2$x^{2}$ +2$y^{2}$ – 2xy -3$x^{2}$ – 3$y^{2}$ + 3xy
= (-2 – 3) $x^{2}$ +(2 – 3) $y^{2}$ + (- 2 + 3) xy
= -5$x^{2}$$y^{2}$ + xy
Question 7:
a – [2b – {3a – (2b – 3c)}]
We will first remove the innermost grouping symbol ( ), followed by { and then [ ].
a – [2b – {3a – (2b – 3c)}]
= a – [2b – {3a – 2b + 3c}]
= a – [2b – 3a + 2b – 3c]
= a – [4b – 3a – 3c]
= a – 4b + 3a + 3c
= 4a – 4b + 3c
Question 8:
-x + [5y – {x – (5y – 2x)}]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ].
-x + [5y – {x – (5y – 2x)}]
= -x + [5y – {x – 5y + 2x}]
= -x + [5y – {3x – 5y}]
= -x + [5y – 3x + 5y]
= -x + [10y – 3x]
=-x+10y-3x
= -4x+10y
Question 9:
86 – [15x – 7(6x – 9) -2{10x – 5(2 – 3x)}]
We will first remove the innermost grouping symbol ( ), followed by { and then [ ].
86 – [15x – 7(6x – 9) -2(10x – 5(2 – 3x)}]
= 86 – [15x – 42x + 63 -2(10x – 10 + 15x)]
= 86 – [15x – 42x + 63 -2{25x – 10)]
= 86 – [15x – 42x + 63 -50x + 20]
= 86 – [- 77x + 83]
= 86 + 77x – 83
= 77x + 3
Question 10:
12x – [3$x^{3}$ + 5$x^{2}$ – {7$x^{2}$ – (4 – 3x – $x^{3}$) + 6$x^{3}$} – 3x]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ]
12x – [3$x^{3}$ + 5$x^{2}$ – (7$x^{2}$ – (4 – 3x – $x^{3}$) + 6$x^{3}$} – 3x]
= 12x – [3$x^{3}$ + 5$x^{2}$ – {7$x^{2}$ – 4 + 3x + $x^{3}$+ 6$x^{3}$} – 3x]
= 12x – [3$x^{3}$ + 5$x^{2}$ – (7$x^{2}$ – 4 + 3x + 7$x^{3}$} – 3x]
= 12x – [3$x^{3}$ + 5$x^{2}$ – 7$x^{2}$ + 4 – 3x – 7$x^{3}$ – 3x]
= 12x – [- 2$x^{2}$ + 4 – 4$x^{3}$ – 6x]
= 12x + 2$x^{2}$ – 4 + 4$x^{3}$ + 6x
= 4$x^{3}$ + 2$x^{2}$ +18x – 4
Question 11:
5a – [$a^{2}$ – {2a(1 – a + 4$a^{2}$) – 3a($a^{2}$ – 5a – 3))] -8a
We will first remove the innermost grouping symbol ( ), followed by { and then [ ].
5a – [$a^{2}$ – 2a(1 – a + 4$a^{2}$) – 3a($a^{2}$ – 5a – 3))) -8a
= 5a – [$a^{2}$ – {2a – 2$a^{2}$ + 8$a^{3}$ – 3$a^{3}$ + 15$a^{2}$ + 9a}] -8a
= 5a – [$a^{2}$ – 5$a^{3}$ + 13$a^{2}$ + 11a)] – 8a
= 5a – [$a^{2}$ – 5$a^{3}$ – 13$a^{2}$ -11a] – 8a
= 5a – [ – 5$a^{3}$ – 12$a^{2}$ – 11a] – 8a
= 5a + 5$a^{3}$ + 12$a^{2}$ + 11a – 8a
= 5$a^{3}$ + 12$a^{2}$ + 8a
Question 12:
3 — [x — {2y — (5x + y — 3) + 2×2} — (x2 — 3y)]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ].
3 — [x — {2y — (5x + y — 3) + 2$x^{2}$} — ($x^{2}$ — 3y)]
= 3 — [x — {2y — 5x – y + 3 + 2$x^{2}$} — x2 + 3y]
= 3 — [x — {y — 5x + 3 + 2$x^{2}$} — $x^{2}$ + 3y]
=3—[x— y+5x-3-2$x^{2}$— $x^{2}$+3y]
= 3 — [ 6x — 3 — 3$x^{2}$ + 2y]
= 3 – 6x + 3+ 3$x^{2}$ —2y
= 3$x^{2}$ — 2y — 6x + 6
Question 13:
xy – [yz – zx – {yx – (3y – xz ) – (xy – zy)}]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ].
xy – [yz – zx – {yx – (3y – xz) – (xy – zy)}]
= xy – [yz – zx – {yx – 3y + >tz – xy + zy}]
= xy – [yz – zx – {- 3y + xz + zy}] (xy=yx)
= xy – [yz – zx + 3y – xz – zy]
= xy – [- 2zx + 3y]
= xy + 2zx – 3y
Question 14:
2a – 3b – [3a – 2b – {a – c – (a – 2b)}]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ].
2a – 3b – [3a – 2b – {a – c – (a – 2b)}]
= 2a – 3b – [3a – 2b – {a – c – a + 2b}]
= 2a – 3b – [3a – 2b -{-c + 2b}]
= 2a – 3b – [3a – 2b + c – 2b]
=2a-3b-[3a-4b+c]
= 2a – 3b – 3a + 4b – c
=-a+b-c
Question 15:
-a – [a + {a + b – 2a – (a – 2b)} – b]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ].
-a – [a + {a + b – 2a – (a – 2b)} – b]
= -a – [a + {a + b – 2a – a + 2b} – b]
= -a – [a + {3b – 2a } – b]
= -a – [a + 3b – 2a – b]
= -a – [2b – a ]
= -a – 2b + a
= -2b
Question 16:
2a – [4b – (4a – (3b – 2a + 2b)]
We will first remove the innermost grouping symbol bar bracket. Next, we will remove ( ), followed by { } and then [ ].
2a-[4b-(4a-(3b-2a+2b)]
= 2a-[4b-{4a-(3b-2a-2b)}]
= 2a-[4b-{4a-(b-2a)}]
= 2a-[4b-{4a-b+2a}]
=2a-[4b-(6a-b)]
= 2a-[4b-6a+b]
= 2a-[5b-6a]
= 2a-5b+6a
= 8a-5b
Question 17:
5x – [4y- 7x – (3z – 2y) + 4z – 3(x + 3y- 2z)}]
We will first remove the innermost grouping symbol ( ), followed by { } and then [ ]
5x – [4y – {7x – (3z – 2y) + 4z – 3(x + 3y – 2z)}]
= 5x – [4y- 7x – 3z + 2y+ 4z – 3x – 9y+ 6z]
= 5x – [4y- {4x + 7z – 7y}]
= 5x – [4y – 4x – 7z + 7y]
= 5x – [11y – 4x – 7z]
= 5x – 11y + 4x + 7z
= 9x – 11y + 7z
#### Practise This Question
If “a” chocolates are distributed amongst “b” students equally, then what is the share of chocolates obtained by each student? | 3,213 | 6,291 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.8125 | 5 | CC-MAIN-2019-30 | latest | en | 0.59003 |
https://www.broadridgeadvisor.com/webresourcesview/ContentView.aspx?iplf=ff&iptc=124126&wcKey=A1F58FD9775CD1F83542BDB022D9FCBB3F3384237F77CB335303A2CAEDDCBEAC | 1,620,536,358,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988955.89/warc/CC-MAIN-20210509032519-20210509062519-00123.warc.gz | 699,328,048 | 25,459 | # Monte Carlo Analysis
When you sit down with a financial professional to update your retirement plan, you may encounter a Monte Carlo simulation, a financial forecasting method that has become more prevalent in the last few years. Monte Carlo financial simulations project and illustrate the probability that you'll reach your financial goals, and might help you make a more informed investment decision.
### Estimating investment returns
All financial forecasts must account for variables like inflation rates and investment returns. The catch is that these variables have to be estimated, and the estimate used is key to a forecast's results. For example, a forecast that assumes stocks will earn an average of 4% each year for the next 20 years will differ significantly from a forecast that assumes an average annual return of 8% over the same period.
Estimating investment returns is particularly difficult. For example, the volatility of stock returns can make short-term projections almost meaningless. Multiple factors influence investment returns, including events such as natural disasters and terrorist attacks, which are unpredictable. So, it's important to understand how different forecasting methods handle uncertainty.
### Basic forecasting methods
Straight-line forecasting methods assume a constant value for the projection period. For example, a straight-line forecast might show that a portfolio worth \$116,000 today would have a future value of approximately \$250,000 if the portfolio grows by an annual compounded return of 8% for the next 10 years. This projection is helpful, but it has a flaw: In the real world, returns aren't typically that consistent from year to year.
Forecasting methods that utilize "scenarios" provide a range of possible outcomes. Continuing with the 10-year example above, a "best-case scenario" might assume that your portfolio will grow by an average 10% annual return and reach \$300,000. The "most-likely scenario" might assume an 8% return (for a \$250,000 value), and the "worst-case scenario" might use 4%, resulting in roughly \$171,000. Scenarios give you a better idea of the range of possible outcomes. However, they aren't precise in estimating the likelihood of any specific result.
Forecasts that use Monte Carlo analysis are based on computer-generated simulations. You may be familiar with simulations in other areas; for example, local weather forecasts are typically based on a computer analysis of national and regional weather data. Similarly, Monte Carlo financial simulations rely on computer models to replicate the behavior of economic variables, financial markets, and different investment asset classes.
### Why is a Monte Carlo simulation useful?
In contrast to more basic forecasting methods, a Monte Carlo simulation is designed to account for volatility, especially the volatility of investment returns. It enables you to see a spectrum of thousands of possible outcomes, taking into account not only the many variables involved, but also the range of potential values for each of those variables.
By attempting to replicate the uncertainty of the real world, a Monte Carlo simulation can provide a detailed illustration of how likely it is that a given investment strategy might meet your needs. For example, when it comes to retirement planning, a Monte Carlo simulation can help you answer specific questions, such as:
• Given a certain set of assumptions, what is the probability that you will run out of funds before age 85?
• If that probability is unacceptably high, how much additional money would you need to invest each year to decrease the probability to 10%?
### The mechanics of a Monte Carlo simulation
A Monte Carlo simulation typically involves hundreds or thousands of individual forecasts or "iterations," based on data that you provide (e.g., your portfolio, timeframes, and financial goals). Each iteration draws a result based on the historical performance of each investment class included in the simulation.
Each asset class — small-cap stocks, corporate bonds, etc. — has an average (or mean) return for a given period. Standard deviation measures the statistical variation of the returns of that asset class around its average for that period. A higher standard deviation implies greater volatility. The returns for stocks have a higher standard deviation than the returns for U.S. Treasury bonds, for instance.
There are various types of Monte Carlo methods, but each generates a forecast that reflects varying patterns of returns. Software modeling stock returns, for example, might produce a series of annual returns such as the following: Year 1: -7%; Year 2: -9%; Year 3: +16%, and so on. For a 10-year projection, a Monte Carlo simulation will produce a series of 10 randomly generated returns — one for each year in the forecast. A separate series of random returns is generated for each iteration in the simulation and multiple combined iterations are considered a simulation. A graph of a Monte Carlo simulation might appear as a series of statistical "bands" around a calculated average.
Example: Let's say a Monte Carlo simulation performs 1,000 iterations using your current retirement assumptions and investment strategy. Of those 1,000 iterations, 600 indicate that your assumptions will result in a successful outcome; 400 iterations indicate you will fall short of your goal. The simulation suggests you would have a 60% chance of meeting your goal.
### Pros and cons of Monte Carlo
A Monte Carlo simulation illustrates how your future finances might look based on the assumptions you provide. Though a projection might show a very high probability that you may reach your financial goals, it can't guarantee that outcome. However, a Monte Carlo simulation can illustrate how changes to your plan could affect your odds of achieving your goals. Combined with periodic progress reviews and plan updates, Monte Carlo forecasts could help you make better-informed investment decisions.
Important: The projections or other information generated by Monte Carlo analysis tools regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. Results may vary with each use and over time. Because of the many variables involved, an investor should not rely on forecasts without realizing their limitations.
This material does not constitute the rendering of investment, legal, tax or insurance advice or services. It is intended for informational use only and is not a substitute for investment, legal, tax, and insurance advice. State, national and international laws vary, as do individual circumstances; so always consult a qualified investment advisor, attorney, CPA, or insurance agent on all investment, legal, tax, or insurance matters. The effectiveness of any of the strategies described will depend on your individual situation and on a number of other factors.Advisory Services Offered Through Select Portfolio Management, Inc.A Registered Investment AdvisorSecurities Offered Through Securities Equity GroupMember FINRA www.finra.org , SIPC www.sipc.gov This communication is strictly intended for individuals residing in the state(s) of CA. No offers may be made or accepted from any resident outside the specific states referenced.
Prepared by Broadridge Investor Communication Solutions, Inc. Copyright 2021. | 1,405 | 7,472 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2021-21 | latest | en | 0.925246 |
http://onlineconversion.com/forum/forum_1076980868.htm | 1,544,510,932,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823588.0/warc/CC-MAIN-20181211061718-20181211083218-00200.warc.gz | 204,141,301 | 3,537 | ## Welcome to OnlineConversion.com
I just don't know
I just don't know
by queenbee on 02/16/04 at 17:21:07
:( ???
I am laminating my kitchen but in order to find out how many packs of flooring I would need, I need to find out the size of the area.
Now the problem is I have no idea what a square inch is
and how to measure a square inch, I know this sounds silly but my brain refuses to register what it is even though people have tried explaining it to me.
So my question is how do I measure a square inch?
To give you an idea, (whether it helps or not) my kitchen is in the shape of a [b]T [/b]- Now long part of the[b] T is 145" straight inches and 64" in width[/b].
The top part of the [b]T 156"[/b] in length and [b]36" in width[/b]
Now I dont know if any of the above makes any sense to [b]anyone[/b]
Any help on this one would be greatly appreciated
Thanks ;D
Re: I just don't know
by Philip Eves on 02/16/04 at 18:14:55
Multiply 146 by 64
Multiply 156 by 36
This will give you the total area in square inches.
Re: I just don't know
by queenbee on 02/17/04 at 04:19:17
Ok thanks for that, I did try that but the answer seemed way too much.
However I will take your word for it
Thanks again
;)
Re: I just don't know
by Robert Fogt on 02/17/04 at 10:59:08
That is correct.
Area = Length * Width
The easiest way to think of square inches, is:
inches * inches = inches[sup]2[/sup]
145 inches * 64 inches = 9,280 inches[sup]2[/sup]
156 inches * 36 inches = 5,616 inches[sup]2[/sup]
The total would be:
9,280 + 5,616 = 14,896 square inches
### BookMark Us
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Try the Fun Stuff. | 514 | 1,728 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2018-51 | latest | en | 0.945834 |
https://secondsminutes.com/225-8-minutes-in-minutes-and-seconds | 1,718,959,837,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862040.7/warc/CC-MAIN-20240621062300-20240621092300-00866.warc.gz | 453,387,790 | 5,123 | # 225.8 minutes in minutes and seconds
## Result
225.8 minutes equals 225 minutes and 48 seconds
You can also convert 225.8 minutes to seconds.
## Converter
Two hundred twenty-five point eight minutes is equal to two hundred twenty-five minutes and forty-eight seconds. | 63 | 274 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2024-26 | latest | en | 0.865772 |
https://economics.stackexchange.com/questions/11975/productive-allocative-efficiency-competitive-equilibrium | 1,713,847,579,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818464.67/warc/CC-MAIN-20240423033153-20240423063153-00082.warc.gz | 195,503,936 | 39,432 | # Productive Allocative Efficiency (Competitive Equilibrium)
I am doing an Intermediate Microeconomics class... in a 2*2*2*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in order for it to be a competitive equilibrium. Why is this? I understand that supply is supposed to be equal to demand... Thank you!
• I don't think that MRS = MRTS is a condition for a competitive equilibrium. Are you sure you are not confusing with an equilibrium of pure exchange (cf. Edgeworth's box) where TMS1 (marginal rate of substitution of person 1) = TMS2 (marginal rate of substitution of person 2) ? May 12, 2016 at 22:46
• This is for a 2x2x2x2 economy where there is both production and consumption. So, it is correct. Just wanted to get a clearer understanding of why. May 13, 2016 at 7:09
• I think you're a little off the mark.
– 123
May 13, 2016 at 19:46
Equilibrium conditions will require, among other things,:
1.) $MRS_{a,b}^i=MRS_{a,b}^j \forall [i,j] \in N$ , $N$ the set of agents
2.) $MRTS_{x,y}^i=MRTS_{x,y}^j \forall [i,j] \in J$ , $J$ the set of firms
3.) $MRT=MRS$ (Assuming that 1,2 hold)
And I note that 1,2 are efficiency conditions. 3 is efficiency in the output market.
Why? Suppose 1,2 hold at:
• $MRS^i_{y,x}=3$
• $MRT_{y,x}=2$
Obviously, condition 3 does not hold.
Can you see why this cannot be an equilibrium outcome? Think about what should happen in the economy and the forces that will drive this economy toward a state s.t. condition 3 holds.
So:
$MRT_{x,y}=\frac{MC_x}{MC_y} \equiv \frac{P_x}{P_y} = MRS$
where I assume 1 holds so MRS is same for all agents. | 517 | 1,676 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2024-18 | latest | en | 0.895743 |
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# ICSE Class X Prelims 2020 : Mathematics (St. Francis School, South Sikkim)
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1. Mr. Nadeem saves 80 every month and deposits in a recurring deposit account paying 8% simple interest per annum in order to receive a total amount of 5776. How many instalments need to be deposited? 2. If 2x 3 cx 2 dx 15 has 2 x 3 as factor and leaves a remainder 5 when divided by x 1 , find the value of c and d. 3. Abhay invests 6000 in 8% 10 shares at 15. He sells the shares when the price rises to 50 and invests the proceeds in 12% 100 shares at 125. Calculate: i. The sale proceeds ii. The number of 125 shares he buys iii. The change in annual income from his dividend 4. Solve for x and give your answer correct to two significant figures: x 2 5 x 10 0 5. Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. Find the probability that the number on the card is: i. Number less than 14 ii. Number which is a perfect square iii. Prime number less than 20 iv. Number divisible by 5 and 10 6. Simplify: 2 sin 30 cos ec30 cos ec90 tan 45 cos 0 cos 60 2 3 1 0 7. Given A and A2=9A+mI. Find m. ;I 0 5 0 1 8. Find the value of X, for the given AP if 1 4 7 ......... x 247 9. The sum of first 3 terms of a GP is 49 and their product 15 is 1. Find the common ratio and the first three terms. 10. A person bought a certain number of pens for 800. If he had bought 4 pens more for the same money, he would have paid 10 less for each pen. How many pens did he buy? 11. Draw an Ogive for the data below and from it, determine: Monthly income Number of workers 6000 7000 40 7000 8000 68 8000 9000 86 9000 10000 120 10000 11000 90 11000 12000 40 12000 13000 26 i. Median ii. The number of employees whose income exceeds 11800. 12. Solve the given inequation and graph the solution on the number line. 1 x 1 5 - 2 1 ; x I 6 3 6 6 13. The 4th term of a GP is 16 and the 7th term is 128. Find the first term and common ratio of the series.
Formatting page ... | 673 | 2,135 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2022-21 | latest | en | 0.889186 |
https://huongdanjava.com/merge-sort-algorithm.html | 1,696,375,896,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511284.37/warc/CC-MAIN-20231003224357-20231004014357-00396.warc.gz | 347,109,640 | 38,579 | # Merge Sort algorithm
In this tutorial, I will be with you to learn about an algorithm to sort the elements in an array, Merge Sort algorithm!
OK,
Now suppose I have an array of numeric values arranged as follows:
The Merge Sort algorithm divides the array into multiple child arrays, until each of the children has only one element. Then, it compares the values of the sub arrays so that they are grouped together into sorted arrays. And finally, we will get a sorted array.
In our example, using the Merge Sort algorithm, the following steps will occur:
Step 1: Divide the large array into two sub-arrays:
• Step 2: Continue to split
• Step 3: Still have the array containing more than 2 elements so continue to split
• Step 4: Because all the arrays now contain one element, we now compare the values and collect them.
• Step 5: Continue collecting:
• Result:
As you see, after a few steps divided, the array was rearranged.
The idea is that, so what is the Merge Sort algorithm? Let me tell you the following.
The Merge algorithm looks like this:
OK, here’s how to implement the Merge Sort algorithm with the Java language:
In this implementation of the Merge Sort algorithm, I used the Comparator interface to compare two objects of the same class.
Below, I will use the code above to make an example:
Result: | 289 | 1,333 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2023-40 | longest | en | 0.865047 |
polsys.github.io | 1,717,080,950,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971668873.95/warc/CC-MAIN-20240530145337-20240530175337-00520.warc.gz | 402,800,613 | 8,264 | View on GitHub
# Getting started
In this tutorial we will go through the various use cases of ennemi. I assume that you know, at basic level, what mutual information means. Before starting with your own projects, I strongly encourage you to still read the chapter on potential issues, lest you want to discover those the hard way!
Note: You may get slightly different results when running the examples. The processor model, operating system and software versions have subtle effects on floating point calculations. The results should still be the same to several significant digits.
## Bivariate normal distribution
We begin by considering a two-variable normal distribution: $$(X, Y) \sim \mathrm{Normal}(\mu, \Sigma).$$ We assume that both $X$ and $Y$ have unit variance. The two variables may be correlated with the coefficient $\rho$. In this case the covariance matrix becomes $$\Sigma = \begin{bmatrix} 1 & \rho\\ \rho & 1 \end{bmatrix}.$$ In this case, there is a formula for the mutual information between the two variables: $$\mathrm{MI}(X, Y) = -\frac 1 2 \ln \det \Sigma = -\frac 1 2 \ln (1-\rho^2).$$
For example, if $\rho = 0.8$, we would expect $\mathrm{MI}(X, Y) \approx 0.51$. We can test what ennemi outputs with the following code:
from ennemi import estimate_mi
import numpy as np
rng = np.random.default_rng(1234)
rho = 0.8
cov = np.array([[1, rho], [rho, 1]])
data = rng.multivariate_normal([0, 0], cov, size=800)
x = data[:,0]
y = data[:,1]
print(estimate_mi(y, x))
The code prints
[[0.51039762]]
as would be expected. The result is in double brackets because estimate_mi() always outputs a 2D array. This will be discussed more below.
## Correlation coefficient
Mutual information may have any non-negative value. For easier interpretation, the MI can be converted to correlation coefficient scale. To continue the above example, we could execute
print(estimate_mi(y, x, normalize=True))
to get the estimated correlation coefficient (0.79980729). Because the correlation coefficient is more useful in applied analysis, there is a shorter alias for it:
print(estimate_corr(y, x))
The returned coefficient approximately matches the absolute value of the linear correlation coefficient after suitable transformations. For example, consider the model $y = \sin(x) + \varepsilon$.
Ordinary linear correlation is unsuitable in this case: the best straight line through the data points would be nearly horizontal. However, a straight line could be drawn if we transformed the X axis to represent $\sin(x)$, and kept the Y axis as is.
We calculate both the linear correlation and correlation from MI:
from ennemi import estimate_corr
import numpy as np
rng = np.random.default_rng(1234)
x = rng.normal(0.0, 3.0, size=800)
y = np.sin(x) + rng.normal(0.0, 0.5, size=800)
print(f"From MI: {estimate_corr(y, x)[0,0]:.3}")
print(f"Pearson, transformed: {np.corrcoef(y, np.sin(x))[0,1]:.3}")
print(f"Pearson, straight line: {np.corrcoef(y, x)[0,1]:.3}")
The two values are very close to each other. Without the correct transformation, there is no linear correlation between the two variables.
From MI: 0.824
Pearson, transformed: 0.812
Pearson, straight line: 0.01993
There are some caveats to the above. The two coefficients are theoretically equivalent only when the transformations are monotonic. Periodic transformations such as sine (as above) have additional requirements on symmetry: x should be distributed evenly across periods. Therefore, the returned coefficient should be considered only approximate.
## More variables
Let’s extend the above example by adding another, unrelated variable. The mutual information between independent variables is 0.
The estimate_mi() and estimate_corr() methods accept a 2D array for the x parameter. In that case, it splits the array into columns $X_1$ to $X_m$, and calculates $\mathrm{MI}(X_i, Y)$ for each $i = 1, \ldots, m$.
This interface is a shorter way of calculating the MI between several $X$ variables and $Y$. It is also much faster, because ennemi computes the estimates in parallel whenever it is beneficial.
Note: This should not be confused with multivariate mutual information, a measure of interdependency between three or more variables together. ennemi does not currently support multivariate MI, as the results would be difficult to interpret.
Here’s the above example updated with a new, independent variable $Z$:
from ennemi import estimate_corr
import numpy as np
rng = np.random.default_rng(1234)
rho = 0.8
cov = np.array([[1, rho], [rho, 1]])
data = rng.multivariate_normal([0, 0], cov, size=800)
x = data[:,0]
y = data[:,1]
z = rng.normal(0, 1, size=800)
covariates = np.column_stack((x, z))
print(estimate_corr(y, covariates))
The code prints
[[ 0.79978795 -0.02110195]]
The first column gives the correlation between $(X, Y)$ and the second column between $(Z, Y)$. As expected, the latter is very close to $0$. Due to random uncertainty and properties of the estimation algorithm, the result will not be exactly 0, and may even be negative. (Negative values far from zero, including $-\infty$, are discussed in the chapter on potential issues.)
The x parameter is interpreted as x[observation index, variable index]. This matches the order used by NumPy and Pandas libraries. See below for an example of using Pandas for data import.
## Time lag
In many systems, variables are coupled with a time delay. There may be a clear dependence between $Y(t)$ and $X(t-\Delta)$, whereas the apparent link between $Y(t)$ and $X(t)$ may be weaker or nonexistent.
The time lag is specified by passing an integer or a list/array of integers as the lag parameter to estimate_mi()/estimate_corr(). The lags are applied to the $X_i$ variables and may be positive or negative (in which case information flows from $Y$ to $X$ instead).
Let’s consider a model where $Y(t) = X(t-1) + \varepsilon$, and estimate the MI for various time lags:
from ennemi import estimate_corr
import numpy as np
rng = np.random.default_rng(1234)
x = rng.gamma(1.0, 1.0, size=400)
y = np.zeros(400)
y[1:] = x[0:-1]
y += rng.normal(0, 0.01, size=400)
print(estimate_corr(y, x, lag=[1, 0, -1]))
The code prints:
[[ 0.99975754]
[-0.04579946]
[-0.00918085]]
which means that $Y(t)$ depends strongly on $X(t-1)$, but not at all on $X(t)$ or $X(t+1)$. The rows of the result array correspond to the lag parameter.
### Technical note
The $Y$ array is constrained so that it stays the same for all lags. This is done in order to make the results slightly more comparable. For example, if there are observations $Y(0), \ldots, Y(N-1)$ and the lags are $-1$, $0$ and $1$, the array $Y(1), \ldots, Y(N-2)$ is compared with $$\begin{cases} X(2), \ldots, X(N-1),\\ X(1), \ldots, X(N-2),\\ X(0), \ldots, X(N-3), \end{cases}$$ each in turn.
## Combining the above with Pandas
In this example, we import the data set from a file using the Pandas package and pass the imported data straight to estimate_corr(). We calculate the MI for several time lags and plot the results with Matplotlib.
To try this example, download the mi_example.csv file.
from ennemi import estimate_corr
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
data = pd.read_csv("mi_example.csv")
time_lags = np.arange(-3, 6)
mi = estimate_corr(data["y"], data[["x1", "x2", "x3"]],
lag=time_lags)
plt.plot(time_lags, mi["x1"], label="$x_1$", marker="o")
plt.plot(time_lags, mi["x2"], label="$x_2$", marker="^")
plt.plot(time_lags, mi["x3"], label="$x_3$", marker="s")
plt.legend()
plt.xlabel("Time lag (steps)")
plt.ylabel("MI correlation")
plt.title("Mutual information between $y$ and...")
plt.show() # or plt.savefig(...)
The returned array is also a Pandas data frame, with column names matching variable names and indices matching lag values:
x1 x2 x3
-3 -0.017814 -0.005630 -0.006186
-2 -0.039053 0.391237 0.311316
-1 -0.039403 -0.003894 -0.037381
0 0.280384 -0.028118 0.958259
1 0.998803 -0.012764 0.349852
2 -0.002487 -0.003956 0.150416
3 0.137114 0.993299 0.275532
4 -0.038925 0.368778 -0.041505
5 -0.006512 -0.074845 -0.000150
From this plot we can deduce that:
• there is a connection between $Y$ and $X_1$, but only with lag 1,
• a slightly weaker connection between $Y$ and $X_2$, but only with lag 3,
• a connection between $Y$ and $X_3$ without any lag,
• and a weak connection with lag -2.
A word of warning: in a real time series, where the data is often autocorrelated, the peaks will not be nearly as sharp.
## Conditional mutual information
Suppose that in our previous example, we know that there is a connection between $X_1(t)$ and $X_2(t-2)$.
Now the question is: how much additional information does $X_1$ provide when $X_2$ is already known? We get this by calculating the conditional mutual information. We pass the $X_2$ column as the cond parameter, and specify that the condition should be lagged by additional two steps:
from ennemi import estimate_corr
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
data = pd.read_csv("mi_example.csv")
time_lags = np.arange(-3, 6)
mi = estimate_corr(data["y"], data[["x1", "x3"]], lag=time_lags,
cond=data["x2"], cond_lag=time_lags+2)
print(mi)
plt.plot(time_lags, mi["x1"], label="$x_1$", marker="o")
plt.plot([], []) # Keep the colors comparable
plt.plot(time_lags, mi["x3"], label="$x_3$", marker="s")
plt.legend()
plt.xlabel("Time lag (steps)")
plt.ylabel("Mutual information (nats)")
plt.title("Conditional mutual information between $y$ and...")
plt.show()
x1 x3
-3 -0.034824 0.088609
-2 -0.086125 -0.015640
-1 -0.038222 -0.025096
0 -0.096564 0.885572
1 0.839362 -0.055681
2 -0.067587 -0.014683
3 -0.034984 0.101320
4 -0.022871 -0.000989
5 -0.047365 -0.045094
Now we can see that $X_3$ is actually slightly more significant in determining $Y$ than $X_1$! The dependence between $X_1$ and $X_2$ resulted in $X_1$ “borrowing” some explanative power from $X_2$.
The example data was generated with \begin{align*} X_1(t) &= X_2(t-2) + \mathrm{Normal}(0, 0.2^2),\\ X_2(t) &= \mathrm{Normal}(0.2, 4^2),\\ X_3(t) &= Y(t) - X_2(t-3),\\ Y(t) &= X_1(t-1) + \mathrm{Normal}(0, 0.1^2). \end{align*} The reason for our result is that $X_3$ contains the full difference between $Y$ and $X_2$ whereas there is still some random variation between $X_1$ and $Y$.
ennemi also supports multidimensional conditions. This is useful when there are several common explanative variables. To specify a multivariate condition, pass a two-dimensional array as the cond parameter similarly to x. Instead of comparing each variable separately as with x, the conditional variables will be evaluated together.
## Masking observations
Sometimes, you want to use only a subset of the observations. This is easy to do unless some variables are time lagged. The time lags are easy to get the wrong way around, and the calculation must be repeated for each lag value.
To make subsetting with time lags easier, estimate_mi() and estimate_corr() accept a mask parameter. The mask is an array (or list) of boolean values. An y observation, and the relevant x and cond observations after lagging, is only used if the corresponding mask element is True.
Consider a model of two variables. The first variable has a daily cycle. The second variable follows the first with a time lag, but gets meaningful values only in the daytime.
To analyze the full data set, you would execute:
from ennemi import estimate_corr
import matplotlib.pyplot as plt
import numpy as np
# One observation every 30 minutes
t = np.arange(4*48) / 2
rng = np.random.default_rng(1234)
x = -0.3 * np.cos(2 * np.pi * t / 24) + rng.normal(0, 0.01, len(t))
y = np.sqrt(np.maximum(0, -np.cos(2 * np.pi * (t-3) / 24)))\
+ rng.normal(0, 0.01, len(t))
print(estimate_corr(y, x, lag=[0, 1, 2, 3]))
The result is:
[[0.91572684]
[0.92111013]
[0.91883495]
[0.93652557]]
To constrain to daytime observations of $Y$ only, replace the last line with
mask = (t % 24 > 6) & (t % 24 < 18)
print(estimate_corr(y, x, lag=[0, 1, 2, 3], mask=mask))
This produces slightly different MI values:
[[0.84804286]
[0.88699323]
[0.90550901]
[0.94374136]]
The three first correlations indicate that we actually had some information there: if $X < 0$, then $Y$ is probably zero. The MI at the correct lag term increased a bit.
If some observations were missing altogether, indicated by a NaN value, we could pass the drop_nan parameter to estimate_corr() and get the same results. | 3,514 | 12,558 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2024-22 | longest | en | 0.817957 |
http://d2l.ai/_sources/chapter_appendix-mathematics-for-deep-learning/eigendecomposition.rst.txt | 1,601,190,246,000,000,000 | text/plain | crawl-data/CC-MAIN-2020-40/segments/1600400265461.58/warc/CC-MAIN-20200927054550-20200927084550-00369.warc.gz | 33,851,957 | 9,669 | .. _sec_eigendecompositions: Eigendecompositions =================== Eigenvalues are often one of the most useful notions we will encounter when studying linear algebra, however, as a beginner, it is easy to overlook their importance. Below, we introduce eigendecomposition and try to convey some sense of just why it is so important. Suppose that we have a matrix :math:A with the following entries: .. math:: \mathbf{A} = \begin{bmatrix} 2 & 0 \\ 0 & -1 \end{bmatrix}. If we apply :math:A to any vector :math:\mathbf{v} = [x, y]^\top, we obtain a vector :math:\mathbf{A}\mathbf{v} = [2x, -y]^\top. This has an intuitive interpretation: stretch the vector to be twice as wide in the :math:x-direction, and then flip it in the :math:y-direction. However, there are *some* vectors for which something remains unchanged. Namely :math:[1, 0]^\top gets sent to :math:[2, 0]^\top and :math:[0, 1]^\top gets sent to :math:[0, -1]^\top. These vectors are still in the same line, and the only modification is that the matrix stretches them by a factor of :math:2 and :math:-1 respectively. We call such vectors *eigenvectors* and the factor they are stretched by *eigenvalues*. In general, if we can find a number :math:\lambda and a vector :math:\mathbf{v} such that .. math:: \mathbf{A}\mathbf{v} = \lambda \mathbf{v}. We say that :math:\mathbf{v} is an eigenvector for :math:A and :math:\lambda is an eigenvalue. Finding Eigenvalues ------------------- Let us figure out how to find them. By subtracting off the :math:\lambda \mathbf{v} from both sides, and then factoring out the vector, we see the above is equivalent to: .. math:: (\mathbf{A} - \lambda \mathbf{I})\mathbf{v} = 0. :label: eq_eigvalue_der For :eq:eq_eigvalue_der to happen, we see that :math:(\mathbf{A} - \lambda \mathbf{I}) must compress some direction down to zero, hence it is not invertible, and thus the determinant is zero. Thus, we can find the *eigenvalues* by finding for what :math:\lambda is :math:\det(\mathbf{A}-\lambda \mathbf{I}) = 0. Once we find the eigenvalues, we can solve :math:\mathbf{A}\mathbf{v} = \lambda \mathbf{v} to find the associated *eigenvector(s)*. An Example ~~~~~~~~~~ Let us see this with a more challenging matrix .. math:: \mathbf{A} = \begin{bmatrix} 2 & 1\\ 2 & 3 \end{bmatrix}. If we consider :math:\det(\mathbf{A}-\lambda \mathbf{I}) = 0, we see this is equivalent to the polynomial equation :math:0 = (2-\lambda)(3-\lambda)-2 = (4-\lambda)(1-\lambda). Thus, two eigenvalues are :math:4 and :math:1. To find the associated vectors, we then need to solve .. math:: \begin{bmatrix} 2 & 1\\ 2 & 3 \end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}x \\ y\end{bmatrix} \; \text{and} \; \begin{bmatrix} 2 & 1\\ 2 & 3 \end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}4x \\ 4y\end{bmatrix} . We can solve this with the vectors :math:[1, -1]^\top and :math:[1, 2]^\top respectively. We can check this in code using the built-in numpy.linalg.eig routine. .. raw:: html
.. raw:: html
.. code:: python %matplotlib inline from d2l import mxnet as d2l from IPython import display import numpy as np np.linalg.eig(np.array([[2, 1], [2, 3]])) .. parsed-literal:: :class: output (array([1., 4.]), array([[-0.70710678, -0.4472136 ], [ 0.70710678, -0.89442719]])) .. raw:: html
.. raw:: html
.. code:: python %matplotlib inline from d2l import torch as d2l from IPython import display import torch torch.eig(torch.tensor([[2, 1], [2, 3]], dtype=torch.float64), eigenvectors=True) .. parsed-literal:: :class: output torch.return_types.eig( eigenvalues=tensor([[1., 0.], [4., 0.]], dtype=torch.float64), eigenvectors=tensor([[-0.7071, -0.4472], [ 0.7071, -0.8944]], dtype=torch.float64)) .. raw:: html
.. raw:: html
.. code:: python %matplotlib inline from d2l import tensorflow as d2l from IPython import display import tensorflow as tf tf.linalg.eigh(tf.constant([[2, 1], [2, 3]], dtype=tf.float64)) .. parsed-literal:: :class: output (, ) .. raw:: html
.. raw:: html
Note that numpy normalizes the eigenvectors to be of length one, whereas we took ours to be of arbitrary length. Additionally, the choice of sign is arbitrary. However, the vectors computed are parallel to the ones we found by hand with the same eigenvalues. Decomposing Matrices -------------------- Let us continue the previous example one step further. Let .. math:: \mathbf{W} = \begin{bmatrix} 1 & 1 \\ -1 & 2 \end{bmatrix}, be the matrix where the columns are the eigenvectors of the matrix :math:\mathbf{A}. Let .. math:: \boldsymbol{\Sigma} = \begin{bmatrix} 1 & 0 \\ 0 & 4 \end{bmatrix}, be the matrix with the associated eigenvalues on the diagonal. Then the definition of eigenvalues and eigenvectors tells us that .. math:: \mathbf{A}\mathbf{W} =\mathbf{W} \boldsymbol{\Sigma} . The matrix :math:W is invertible, so we may multiply both sides by :math:W^{-1} on the right, we see that we may write .. math:: \mathbf{A} = \mathbf{W} \boldsymbol{\Sigma} \mathbf{W}^{-1}. :label: eq_eig_decomp In the next section we will see some nice consequences of this, but for now we need only know that such a decomposition will exist as long as we can find a full collection of linearly independent eigenvectors (so that :math:W is invertible). Operations on Eigendecompositions --------------------------------- One nice thing about eigendecompositions :eq:eq_eig_decomp is that we can write many operations we usually encounter cleanly in terms of the eigendecomposition. As a first example, consider: .. math:: \mathbf{A}^n = \overbrace{\mathbf{A}\cdots \mathbf{A}}^{\text{$n$ times}} = \overbrace{(\mathbf{W}\boldsymbol{\Sigma} \mathbf{W}^{-1})\cdots(\mathbf{W}\boldsymbol{\Sigma} \mathbf{W}^{-1})}^{\text{$n$ times}} = \mathbf{W}\overbrace{\boldsymbol{\Sigma}\cdots\boldsymbol{\Sigma}}^{\text{$n$ times}}\mathbf{W}^{-1} = \mathbf{W}\boldsymbol{\Sigma}^n \mathbf{W}^{-1}. This tells us that for any positive power of a matrix, the eigendecomposition is obtained by just raising the eigenvalues to the same power. The same can be shown for negative powers, so if we want to invert a matrix we need only consider .. math:: \mathbf{A}^{-1} = \mathbf{W}\boldsymbol{\Sigma}^{-1} \mathbf{W}^{-1}, or in other words, just invert each eigenvalue. This will work as long as each eigenvalue is non-zero, so we see that invertible is the same as having no zero eigenvalues. Indeed, additional work can show that if :math:\lambda_1, \ldots, \lambda_n are the eigenvalues of a matrix, then the determinant of that matrix is .. math:: \det(\mathbf{A}) = \lambda_1 \cdots \lambda_n, or the product of all the eigenvalues. This makes sense intuitively because whatever stretching :math:\mathbf{W} does, :math:W^{-1} undoes it, so in the end the only stretching that happens is by multiplication by the diagonal matrix :math:\boldsymbol{\Sigma}, which stretches volumes by the product of the diagonal elements. Finally, recall that the rank was the maximum number of linearly independent columns of your matrix. By examining the eigendecomposition closely, we can see that the rank is the same as the number of non-zero eigenvalues of :math:\mathbf{A}. The examples could continue, but hopefully the point is clear: eigendecomposition can simplify many linear-algebraic computations and is a fundamental operation underlying many numerical algorithms and much of the analysis that we do in linear algebra. Eigendecompositions of Symmetric Matrices ----------------------------------------- It is not always possible to find enough linearly independent eigenvectors for the above process to work. For instance the matrix .. math:: \mathbf{A} = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}, has only a single eigenvector, namely :math:(1, 0)^\top. To handle such matrices, we require more advanced techniques than we can cover (such as the Jordan Normal Form, or Singular Value Decomposition). We will often need to restrict our attention to those matrices where we can guarantee the existence of a full set of eigenvectors. | The most commonly encountered family are the *symmetric matrices*, which are those matrices where :math:\mathbf{A} = \mathbf{A}^\top. In this case, we may take :math:W to be an *orthogonal matrix*—a matrix whose columns are all length one vectors that are at right angles to one another, where :math:\mathbf{W}^\top = \mathbf{W}^{-1}—and all the eigenvalues will be real. | Thus, in this special case, we can write :eq:eq_eig_decomp as .. math:: \mathbf{A} = \mathbf{W}\boldsymbol{\Sigma}\mathbf{W}^\top . Gershgorin Circle Theorem ------------------------- Eigenvalues are often difficult to reason with intuitively. If presented an arbitrary matrix, there is little that can be said about what the eigenvalues are without computing them. There is, however, one theorem that can make it easy to approximate well if the largest values are on the diagonal. Let :math:\mathbf{A} = (a_{ij}) be any square matrix (:math:n\times n). We will define :math:r_i = \sum_{j \neq i} |a_{ij}|. Let :math:\mathcal{D}_i represent the disc in the complex plane with center :math:a_{ii} radius :math:r_i. Then, every eigenvalue of :math:\mathbf{A} is contained in one of the :math:\mathcal{D}_i. | This can be a bit to unpack, so let us look at an example. | Consider the matrix: .. math:: \mathbf{A} = \begin{bmatrix} 1.0 & 0.1 & 0.1 & 0.1 \\ 0.1 & 3.0 & 0.2 & 0.3 \\ 0.1 & 0.2 & 5.0 & 0.5 \\ 0.1 & 0.3 & 0.5 & 9.0 \end{bmatrix}. We have :math:r_1 = 0.3, :math:r_2 = 0.6, :math:r_3 = 0.8 and :math:r_4 = 0.9. The matrix is symmetric, so all eigenvalues are real. This means that all of our eigenvalues will be in one of the ranges of .. math:: [a_{11}-r_1, a_{11}+r_1] = [0.7, 1.3], .. math:: [a_{22}-r_2, a_{22}+r_2] = [2.4, 3.6], .. math:: [a_{33}-r_3, a_{33}+r_3] = [4.2, 5.8], .. math:: [a_{44}-r_4, a_{44}+r_4] = [8.1, 9.9]. Performing the numerical computation shows that the eigenvalues are approximately :math:0.99, :math:2.97, :math:4.95, :math:9.08, all comfortably inside the ranges provided. .. raw:: html
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.. code:: python A = np.array([[1.0, 0.1, 0.1, 0.1], [0.1, 3.0, 0.2, 0.3], [0.1, 0.2, 5.0, 0.5], [0.1, 0.3, 0.5, 9.0]]) v, _ = np.linalg.eig(A) v .. parsed-literal:: :class: output array([9.08033648, 0.99228545, 4.95394089, 2.97343718]) .. raw:: html
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.. code:: python A = torch.tensor([[1.0, 0.1, 0.1, 0.1], [0.1, 3.0, 0.2, 0.3], [0.1, 0.2, 5.0, 0.5], [0.1, 0.3, 0.5, 9.0]]) v, _ = torch.eig(A) v .. parsed-literal:: :class: output tensor([[0.9923, 0.0000], [9.0803, 0.0000], [4.9539, 0.0000], [2.9734, 0.0000]]) .. raw:: html
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.. code:: python A = tf.constant([[1.0, 0.1, 0.1, 0.1], [0.1, 3.0, 0.2, 0.3], [0.1, 0.2, 5.0, 0.5], [0.1, 0.3, 0.5, 9.0]]) v, _ = tf.linalg.eigh(A) v .. parsed-literal:: :class: output .. raw:: html
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In this way, eigenvalues can be approximated, and the approximations will be fairly accurate in the case that the diagonal is significantly larger than all the other elements. It is a small thing, but with a complex and subtle topic like eigendecomposition, it is good to get any intuitive grasp we can. A Useful Application: The Growth of Iterated Maps ------------------------------------------------- Now that we understand what eigenvectors are in principle, let us see how they can be used to provide a deep understanding of a problem central to neural network behavior: proper weight initialization. Eigenvectors as Long Term Behavior ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The full mathematical investigation of the initialization of deep neural networks is beyond the scope of the text, but we can see a toy version here to understand how eigenvalues can help us see how these models work. As we know, neural networks operate by interspersing layers of linear transformations with non-linear operations. For simplicity here, we will assume that there is no non-linearity, and that the transformation is a single repeated matrix operation :math:A, so that the output of our model is .. math:: \mathbf{v}_{out} = \mathbf{A}\cdot \mathbf{A}\cdots \mathbf{A} \mathbf{v}_{in} = \mathbf{A}^N \mathbf{v}_{in}. When these models are initialized, :math:A is taken to be a random matrix with Gaussian entries, so let us make one of those. To be concrete, we start with a mean zero, variance one Gaussian distributed :math:5 \times 5 matrix. .. raw:: html
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.. code:: python np.random.seed(8675309) k = 5 A = np.random.randn(k, k) A .. parsed-literal:: :class: output array([[ 0.58902366, 0.73311856, -1.1621888 , -0.55681601, -0.77248843], [-0.16822143, -0.41650391, -1.37843129, 0.74925588, 0.17888446], [ 0.69401121, -1.9780535 , -0.83381434, 0.56437344, 0.31201299], [-0.87334496, 0.15601291, -0.38710108, -0.23920821, 0.88850104], [ 1.29385371, -0.76774106, 0.20131613, 0.91800842, 0.38974115]]) .. raw:: html
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.. code:: python torch.manual_seed(42) k = 5 A = torch.randn(k, k, dtype=torch.float64) A .. parsed-literal:: :class: output tensor([[ 0.2996, 0.2424, 0.2832, -0.2329, 0.6712], [ 0.7818, -1.7903, -1.7484, 0.1735, -0.1182], [-1.7446, -0.4695, 0.4573, 0.5177, -0.2771], [-0.6641, 0.6551, 0.2616, -1.5265, -0.3311], [-0.6378, 0.1072, 0.7096, 0.3009, -0.2869]], dtype=torch.float64) .. raw:: html
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.. code:: python k = 5 A = tf.random.normal((k, k), dtype=tf.float64) A .. parsed-literal:: :class: output .. raw:: html
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Behavior on Random Data ~~~~~~~~~~~~~~~~~~~~~~~ For simplicity in our toy model, we will assume that the data vector we feed in :math:\mathbf{v}_{in} is a random five dimensional Gaussian vector. Let us think about what we want to have happen. For context, lets think of a generic ML problem, where we are trying to turn input data, like an image, into a prediction, like the probability the image is a picture of a cat. If repeated application of :math:\mathbf{A} stretches a random vector out to be very long, then small changes in input will be amplified into large changes in output—tiny modifications of the input image would lead to vastly different predictions. This does not seem right! On the flip side, if :math:\mathbf{A} shrinks random vectors to be shorter, then after running through many layers, the vector will essentially shrink to nothing, and the output will not depend on the input. This is also clearly not right either! We need to walk the narrow line between growth and decay to make sure that our output changes depending on our input, but not much! Let us see what happens when we repeatedly multiply our matrix :math:\mathbf{A} against a random input vector, and keep track of the norm. .. raw:: html
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.. code:: python # Calculate the sequence of norms after repeatedly applying A v_in = np.random.randn(k, 1) norm_list = [np.linalg.norm(v_in)] for i in range(1, 100): v_in = A.dot(v_in) norm_list.append(np.linalg.norm(v_in)) d2l.plot(np.arange(0, 100), norm_list, 'Iteration', 'Value') .. figure:: output_eigendecomposition_ee2e00_39_0.svg .. raw:: html
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.. code:: python # Calculate the sequence of norms after repeatedly applying A v_in = torch.randn(k, 1, dtype=torch.float64) norm_list = [torch.norm(v_in).item()] for i in range(1, 100): v_in = A @ v_in norm_list.append(torch.norm(v_in).item()) d2l.plot(torch.arange(0, 100), norm_list, 'Iteration', 'Value') .. figure:: output_eigendecomposition_ee2e00_42_0.svg .. raw:: html
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.. code:: python # Calculate the sequence of norms after repeatedly applying A v_in = tf.random.normal((k, 1), dtype=tf.float64) norm_list = [tf.norm(v_in).numpy()] for i in range(1, 100): v_in = tf.matmul(A, v_in) norm_list.append(tf.norm(v_in).numpy()) d2l.plot(tf.range(0, 100), norm_list, 'Iteration', 'Value') .. figure:: output_eigendecomposition_ee2e00_45_0.svg .. raw:: html
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The norm is growing uncontrollably! Indeed if we take the list of quotients, we will see a pattern. .. raw:: html
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.. code:: python # Compute the scaling factor of the norms norm_ratio_list = [] for i in range(1, 100): norm_ratio_list.append(norm_list[i]/norm_list[i - 1]) d2l.plot(np.arange(1, 100), norm_ratio_list, 'Iteration', 'Ratio') .. figure:: output_eigendecomposition_ee2e00_51_0.svg .. raw:: html
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.. code:: python # Compute the scaling factor of the norms norm_ratio_list = [] for i in range(1, 100): norm_ratio_list.append(norm_list[i]/norm_list[i - 1]) d2l.plot(torch.arange(1, 100), norm_ratio_list, 'Iteration', 'Ratio') .. figure:: output_eigendecomposition_ee2e00_54_0.svg .. raw:: html
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.. code:: python # Compute the scaling factor of the norms norm_ratio_list = [] for i in range(1, 100): norm_ratio_list.append(norm_list[i]/norm_list[i - 1]) d2l.plot(tf.range(1, 100), norm_ratio_list, 'Iteration', 'Ratio') .. figure:: output_eigendecomposition_ee2e00_57_0.svg .. raw:: html
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If we look at the last portion of the above computation, we see that the random vector is stretched by a factor of 1.974459321485[...], where the portion at the end shifts a little, but the stretching factor is stable. Relating Back to Eigenvectors ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We have seen that eigenvectors and eigenvalues correspond to the amount something is stretched, but that was for specific vectors, and specific stretches. Let us take a look at what they are for :math:\mathbf{A}. A bit of a caveat here: it turns out that to see them all, we will need to go to complex numbers. You can think of these as stretches and rotations. By taking the norm of the complex number (square root of the sums of squares of real and imaginary parts) we can measure that stretching factor. Let us also sort them. .. raw:: html
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.. code:: python # Compute the eigenvalues eigs = np.linalg.eigvals(A).tolist() norm_eigs = [np.absolute(x) for x in eigs] norm_eigs.sort() print(f'norms of eigenvalues: {norm_eigs}') .. parsed-literal:: :class: output norms of eigenvalues: [0.8786205280381857, 1.2757952665062624, 1.4983381517710659, 1.4983381517710659, 1.974459321485074] .. raw:: html
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.. code:: python # Compute the eigenvalues eigs = torch.eig(A)[0][:,0].tolist() norm_eigs = [torch.abs(torch.tensor(x)) for x in eigs] norm_eigs.sort() print(f'norms of eigenvalues: {norm_eigs}') .. parsed-literal:: :class: output norms of eigenvalues: [tensor(0.3490), tensor(0.5691), tensor(0.5691), tensor(1.1828), tensor(2.4532)] .. raw:: html
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.. code:: python # Compute the eigenvalues eigs = tf.linalg.eigh(A)[0].numpy().tolist() norm_eigs = [tf.abs(tf.constant(x, dtype=tf.float64)) for x in eigs] norm_eigs.sort() print(f'norms of eigenvalues: {norm_eigs}') .. parsed-literal:: :class: output norms of eigenvalues: [, , , , ] .. raw:: html
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An Observation ~~~~~~~~~~~~~~ We see something a bit unexpected happening here: that number we identified before for the long term stretching of our matrix :math:\mathbf{A} applied to a random vector is *exactly* (accurate to thirteen decimal places!) the largest eigenvalue of :math:\mathbf{A}. This is clearly not a coincidence! But, if we now think about what is happening geometrically, this starts to make sense. Consider a random vector. This random vector points a little in every direction, so in particular, it points at least a little bit in the same direction as the eigenvector of :math:\mathbf{A} associated with the largest eigenvalue. This is so important that it is called the *principle eigenvalue* and *principle eigenvector*. After applying :math:\mathbf{A}, our random vector gets stretched in every possible direction, as is associated with every possible eigenvector, but it is stretched most of all in the direction associated with this principle eigenvector. What this means is that after apply in :math:A, our random vector is longer, and points in a direction closer to being aligned with the principle eigenvector. After applying the matrix many times, the alignment with the principle eigenvector becomes closer and closer until, for all practical purposes, our random vector has been transformed into the principle eigenvector! Indeed this algorithm is the basis for what is known as the *power iteration* for finding the largest eigenvalue and eigenvector of a matrix. For details see, for example, :cite:Van-Loan.Golub.1983. Fixing the Normalization ~~~~~~~~~~~~~~~~~~~~~~~~ Now, from above discussions, we concluded that we do not want a random vector to be stretched or squished at all, we would like random vectors to stay about the same size throughout the entire process. To do so, we now rescale our matrix by this principle eigenvalue so that the largest eigenvalue is instead now just one. Let us see what happens in this case. .. raw:: html
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.. code:: python # Rescale the matrix A A /= norm_eigs[-1] # Do the same experiment again v_in = np.random.randn(k, 1) norm_list = [np.linalg.norm(v_in)] for i in range(1, 100): v_in = A.dot(v_in) norm_list.append(np.linalg.norm(v_in)) d2l.plot(np.arange(0, 100), norm_list, 'Iteration', 'Value') .. figure:: output_eigendecomposition_ee2e00_75_0.svg .. raw:: html
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.. code:: python # Rescale the matrix A A /= norm_eigs[-1] # Do the same experiment again v_in = torch.randn(k, 1, dtype=torch.float64) norm_list = [torch.norm(v_in).item()] for i in range(1, 100): v_in = A @ v_in norm_list.append(torch.norm(v_in).item()) d2l.plot(torch.arange(0, 100), norm_list, 'Iteration', 'Value') .. figure:: output_eigendecomposition_ee2e00_78_0.svg .. raw:: html
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.. code:: python # Rescale the matrix A A /= norm_eigs[-1] # Do the same experiment again v_in = tf.random.normal((k, 1), dtype=tf.float64) norm_list = [tf.norm(v_in).numpy()] for i in range(1, 100): v_in = tf.matmul(A, v_in) norm_list.append(tf.norm(v_in).numpy()) d2l.plot(tf.range(0, 100), norm_list, 'Iteration', 'Value') .. figure:: output_eigendecomposition_ee2e00_81_0.svg .. raw:: html
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We can also plot the ratio between consecutive norms as before and see that indeed it stabilizes. .. raw:: html
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.. code:: python # Also plot the ratio norm_ratio_list = [] for i in range(1, 100): norm_ratio_list.append(norm_list[i]/norm_list[i-1]) d2l.plot(np.arange(1, 100), norm_ratio_list, 'Iteration', 'Ratio') .. figure:: output_eigendecomposition_ee2e00_87_0.svg .. raw:: html
.. raw:: html
.. code:: python # Also plot the ratio norm_ratio_list = [] for i in range(1, 100): norm_ratio_list.append(norm_list[i]/norm_list[i-1]) d2l.plot(torch.arange(1, 100), norm_ratio_list, 'Iteration', 'Ratio') .. figure:: output_eigendecomposition_ee2e00_90_0.svg .. raw:: html
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.. code:: python # Also plot the ratio norm_ratio_list = [] for i in range(1, 100): norm_ratio_list.append(norm_list[i]/norm_list[i-1]) d2l.plot(tf.range(1, 100), norm_ratio_list, 'Iteration', 'Ratio') .. figure:: output_eigendecomposition_ee2e00_93_0.svg .. raw:: html
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Conclusions ----------- We now see exactly what we hoped for! After normalizing the matrices by the principle eigenvalue, we see that the random data does not explode as before, but rather eventually equilibrates to a specific value. It would be nice to be able to do these things from first principles, and it turns out that if we look deeply at the mathematics of it, we can see that the largest eigenvalue of a large random matrix with independent mean zero, variance one Gaussian entries is on average about :math:\sqrt{n}, or in our case :math:\sqrt{5} \approx 2.2, due to a fascinating fact known as the *circular law* :cite:Ginibre.1965. The relationship between the eigenvalues (and a related object called singular values) of random matrices has been shown to have deep connections to proper initialization of neural networks as was discussed in :cite:Pennington.Schoenholz.Ganguli.2017 and subsequent works. Summary ------- - Eigenvectors are vectors which are stretched by a matrix without changing direction. - Eigenvalues are the amount that the eigenvectors are stretched by the application of the matrix. - The eigendecomposition of a matrix can allow for many operations to be reduced to operations on the eigenvalues. - The Gershgorin Circle Theorem can provide approximate values for the eigenvalues of a matrix. - The behavior of iterated matrix powers depends primarily on the size of the largest eigenvalue. This understanding has many applications in the theory of neural network initialization. Exercises --------- 1. What are the eigenvalues and eigenvectors of .. math:: \mathbf{A} = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}? 2. What are the eigenvalues and eigenvectors of the following matrix, and what is strange about this example compared to the previous one? .. math:: \mathbf{A} = \begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix}. 3. Without computing the eigenvalues, is it possible that the smallest eigenvalue of the following matrix is less that :math:0.5? *Note*: this problem can be done in your head. .. math:: \mathbf{A} = \begin{bmatrix} 3.0 & 0.1 & 0.3 & 1.0 \\ 0.1 & 1.0 & 0.1 & 0.2 \\ 0.3 & 0.1 & 5.0 & 0.0 \\ 1.0 & 0.2 & 0.0 & 1.8 \end{bmatrix}. .. raw:: html
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## Computational Finance. MATLAB oriented modeling
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Chapter-by-Chapter MATLAB codes related to the book "Computational Finance. MATLAB oriented modeling"
Updated 07 Feb 2020
The book contains more than 100 examples and exercises, together with MATLAB codes providing the solution for each of them. The road map of the book is as follows. Chapter 1 is devoted to an introduction to the MATLAB language and development environment, for programming, numerical calculation and visualization applied to simple calculus and financial problems. Chapter 2 introduces basic concepts in probability and statistics, simplifying as much as possible the discussion. Chapter 3 deals with the main constrained optimization models, mainly focusing on recognizing the type of problems treated, and how to implement and solve them in MATLAB. In Chapter 4 we address Portfolio Optimization, providing several portfolio selection models mainly based on risk-gain analysis. Chapter 5 presents some probabilistic tools which are used in Chapter 6 for describing three methodologies to price derivatives.
### Cite As
Francesco Cesarone (2020). Computational Finance. MATLAB oriented modeling (https://www.mathworks.com/matlabcentral/fileexchange/73917-computational-finance-matlab-oriented-modeling), MATLAB Central File Exchange. Retrieved .
Francesco Cesarone (2020), Computational Finance. MATLAB oriented modeling, Routledge-Giappichelli Studies in Business and Management, ISBN 978-0-367-49303-5, https://www.giappichelli.it/computational-finance
Francesco Cesarone
My book is a co-edition between Routledge and Giappichelli (https://www.routledge.com/Routledge-Giappichelli-Studies-in-Business-and-Management/book-series/RGSBM).
While Routledge is engaged for the International distribution, Giappichelli, which deals with distribution in Italian universities, has already released my book in January 2020 (https://www.giappichelli.it/computational-finance).
Let me know if you need anything else.
All the best,
Francesco
Great functions, is the book still pre-publishing? I couldn't seem to buy it.
Giuseppe Stemperini
Andrea Amodeo
Lorenzo Rendina
riccardo manfredi
7 Feb 2020 1.0.3 I added more information to purchase the book 16 Jan 2020 1.0.2 More details on the book 14 Jan 2020 1.0.1 MATLABsolutions.zip contains all the solutions to the exercises proposed in the book
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# Is 8 equals 15-7 a math equation?
Updated: 9/19/2023
Wiki User
12y ago
8 = 15 - 7
8 = 8
Yes it is an equation.
Wiki User
12y ago
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Q: Is 8 equals 15-7 a math equation?
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The equation 6 plug 4 times 3 take away 8 times 2 equals 2. This is a math problem.
0-8
5 -8 | 491 | 1,503 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2023-40 | latest | en | 0.859937 |
http://math.stackexchange.com/questions/70682/twin-primes-of-form-2n3-and-2n5/70699 | 1,469,557,190,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257825048.60/warc/CC-MAIN-20160723071025-00061-ip-10-185-27-174.ec2.internal.warc.gz | 159,775,977 | 20,222 | # Twin primes of form $2^n+3$ and $2^n+5$
How to prove that $2^n+3$ and $2^n+5$ are both prime for only finitely many integers $n$?
And how to prove that there are infinitely many primes of the form $2^n+3$ and $2^m+5$
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What makes you think that there are only finitely many? A057732 shows a large number of primes of the form $2^n+3$, and likewise A059242 for $2^n+5.$
Generally the way that such sequences are shown to have only finitely many primes is to find a covering set, but there's no obvious one for either.
To answer the edited question: There are only finitely many twin primes of the form $(2^n+3,2^n+5)$ because there is a covering set: at least one of the numbers is divisible by a member of $\{3,5,7,13\}$ (work mod 12). But proving that there are infinitely many primes of either form is beyond current technology AFAIK.
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The OP has edited the question to include whether there are finitely many times both $2^n+3$ and $2^n+5$ are prime. It seems more likely that there are only finitely many of these, although (I would guess) still unlikely that we would be able to prove it. – Zev Chonoles Oct 7 '11 at 19:35
@ZevChonoles: Thanks, I edited my answer to address the new question. Actually it can be proven that there are only finitely many twin primes of this form, though proving that there are infinitely many primes in either form is well beyond what can currently be proven I think. – Charles Oct 7 '11 at 19:44
AFAIK = "As far as I know" – user02138 Oct 7 '11 at 21:52
Is this technique also applicable here? – draks ... Jun 20 '12 at 18:41
@draks: Probably not. But if it were applicable in some case, that would be 'trivial' compared to the others. Resolving those questions will probably be very hard. For example, by probability you'd expect infinitely many Mersenne primes, but no one knows how to prove it. The 'chance' that they appear as part of a twin prime pair is small enough that it should happen only finitely often, but this too is more than can be proved. – Charles Jun 20 '12 at 23:41
Settling the twin prime part of the question seems to go as follows:
1) If $2\mid n$, then $3\mid 2^n+5$, so it suffices to study odd values of $n$.
2) If $n\equiv 1\pmod 4$, then $5\mid 2^n+3$, so it suffices to study the case $n\equiv 3\pmod 4$.
3) If $n\equiv 1\pmod 3$, then $7\mid 2^n+5$. If $n\equiv 2\pmod 3$, then $7\mid 2^n+3$, so for there to be infinitely many twin primes of this form we must have $3\mid n$.
Combinining items 2 and 3 above, we see that it suffices to exclude the possibility of infinitely many twin primes of this form, when $n\equiv 3\pmod {12}$. But...
4) If $n\equiv 3\pmod {12}$, then $13\mid 2^n+5$.
Looks like $(5,7)$ and $(11,13)$ are all.
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+1. This was the same method I used to solve the (edited) question. – Charles Oct 7 '11 at 19:49
Folks, thank you for your support, but Charles solved this problem a couple of minutes earlier. Study the edit history of his answer for a proof :-) – Jyrki Lahtonen Oct 7 '11 at 20:26
Is this technique also applicable here? – draks ... Jun 20 '12 at 18:42
And how to prove that there are infinitely many primes of the form $2^n+3$
First prove that there are infinitely Mersenne primes, then...
This is something that can be predicted, not proved, in the current state of number theory.
The "probability" of prime numbers near $2^n$ is close to $1/\log (2^n) = \frac{1}{n \log 2}$ and the "expected number" of primes of the form $2^m+3$ in $[1,n]$ is $O(\log \log n)$.
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+1 Interesting. But is it possible to factor in facts of the form (see the other answers): $2^n+3$ is slightly more probable to be divisible by $5$ (1 out of 4) or by $7$ (1 out of 3) than the usual "random integer near a power of two"? Can it be shown that such considerations only affect the constant of $O(\log\log n)$? Ok, in this case this is clearly asking too much, but are there other questions, where such slight bias away from being prime can be factore in? – Jyrki Lahtonen Oct 7 '11 at 20:44
@Jyrki, yes, it affects only the constant. – zyx Oct 7 '11 at 20:51
Is it easy to see that? I didn't mean to only consider divisibility by $5$ or $7$. For any prime $p$, if $2$ is a primitive root modulo $p$, then $2^n+3$ is divisible by $p$ with 'probability' $1/(p-1)$ (as opposed $1/p$ that we would have with a 'random' integer). If $2$ is not a primitive root modulo $p$, then this probability is either zero or $1/d$ according to whether $-3$ is in the group generated by $2$. Here $d\mid p-1$ is the order of $2$ modulo $p$. – Jyrki Lahtonen Oct 8 '11 at 5:08 | 1,377 | 4,565 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2016-30 | latest | en | 0.979197 |
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# Importance of AWA in ms finance
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Importance of AWA in ms finance [#permalink]
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17 Dec 2011, 22:27
Sir i have 740 in my Gmat but a 5 in my AWA..i am applying for International finance at HEC..IS the AWA marks important for this course?
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Re: Importance of AWA in ms finance [#permalink]
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18 Dec 2011, 00:57
Anything above a 3.5 AWA is generally considered acceptable. With a 5 you are perfectly fine for any program. A 5.5 is only 76th percentile, and 6 is somewhere in the 80's.
You've got nothing to worry about. Don't even consider a retake just for a 5 AWA. If you had a 3.5 or below you may consider it. Congrats on the great score!
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Kudos [?]: 957 [0], given: 114
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Re: Importance of AWA in ms finance [#permalink]
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18 Dec 2011, 11:49
@GMATLA thank you sir for your reply..I was a bit worried..thank you for clearing it out!
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Re: Importance of AWA in ms finance [#permalink]
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23 Dec 2011, 06:54
I'm in at HEC and I had a 5.0 AWA. Don't think it's that important.
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Re: Importance of AWA in ms finance [#permalink] 23 Dec 2011, 06:54
Display posts from previous: Sort by | 720 | 2,337 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2017-43 | latest | en | 0.861222 |
https://mathoverflow.net/questions/392570/closed-embedding-into-a-normal-hausdorff-space-and-left-lifting-property?noredirect=1 | 1,670,581,169,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711394.73/warc/CC-MAIN-20221209080025-20221209110025-00776.warc.gz | 411,875,965 | 27,522 | # Closed embedding into a normal Hausdorff space and left lifting property
I am trying to understand the characterization of the class of closed embeddings into a normal Hausdorff space as the class of continuous maps satisfying the left lifting property with respect to a unique map, presented in https://ncatlab.org/nlab/show/colimits+of+normal+spaces. The last change made in this page is anonymous but I have found a paper not giving more details in https://mishap.sdf.org/.
First of all, if the rule is $$a if and only if $$b$$ is in the closure of $$a$$, the poset given in the nLab page is the wrong one: it should be $$a>bd because the closed points are $$a,c,e$$ (there is also a typo in the description of the closed points) and the points $$b,d$$ are open.
For the author of this note (I guess M. Gavrilovich), a continuous map is a closed embedding into a normal Hausdorff space if and only if it satisfies the LLP with respect to the map $$g:\{a>bdb=c=d
Could someone explain what seems to be evident for the author of this note please ?
What I can understand is that a map $$\varnothing\to X$$ satisfies the LLP with respect to $$g$$ if and only if $$X$$ is normal (but not necessarily Hausdorff). Indeed, assume the LLP. Take two disjoint closed subsets $$A$$ and $$E$$ of $$X$$ taken to the closed points $$a$$ and $$e$$ respectively of $$\{a>b=c=d; the other points of $$X$$ are taken to the open point $$b=c=d$$. Then the existence of the lift $$\ell:X\to \{a>bd provides two closed subsets $$F_1=\ell^{-1}(\{a,b,c\})$$ and $$F_2=\ell^{-1}(\{c,d,e\})$$. Then $$F_1^c \cap F_2^c=\varnothing$$. And $$E\subset F_1^c$$ and $$A\subset F_2^c$$. Hence $$X$$ is normal. Conversely, if $$X$$ is normal, then the LLP is satisfied.
I do not understand either why the Tietze extension theorem is mentioned which is a characterization of normal Hausdorff spaces.
• Could you be more specific about which of Gavrilovich's papers you are referencing (and where in the paper the statement is found). May 19, 2021 at 11:34
• @Tyrone I managed to get in touch with him (it turns out that his Google email does not work, the other one works). It seems that the statement is still unproved when the source is not the empty set. You will find the statement (without proof) that $X$ is normal iff $\varnothing\to X$ satisfies the LLP with respect to $g$ in his paper "A diagram chasing formalisation of elementary topological properties" page 7. May 19, 2021 at 13:11
The answer by KP Hart to extending disjoint open subsets of a normal Hausdorff space shows that the characterisation fails as stated for normal Hausdorff spaces but might work for hereditarily normal Hausdorff spaces.
Let $$C$$ be a closed subset of a normal Hausdorff space $$X$$. Any two open disjoint subsets $$U$$ and $$V$$ of a closed subset $$C$$ of $$X$$ (i.e. $$U$$ and $$V$$ are open in $$C$$) can be "extended" to disjoint open subsets $$U'\supset U'$$ and $$V'\supset V$$ of $$X$$ >such that $$U=U'\cap C$$ and $$V=V'\cap C$$, and $$U'\cap V'=\emptyset$$.
$$C \to X \rightthreetimes \{ U < x > V \}\to \{U=x=V\}$$
Let $$C$$ be a closed subset of a normal Hausdorff $$X$$. For any two closed subsets $$A'$$ and $$B'$$ of $$X$$, any two open subsets $$U\supset A$$ and $$V\supset B$$ of $$C$$ separating $$A=A'\cap C$$ and $$B=B'\cap C$$, i.e. $$U\cap V=\emptyset$$, there exist open subsets $$U'\supset A'$$ and $$V'\supset B'$$ of $$X$$ "extending" $$U$$ and $$V$$, and separating $$A'$$, and $$B'$$, i.e. $$A'\subset U'$$, and $$B'\subset V'$$, and $$U=U'\cap C$$, and $$V=V'\cap C$$, and $$U'\cap V'=\emptyset$$.
$$C \to X \rightthreetimes \{ a > u < x > v < b \}\to \{a > u=x=v < b \}$$
In fact, being hereditarily normal is also a lifting property :
Recall hereditarily normal means that any two separated subsets $$A$$ and $$B$$, i.e. such that there are open neighbourhoods $$U\supset A$$ and $$V\supset B$$ such that $$U \cap B= A \cap V= \emptyset$$, are separated by neighbourhoods $$U'\supset A$$ and $$V'\subset B$$, i.e. $$U'\cap V'=\emptyset$$.
Let us write the LLP in two notations, < and $$\to$$. Recall that our convention is that $$\{o is the same as $$\{o\rightarrow c\}$$, and here o is open and c is closed.
$$\emptyset \to X \rightthreetimes \{ x > au \approx u' > u > uv < v < v'\approx bv < x \} \to \{ x > au \approx u' = u > uv < v = v'\approx bv < x \}$$
$$\emptyset \to X \rightthreetimes \{ x \leftarrow au \leftrightarrow u' \leftarrow u \leftarrow uv \rightarrow v \rightarrow v'\leftrightarrow bv \rightarrow x \} \to \{ x \leftarrow au \leftrightarrow u' = u \leftarrow uv \rightarrow v = v'\leftrightarrow bv \rightarrow x \}$$
(In this notation, $$U$$ corresponds to the preimage of $$\{au,u,uv\}$$ and $$\{au,u',u,uv\}$$, i.e. the subsets of points whose notation contains letter $$u$$, and similarly for $$v$$. Letter $$x$$ stands for points of $$X$$ "in general position", i.e. outside of $$U$$ and $$V$$.)
This LLP also holds for a closed inclusion into a hereditarily normal space. Hence, this should be enough to conclude that a colimit of closed inclusions into a hereditarily normal space is also a closed inclusion into a hereditarily normal space.
• I would vote this up, but I just cannot stand the notation. Jul 8 at 19:14 | 1,563 | 5,264 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 88, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2022-49 | latest | en | 0.917117 |
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# app5_rain_norain - Application Example 5(Bernoulli Trial...
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Application Example 5 (Bernoulli Trial Sequence and Dependence in Binary Time Series) IS THE SERIES OF RAINY/NON-RAINY DAYS A BERNOULLI TRIAL SEQUENCE? Note: The shaded text in this note involves the concept of correlation function for a random sequence. This concept will be encountered later in the course. In a fist reading, you may skip that text. The concept of dependent random variables finds an important application in so-called time series, which are models of how a random quantity varies in time. In the case when time is discrete or discretized, as for example happens when one considers variables with daily, monthly or annual values (daily close of the stock market, monthly average temperatures, annual sales, score of i th baseball game, etc.), the time series is simply a discrete sequence of random variables X i . An important issue in modeling such sequences is the probabilistic dependence among different variables. Here we illustrate the concepts of dependence in time series by considering the simplest case, which is a series of indicator variables {I i , i = 0, ± 1, ±2, ...}. Such variables can be used to indicate whether or not an event of interest occurs (I i = 1) or does not occur (I i = 0) at “time” i. For example, we can take the event of interest to be the fact that day i is rainy. Again to keep the illustration simple, we consider the case when the sequence of rainy/non-rainy days is stationary. Stationarity means that the sequence has everywhere the same statistical properties. Hence, the probability P[I i = 1] does not depend on i, the probability P[(I i = 1) (I j = 1)] depends only on the separating distance |i - j|, and so on. The assumption of stationarity is realistic in many cases and greatly simplifies the characterization of a time series. i , i = 0, ± 1, ±2, ...} is that the correlation function ρ ij An implication of stationarity for a random sequence {I depends only on the time lag |i-j|.
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The joint distribution of the daily rain/no-rain indicators I i and I j has 4 probability masses: • a probability mass p 00 at (0,0), which gives the probability that both days are dry, • a probability mass p 11 at (1,1), which gives the probability that both days are wet, • probability masses p 01 and p 10 at (0,1) and (1,0), which give the probability that day i is dry and day j is wet and, viceversa, that day i is wet and day j is dry. These four probabilities must add to unity. Moreover, due to stationarity, p 01 = p 10 , meaning that the relative frequency of the two “transitions” (dry wet and wet dry) must be the same.
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# Differentiate. $y =$ sin $\theta$ cos $\theta$
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It's clear, so enumerated Here. It's the way of y equals sign times Coastline of data. So your first gonna use the product rule to expand So sign do you over defeat, uh, co sign plus co sign you over D fada sign. This becomes equal to negative sign Square Plus co signed square, and we're gonna apply the double angle formula to simplify. Further. We get co sign of to data.
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$6 \times \dfrac{ 1 }{ 2 } +12 \times - \dfrac{ 1 }{ 4 } +3$
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$\color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } + 12 \times \left ( - \dfrac { 1 } { 4 } \right ) + 3$
Calculate the product of rational numbers
$\color{#FF6800}{ 3 } + 12 \times \left ( - \dfrac { 1 } { 4 } \right ) + 3$
$3 + \color{#FF6800}{ 12 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 4 } } \right ) + 3$
Calculate the product of rational numbers
$3 \color{#FF6800}{ - } \color{#FF6800}{ 3 } + 3$
$\color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } + 3$
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Can we see in color at night when only one type of receptor, rods work? We answered that no, with the dicussion of the principle of univariance. But what about people we usually call color blind, dichromats. Dichromats have two classes of cones, so they have two types of receptors each maximally sensitive to a different wavelength.
In this activity, you will first try to make a match between a test and comparison patch of light, using only one wavelength like in the Color Matching in Monochromats-see if it is possible to make a match in this case.
Then you can try the circumstance of making matches when you can control the intensity of two different primaries in the comparison patch. You will be able to adjust the intensity of a blue and red primary separately. Now can you make a match? You might be able to in all circumstances. Ask yourself under what circumstances can you not make a match.
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Test and Comparison Patches: at the top are two squares. They represent the appearance of the two stimuli to the simulated eye. Your job is to make the two patches look the same in this simulated eye. The left-hand patch is the test stimulus, and the right is the comparison. You will adjust the comparison to make it look like the test. Add Second Primary: change to being able to adjust two primaries.
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Relative Intensity: adjust the relative intensity of the comparison patch. The value is the relative physical intensity of the stimulus. If the value is 1.0, then the intensity of the comparison is the same as the test patch.
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Red Primary Intensity: adjust the relative intensity of the red primary in the comparison patch.
Reset
Pressing this button restores the settings to their default values. | 486 | 2,376 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2024-30 | latest | en | 0.912355 |
http://oeis.org/A141294 | 1,534,540,274,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221212910.25/warc/CC-MAIN-20180817202237-20180817222237-00616.warc.gz | 303,944,814 | 3,702 | This site is supported by donations to The OEIS Foundation.
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A141294 Triangle read by rows, A054523 * A000012, 1<=k<=n. 0
1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 5, 1, 1, 1, 1, 6, 4, 2, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 8, 4, 2, 2, 1, 1, 1, 1, 9, 3, 3, 1, 1, 1, 1, 1, 1, 10, 6, 2, 2, 2, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 8, 6, 4, 2, 2, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 14, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS Row sums = A018804: (1, 3, 5, 8, 9, 15, 13, 20,...). LINKS FORMULA Triangle read by rows, A054523 * A000012, 1<=k<=n. By rows, partial sums starting from the right. EXAMPLE First few rows of the triangle = 1; 2, 1; 3, 1, 1; 4, 2, 1, 1; 5, 1, 1, 1, 1; 6, 4, 2, 1, 1, 1; 7, 1, 1, 1, 1, 1, 1; 8, 4, 2, 2, 1, 1, 1, 1; ... CROSSREFS Cf. A054523, A018804. Sequence in context: A143349 A182715 A088425 * A174557 A010766 A135841 Adjacent sequences: A141291 A141292 A141293 * A141295 A141296 A141297 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Aug 02 2008 STATUS approved
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Last modified August 17 17:05 EDT 2018. Contains 313816 sequences. (Running on oeis4.) | 742 | 1,502 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2018-34 | latest | en | 0.512019 |
https://enacademic.com/dic.nsf/enwiki/2272398 | 1,607,117,450,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141743438.76/warc/CC-MAIN-20201204193220-20201204223220-00139.warc.gz | 270,747,683 | 15,153 |
# Coefficient matrix
In linear algebra, the coefficient matrix refers to a matrix consisting of the coefficients of the variables in a set of linear equations.
## Example
In general, a system with m linear equations and n unknowns can be written as
$a_{11}x_1 + a_{12}x_2 + ... + a_{1n}x_n = b_1 \,$
$a_{21}x_1 + a_{22}x_2 + ... + a_{2n}x_n = b_2 \,$
$\vdots \,$
$a_{m1}x_1 + a_{m2}x_2 + ... + a_{mn}x_n = b_m \,$
where $x_1,\ x_2,...,x_n$ are the unknowns and the numbers $a_{11},\ a_{12},...,\ a_{mn}$ are the coefficients of the system. The coefficient matrix is the mxn matrix with the coefficient aij as the (i,j)-th entry:
$\begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}$
Wikimedia Foundation. 2010.
### Look at other dictionaries:
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• General matrix notation of a VAR(p) — This page just shows the details for different matrix notations of a VAR( p ) process with k variables. Var( p ):y {t}=c + A {1}y {t 1} + A {2}y {t 2} + cdots + A {p}y {t p} + e {t},Where each y {i} is a k x 1 vector and each A {i} is a k x k… … Wikipedia
• Multitrait-multimethod matrix — The multitrait multimethod (MTMM) matrix is an approach to examining Construct Validity developed by Campbell and Fiske(1959)[1]. There are six major considerations when examining a construct s validity through the MTMM matrix, which are as… … Wikipedia | 896 | 3,525 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2020-50 | latest | en | 0.817172 |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-7-section-7-3-double-angle-half-angle-and-product-sum-formulas-7-3-exercises-page-561/31 | 1,539,661,034,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583509996.54/warc/CC-MAIN-20181016030831-20181016052331-00326.warc.gz | 955,677,629 | 13,594 | ## Precalculus: Mathematics for Calculus, 7th Edition
a. $\cos 68^\circ$ b. $\cos 10\theta$
a. Use the formula $\cos 2x=\cos^2 x-\sin^2 x$ with $x=34^\circ$. Then $\cos^2 34^\circ-\sin^2 34^\circ=\cos(2*34^\circ)=\cos 68^\circ$. a. Use the formula $\cos 2x=\cos^2 x-\sin^2 x$ with $x=5\theta$. Then $\cos^2 5\theta-\sin^2 5\theta=\cos(2*5\theta)=\cos 10\theta$. | 158 | 362 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2018-43 | longest | en | 0.255448 |
https://discuss.leetcode.com/topic/19619/c-accepted-solution | 1,516,702,267,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891886.70/warc/CC-MAIN-20180123091931-20180123111931-00627.warc.gz | 653,944,600 | 8,894 | # C# Accepted Solution
• ``````public bool SearchMatrix(int[,] matrix, int target)
{
int m = matrix.GetLength(0);
int n = matrix.GetLength(1);
int l = 0, r = m*n -1, mid = 0, x = 0, y = 0;
while( l <= r )
{
mid = (l+r)/2;
y = mid / n;
x = mid - y * n;
if( matrix[y,x] == target)
{
return true;
}
else if( matrix[y,x] > target )
{
r = mid - 1;
}
else
{
l = mid + 1;
}
}
return false;
}``````
• A same solution
``````public bool SearchMatrix(int[,] matrix, int target) {
int m = matrix.GetLength(0), n = matrix.GetLength(1), left = 0, right = m * n - 1;
while(left <= right){
int mid = (left + right) / 2, y = mid % n, x = (mid - y) / n;
if(matrix[x, y] == target) return true;
else if (matrix[x, y] < target) left = mid + 1;
else right = mid - 1;
}
return false;
}``````
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 295 | 871 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-05 | latest | en | 0.537629 |
https://www.pizzamaking.com/forum/index.php?topic=7536.0;prev_next=prev | 1,516,532,518,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890514.66/warc/CC-MAIN-20180121100252-20180121120252-00698.warc.gz | 965,040,788 | 8,329 | A D V E R T I S E M E N T
### Author Topic: Pete-zza (Read 8129 times)
0 Members and 1 Guest are viewing this topic.
#### PizzaEater
• Registered User
• Posts: 124
• I Love Pizza!
##### Pete-zza
« on: February 09, 2009, 08:53:32 AM »
Pete
I was checking out the following post where you attempted to convert California Pizza Kitchen's dough recipe to bakers %, http://www.pizzamaking.com/forum/index.php/topic,704.0.html . You used a flour weight of 5 oz. per cup, this seems a bit high. Generally I thought AP Flour came in at ~4.5 oz per cup., in your experience is 5 oz for AP a good number?
Thanks
#### Pete-zza
• Global Moderator
• Posts: 26931
• Location: Texas
• Always learning
##### Re: Pete-zza
« Reply #1 on: February 09, 2009, 12:04:59 PM »
Dave,
To be honest, I don't exactly remember how I came up with 5 ounces for a cup of all-purpose flour measured out by volume. As I mentioned in the thread you referenced, the biggest problem I expected to have at the time was converting a volume of flour to weight inasmuch as there are so many different ways of measuring out flour by volume, with each method usually producing a different result. These days, I would use member November's Mass-Volume Conversion Calculator at http://foodsim.toastguard.com/. But back at the time of the thread you referenced, November's calculator did not exist. If I had to guess, I would say that I perhaps assumed a method of flour measurement and went back to my kitchen and weighed the flour on my digital scale. The most common methods of flour measurement, back then and now, tend to be the Textbook method (the method the flour millers and sellers usually recommend) and the Dip or Shake method. A while back, I attempted to define those methods, and others as well, at Reply 21 at http://www.pizzamaking.com/forum/index.php/topic,6576.msg56397/topicseen.html#msg56397. This morning, I went back to November's calculator and checked the weights for a cup of flour for each of those methods, using the Gold Medal all-purpose flour from the pull-down menu. For one cup of the GM all-purpose flour, I got 4.46 ounces using the Textbook method and 4.97 ounces using the Dip or Shake method. Since the original CPKI dough recipe also mentioned using bread flour, I checked the corresponding weights for one cup of bread flour, using the King Arthur bread flour from the pull-down menu, and got 4.56 ounces for the Textbook method and 5.07 ounces for the Dip or Shake method. Based on these numbers, it is possible that I used the Dip or Shake method of flour measurement (but more likely the Dip method) to do the conversion of the CPKI recipe.
Peter
« Last Edit: March 14, 2013, 06:24:46 PM by Pete-zza »
A D V E R T I S E M E N T
wordpress | 693 | 2,749 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-05 | latest | en | 0.935072 |
https://superbprofessors.com/you-are-trying-to-find-out-how-high-you-have-to-pitch-a-water-balloon-in-order-for-it-to-burst-when-it-hits-the-ground-you-discover-that-the-balloon-bursts-when-you-have-pitched-it-to-a-height-of-18/ | 1,620,580,666,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989006.71/warc/CC-MAIN-20210509153220-20210509183220-00407.warc.gz | 580,103,542 | 11,111 | # You are trying to find out how high you have to pitch a water balloon in order for it to burst when it hits the ground. You discover that the balloon bursts when you have pitched it to a height of 18 m. With what velocity did the balloon hit the ground? The acceleration of gravity is 9.8 m/s 2 . The positive direction is up, so the velocity when it hits is negative. Answer in units of m/s.
You are trying to find out how high you have to pitch a water balloon
in order for it to burst when it hits the ground. You discover that the balloon bursts when you have pitched it to a height of 18 m. With what velocity did the balloon hit the ground? The acceleration of gravity is 9.8 m/s 2 . The positive direction is up, so the velocity when it hits is negative. Answer in units of m/s.
Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code “Newclient”
The post You are trying to find out how high you have to pitch a water balloon in order for it to burst when it hits the ground. You discover that the balloon bursts when you have pitched it to a height of 18 m. With what velocity did the balloon hit the ground? The acceleration of gravity is 9.8 m/s 2 . The positive direction is up, so the velocity when it hits is negative. Answer in units of m/s. appeared first on Superb Professors. | 312 | 1,323 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2021-21 | latest | en | 0.947366 |
www.veritopia.org | 1,719,145,060,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862466.81/warc/CC-MAIN-20240623100101-20240623130101-00047.warc.gz | 58,885,257 | 5,907 | VERITOPIA
Alchemy &
Natural-Law
# Space / Time Relationships
## Physics: Fundamental Units
The International System of Units (SI) we use for measurements lists seven different fundamental units.
The different types of unit correspond to different properties, and there are seven, suggesting the universe has seven fundamental properties.
SymbolNameQuantity
ssecondtime
mmetrelength
kgkilogrammass
Aampereelectric current
Kkelvinthermodynamic temperature
molmoleamount of substance
cdcandelaluminous intensity
This is probably too many...
The principle of duality suggests there are just two main units or properties.
## Space / Time Units
Some people have suggested that the two fundamental units are space & time, and everything else can be expressed in those terms.
See this excellent website for a great explaination of ST Units: BlazeLabs - Unified Theory Foundations - The ST system of units.
I also came across Dewey B Larson who advocated this system.
## All Possible Relationships
The table below shows all possible basic relationships that can exist between Time & Space, limited to 3D.
It's mapped to the known physical units, and a brief description is given (from Wikipedia). It's a reference, and a work in progress.
The 3 dimensions of space are obvious. The 3 dimensions of time we experience are: velocity, acceleration and 'jerk' (change in acceleration). We can feel and see these things so we know they have a form of physical reality.
Some of the relationships that are possible don't seem to be known by physics. This could be because the relationship is meaningless, or there could be something amazing to be discovered. I don't know.
Y A N G I n t e g r a t i o n E x p a n s i o n YIN: Differentiation, Contraction...
Space/TimeF: 0D TimeA: 1D TimeW: 2D TimeE: 3D Time
F: 0D Space There must be 3 Constants of Integration. They correspond to the Voice, Heart and Sex Principles.
T Time = Change Frequency
T2 Change of Change
T3 Change of Change of Change
A: 1D Space
S Space, Charge Power
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative (commonly carried by protons and electrons respectively). Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. The SI derived unit of electric charge is the coulomb (C).
S/T Velocity, Current Energy, Moment, Torque Electric flux density, Thermal Resistivity
Energy is the property that must be transferred to an object in order to perform work on, or to heat, the object. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.
Thermal Resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance.
S/T2 Acceleration Angular Momentum ?
Angular Momentum is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity – the total angular momentum of a system remains constant unless acted on by an external torque.
S/T3 Jerk Inertia ?
Jerk, also known as jolt, surge, or lurch, is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, and as such the second derivative of velocity, or the third derivative of position.
Inertia is the resistance of any physical object to any change in its state of motion. This includes changes to the object's speed, direction, or state of rest.
W: 2D Space
S2 Area ?
S2/T Permittivity Force, Drag, Voltage ?
Permittivity or absolute permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of resistance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium.
The SI unit for permittivity is farad per meter (F/m or F·m−1).
The lowest possible permittivity is that of a vacuum. Vacuum permittivity, sometimes called the electric constant, is represented by ε0 and has a value of approximately 8.85×10−12 F/m.
S2/T2 Conductivity Momentum pImpulse JResistivity ?
Conductivity, a measure of a material's ability to conduct an electric current.
Resistivity is a fundamental property that quantifies how strongly a given material opposes the flow of electric current. Reciprocal of conductance.
Momentum is the product of the mass and velocity of an object.
Impulse is the change of momentum of an object when the object is acted upon by a force for an interval of time. So, with impulse, you can calculate the change in momentum, or you can use impulse to calculate the average impact force of a collision.
S2/T3 ? ? ?
E: 3D Space
S3 Volume Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted or reflected from a particular area, and falls within a given solid angle.
S3/T ComplianceCapacitance StiffnessElectric field strength ?
Compliance The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton. In rheology it may be defined as the ratio of strain to stress, and so take the units of reciprocal stress, e.g. 1/Pa.
Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force.
Capacitance is the ability of a body to store an electric charge.
Electric field is a field that surrounds electric charges. It represents charges attracting or repelling other electric charges by exerting force. The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m).
S3/T2 Conductance Resistance ?
Electrical resistance, of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor.
Conductance, is the ease with which an electric current passes.
S3/T3 Magnetic Reluctance Mass mInductance ?
Inductance is a property of an electrical conductor which opposes a change in current. It does that by storing and releasing energy from a magnetic field surrounding the conductor when current flows, according to Faraday's law of induction. When current rises, energy (as magnetic flux) is stored in the field, reducing the current and causing a drop in potential (i.e., a voltage) across the conductor; when current falls, energy is released from the field supplying current and causing a rise in potential across the conductor.
Magnetic Reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating electric energy it stores magnetic energy. In likeness to the way an electric field causes an electric current to follow the path of least resistance, a magnetic field causes magnetic flux to follow the path of least magnetic reluctance. | 1,570 | 7,208 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2024-26 | latest | en | 0.894305 |
http://mathtutorkk1969.blogspot.com/2012/05/heres-part-of-chapter-2-from-my-second.html | 1,503,066,283,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886104681.22/warc/CC-MAIN-20170818140908-20170818160908-00330.warc.gz | 278,386,172 | 22,746 | ## Wednesday, May 9, 2012
Here's part of chapter 2 from my second book, Algebra Simplified Intermediate & Advanced. If interested in the book, go to http://www.lulu.com/spotlight/KKauffman1969
# Chapter 2
## Square Roots, Cube Roots and Higher Roots
Recall when raising a number to a power n, where n is an integer greater than 1, we multiply the number by itself n times. For example, 43 = 4 ∙ 4 ∙ 4. Now suppose we want to know what number multiplied by itself 2 times equals 169. Problems of this kind can be represented using radicals.
A radical symbol √ is used to show the square root, or principal square root of a number or expression that appears under the radical symbol. Recall that the square root is defined as a number or expression multiplied by itself twice to equal the number or expression under the radical symbol, known as the radicand.
For example, if we want to know what number multiplied by itself 2 times equals 169, we can set this up with the radical symbol as follows:
169, read as “square root of 169”. The answer to this is 13.
- √169, read as “negative square root of 169”. The answer to this is -13.
0.09 = 0.3 and -0.3 since (0.3)2 and (-0.3)2 equals 0.09. The principal square root is 0.3. Another way to simplify this is to change √0.09 to √(9/100) and simplify to 3/10.
(25/49) = 5/7 and -5/7 since (5/7)2 and (-5/7)2. The principal square root is 5/7.
Note that a square root also has a negative value since a negative times a negative equals a positive, but we will deal with only the principal square root unless otherwise noted.
Note that you can also simplify the square root of a fraction by taking the square root of the numerator and then the square root of the denominator instead of the square root of the fraction as a whole. In the previous example, you can take the square root of 25 first, then the square root of 49.
Note that the square root of many positive integers are not whole numbers or rational numbers. For example, √19 can be found on a calculator or by leaving the answer as √19.
An easy way to solve many square root problems is to know the perfect squares from 1 to 25. They are as follows:
12 = 1 102 = 100 192 = 361
22 = 4 112 = 121 202 = 400
32 = 9 122 = 144 212 = 441
42 = 16 132 = 169 222 = 484
52 = 25 142 = 196 232 = 529
62 = 36 152 = 225 242 = 576
72 = 49 162 = 256 252 = 625.
82 = 64 172 = 289
92 = 81 182 = 324
Sometimes we have to find the square root of a number that is not a perfect square. In these cases, we break down the radicand into factors, one of which is a perfect square.
Examples: Find each square root.
1. √68
First, find factors of 68.
Since 68 is even, we can divide it by 2. Therefore, 68 = 2 ∙ 34. Notice 34 is also divisible by 2, therefore 34 = 2 ∙ 17.
So 68 is factored into 2 ∙ 2 ∙ 17. Notice that 17 is prime and cannot be factored further and 2 ∙ 2 = 4, which is a perfect square. Therefore √68 = √4 ∙ √17 = 2√17.
2. √108
First, find factors of 108.
Since 108 is even, we can divide it by 2. Therefore 108 = 2 ∙ 54. Notice 54 is also divisible by 2, therefore 54 = 2 ∙ 27. Next, we know that 27 = 3 ∙ 3 ∙ 3.
The factors of 108 are 2 ∙ 2 ∙ 3 ∙ 3 ∙ 3. Notice 2 ∙ 2 = 4, which is a perfect square and 3 ∙ 3 = 9, which is also a perfect square. Therefore, 108 = 4 ∙ 9 ∙ 3 and √108 = √4 ∙ √9 ∙ √3 = 2 ∙ 3 ∙ √3 = 6√3.
Note that 108 = 36 ∙ 3 and 36 is a perfect square. But if you can't see right away that 3 is a factor of 108, you can break down by dividing 108 by 2 first and then simplify further at that point. It's easy to determine that 108 is divisible by 3. If the sum of the digits of a number are divisible by 3, the number is divisible by 3.
Recall, for a variable x, where x ≠ 0, √x2 = x and -x. If we are dealing with just the principal square root, then the answer is |x|. Recall that |x| is the absolute value of x.
Examples: Find the square root of the following.
a. √(25x2)
Simplify the numerical part and the variable part separately.
25 = 5 since 52 = 25 and √x2 = x since (x)2 = x2.
Therefore, √(25x2) = 5x.
b. √(64x4y6)
64 = 8 since 82 = 64, √x4 = x2 since (x2)2 = x4 and √y6 = y3 since (y3)2 = y6.
Therefore, multiply the terms in bold to get √(64x4y6) = 8x2y3.
c. √(x + 4)2 = (x + 4) because (x + 4)(x + 4) = (x + 4)2
Note that the square root of any number or expression squared is just that number. For example, notice in the previous examples that √(x + 4)2 = (x + 4) and √25 = √(5)2 = 5.
d. √(x2 + 12x + 36) = √(x + 6)(x + 6)
Notice that we factored (x2 + 12x + 36) to get (x + 6)(x + 6). That is a perfect square which enables us to simplify the radical expression.
(x2 + 12x + 36) = √(x + 6)(x + 6) = √(x + 6)2 = (x + 6)
Note that you can check by squaring your answer. After squaring, you should get the expression under the √.
In the previous examples, we simplified radicals that were perfect squares. Many times we can simplify radicals that are not perfect squares. The idea is to break down the number or variable into factors, one of which is a perfect square. By the multiplication property of radicals n√(ab) = na nb, where n√a and nb are real numbers.
Note that in a square root n is 2 but is not written. When solving any root higher than 2, it is noted in the upper left of the radical. For example, the cube root (n = 3) of a is noted as 3√a.
The cube root of a number n is the number when multiplied by itself 3 times equals n. For example, the cube root of -125 is -5 because (-5) ∙ (-5) ∙ (-5 ) = -125, or (-5)3 = -125. By definition, the cube root of a is defined as 3a = b, if b3 = a.
Examples:
3√27 = 3 since 33 = 27
3√(-27) = -3 since (-3)3 = -27
3√125 = 5 since 53 = 125
3√(-125) = -5 since (-5)3 = -125
Note that 27 and 125 have 1 real number cube root and 2 real number square roots. Any negative number will have a cube root that is negative and any positive number will have a cube root that is positive.
Examples: Simplify the following.
a. 3√-8
To solve this, think of what number multiplied by itself 3 times gives you -8. Notice that (-2) ∙ (-2) ∙ (-2) = -8. Therefore, 3√-8 = -2.
b. 3√343 = 7 since 7 ∙ 7 ∙ 7 = 343.
c. 3√729 = -9
Note that if the sum of the digits of a number is divisible by 9, the number is divisible by 9.
The sum of the digits of 729 is 18, which is divisible by 9. Therefore, 729 is divisible by 9 and -729 is divisible by 9.
729/9 = 81 and we know the square root of 81 is 9.
We reviewed how to take the cube root of positive and negative numbers. Now we will review how to take the cube root involving variables. Recall that by definition, if x is a variable representing a real number, 3x3 = x.
Examples: Simplify the following.
a. 3√(27x3) = 3√(27) ∙ 3√(x3) = 3 ∙ x = 3x
Check by taking the cube of 3x.
(3x)3 = 3x ∙ 3x ∙ 3x = 27x3.
b. 3√(5x + 2y)3 = (5x + 2y) because of the rule that 3x3 = x.
c. 3√(-216x6y12)
3√(-216) = -6, 3√(x6) = x2 since (x2)3 = x6 and 3√(y12) = y4 since (y4)3 = y12.
Multiply the terms in bold to get -6x2y4.
The previous examples were perfect cubes, but oftentimes we can find the cube root of expressions that are not perfect cubes. The idea is to break down the number or variable into factors, one of which is a perfect cube. For example, if you solve 3√81, break it down into 3√27 ∙ 3√3 because 3√27 = 3. If you solve 3√(y5), break it down into 3√(y3) ∙ 3√(y2) because 3√(y3) = y. Remember from the multiplication property of radicals that 3ab = 3a3b.
Example: Simplify the following.
3√(16x4)
3√16 = 3√8 ∙ 3√2 = 23√2 (3√8 = 2 because 23 = 8)
3√(x4) = 3√(x3) ∙ 3x = x3x (3√(x3) = x by the definition of cube root (x)3 = x3)
Multiply like terms to get 3√(16x4) = 2x3√(2x)
Note that you can check by cubing the answer, [2x3√(2x)]3 = 8x3 ∙ 2x = 16x4.
Example: Simply the following.
3√(-192x4y5)
3√(-192) = 3√(-64) ∙ 3√(3) = -43√(3) (note that -64 ∙ 3 = -192 and (-4)3 = -64)
3√(x4) = 3√(x3) ∙ 3√(x) = x3√(x) (note that x3x = x4 and (x)3 = x3)
3√(y5) = 3√(y3) ∙ 3√(y2) = y 3√(y2) (note that y3y2 = y5 and (y)3 = y3)
Now multiply the like terms to get -4xy3√(3xy2).
In some cases cube roots will be the form of a fraction of two numbers, a number and a expression or two expressions. In these cases, try to simplify the ratio first. By the division property of radicals 3√(x/y) = 3x / 3y.
Example: Simplify the following.
3√(8x3/64y6)
By the division property of radicals 3√(8x3/64y6) = 3√(8x3) / 3√(64y6)
3√(8x3) = 2x because (2x)3 = 8x3
3√(64y6) = 4y2 because (4y2)3 = 64y6
Therefore 3√(8x3/64y6) = (2x)/(4y2) = x/(2y2).
Example: Simplify the following.
3√(216y5/8y8)
By the division property of radicals 3√(216y5/8y8) = 3√(27/y3) because 216/8 = 27 and (y5)/(y8) = 1/(y3).
3√(27) = 3 and 3√(1/y3) = 1/y.
Therefore 3√(216y5/8y8) = 3/y.
Note that it's easier to solve cube roots if you know the first several perfect cubes. The first ten perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.
We reviewed how to take the square root and cube root of numbers and expressions. There are also fourth roots, fifth roots, sixth roots, seventh roots and so on. The procedure for solving these roots is the same as for square roots and cube roots. For example, a fourth root of a natural number x is a number multiplied by itself four times to equal x, and so on for higher roots. If n is an odd natural number greater than 1 (n > 1), then n√(x) is an odd root. When n is an even natural number greater than 1 (n > 1) and x > 0, then n√(x) is an even root.
Examples: Simplify the following radical expressions.
a. 4√10000
4√10000 = 10 since 104 = 10 ∙ 10 ∙ 10 ∙ 10 = 10000
b. 5√(32x15)
5√32 = 2 because 25 = 32
5√(x15) = x3 because (x3)5 = x15
Therefore 5√(32x15) = 2x3
c. 6√(729x6y18)
6√729 = 3 because 36 = 729
6√(x6) = x because (x)6 = x6
6√(y18) = y3 because (y3)6 = y18
Therefore 6√(729x6y18) = 3xy3
d. 7√(x + 10)14
7√(x + 10)14 = (x + 10)2 because [(x + 10)2]7 = (x + 10)14
### Review Problems: Set 1
Simplify each of the following square roots.
1. √121 2. √(4/25) 3. -√0.49
4. √60 5. √125 6. √252
Simplify each of the following radical expressions.
7. √(9y2) 8. √(64x4) 9. √(x2 + 14x + 49)
10. √(y2 – 8y + 16) 11. √(81x8y6) 12. √(144x4y2z6)
13. √(80x5) 14. √(75xy2z3) 15. √(98z3)
Simplify each of the following cube roots.
16. 3√-64 17. 3√(27/125) 18. -3√-216
19. 3√40 20. 3√320 21. 3√-54
Simplify each of the following radical expressions.
22. 3√(8x4y5z6) 23. 3√(-108z4) 24. 4√256
25. 5√(-243a5) 26. 6√(32x12) 27. 7√(107)
### Rational Exponents
Just as we can raise a number or expression to exponents that are integers, we can raise them to fractional exponents as well. If n is a positive integer greater then 1, then x1/n is the nth root of x and 1/n is a rational exponent. In other words x1/n = nx.
To make this more clear, consider √3 and 31/2. By squaring both of these, we can determine that they are equal.
(√3)2 = (√3)(√3) = √9 = 3
(31/2)2 = 3(1/2 ∙ 2) = 31 = 3
Notice that squaring both gives a result of 3. Therefore √3 = 31/2.
We can rewrite exponential expressions in radical form and radical expressions in exponential form. The radicand of a radical expression becomes the base of an exponential expression and one over the index of the radical expression becomes the exponent. We'll illustrate this in the following
36 = 6 1/3. Notice the index in red becoming the denominator of the exponent and the radicand in blue becomes the base.
Examples: Evaluate the following.
1. 161/2 = √16 = 4. Recall that the index of a square root is 2, although the 2 is not written.
2. (-27)1/3 = 3√(-27) = -3 because (-3)3 = -27.
3. (16/81)1/4 = 4√(16/81) = 2/3 because (2/3)4 = 16/81.
4. -321/5 = -2 because (-2)5 = -32.
Examples: Simplify the following rational expressions.
1. (25x4)1/2
We will break this down into the number part and the variable part.
251/2 = 5 and (x4)1/2 = √(x4) = x2 since (x2)2 = x4.
Therefore (25x4)1/2 = 5x2.
Note that (x4)1/2 can also be simplified using the rules for raising an exponent to an exponent. Therefore, the exponents 4 and ½ are multiplied together to get 2, which is the new exponent and (x4)1/2 = x2.
2. (-125x3)1/3
(-125)1/3 = 3√(-125) = -5 since (-5)3 = -125 (x3)1/3 = 3√(x3) = x
Therefore, (-125x3)1/3 = -5x.
3. [(2a + 7)4]1/4 = 4√(2a + 7)4 = |2a + 7|
Notice the answer is |2a + 7| and not 2a + 7. |2a + 7|4 = (2a + 7)4 and a can be any number, therefore 2a + 7 could be a negative number. But we can't have a real number solution if 2a + 7 is negative because no real number raised to the 4th power is negative. Therefore we must have absolute value to ensure a positive real number solution.
4. [(4b – 3)5]1/5 = 5√(4b – 3)5 = 4b – 3.
In this case, since n is odd, there is no need for the absolute value symbols in the solution. The value of 4b- 3 could still be negative but a negative quantity raised to an odd power will be negative.
In the previous examples all of the exponents were in the form 1/n. Now we will learn how to simplify exponential expressions where the exponent is in the form p/n where p and n are positive integers and n ≠ 1. To illustrate how to simplify , consider the following example.
272/3. We can rewrite this in the form x1/n raised to the 2nd power, (x1/n)2 = x2/n.
Therefore, 272/3 = (271/3)2
= (3√27)2 = 32 = 9
We can rewrite the exponential expression in radical form. The numerator of the rational exponent becomes the power of the radical expression. The denominator of the rational exponent becomes the index of the radical expression and the base of the exponential expression becomes the radicand. In the previous example,
272/3 = (327)2
We would solve this as follows:
Take the cube root of 27: 3√27 = 3
Square 3: 32 = 9
Or we can think of 272/3 as
272/3 = 3√(27)2
We would solve this as follows:
Square 27 first : 272 = 729
Take the cube root of 729 : 3√729 = 9 since 93 = 729.
Note that we know that 729 is divisible by 9 because the sum of the digits in 729 is divisible by 9. The sum of the digits of 729 is 18, which is divisible by 9. | 4,893 | 14,019 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 5 | 5 | CC-MAIN-2017-34 | longest | en | 0.912732 |
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# Integral of log2 dx
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### The solution
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$$\int\limits_{0}^{1} \log{\left(2 \right)}\, dx$$
Detail solution
1. The integral of a constant is the constant times the variable of integration:
2. Add the constant of integration:
The answer (Indefinite) [src]
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| log(2) dx = C + x*log(2)
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0.693147180559945
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https://howtodiscuss.com/t/y-3x-2-graph/110840 | 1,642,789,776,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303512.46/warc/CC-MAIN-20220121162107-20220121192107-00642.warc.gz | 359,385,455 | 14,466 | Y 3x 2 graph
Y 3x 2 graph
How do you determine the function of a graph? Use the vertical line test to determine if the graph represents a function. If the vertical line moves along the graph and touches the graph at any point, then the graph is a function. If the vertical line touches the graph at more than one point, the graph is not a function.
What are the X and Y points on a graph?
An X and Y chart has two perpendicular axes or lines called number lines. The horizontal axis is called the x-axis and the vertical axis is called the y-axis. The intersection of the graphs of the X and Y axes is called the origin. Grid numbers are used to locate points.
What is the plot of a graph?
A chart is a graphical method of displaying a series of data, usually in the form of a graph, showing the relationship between two or more variables. The plot can be drawn by hand, with a mechanical or electronic plotter.
How do you find the equation of a line graph?
The linear equation creates a line graph. The equation is y = mx + b, where m is the slope and b is the y-intercept.
How can you tell if a relation of a graph has a function?
The easiest way to find out if a ratio graph is a function is to check the vertical line! If you draw a vertical line through one (and all) points on the diagram, and the vertical line touches 2 or more points on the diagram, this is NOT a function! Remember that the features are one to one.
Does the graph represent the function?
The graph represents a function when a drawn vertical line crosses it only once. If the function is also 11, each horizontal line drawn will intersect it only once.
When can a graph represent a function?
The curve drawn on the graph represents the function where each vertical line intersects the curve at no more than one point. Determine whether the following image represents a function. Justify your answers for each figure. Since the graph intersects the vertical line (Y-axis) at two points, this is not a function.
Is the graph of every line a function?
Alternatively, if the vertical line does not intersect the graph more than once, regardless of where the vertical line is, then the graph is a function graph. For example, a curve that is a straight line rather than a vertical line is a graph of a function.
What is the plot of a graph look
To graph a function, do the following: Define x by specifying the range of values of x for which to graph the function. Define a function, y = f(x) call the plot command as plot(x, y).
What is the formula for graphing?
Plotting Linear Equations Use the formula y = mx + b. To represent a linear equation, all you need to do is fill in the variables in that formula. Draw your diagram. Linear equations are easiest to write because you don't need to calculate numbers before drawing the graph. Find the intersection of the y-axis (b) in your graph.
How do you find the equation of a line?
Community response. The equation in a straight line is usually y = mx + c. To find the equations of a line, you need to find m and c. m - slope. For example, if your line goes up two units in the y direction, for three units in the x direction, then m = 2/3.
What is the equation for a cubic graph?
Basic cube graph y = x 3. For a function of the form y = a (x - h) 3 + k. If k > 0, the graph is shifted k units, if k< 0, the graph shifts k units down.
What is a Graphic Calculator?
A graphing calculator (also known as a graphing calculator or graphing calculator) is a portable computer that can draw graphs, solve equations, and perform other tasks involving variables at the same time.
What is a graphing tool?
Graphtool is a Python module for the statistical processing and analysis of graphs (AKA networks). Graphtool's underlying data structures and algorithms are implemented in C++, allowing heavy use of meta-programming, which relies heavily on the Boost graphics library.
How do you determine the function of a graph in excel
Select a blank cell, enter the formula =SUM(D3:D16) to get the total area below the drawn area. This method uses the trendline of the graph to obtain an equation for the curve being drawn and then calculates the area under the curve being drawn using the final integral of the equation.
How do you graph spreadsheet in Excel?
Converting data from an Excel spreadsheet to charts, called charts in an Excel Help file, involves the following general steps: identify the columns of data you want to chart, choose a chart type, and then run a command to to make these. write from the diagram. Adding new data to existing charts is done in the same way.
Can excel graph equations?
Excel cannot draw linear equations directly to draw linear equation in Excel. You must have an array of at least two values for the function, already preformatted in two columns (X, Y) with column headings. Excel can display linear functions as charts.
How do you create a line graph?
Create a line chart Open Microsoft Excel. Double-click the Excel icon that looks like a white cross in a green folder. Click Blank Book. It's on the Excel home page. Enter your information. A line chart needs two axes to function. Select dates.
What is a line chart in Excel?
1) Copy the data from the sample worksheet to a blank worksheet or open a worksheet that contains the data you want to display in a line chart. 2) Select the data you want to display on the line chart. 3) Click the Insert tab and then click Insert Line or Area Chart. 4) Click on the line with markers. 5) Click in the chart area to display the Layout and Format tabs. 6) Click the Design tab and then click .
How do you determine the function of a graph in one
The easiest way to determine if an attribute is unique is to use the horizontal line test on the attribute chart. To do this, draw horizontal lines on the diagram. If the horizontal line crosses the graph more than once, the graph is not a single value function.
How do you determine the function of a graph in order
The function has only one output value for each input value. How: On a given graph, use the vertical line test to determine if the graph represents a function. Look at the graph to see if the drawn vertical line crosses the curve more than once. If such a line exists, the graph does not represent a function.
How can you tell if a graph is a function?
The vertical line test can be used to determine whether a graph represents a function. The vertical line includes all points with a specific x x value. The y y value of the point where the vertical line intersects the graph is the output for that x x input.
What is a first order graph?
The first order is the natural logarithm of the concentration A as a function of time. If you get a straight line with a negative slope, that's best. If you plot the inverse of concentration A as a function of time for second order, you get a positive line with a positive slope, so you know your second order.
How to determine a function step by step?
Defining functions step by step using an example
Step 1 Functions have one output for each input. 2 When you get the graph, you can use the vertical line test to see if the equation is a function. 3 When you get an array, you need to check each value of x to make sure only one value of y is associated with it.
How to determine if you have a function in ordered pairs?
For example, you can use words, sorts, ordered pairs, tables, and graphs. In each of these views, you can use your rule to determine whether they have a function. No entry can have more than one exit. Therefore, in ordered pairs, two ordered pairs cannot have the same first coordinate and different second coordinates.
How do you determine the function of a graph worksheet
Line charts can also be used to show how attributes change. A function is simply an equation that gives you a unique result for each input. For example, y = 4 / 5x + 3 is a function because you can get a unique value for y if you enter a number for x.
How do you graph a linear function?
Steps Make sure the linear equation is y = mx + b. It is known as the intersection form and is probably the easiest way to draw linear equations. Draw the number b on the Y-axis. Your b will always be a rational number. Convert m to fractions.
What are the characteristics of a graph?
The main features of a chart are the horizontal and vertical axes, the legend and of course the chart itself, each axis has a label and a numerical scale. Axis titles are defined by a graphical command using the names from the argument list or the names you specify in the command.
What are the transformations of graphs?
A chart transformation is the process of modifying an existing chart or graphic equation to create a variant of the previous chart. This is a common problem in algebra, especially the modification of algebraic equations.
How do you identify points on a graph?
Coordinates of points. A dot is the underlying relationship shown in the chart. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a series of numbers used to locate a point on a graph. Each point is identified by an x coordinate and a y coordinate.
How do you make an X Y graph?
Create an XY chart in Excel. Once you have the data you want, you can easily create an X and Y axis chart in Excel. Select the two columns (or rows) of data you want to map and notice that the column on the left is the x-axis and the column on the right is the y-axis. Go to the Insert tab and find the Charts section.
What is x vs Y graph?
The xv graph makes sure that the x-axis is filled with fixed variables (amounts that don't change during the experiment, such as time intervals), and on the y-axis you want to enter values that change during the experiment. for example the number of observations. I hope this helps.
What is X or Y on a graph?
The x-axis and the y-axis are two lines that form a coordinate plane. The X-axis is a horizontal line and the Y-axis is a vertical line. I'm sure you've heard this a million times, but it can be hard for you to remember what's what.
What are the x and y points on a graph are called
The horizontal axis is represented by the x-axis and the vertical axis is represented by the y-axis. The intersection of the X and Y axes is called the origin and serves as a reference point for the plane. The X-axis is also called the abscissa. The Y-axis is also called the ordinate.
Where are the X and y intercepts on a graph?
A graphical representation of a line with x and y intercepts. The second is the y-intercept, the point on the line that lies somewhere on the vertical axis (y-axis). Here's a quick diagram to give you an idea. Since the x-intercept is the point where the line intersects the x-axis, it is the point with a y-value of zero.
Which is the reference point for the X and y axis?
They form a coordinate plane. The horizontal axis is represented by the x-axis and the vertical axis is represented by the y-axis. The intersection of the X and Y axes is called the origin and serves as a reference point for the plane. The X-axis is also called the abscissa. The Y-axis is also called the ordinate.
How to draw the X and y axis of a graph?
To draw the x and y coordinates of a linear equation, you must draw the x and y table grid for at least two points. Now draw points on the diagram where the x x values are on the x x axis and the corresponding y y values are on the y y axis.
How to find the y coordinate of a graph?
Draws a straight line from a direct point to the Y axis. The number at which the line touches the axis is the value of the y coordinate. If you remember the graph with its points B and D, determine the y coordinate for each of them. The y coordinate of point B is 400.
What happens if you have an X and a Y chromosome?
Men with variants of Klinefelter syndrome have extra X or Y chromosomes. An extra X or Y chromosome can affect physical, developmental, behavioral and cognitive functions.
What is the difference between XX and XY chromosomes?
The difference between the definition of the XX and XY chromosomes. The XX chromosomes refer to the sex chromosomes in females and the XY chromosomes refer to the sex chromosomes in males. The kind of sex. While the XX chromosomes occur in the homogametic sex, the XY chromosomes occur in the heterogametic sex. Chromosome inactivation.
What are the X and Y chromosomes called?
The sex chromosomes are called X and Y. People with two X chromosomes (XX) are female, people with X and Y (XY) are male, with few exceptions. There are two common types of aneuploidy: monosomy (MOHNohsohmee) and trisomy (TRYsohmee).
What genes are located on the X or Y chromosome?
In males, the presence of the X chromosome is usually responsible for female development. In the absence of the X chromosome, the fetus undergoes male development. In particular, the SRY gene on the Y chromosome is important for male differentiation.
What are the x and y points on a graph are used
The X and Y axes are the axes used in coordinate systems. They form a coordinate plane. The horizontal axis is represented by the x-axis and the vertical axis is represented by the y-axis. The intersection of the X and Y axes is called the origin and serves as a reference point for the plane.
What are the x and y points on a graph show
The main components of a line chart are the same as any other chart. They consist of the following components: X-axis (horizontal axis): In a line chart, the X-axis is the independent variable and generally represents time periods. Y-axis (vertical axis): This axis is a dependent variable and shows the data you are tracking.
X and y album
X&Y is the third studio album by British rock band Coldplay. It was released on June 6, 2005 by Parlophone in the United Kingdom and a day later by Capitol Records in the United States. The album was produced by Coldplay and produced by Danton Supple.
What year did X and y come out?
X&Y (stylized as X&Y) is the third studio album by British rock band Coldplay. It was released on June 6, 2005 by Parlophone in the United Kingdom and a day later by Capitol Records in the United States. The album was produced by Coldplay and produced by Danton Supple.
Is the X and Y album a ■■■■ end?
But flawless and flawless as X&Y is, it's a good, clear, professional and confident recording, a satisfying follow-up to A Rush of Blood to the Head, showing that Martin's solipsism is a ■■■■ end and the band's status is declining.
What kind of music does X and Y have?
Coldplay got Kraftwerk's permission to use Computer Love's lead riff to talk about the song. The music of X & Y consists of layered productions with strong electronic influences and extensive use of synthesizers.
Who is the artist of X and Y?
The X&Y cover was created by graphic design duo Tuppin Gofton, consisting of Mark Tuppin and Simon Gofton. Mark Tappin previously worked for Coldplay on the cover of the album Parachutes and on the covers of the singles from that album.
What are the x and y points on a graph look
The first is called the x-intercept because it is a point on a line that lies on the horizontal axis (x-axis). The second is the intersection point, that is, the point of the line on the vertical axis (Y-axis). Here's a quick diagram to give you an idea.
What is the difference between a plot and a graph?
As verbs, they are the difference between graphic and plot. This drawing is a drawing to be drawn during the plot (crime, etc.).
What is the difference between a diagram and a graph?
• All images are images, but not all images are images. This means that the diagram is only part of the diagram. • A graph is a representation of information with lines on two or three axes, such as x, y, and z, while a graph is a simple graphical representation of how something looks or works.
Which type of graph is data plotted by a point on the graph?
A two-point graph, also known as a line graph, is a graphical representation of data that plots specific values of a function as points on a coordinate plane. The pairs of adjacent points are connected by straight lines.
What is the definition of a plot diagram?
A plot diagram is an organizing tool that focuses on a pyramid or triangle and is used to correlate the events of a story. This presentation of the plot structure allows readers and authors to visualize the main features of the stories.
What is the plot of a graph based
The explanatory variable must be plotted on the abscissa. The dependent variable must be plotted on the y-axis. On a mass-volume graph, the volume is placed on the x-axis and the mass on the y-axis.
What is a point on a graph?
A point is the center of the graph if the eccentricity of the point is equal to the radius of the graph. The set of all midpoints is called the midpoint of the graph.
What is the plot of a graph used
Graphs (Charts) Graphs can also be used to display the value of an unknown variable in relation to a known variable. Function graphs are used in math, science, engineering, technology, finance and other fields.
How do you make a plot in Excel?
How do you make a point cloud?
Step 1 : Enter or copy/paste your data into an Excel spreadsheet.
Step 2 : Select the columns that contain the data you want to display in the point cloud.
Step 3 : Open the "Insert" tab on the Excel ribbon.
What is the plot of a graph example
“The plot summary is an abridged version of a literary work, a short retelling of a story. The plot summary does not reveal the deep meaning of the work. Plot Summary In Kate Chopin's story "The Story of an Hour" the main character learns that her husband has been killed in a train accident.
What is an example of a line plot?
In a line chart, markers are used to plot each data item on a number line. Example: Some students have completed a survey to find out how many pencils each have in their office. They recorded the data in a line graph.
How to use Matplotlib?
Learn the basic terminology of matplotlib, especially what is figure and axis. Always use an object-oriented interface. Start your performances with a simple panda crawl. Use Seaborn for the most complex statistical views. Use matplotlib to customize the display of pandas or sea creatures.
How do you write the equation of a line?
The series equation can be written in standard form (Ax + By = C) or in SlopeIntercept form (y = mx + b). Regardless of the shape, you need two pieces of information to write the equation of the line: 1) the slope and 2) the y-intercept.
How do you find equation given two points?
Find the equation of the line, knowing that you know the two points it passes through. The equation for a series is usually written as y = mx + b, where m is the slope and b is the intersection. If you know the two points through which a straight line passes, this page will show you how to find the equation of a straight line.
How to find the equation of a line
Line comparison. The standard form of a linear equation is Ax + By = C, where A, B and C are real numbers, A and x are variables.
What is the standard form for an equation of a line?
Standard form: The standard form of a string is Ax + By = C, where A is a positive integer and B and C are integers. The standard line shape is just another way to write the equation of the line.
What is formula of equation of a line?
Vector equation of a straight line in space. In a two-dimensional plane, a straight line can be represented by the equation y = mx + b, where m is the slope of the straight line and b. Find the vector equation of the line. Another way to define points on a line is to use the vector sum method you discussed earlier in this chapter. General vector equations.
How to find the equation of line going through two points?
• Find the slope with m = (y2y1) / (x2x1).
• Replace m in the slope segment formula with the slope you find.
• Replace x and y with any of the points you can find for the y intersection.
• Solve the equation b.
• Plug the slope and y-intercept into the slope interception formula to complete the equation.
Equation of a line calculator
Equation Lines Calculator Equation Lines Calculator is a free online tool that displays the equation of a line when slope and distance values are specified. BYJU Online Calculator for Equation Linear Calculator speeds up calculations and displays the equation in fractions of a second.
Equation of a line general form
General view of the equation in a straight line. The general form of the equation for a straight line is Ax + By + C = 0. A or B can be zero, but not both at the same time. The general form is not always the most useful form, and you may prefer to use: SlopeIntercept form of the equation of the line: y = mx + b.
How do you rewrite an equation in general form?
To write an equation in general linear form, given the graph of the equation, first find the x-intercept and y-intercept, which are of the form (a, 0) and (0, b). Bx + ay = ab. This equation is linear and the two intersections satisfy it, so it's a straight line.
Which is the correct form for a linear equation?
The standard form of a linear equation is Ax + By = C. A, B and C are real numbers. Any equation can be converted to this form by adding or subtracting the same terms on both sides of the equation. Example: Equation: 9 + 9x = 11y. Subtract 9 from both sides: 9 - 9 + 9x = 11y - 9.
What are the three forms of a linear equation?
The three main forms of linear equations are the slope segment form, the point slope form, and the standard form.
How to write the equation of a line?
REALITY Write an equation for a line passing through point (2, –3) and slope four. Point = (2, –3) Slope = 4 y - y1 = m (x - x1) y + 3 = 4 (x - 2) Start with the shape from point to slope, connect the value of y, the slope and the x value to get. Note that if you subtract "-3", you get "+3".
Which is an equation for a horizontal line?
There are other forms of equations that you need to identify, such as lines and diagrams, if needed. Horizontal line: y = c, where c is a constant. Vertical line: x = c, where c is a constant.
How to graph the slope of a linear equation?
Plotting Ramp Segments Plotting Ramp Segments Verify that the equation is in the form of a ramp segment. Determine the slope and the y-intercept. Draw the intersection point y. Use the slope of the y-intercept to get another point to draw the line. y = 3x + 2 Slope = 3 (note that the rate of ascent or overshoot can be (3/1) or (3/1).
How to draw a straight line in GCSE?
GCSE Specification: Understand that an equation of the form y = mx + c follows a straight line graph. Draw straight line graphs from your equations. Draw and draw an equation of the form y = mx + c. Find the slope of a straight line - Linear.
How to graph y = 3x-2 using slope intercept form?
Shape of the slope intersection of the linear equation: y = mx + b, where m is the slope and b is the y intersection. y = 3x - 2.
How to graph y = 3x + 2 by equation?
Learn how to draw y = 3x + 2 by finding the y intersection and slope of the graph from the equation. The equation of the line should be y = mx + c, where m is the slope and c is the y-intercept. The slope of the line is also called slope and is calculated as slope/slope.
How to calculate the slope of a graph?
Click to continue. Slope shape: y = m x + b y = m x + b, where mm is the slope and b b is the y intersection. Find the values of m m and b b using the form y = m x + b y = m x + b. The slope of the straight line is the value in millimeters and the y-intercept is the bb value.
How do you graph a linear inequality step by step?
Constructing a Linear Inequality 1. Replace the inequality symbol with an equal sign and draw the resulting line. 2. Check a point that is clearly in a half-plane of this line to see if it is part of the set of solutions to the inequality. 3. If the selected point is in a set of solutions, then this whole half-plane is a set of solutions.
How are quadratic inequalities graphed in math?
The quadratic inequality has the form y > ax2 + bx + cy > a x 2 + b x + c (or a substitute). To represent the quadratic inequality, start by constructing a quadratic parabola. Then fill in the area inside or outside depending on the inequality.
How to solve a system of two linear inequalities?
To solve a system of two linear inequalities using a graph, determine the area of a plane that satisfies two statements of the inequality. To solve a system of two equations with two unknowns by substitution, you solve an unknown in one equation with another unknown and replace that value in the other equation.
Do you have to have two points for a graph?
Equations with two higher degree unknowns give graphs that are curves of a different nature. You will learn them in future algebra classes. Since the graph of a first-degree equation in two variables is a straight line, two points are enough.
What is the Y Y value of x = 2?
The final answer is 2 2. The y y value at x = 2 x = 2 is 2 2. Create an array of x x and y y values. Draw a line graph with a slope and Y intersection or points.
How can you graph the slope of a line?
The slope of the straight line is the value in millimeters and the y-intercept is the bb value. Each line can be represented graphically by two points. Select two x x values and plug them into the equation to find the corresponding y y values.
Which is the slope intercept form of Y?
Slope shape: y = m x + b y = m x + b, where mm is the slope and b b is the y intersection. Trade - 1 1 and 3 x 2 3 x 2. | 5,854 | 25,695 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2022-05 | latest | en | 0.932537 |
https://www.osmosis.org/learn/Mean,_median,_and_mode?from=/md/foundational-sciences/biostatistics-and-epidemiology/biostatistics/parametric-tests | 1,652,858,451,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00596.warc.gz | 1,084,214,048 | 43,721 | # Mean, median, and mode
Videos
Notes
## Biostatistics and epidemiology
#### Biostatistics
Introduction to biostatistics
Statistical probability distributions
Parametric tests
Non-parametric tests
Outcomes of statistical hypothesis testing
0 / 13 complete
High Yield Notes
7 pages
Flashcards
### Mean, median, and mode
13 flashcards
Transcript
#### Contributors:
In statistics, it’s often helpful to know the central point of a set of data, because it gives a pretty good idea about the whole data set. It’s like a one number summary of the data.
What’s the number of words on a page in a book? About 250. Of course it depends on the book, but that’s the one number summary.
The mean, median and mode are the most commonly used ways to measure this central point.
You can calculate the mean by adding up each value in a data set and then dividing by the total number of data points.
Let’s look at an example. Let’s say 7 students took a test on biostatistics and out of 100 possible points, one student got 17, another got 19, two got 20, two more got 61 and the last student got 62.
The mean score would be the total number of points they all got added up together divided by the number of students, which is 7.
So that’s: 17+19+20+20+61+61+62 = 260 = 37.14
To show this as a formula, we can say that the mean, written as X with a bar over it, is the total sum of the individual data points X1, X2, ......., Xn, divided by n, which is the number of data points.
A mean test score of 37.14, quickly tells us that overall, these students didn’t do well on this test.
But, the problem with the mean, is that it can be influenced by an extreme value called an outlier.
Let’s say that another student comes along and get a perfect 100 out of 100 on the test.
That means that the average is now: 17+19+20+20+61+61+62+100 = 360 divided by 8, which is 45.
This one number summary isn’t a very good summary because the only reason that it is so high is due to this one high-scoring student.
In this case, 100 is an outlier, and any data set with an outlier is called skewed data.
To calculate the central point when there may be outliers, you can use the median. | 550 | 2,178 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2022-21 | longest | en | 0.922167 |
http://www.reddit.com/user/RokSeouljah420 | 1,406,115,597,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1405997877693.48/warc/CC-MAIN-20140722025757-00157-ip-10-33-131-23.ec2.internal.warc.gz | 1,040,324,615 | 17,098 | # reddit is a platform for internet communities
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pm'd
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Confirmed.
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60% of the time, I look at it every time.
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Looks like tetanus.
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VCR's...
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Here's a better description of the 'rollover' bonus. Edit *sorry for the wall of text, it was a shitty c&p job.
MTURK ROLLOVER
1. MTurk Rollover Benefits:
A 2-week rolling average of 1000 HITs earns \$0.05 on all approved HITs the following week. A 2-week rolling average of 500 HITs earns \$0.04 on all approved HITs the following week. As long as you maintain an average of 500 HITs each week... the rollover continues! . . 2. MTurk Rollover Example: . Week 1 = you worked 450 HITs for a bonus of \$18 (450 HITs x \$.04 ) Week 2 = you worked 1150 HITs for a bonus of \$57.50 (1150 HITs x \$.05) Week 3 = your rolling two week average equals 800 HITs (1150+450 / 2) which qualifies you for a Rollover base rate of \$.04 in week 3. . . 3. Example Details: In the above example . You started week 3 with a Rollover base bonus of \$.04 per HITs regardless of volume, if you worked 100 HITs you would receive a bonus of \$4 (100 x \$.04). Without Rollover you would have received a \$2 bonus (100 x \$.02). If you worked 1000 HITs in week 3 you would qualify for the higher base volume bonus of \$.05 per HIT giving you a bonus of \$50 (1000 x \$.05) rather than the base Rollover bonus of \$40 (1000 x \$.04).
*Please note that these are not compounding bonuses you will always receive the higher of the two rates.
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It's cumulative. So I guess it could be presented as, "First bonus rate achieved at 100 HITs, any day of the week."
So in other words, whatever day you reach 100 cumulative HITs, you earn the first bonus (paid out the following Monday unless otherwise specified) of \$2.00.
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C&P'd
The MTurk Weekly Volume Bonus! First bonus rate achieved at 100 HITs any day of the week. Each HIT has a prorated bonus after HIT 300! Highest rate applies - rollover, bonus tiers, and prorates are not cumulative Weekly Bonus Rates!
\$2.00 for 100 HITs approved \$5.00 for 200 HITs approved \$9.00 for 300 HITs approved (\$0.03 on every approved HIT 301-499) \$20.00 for 500 HITs approved (\$0.04 on every approved HIT 501-999) \$50.00 for 1000 HITs approved (\$0.05 on every approved HIT 1001+)
Rollover Rates Example:
An average 500 HITs per week earns \$0.04 on ALL APPROVED HITs worked between June 30, 12:00 am and July 6, 11:59pm PST. An average 1000 HITs per week earns \$0.05 on ALL APPROVED HITs worked between June 30, 12:00 am and July 6, 11:59pm PST. As long as you maintain an average of 500 HITs for the previous 2 weeks...the rollover continues! Terms & Conditions
Approved transcription HITs only (*not applicable to Transcription Review HITs). Highest rate applies - bonus rates, rollover, and prorates are not cumulative. Please see General Guidelines to increase approved HITs. Details Here. Bonus Effective 12:00 AM PST Monday, July 7, through 11:59 PM PST Sunday, July 13, 2014. Bonus payable Monday July 14, 2014.
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As a few others have said, the biggest difficulty in hitting that magic 1k mark is finding a batch of transcriptions that you can blow through to stack up the numbers. I do a lot of CrowdSurf stuff so here are a few tips to try and make that 1000 a more seemingly manageable number.
• I find it easier to tackle the 1000 HITs as smaller groups. I tend to try and bang out 50 at a time, so 20 sessions of 50. Assuming you're a relatively skilled transcriber and you have a relatively easy batch of hits, this should take no more than 2 to 2 and a half hours. (I use multiple tabs to preview multiple HITs, difficulties, etc.) Experiment with the number...maybe 40 sessions of 25 HIT's will work out better for you.
As a side note, I tend to also shoot for banging out these 'blocks' earlier in the week if possible. Sometimes the selection of HITs is not the greatest over the weekend and if you try to push all your HITs to Sat/Sun you may find yourself short.
• Smaller paying hits. I know, this one goes against the common side sense of your brain, but think about it. Those two and four cent HITs count to your total HITs count for the bonus. Try and keep an eye out for batches of .02, .04, or even .06 (low difficulty pay rate example) as they take far less time than doing the .08 or .12 HITs.
As the bonus stands, if you can maintain the 500 HIT average for two weeks, those .04 HITs start out at .08 a piece with the rollover. That's the equivalent of doing the .08 HITs for 40% of the transcription time!
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What if I'm being sarcastic AND I'm afraid of not being paid?
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5 even
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So I can get 125 bb/an hour (equivalent of \$.05) if I play 1/2....but only 25 bb/hour (equivalent of \$.11) if i move up stakes?
This sounds too good to be true!
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Damn bro, hope this works out for you. While I agree, escrow can be a very useful tool if used properly, I don't necessarily feel that it should generally be applied to all transactions. That being said, I would rather stress the importance of due diligence when trading.
Not trying to kick you while your down, but a few minutes of checking out /u/Luxuryhippo shows him to be a year old account, with activity only kicking in 8 days ago. And most of his comments are clearly fluff to pad karma.
It's true we are a community, and one of the best around imo, but when it comes down to it, you and you alone are the last line of defense against you getting scammed.
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pming
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Pming
[BG] Pizza for Dogecoin by in dogemarket
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IIRC, at least in my state, that's perfectly legal as long as you sign your OWN name. If you try to sign the person's name on the card, that can constitute credit card fraud. | 1,668 | 5,999 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2014-23 | latest | en | 0.905895 |
https://community-forums.domo.com/main/discussion/57450/division-by-zero-be-aware-failed-iferror-ifnull-and-groupby | 1,726,250,942,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651535.66/warc/CC-MAIN-20240913165920-20240913195920-00505.warc.gz | 164,178,498 | 98,471 | # Division By Zero - Be Aware - Failed IFERROR, IFNULL, and GROUPBY
Member
When you're performing calculations over 100s of millions or records sometimes you come across division by zeros in which you're hoping the software you're using would manage accordingly, I ran into a scenario in an ETL scenario where it lead to having more than a 10% revenue shortfall in my numbers.
Generally in Domo if there is no data or if there is an error it will return a NULL in the output variable; however, if it is a division by zero, several functions fail to work with the output.
`Figure 1: Input and Output`
• Ratio = Num / Denom
• Ratio IFERROR = IFERROR(Num / Denom, 0 )
• Ratio IFNULL = IFULL( Num/Denom , 0)
• Ratio Backfill IFERROR = IFERROR(IFERROR(Num / Denom, 0 ),0)
In Figure 1 you can see in row 4 that the Ratio of `Num` and `Denom` yielded a blank calculation, however, both the IFERROR and IFNULL failed to backfill with the assigned zero.
Compared to Row 6 where the Ratio is also blank, but the IFNULL was able to backfill with zero. Not that a blank / blank for Domo is not necessarily an error, hence it did not meet the criteria for Ratio IF ERROR result of 0.
The real problem came when it was time to Group BY.
`Figure 2: GroupBY Node`
When I grouped by Products and sum `Ratio` and `Ratio IFERROR`, Product Y failed to sum in Figure 2 Row 3 because of the blank in row 4 (Division by Zero) from Figure 1, as opposed to Product Z which also had a blank cell in row 6, but was able to sum as seen in row 1 in Figure 2.
As a workaround, I used a case statement to check the denominator before computing the ratio.
`case`
` when Denom = 0 then 0`
` else Num / Denom`
`end`
Domo is aware of the issue, but be aware that IFERROR, IFNULL, and GROUP BY fails at managing division by zero errors.
Think about it this way, if Product Y was 1 million records and just 1 of those 1 million records had a division by zero, the sum of all 1 million records would result with a BLANK.
Tagged: | 518 | 2,008 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2024-38 | latest | en | 0.940062 |
https://thirdspacelearning.com/gcse-maths/statistics/frequency-diagram/ | 1,723,045,238,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640694594.35/warc/CC-MAIN-20240807143134-20240807173134-00833.warc.gz | 452,799,617 | 54,794 | # Frequency Diagram
Here we will learn about frequency diagrams, including what they are and how to construct them.
There are also frequency diagram worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
## What is a frequency diagram?
A frequency diagram is a way of representing data from a frequency table.
Frequency diagrams are usually bar charts, vertical line charts or frequency polygons with frequency displayed on the vertical axis.
### Bar charts
Bar charts represent data using rectangular bars that are the same width. They can be used for categorical data (such as favourite colour, types of food, or makes of car) or numerical data (such as goals scored, height, or time).
Bar charts can also be used for grouped numerical data.
Step-by-step guide: Bar charts
### Vertical line charts
Vertical line charts represent data by drawing straight lines to a given frequency.
They can be used for ungrouped numerical data.
### Frequency polygons
A frequency polygon is a graph that shows the frequencies of grouped data. It is a type of frequency diagram that plots the midpoints of the class intervals against the frequencies and then joins up the points with straight lines.
Step-by-step guide: Frequency polygon
## How to draw a frequency diagram
In order to draw a frequency diagram:
1. Draw a pair of axes and label them.
2. Draw a bar (or vertical line) for each of the items.
### Related lessons on representing data
Frequency diagram is part of our series of lessons to support revision on representing data. You may find it helpful to start with the main representing data lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
## Frequency diagram examples
### Example 1: categorical data – bar chart
Draw a bar chart for this data:
1. Draw a pair of axes and label them.
Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. The categories should be evenly spaced along the horizontal axis.
2Draw a bar (or vertical line) for each of the items.
The heights of the bars need to correspond with their frequencies. The bars should have equal width.
### Example 2: categorical data – bar chart
Draw a bar chart for this data:
Draw a pair of axes and label them.
Draw a bar (or vertical line) for each of the items.
### Example 3: ungrouped numerical data – vertical line chart
Draw a vertical line chart for this data:
Draw a pair of axes and label them.
Draw a bar (or vertical line) for each of the items.
### Example 4: ungrouped numerical data – vertical line chart
Draw a vertical line chart for this data:
Draw a pair of axes and label them.
Draw a bar (or vertical line) for each of the items.
### Example 5: grouped numerical data – bar chart
Draw a bar chart for this grouped data:
Draw a pair of axes and label them.
Draw a bar (or vertical line) for each of the items.
### Example 6: grouped numerical data – bar chart
Draw a bar chart for this grouped data:
Draw a pair of axes and label them.
Draw a bar (or vertical line) for each of the items.
### Common misconceptions
• Equal widths
The bars for frequency diagrams should all have the same width. The vertical lines should also have the same thickness.
• Frequencies are whole numbers
Since frequencies are a count of how many times an item occurs, they will always be integers. They are not decimals.
• Gaps between bars
For categorical data, there should be a gap between each bar on a bar chart. This allows the data to be easier to interpret.
### Practice frequency diagram questions
1. Choose the correct frequency table for the following frequency diagram:
The frequency for Blonde is 4, the frequency for Brown is 5, the frequency for Black is 3 and the frequency for Red is 1.
2. Choose the correct frequency table for the following frequency diagram:
The frequency for Sheep is 5 , the frequency for Cow is 3 , the frequency for Pig is 1 and the frequency for Chicken is 6 .
3. Choose the correct frequency table for the following frequency diagram:
The frequency for 0 siblings is 7 , the frequency for 1 sibling is 5 and the frequency for 2 siblings is 2 .
4. Choose the correct frequency table for the following frequency diagram:
The frequency for 3 apples is 7 , the frequency for 4 apples is 9 , the frequency for 5 apples is 6 , the frequency for 6 apples and the frequency for 7 apples is 1 .
5. Choose the correct grouped frequency table for the following grouped frequency diagram:
The frequency is 2 for values in the range 0-100cm , the frequency is 4 for values in the range of 100-200cm, the frequency is 7 for values in the range of 200-300cm and the frequency is 3 for values in the range of 300-400cm.
6. Choose the correct grouped frequency table for the following grouped frequency diagram:
The frequency for 0-10 \; kmph is 5 , the frequency for 10-20 \; kmph is 8 , the frequency for 20-30 \; kmph is 4 and the frequency for 30-40 \; kmph is 1.
### Frequency diagram GCSE questions
1. Will recorded the different types of birds visiting his garden.
The table shows his results.
(a) Complete the bar chart to show Will’s results.
(b) How many more sparrows than robins were there?
(3 marks)
(a)
(2)
(b)
12
(1)
2. Laine recorded the number of bedrooms in different houses on an estate.
The table shows her results.
(a) Complete the vertical line chart to show Laine’s results.
(b) How many houses have at least 3 bedrooms?
(3 marks)
(a)
(2)
(b)
30
(1)
3. Here is a frequency diagram showing the times of people solving a sudoku problem.
(a) Complete the grouped frequency table.
(b) How many people were there altogether who did the sudoku?
(3 marks)
(a)
(2)
(b)
18
(1)
## Learning checklist
You have now learned how to:
• Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, and bar charts for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data.
## Still stuck?
Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.
Find out more about our GCSE maths tuition programme. | 1,441 | 6,424 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2024-33 | latest | en | 0.867864 |
https://homework.cpm.org/category/CCI_CT/textbook/int2/chapter/12/lesson/12.2.1/problem/12-70 | 1,723,704,316,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641151918.94/warc/CC-MAIN-20240815044119-20240815074119-00178.warc.gz | 234,990,750 | 16,208 | Home > INT2 > Chapter 12 > Lesson 12.2.1 > Problem12-70
12-70.
$x^2 - 6x + 11 = 0$
Use the example below.
Example: Solve $x^2+5x+4=0$ by completing the square.
Solution: This method works most efficiently when the coefficient of $x^2$ is $1$.
Rewrite the equation as $x^2+5x=-4$. Rewrite the left side as an incomplete square:
$2.5$$+$$x$ $2.5x$ $=-4$ $x^2$ $2.5x$ $x+2.5$
Complete the square and rewrite as
$(x+2.5)^2-6.25=-4$ or $(x+2.5)^2=2.25$
Take the square root of both sides, $x+2.5=\underline{+}1.5$. Solving for $x$ reveals that
$x=-1$ or $x=-4$. | 226 | 565 | {"found_math": true, "script_math_tex": 19, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2024-33 | latest | en | 0.743155 |
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## Details
Chapter 9 - Descriptive Statistics
Chapter 9 IACA
33
Criminal Justice
Professional
09/05/2014
Term
Statistics
Definition
science of collection and organizing data to then draw conclusions based on data
Term
Types of stats
Definition
descriptive, multivariate, inferential
Term
Descriptive statistics
Definition
summary of large data sets to be put into an easy to read manner
Term
Multivariate
Definition
allows comparisons of factors by isolating the effect of one variable from others
Term
Inferential
Definition
statements of a population based on a sample
Term
Levels of measurement
Definition
nominal, ordinal, interval and ratio
Term
Characteristics of nominal data
Definition
lowest level, must be exhaustive, mutually exclusive, only classified one way, provides names or labels (race, gender), can only be one of something
Term
Characteristics of ordinal data
Definition
exhaustive, mutually exclusive, exhibits a degree of difference, the degree of difference indicates order/rank, ordering distance has no meaning (good, better, best/agree, disagree, neutral)
Term
Characteristics of interval
Definition
assumes all items on scale have equal units of measurement, distance between categories have meaning, logical distances (temp readings, IQ score)
Term
Characteristics of Ratio
Definition
has all the characteristics of the other levels plus a true "zero" point. highest level of measurement. (income, weight, time, age)
Term
Frequency distribution
Definition
lists the number or frequency of scores/labels for each case
Term
Range
Definition
summary statistic with limited information. Highest score-lowest score= range
Term
Class interval
Definition
i= range/"n" of desired intervalsexample:i=12-1/4=1111/4= 2.75i=2.75
Term
Mean
Definition
average
Term
Median
Definition
midpoint/middle score
Term
Mode
Definition
most frequent score/label
Term
Variance
Definition
sum squared (S^2)deviations of each score from the mean divided by the total number
Term
Standard deviation
Definition
average distance each data item is away from the mean of the all the data items. Provides comparison insight between two distributions.
Term
Skewness
Definition
the spread of scores weighted to one side of the mean.
Term
Normal skewness
Definition
bell shape, the curve doesn't touch the x-axis, curve is symmetrical. Mean, median, mode are equal.
Term
Positive skewness
Definition
unimodial scores weighted to the left. Hump to the left, tail to the right. Mode is the largest, followed by the median, and then mean.
Term
Negative skewness
Definition
unimodial weighted to the right (hump to the right, tail to the left). Mean largest value, then median, then mode.
Term
Rates
Definition
used to standardize measure for comparison between two different items of size. (compare car theft rates between two cities with significant difference in population size).
Term
Proportions
Definition
example:60 officers / 15 sgts(15/75)= .20 portion of sgts(60/75) = .80 portion of officers
Term
Percent changes
Definition
subtract old value from new value then divide by old value then multiply by 100.
Term
Correlation analysis
Definition
measures the relative fit or degree of association between two variable or 3 or more variables to determine the quality of regression line or reliability of prediction.
Term
Pearson's product moment coefficient
Definition
=roperates within range 1.0, the closer to one the stronger the value. Zero = no correlation.
Term
Regression analysis
Definition
seeks general pattern evident in observation relationships through pattern recognition and placement on a trendline.
Term
Regression analysis and correlation analysis are similar except regression
Definition
locates the best line through the points.
Term
Linear function
Definition
is one in which data points, x & y coordinates, make more a less straight line.
Term
Non-linear function
Definition
is one which the data points, x & y data, make some type of curve shape that can be expressed by an algebraic formula.
Term
Linear regression
Definition
to find the best straight line through the points and has the smallest variance, reflecting gaps between the actual placement of the data points on the graph.
Term
Statistical analysis
Definition
is multivariate in nature when two or more variables (usually of ratio or interval type) are examined together with the focus on observable relationships or patterns of association, between or among the variables.
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# (3 X 100) + (4 X 1) + (5 X 1,000) + (6 X 10) = (A) 3,456 (D
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(3 X 100) + (4 X 1) + (5 X 1,000) + (6 X 10) = (A) 3,456 (D [#permalink] 13 Aug 2019, 07:44
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(3 X 100) + (4 X 1) + (5 X 1,000) + (6 X 10) =
(A) 3,456
(B) 3,564
(C) 4,635
(D) 5,346
(E) 5,364
[Reveal] Spoiler: OA
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Re: (3 X 100) + (4 X 1) + (5 X 1,000) + (6 X 10) = (A) 3,456 (D [#permalink] 16 Aug 2019, 00:53
1
KUDOS
It is obvious that the unit's digit will be 4. Eliminate A,C,D
It is also very obvious that the thousand's digit will be 5. Eliminate B
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Re: (3 X 100) + (4 X 1) + (5 X 1,000) + (6 X 10) = (A) 3,456 (D [#permalink] 19 Aug 2019, 09:54
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Re: (3 X 100) + (4 X 1) + (5 X 1,000) + (6 X 10) = (A) 3,456 (D [#permalink] 19 Aug 2019, 09:54
Display posts from previous: Sort by | 711 | 1,859 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2019-51 | latest | en | 0.833208 |
https://www.cnblogs.com/rgvb178/p/9181630.html | 1,566,087,720,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313501.0/warc/CC-MAIN-20190817222907-20190818004907-00273.warc.gz | 782,943,808 | 5,377 | # Reject Inference: Your Data is Deceiving You
Keyword: Reject Inference
Suppose there is a dataset of several attributes, including working conditions, credit history, and property, that have been provided by the bank. The sample classified the customers according to whether they paid off their loans on time. Those who paid off their loans on time were classified as “good customers”, and those who did not pay off their loans on time were classified as “bad customers”.
If Rick, an employee of the bank, uses this dataset to do data analysis directly, what will happen?
Take one of these attributes as an example.
1 : unemployed
2 : skilled employee
3 : management/ highly qualified employee/ officer
Which of these three groups of people, by instinct, should have the best credit? Most people would think it is the second or the third category. However, the data give us a different answer.
As the data shows, the first group of customers is “better than” the third group of customers. After looking at the data, Rick might reach the conclusion that lending more money to the unemployed people is better than lending money to those who are the highly qualified employee, officer, or management board. Is it correct? Let’s think about it a little bit.
Let’s review the process of collecting data:
1. Rick’s Customer applies for a personal loan
2. If it is approved, go to step 3. Otherwise, it will not be counted as a data point in Rick’s data set.
3. If a customer pays off the loan on time, he will be labeled as a “Good Customer”. Otherwise, he will be labeled as a “Bad Customer”.
Before collecting data, there is a crucial step - Step 2. That is to say, the customers who are collected by Rick have already been selected by the bank. Those who applied for a personal loan but didn’t get approved are not in this dataset.
Here I would like to ask you a question: which has the greater risk, jumping from the 4th floor or the 70th floor? (Please do not try it, it is just an example.) You may reply immediately: “The 70th floor, of course!”
You are wrong. I am not asking about the probability of death. I am asking about risk. Suppose someone will offer you 10 billion if you can jump from 70th floor without dying, then you probably won’t bet with him. However, suppose someone will offer you 10 billion if you can jump from 4th floor without dying, then you might want to give it a shot because you know you may not die.
The customers who make the bank feel like jumping from the 70th floor, are most likely rejected by the bank from the beginning. The bank usually has a hard time to make decisions on the application of the customers who make the bank feel like jumping from the 4th floor.
“The 70th floor” customers are likely existing in the first group of customers. So if the bank approved their application, then there must be some reasons support the bank to believe they will pay off their loans. If the bank approved every first-group customer’s application, the data may be different from current data.
Using the data analysis before didn't really understand the meaning of the data may result in you are deceived by your data.
There are lots of factors should be taken into consideration in an evaluation, but I have to simplify the explanation here. If there are any mistakes or anything make you uncomfortable, please let me know so that I can fix it.
posted @ 2018-06-14 09:55 rgvb178 阅读(...) 评论(...) 编辑 收藏 | 757 | 3,441 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2019-35 | longest | en | 0.973766 |
http://www.math-only-math.com/worksheet-on-probability.html | 1,537,918,183,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267162563.97/warc/CC-MAIN-20180925222545-20180926002945-00195.warc.gz | 374,353,441 | 7,181 | # Worksheet on Probability
In math worksheet on probability we will solve various types of practice probability questions to find the probability of occurrence of an event.
1. What is the probability of occurrence of an event?
2. A coin is tossed 125 times and head is obtained 64 times. Now, if a coin is tossed at random, what is the probability of getting a head?
3. A corn is tossed 200 times and tails obtained 128 times. Now, if a coin is tossed at random, what is the probability of getting a tail?
4. In 60 throws of a dice, 6 is obtained 24 times. Now, in a random throw of a dice, what is the probability of getting 6?
5. In 100 throws of a dice, 5 is obtained 42 times. In a random throw of a dice, what is the probability of getting 5?
6. In 150 throws of a dice, 2 is obtained 76 times. In a random throw of a dice, what is the probability of getting 2?
7. In 2010, there was a survey of 200 people, it was found that 82 like orange juice while 118 dislike it. From these people, one is chosen at random. What is the probability that the chosen people dislikes orange juice?
Answers on probability are given below to check the exact answers of the questions.
2. ⁶⁴/₁₂₅
3. ¹⁶/₂₅
4. ²/₅
5. ²¹/₅₀
6. ³⁸/₇₅
7. ⁵⁹/₁₀₀
`
Probability
Probability
Probability - Worksheets
Worksheet on Probability | 369 | 1,321 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2018-39 | latest | en | 0.943379 |
https://usacourseworkhelp.com/questions/a-3-20-kg-box-is-sliding-across-the-horizontal-flo/ | 1,601,588,773,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402132335.99/warc/CC-MAIN-20201001210429-20201002000429-00479.warc.gz | 653,389,437 | 6,501 | # A 3.20-kg box is sliding across the horizontal flo…
### Question Description:
25.50
A 3.20-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.460. Determine the kinetic frictional force that acts on the box for each of the following cases. (a) The elevator is stationary. ___________ N (b) The elevator is accelerating upward with an acceleration whose magnitude is 2.90 m/s2. ________ N (c) The elevator is accelerating downward with an acceleration whose magnitude is 2.90 m/s2. ___________N | 141 | 580 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2020-40 | latest | en | 0.860655 |
http://www.brainbashers.com/showanswer.asp?ref=ZJYH | 1,481,457,222,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698544678.42/warc/CC-MAIN-20161202170904-00165-ip-10-31-129-80.ec2.internal.warc.gz | 359,545,649 | 3,369 | [OK] We use cookies to personalise content and adverts. We also share information about your use of our site with our advertising partners who may combine it with other information you’ve provided to them or they’ve collected from your use of their services. You also agree to our terms and conditions (T&C).
Mr Smith has lots of pound coins, ten boxes in all. Each box contains 100 pound coins, but one box contains coins which are all counterfeit and are slightly lighter, 1/16 of an ounce lighter to be exact.
The problem lies in the fact that they all look identical, the only way to tell them apart is to weigh them.
Mr Smith knows the correct weight for a box, but how many weighings are required to determine which box contains the counterfeit ones?
[Ref: ZJYH]
Take one coin from the first box, two from the second and so on.
When the coins are weighed, the number of 1/16ths light will tell us which box contains the counterfeits.
For example if it was box 5, the weighing would be 5/16 too light.
Back to the puzzles...
Our Favourite Illusions
Shadow Illusion What Am I? Hidden Faces Impossible Waterfall? Same Eyes? Impossible Prongs?
Duck Or Rabbit? Spinning Dancer Who Turned To? Blind Spot The Butterfly Parallel Cafe Wall Lines? | 283 | 1,255 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2016-50 | latest | en | 0.9447 |
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# Reconstruction of a Tree
Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.
## Input
In the first line, an integer $n$, which is the number of nodes in the binary tree, is given.
In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters.
In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.
Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.
## Output
Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.
## Constraints
• $1 \leq n \leq 40$
## Sample Input 1
5
1 2 3 4 5
3 2 4 1 5
## Sample Output 1
3 4 2 5 1
## Sample Input 2
4
1 2 3 4
1 2 3 4
## Sample Output 2
4 3 2 1 | 288 | 1,063 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-22 | latest | en | 0.882316 |
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2019-September/001716.html | 1,702,158,793,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100972.58/warc/CC-MAIN-20231209202131-20231209232131-00526.warc.gz | 592,599,765 | 2,349 | # [R-meta] How to define Rosenthal & Rubin's Proportion Index?
Patrizio Tressoldi p@tr|z|o@tre@@o|d| @end|ng |rom un|pd@|t
Thu Sep 5 17:20:29 CEST 2019
```Il 05/09/2019 00:00, r-sig-meta-analysis-request using r-project.org ha scritto:
> ......................
>
> ..........................
>
> This isn't built into metafor. But the computations are easy to carry out 'by hand'. Let's say you have data like this:
>
> dat <- data.frame(study = 1:4, ni = c(32, 10, 14, 7), hits = c(14, 3, 0, 6), ki = c(4, 6, 5, 4))
>
> which is actually Table 5 in the paper.
>
> Then we can compute this outcome measure and the corresponding sampling variances with:
>
> dat\$Pi <- with(dat, ifelse(hits == 0, 0.5 / (ni + 1), hits / ni))
> dat\$yi <- with(dat, Pi*(ki-1) / (1 + Pi*(ki-2)))
> dat\$vi <- with(dat, 1/ni * yi^2*(1-yi)^2 / (Pi*(1-Pi)))
> dat
>
Thank you for this implementation in metafor, however a trick of this
effect size is that values above .5 are related to a positive effect
(hits above chance) and viceversa.
Running a fixed or random model in metafor, all values are considered
as positive. Do I have to calculate the dat\$yi subtracting .5?
And if this adjustment is correct, the calculation of dat\$vi remains the
same?
Patrizio
--
Patrizio E. Tressoldi Ph.D.
Dipartimento di Psicologia Generale
via Venezia 8 | 439 | 1,327 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2023-50 | latest | en | 0.658743 |
http://researchmaniacs.com/Calculator/PrimeFactors/Prime-Factorization-of-1500.html | 1,496,003,491,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463611560.41/warc/CC-MAIN-20170528200854-20170528220854-00136.warc.gz | 373,862,078 | 3,396 | Prime Factorization of 1500
What are the prime factors of 1500?
The prime factors of 1500 are the prime numbers that can be divided into 1500 exactly, with no remainder. The prime factorization of 1500 is the list of prime factors of 1500.
If you multiply all the prime factors of 1500 you will get 1500.
To find all the prime factors of 1500, divide it by the lowest prime number possible. Then divide that result by the lowest prime number possible. Keep doing this until the result itself is a prime number. The prime factorization of 1500 will be all the prime numbers you used to divide, in addition to the last result, which is a prime number. The math and the solutions to prime factorization of 1500 is as follows: 1500 / 2 = 750750 / 2 = 375375 / 3 = 125125 / 5 = 2525 / 5 = 5 2 x 2 x 3 x 5 x 5 x 5 NOTE: The solution above must be correct, because they are all prime numbers and if you multiply them together you will find that they equal 1500.
Prime Factorization Calculator For a different number, simply enter it in the box below and press "Factorization". Prime Factorization of 1501 Do you think you can do it without our calculator, based on how we got the prime factorization of 1500 on this page? If so, try one number higher and check your answer here. Factors of 1500 Don't confuse prime factors with factors! Go here if you want to see all the factors of 1500. | 356 | 1,387 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-22 | longest | en | 0.915254 |
https://study.com/academy/topic/geometry-in-trigonometry-tutoring-solution.html | 1,563,411,789,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195525483.62/warc/CC-MAIN-20190718001934-20190718023934-00122.warc.gz | 559,301,839 | 24,003 | # Ch 21: Geometry in Trigonometry: Tutoring Solution
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2 Lessons in Chapter 21: Geometry in Trigonometry: Tutoring Solution
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Test your knowledge of this chapter with a 30 question practice chapter exam.
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This is just one of the solutions for you to be successful. Complex Numbers Worksheets with Answer Keys. Complex Numbers Worksheet With Answers Pdf. In this article, you’ll learn how easy and fun it is to create your own complex number worksheet with an answer key. Enjoy these free printable sheets focusing on the complex and imaginary numbers, typically covered unit in Algebra 2.Each worksheet has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Resources Academic Maths Arithmetic complex numbers are built on the worksheet again simplifying complex numbers worksheet with answer,! All the digits that are on the worksheet from the answers take you right to... Numbers worksheet with answer key on complex numbers worksheet with answer key and negative radicals it to. Like to use the software that you may find useful if you ’ ll find that they are helpful you. Be concerned about your password because it ’ s not stored anywhere your. Can determine how much you know about an argument of complex numbers, a + bi forms, negative... Numbers worksheets with answers pdf Here 's a graphical preview for all workbooks with complex can! May also want to invest in one of the solutions for you to be.. Sure that you can also use these complex worksheets, you will have to type in the end offers... Come with an answer key, source: pinterest.com may be hesitant to save your complex worksheets. Here and check out the link into the text boxes that are in... Answers or Exponential worksheets Kidz Activities the information is incorrect the end not stored on! Your questions from the complex number worksheet with answers the complex numbers worksheet – Fronteirastral from numbers. ’ re a newbie at creating complex worksheets without any hassle at all offers a great way can. Worksheet, you can easily get answers to your needs the first step to creating a complex number,! Ability to quickly understand the concepts behind those terms and using complex number worksheets negative one some complex.. But, what many people like to use them to learn about imaginary numbers, complex numbers enjoy research. Ll find that they are helpful to you complex worksheets without any hassle at all you look... These are only a few of the imaginary number i from complex numbers in polar form concepts from expressing numbers... Your knowledge of dividing and multiplying complex numbers complex number worksheets it is to pick a number that a... Access them when you need them use them, you can use to... Anywhere on your computer and a free video tutorial BEFORE you buy fill the boxes... Same process as using formulas in Math class imaginary number i from complex worksheet. ’ re a newbie at creating complex worksheets, then you will have to type in your worksheet. You ’ ll have your complex number worksheets according to your financial needs is something you... Really do help you make investments as you such as … algebra 2 numbers. Need them is the complex numbers in polar form: hasshe.com are included in that particular.... That many people don ’ t have the ability to quickly understand the concepts those. Really do help you with your calculations what to do in case the information incorrect., source:1proga.info we present the book compilations in this website to be concerned about investment., this is just one of the expression below can create complex number worksheet is to pick a that. We present the book compilations in this website Academic Maths Arithmetic complex numbers worksheet with answer key,:! That many people don ’ t know is how simple it is to pick number! To type in the number and click the “ complex number worksheet with answers ” button form, irrational,. A little more difficult useful if you ’ ve done any research on making your own worksheets, you have! Need them, you will have to type in the end solutions for you be! Your calculations is my favorite television show but i also love true blood in website! Negative one great way you can also use these complex worksheets without hassle.
complex number worksheet with answers 2021 | 4,033 | 19,031 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2021-25 | latest | en | 0.912943 |
https://physics.stackexchange.com/questions/468019/why-does-the-motion-of-the-emitter-doppler-shift-impact-the-energy-of-the-phot | 1,716,957,714,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059206.29/warc/CC-MAIN-20240529041915-20240529071915-00445.warc.gz | 378,972,379 | 43,018 | # Why does the motion of the emitter (doppler shift) impact the energy of the photons
(a) When there is a red or blue shift, is there an actual change in the energy of the photons or not?
(b) If there are two observers, one moving toward the light source and one away from it, they would see different red/blue shifts of the same set of photons from the same source, so that gives me a clue that actually the energy of the batch of photons is not changing, this is just some apparent effect that we are seeing. Then how can we say for both observers that the energy of the photons is proportional to the frequency? (the frequency observed by both observers is different, but it is the same batch of photons from the same light source presumably having the same energy)
(c) Assuming light is emitted by a bandgap transition, and the emitted photons have energy equal to the bandgap, then intuitively speaking, why does the motion of the emitter alter that energy?
I can understand how a number of cycles of waves can get compressed or expanded into a smaller or larger space depending on the motion of the emitter and hence change the wavelength. I can also understand how, if a gun is firing a bullet, and the gun is mounted on a fast-moving train, then the velocity and KE of the bullet will change as a result.
However, the photons travel at fixed velocity, and being massless, have no KE resulting from mass. So how is it possible that the physical motion of the emitter "relative to the observer" translates into a different energy of the photons than the bandgap energy from which they were emitted?
(d) If it is the observer that is accelerating towards the light source (e.g. the observer is in an accelerating rocket ship), then why would the energy of the distant photons change or why would the observer see a continuous change in red/blue shift?
• It is preferable to ask one question at a time. To answer a) and b), E=hf. So yes the energy changes. Mar 22, 2019 at 10:10
• I think is all about duality. Propagation as a wave and interaction as a photon. More formal answer needed, of course. It is always tricky to transition from a train of waves to single photons, there are already questions different from yours but boiling to the same point. Mar 22, 2019 at 10:12
• Not all observers will measure the same energy of the photon, it doesn't lose energy until it collides with something else. Mar 22, 2019 at 10:12
• The question is, if the photon has energy X, why would different observers measure it as having different energy? Mar 22, 2019 at 10:28
• @KhushroShahookar, different observers in different frames of reference. Mar 22, 2019 at 12:05
You ask why it is that the energy of the photon/wave packet is not the same in different frames of reference. I cannot offer a good explanation for the why but I think the following might "fix" the intuition where the question seems to originate.
Imagine an object just standing there in vacuum. Its energy is zero. But what would another observer (moving with constant velocity with respect to it) think its energy is? Well, not zero. The situation of a photon (i.e., a massless object which is not just standing there) is not the same, sure, but still the same question applies to both situations: Why would its energy be the same in reference frames moving at different velocities anyway? It simply would not.
I'll speculate that perhaps you are thinking "Energy is a conserved quantity; it must be the same." If that is the case, you must remember that implicit or explicit in such statements of invariance there is a transformation in mind. The transformation relevant to your question is the one that converts quantities from one (inertial) observer's reference frame to another's. Namely the Lorentz transformation. And energy of a particle (or the sum of energies of a bunch of particles) does not remain the same under this transformation. A quantity made out of both the energy and the momentum does, but this is perhaps not the place to dig into that.
If you would still appreciate an itemized answer, in light of the discussion above:
(a) There is an actual change in the energy of the photons.
(b) The energy of the batch of photons is changing. The intuition you voice in your parenthetical remark about the same batch of photons having the same energy is flawed. That's how intuition is sometimes.
(c) I would avoid the bullet analogy because the addition of velocities there does not apply to light at all. So it would only increase confusion. However your contemplations about the wavelength getting stretched or compressed are quite well-placed. In your band-gap transition example (which is a good one), it's not so much the motion of the emitter that affects the energy of the emitted photon (because the emitter is stationary according to its own reference frame!), rather it's the motion of an observer relative to it. As you pointed out, the wavelength of the oscillation will be different in that observer's frame. (This is true even for slow waves, not just photons, but the relation of the new wavelength to the old one is a bit more sophisticated in the latter case.)
(d) I'm not sure I understand this one. But perhaps once it fixes itself once you are not worried about the energy of a photon being different in reference frames with different velocities.
• It is virtually impossible to believe that a body can have different KEs when viewed from different frames of reference. Suppose the observer is in a rocket ship and is accelerating towards an object with no external force acting on it, he would know that he is increasing his own KE, but he would see the other object's KE increase with no source of energy being supplied to it. How is that possible? Mar 22, 2019 at 15:58
• @KhushroShahookar KE is not an absolute thing, it is frame dependent. If the object is moving with respect to you, you can harvest energy from its KE (perhaps with a rope and a generator). If you are both moving at the same speed, there is no relative motion and no energy is there for you to harvest. Mar 22, 2019 at 16:03
• Also, suppose a light source is on an accelerating rocket ship, then its dopler shift is continuously increasing, as its velocity increases relative to an observer moving without any acceleration. Now the mere motion of the light emitter does really change the energy of the emitted photons, beyond the bandgap due to which they are emitted. Why? I am using acceleration (which can be detected in absolute terms) to prove that it is really the light source's motion that contributes to change in energy, instead of anything else. Mar 22, 2019 at 16:04
• If KE is frame-dependent and not absolute then energy is not conserved. In the above example, the observer accelerating in a rocket towards an object with no force acting on it, the observer observes that the observed object is increasing in KE, (at least relative to the observer the object seems to increase its speed), although it has no source of energy to provide this increasing KE. True the observer can detect in absolute terms that he is accelerating and the object is not, but based on the speed of the object relative to himself he does observe increase in objects KE with no power source Mar 22, 2019 at 16:18
• @KhushroShahookar, you are thinking of (kinetic) energy as absolute; as though something has a "true" value of it. But no inertial frame is more true than another, and since observed velocities depend on the frame, so does the energy. As for when your frame itself is accelerating (noninertial), a system viewed in that frame is not supposed to have a conserved energy. In fancy terms, the Hamiltonian depends explicitly on time. Also, your example of accelerating the emitter doesn't make the effect special to the acceleration of the emitter: the effect remains if the observer is accelerating. Mar 22, 2019 at 16:25
The photon is a relativistic elementary particle and is described by a four vector:
The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.
E is the total energy, of which the kinetic part is the one carrid by the momentum vector. The only invariants in frame changes is the mass, the vector itself changes according to the Lorentz transformation
which depends on the velocity. So the mass is the only invariant to velocity changes, the momentum vector changes to p', and for the photon this means that the energy changes , according to the equation for the mass. | 1,864 | 8,601 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2024-22 | longest | en | 0.95328 |
https://community.anaplan.com/t5/Anaplan-Platform/Formula-to-take-1-unit-data-to-another/m-p/54683/highlight/true | 1,656,644,619,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103917192.48/warc/CC-MAIN-20220701004112-20220701034112-00000.warc.gz | 234,565,750 | 28,554 | Contributor
Formula to take 1 unit data to another
Hi Anaplan,
I am trying to create a model to summarize the volume from the region and paste back into manufacturing unit, not sure what formula should work in this situation.
For example, Australia (Reporting Unit) and New Zealand (Reporting Unit) purchase plastic cup from Hong Kong (Manufacturing Unit) by 300 cases, I want to put this 300 cases back into Hong Kong (Reporting Unit). How can I create the formula to pick up all the demand 300 cases under Hong Kong (Reporting Unit) ??
Thanks,
Kiwi
1 ACCEPTED SOLUTION
Accepted Solutions
Moderator
Here's an example using @DavidSmith and @Misbah
You will want to set up system modules first for the manufacturing units and reporting units.
See the DISCO method for more details.
Here is the system module for manufacturing. Super simple.
You will need this to do the Sum on demand.
Then we enter demand as you suggest up above.
Next, you add a formula in your supply module that sums the demand by manufacturing plant.
Demand = Demand[SUM: List formatted line item for manufacturing units]
And the result:
Jared Dolich
4 REPLIES 4
Community Boss
SUM and LOOKUP are what you are going to need.
https://help.anaplan.com/anapedia/Content/Calculation_Functions/All/SUM.html
https://help.anaplan.com/anapedia/Content/Calculation_Functions/All/LOOKUP.html
If you take the new Level 1 training, we do cover this in a lot of detail too
Also, take a look at the following and also the attached slide deck I've created to help with the understanding
https://community.anaplan.com/t5/Anaplan-Platform-Discussions/Converting-data-between-line-items-wit...
https://community.anaplan.com/t5/Anaplan-Platform-Discussions/Lookup-Sum-and-Textlist-Cheat-Sheet/td...
https://community.anaplan.com/t5/Anaplan-Platform-Discussions/Dimension-Mismatch/m-p/53248
If you can master these techniques (with System modules), you'll build efficient and flexible Anaplan models
I hope that helps
David
Moderator
Is there any hierarchy in place? Connection between Region & manufacturing unit or reporting unit?
Thanks,
Misbah
Moderator
Here's an example using @DavidSmith and @Misbah
You will want to set up system modules first for the manufacturing units and reporting units.
See the DISCO method for more details.
Here is the system module for manufacturing. Super simple.
You will need this to do the Sum on demand.
Then we enter demand as you suggest up above.
Next, you add a formula in your supply module that sums the demand by manufacturing plant.
Demand = Demand[SUM: List formatted line item for manufacturing units]
And the result:
Jared Dolich
Contributor
Thank you, this is much more clear to my mind 🙂 | 642 | 2,733 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2022-27 | latest | en | 0.846794 |
https://gimpppa.org/intersection-of-a-column-and-a-row/ | 1,653,438,142,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662577757.82/warc/CC-MAIN-20220524233716-20220525023716-00483.warc.gz | 306,883,129 | 7,882 | ## What is the reference to the intersection the a column and row?
CELLThe INTERSECTION the a row and also column is referred to as a CELL. Additionally called a spreadsheet.
You are watching: Intersection of a column and a row
## What is it referred to as when a row and also column crossing in a spreadsheet?
A cabinet is an intersection that a column and row. Every cell has actually a unique cell address. The hefty border approximately the selected cabinet is called the cell pointer.
## What is the cell recommendation for the encircled cell?
Each cell have the right to be referenced by start the pillar letter followed by the row variety of the wanted cell. For example, the encircled cabinet in the over image is well-known as cabinet A2, due to the fact that the cell lies in ~ the intersection of tower A and also row 2.
## Is one intersection that a column and row?
A cell is the intersection the a row and also a column—in various other words, whereby a row and also column meet. Columns are established by letters (A, B, C), if rows are figured out by number (1, 2, 3). Every cell has its very own name—or cell address—based top top its column and also row.
## Are the box created by intersection the row and column?
The crate that is developed at the intersection the a column and also a row is dubbed a cell.
## When two or an ext cells are selected it is called?
Answer: When more than one cabinet is selected, the an option is referred to as a range of cells.
## What we call developed in formula?
Introduction. A role is a predefined formula that performs calculations using certain values in a particular order. Every spreadsheet program include common functions that deserve to be provided for conveniently finding the sum, average, count, best value, and also minimum worth for a variety of cells.
## Why is it better to usage cell recommendation in a formula?
Modifying values through cell references. The true benefit of cell recommendations is the they allow you to upgrade data in your worksheet without having to rewrite formulas. The formula in B3 will instantly recalculate and also display the new value in cell B3.
## Is the cell address of tower A and also row 3?
Understanding cell Columns are determined by letters (A, B, C), while rows are determined by number (1, 2, 3). Each cell has its own name—or cabinet address—based on its column and row. In the instance below, the selected cell intersects obelisk C and row 5, for this reason the cell resolve is C5.
## Is a rectangular box created by the intersection the a row and also column?
A cell is the rectangular box developed at the intersection the a row and also a column.
## Is the intersection the a row v a column Mcq?
The intersections that a column and row is referred to as a_____. Alternative is= BORDER,TABLE,CELL.
## How plenty of row and also column in multiple sclerosis Excel?
1,048,576 rowsWorksheet and also workbook specifications and limits
FeatureMaximum limit
Total number of rows and columns ~ above a worksheet1,048,576 rows by 16,384 columns
Column width255 characters
Row height409 points
Page breaks1,026 horizontal and also vertical
## Which is called combination of cell?
Solution. The combination of two or more cells is dubbed a battery. To do a battery, the an adverse terminal that one cabinet is connected to the confident terminal the the following cell and so on.
## What is the mix of cabinet is called and what is that symbol?
(a) A longer line in the symbol for a cabinet represents its optimistic terminal. (b) The combination of 2 or more cells is dubbed a battery.
## What room the two means to reference cells in other sheets?
To recommendation a cell or variety of cell in one more worksheet in the very same workbook, put the worksheet name adhered to by an exclamation note (!) before the cell address. Because that example, to describe cell A1 in Sheet2, you kind Sheet2! A1.
## How carry out you keep one cell consistent in a formula?
To store cell reference constant in formula, you simply need to add the \$ symbol come the cell recommendation with pushing the F4 key. Please perform as follows. 1. Select the cell v the formula you want to do it constant.
## What is the formula to calculation sales?
Gross sales space calculated simply as the units marketed multiplied by the sales price per unit….Net Sales vs. Gross Sales.
Net SalesGross Sales
FormulaGross Sales – DeductionsUnits marketed x Sales Price
## What is average mean in math?
In maths, the average value in a collection of numbers is the center value, calculated by splitting the total of every the values by the variety of values. As soon as we need to find the mean of a set of data, we add up all the values and then divide this full by the variety of values.
## Where an median is supplied for comparing situations?
Give three examples where an typical is offered for to compare situations. Answer: elevation of students in a course with a huge number of students, income of human being of a state, forest cover in a country, etc. Are some instances where averages are offered for to compare situations.
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The intersection the a upright column and horizontal row is dubbed a cell. The location, or address, the a certain cell is established by using the headers of the column and also row involved. Because that example, cabinet “F2” is located at the point out where column “F” and row “2” meet.
## What are the two ways of referencing cabinet in various other worksheets?
There are two means to reference cells in other sheets: by entering the formula directly using the key-board or by making use of the mouse.
## How execute I connect a formula in Excel?
Select the cell wherein you want the linking formula, kind = (equal sign), and then click the cell v the consistent (text or number) or the formula that you desire to lug forward to the cell. Complete the cabinet entry by clicking the Enter button on the Formula bar or pushing the go into key.
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one year
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See more: How Do You Make Locomotive In Doodle God How To Make Ice In Doodle God Blitz
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http://www.velocityreviews.com/forums/t748286-i-dont-understand-generator-send.html | 1,386,299,900,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163049340/warc/CC-MAIN-20131204131729-00077-ip-10-33-133-15.ec2.internal.warc.gz | 587,516,971 | 11,105 | Velocity Reviews > I don't understand generator.send()
# I don't understand generator.send()
Victor Eijkhout
Guest
Posts: n/a
05-15-2011
#! /usr/bin/env python
def ints():
i=0
while True:
yield i
i += 1
gen = ints()
while True:
i = gen.next()
print i
if i==5:
r = gen.send(2)
print "return:",r
if i>10:
break
I thought the send call would push the value "2" at the front of the
queue. Instead it coughs up the 2, which seems senseless to me.
1/ How should I view the send call? I'm reading the manual and dont' get
it
2/ Is there a way to push something in the generator object? So that it
becomes the next yield expression? In my code I was hoping to get
0,1,2,3,4,5,2,6,7 as yield expressions.
Victor.
--
Victor Eijkhout -- eijkhout at tacc utexas edu
OKB (not okblacke)
Guest
Posts: n/a
05-15-2011
Victor Eijkhout wrote:
> #! /usr/bin/env python
>
> def ints():
> i=0
> while True:
> yield i
> i += 1
>
> gen = ints()
> while True:
> i = gen.next()
> print i
> if i==5:
> r = gen.send(2)
> print "return:",r
> if i>10:
> break
>
> I thought the send call would push the value "2" at the front of
> the queue. Instead it coughs up the 2, which seems senseless to me.
>
> 1/ How should I view the send call? I'm reading the manual and
> dont' get it
> 2/ Is there a way to push something in the generator object? So
> that it becomes the next yield expression? In my code I was hoping
> to get 0,1,2,3,4,5,2,6,7 as yield expressions.
You can't usefully use send() unless the generator is set up to
make use of the sent values. You can't just push values into any old
generator. For it to do anything, you need to use assign the result of
the yield to something within your generator and make use of it. See
http://docs.python.org/whatsnew/2.5....rator-features
for an example.
--
--OKB (not okblacke)
Brendan Barnwell
"Do not follow where the path may lead. Go, instead, where there is
no path, and leave a trail."
--author unknown
Chris Rebert
Guest
Posts: n/a
05-15-2011
On Sat, May 14, 2011 at 5:08 PM, Victor Eijkhout <(E-Mail Removed)> wrote:
> #! /usr/bin/env python
>
> def ints():
> Â* Â*i=0
> Â* Â*while True:
> Â* Â* Â* Â*yield i
> Â* Â* Â* Â*i += 1
>
> gen = ints()
> while True:
> Â* Â*i = gen.next()
> Â* Â*print i
> Â* Â*if i==5:
> Â* Â* Â* Â*r = gen.send(2)
> Â* Â* Â* Â*print "return:",r
> Â* Â*if i>10:
> Â* Â* Â* Â*break
>
> I thought the send call would push the value "2" at the front of the
> queue. Instead it coughs up the 2, which seems senseless to me.
>
> 1/ How should I view the send call? I'm reading the manual and dont' get
> it
`yield` is an expression. Within the generator, the result of that
expression is [, ignoring the complications of .throw() etc.,] the
argument to .send(). You're currently using `yield` only as a
statement, so it's no wonder you're not quite understanding .send(). I
think this example should clarify things somewhat:
>>> def example(start):
.... i = ord(start)
.... while True:
.... sent = (yield chr(i)) # Note use of yield as expression
.... print('was sent', sent)
.... i += 1
....
>>> g = example('a')
>>> g.send(3)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: can't send non-None value to a just-started generator
>>> # Ok, so we can't send something back to `yield`
>>> # until we hit the first `yield`.
>>> g.send(None) # Follow the error message's advice
'a'
>>> g.send(3) # Let's try again now.
was sent 3
'b'
>>> g.send(5)
was sent 5
'c'
>>> g.send(9)
was sent 9
'd'
>>>
Cheers,
Chris
--
http://rebertia.com
Chris Angelico
Guest
Posts: n/a
05-15-2011
On Sun, May 15, 2011 at 10:08 AM, Victor Eijkhout <(E-Mail Removed)> wrote:
> * * * *yield i
> * * * *r = gen.send(2)
When you send() something to a generator, it becomes the return value
of the yield expression. See the example here:
http://docs.python.org/whatsnew/2.5....rator-features
For what you're doing, there's a little complexity. If I understand,
you want send() to be like an ungetc call... you could do that like
this:
def ints():
i=0
while True:
sent=(yield i)
if sent is not None:
yield None # This becomes the return value from gen.send()
yield sent # This is the next value yielded
i += 1
This lets you insert at most one value per iteration. Supporting more
than one insertion is more complicated, but changing the loop
structure entirely may help:
def ints():
i=0
queue=[]
while True:
if queue: # see other thread, this IS legal and pythonic and
quite sensible
sent=(yield queue.pop(0))
else:
sent=(yield i)
i+=1
if sent is not None:
yield None # This is the return value from gen.send()
queue.append(sent)
With this generator, you maintain a queue of sent values (if you want
it to be a LIFO stack rather than a FIFO queue, just change the pop(0)
to just pop()), and if the queue's empty, it produces sequential
integers. (Incidentally, the sent values don't have to be integers. I
leave it to you to decide whether that's any use or not.)
Hope that helps!
Chris Angelico
Ian Kelly
Guest
Posts: n/a
05-15-2011
On Sat, May 14, 2011 at 6:08 PM, Victor Eijkhout <(E-Mail Removed)> wrote:
> I thought the send call would push the value "2" at the front of the
> queue. Instead it coughs up the 2, which seems senseless to me.
>
> 1/ How should I view the send call? I'm reading the manual and dont' get
> it
There is no queue unless you create one inside the generator. The
generator by itself behaves more like a coroutine.
> 2/ Is there a way to push something in the generator object? So that it
> becomes the next yield expression? In my code I was hoping to get
> 0,1,2,3,4,5,2,6,7 as yield expressions.
This will do what you're asking for:
def ints():
i=0
while True:
next_yield = (yield i)
while next_yield is not None:
next_yield = (yield next_yield)
i += 1
However, I don't think this is what you want. The send call returns a
yield expression, which will then be the value that you just passed
in, which seems a bit silly. Probably you want something more like
this:
def ints():
i=0
while True:
next_yield = (yield i)
while next_yield is not None:
yield None
next_yield = (yield next_yield)
i += 1
Then the send() call will return None, and the next next() call will
return the value you passed in. Note though that this is too simple
to work correctly if you call send() more than once before calling
next() again.
In general, I think it is a bad idea to mix calling next() and send()
on the same generator. It makes the generator logic too complicated,
and I think it's better just to create a stateful iterator class
instead, where send() and next() are two entirely separate methods.
Cheers,
Ian
Ian Kelly
Guest
Posts: n/a
05-15-2011
On Sat, May 14, 2011 at 6:47 PM, Chris Angelico <(E-Mail Removed)> wrote:
> def ints():
> * *i=0
> * *queue=[]
> * *while True:
> * * * *if queue: *# see other thread, this IS legal and pythonic and
> quite sensible
> * * * * * *sent=(yield queue.pop(0))
> * * * *else:
> * * * * * *sent=(yield i)
> * * * * * *i+=1
> * * * *if sent is not None:
> * * * * * *yield None *# This is the return value from gen.send()
> * * * * * *queue.append(sent)
>
> With this generator, you maintain a queue of sent values (if you want
> it to be a LIFO stack rather than a FIFO queue, just change the pop(0)
> to just pop()), and if the queue's empty, it produces sequential
> integers. (Incidentally, the sent values don't have to be integers. I
> leave it to you to decide whether that's any use or not.)
Actually, this won't work, because the value of the "yield None" gets
ignored. Thus if you try to call send() twice in a row, the generator
the treats second send() as if it were a next(), and it is not
possible to have more than one item in the queue.
Chris Angelico
Guest
Posts: n/a
05-15-2011
On Sun, May 15, 2011 at 11:05 AM, Ian Kelly <(E-Mail Removed)> wrote:
> Actually, this won't work, because the value of the "yield None" gets
> ignored. *Thus if you try to call send() twice in a row, the generator
> the treats second send() as if it were a next(), and it is not
> possible to have more than one item in the queue.
You're right. It needs a while loop instead of the if (and some slight
reordering):
def ints():
i=0
queue=[]
while True:
if queue: # see other thread, this IS legal and pythonic and
quite sensible
sent=(yield queue.pop(0))
else:
sent=(yield i)
i+=1
while sent is not None:
queue.append(sent)
sent=(yield None) # This is the return value from gen.send()
That should work.
Chris Angelico
Victor Eijkhout
Guest
Posts: n/a
05-15-2011
Chris Angelico <(E-Mail Removed)> wrote:
> For what you're doing, there's a little complexity. If I understand,
> you want send() to be like an ungetc call... you could do that like
> this:
>
>
> def ints():
> i=0
> while True:
> sent=(yield i)
> if sent is not None:
> yield None # This becomes the return value from gen.send()
> yield sent # This is the next value yielded
> i += 1
I think this will serve my purposes.
Thanks everyone for broadening my understanding of generators.
Victor.
--
Victor Eijkhout -- eijkhout at tacc utexas edu
Ian Kelly
Guest
Posts: n/a
05-15-2011
On Sat, May 14, 2011 at 7:17 PM, Chris Angelico <(E-Mail Removed)> wrote:
> You're right. It needs a while loop instead of the if (and some slight
> reordering):
>
> def ints():
> * i=0
> * queue=[]
> * while True:
> * * * if queue: *# see other thread, this IS legal and pythonic and
> quite sensible
> * * * * * sent=(yield queue.pop(0))
> * * * else:
> * * * * * sent=(yield i)
> * * * * * i+=1
> * * * while sent is not None:
> * * * * * queue.append(sent)
> * * * * * sent=(yield None) *# This is the return value from gen.send()
>
> That should work.
Yeah, that should do it. But this is so much easier to get right and
to understand:
import itertools
class Ints(object):
def __init__(self):
self.ints = itertools.count()
self.queue = []
def __iter__(self):
return self
def next(self):
if self.queue:
return self.queue.pop(0)
else:
return self.ints.next()
def insert(self, x):
self.queue.append(x) | 2,987 | 10,037 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2013-48 | longest | en | 0.875913 |
https://charmestrength.com/how-do-i-create-an-interaction-term-in-r/ | 1,653,555,997,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662604495.84/warc/CC-MAIN-20220526065603-20220526095603-00794.warc.gz | 225,605,064 | 24,127 | # How Do I Create An Interaction Term In R?
How do I create an interaction term in R?
• Step 1: Centering. To center a variable, simply subtract its mean from each data point and save the result into a new R variable, as demonstrated below. > #center the input variables.
• Step 2: Multiplication. Once the input variables have been centered, the interaction term can be created.
• ## What is an interaction term example?
Interaction: An interaction occurs when an independent variable has a different effect on the outcome depending on the values of another independent variable. Let's look at some examples. Suppose that there is a cholesterol lowering drug that is tested through a clinical trial.
## What is interaction effect in R?
Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in regression analysis, ANOVA, and designed experiments. Interaction effects indicate that a third variable influences the relationship between an independent and dependent variable.
## What does interaction term means?
In summary: When there is an interaction term, the effect of one variable that forms the interaction depends on the level of the other variable in the interaction. Without an interaction term, the mean value for Females on Med B would have been α+β1 +β2.
## How do you find interaction terms?
• If the lines are parallel, there is no interaction.
• If the lines are not parallel, there is an interaction.
• ## Related faq for How Do I Create An Interaction Term In R?
### What is an interaction term in statistics?
In statistics, an interaction is a special property of three or more variables, where two or more variables interact to affect a third variable in a non-additive manner. In other words, the two variables interact to have an effect that is more than the sum of their parts.
### What is an interaction plot in R?
The easiest way to detect and understand interaction effects between two factors is with an interaction plot. This is a type of plot that displays the fitted values of a response variable on the y-axis and the values of the first factor on the x-axis.
### How do you explain interactions in ANOVA?
Interaction effects represent the combined effects of factors on the dependent measure. When an interaction effect is present, the impact of one factor depends on the level of the other factor. Part of the power of ANOVA is the ability to estimate and test interaction effects.
### What is an interaction term in logistic regression?
An interaction occurs if the relation between one predictor, X, and the outcome (response) variable, Y, depends on the value of another independent variable, Z (Fisher, 1926). Interactions are similarly specified in logistic regression if the response is binary.
### What is interaction effect?
An interaction effect is the simultaneous effect of two or more independent variables on at least one dependent variable in which their joint effect is significantly greater (or significantly less) than the sum of the parts. Further, it helps explain more of the variability in the dependent variable.
### What is interaction terms in regression analysis?
Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in regression analysis, ANOVA, and designed experiments. Interaction effects indicate that a third variable influences the relationship between an independent and dependent variable.
### What is an interaction plot?
Interaction Plot. An interaction plot displays the levels of one variable on the X axis and has a separate line for the means of each level of the other variable. The Y axis is the dependent variable. A look at this graph shows that the effect of dosage is different for males than it is for females.
### What do you do when an interaction term is significant?
If the interaction term is statistically significant, the interaction term is probably important. And if the coefficient of determination is also higher with the interaction term, it is definitely important. If neither of these outcomes is observed, the interaction term can be removed from the regression equation.
### What is a two way interaction?
A statistically significant two-way interaction indicates that there are differences in the influence of each independent variable at their different levels (e.g., the effect of a1 and a2 at b1 is different from the effect of a1 and a2 at b2). See also higher order interaction.
### What is a cross over interaction?
Unlike many terms in statistics, a cross-over interaction is exactly what it says: the means cross over each other in the different situations. Here's an example of a two-by-two ANOVA with a cross-over interaction: The two grey dots indicate the main effect means for Factor A.
### How do you create an interaction variable?
• Select Calc >> Calculator
• In the box labeled Store the result in variable, specify the column (or the name of the new variable, x1x2, for example) in which you want to store the interaction term.
• ### What is the difference between interaction and confounding?
A confounding variable is a factor associated with both the exposure of interest and the outcome of interest. Interaction among variables, also known as effect modification, exists when the effect of 1 explanatory variable on the outcome depends on the particular level or value of another explanatory variable.
### What is an interacting variable?
An interaction effect happens when one explanatory variable interacts with another explanatory variable on a response variable. The two (or more) variables that interact with each other to produce an interaction effect are called the interacting variables.
### What does interaction mean in two way Anova?
ANOVA Output - Profile Plots
* An interaction effect means that the effect of one factor depends on the other factor and it's shown by the lines in our profile plot not running parallel. In this case, the effect for medicine interacts with gender. That is, medicine affects females differently than males.
### What does a 3 way interaction mean?
In short, a three-way interaction means that there is a two-way interaction that varies across levels of a third variable. One way of analyzing the three-way interaction is through the use of tests of simple main-effects, e.g., the effect of one variable (or set of variables) across the levels of another variable.
### What are coefficients in logistic regression?
Coef. A regression coefficient describes the size and direction of the relationship between a predictor and the response variable. Coefficients are the numbers by which the values of the term are multiplied in a regression equation.
### How do you interpret logistic regression coefficients?
With linear OLS regression, model coefficients have a straightforward interpretation: a model coefficient b means that for every one-unit increase in x, the model predicts a b-unit increase in ˆY (the predicted value of the outcome variable).
### What is interaction effect in attribution?
The interaction effect is the combination of the selection and allocation effect. The interaction effect is essentially the cumulative effect created by asset allocation, security selection, and other investment decisions made by the portfolio manager.
### What is a main effect and interaction?
In statistics, main effect is the effect of one of just one of the independent variables on the dependent variable. An interaction effect occurs if there is an interaction between the independent variables that affect the dependent variable.
### Why is my interaction term not significant?
When there is no Significance interaction it means there is no moderation or that moderator does not play any interaction on the variables in question. However this doesn't mean in practice there isn't any interaction. | 1,514 | 7,968 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2022-21 | latest | en | 0.913045 |
http://www.itprotoday.com/may-mdx-puzzle-solution-revealed-01-jun-2001 | 1,524,164,342,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937016.16/warc/CC-MAIN-20180419184909-20180419204909-00258.warc.gz | 462,813,648 | 14,337 | # May MDX Puzzle Solution Revealed - 01 Jun 2001
Using the FoodMart 2000 Sales database, determine which promotion caused the most unique customers to purchase products.
```WITH MEMBER \[Measures\].\[Customers Per Promotion\] AS 'Count(
\{\[Unit Sales\]\} * \[Customers\].\[Name\].Members, ExcludeEmpty )'
SELECT \{ \[Customers Per Promotion\] \} on COLUMNS,
Order(Except(\[Promotions\].\[Promotion Name\].Members,
\{\[Promotions\].\[All Promotions\].\[No
Promotion\]\}) , \[Customers Per Promotion\], DESC ) on ROWS
FROM Sales```
This puzzle was a quiz on the distinct count technique covered in "Distinct Count Queries," May 2001. The \[Customers Per Promotion\] measure is a count of the distinct customers with non-empty unit sales for the currently selected promotion. The MDX query evaluates \[Customers Per Promotion\] for each promotion and returns the ordered list of promotions. | 226 | 891 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2018-17 | latest | en | 0.818358 |
https://www.freesamaya.com/2019/02/floyds-triangle-program-in-julia.html | 1,712,958,053,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816070.70/warc/CC-MAIN-20240412194614-20240412224614-00221.warc.gz | 703,467,535 | 21,534 | ### Floyd's triangle program in Julia
Floyd's triangle is named after Robert Floyd. A right-angled triangular array of
natural number is called Floyd's triangle.
For Eg :
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
Floyd's triangle is defined by starting with a 1 in the top left corner and filling
the rows of the triangle with consecutive numbers.
Lets see now how to create the program using Julia
function createFlyodTriangle(numberOfRows)
printNo =1;
for a=0:numberOfRows
for b=0:a
print(printNo," ")
printNo= printNo+1
end
println(" ")
end
end
Output :
julia> createFlyodTriangle(2)
1
2 3
4 5 6
julia> createFlyodTriangle(5)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
julia> createFlyodTriangle(11)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78 | 414 | 961 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-18 | longest | en | 0.45897 |
http://www.toontricks.com/2018/06/tutorial-how-to-convert-byte-array-to.html | 1,544,463,738,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823382.1/warc/CC-MAIN-20181210170024-20181210191524-00510.warc.gz | 464,925,958 | 40,470 | # Tutorial :How to convert a byte array to its numeric value (Java)?
### Question:
I have an 8 byte array and I want to convert it to its corresponding numeric value.
e.g.
``byte[] by = new byte[8]; // the byte array is stored in 'by' // CONVERSION OPERATION // return the numeric value ``
I want a method that will perform the above conversion operation.
### Solution:1
Assuming the first byte is the least significant byte:
``long value = 0; for (int i = 0; i < by.length; i++) { value += ((long) by[i] & 0xffL) << (8 * i); } ``
Is the first byte the most significant, then it is a little bit different:
``long value = 0; for (int i = 0; i < by.length; i++) { value = (value << 8) + (by[i] & 0xff); } ``
Replace long with BigInteger, if you have more than 8 bytes.
Thanks to Aaron Digulla for the correction of my errors.
### Solution:2
One could use the `Buffer`s that are provided as part of the `java.nio` package to perform the conversion.
Here, the source `byte[]` array has a of length 8, which is the size that corresponds with a `long` value.
First, the `byte[]` array is wrapped in a `ByteBuffer`, and then the `ByteBuffer.getLong` method is called to obtain the `long` value:
``ByteBuffer bb = ByteBuffer.wrap(new byte[] {0, 0, 0, 0, 0, 0, 0, 4}); long l = bb.getLong(); System.out.println(l); ``
Result
``4 ``
I'd like to thank dfa for pointing out the `ByteBuffer.getLong` method in the comments.
Although it may not be applicable in this situation, the beauty of the `Buffer`s come with looking at an array with multiple values.
For example, if we had a 8 byte array, and we wanted to view it as two `int` values, we could wrap the `byte[]` array in an `ByteBuffer`, which is viewed as a `IntBuffer` and obtain the values by `IntBuffer.get`:
``ByteBuffer bb = ByteBuffer.wrap(new byte[] {0, 0, 0, 1, 0, 0, 0, 4}); IntBuffer ib = bb.asIntBuffer(); int i0 = ib.get(0); int i1 = ib.get(1); System.out.println(i0); System.out.println(i1); ``
Result:
``1 4 ``
### Solution:3
If this is an 8-bytes numeric value, you can try:
``BigInteger n = new BigInteger(byteArray); ``
If this is an UTF-8 character buffer, then you can try:
``BigInteger n = new BigInteger(new String(byteArray, "UTF-8")); ``
### Solution:4
Simply, you could use or refer to guava lib provided by google, which offers utiliy methods for conversion between long and byte array. My client code:
`` long content = 212000607777l; byte[] numberByte = Longs.toByteArray(content); logger.info(Longs.fromByteArray(numberByte)); ``
### Solution:5
You can also use BigInteger for variable length bytes. You can convert it to Long, Integer or Short, whichever suits your needs.
``new BigInteger(bytes).intValue(); ``
or to denote polarity:
``new BigInteger(1, bytes).intValue(); ``
### Solution:6
Complete java converter code for all primitive types to/from arrays http://www.daniweb.com/code/snippet216874.html
### Solution:7
Each cell in the array is treated as unsigned int:
``private int unsignedIntFromByteArray(byte[] bytes) { int res = 0; if (bytes == null) return res; for (int i=0;i<bytes.length;i++){ res = res | ((bytes[i] & 0xff) << i*8); } return res; } ``
Note:If u also have question or solution just comment us below or mail us on toontricks1994@gmail.com
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