url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
http://www.angelfire.com/scifi2/zpt/chapter3.html | 1,534,269,412,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221209216.31/warc/CC-MAIN-20180814170309-20180814190309-00422.warc.gz | 437,232,374 | 13,630 | Pg_1
go to page number 1 2 3 4 5 6 7 8 910
Chapter Three
I have just released a paper back at Amazon. The book,"Energy, Antigravity, and Cold Fusion", is also available on Kindle. Please purchase a copy of this historic work.
LEVITATIONAL TECHNOLOGIES
Conventional, unconventional, and antigravitational
THE LIMITATIONS OF A ROCKET
Rockets operate on the basis of Newton's second law. This law states that every action produces an equal and opposite reaction. The force that drives a rocket forward is produced in opposition to the ejection of a rocket's exhaust. In more exact terms, the momentum of the gas exiting a rocket equals the forward momentum delivered to the rocket.
The momentum of the rocket = The momentum of the exhaust
MassrocketVelocityrocket = MassexhaustVelocityexhaust
The momentum delivered to a rocket varies directly with the mass and velocity of the gas ejected from the rocket. The mass that is ejected from a rocket is carried by the rocket in the form of a propellant fuel. There is a limit to the amount of fuel that can be carried by a rocket. Consequentially, a rocket can only exhaust a limited number of pounds of gas. In order to get sufficient thrust from a limited weight of gas, rockets must exhaust gas at very high velocities. The kinetic energy of moving matter increases with the square of the exhaust's velocity.
KINETIC ENERGY = 1/2 Mv2
Most of the energy contained in a rocket's fuel is expended in the rocket's high velocity exhaust stream. Only a small portion of the fuel's energy is actually imparted to the rocket. This is a limitation inherent to all rockets. This limitation restricts the weight of a rocket's payload to a small percentage of the rocket's weight. One way to increase a rocket's efficiency would be to expel more mass from its exhaust stream. The ejection of additional mass would deliver more momentum to the rocket and reduce the kinetic energy thrown away to its exhaust stream. Additional mass cannot be obtained by placing more fuel into a rocket. Additional fuel will make the rocket heavier. The additional weight will negate any gains in efficiency that were obtained from the more massive exhaust stream.
Mass can be obtained from the atmosphere. Airplanes, for example, grab air with their wings, propellers, and jet engines. The weight of the air thrown down by an airplane greatly exceeds the weight of the plane's fuel. Airplanes are, therefore, much more efficient than rockets. In order to get into space, rockets must travel at hypersonic velocities. It is difficult to get a stable flame in air breathing jet engines at hypersonic velocities. Hypersonic engine technology is, however, being developed. This technology will allow a single stage vehicle to reach orbit.
Better, more efficient launch vehicles are needed to colonize space. The engines in these vehicles must be very efficient. The most efficient engine would not expel a light gas. It would push away from a heavy object. In the future, advanced propulsion systems will push down upon the large mass of the earth. Very little kinetic energy will be transferred to the earth. All of the fuel's energy will be imparted to the vehicle. These engines will be very efficient.
Pg_2 UP
THE MAGNOCRAFT
The idea of magnetically propelling a space craft as been around for a long time.
In 1950, Frank Scully wrote in "Behind the Flying Saucers"
"Now that we have learned that these ships from another world fly magnetically, it is my opinion that our own magnetic engieers will solve the problem magnetic flight and match the ships of the visitors with saucers made on this earth."
More recently, Dr. Jan Pajak of Invercargill New Zealand spent many years developing methods of using the earth's magnetic field to propel a spacecraft. He designed a machine called the magnocraft. Pajak's magnocraft is a simple device that operates on the principle of magnetic repulsion. 1, 2
Pajak tried to design a magnet strong enough to push away from one of the earth's magnetic poles. The required strength was called, by Pajak and his associates in Poland, the starting flux. After many years of work, Pajak uncovered some serious problems. The problems have to do with dipole forces. An example will be offered to explain the problems Pajak encountered. An attractive force is developed between the opposite poles of a dipole, and a repulsive force is developed between the like poles of a dipole.
TWO CLOSELY SPACED DIPOLES
In the figure above, an attractive force is developed between poles #1 & #3 and poles #2 & #4. A repulsive force is developed between poles #2 & #3, and poles #1 & #4. The repulsive force between poles #2 & #3 is much stronger than the forces developed between the other poles. A stronger force is produced because the distance between poles #2 & #3 is the least. As the general rule, the force between two dipoles, which are separated by a distance shorter than their length, drops off with the square of their separation distance.
TWO DIPOLES SPACED AT A DISTANCE
The figure below depicts two dipoles separated by a distance longer than their length.
In this second example, the distance separating the dipole's opposite poles is about the same as the distance separating the dipole's like poles. The attractive force between poles #1 & #3, and poles #2 & #4 is about equal to the repulsive force between poles #2 & #3 and poles #1 and #4. As a general rule, the force between two dipoles, which are separated by a distance greater than their length, drops off with the forth power of their separation distance. Any force that decreases with the fourth power drops off to almost nothing in rather short order. This is the reason that inductance is a local phenomena. Dr. Pajak found that the only real force produced by dipoles, separated by a distance greater then their length, is rotational. The magnocraft would not levitate, it would only spin on the ground like a compass. Pajak is still working on the problem, he is examining every detail in his search for a solution. 8
Pg_3 UP
THE BEAMSHIP
Literature abounds with descriptions of spaceships that "ride a beam".2
"He found he was getting a strong 3000 mcs signal from about there 2 o'clock position, just the relative bearing at which the unknown luminous source had blinked out moments earlier."
Astronautics & Aeronautics July 1971, http://homepage.ntlworld.com/ufophysics/jimcd.htm
Pick the icon to view the various types of proposed propulsion systems.
A beam ship operates by ejecting a beam of energy. The momentum carried by a beam of electromagnetic energy is equal to the energy in the beam divided by the speed of light. Any means no exceptions, This author should know; he spent years in a misguided effort attempting to produce a high momentum beam of electromagnetic energy. Any includes light beams, radar beams, laser beams, and X-ray beams. Flows of energy are measured in watts. The relationship between the flow of energy in watts and the momentum of the energy flow is:
Momentum = (Watts) / (3 x 108 meters/second)
A large power plant burning 600 tons of coal an hour can produce 1,800,000,000 watts of energy. If the entire output of the plant was channeled into a beam of energy, this beam would generate a meager 6 newtons of thrust. Six newtons of thrust will just about lift a two ounce mass. The efficiency of a beam ship is very low. Rockets are better, at least a rocket can get off of the ground.
Pg_4 UP
GRAVITOMAGNETIC LEVITATION
A sensitive experiment performed by Hideo Hayasaka and Sakae Takeuchi of the engineering faculty at Tohoku University Sendai, Japan, detected a faint gravitomagnetic that was induced by a super high speed Gyroscope. They found that rapidly spinning gyroscopes tended to loose weight. Gyroscopes weighing 176 grams lost 11 thousandths of a gram when spun at 216 revolutions/second. 3 General Relativity states that a gravitomagnetic field will be produced by a spinning mass. The gravitomagnetic field is similar in structure to the magnetic field produced by an electron moving in a circle. The gravitomagnetic field, however, is very much weaker than its electromagnetic counterpart.
Pick the icon to view various induced fields.
The gravitomagnetic field of a spinning mass is attached to the kinetic energy of the spinning mass and is very weak. Sensitive satellite experiments (ie the Stanford Gravity Probe-B Experiment) are just barely able to detect the gravitomagnetic field associated with the whole of the spinning earth.
In 1992, a strong gravitomagnetic field was detected above a rotating superconductive disk by researchers at the Tampere University in Finland. This effect was 300 million times stronger than the effect observed with the gyroscope in Japan. This gravitomagnetic field is is attached to the mass energy of the spinning superconductor (not the kinetic energy as in the case of the spinning gyroscope) and is very much stronger. The will be explained in detail in later chapters.
Pick the icon to view the gravitational devices invented by Dr. Eugene Podkletnov at Tampere University. This device produces a local gravitomagnetic field. Note: For the gravitomagnetic field local is less than a hundred meters.
This device generates a strong local gravitomagnetic field.
In an historic new release in September of 1996, Robert Matthews and Ian Sample of the 'Sunday Telegraph' UK reported 4 :
"Scientists in Finland are about to reveal details of the world's first anti- gravity device. Measuring about 12in across, the device is said to reduce significantly the weight of anything suspended over it.....
According to Dr. Eugene Podkletnov (right), who led the research, the discovery was accidental................
The team was carrying out tests on a rapidly spinning disc of superconducting ceramic suspended in the magnetic field of three electric coils, all enclosed in a low-temperature vessel called a cryostat.
"One of my friends came in and he was smoking his pipe," Dr Eugene Podkletnov said. "He put some smoke over the cryostat and we saw that the smoke was going to the ceiling all the time. It was amazing - we couldn't explain it."
Pg_5 UP
In February of 1997 'Final Frontier' Magazine reported that Ning Li was following up on Podkletnov's work at NASA Marshall.
"NASA is working with theorist Ning Li of the University of Alabama at Huntsville. Equipment and test materials are being prepped for a set of experiments that could, if successful, lead to new knowledge about gravity fields. If Li's ideas work, modifying and controlling gravity may be the outcome........."
In NASA Technical Memorandum 107,289, "The Challenge to Create the Space Drive",
Marc G. Millis of NASA Lewis writes:
"New theories have emerged suggesting that gravitational an inertial forces are caused by interaction with the electromagnetic fluctuations of the vacuum. There have also been studies suggesting experimental tests for mass altering affects.......it may be time to revisit the notion of creating the visionary "space drive." Space drive, as defined here, is an idealized form of propulsion where the fundamental properties of matter and space-time are used to create propulsive forces anywhere in space without having to carry and expel a reaction mass."
Scientists around the world are following up on Dr. Podkletnov's discovery.5 The team lead by Dr. Ning Li 6 of the University of Alabama attempted to replicate the experiment. NASA Marshall is also experimenting with the technology. This author expects the results of this work to be slow in coming and revolutionary in scope.
Historic picture. Pick the icon to view a picture of Witt Brantley Chief of NASA's Advanced Concepts Office showing Frank Znidarsic one of the mechanisms used to spin superconductive disks.
Historic picture. Pick the icon to view a NASA scientist Glen A. Robinson showing one of the test superconductive disks. One of the problems has been that the disks shatter when spun at high velocities. The ring around the disk is part of the press used to make the disk. Glen went on to establish the Space and Propulsion International Forum.
Historic picture. Pick the icon to view another of the NASA machines designed to spin superconductive disks.
NASA'S CONCLUSIONS
Nasa has completed its gravitational experiments. NASA applied a magnetic field to a high temperature superconductor and searched for a gravitational anomaly. No anomaly was found. NASA did not rotate or apply a radio frequency field to the superconductor. NASA did not follow Podkletnov's suggestions. The author has obtained a copy of Ning Li's unpublished paper, "Gravitomagnetic fields arising from the lattice ion rotations of superconductors." Ning's method does not require rotation or the application of a radio frequency field. Li may have led NASA down the wrong path. Just as a spinning charge generates an electromagnetic field, a rotating mass generates a gravitomagnetic field. The gravitational field is 1039 weaker than the electromagentic field. To get an idea of how weak the gravitomagnetic field is, envision the mass of the earth rotating. The gravitomagnetic field produced by the rotation of the entire mass of the earth is just barely detectable using the most sensitive satellite experiments. No mechanical machine on earth could ever spin fast enough to generate a useable gravitomagnetic field. Ning Li suggested that nucleons could be spun up by a factor of 1045. This author does not appreciate her mechanism for adding spin to the nucleus. As with the electron each level of spin is accompanied by a higher level of energy. It would be impossible to maintain energy levels that are a factor of 1045 above the ground state. The energy would be released long before this level of spin was obtained through the decay of the state and the emission of a photon. Gravity is normally a very weak force.
AN OVERVIEW OF GRAVITOMAGNETIC PROPULSION
There is one instance, however, when all of the fields, including gravity, strongly interact. That instance is during the quantum transition. Lot Brantly asked Znidarsic, "What purpose does the radio frequency stimulation serve." If Brantly or Znidarsic had known the answer NASA may have followed a different path and mankind would have gravitomagnetic propulsion. Lot's question proved to be a vital clue. Znidarsic discovered that the quantum transition is proceeds at a velocity of 1.094 million meters per second. This understanding will be applied in later chapters to demonstrate how to place a macroscopic object into a state of quantum transition. Millions of atoms will be adjoined into a single state of quantum transition. Strong local gravitomagnetic fields will be induced. The gravitomagnetic field will tend to align the protons of the matter in which it comes into contact. This alignment requires energy. This expenditure of energy indicates the gravitomagnetic field is repulsive in nature. The repulsive effect can be used to levitate a spacecraft a hundred or so meters above the surface of the earth. A stronger gravitomagnetic field may be able to repel off of the atmosphere. Longer range repulsive effects may be obtained above the rotational poles of the earth. The range of the translational force above the poles of the earth should approximate the radius of the earth. In order to obtain thrust over interstellar distances the spacecraft engine could rotate with respect to the rest of the universe. This rotation will induce a weak gravitomagnetic field. The strong gravtomagnetic field of the spacecraft will interact with the weak gravitomagnetic field of the universe. The gravitation field is monopolar (it does not contain a field of opposite polarity). The interactions of a monopolar field should induce a long range translational force. The translational force can be employed for propulsion.
There is the possibility that the reaction of strong local gravitomagnetic field and the long range gravitomagnetic field of the universe will be purely rotational. There is another method, abet more difficult, to obtain a translational thrust. Strong local gravitomagnetic structures may be modulated and arranged into an array. This array will resemble a directional electromagnetic antenna. An electromagnetic antenna emits a beam of energy. A gravitomagnetic antenna should emit a beam of momentum.
The relationship between force, gravity, and the gravitomagnetic field has been known for 100 years. This author was the first to place force in a model of matter. This author's work is fundamental to the development of zero point levitational technologies. Published November 1998, INFINITE ENERGY, Volume 4, Issue 22.
Pg_6 UP
The Legend of air force base Area-51
Stories abound about the top secret air force base Area-51. It has been said that flying saucers, aliens, and Roswell crash debris are located there. Physist Bob Lazar claims to have seen captured alien spacecraft at the base. Lasar claims that spacecraft fly with the help of Element-X. This author questions this claim. What could Element-X be? All of the stable elements have been identified. Unknown elements heavier that uranium have very short half lives. The laws of physics are known well enough to rule out the existence of reasonably stable unknown elements. Lasar's claim does not ring true.
Air Force consultant Edgar Fouche claims that Aurora program has developed a craft known as the TR-3B. Picture of the TR-3B courtesy of Edgar Fouche. 7 Fouche states,. "Sandia and Livermore laboratories developed the reverse engineered MFD technology. The plasma, mercury based, is pressurized at 250,000 atmospheres at a temperature of 150 degrees Kelvin and accelerated to 50,000 rpm to create a super-conductive plasma with the resulting gravity disruption." 7 This author has shown that the rotation of a superconductor (a bose condensate) will induce a gravitomagnetic field. Indeed the Advanced Concepts Group at NASA Marshall is currently experimenting with this idea. Could Fouche's rotating plasma be a Bose condensate? Plasmas tends to condense into liquids and solids under high pressure and low temperature. What keeps the TR-3B's plasma from condensing? This author has many more questions than answers, however, Fouche's claim has some technical basis and just could be true.
Pg_7 UP
CONCLUSION
Interseller space travel is impossible with conventional methods of propulsion. Promising graviational technologies appear to have been discovered. It appears that small engines, producing several newtons of thrust, will soon be built. More powerful engines, capable of lifting off from earth, will require extensive development. These engines do not expel mass. They push off of other matter. They will be efficient. Their only requirement is energy. Someday soon man will begin to colonize the universe. He will do this in spaceships that are propelled by gravtomagnetic engines. These engines will be powered by "zero point" cold fusion technology. This author is looking forward to a bright new future. In this future limitless energy will be available from new energy machines and the galaxy will be traversed in spaceships propelled by gravitomagnetic engines.
Pg_8 UP
NOTES
The Latest from NASA
http://www.imglmb1.com/tribune/0207/tld_att_latimes.html
1. "The Oscillatory Chamber" Jan Pajak , ISBN 0-9597698-2-X, 50 pages, 1984 New Zealand
2. "Flyiing Saucers Uncensured" Harold T. Wilkins, Citadel Press, 1955, Page 19
3. Physical Review Letters December 18, 1989
4. The Sunday Telegraph may be directly accessed on the Internet at http:// www.telegraph.co.uk/et Then search for Podkletnov
5. Popular Mechanics, December 1997, page 44
6. "Gravitatioanl effects on the magnetic attenuation of superconductors" Ning Li and D. G. Torr, Physical Review B, Vol 46, # 9 Sept. 1992
"Effects of a gravitomagnetic field on pure superconductors" N. Li and D.G. Torr, Physical Review D, vol 43 # 2 January 1991
Li,N. Noever, D.A., Koczor, R. Robertson, T, Brantley, W, "Static test for a gravitational force coupled to type II YBCO superconductors," Physica C 281 (1997) 260-267.
Noever, D., Koczor, R. "Superconductor-mediated Modification of gravity? AC Motor Experiments with Bulk YBCO Disks in Rotating Magnetic Fields," AIAA 98-3139, Proceedings, 1998 AIAA/AASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH July 13-15, 1998.
Noever, D., Koczor, R. "Test Status for Proposed Coupling of A Gravitational Force to Extreme Type II YBCO Ceramic Superconductors" NASA/CP-1999-208694, NASA Breakthrough Propulsion Physics Workshop Proceedings, August 12-14, 1997, Lewis Research Center, Cleveland, OH.
David Noever, Neural Net Method for HTS Combinatorial Optimization Bi:Cu:Sr:Ca Ratio, presentation at the 3rd European Conference on Applied Superconductivity 7-9 July 1997
David Noever and Ron Koczor, Radio-frequency illuminated superconductive disks: Reverse Josephson effects and implications for precise measuring of proposed gravity effects, NASA JPL-Ninth Advanced Space Propulsion Research Workshop and Conference, Pasadena, CA March 11-13, 1998
D. Noever and C. Bremner, Large-Scale Sakharov Condition, 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Los Angeles, CA, 20-23 June, 1999
R. Koczor, Noever, D, Fabrication of large YBCO superconducting disks, Physica C: Superconductivity, (submitted, 1999)
Dr. Harrald Reiss , "Weight Anomalies Observed During the Cool-Down of High Temperature Superconductors"
, Vol 16, No. 2 June 2002
Replication at the European Space Agency
http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:gr-qc/0003011
7. "Alien Rapture", Edgar Fouche, Box 760094, San Antionio TX, 78245
Edgar Fouche appeared on the TLC program "Alien Invasion" on March 5, 1999
Reference provided as required in exchange for this use of the TR-3B picture.
7. "Alien Rapture", Edgar Fouche, Box 760094, San Antionio TX, 78245
Edgar Fouche appreared on the TLC program "Alien Invision" on March 5, 1999
Reference provided as required in exchange for this use of the TR-3B picture.
8. "Scientific American", Aug. 2004, Pg. 51
Tethers in Space
50 KM long tethers may produce some thrust.
Pg_9 UP
THE MATHEMATICS
Given
F = The gravitomagnetic field in newtons/ (kg/sec)
Mearth = Mass of the Earth = 5.98 x 1024 kg
re = The gravitational radius of the earth = 5 x 106 meters
R = Radius of the spinning disc or gyroscope = .2 meters
Note: the gravitomagnetic field is induced by the movement of a collimated energy field. Note R & re also define the length of the collimated energy field. Only the kinetic energy of the spinning earth and gyroscope are colliminated.
m = Mass of spinning disc or gyroscope = 700 grams
THE GYROSCOPE CALCULATION
v = velocity at the edge of the gyroscope = 2p (f) (R)
v = 2p (216rev/sec)(.2 meters)
v = 271 meters/second
For the sake of analysis this velocity will be split evenly between the earth and the spinning gyroscope.
v = v / 2 = 135 meters/second
The gravitomagnetic field "F" is similar to the electro-magnetic field in that it is induced by motion. It is induced by the movement of mass "dm/dt" not charge "dq/dt". The gravitomagnetic is very weak and involves the very large constants "G" and c2. The gravitomagnetic field "F" is given by:
F = (G/c2) dm/dt
F = (G/c2r) Mv
Fearth = (6.67 x 10-11) / [(9 x 1016)(3 x 106)](5.98 x 1024)(135)
The field density B is given in units of 1/meters.
B = F /meter
Bearth = 2 x 10-7 newtons/(kg-meter/sec)
The electro-magnetic field tends to repel like charges moving in opposite directions. Likewise the gravitomagnetic field tends to repel masses moving in opposite directions. The gravitomagnetic effect is ordinarily to weak to be detected.
Force on gyroscope = Bearth Mv
Force on gyroscope = (2 x 10-7)(.7KG)(135m/s)
Force on gyroscope = 2 x 10-5 newtons
Converting newtons to grams.
Weight loss = (100 grams/newton) (2 x 10-5newtons)
Weight loss = 2 milligrams
The results of the gyroscope experiment are consistent with those expected from the interaction of the gravitomagnetic field.
Pg_10 UP
THE SUPERCONDUCTIVE DISC CALCULATIONS
In the gyroscope experiment, the kinetic rotational kinetic energy of the gyroscope is collimated produced the effect. The mass energy of a superconductor is collimated. The mass energy of a rotating superconductor is much larger than its kinetic energy. The antigravitational effect will therefore be much larger. For a disc with a radius of .2 meters rotatating at 2 revolutions per second the calculation is:
For the sake of analysis this velocity will be split evenly between the earth and the spinning disc.
v = velocity at the edge of the disc = 2p (f) (R)
v = 2p(.2)(2rev/sec) = 2.51 meters/second
The induced gravitomagnetic field is given by:
F = (G/c2r) Mv
Fearth = (6.67 x 10-11)/[(9 x 1016)(3 x 106)](5.98 x 1024)(1.25 m/sec)
Fearth = 1.8 x 10-9 newtons/(kg-meter/sec)
B = F /meter
Force on disc = Bearth Mv
Due to the collimation of the mass energy of a superconductor momentum "P" is substituted for "Mv". The kinetic contribution to "P" is small and was not included with the calculation. As before the mass of the disc is .7kg.
Force on disc = Bearth P
Force on disc = Bearth E/c
Force on disc = Bearth (Mc2)/c
Force on disc = ( 1.8 x 10-9) (.7kg) (3 x 108)
Force on disc = .37 newtons
Converting newtons to grams.
Weight loss = (100 grams/newton) (.37 newtons) = 37 grams
% weight change = (37 grams/ 700 grams)(100%) = 5.4 %
The weight loss is consistent with the weight loss observed in spinning disks. This consistency indicates that the gravitational effects are the result of an induced gravitomagnetic field.
// end of Chapter 3 ........................................................................... | 5,961 | 25,847 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2018-34 | latest | en | 0.927239 |
https://share.cocalc.com/share/5d54f9d642cd3ef1affd88397ab0db616c17e5e0/www/168/notes/2005-09-28/sage-find-points-on-curve.txt?viewer=share | 1,600,950,454,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400217623.41/warc/CC-MAIN-20200924100829-20200924130829-00474.warc.gz | 588,233,096 | 2,951 | CoCalc Public Fileswww / 168 / notes / 2005-09-28 / sage-find-points-on-curve.txt
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
1[email protected]:~/www/168/notes/2005-09-28\$ sage
2------------------------------------------------------------------------
3 SAGE Version 0.7.5, Export Date: 2005-09-29-0607
4 Distributed under the terms of the GNU General Public License (GPL)
5 IPython shell -- for help type <object>?, <object>??, %magic, or help
6 ------------------------------------------------------------------------
7
8 sage: E = EllipticCurve([0,0,1,-1,0])
9 sage: E
10 _4 = Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field
11 sage: P = E([0,0])
12 sage: P
13 _7 = (0, 0)
14 sage: P+P
15 _8 = (1, 0)
16 sage: P+P+P
17 _9 = (-1, -1)
18 sage: P+P+P+P
19 _10 = (2, -3)
20 sage: P+P+P+P+P
21 _11 = (1/4, -5/8)
22 sage: P+P+P+P+P+P
23 _12 = (6, 14)
24 sage: 6*P
25 _13 = (6, 14)
26 sage: 7*P
27 _14 = (-5/9, 8/27)
28 sage: 8*P
29 _15 = (21/25, -69/125)
30 sage: 9*P
31 _16 = (-20/49, -435/343)
32 sage: 10*P
33 _17 = (161/16, -2065/64)
34 sage: 20*P
35 _18 = (683916417/264517696, -18784454671297/4302115807744)
36
37 | 497 | 1,257 | {"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} | 2.625 | 3 | CC-MAIN-2020-40 | latest | en | 0.501539 |
http://oeis.org/A317411 | 1,576,506,361,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540565544.86/warc/CC-MAIN-20191216121204-20191216145204-00052.warc.gz | 103,166,273 | 4,326 | This site is supported by donations to The OEIS Foundation.
Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317411 Expansion of e.g.f. tanh(x/(1 - x)). 0
0, 1, 2, 4, 0, -104, -1200, -10352, -68992, -177536, 5310720, 145374208, 2512029696, 33484862464, 294806779904, -1053894275072, -133585065738240, -4148745576218624, -92116699894185984, -1510783598900412416, -11327731683300474880, 414155615537321476096, 25541948643911385219072 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,3 COMMENTS Lah transform of the sequence 0, 1, 0, -2, 0, 16, 0, -272, ... (A155585 with initial term 0). LINKS N. J. A. Sloane, Transforms MAPLE a:=series(tanh(x/(1 - x)), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019 MATHEMATICA nmax = 22; CoefficientList[Series[Tanh[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[Binomial[n - 1, k - 1] 2^k EulerE[k, 1] n!/k!, {k, n}], {n, 0, 22}] CROSSREFS Cf. A000182, A155585, A219613. Sequence in context: A012710 A287761 A009512 * A309598 A305570 A287651 Adjacent sequences: A317408 A317409 A317410 * A317412 A317413 A317414 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jul 27 2018 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.) | 640 | 1,880 | {"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} | 2.890625 | 3 | CC-MAIN-2019-51 | latest | en | 0.679138 |
https://math.answers.com/Q/How_do_you_simplify_the_fraction_10_over_40 | 1,656,257,413,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103269583.13/warc/CC-MAIN-20220626131545-20220626161545-00074.warc.gz | 430,028,812 | 40,377 | 0
# How do you simplify the fraction 10 over 40?
Wiki User
2011-04-27 04:45:07
10/40 = 1/4 = .25 = 25%
Wiki User
2011-04-27 04:45:07
Study guides
20 cards
➡️
See all cards
3.74
1018 Reviews | 84 | 197 | {"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-2022-27 | latest | en | 0.677135 |
https://www.divorce-attorney-fort-worth.net/unit-rates-calculator/ | 1,695,286,193,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233505362.29/warc/CC-MAIN-20230921073711-20230921103711-00817.warc.gz | 831,485,169 | 13,196 | # Unit Rates Calculator
### Contents
A lesson that parents can work through with their children to help them learn how to work with unit rates. Includes an introduction on ratios as well as two related worksheets and.
By (date), when given problems with hints on solving rate problems (e.g. Khan Academy – Rate Problems with Fractions 1), (name) will use a. checklist to correctly calculate unit rates using ratios, including ratios of fractions with quantities measured in like units for (4 out of 5) problems.
Guidelines to follow when using the calculator: Each table has two boxes. The box on top is the numerator and the box at the bottom is the denominator. Therefore, each table represents a ratio Enter a ratio with two values in either box. Then enter only one value in the other box Hit the calculate button and the fourth value will be computed!
Unit rates with fractions : We can use unit rates to simplify rates and ratios that appear complicated, such as those containing fractions in both the numerator and denominator. To have better understanding on "Unit rates with fractions ", let us look at the example given below.
Commercial Financing Real Estate 300000 Morgage 25 Year Amortization 25 Year vs. 40 year Amortization – revnyou.com – * Amortization is 25 years * Payments are \$1,569.92/month * Total interest paid over 25 years = \$220,974 * Amortization is 40 years * Payments are \$1,328.97/month * Total interest paid over 40 years = \$387,908.4 Mortgage Misunderstandings That Could Cost You – . is a premium that’s added to your monthly mortgage payment when you don’t manage to put 20% down. PMI will typically equal 0.5% to 1% of your loan’s value, which means that if you’re looking at a.Bank Rate Amortization Loan Calculator Amortization Bankrate GRAND COUNTY – GRAND COUNTY’s 4,440 members currently have \$27.1 million in shares with the credit union. Overall, Bankrate believes that, as of December 31, 2017, grand county exhibited a good condition, earning 4.buy commercial space apartment complex loans apartment loans – 7 Best Rate Multifamily Mortgages – Since 1997, we have shopped our network of affiliated lenders to land our clients the best deals on apartment loans for buildings of 5 units or more, and \$500,000 plus.. apartment loan store has specialized in the lowest rate multifamily loans for over 20 years.Commercial property in Hyderabad – Commercial property for. – Find Commercial property in Hyderabad within your budget on 99acres.com, India’s No.1 real estate portal.. buy. buy rent P.G. Lease.. Description : Commercial space north facing, main road 100 feet road, with all permission for construction,Personal Loan – Security Bank Philippines – Apply for a personal loan online and loan up to P1,000,000 at low interest. No credit card or existing credit history required to apply. Not sure how much you can borrow? Try our personal loan calculator to.Types of Commercial Real Estate Loans – thebalancesmb.com – · Real estate purchase loans are similar to fixed-rate and adjustable-rate commercial mortgages. Borrowers must have excellent credit to qualify for this type of loan-a credit score of 700 or higher-and significant savings in both business and personal bank accounts.
The Windows Calculator app included in Windows 10 is a simple yet powerful calculator that includes standard, scientific, and.
Business Calculator Free Commercial Property Equity Loan Bank Loan For Commercial Property Amortization Bankrate Loan Amortization Calculator – Loan Amortization Calculator. This calculator will figure a loan’s payment amount at various payment intervals — based on the principal amount borrowed, the length of the loan and the annual interest rate. Then, once you have computed the payment, click on the "Create Amortization Schedule" button to create a printable report.
Commercial Equity Line – City National Bank – With our Commercial Equity Line of Credit, you can tap into the equity of eligible. Maximum loan-to-value depends on the type of commercial real property.Whatever it is, it’s important to remember your sexual history is your own business. No one may feel pressured to adhere..
The Unit Rate Calculator an online tool which shows Unit Rate for the given input. Byju’s Unit Rate Calculator is a tool which makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number.
Non-Agriculture Rates Agriculture Rates District Select District ANANTAPUR CHITOOR CUDDAPAH EAST GODAVARI GUNTUR KRISHNA KURNOOL NELLORE PRAKASAM SRIKAKULAM VISAKHAPATNAM VIZIANAGARAM WEST GODAVARI
The report also consists of the facts and key values of the global Hydraulic Workover Unit market in terms of sales and.
UPS’s shipping calculator estimates the time and cost of delivery based on the destination and service. Get a quote for your next shipment.
Currency converter: Exchange rates of European Central Bank are now used as source. They are updated around 16:00 CET on every working day. x. Tips. To add the Unit Converter to your iPhone or iPad home screen. Open the Unit Converter in Safari, click the "Share" button and select "Add to Home.
The unit will have two SPs. “It will increase the crime rate but will provide justice for all,” Gehlot said. | 1,139 | 5,294 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2023-40 | latest | en | 0.927325 |
http://www.transum.org/Maths/Puzzles/Pick_up_sticks/ | 1,521,934,800,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257651465.90/warc/CC-MAIN-20180324225928-20180325005928-00775.warc.gz | 470,944,631 | 10,484 | # Pick Up Sticks
#
#
#
#
#
#
#
#
#
If you were to pick up the sticks from this pile so that you were always removing the top stick what calculation would you create? Type the answer to this calculation into this box:
Don't forget the order of operations (BIDMAS).
## Transum.org
This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.
## More Activities:
Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?
Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :
"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"
Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:
"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"
#### Great Expectation
An interactive online activity requiring logical thinking and a certain amount of luck. Numbers 1 to 6 are presented randomly and are to be used to produce two 2-digit numbers. Can you ensure that the first number is greater than the second?
## Numeracy
"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."
Secondary National Strategy, Mathematics at key stage 3
## Go Maths
Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.
## Teachers
If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
For Students:
For All: | 609 | 2,960 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2018-13 | longest | en | 0.955067 |
https://www.lessonup.com/nl/lesson/CdiXifCDFJmiivmEd | 1,721,720,965,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518029.81/warc/CC-MAIN-20240723072353-20240723102353-00473.warc.gz | 735,022,982 | 41,306 | # Y2_T4_REVIEW§4.1-§4.3
HW CHECK
§4.1
§4.2
§4.3
FORCES WORKSHEET
timer
30:00
1 / 20
Slide 1: Tekstslide
ScienceMiddelbare schoolhavo, vwoLeerjaar 2
In deze les zitten 20 slides, met interactieve quizzen en tekstslides.
Lesduur is: 90 min
## Onderdelen in deze les
HW CHECK
§4.1
§4.2
§4.3
FORCES WORKSHEET
timer
30:00
#### Slide 1 -Tekstslide
§4.1 - Learning Goals:
• I can explain what a force is and can identify different types of forces.
• I can calculate the gravitational force acting on an object.
• I can draw arrows on a force diagram with the correct point of application, magnitude and direction.
• I can calculate the resultant force of forces going in the same direction or opposite directions of each other.
• VWO ONLY - I can calculate the resultant force of two perpendicular forces
P.154-157
#### Slide 2 -Tekstslide
§4.1 - Keywords:
• Gravity
• Applied force
• Air resistance
• Friction
• Tension force
• Spring force
• Normal force
• Resultant force
• Point of application
• Direction
• Magnitude
P.154-157
Fg
Fa
Fair
Ff
Ft
Fs
Fn
Fres
#### Slide 3 -Tekstslide
How does air resistance affect the motion of a skydiver as they fall towards the ground?
A
Air resistance decreases a skydivers rate of falling.
B
Air resistance decreases a skydivers rate of acceleration.
C
Air resistance increases a skydivers rate of acceleration.
D
Air resistance stops a skydivers from falling.
#### Slide 4 -Quizvraag
What is the force of gravity on a 50 kg object on Earth's surface, where the force due to gravity is approximately 9.81 N/kg?
#### Slide 5 -Open vraag
If a person has a mass of 70 kg and is standing on the surface of the moon, where the force due to gravity is approximately 1.62 N/kg, what is the force of gravity acting on them?
#### Slide 6 -Open vraag
Two forces of 5 N (left) and 8 N (right) are acting on an object in opposite directions. What is the magnitude and direction of the resultant force acting on the object?
#### Slide 7 -Open vraag
§4.2 - Learning Goals:
• I can describe the concept of speed and understand which measurements and units are necessary to calculate it.
• I can calculate the speed (or distance or time) of an object using the speed formula.
• I can convert speed between the units of m/s and km/h.
• I can create and interpret s,t-diagrams relating to an object’s motion.
P.162-165
§4.2 - Keywords:
• Speed
• s,t-diagram
P.162-165
#### Slide 9 -Tekstslide
A car travels a distance of 240 km in 4 hours. What is the average speed of the car in kilometers per hour (km/h)?
#### Slide 10 -Open vraag
A train covers a distance of 400 meters in 20 seconds. What is the speed of the train in kilometers per hour (km/h)?
#### Slide 11 -Open vraag
A car travels at a speed of 60 km/h. How many minutes will it take to travel a distance of 18 km?
#### Slide 12 -Open vraag
A train travels at a speed of 80 km/h. How far will it travel in 100 minutes?
#### Slide 13 -Open vraag
§4.3 - Learning Goals:
• I can describe the concept of acceleration and understand which measurements and units are necessary to calculate it.
• I can calculate the acceleration of an object using the acceleration formula.
• I can create and interpret v,t-diagrams relating to an object’s change in motion.
• I can use an object’s resultant force to determine what type of motion it has.
P.172-175
§4.3 - Keywords:
• Acceleration
• Deceleration
• v,t-diagram
P.172-175
#### Slide 15 -Tekstslide
A car traveling at 60 km/h suddenly hits the brakes and comes to a complete stop in 5 seconds. What is the car's acceleration?
#### Slide 16 -Open vraag
A rock is thrown off a cliff with an initial velocity of 30 m/s. After 5 seconds it has a velocity of 79 m/s, what is its acceleration during the fall?
#### Slide 17 -Open vraag
A car is traveling along a straight road with a constant speed of 30 m/s. If the engine provides a driving force of 5000 N, and air resistance provides a drag force of 2000 N in the opposite direction, what is the resultant force acting on the car? Calculate and explain what other force is acting on the car.
#### Slide 18 -Open vraag
A cyclist is pedaling a bicycle on a flat road with a constant applied force of 200 N. The bicycle experiences resistive forces of 250 N. What is the resultant force acting on the bicycle? Is the cyclist accelerating, decelerating, or moving at a constant speed?
#### Slide 19 -Open vraag
Study for the quiz:
• study all the glossaries
• study the notes
• review all the hw exercises
Make sure you bring:
• ruler/triangle
• calculator
• pen
• highlight marker | 1,232 | 4,588 | {"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-2024-30 | latest | en | 0.734432 |
https://www.coursehero.com/file/224886/06-differential-forms-on-manifolds/ | 1,516,782,566,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084893530.89/warc/CC-MAIN-20180124070239-20180124090239-00567.warc.gz | 854,314,238 | 24,365 | 06 - differential forms on manifolds
# 06 - differential forms on manifolds - FORMS AND...
This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: FORMS AND INTEGRATION — I Differential forms: definitions Part I: Linear Theory Let V ’ R n be a linear space: we avoid the symbol R n since the latter implicitly implies some coordinates. ♥ Definition. An exterior k-form on V is a map ω : V × · × V | {z } k times → R , ( v 1 ,...,v k ) 7→ ω ( v 1 ,...,v k ) , which is: • linear in each argument, and • antisymmetric: if σ ∈ S k is a permutation on k symbols, and | σ | = ± 1 its parity, then ω ( v σ (1) ,...,v σ ( k ) ) = (- 1) | σ | ω ( v 1 ,...,v k ) . The space of all k-forms on V is denoted by ∧ k ( V * ): it is a linear space over R . / ♦ Example. Linear forms are 1-forms: ∧ 1 ( V * ) = V * . ♦ Example. If dim V = k and a coordinate system in V is chosen, and v j = ( v j 1 ,...,v jk ), then ω ( v 1 ,...,v k ) = det fl fl fl fl fl fl v 11 ... v k 1 . . . . . . . . . v 1 k ... v kk fl fl fl fl fl fl is a k-form. We denote it by det x , x explicitly indicating the coordinate system. ♣ Problem 1. Prove that for any u,v ∈ R 3 the two formulas, ω 2 = det x ( u, · , · ) , ω 1 = det x ( u,v, · ) define 2- and 1-forms respectively. In any coordinate system ( x 1 ,...,x n ) on V ’ R n a k-form can be associated with a tuple of reals: if α : { 1 ,...,k } → { 1 ,...,n } is an index map , and ( e 1 ,..., e n ) a basis in V , then we define a α = ω ( e α (1) ,..., e α ( k ) ) and consider the collection { a α } with α ranging over all possible index maps.possible index maps....
View Full Document
{[ snackBarMessage ]}
### Page1 / 4
06 - differential forms on manifolds - FORMS AND...
This preview shows document pages 1 - 2. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 631 | 2,056 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2018-05 | latest | en | 0.734088 |
http://perplexus.info/show.php?pid=5291&cid=35698 | 1,534,393,124,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221210413.14/warc/CC-MAIN-20180816034902-20180816054902-00097.warc.gz | 310,904,297 | 5,542 | All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
perplexus dot info
Snookered! (Part I) (Posted on 2007-01-01)
Billiards experts work their magic on a pool table without any exact knowledge of distances, angles or speeds. Can you?
A regulation billiards table is twice as long as it is wide, has six pockets in the conventional positions, and a total of 18 “rail sights” (the little aiming circles or diamonds along all four sides). Rail sights and pockets form 24 equally spaced divisions around the table. You are at the “head” of the table, and desire to hit the cue ball from against your rail (the head rail), over the “foot spot” (that little dot near the other end), off the far (foot) rail, and back into one of the corner pockets on your end. For non-experts, (including me!), the foot spot is always two rail sight marks from the from the foot rail and centered between the two long sides.
Assume the following:
The ball rolls only – no sliding, no “english”, no leaving the table, therefore all shots go straight since the table is level Coefficient of friction of the rolling ball on the table is 0.05 (a realistic value)
The ball always makes a perfect collision with the bumper (i.e. no energy loss and no friction while in contact) Ignore the size of the ball and pockets – treat both as point entities.
Mass of the ball = OOOPS!, some pool shark has switched your cue ball for one of unknown weight (mass).
Q1: Where do you place the cue ball in order to make the bank shot?
Q2: What is the minimum initial speed you must give to the ball on this trajectory in order to make the shot (assume that if the ball stops exactly at the pocket, you succeeded)
See The Solution Submitted by Kenny M Rating: 3.0000 (1 votes)
Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution Comment 3 of 3 |
(In reply to solution by Charlie)
In response to Kenny's comment, the following is a correction to my original solution. When taking the square root of t^2, I had taken the square root of the coefficient of w, but not of w itself. That is corrected below. Further precision could probably be gained by using the 32.174 value for g, rather than the 32 I used.
The foot spot is 1/4 of the table length from the foot rail, so the path from the foot spot to the foot rail will need to take it 1/5 of the way from the center-line of the table, or 1/10 of the table width, while the trip back to the head rail will take up the remaining 4/10 of the width. Traveling backward from the foot spot to the point where the cue hit the ball will require 3/10 of the width, and thus 2/10 of the width of the table from the opposite pocket to that aimed at.
The total distance to be traveled by the ball is the hypotenuse of a triangle 4 table widths long and .8 table widths wide, or a total length of 4.079215610874228 table widths, to the accuracy shown.
I'm not sure how kilograms of mass are related to kilograms of weight, but in the English system used in the U.S., in which I learned physics, mass, measured in slugs is 1/32 the weight in pounds on the earth's surface (32.174 in the denominator actually).
The frictional force is .05 the weight, so since f = ma, .05w = (w/32) a, and
a = 1.6 ft/s^2
v = 1.6 t ft/s
d = .8 t^2 ft
If w is the table width,
4.079215610874228 w = .8 t^2
t = 2.258100864353226 sqrt(w) s
v = 1.6 * 2.258100864353226 * sqrt(w) = 3.612961382965161 * sqrt(w) ft/s initially.
So it depends on the width of the table, being about 3.613 times the square root of the table width, in feet per second, when the table width is measured in feet.
Posted by Charlie on 2007-01-06 11:16:34
Search: Search body:
Forums (0) | 958 | 3,724 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2018-34 | latest | en | 0.925871 |
https://stacks.math.columbia.edu/tag/0EQW | 1,685,715,363,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648695.4/warc/CC-MAIN-20230602140602-20230602170602-00130.warc.gz | 601,528,971 | 7,130 | 81.21 Intersecting with an invertible sheaf and rational equivalence
This section is the analogue of Chow Homology, Section 42.28. Applying the key lemma we obtain the fundamental properties of intersecting with invertible sheaves. In particular, we will see that $c_1(\mathcal{L}) \cap -$ factors through rational equivalence and that these operations for different invertible sheaves commute.
Lemma 81.21.1. In Situation 81.2.1 let $X/B$ be good. Assume $X$ integral and $\dim _\delta (X) = n$. Let $\mathcal{L}$, $\mathcal{N}$ be invertible on $X$. Choose a nonzero meromorphic section $s$ of $\mathcal{L}$ and a nonzero meromorphic section $t$ of $\mathcal{N}$. Set $\alpha = \text{div}_\mathcal {L}(s)$ and $\beta = \text{div}_\mathcal {N}(t)$. Then
$c_1(\mathcal{N}) \cap \alpha = c_1(\mathcal{L}) \cap \beta$
in $\mathop{\mathrm{CH}}\nolimits _{n - 2}(X)$.
Proof. Immediate from the key Lemma 81.20.1 and the discussion preceding it. $\square$
Lemma 81.21.2. In Situation 81.2.1 let $X/B$ be good. Let $\mathcal{L}$ be invertible on $X$. The operation $\alpha \mapsto c_1(\mathcal{L}) \cap \alpha$ factors through rational equivalence to give an operation
$c_1(\mathcal{L}) \cap - : \mathop{\mathrm{CH}}\nolimits _{k + 1}(X) \to \mathop{\mathrm{CH}}\nolimits _ k(X)$
Proof. Let $\alpha \in Z_{k + 1}(X)$, and $\alpha \sim _{rat} 0$. We have to show that $c_1(\mathcal{L}) \cap \alpha$ as defined in Definition 81.18.1 is zero. By Definition 81.15.1 there exists a locally finite family $\{ W_ j\}$ of integral closed subspaces with $\dim _\delta (W_ j) = k + 2$ and rational functions $f_ j \in R(W_ j)^*$ such that
$\alpha = \sum (i_ j)_*\text{div}_{W_ j}(f_ j)$
Note that $p : \coprod W_ j \to X$ is a proper morphism, and hence $\alpha = p_*\alpha '$ where $\alpha ' \in Z_{k + 1}(\coprod W_ j)$ is the sum of the principal divisors $\text{div}_{W_ j}(f_ j)$. By Lemma 81.19.4 we have $c_1(\mathcal{L}) \cap \alpha = p_*(c_1(p^*\mathcal{L}) \cap \alpha ')$. Hence it suffices to show that each $c_1(\mathcal{L}|_{W_ j}) \cap \text{div}_{W_ j}(f_ j)$ is zero. In other words we may assume that $X$ is integral and $\alpha = \text{div}_ X(f)$ for some $f \in R(X)^*$.
Assume $X$ is integral and $\alpha = \text{div}_ X(f)$ for some $f \in R(X)^*$. We can think of $f$ as a regular meromorphic section of the invertible sheaf $\mathcal{N} = \mathcal{O}_ X$. Choose a meromorphic section $s$ of $\mathcal{L}$ and denote $\beta = \text{div}_\mathcal {L}(s)$. By Lemma 81.21.1 we conclude that
$c_1(\mathcal{L}) \cap \alpha = c_1(\mathcal{O}_ X) \cap \beta .$
However, by Lemma 81.18.2 we see that the right hand side is zero in $\mathop{\mathrm{CH}}\nolimits _ k(X)$ as desired. $\square$
In Situation 81.2.1 let $X/B$ be good. Let $\mathcal{L}$ be invertible on $X$. We will denote
$c_1(\mathcal{L})^ s \cap - : \mathop{\mathrm{CH}}\nolimits _{k + s}(X) \to \mathop{\mathrm{CH}}\nolimits _ k(X)$
the operation $c_1(\mathcal{L}) \cap -$. This makes sense by Lemma 81.21.2. We will denote $c_1(\mathcal{L}^ s \cap -$ the $s$-fold iterate of this operation for all $s \geq 0$.
Lemma 81.21.3. In Situation 81.2.1 let $X/B$ be good. Let $\mathcal{L}$, $\mathcal{N}$ be invertible on $X$. For any $\alpha \in \mathop{\mathrm{CH}}\nolimits _{k + 2}(X)$ we have
$c_1(\mathcal{L}) \cap c_1(\mathcal{N}) \cap \alpha = c_1(\mathcal{N}) \cap c_1(\mathcal{L}) \cap \alpha$
as elements of $\mathop{\mathrm{CH}}\nolimits _ k(X)$.
Proof. Write $\alpha = \sum m_ j[Z_ j]$ for some locally finite collection of integral closed subspaces $Z_ j \subset X$ with $\dim _\delta (Z_ j) = k + 2$. Consider the proper morphism $p : \coprod Z_ j \to X$. Set $\alpha ' = \sum m_ j[Z_ j]$ as a $(k + 2)$-cycle on $\coprod Z_ j$. By several applications of Lemma 81.19.4 we see that $c_1(\mathcal{L}) \cap c_1(\mathcal{N}) \cap \alpha = p_*(c_1(p^*\mathcal{L}) \cap c_1(p^*\mathcal{N}) \cap \alpha ')$ and $c_1(\mathcal{N}) \cap c_1(\mathcal{L}) \cap \alpha = p_*(c_1(p^*\mathcal{N}) \cap c_1(p^*\mathcal{L}) \cap \alpha ')$. Hence it suffices to prove the formula in case $X$ is integral and $\alpha = [X]$. In this case the result follows from Lemma 81.21.1 and the definitions. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 1,553 | 4,383 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "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": 2, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2023-23 | latest | en | 0.666052 |
https://www.geeksforgeeks.org/number-among-n-numbers-numbers-divisible/?type=article&id=175487 | 1,708,859,543,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474595.59/warc/CC-MAIN-20240225103506-20240225133506-00317.warc.gz | 784,963,380 | 61,989 | # Find an array element such that all elements are divisible by it
Given an array of numbers, find the number among them such that all numbers are divisible by it. If not possible print -1.
Examples:
Input : arr = {25, 20, 5, 10, 100}
Output : 5
Explanation : 5 is an array element
which divides all numbers.
Input : arr = {9, 3, 6, 2, 15}
Output : -1
Explanation : No numbers are divisible
by any array element.
Method 1:(naive): A normal approach will be to take every element and check for division with all other elements. If all the numbers are divisible then return the number.
Implementation:
## C++
// CPP program to find an array element that // divides all numbers in the array using // naive approach #include using namespace std; // function to find smallest num int findSmallest(int a[], int n) { // traverse for all elements for (int i = 0; i < n; i++) { int j; for (j = 0; j < n; j++) if (a[j] % a[i]) break; // stores the minimum if // it divides all if (j == n) return a[i]; } return -1; } // driver code int main() { int a[] = { 25, 20, 5, 10, 100 }; int n = sizeof(a) / sizeof(int); cout << findSmallest(a, n); return 0; }
## Java
// Java program to find an array element // that divides all numbers in the array // using naive approach import java.io.*; class GFG { // function to find smallest num static int findSmallest(int a[], int n) { // traverse for all elements for (int i = 0; i < n; i++) { int j; for (j = 0; j < n; j++) if (a[j] % a[i]>=1) break; // stores the minimum if // it divides all if (j == n) return a[i]; } return -1; } // driver code public static void main(String args[]) { int a[] = { 25, 20, 5, 10, 100 }; int n = a.length; System.out.println(findSmallest(a, n)); } } // This code is contributed by Nikita Tiwari.
## Python3
# Python 3 program to find an array # element that divides all numbers # in the array using naive approach # Function to find smallest num def findSmallest(a, n) : # Traverse for all elements for i in range(0, n ) : for j in range(0, n) : if ((a[j] % a[i]) >= 1) : break # Stores the minimum # if it divides all if (j == n - 1) : return a[i] return -1 # Driver code a = [ 25, 20, 5, 10, 100 ] n = len(a) print(findSmallest(a, n)) # This code is contributed by Nikita Tiwari.
## C#
// C# program to find an array element // that divides all numbers in the array // using naive approach using System; class GFG { // function to find smallest num static int findSmallest(int []a, int n) { // traverse for all elements for (int i = 0; i < n; i++) { int j; for (j = 0; j < n; j++) if (a[j] % a[i] >= 1) break; // stores the minimum if // it divides all if (j == n) return a[i]; } return -1; } // Driver code public static void Main() { int []a = { 25, 20, 5, 10, 100 }; int n = a.Length; Console.WriteLine(findSmallest(a, n)); } } // This code is contributed by vt_m.
## PHP
## Javascript
Output
5
Time Complexity: O(n2)
Auxiliary Space: O(1)
Method 2 : (Efficient): An efficient approach is to find smallest of all numbers, and check if it divides all the other numbers, if yes then the smallest number will be the required number.
Implementation:
## C++
// CPP Program to find the smallest number // that divides all numbers in an array #include using namespace std; // function to find smallest num int findSmallest(int a[], int n) { // Find the smallest element int smallest = *min_element(a, a+n); // Check if all array elements // are divisible by smallest. for (int i = 1; i < n; i++) if (a[i] % smallest) return -1; return smallest; } // Driver code int main() { int a[] = { 25, 20, 5, 10, 100 }; int n = sizeof(a) / sizeof(int); cout << findSmallest(a, n); return 0; }
## Java
// Java Program to find the // smallest number that divides // all numbers in an array import java.io.*; class GFG { // function to find the smallest element static int min_element(int a[]) { int min = Integer.MAX_VALUE, i; for (i = 0; i < a.length; i++) { if (a[i] < min) min = a[i]; } return min; } // function to find smallest num static int findSmallest(int a[], int n) { // Find the smallest element int smallest = min_element(a); // Check if all array elements // are divisible by smallest. for (int i = 1; i < n; i++) if (a[i] % smallest >= 1) return -1; return smallest; } // Driver code public static void main(String args[]) { int a[] = {25, 20, 5, 10, 100}; int n = a.length; System.out.println(findSmallest(a, n)); } } // This code is contributed by Nikita Tiwari.
## Python3
# Python3 Program to find the # smallest number that divides # all numbers in an array # Function to find the smallest element def min_element(a) : m = 10000000 for i in range(0, len(a)) : if (a[i] < m) : m = a[i] return m # Function to find smallest num def findSmallest(a, n) : # Find the smallest element smallest = min_element(a) # Check if all array elements # are divisible by smallest. for i in range(1, n) : if (a[i] % smallest >= 1) : return -1 return smallest # Driver code a = [ 25, 20, 5, 10, 100 ] n = len(a) print(findSmallest(a, n)) # This code is contributed by Nikita Tiwari.
## C#
// C# Program to find the // smallest number that divides // all numbers in an array using System; class GFG { // function to find the smallest element static int min_element(int []a) { int min = int.MaxValue; int i; for (i = 0; i < a.Length; i++) { if (a[i] < min) min = a[i]; } return min; } // function to find smallest num static int findSmallest(int []a, int n) { // Find the smallest element int smallest = min_element(a); // Check if all array elements // are divisible by smallest. for (int i = 1; i < n; i++) if (a[i] % smallest >= 1) return -1; return smallest; } // Driver code public static void Main() { int []a = {25, 20, 5, 10, 100}; int n = a.Length; Console.WriteLine(findSmallest(a, n)); } } // This code is contributed by vt_m.
## PHP
## Javascript
Output
5
Time Complexity: O(n)
Auxiliary Space: O(1)
Previous
Next | 2,220 | 7,446 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2024-10 | latest | en | 0.346969 |
https://www.nandantechnicals.com/2021/07/actuators-multiple-choice-questions.html | 1,726,374,860,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651614.9/warc/CC-MAIN-20240915020916-20240915050916-00561.warc.gz | 846,605,113 | 34,460 | # Actuators
1. A pressure control process using proportional plus integral control has a time constant of 10 seconds. The best choice of actuator would be
a) An electric motor
b) A pneumatic diaphragm
c) A piston and cylinder
d) A solenoid electrical
2. An electronic controller creates a 4 to 20mA dc signal that must actuate a steam valve for temperature control. The best and most economical choice would be to
a) Use an all-electric actuator system
b) Convert to a pneumatic signal at the controller and use a pneumatic actuator.
c) Use pneumatic actuator with an electric to pneumatic valve positioner
d) None of the above
Answer: Use pneumatic actuator with an electric to pneumatic valve positioner
3. The basic function of the spring in a control valve is to
a) Characterize flow
b) Oppose the diaphragm so as to position the valve according to signal pressure
c) Close the valve if air failure occurs
d) Open the valve if air failure occurs
Answer: Oppose the diaphragm so as to position the valve according to signal pressure
4. A single seated globe valve containing a plug 1 1/2 inches in diameter is used in a line pressurized to 500 psi. What actuator force is required for tight Shutoff.?
a) 884 pounds
b) 2,000 pounds
c) Depends upon direction of flow through the valved
d) None of the above
Answer: Depends upon direction of flow through the valved
5. A diaphragm actuator has a diaphragm area of 50 square inches and is adjusted to stroke a valve when a 3 to 15 psi (20 to 100 k Pa) Signal is applied. If the signal is 15 psi (100 k pa) the force on the valve stem will be
a) 750 pounds
b) 750 pounds less than the opposing spring force
c) Dependent on hysteresis
d) None of the above
Answer: 750 pounds less than the opposing spring force
6. Assume that a control valve regulates stream flow to a process and that high temperature makes the reaction hazardous. The usual pneumatically operated control valve utilizes the following action for fail-safe operation
a) Air to open
b) Air to close
c) 3 psi (20 kpa) to fully open
d) 15 psi (100 kpa) to fully close
7. One advantage of an electric to pneumatic valve positioner is
a) It can be used on flow control
b) It produces positive valve position
c) It conserves energy
d) It dampers valve travels
Answer: It produces positive valve position
8. A valve positioner
a) Takes the place of a cascade control system
b) Provides more precise valve position
c) Makes a pneumatic controller in necessary
d) Provides a remote indication of valve position
Answer: Provides more precise valve position
9. A diaphragm actuator has a diaphragm area of 115 square inches. A valve positioner is attached to the actuator and fed with 22 psi air supply. If after 9 psi signal is received from the controller the signal changes to 10 psi and the valve fails to move. What is the force applied to the valve stem?
a) 2.530 pounds
b) 1.495 pounds
c) 1.035 pounds
d) None of the above
10. A high- pressure flow process requires a valve with tight packing. This would suggest that
a) A valve positioner should be employed
b) The actuator must be sized to provide adequate force
c) Oversized pneumatic signals lines are required
d) The controller supplying the signal to the valve must have a very narrow proportional band.
11. Actuators are used to
a) sense an object
b) activate a chemical
c) make a mechanical movement
d) All of the above
Answer: Option make a mechanical movement
## Hydraulic Actuating Systems
1. What is the formula of speed control valve during extension of a flow control valve?
a) V=(Q/A)
b) V=Q.A
c) V=A/Q
d) V=Q(A-a)
2. Which among the following are not the main selection criteria of the control valves?
a) Type of actuation
b) Environmental conditions
c) Space requirement
d) Software support
3. The valve packing of control valves is used ____
a) to prevent the fluid from escaping
b) to control the force generated by actuators
c) to control different parameters of the fluid
d) to control the direction of flow
Answer: to prevent the fluid from escaping
4. Which among the following fluid parameters are not controlled by the control valves?
a) Pressure
b) Rate of flow
c) Speed
d) Direction of flow
5. What is the formula of speed control valve during retraction of a flow control valve?
a) V=(Q/A)
b) V=Q.A
c) V=A/Q
d) V=Q/(A-a)
6. What is the function of the pressure control valve?
a) To control the force generated by actuators
b) To perform two operations in sequence
c) To control the direction of flow
d) To avoid the development of excess of pressure
Answer: To control the force generated by actuators
7. What is the function of the control valve?
a) To control different parameters of the fluid
b) To perform two operations in sequence
c) To control the direction of flow
d) To avoid the development of excess of pressure
Answer: To control different parameters of the fluid
8. Which among the following are not the ‘work parameters’ of the fluid?
a) Direction
b) Speed
c) Pressure
d) Temperature of flow | 1,254 | 4,996 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-38 | latest | en | 0.847838 |
https://www.meritnation.com/ask-answer/question/please-solve-this-first-question-of-gay-lussac-based-problem/mole-concept-and-stoichiometry/14062073 | 1,656,619,590,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103877410.46/warc/CC-MAIN-20220630183616-20220630213616-00529.warc.gz | 961,210,936 | 8,281 | please solve this first question of gay-lussac based problem
Dear student,
Gay Lussac's law called the Law of combining volumes and it states that, The ratio between the volumes of the reactant gases and the products can be expressed in simple whole numbers.
If we write balance chemical equation for reaction of H2 with Cl2. We find that 1 mol of H2 reacts with 1 mol of Cl2 to give 2 moles of HCl.
H 2 (g) + Cl 2 (g) -------> 2HCl (aq)
That is 1 volume of H2 reacts with 1 volume of Clto give 2 volume of HCl.
5.6 L of Cl2 will combine with 5.6 L of H2 and hence 11.2 L of HCl is formed.
Hydrogen will be present in excess, so residual hydrogen will be =6-5.6=0.4 L
Volume of H2 left = 0.4L | 234 | 720 | {"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-2022-27 | latest | en | 0.850444 |
https://whatisconvert.com/8-milliseconds-in-weeks | 1,600,734,260,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400202686.56/warc/CC-MAIN-20200922000730-20200922030730-00182.warc.gz | 713,249,112 | 7,229 | # What is 8 Milliseconds in Weeks?
## Convert 8 Milliseconds to Weeks
To calculate 8 Milliseconds to the corresponding value in Weeks, multiply the quantity in Milliseconds by 1.6534391534392E-9 (conversion factor). In this case we should multiply 8 Milliseconds by 1.6534391534392E-9 to get the equivalent result in Weeks:
8 Milliseconds x 1.6534391534392E-9 = 1.3227513227513E-8 Weeks
8 Milliseconds is equivalent to 1.3227513227513E-8 Weeks.
## How to convert from Milliseconds to Weeks
The conversion factor from Milliseconds to Weeks is 1.6534391534392E-9. To find out how many Milliseconds in Weeks, multiply by the conversion factor or use the Time converter above. Eight Milliseconds is equivalent to zero point zero zero zero zero zero zero zero one three two three Weeks.
## Definition of Millisecond
A millisecond (from milli- and second; symbol: ms) is a thousandth (0.001 or 10−3 or 1/1000) of a second.
## Definition of Week
A week (symbol: wk) is a time unit equal to seven days. It is the standard time period used for cycles of rest days in most parts of the world, mostly alongside—although not strictly part of—the Gregorian calendar. The days of the week were named after the classical planets (derived from the astrological system of planetary hours) in the Roman era. In English, the names are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.
## Using the Milliseconds to Weeks converter you can get answers to questions like the following:
• How many Weeks are in 8 Milliseconds?
• 8 Milliseconds is equal to how many Weeks?
• How to convert 8 Milliseconds to Weeks?
• How many is 8 Milliseconds in Weeks?
• What is 8 Milliseconds in Weeks?
• How much is 8 Milliseconds in Weeks?
• How many wk are in 8 ms?
• 8 ms is equal to how many wk?
• How to convert 8 ms to wk?
• How many is 8 ms in wk?
• What is 8 ms in wk?
• How much is 8 ms in wk? | 495 | 1,894 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2020-40 | longest | en | 0.897114 |
https://arundquist.wordpress.com/2011/09/02/more-brute-force-probability/ | 1,669,576,018,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710417.25/warc/CC-MAIN-20221127173917-20221127203917-00872.warc.gz | 146,227,953 | 30,056 | ## More brute force probability
Last night a tweep of mine posted this:
I thought about it for a while with factorials running through my head but, as more people were commenting that it’s not trivial, I thought I’d try a brute force approach just to see what the answer was.
I’ve blogged about a brute force approach to probability before. The basic idea is that computers are plenty fast these days to just try all combinations of things and count whatever it is you’re looking for.
### My approach
So I scratched my head for a bit to see how to get Mathematica to do the counting for me. My first approach worked so I went with it:
• Make an array with 8 different numbers (orig=Range[8])
• Find all permutations and store them (all=Permutations[orig])
• make a function to check how many characters are in their original location (check[list_]:=Count[list-orig, 0])
• What this does is term-by-term subtract the original array from the test permutation (“list”). If there are any zeros, then there was a digit in the correct place. This function simply counts how many zeros there are.
• Run all the permutations through the function (checklist=check/@all;)
• Note, the semicolon is important because it’s a long list you don’t want to display. You should do the same with the permutation command above
• Check how many of those came up with zero zeros (meaning no digit was in its original place): (total=Count[checklist, 0])
Using that, I got 14,833 permutations out of the 40,320 (or 8!) total where the no digit was in its original place.
### Analytical solution
Professor Wright has since posted his analytical solution. Note that he also has a link to a cool screencast of a different analytical solution. These are very thorough and very cool. I learned a lot working my way through them. I especially like that, if you start to use a lot of letters (or hats or digits or whatever), the number of deranged permutations is given by $\approx \frac{N!}{e}$ and so the probability of finding one is $\approx \frac{1}{e}$. That’s cool!
### Pattern solution
Another excellent contribution to the conversation last night can be seen here:
This was very cool. He did it for 2 and then 3 letters and then just put the pattern he saw into an awesome web page that finds known series that match the pattern. UPDATE: HERE’S HIS BLOG POST ON IT. Check the web page out, it’s very cool.
### Discussion
So what do all these approaches bring to the table. There’s no question that the analytical approaches really make you think clearly about the problem, and allow you to get a result for any number of letters (or hats, digits, . . .). It’s the most thorough and, some would say, satisfying.
However, the analytical approaches are difficult, especially as you think about asking this question to an audience that might not be able to handle some of the probability jargon.
Next, what about the pattern matching way? I think getting students to start seeing patterns is an important goal of mine. It reminds me of teaching differential equations. We want students to say things like “hey, this is the Bessel equation! I know the solutions to that” even when they’re studying a brand new physical system.
Finally, the brute force way. It certainly true that it gives you the answer you’re looking for quite quickly, but is there any more? I think so (hence the blog post 😉 For me, figuring out how to get Mathematica to do what I wanted took a little head-scratching. How do I mathematically determine whether a pattern meets my criteria? Figuring that out was fun, and, I think, could be a useful thing to do with students if you throw a problem like this at them.
Another great thing about the brute force approach is that, once you have the basic code together, it’s easy to ask different questions, some of whom may not have analytical solutions. For example, what if you wanted to calculate how many derangements have two people with the correct hat (Count[checklist, 2] = 7420). Or, how many ways can the second person and one other have the correct hat, or how often do the 4th, 5th, and 6th people (only) have the correct hats? I think it would be fun to work with students in a computer lab doing things like that.
### My son
As I was typing this up, I asked my 11 year old son how he’d do it. I posed it as the hats version to give him context. I told him to do 8 people and he balked a little but I encouraged him to do 2 people (he nailed it). Then I said, how about 3 people. Almost immediately he said “2 ways” with great confidence. I asked him how he did it. He put up three fingers in a triangle with the point at the bottom. He pointed to the bottom “guy” and said he could either move his hat clockwise or counterclockwise, so, two ways. Cool huh?
Professor of physics at Hamline University in St. Paul, MN
This entry was posted in fun, math, mathematica, twitter. Bookmark the permalink.
### 14 Responses to More brute force probability
1. I wrote a blog post about an approach to this problem using integrals. You might find it interesting. http://mathblag.wordpress.com/2010/12/23/counting-with-integrals-2/
• Andy "SuperFly" Rundquist says:
Thanks, David, that’s a really cool way of thinking about things. I love the line about how people don’t usually think about integrals being a way to count things.
2. rhettallain says:
Here is a brute force solution to an algebra problem I did with my daughter using Scratch (from MIT). Actually, this is just a screencast of how to make it.
• Andy "SuperFly" Rundquist says:
This is great. “What’s it called? (I told you before)” “Oh, Brute Force!”. Love it.
3. R. Wright says:
He pointed to the bottom “guy” and said he could either move his hat clockwise or counterclockwise, so, two ways.
Whoa, deep.
4. Pingback: Deranged « Dethorning STEM
5. R. Wright says:
Another great thing about the brute force approach is that… it’s easy to ask different questions, some of whom may not have analytical solutions. For example, what if you wanted to calculate how many derangements have two people with the correct hat…
Actually, if I were to teach the problem of derangements to undergraduates*, and wanted to test whether they really understood my derivation of the solution, this would be a nice tractable little question to do so. I’ll have to keep it in mind. (Your point about questions that don’t have analytical solutions is also well-taken, though.)
* Unfortunately I opted not to cover the problem of derangements in my discrete math class this year. I think the level of difficulty is appropriate for the course, but it’s a bit too time-consuming for a rather non-standard topic.
• Andy "SuperFly" Rundquist says:
It’s funny, I knew that the 2 hats one was likely analytical but I couldn’t quickly come up with one that definitely wouldn’t be analytical. Can you? Thanks again for getting me going on this!
• R. Wright says:
Huh, I guess I forgot to subscribe to comments. Sorry for the delay. To get an ordering in which exactly two people have the right hat, you pick the two who keep their hats and “derange” the other 6 hats. The number of ways to do this is 8C2 times the number of ways can I rearrange 6 letters so that no letter is in its original position: 28 * 265 = 7420.
• R. Wright says:
Also,
How many ways can the second person and one other have the correct hat…
Choose the “one other” person and derange the other 6. There are 8 * 265 = 2120 ways to do this.
…or how often do the 4th, 5th, and 6th people (only) have the correct hats?
Derange the other 5 people. There are 44 ways to do this.
• R. Wright says:
Here’s a derangement-like problem whose analytical solution does not immediately occur to me (but, to be honest, probably exists): If 8 people sit in a row, how many ways can you rearrange their hats so that no one receives a hat from one of their neighbors?
6. This sequence is http://oeis.org/A001883 (if a person cannot get his own hat or his neighbor’s hat) or http://oeis.org/A078480 (if a person can get his own hat but not his neighbor’s hat). The latter sequence has an explicit formula.
• R. Wright says:
That was astoundingly fast. How did you do that? Brute force then OEIS search?
7. Yes. That’s my usual approach to counting problems when the answer isn’t immediately obvious. | 1,971 | 8,335 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2022-49 | latest | en | 0.924348 |
http://nrich.maths.org/public/leg.php?code=-9&cl=3&cldcmpid=4956 | 1,484,636,466,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279489.14/warc/CC-MAIN-20170116095119-00428-ip-10-171-10-70.ec2.internal.warc.gz | 210,602,777 | 4,872 | # Search by Topic
#### Resources tagged with Sets similar to The Mean Problem:
Filter by: Content type:
Stage:
Challenge level:
##### Other tags that relate to The Mean Problem
Subgroups. Groups. Integers. Harmonic mean. Geometric mean. Inverses. Experimental probability. Mean. Number theory. Golden ratio.
### There are 2 results
Broad Topics > Algebra > Sets
### Spot the Card
##### Stage: 4 Challenge Level:
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
### Smith and Jones
##### Stage: 4 Challenge Level:
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not! | 195 | 845 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2017-04 | longest | en | 0.853804 |
https://discourse.mc-stan.org/t/sampling-issues-when-modeling-a-proxy-variable/26431 | 1,713,238,966,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817043.36/warc/CC-MAIN-20240416031446-20240416061446-00740.warc.gz | 179,450,786 | 6,149 | # Sampling issues when modeling a proxy variable
I am trying to model the difference between two variables, y1 and y2:
y1 -y2 = N(\mu, \sigma)
What makes this tricky for me is that both y1 and y2 are measured variables, but the measures are proxies. I don’t have the “true” measurement, but I do have data from a previous study that tells me how the use of that proxy relates to “true” measurement:
proxy = \alpha + \beta * measured + \rho
I wrote a model (below) that treats the “true” measurement as a parameter whose mean is the proxy value and whose standard deviation is \rho from above.
The model compiles and samples but I got several issues related to sampling efficiency, which makes me think I wrote the model wrong. Here’s the model:
data {
int<lower=0> N; // length of both y1_obs and y2_obs
vector[N] y1_obs;
vector[N] y2_obs;
// rho from the above model relating proxy measure to a true measure
real<lower=0> meas_error;
}
parameters {
vector[N] y1_true; // the unobserved true measure of y1
vector[N] y2_true; // the unobserved true measure of y2
real mu;
real<lower=0> sigma;
}
transformed parameters {
vector[N] y_diff = y1_true - y2_true;
}
model {
for (n in 1:N) {
y1_true[n] ~ normal(y1_obs[n], meas_error);
}
for (n in 1:N) {
y2_true[n] ~ normal(y2_obs[n], meas_error);
}
y_diff ~ normal(mu, sigma);
}
These are the errors:
Warning messages:
1: There were 3 chains where the estimated Bayesian Fraction of Missing Information was low. See
https://mc-stan.org/misc/warnings.html#bfmi-low
2: Examine the pairs() plot to diagnose sampling problems
3: The largest R-hat is 1.06, indicating chains have not mixed.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#r-hat
4: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#bulk-ess
5: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess
And this is the R code I used with some reproducible data:
data = list(
N = 200,
meas_error = 2.58,
y1_obs = rnorm(200,8.88,7.21),
y2_obs = rnorm(200,10.33,8.32)
)
stan(file = "diff-model-meas-err.stan",
data = data,
iter = 5000,
warmup = 2000,
chains = 3,
control = list(adapt_delta = 0.99,
max_treedepth = 15)
)
Does anything stand out as a clear error I’m making in thinking about how to generate a “true observed” variable for which each of the values is a distribution determined by the measured proxy value and rho?
Thank you. | 738 | 2,714 | {"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} | 2.71875 | 3 | CC-MAIN-2024-18 | latest | en | 0.837278 |
http://stackoverflow.com/questions/2849045/if-in-prolog/6314926 | 1,419,655,261,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1419447550298.151/warc/CC-MAIN-20141224185910-00011-ip-10-231-17-201.ec2.internal.warc.gz | 86,693,912 | 20,367 | # 'if' in prolog?
Probably a stupid question, but I can't find any documentation anywhere for it. Is there a way to do an if in prolog, e.g. if a variable is 0, then to do some actions (write text to the terminal). An else isn't even needed, but I can't find any implementation of if.
-
See if-then-else from www.learnprolognow.org – adamo Jun 12 '11 at 13:32
Prolog has a builtin `if-then-else` syntax. But it is not declarative to really use it. – CommuSoft Aug 22 at 17:12
A standard prolog predicate will do this.
`````` isfive(5).
``````
will evaluate to true if you call it with 5 and fail(return false) if you run it with anything else. For not equal you use \=
``````isNotEqual(A,B):- A\=B.
``````
Technically it is does not unify, but it is similar to not equal.
Learn Prolog Now is a good website for learning prolog.
``````isEqual(A,A).
``````
-
+1 for enforcing logic programming style instead of imperative one :-) – Agnius Vasiliauskas Aug 14 '12 at 7:53
Yes, there is such a control construct in ISO Prolog, called `->`. You use it like this:
``````( condition -> then_clause ; else_clause )
``````
Here is an example that uses a chain of else-if-clauses:
``````( X < 0 ->
writeln('X is negative. That's weird! Failing now.'),
fail
; X =:= 0 ->
writeln('X is zero.')
; writeln('X is positive.')
)
``````
Note that if you omit the else-clause, the condition failing will mean that the whole if-statement will fail. Therefore, I recommend always including the else-clause (even if it is just `true`).
-
In ISO, the control construct is actually called (;)/2 - if-then-else (7.8.8) because the principal functor is the (;)/2. This is a bit irritating since there is another control construct with the same principal functor: (;)/2 - disjunction (7.8.6). You can see it like this `(if->then;else) == ((if->then);else).` succeeds. – false Feb 17 '12 at 0:29
Prolog predicates 'unify' -
So, in an imperative langauge I'd write
``````function bazoo(integer foo)
{
if(foo == 5)
doSomething();
else
doSomeOtherThing();
}
``````
In Prolog I'd write
``````bazoo(5) :- doSomething.
bazoo(Foo) :- Foo =/= 5, doSomeOtherThing.
``````
which, when you understand both styles, is actually a lot clearer.
"I'm bazoo for the special case when foo is 5"
"I'm bazoo for the normal case when foo isn't 5"
-
I found this helpful for using an if statement in a rule.
max(X,Y,Z) :- ( X =< Y -> Z = Y ; Z = X ).
-
Prolog program actually is big condition for "if" with "then" which prints "Goal is reached" and "else" which prints "No sloutions was found". `A, B`means "A is true and B is true", most of prolog systems will not try to satisfy "B" if "A" is not reachable (i.e. `X=3, write('X is 3'),nl` will print 'X is 3' when X=3, and will do nothing if X=2).
-
Well, the best thing to do is to use the so cold cuts.(symbol for that is `!`).
``````if_then_else(Condition, Action1, Action2) :- Condition, !, Action1.
if_then_else(Condition, Action1, Action2) :- Action2.
``````
This is the basic structure of a condition function.
To exemplify it:
• the `max` function:
```max(X,Y,X):-X>Y,!. max(X,Y,Y):-Y=<X.```
Read more documentation on cuts, but mainly they are like breakpoints.
Ex.: In case the first `max` function returns a true value, the second function is not verified.
PS: I'm fairly new to Prolog, but this is what I found.
-
Not sure why this post was voted down. cold cuts are the most powerful way to handle conditions in prolog. – gaurav.singharoy Jun 2 at 8:49
``````( A == B ->
writeln("ok")
;
writeln("nok")
),
``````
The else part is required
-
It is certainly a good idea to indicate an else-part, but it is not required. – false Jul 7 at 22:03 | 1,088 | 3,712 | {"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} | 2.671875 | 3 | CC-MAIN-2014-52 | latest | en | 0.867645 |
http://www.enotes.com/homework-help/what-answer-question-1-http-postimg-org-image-448369 | 1,386,290,476,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163048688/warc/CC-MAIN-20131204131728-00092-ip-10-33-133-15.ec2.internal.warc.gz | 322,000,168 | 6,847 | Homework Help
# What is the answer for question 1) ? http://postimg.org/image/jjjnw5hzr/ It's all...
Student
Valedictorian
• Up
• 1
• Down
What is the answer for question 1) ?
http://postimg.org/image/jjjnw5hzr/
It's all only one question.
Posted by lkballer24 on August 19, 2013 at 1:46 AM via web and tagged with math
High School Teacher
Valedictorian
• Up
• 0
• Down
`sin^2(x)=1/2`
`sin(x)=+-1/sqrt(2)`
`sin(x)=+-sin(45^0)`
`x=45^0 and 225^0`
2. `cos^2(x)=-cos(x)`
`cos^2(x)+cos(x)=0`
`cos(x)(cos(x)+1)=0`
`either`
`cos(x)=0`
`x=0^0 and 360^0`
`or`
`cos(x)+1=0`
`cos(x)=-1`
`x=180^0`
Please for other two parts repost problems. eNotes rule does not permit us to answer more than one.
Posted by aruv on August 19, 2013 at 3:11 AM (Answer #1) | 297 | 770 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2013-48 | longest | en | 0.817331 |
https://converter.ninja/volume/metric-teaspoons-to-imperial-quarts/269-brteaspoon-to-imperialquart/ | 1,623,528,723,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487586390.4/warc/CC-MAIN-20210612193058-20210612223058-00494.warc.gz | 190,999,667 | 5,457 | # 269 metric teaspoons in imperial quarts
## Conversion
269 metric teaspoons is equivalent to 1.18343455584909 imperial quarts.[1]
## Conversion formula How to convert 269 metric teaspoons to imperial quarts?
We know (by definition) that: $1\mathrm{brteaspoon}\approx 0.00439938496598176\mathrm{imperialquart}$
We can set up a proportion to solve for the number of imperial quarts.
$1 brteaspoon 269 brteaspoon ≈ 0.00439938496598176 imperialquart x imperialquart$
Now, we cross multiply to solve for our unknown $x$:
$x\mathrm{imperialquart}\approx \frac{269\mathrm{brteaspoon}}{1\mathrm{brteaspoon}}*0.00439938496598176\mathrm{imperialquart}\to x\mathrm{imperialquart}\approx 1.1834345558490935\mathrm{imperialquart}$
Conclusion: $269 brteaspoon ≈ 1.1834345558490935 imperialquart$
## Conversion in the opposite direction
The inverse of the conversion factor is that 1 imperial quart is equal to 0.844998141263941 times 269 metric teaspoons.
It can also be expressed as: 269 metric teaspoons is equal to $\frac{1}{\mathrm{0.844998141263941}}$ imperial quarts.
## Approximation
An approximate numerical result would be: two hundred and sixty-nine metric teaspoons is about one point one seven imperial quarts, or alternatively, a imperial quart is about zero point eight four times two hundred and sixty-nine metric teaspoons.
## Footnotes
[1] The precision is 15 significant digits (fourteen digits to the right of the decimal point).
Results may contain small errors due to the use of floating point arithmetic.
Was it helpful? Share it! | 425 | 1,569 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "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} | 3.90625 | 4 | CC-MAIN-2021-25 | latest | en | 0.684601 |
https://physics.stackexchange.com/questions/tagged/doppler-effect | 1,720,977,477,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514635.58/warc/CC-MAIN-20240714155001-20240714185001-00121.warc.gz | 394,906,892 | 52,032 | Skip to main content
# Questions tagged [doppler-effect]
The Doppler effect refers to change in the observed frequency of a wave if the observer and source are in relative motion.
541 questions
Filter by
Sorted by
Tagged with
1 vote
0 answers
14 views
### Confusion about signs of the velocities in Doppler formula
Wikipedia gives the Doppler formula as: $f = \left( \frac{c \pm v_r}{c \pm v_s} \right) f_0$ c is the propagation speed of waves in the medium. $v_r$ is the speed of the receiver relative to the ...
• 5,706
-1 votes
0 answers
16 views
### Doppler effect for multiple sources [closed]
Given the figure below, how can I determine the speed from the two sources given that they both produce a frequency of 1000 Hz, and the speed of sound can be assumed to 340 m/s. The sources are both ...
0 votes
2 answers
40 views
### Doppler shift from a moving reflector and source if only the relative velocity is known?
Suppose there is a device which is producing and listening to sound (sonar), a reflector is moving with respect to device and the velocity of reflector and device with respect to the air is not known, ...
• 910
2 votes
1 answer
74 views
### Doppler Effect and the concept of relative velocity in GR
While reading Sean Carroll's book on General Relativity, I understood that the concept of velocity is ill-defined over large distances in arbitrarily curved manifolds, like the one used to describe ...
• 442
0 votes
1 answer
30 views
### ${}$Doppler shift
If observer is moving and source is at rest then i can treat the scenario with approach in which observer is at rest and source is moving since this is what will be happening according to the observer ...
0 votes
1 answer
47 views
### How does doppler cooling work?
I have trouble understanding how doppler cooling works. I understand that an atom moving towards laser sees the laser light blue-shifted and if the laser frequency is slightly below the atom's ...
1 vote
0 answers
40 views
### Oscillating body and Doppler effect
Say we have a body attached to a spring, oscillating with some frequency $\nu$. This is one of the simplest problems studied in elementary Physics, and yet I've noticed we always study it positioning ...
• 1,631
1 vote
0 answers
67 views
### Relativistic Doppler shift moving source in a circle
I am looking to understand the value for the relativistic doppler shift in the following scenario. We have a source moving in a circular pattern around a center. Now, if the observer would be in the ...
• 21
1 vote
0 answers
21 views
### $I_{\nu}/\nu^{3}$ which is Lorentz invariant is also invariant for cosmological redshift?
$I_{\nu}/\nu^{3}$ is Lorentz invariant, therefore an observed intensity is boosted by $\delta^{3}$, where $\delta$ is the Doppler factor. If the cosmological redshift is same physical process with ...
1 vote
0 answers
27 views
0 votes
3 answers
161 views
### Why do we cool atoms with laser light opposed to normal light?
When we use laser light to cool atoms, we get into some problems, because when atom beam slows down the Doppler shift changes the frequency of light in atom's frame of reference, so they can't ... | 754 | 3,171 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2024-30 | latest | en | 0.919651 |
https://napavalleyartfestival.com/what-is-0-25-in-percentage-update-new/ | 1,653,292,282,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662556725.76/warc/CC-MAIN-20220523071517-20220523101517-00297.warc.gz | 482,168,888 | 31,392 | Home » What Is 0.25 In Percentage? Update New
# What Is 0.25 In Percentage? Update New
Let’s discuss the question: what is 0.25 in percentage. We summarize all relevant answers in section Q&A of website Napavalleyartfestival in category: MMO. See more related questions in the comments below.
## How do you convert 0.25 to a percentage?
Explanation: 0.25=25100=25% You can also use the method of multiplying by 1, with 1 written as 100% 0.25×1. 0.25×100% 25% 22 thg 11, 2016
## What is the percent of 0.25 *?
You can get percentage by multiplying 0.25 with 9.5 i.e. 2.38 percentage.
## What is 0.25 as a?
Answer: 0.25 as a fraction is written as 1/4.
## How do you find 0.25 of a number?
Find the percentage one number is of another Step 1 – Divide. Divide the first number by the number it is a percentage of. ( 15 / 60 = 0.25) This gives us a number (0.25) Step 2 – Multiply. Multiply the number we calculated in step 1 by 100. ( 0.25 * 100 = 25)
## What is 0.45 as a percent?
45% We’ve finished converting our decimal into a percent. 0.45 is equal to 45%.
## Is 0.25 a real number?
It’s written as a ratio of two integers, so it’s a rational number and not irrational. All rational numbers are real numbers, so this number is rational and real. … Type of Decimal Rational or Irrational Examples Terminating Rational 0.25 (or ) 1.3 (or ) Nonterminating and Repeating Rational 0.66… (or ) 3.242424… (or) 1 hàng khác
How To Change Decimal To Fraction
How To Change Decimal To Fraction
## What is 0.25 percent as a fraction in simplest form?
2. What is 0.25% in the fraction form? 0.25% in the fraction form is 0.25/100. If you want you can simplify it further as 1/400.
## How do you write 0.25 as a fraction in lowest terms?
Answer: 0.25 as a fraction would be written as 1/4.
## What is 25 over 100 as a decimal?
0.25 If you divide 25 by 100, you get 0.25, which is a decimal. 17 thg 2, 2022
## How do you find a percentage?
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.
## What is 0.125 as a percent?
125 becomes −12.5% . 23 thg 5, 2016
## What is the decimal 0.125 written as a percent?
12.5% To find the percent of 0.125 we had to multiply its fraction by 100. So, the percentage of 0.125 is 12.5% and the fraction is \[\dfrac{1}{8}\].
## What is 0.4 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.4 to its equivalent percent value 0.004% in no time along with the detailed steps.
## Is 0.25 a terminating decimals?
A terminating decimal, true to its name, is a decimal that has an end. For example, 1 / 4 can be expressed as a terminating decimal: It is 0.25.
## Is 0.125 a rational number?
A rational number is any number that can be written as a ratio between two numbers (hence rational). For example, 1/8 is a rational number, which makes 0.125. 3 thg 2, 2013
## When we change 0.25 to the rational number we get?
The answer is 1\4. 25 thg 8, 2020
## What is 0.125 as a fraction?
1/8 0.125 = 125/1000. We can reduce this to lowest terms by dividing the numerator and denominator by 125 to get the equivalent fraction 1/8. 21 thg 12, 2020
## What’s 1 as a percent?
100% Example Values Percent Decimal Fraction 100% 1 125% 1.25 5/4 150% 1.5 3/2 200% 2 12 hàng khác
## What is 0.8 in a fraction?
4/5 0.8 is the same thing as 8/10, which is the same thing as 4/5.
## Is 0.25 a rational number?
When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number is 0.25 and it has terminating digits. We can also express it in fraction form as 25⁄100. Hence, the given number is a rational number. 17 thg 8, 2021
## How can calculate marks percentage?
To calculate how to compute a student’s percentage of marks in an exam, a student’s total marks should be divided by the maximum marks, and then multiplied by 100. For instance, if a student receives 95 out of 100 in English, 85 out of 100 in Hindi, 75 out of 100 in history. 22 thg 12, 2021
## How do you take percentages off a calculator?
To subtract any percentage from a number, simply multiply that number by the percentage you want to remain. In other words, multiply by 100 percent minus the percentage you want to subtract, in decimal form. To subtract 20 percent, multiply by 80 percent (0.8). 26 thg 7, 2019
## What is .25 percent as a decimal?
25% can be written as the decimal 0.25. The word ‘percent’ means ‘per 100.
## How do you write .25 as a decimal?
To convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25.
## What is 25 over 100 as a percent?
Therefore the fraction 25/100 as a percentage is 25%.
## What is percentage of a number?
In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol “%” or simply as “percent” or “pct.” For example, 35% is equivalent to the decimal 0.35, or the fraction. 35.
## How do you find 1 percent of a number?
To find 1% of something (1/100 of something), divide by 100. Remember how to divide by 100 mentally: Just move the decimal point two places to the left. For example, 1% of 540 is 5.4. And 1% of 8.30 is 0.083.
## What’s my average percentage?
To calculate the average percentage, you need to: Determine the sample sizes corresponding to each percentage. For each percentage, multiply it by its sample size. Add all the numbers obtained in step 2. 8 thg 12, 2021
## What number is 50% of 150?
Percentage Calculator: What is 50 percent of 150? = 75.
## What is 0.1 as a percent?
10% Answer: 0.1 as a percent is 10%. Here, we will express the decimal number 0.1 as a percent.
## What is 1 in 25 as a percent?
Now we can see that our fraction is 4/100, which means that 1/25 as a percentage is 4%.
## How do you turn 1.125 into a percent?
Convert to decimal. Multiply 1.125 by 100 to convert to a percentage. Simplify 1.125⋅100 1.125 ⋅ 100 .
## What is 25 as a percentage of 50?
Percentage Calculator: 25 is what percent of 50? = 50.
## What is 0.15 as a percent?
15% For example, 15% is equivalent to the decimal 0.15.
## What is 0.12 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.12 to its equivalent percent value 0.0012% in no time along with the detailed steps.
## What is 0.02 as a percentage?
What is .05 as a percent? Decimal Percent 0.02 2% 0.03 3% 0.04 4% 0.05 5% 30 thg 11, 2021
## How do you write 0.5 as a percentage?
Multiply 0.5 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number. 50/100 is 50 over 100 and means 50 per 100. 50 “per 100” means 50 “percent” or 50%.
## Is 0.125 a repeating decimal?
For 1/11, k = 2, since 11 divides evenly into 99. Note: There must be two repeating digits in this case (since k=2), and they are: 09. … The Decimal Expansion. of All Fractions (1/d) from 1/2 through 1/70. Fraction Exact Decimal Equivalent or Repeating Decimal Expansion 1 / 8 0.125 72 hàng khác
## Is 0.5 a terminating decimal?
Since the 0.5 can be expressed (written as) as the fraction 1/2, 0.5 is a rational number. That 0.5 is also called a terminating decimal. 7 thg 12, 2021
## How do you calculate terminating decimals?
Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal.
## Is negative 0.125 rational?
It is a rational number. 19 thg 4, 2020
## Is 0.125 a natural number?
0.125 is a terminating decimal, so 0.125 is a rational number. Step 3 Square roots of non-perfect squares are irrational.
## Is 0.3 a rational number?
0.3 is a Rational Number written in Decimal Form 0.3 is neither an Integer nor a Whole number. Integers are like whole numbers, but they also include Negative Numbers (Fractions not allowed). 9 thg 4, 2015
## Is negative 0.25 repeating a rational number?
(I see the decimal 0.25 as repeating since it can be written 0.25000…) Also any decimal number that is repeating can be written in the form a/b with b not equal to zero so it is a rational number.
## Is 0.5 a rational number?
For example, 0.5 is a rational number. It is not a whole number, natural number, or integer, but it can be expressed as 1/2, which a fraction of two other integers: 1 is the numerator and 2 is the denominator. So, 0.5, or 1/2, is a rational number. 23 thg 3, 2021
## Is 0.36 a rational number?
1. The number 36 36 is a perfect square, since 62=36 6 2 = 36 . So √36=6 36 = 6 . Therefore √36 36 is rational.
## What is 1.25 percent as a fraction?
Answer: 1.25 as a fraction is expressed as 5/4.
## What is 0.31 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.31 to its equivalent percent value 0.0031% in no time along with the detailed steps.
## What is 0.24 as a percent?
24% Answer: 0.24 in per cent form is 24%.
## What number is 25 percent of 32?
Percentage Calculator: What is 25 percent of 32? = 8.
0.25 as a Fraction ||Decimal as a Fraction||Express 0.25 in the form of p/q
0.25 as a Fraction ||Decimal as a Fraction||Express 0.25 in the form of p/q
## What is 0.45 as a fraction?
920 We drop the decimal and write the number 45 as the numerator of a fraction. Step 4: So, 0.45=920 as a proper fraction in simplest form.
## What is 48 percent as a fraction?
12/25 Answer: 48% as a fraction in simplest form is 12/25.
## What is 0.16 as a fraction?
4/25 Answer: 0.16 as a fraction in its simplest form is 4/25.
## Is 25 a real number?
Answer: Since, the whole numbers are set of real numbers that includes zero and all positive counting numbers, such as 0,1,2,3,4, etc. Whereas , excludes fractions, negative integers, fractions, and decimals. Therefore, 25 being a part of real number is a whole number. 5 thg 8, 2021
## Why is .25 a rational number?
Answer. 25 is a rational number because it can be expressed as the quotient of two integers: 25 ÷ 1.
## Is 25 a natural number?
25 (twenty-five) is the natural number following 24 and preceding 26.
## How do you calculate 40 percentage marks?
The percentage of marks obtained out of 40 will be (marks obtained×100/40). 8 thg 12, 2020
## How much off is 30 percent?
To take 30 percent off a number: Divide the number by 10. Triple this new number. Subtract your triple from your starting number. 10 thg 3, 2022
## How do you subtract 25 percent from a price?
Percent Off Price Formula Convert 25% to a decimal by dividing by 100: 25/100 = 0.25. Multiply list price by decimal percent: 130*0.25 = 32.50. Subtract discount amount from list price: 130 – 32.50 = 97.50. With the formula: 130 – (130*(25/100)) = 130 – (130*0.25) = 130 – 32.50 = 97.50. 25% off \$130 is \$97.50.
## How much is 20% off?
First, convert the percentage discount to a decimal. A 20 percent discount is 0.20 in decimal format. Secondly, multiply the decimal discount by the price of the item to determine the savings in dollars. For example, if the original price of the item equals \$24, you would multiply 0.2 by \$24 to get \$4.80. 13 thg 3, 2018
## How do you calculate percentage manually?
Finding the percentage For this type of problem, you can simply divide the number that you want to turn into a percentage by the whole. So, using this example, you would divide 2 by 5. This equation would give you 0.4. You would then multiply 0.4 by 100 to get 40, or 40%. 2 thg 11, 2021
## How do I get a percentage from two numbers?
Answer: To find the percentage of a number between two numbers, divide one number with the other and then multiply the result by 100.
## What is the ratio of 25%?
1:3 Following the same logic 25% is 1:3 and not 1:4, else 50% would end up being 1:2 (but 1 in 2 is the proportion and not ratio).
## What is the fraction of 25 percent?
1/4 Answer: 25% as a fraction is 1/4.
## What fraction of decimal is 25%?
1/4 Answer: 25% can be represented as 1/4 in fraction form, and 0.25 in decimal form.
## What is 35 in a decimal?
0.35 Example: To change 75.6% to a decimal, shift the decimal two places left, remove the percent sign and you get the answer of 0.756. The other method is to take the percent total, divide it by 100 and, of course, remove the percent sign. … Table of Conversions. Percent Decimal 25% 0.25 30% 0.30 35% 0.35 40% 0.40 20 hàng khác • 21 thg 4, 2014
## What number is 25 percent of 80?
25 percent of 80 is 20.
## What is a 25 out of 30 grade?
83.33% The percentage score for 25 out of 30 is 83.33%. This is an B grade.
## What number is 25 of 92?
25 percent of 92 is 23.
## What number is 25 percent of 60?
15 Answer: 25% of 60 is 15.
## What number is 40% of 80?
32 Answer: 40% of 80 is 32.
## What is 60 out of 100 as a percentage?
60% Convert the fraction 60/100 to a percentage This implies that 60/100 = 0.6. Then, multiply 0.6 by 100 = 60%. 22 thg 2, 2021
## How do you find 0.5 of a number?
1 Answer 1) Convert that percentage to either fraction or decimal: 0.5%=0.005. 2) Simply multiply your result by the total number. … 3) Therefore 5%of 250=1.25. In this case it is 2.5 because 250100=2.5. We know that the question is asking for 0.5% and NOT 1%. It should be easy enough to know 0.5 is half of 1 . … 2.52=1.25. 21 thg 12, 2016
## How do you find 60 percent of a number?
You have learned that to find 1% of a number means finding 1/100 of it. Similarly, finding 60% of a number means finding 60/100 (or 6/10) of it. 60% of \$700 → 60% × \$700. 60% of \$700 → 0.6 × \$700.
दशमलव को प्रतिशत में बदलने का (ट्रिक ) logon Ko pratishat mein badalne ka Tarika , study 5.6
दशमलव को प्रतिशत में बदलने का (ट्रिक ) logon Ko pratishat mein badalne ka Tarika , study 5.6
## How can I calculate my grades?
Steps for Computing Grades Get the total score for each component. Divide the total raw score by the highest possible score then multiply the quotient by 100%. Convert Percentage Scores to Weighted Scores. … Add the Weighted Scores of each component. … Transmute the Initial Grade using the Transmutation Table.
## How can calculate marks percentage?
To calculate how to compute a student’s percentage of marks in an exam, a student’s total marks should be divided by the maximum marks, and then multiplied by 100. For instance, if a student receives 95 out of 100 in English, 85 out of 100 in Hindi, 75 out of 100 in history. 22 thg 12, 2021
## How do you calculate card grades?
Grade Calculator Example: A. Divide the mark given for each small assignment by the possible mark for each small assignment. B. Add the marks given for each assignment. Then add the possible marks given for each assignment. … C. Multiply the decimal by 100 to calculate the percentage.
## What is a third of 300?
Therefore, the answer is 90. If you are using a calculator, simply enter 30÷100×300 which will give you 90 as the answer. 13 thg 12, 2021
## What percent is 3 out of 29?
10.34% Hence, 10.34% of 29 is 3. So, the correct answer is “10.34%”.
## What is 30 out of 40 as a percentage?
Solution and how to convert 30 / 40 into a percentage 0.75 times 100 = 75. That’s all there is to it!
## What is 0.125 as a percent?
125 becomes −12.5% . 23 thg 5, 2016
## What is 0.25 as a fraction?
1/4 0.25 = 1/4 It is often denoted using the per cent. To convert fraction to a per cent, you just need to multiply the fraction by 100 and reduce it to per cent.
## What is 0.125 as a fraction?
1/8 0.125 = 125/1000. We can reduce this to lowest terms by dividing the numerator and denominator by 125 to get the equivalent fraction 1/8. 21 thg 12, 2020
## What is the percentage of 4 in 25?
What is this? Now we can see that our fraction is 16/100, which means that 4/25 as a percentage is 16%.
## What is 8 25 as a percent?
Solution and how to convert 8 / 25 into a percentage 0.32 times 100 = 32. That’s all there is to it!
## What is 0.04 as a percent?
4% Answer: 0.04 as a percentage is 4%.
## What is 0.4 in a fraction?
2/5 Answer: 0.4 can be written in a fraction as 4/10 or 2/5.
## What is 0.2 as a fraction?
1/5 Answer: 0.2 as a fraction is 1/5.
## What is 25 out of 100 as a percentage?
Therefore the fraction 25/100 as a percentage is 25%.
## What number is 25 percent of 40?
10 Answer: 25% of 40 is 10.
## What is 0.75 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.75 to its equivalent percent value 0.0075% in no time along with the detailed steps.
## What is 0.1 as a percent?
10% Answer: 0.1 as a percent is 10%. Here, we will express the decimal number 0.1 as a percent.
## What is 0.44 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.44 to its equivalent percent value 0.0044% in no time along with the detailed steps.
## What is 0.14 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.14 to its equivalent percent value 0.0014000000000000002% in no time along with the detailed steps.
## What number is 0.45 percent of 80?
Percentage Calculator: What is 0.45 percent of 80? = 0.36.
## What is 0.45 as a percent?
45% We’ve finished converting our decimal into a percent. 0.45 is equal to 45%.
## What is 0.02 as a percentage?
What is .05 as a percent? Decimal Percent 0.02 2% 0.03 3% 0.04 4% 0.05 5% 30 thg 11, 2021
## What is 0.4 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.4 to its equivalent percent value 0.004% in no time along with the detailed steps.
## Is 0.25 a terminating or repeating decimal?
Therefore, 1/4 is terminating and 0.25 is a terminating decimal.
## Is 0.125 terminating or repeating?
Let’s look at the fraction 1/8. In decimal form it is 0.125, which is a terminating decimal. 17 thg 10, 2021
## Is 0.25 a rational number?
When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number is 0.25 and it has terminating digits. We can also express it in fraction form as 25⁄100. Hence, the given number is a rational number. 17 thg 8, 2021
## Is 0.5 Terminating or non terminating?
Terminating decimals: Terminating decimals are those numbers which come to an end after few repetitions after decimal point. Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals.
## Is 0.125 a repeating decimal?
For 1/11, k = 2, since 11 divides evenly into 99. Note: There must be two repeating digits in this case (since k=2), and they are: 09. … The Decimal Expansion. of All Fractions (1/d) from 1/2 through 1/70. Fraction Exact Decimal Equivalent or Repeating Decimal Expansion 1 / 8 0.125 72 hàng khác
## Is 0.5 a terminating decimal?
Since the 0.5 can be expressed (written as) as the fraction 1/2, 0.5 is a rational number. That 0.5 is also called a terminating decimal. 7 thg 12, 2021
## Is 0.125 irrational or rational?
A rational number is any number that can be written as a ratio between two numbers (hence rational). For example, 1/8 is a rational number, which makes 0.125. Also, 1/3 is a rational number which makes 0.333333. 3 thg 2, 2013
## Is 0.125 a natural number?
0.125 is a terminating decimal, so 0.125 is a rational number. Step 3 Square roots of non-perfect squares are irrational.
## Is negative 0.125 rational?
It is a rational number. 19 thg 4, 2020
## Are decimals real numbers?
Therefore, all of these rational and irrational numbers, including fractions, are considered real numbers. Real numbers that include decimal points are known as floating point numbers because the decimal floats within the numbers. Integers or whole numbers cannot be floating point numbers. 15 thg 1, 2014
See also Forwards Im Heavy Backwards Im Not What Am I? New Update
## Is .3 a real number?
The real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers. The set of real numbers is all the numbers that have a location on the number line. Integers …, −3, −2, −1, 0, 1, 2, 3, …
## What’s 0.3 as a percent?
30 % So, 0.3 as a percent is 30 %. We can write in just two steps to calculate any decimal into a percent.
## Is 0.23 a rational number?
Yes, 0.23 and 0.9 are rational numbers. 2 thg 5, 2018
## When we change 0.25 to the rational number we get?
The answer is 1\4. 25 thg 8, 2020
## How do you convert a 0.25 bar to a rational number?
R D Sharma – Mathematics 9 Hence, 0.25 ( bar on 25) is in the form of 25/99 which is in the form of P/Q. 7 thg 6, 2018
## Is 25 a rational number?
The number 25 is a rational number. It is a whole number that can be written as the fraction 25/1.
## IS /- 2 rational or irrational?
2 is a rational number because it can be expressed as the quotient of two integers: 2 ÷ 1.
## Is 1.4142135 a rational number?
Its decimal equivalent is 1.4142135… The decimal never repeats and never terminates. It cannot be written as a ratio of two integers. It is an irrational square root number.
## Is 0.36 repeating a irrational number?
Also any decimal number that is repeating can be written in the form a/b with b not equal to zero so it is a rational number. … Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers. 1 thg 12, 2021
## Can decimals be irrational numbers?
An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point.
## How do you write 0.36 repeating as a fraction?
Answer and Explanation: The repeating decimal 0.36363636. . . is written as the fraction 411 .
## Is 1.25 the same as 25 percent?
Step 1: In the given case Output Value is 1.25. Step 2: Let us consider the unknown value as x. Step 3: Consider the output value of 1.25 = 100%. Step 4: In the Same way, x = 25%. … Nearby Results. 25% of Result 1.25 0.3125 1.26 0.315 1.27 0.3175 1.28 0.32 21 hàng khác
## What is 1 25 as a decimal and percent?
1 / 25 = 0.04. That’s all there is to it.
## Is 1.25 a real number?
1.25 is a rational number. A rational number is any number that can be written as a fraction.
## What is 0.4 percent as a decimal?
Any percentage is a number divided by 100 . So 0.4%=0.4100 . Dividing 0.4 by 100 gives 0.004 . 4 thg 3, 2018
## How do you turn 1.27 into a percent?
Express 1.27 as a percent Multiply both numerator and denominator by 100. 1.27 × 100100. = (1.27 × 100) × 1100 = 127100. Write in percentage notation: 127%
## What is 0.92 to a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.92 to its equivalent percent value 0.0092% in no time along with the detailed steps.
## What is .06 as a percent?
Multiply the decimal 0.06 by 100 to get 6 percent. 24 thg 4, 2017
## What is 0.12 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.12 to its equivalent percent value 0.0012% in no time along with the detailed steps.
## What is 0.96 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.96 to its equivalent percent value 0.0096% in no time along with the detailed steps.
## What number is 25 percent of 80?
25 percent of 80 is 20.
## What number is 25 percent of 60?
15 Answer: 25% of 60 is 15.
## What number of 80% is 45?
Percentage Calculator: What is 80 percent of 45? = 36.
## What is the ratio of 25%?
1:3 Following the same logic 25% is 1:3 and not 1:4, else 50% would end up being 1:2 (but 1 in 2 is the proportion and not ratio).
## What is the decimal of 45%?
0.45 Table of Conversions Percent Decimal 30% 0.30 35% 0.35 40% 0.40 45% 0.45 20 hàng khác • 21 thg 4, 2014
## What is 0.5 As a decimal?
Percent to decimal conversion table Percent Decimal 20% 0.2 30% 0.3 40% 0.4 50% 0.5 20 hàng khác
## What is .24 as a fraction?
This is your decimal form of 24% . Note: To turn a decimal into a percent, simply multiply by 100%. 24100 can be simplified to 625 which is your final fraction form. 22 thg 11, 2015
## How do you write 0.05 as a percentage?
To change a decimal to a percentage, multiply it by 100. For example 0.05 is equivalent to 5%, because 0.05 × 100 = 5. 2 thg 10, 2007
## What is 0.05 as a percent?
5 % Answer: 0.05 as a percent is equal to 5 %
## What is 4/25 as a decimal?
0.16 Answer: 4/25 as a decimal is equal to 0.16.
## What is 0.16 as a percent?
Make use of the Free Decimal to Percent Calculator to change decimal value 0.16 to its equivalent percent value 0.0016% in no time along with the detailed steps.
## What is the simplest form of 4 25?
425 is already in the simplest form. It can be written as 0.16 in decimal form (rounded to 6 decimal places).
## What is .25 as a whole number?
Example Problem Write 25% as a simplified fraction and as a decimal. Simplify the fraction by dividing the numerator and denominator by the common factor 25. Write as a decimal. 25% = = 0.25 You can also just move the decimal point in the whole number 25 two places to the left to get 0.25. Answer 25% = = 0.25 1 hàng khác
## Is 0.5 a natural number?
Real numbers (R), (also called measuring numbers or measurement numbers). This includes all numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or 2.142857. It also includes all the irrational numbers such as π, √2 etc.
## Is sqrt 25 a natural number?
Since 25 is a natural number and the square root of 25 is a natural number (5), 25 is a perfect square. 4 thg 2, 2020
## Is 0.25 a integer number?
The decimal 0.25 is a rational number. It represents the fraction, or ratio, 25/100. Both 25 and 100 are integers.
How do you write 0.25 in fraction form?
How do you write 0.25 in fraction form?
## Is negative 25 a whole number?
Negative numbers are not considered “whole numbers.” All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
## Is negative 25 a real number?
Answer: Since, the whole numbers are set of real numbers that includes zero and all positive counting numbers, such as 0,1,2,3,4, etc. Whereas , excludes fractions, negative integers, fractions, and decimals. Therefore, 25 being a part of real number is a whole number. 5 thg 8, 2021
## How can we write root 25?
The square root of 25 is expressed as √25 in the radical form and as (25)½ or (25)0.5 in the exponent form. The square root of 25 is 5.
## Is 0.4 a real number?
If result’s adequate to zero then the amount may be a integer . The first digit after the decimal point is 4, therefore 0.4 is not a whole number. 1 thg 9, 2021
## What’s special about the number 25?
Manganese has the atomic number of 25. The smallest square that can be written by adding two consecutive squares is 25 (32+42=52). In Portugal, the maximum life sentence is 25 years imprisonment. According to a 2016 World Happiness Report, Panama is the 25th happiest country in the world. 3 ngày trước
Related searches
• 0.25 as a percentage of 100
• 1 25 as a percent
• 0.25 as a percent calculator
• what is 0 25 in percentage excel
• 0 25 as a percent calculator
• 0 2 as a percent
• 1.25 as a percent
• decimal to percent
• 0 125 as a percent
• 0.025 as a percent
• 0 025 as a percent
• 0 25 as a fraction in simplest form
• 0.125 as a percent
• what is 0 25 in percentage form
• 0 25 as a percentage of 100
You have just come across an article on the topic what is 0.25 in percentage. If you found this article useful, please share it. Thank you very much. | 8,294 | 27,862 | {"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-2022-21 | latest | en | 0.891181 |
https://www.ipac.caltech.edu/2mass/releases/second/doc/sec4_8.html | 1,725,993,403,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651303.70/warc/CC-MAIN-20240910161250-20240910191250-00516.warc.gz | 787,553,133 | 3,009 | IV. 2MASS Data Processing
8. Photometric Calibration
a. Photometric Zeropoint Evaluation
The transformation between instrumental and calibrated 2MASS magnitudes applied to all point and extended sources is:
Mcal = Minst + c1 - c2(X-1.0)
where
• c1 is the photometric zeropoint offset (magnitudes)
• c2 is extinction coefficient (magnitudes/airmass)
• X is airmass (sec z)
• Minst is measured instrumental magnitude of star, and
• Mcal is the calibrated magnitude.
Each of the coefficients is a function of wavelength. Note that no color coefficients are included in the 2MASS photometric transformations, so all photometry is reported in the natural "2MASS system."
The photometric zeropoint offsets, c1(J,H,Ks), are evaluated each night at each observatory using the nightly calibration observations. The nightly H and Ks band zeropoints are fit to a constant value that is evaluated from the average difference between the "true" catalog (Mcat) and extinction-corrected instrumental (Minst´) magnitudes for all primary and secondary standards measured during the night:
c1(H,Ks) = < Mcat - Minst´ >
where
Minst´ = Minst - c2(H,Ks)(X-1.0)
The plots of photometric zeropoint offsets vs. survey day number, shown in Section III.1.c, illustrate that the J-band offset varies night-to-night by nearly a factor of two more than the those at H and Ks, and therefore probably changes within a night more than the longer wavelength values. Thus, the nightly J-band zeropoint offset is derived by fitting the differences between catalog and extinction-corrected instrumental magnitudes as a linear function of time (T):
c1(J,T) = c10 + (Mcat - Minst´) * T
where again
Minst´ = Minst - c2(J)(X-1.0).
As an example, Figure 1 and Figure 2 show the the photometric zeropoint offset solutions for the night of 1998 October 11 UT in the north and south, respectively. Each green point in these figures shows the average value of Minst´ from a calibration scan plotted as a function of time (in UT hours), with J-band on the top, H-band in the middle and Ks on the bottom. Each cluster of green points represents the six scans in a calibration observation. The black points between the calibration scan points indicate the zeropoint solution that is applied to the scans of Survey Tiles made at the indicated time. The error bars on the black points represent the RMS uncertainty in the zeropoint solution for the night. The derived zeropoint coefficent solutions for each hemisphere on this night are:
North:
c1(J) = 0.0570 + 0.0003 * T(hr)
c1(H) = 0.0158 + 0.0033
c1(Ks) = 0.0428 + 0.0066
South:
c1(J) = 0.0461 + 0.0024 * T(hr)
c1(H) = -0.0011 + 0.0085
c1(Ks) = 0.0013 + 0.0077
The photometric zeropoint coefficients derived for each night included in the 2MASS Second Incremental Data Release are tabulated in the Scan Information Table (cf II.6.d).
The nightly zeropoint offset coefficents are a measure of atmospheric transparency. Large (more positive) values indicate higher atmospheric transparency and better effective sensitivity. The long-term zeropoint plots shown in Section III.1.c illustrate seasonal variations in the zeropoints. Most pronounced are the transparency drops during the July-August period at Mt. Hopkins, corresponding to the southern Arizona "monsoon" season when atmospheric water vapor content is high.
b. Extinction Coefficients
The atmospheric extinction coefficients (c2 above) used in the nightly calibration solutions are not derived solely from the nights' data. Rather, all calibration observations are combined in a global 2 minimization process to derive internally consistent photometry and long-term averaged extinction coefficients. The extinction coefficients used to calibrate the 2MASS Second Incremental Data Release photometry are:
North:
c2(J) = 0.109 mag/airmass
c2(H) = 0.031 mag/airmass
c2(Ks) = 0.061 mag/airmass
South:
c2(J) = 0.100 mag/airmass
c2(H) = 0.060 mag/airmass
c2(Ks) = 0.080 mag/airmass
c. Calibration Uncertainties
Photometric uncertainties quoted in the 2MASS Second Incremental Data Release Point and Extended Source Catalogs have the contribution of the nightly Photometric Calibration RMS uncertainties incorporated. For the PSC, the calibration uncertainty is combined in quadrature with the measurement errors ("<band>_msig") and other systemmatic terms in the "<band>_msigcom" fields. The uncertainties quoted for all magnitudes in the XSC have the calibration uncertainty combined in quadrature with measurement and other systematic errors.
Figure 1 Figure 2
[Last Update: 2000 February 9; by R. Cutri]
Previous page. Next page. | 1,160 | 4,655 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-38 | latest | en | 0.882665 |
http://2ndskiesforex.com/strategies-for-forex-trading/forex-articles/using-the-ichimoku-cloud-for-reversals/ | 1,371,695,946,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368710115542/warc/CC-MAIN-20130516131515-00017-ip-10-60-113-184.ec2.internal.warc.gz | 1,903,758 | 14,195 | # Using the Ichimoku Cloud for Reversals
Using the Ichimoku Cloud to discover Reversals
One of the amazing things about the Ichimoku Cloud is the actual Cloud or ‘Kumo’ which is something unique wherein nothing like it was created before and nothing sense has come after.The Ichimoku Cloud or Kumo is designed to represent support or resistance but in a different form the western world has seen – to view support and resistance as evolving or dynamic and not static like pivot lines, Fibonacci lines, support lines or trend lines.
To the creator (Goichi Hosada), support and resistance was evolving and really based upon previous price action.Particularly, the highs and lows of previous price action was of great concern to Hosada (along with the opens and closes) which showed levels of rejection where the market would not accept price.The previous highs and lows would also give traders the range where the market was accepting price.
So the real question is ‘how’ does the Ichimoku Cloud or Kumo represent support and resistance?The answer lies in the construction of the Cloud or Kumo.
Kumo Composition
There are two main lines of the Kumo which are referred to as Senkou Span A and Senkou Span B. For the purposes of efficiency, we will refer to them as Span A and Span B. The space or value in between these two lines is what forms the Kumo.
Span A is formed by taking the Tenkan Line and adding it to the Kijun Line (white and red lines respectively from chart above), then dividing that value by 2 and plotting it 26 periods ahead. The formula is;
(Tenkan Line + Kijun Line) / 2 placed 26 periods ahead
Span B is formed by taking the highest high (over the last 52 periods), adding to it the lowest low (over the last 52 periods), dividing that by 2 and plotting that 26 time periods ahead. The formula is;
(Highest High + Lowest Low for the last 52 periods) / 2 and plotted 26 time periods ahead.
Now, before we fully get into the construction of the Kumo, we have to talk about what the Tenkan and Kijun lines are which help to form the ever changing Senkou Span A.
The Tenkan Line or Tenkan Sen (Sen means line in Japanese) is known as the conversion line or turning line is similar to a 9SMA but actually is quite different. Remember a SMA (simple moving average) will smooth out all the data and make it equal but the Tenkan Line will take the highest high and lowest low over the last 9 periods. The explanation for this is Hosada felt price action and its extremes were more important than smoothing any data because price action represented where buyers/sellers entered and directed the market, thus being more important than averaging or smoothing the data out.
As you can see by the chart below, the Tenkan Line is quite different than a 9SMA. Because the TL (Tenkan Line) uses price instead of an averaging or the closing prices, it mirrors price better and is more representative of it. You can see this when the TL flattens in small portions to move with price and its moments of ranging.
The Kijun Line (or Kijun Sen) is known as the datum line, standard line or trend line designed to indicate the overall trend for the instrument or pair. The formula behind it is the same as the Tenkan line using price action and the highest high + lowest low with the only change being in the periods as it does it over the last 26 periods.
Other Notes About the Tenkan and Kijun
As a whole, if the Kijun has been climbing – it means price has been gaining ground for the last month. If it is flat, then it will be the midpoint of the range of price for the last month of price action (or representative of the price equilibrium).
Now that we have uncovered the composition of the Tenkan and the Kijun lines, lets talk about how they form the Senkou Span A.
Going back to its construction:
Span A is formed by taking the Tenkan Line and adding it to the Kijun Line (white and red lines respectively from chart above), then dividing that value by 2 and plotting it 26 periods ahead. The formula is;
(Tenkan Line + Kijun Line) / 2 placed 26 periods ahead
So the Tenkan line (which is the momentum line) and the Kijun line (which is the trend line) that are based upon price action are moving.Their valued added together, divided by 2 and sent 26periods ahead is what forms the Senkou Span A or Span A.So the first portion of the Ichimoku Cloud or Kumo is based upon evolving price action lines which are half momentum, half trend monitoring.When you put these two together, you get the Span A which is always changing based upon the acceleration or deceleration of price based upon how they effect the Tenkan/Kijun lines (and in turn, the Senkou Span A).
The second line is the Senkou Span B which is a little different.Its based solely upon price action, particularly the last 52 candles of whatever time period you are on.If you are working with a daily chart, we are talking about the last 52 days, for a 1hr chart, the last 52 hours of price action.After taking the high and low for the last 52 candle range, it takes their values, divides them in half, and shoots them 26 time periods ahead.
The shading in between is called the Cloud or Kumo.
If the Ichimoku Cloud or Kumo represents support and resistance, then the thicker the Cloud, the thicker the S/R it offers.If price is below the Kumo, it will act as resistance, if price is above the Kumo, it will act as support.The Cloud can take many forms and shapes (virtually infinite) which is what makes it tricky but thick Kumo’s often will reject price and the longer the time frame (4hr, Daily, Weekly), the more powerful the Kumo will act as support or resistance.
Take a look at some examples below.
USDJPY 4hr Charts
Notice how the pair rejects off the really thick Cloud but when it reverses is where the Cloud was the weakest or most thin.
Taking a look at another example, the USDCAD after its initial fall, rejected off a really thick Kumo twice telling us a reversal was less likely.However the Kumo starts to thin out giving us a window to break through the Kumo and likely reversal point.
So the key tactic in both is to look for thinner Cloud formations which offer a window or glimpse into an upcoming reversal.Remember the Kumo is sent 26time periods ahead so you have plenty of warning when the window is opening.If you are in the current trend, the window in the Kumo could be a warning to take some profits or if you are looking for a reversal, then the Cloud offers you a good location and method to time a reversal which is one of the hardest things to do in trading.
Another clue hidden in the Cloud can be the flipping of the Senkou Span A and B which can indicate a reversal but do not always.The other main point is price does not always reject off a thick Kumo so its important to watch price action as well but the Ichimoku Cloud is excellent at spotting and timing reversals. | 1,550 | 6,909 | {"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-2013-20 | latest | en | 0.949737 |
https://www.thestudentroom.co.uk/showthread.php?page=24&t=2029168 | 1,500,808,445,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549424549.12/warc/CC-MAIN-20170723102716-20170723122716-00394.warc.gz | 854,199,493 | 38,706 | You are Here: Home >< Maths
# Mr M’s Edexcel GCSE Mathematics A Higher Linear Paper 1 Answers June 2012 Watch
1. A large number of posts have been removed from this thread due to discussion of the June 13th Calculator exam. Please refrain from discussing ANY Edexcel exam until either 12AM for AM exams or 4.30AM for PM exams. Edexcel exams are taken all over the world, and so by discussing them you are possibly giving other students an advantage over those who have already taken the exam.
2. (Original post by Mr M)
Mr M’s Edexcel GCSE Mathematics A Higher Linear Paper 1 Answers June 2011
1. Questionnaire
a) Suitable table (2 marks)
b) Sample too small OR not representative (1 mark)
2. Paving slabs
a) Yes (he needs 30 slabs) (3 marks)
b) £276.16 (3 marks)
3. Parcels
a) £10 (1 mark)
b) Ed is cheaper than Bill for distances under 20 miles and more expensive for distances over 20 miles. The cost is the same for a distance of 20 miles. (3 marks)
4. Stem and leaf diagram
2 | 9
3 | 1 3 5 6 9
4 | 2 3 3 4 6 8 9
5 | 2 4 5
Key: 2 | 9 = 29 mph (3 marks)
5. Medicine
8 (2 marks)
6. Shortcakes
a) 30 (2 marks)
b) 60 (2 marks)
7. Buses
11.00 a.m. (3 marks)
8. Algebra
a) (1 mark)
b) (2 marks)
c) (2 marks)
9. Rotation
Rotation 180 degrees about (3, 3) (3 marks)
10. Train tickets
Railtickets (65p cheaper) (4 marks)
11. Parallelogram
39 (3 marks)
12. Orange juice
4 (3 marks)
13. Hexagon and octagon
105 degrees (4 marks)
14. Lighthouse and harbour
a) 35 km (1 mark)
b) 110 degrees (1 mark)
c) Position marked 4 cm away on correct bearing (2 marks)
15. Cumulative frequency
a) 170 g (1 mark)
b) Correct box plot (3 marks)
c) Median of group A is higher than that of group B and interquartile range of A is bigger than B or other correct comparisons (2 marks)
16. More algebra
a) (1 mark)
b) (2 marks)
17. Standard form
a) 1 (1 mark)
b) 0.000067 (1 mark)
c) (2 marks)
18. Area of enlarged shape
1.5 (3 marks)
19. Probability tree diagram
a) Missing numbers: 0.6, 0.7, 0.3, 0.7 (2 marks)
b) 0.12 (2 marks)
20. Simultaneous equations
x = 3 and y = -2 (4 marks)
21. Circle theorems
Radius and tangent are perpendicular so angles OBA and ODA are 90 degrees
Angles in a quadrilateral sum to 360 degrees so angles DOB = 130 degrees
Angle BCD = 65 degrees as angle at circumference is half the angle at the centre of the circle (4 marks)
22. Histogram
a) Correct bars (frequency densities 3, 5, 3.6, 1.2) (3 marks)
b) 18 (2 marks)
23. Algebraic fractions
a) (3 marks)
b) (3 marks)
24. Recurring decimal
(3 marks)
25. Cylinder and sphere
r = 3x (3 marks)
26. Graph transformations
a) Translation 3 units in the positive x direction (2 marks)
b) Stretch scale factor 2 in the y direction (2 marks)
hello Mr M, do you have the calculator version of this paper?
3. (Original post by tayyabkhan786)
hello Mr M, do you have the calculator version of this paper?
There is a thread for it. You will just need to search.
4. Is there a ms for the march 2012 calculator paper please?
5. (Original post by vet_hopeful!_worried)
Is there a ms for the march 2012 calculator paper please?
6. Is their an un-official markscheme any-where on the internet where i can view the workings out?
7. where do you get the paper from
8. (Original post by Mr M)
There is a thread for it. You will just need to search.
where can you find the calculator paper
Updated: June 24, 2015
TSR Support Team
We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.
This forum is supported by:
Today on TSR
### Stuck for things to do this summer?
Come and get some inspiration.
Poll
Useful resources | 1,112 | 3,747 | {"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-2017-30 | latest | en | 0.801772 |
https://gmatclub.com/forum/maria-uses-a-recipe-for-36-cupcakes-that-requires-8-cups-of-flour-300713.html?kudos=1 | 1,579,351,865,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250592565.2/warc/CC-MAIN-20200118110141-20200118134141-00485.warc.gz | 460,485,025 | 152,690 | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 18 Jan 2020, 05:49
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12
Author Message
TAGS:
### Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 60463
Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 [#permalink]
### Show Tags
22 Jul 2019, 00:21
00:00
Difficulty:
5% (low)
Question Stats:
90% (00:54) correct 10% (01:06) wrong based on 105 sessions
### HideShow timer Statistics
Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 cups of milk, and 4 cups of sugar. How many cups of milk would Maria require for a batch of 9 cupcakes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9042
Location: United States (CA)
Re: Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 [#permalink]
### Show Tags
11 Aug 2019, 19:23
1
Bunuel wrote:
Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 cups of milk, and 4 cups of sugar. How many cups of milk would Maria require for a batch of 9 cupcakes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Since 9 cupcakes is 1/4 of 36, for 9 cupcakes Maria would need 1/4 of the 12 cups of milk, or 3 cups of milk.
_________________
# Scott Woodbury-Stewart
Founder and CEO
Scott@TargetTestPrep.com
181 Reviews
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.
SVP
Joined: 03 Jun 2019
Posts: 1936
Location: India
GMAT 1: 690 Q50 V34
Re: Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 [#permalink]
### Show Tags
22 Jul 2019, 00:32
Bunuel wrote:
Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 cups of milk, and 4 cups of sugar. How many cups of milk would Maria require for a batch of 9 cupcakes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Given: Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 cups of milk, and 4 cups of sugar.
Asked: How many cups of milk would Maria require for a batch of 9 cupcakes?
Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 cups of milk, and 4 cups of sugar.
=> Maria uses a recipe for 9 cupcakes that requires 2 cups of flour, 3 cups of milk, and 1 cups of sugar.
IMO B
VP
Joined: 14 Feb 2017
Posts: 1364
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 650 Q48 V31
GMAT 6: 600 Q38 V35
GMAT 7: 710 Q47 V41
GPA: 3
WE: Management Consulting (Consulting)
Re: Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 [#permalink]
### Show Tags
04 Aug 2019, 16:48
Don't think is a mixture question. It's more a ratio question.
Flour: Sugar: Milk: Total
Cups: 8 : 4 : 12 : 24
Ratio: 2x: x : 3x : 6x
This produces 36 cupcakes, and we require 12/24 Milk for this mix.
If we want to make 1/4 th of the cupcakes i.e. 9 cupcakes, then we need 1/4th the total number of cups.
1/4 *24 = 6
We then need to maintain the same proportions (proportions) of each part.
Flour: Sugar: Milk: Total
Cups: 2 : 1 : 3 : 6
Milk = (12/24)*6 = 3
Sugar = 4/24 *6 = 1/6*6 = 1
Flour = 8/24*6 = 1/3 *6 = 2
I added the others for reference
_________________
Here's how I went from 430 to 710, and how you can do it yourself:
Re: Maria uses a recipe for 36 cupcakes that requires 8 cups of flour, 12 [#permalink] 04 Aug 2019, 16:48
Display posts from previous: Sort by | 1,320 | 4,197 | {"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-2020-05 | latest | en | 0.878004 |
http://www.mathisfunforum.com/viewtopic.php?pid=250504 | 1,419,654,834,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1419447550298.151/warc/CC-MAIN-20141224185910-00053-ip-10-231-17-201.ec2.internal.warc.gz | 290,274,538 | 6,217 | Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
## #7151 2013-01-27 02:48:03
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
I am just thinking, I would not like to be that guy in Cyprus being strung along by a 1000 mile-long string.
## #7152 2013-01-27 02:51:54
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Cheating is widespread. You will have to deal with it in every relationship from now on.
Remember what you have learned, serve you it can-Yoda
A good maxim is "Hope for the best and expect the worst!"
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7153 2013-01-27 10:50:29
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
Okay, some progress I think.
I've learned more about the situation with her boyfriend. She said that she definitely does not want a relationship with him, and that she's been wanting to break up with him for a while but has been waiting to tell him in person when she goes to Cyprus in the next couple of weeks. That's the reason she hasn't broken up with him yet, apparently.
She also admits that she finds me attractive and wants to get to know me more too. She says she thought she only prefers girls, but in terms of physical attraction, she mentioned that I have a small build and she likes it, so she says she's beginning to think she prefers both genders but perhaps with a slight preference for girls.
## #7154 2013-01-27 10:52:52
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
How will you know that breakup has actually happened?
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7155 2013-01-27 11:09:49
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
Well, I can't possibly know for certain. All I can do is trust that she is telling the truth. How else can I be certain? I cannot go all the way to Cyprus with her.
## #7156 2013-01-27 11:11:57
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
It probably will not matter whether she does unless he makes a trip to England.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7157 2013-01-27 11:21:32
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
Yeah, I was thinking about that, which is why I confirmed with adriana whether or not it was her going to him, or him going to her. I didn't want him to come to London. But from the sounds of it she doesn't really like the guy that much, she's just afraid of his reaction when she breaks up with him. She says she'd much rather be with me.
## #7158 2013-01-27 11:27:23
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Yes, him thousands of miles away is best. I am going to take about a half hour break becuase I am hungry. See you then.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7159 2013-01-27 11:29:09
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
Okay, see you later.
## #7160 2013-01-27 11:43:13
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
I have the soup made I just will be a little slow posting replies.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7161 2013-01-27 11:53:18
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
That is okay, have you recovered yet?
## #7162 2013-01-27 11:54:31
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
I thought I did but I had to go shopping yesterday and had a small relapse. Only lasted a couple of hours.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7163 2013-01-27 11:56:46
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
So you are fine now?
## #7164 2013-01-27 11:58:26
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Almost, except for the surgery. That still bothers me but no more migraine.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7165 2013-01-28 03:13:39
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
I am sorry to hear that. I hope the pain passes soon. My mother is suffering from damage to her teeth but probably not as serious as yours, although she did have to have surgery.
Today I ran into a girl I hadn't seen for a couple of years. I used to have a crush on her 5 years ago but she rejected me. However, when I ran into her, we were both 17/18 and we'd both matured a bit more. She wasn't flirty but she did talk a lot about her life, how her now school was, and how this boy she liked treated her like rubbish. So I comforted her, and we just talked about relationships and things like that. She waited with me for my bus in the rain, and when I had to go she hugged me tight and said she'd love to catch up again sometime, and we exchanged numbers. I really was not expecting this kind of encounter today, just out of nowhere...
## #7166 2013-01-28 07:34:24
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Like rubbish? She must be in heaven.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7167 2013-01-28 07:36:58
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
She was talking about him to me while we walked. I don't know, I guess we are just friends who never got the chance to meet up properly, we used to talk every day a number of years ago through online chat but not much thereafter.
As for adriana we're still talking plenty, at least 30 e-mails per day. And still a fair amount of light flirting.
## #7168 2013-01-28 07:40:34
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Seems like you have a lot on your plate. Careful you do not over indulge.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7169 2013-01-28 07:41:05
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
What do you mean?
## #7170 2013-01-28 07:46:56
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Looks like adriana is going to demand much of your time. She also feels like the jealous type.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7171 2013-01-28 07:52:30
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
Yes, that is a bit of a concern. But really, I think I can afford that for the time being. I have a definite place to read maths at a good university close to home. The only way that would be stopped is if it burnt down, in which case I am also guaranteed a place at another great uni.
She's not really eating into my leisure time, because I don't often do much anyway...
## #7172 2013-01-28 07:54:07
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
Okay, you know best.
You like to go there and stay in the math section?
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline
## #7173 2013-01-28 07:58:13
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
You mean in their library? You have to be a student there to do that, unfortunately I'm not a student yet so I can't... it's in central London so there are lots of bookstores around there (not exactly cheap though). I did join the UCL maths society online though, but then I got an e-mail telling me to go away because I do not even go to UCL.
## #7174 2013-01-28 07:58:53
zetafunc.
Guest
### Re: Linear Interpolation FP1 Formula
Admittedly UCL's maths building is not that good, it is sort of fudged with the student union and pretty claustrophobic. The people are nice though and it's a clean environment.
## #7175 2013-01-28 07:59:37
bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799
### Re: Linear Interpolation FP1 Formula
They will not even let visitors in the library?
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
Offline | 2,896 | 10,874 | {"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-2014-52 | latest | en | 0.970397 |
https://gmatclub.com/forum/in-order-to-protect-its-semi-conductor-industry-taiwan-has-74843.html | 1,529,679,917,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864546.30/warc/CC-MAIN-20180622143142-20180622163142-00404.warc.gz | 599,604,433 | 48,479 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 22 Jun 2018, 08:05
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# In order to protect its semi-conductor industry, Taiwan has
Author Message
Senior Manager
Joined: 19 Nov 2007
Posts: 433
In order to protect its semi-conductor industry, Taiwan has [#permalink]
### Show Tags
Updated on: 16 Jan 2009, 06:50
00:00
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct 100% (00:47) wrong based on 6 sessions
### HideShow timer Statistics
In order to protect its semi-conductor industry, Taiwan has imposed high tariffs on chips from American manufacturers. Nevertheless, the Taiwanese continue to buy a higher number of American chips.
Which of the following helps explain why the Taiwanese continue to buy American chips?
A) American chip sales have increase this year by 25%
B) The high tariffs have created tensions between the two nations
C) American made chips are the best in the world and required for Taiwanese computer manufacturers
D) Taiwanese labor costs are considerably lower than in America
E) The Taiwanese standard of living is far below the U.S
--== Message from GMAT Club Team ==--
This is not a quality discussion. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
_________________
-Underline your question. It takes only a few seconds!
-Search before you post.
Originally posted by vscid on 15 Jan 2009, 20:23.
Last edited by vscid on 16 Jan 2009, 06:50, edited 1 time in total.
Intern
Joined: 16 Mar 2008
Posts: 17
### Show Tags
15 Jan 2009, 20:38
IMO C. Only C has some logic explanation why Taiwanese would continue to buy american chip despite price increase.
VP
Joined: 18 May 2008
Posts: 1181
### Show Tags
15 Jan 2009, 23:53
yes C for me too. Only C gives an explanation y Taiwanese still purchase ameriacn chips.
Senior Manager
Joined: 23 May 2008
Posts: 387
### Show Tags
16 Jan 2009, 00:01
Clear C.........rest every other answer choice is out of scope
Senior Manager
Joined: 02 Nov 2008
Posts: 254
### Show Tags
16 Jan 2009, 01:36
vscid wrote:
In order to protect its semi-conductor industry, Taiwan has imposed high tariffs on chips from American manufacturers. Nevertheless, the Taiwanese continue to buy a higher number of American chips.
Which of the following helps explain why the Taiwanese continue to buy American chips?
A) American chip sales have increase this year by 25%
This is nice information however it has nothing to do with explaining why Taiwan continues to purchase American chips.
B) The high tariffs have created tensions between the two nations
That's real unfortunate and if anything makes the situation more puzzling. Why would Taiwan continue to buy American chips if there tensions between the 2 nations?
C) American made chips are the best in the world and required for Taiwanese computer manufacturers
Bingo! This is a valid reason.
D) Taiwanese labor costs are considerably lower than in America
This would enhance the mystery of why American chips are purchased.
E) The Taiwanese standard of living is far below the U.S
Standard of living between the 2 nations has nothing to do with the increased demand in American chips
Although the OP confused me at first with his SC title, I figured it out and my analysis is above (in red)
Senior Manager
Joined: 19 Nov 2007
Posts: 433
### Show Tags
16 Jan 2009, 06:51
chicagocubsrule wrote:
vscid wrote:
In order to protect its semi-conductor industry, Taiwan has imposed high tariffs on chips from American manufacturers. Nevertheless, the Taiwanese continue to buy a higher number of American chips.
Which of the following helps explain why the Taiwanese continue to buy American chips?
A) American chip sales have increase this year by 25%
This is nice information however it has nothing to do with explaining why Taiwan continues to purchase American chips.
B) The high tariffs have created tensions between the two nations
That's real unfortunate and if anything makes the situation more puzzling. Why would Taiwan continue to buy American chips if there tensions between the 2 nations?
C) American made chips are the best in the world and required for Taiwanese computer manufacturers
Bingo! This is a valid reason.
D) Taiwanese labor costs are considerably lower than in America
This would enhance the mystery of why American chips are purchased.
E) The Taiwanese standard of living is far below the U.S
Standard of living between the 2 nations has nothing to do with the increased demand in American chips
Although the OP confused me at first with his SC title, I figured it out and my analysis is above (in red)
Thanks for pointing that out.
Corrected!
_________________
-Underline your question. It takes only a few seconds!
-Search before you post.
Director
Joined: 01 Aug 2008
Posts: 651
### Show Tags
16 Jan 2009, 12:03
this is easy one....C.
Senior Manager
Joined: 12 Oct 2008
Posts: 491
### Show Tags
17 Jan 2009, 15:23
I guess only C has some meaning......
Intern
Joined: 15 Aug 2008
Posts: 3
### Show Tags
18 Jan 2009, 03:55
seems only C has something to do with stimulus above...
that would be my pick
--== Message from GMAT Club Team ==--
This is not a quality discussion. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: CR-Taiwan [#permalink] 18 Jan 2009, 03:55
Display posts from previous: Sort by
# In order to protect its semi-conductor industry, Taiwan has
Moderators: GMATNinjaTwo, GMATNinja
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 1,576 | 6,743 | {"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-2018-26 | latest | en | 0.917213 |
https://cstheory.stackexchange.com/questions/tagged/dc.distributed-comp?sort=frequent&pageSize=50 | 1,571,690,342,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987787444.85/warc/CC-MAIN-20191021194506-20191021222006-00513.warc.gz | 442,152,924 | 30,341 | The Stack Overflow podcast is back! Listen to an interview with our new CEO.
# Questions tagged [dc.distributed-comp]
Theoretical questions in Distributed Computing
14 questions
Filter by
Sorted by
Tagged with
2k views
### Why have we not been able to develop a unified complexity theory of distributed computing?
The field of distributed computing has fallen woefully short in developing a single mathematical theory to describe distributed algorithms. There are several 'models' and frameworks of distributed ...
910 views
### Correctness proofs of classic Paxos and Fast Paxos
I am reading the "Fast Paxos" paper by Leslie Lamport and get stuck with the correctness proofs of both classic Paxos and Fast Paxos. For consistency, the value $v$ picked by the coordinator in phase ...
572 views
### Infinitely large but locally finite computation problems
This question is inspired by a comment Jukka Suomela made on another question. What are examples of infinitely large but locally finite computation problems (and algorithms)? In other words, what ...
1k views
### Current parallel models for computation
The 1980's gave rise to both the PRAM and the BSP models of parallel computation. It seems that both model's heyday were during the late 80s and early 90s. Are these areas still active in terms of ...
557 views
### Decentralized algorithm for determining influential nodes in social networks
In this paper by Kempe-Kleinberg-Tardos, the Authors propose a greedy algorithms based on submodular functions to determine the $k$ most influential nodes in a graph, with applications to social ...
373 views
### Modern distributed computing book
Lynch's Distributed Algorithms book is a classic but it is from 1996 and rather out of date. Are there any recent distributed computing books that can be used as textbooks for a graduate distributed ...
193 views
### Existence of “colouring matrices”
Edit: there is now a follow-up question related to this post. Definitions Let $c$ and $k$ be integers. We use the notation $[i] = \{1,2,...,i\}$. A $c \times c$ matrix $M = (m_{i,j})$ is said to be ...
413 views
### Is This Scheduling Problem NP-Hard?
The scheduling problem (arising from distributed computing) is defined as a decision problem as follows: Instance: A trace is comprised of $n$ processes histories (denoted \$p_0, p_1, \ldots, p_{n-...
256 views
### Existence of “colouring matrices” — a generalisation
This is a generalisation of the following post: Existence of "colouring matrices". As the base case turned out to be fairly straightforward (in essence, precisely equal to the existence of Sperner ...
179 views
### Confusion about a formal definition of PRAM consistency
I am reading the paper "Consistency in Non-Transactional Distributed Storage Systems" by Paolo Viotti and Marko Vukolić. The authors provide a comprehensive survey of various consistency semantics ...
422 views
### What is “distributed computing” as a field of computer science?
I think it's field that studies distributed systems as described at http://en.wikipedia.org/wiki/Distributed_computing. There are distributed systems such as clusters and grids on top of this field. ...
213 views
### The proof of P2b in Paxos made simple
I am reading Paxos Made Simple. I am quite confused about the proof of P2b. It said We would make the proof easier by using induction on n, so we can prove that proposal number n has value v under ... | 761 | 3,450 | {"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} | 2.65625 | 3 | CC-MAIN-2019-43 | latest | en | 0.928106 |
https://www.teacherspayteachers.com/Browse/Search:intro%20to%20systems%20of%20equations | 1,623,895,790,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487626465.55/warc/CC-MAIN-20210617011001-20210617041001-00227.warc.gz | 932,565,258 | 63,779 | DID YOU KNOW:
Seamlessly assign resources as digital activities
Learn how in 5 minutes with a tutorial resource. Try it Now
You Selected:
Keyword
intro to systems of equations
See All Formats
Other
#### Subjects
Arts & Music
English Language Arts
Foreign Language
Holidays/Seasonal
Math
Science
Social Studies - History
Specialty
For All Subject Areas
#### Resource Types
See All Resource Types
#### All Resource Types
Don't see what you looking for?
Some filters moved to Formats filters, which is at the top of the page.
Results for
# intro to systems of equations
2,970 results
## Introduction to Systems of Equations
Students seem to struggle with systems of equations and I wanted to come up with something fun and visual to help them get the hang of them. This worksheet was the result. It takes simple clip-art pictures and relates them with two equations. The students then have to figure out what the value of
Subjects:
8th - 11th
Types:
## Introduction to Systems of Equations - Guided Notes and Homework
This 4-page lesson contains 2 pages of guided notes and 2 pages of HW. It is part of my Systems of Equations Unit * Click the preview for details! Answer key included! * In this lesson, students will: - Learn the definition of a system of equations - Explore what it means for an ordered pair to be
Subjects:
7th - 10th
Types:
CCSS:
## Intro to Solving System of Equations Foldable
This foldable contains the three methods for solving a system of equations (graphing, substitution, and elimination). Steps and two examples are included for each type. Answer key is attached. Enjoy!
Subjects:
8th - 9th
Types:
## Introduction to Systems of Linear Equations, free, Common Core
Introduce students to real world systems of equations with this activity. Students will create one graph from a table of values and one graph from an equation to create a system of equations. They will interpret the meaning of the solution to the system of equations. I have used this handout as
Subjects:
8th - 9th
Types:
CCSS:
## Introduction to Systems of Equations For Google Drive™
Instructions:Included in this set of digital pages are 3 pages introducing systems of equations. The first page introduces what systems are, and what a solution of a system is. The 2nd and 3rd review types of solutions and has students determine how many solutions each given system has. Colored and
Subjects:
8th - 11th
Types:
## Intro to 8 EEC 7 & 8 - Introduction to Solving Systems of Equations by Graphing
This packet was created with the idea that putting equations in a real world context would make it easier for students to understand the concept of 1 solution, no solution, and infinitely many solutions. The 4 page packet is a great way to introduce systems of equations and solving them through gra
Subjects:
8th
Types:
CCSS:
## Introduction to Systems of Equations Worksheet
Students find the solution to a system of linear equations by graphing; word problems included.What is covered:- Students review identifying slope and y-intercept from a linear equation in slope-intercept form- Students review graphing a linear equation- Students graph four systems of equations, ide
Subjects:
7th - 10th
Types:
CCSS:
## Introduction to Systems of Equations Task Cards (Digital and Print)
These task cards about introducing systems of equations provide a motivating way for your students to practice a variety of skills. I love using the PDF version as stations, homework, or for early-finishers. It's also been a life-saver for distance learning when I can assign the Google Form version
Subjects:
7th - 10th
Types:
## Introduction to Solving Systems of Linear Equations- 3 Tiers
Power point working through 3 levels. Could be broken up into 3 separate files and set up for use in a centers activity. Each level includes a quiz to assess whether or not the student it ready to proceed. If they are not, the student completes the tutorials session before going on. Beginners level
Subjects:
9th
## Intro to Systems of Equations Boom Cards
These BOOM CARDS™ about introducing systems of equations provide a motivating way for your students to practice a variety of skills through fun, interactive activities.This product includes:1. Determining if a coordinate is a solution to a system of equations.2. Determining the value of the solution
Subjects:
7th - 10th
## Intro to Systems of Equations Notes
This guided note sheet is intended for the first day of solving systems. (I originally made this for when I had a sub, but found it to be helpful). This includes what a system is, an example of graphing and how to check. Answers/key points to mention included.
Subjects:
7th - 11th
## Introduction to Systems of Equations Interactive Notebook Guided Notes & Video
Distance Learning Friendly!Your kiddos will love this notes page for Introduction to Systems of Equations! Everything you need to teach and engage your Algebra 1 students for Introduction to Systems of Equations has been organized into this section of notes.(1) Links to instructional videos. Videos
Subjects:
8th - 11th
## Intro to Solving Systems of Equations by Elimination Foldable
This set of solving systems by elimination problems comes complete with easy to follow instructions and 5 examples of solving systems by elimination, all in varying levels of difficulty! Students are encouraged to check their work on every problem!Buyer's Note (Read Before You Buy): Instead of encou
Subjects:
8th - 10th
## Intro to Graphing Systems of Equations Gallery Walk
Students in groups (optional) go around the room from station to station following the set of instructions. At each station students will (individually) graph the equation provided. I have my students in groups so they can check each others work or help each other out. I do this on the first day of
Subjects:
9th
## Intro to Systems of Equations (Hard Copy or Digital)
Introduce Systems of Equations using this real-world example. Students will use prior knowledge and reasoning to determine the better "deal" when trying to save money to buy a calculator. Some students might solve algebraically, create a table, or make a graph. The problem opens up discussion on a p
Subjects:
7th - 12th
Types:
CCSS:
## Introduction to Systems of Equations using Real World Problems
Three different problems, one on each page, allowing students to figure out the systems of equation problems without solving the equations (although I added an extension to each page for the students to try to solve algebraically).
Subjects:
7th - 10th
Types:
## Introduction to System of Linear Equations
The four problems in this document is an excellent activity to introduce system of linear equations using a table of values. The table of values are already created for students to fill in as well as guidelines to help students discover the point of intersection.
Subjects:
7th - 9th
Types:
## Intro to System of Equations Foldable INB
Intro to systems of equations foldable for interactive notebook with answer keys.- Two word problems to get students thinking about systems- Identify if an ordered pair is a solution to the given system
Subjects:
8th - 9th
CCSS:
## Introduction to Solving Systems of Linear Equations with Elimination
My students have always had issues with understanding why we can add two equations together and get the solution to the system. This guided worksheet helps show the students that manipulating the equations will maintain the solution. I like to give this to my students as the work in groups of th
Subjects:
8th - 12th
Types:
## Intro to Systems of Equations (How many solutions?)
Students will convert all equations into slope-intercept form and then graph each system of equations in the corresponding coordinate plane. Students will then need to analyze the equations and graphs for any patterns they many notice. Students will use these patterns to develop rules that help them
Subjects:
7th - 11th
Types:
## Introduction to Systems of Linear Equations Activity
In this activity, students take graphs (printed on transparency film) and lay them on top of graphs on their handout to visualize the solution to the system. They will also check the solution in the equations to verify it works. This works great as a partner activity at the beginning of a unit on
Subjects:
9th
Types:
## Introduction to substitution system of equations
This power point serves to develop a conceptual understanding of solving a system of two equations using substitution. Starting with word problems allows students to have a concrete reference for an abstract concept. The power point also includes some extra word problems to solve as a whole class, s
Subjects:
7th - 9th
CCSS:
## Introduction to Systems of Equations
Printable note sheet
Subjects:
9th - 12th
## Introduction to systems of equations
Introduction to systems (after students have mastered solving for variable in algebraic equations). Incorporates different representations of data.
Subjects: | 1,925 | 9,027 | {"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-2021-25 | latest | en | 0.912013 |
https://csbnews.org/bridge-for-the-improver-by-ron-klinger/?lang=en | 1,712,946,649,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816045.47/warc/CC-MAIN-20240412163227-20240412193227-00013.warc.gz | 166,668,693 | 19,865 | # Bridge for the Improver by Ron Klinger
0
121
2014 Gold Coast Official Site
Q 5 J 9 8 3 2
South opened 1NT and North raised to 3NT. West leads the 3.
Problem 1: Declarer plays the queen from dummy. East covers with the king and South wins with the ace. Who has the ten?
Problem 2: Declarer plays the 5 from dummy, ten from East and South wins with the ace. Who has the king?
Solution 1: If the situation is like this:
Q 5 J 9 8 3 2 K 7 4 A 10 6
or similar, declarer would have played low from dummy to make guarantee two tricks. The ten is very likely to
be with East. Only if South began with 10 doubleton
Solution 2: If the situation were like this:
Q 5 J 9 8 3 2 K 10 4 A 7 6
Declarer would have played the queen from dummy.
South has the king and the position is something like this:
Q 5 J 9 8 3 2 10 7 4 A K 6 | 265 | 833 | {"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-2024-18 | latest | en | 0.958012 |
https://forum.powerscore.com/lsat/viewtopic.php?t=11844&&start=10 | 1,558,926,052,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232260658.98/warc/CC-MAIN-20190527025527-20190527051527-00072.warc.gz | 488,502,243 | 9,615 | ## #19- Nearly all mail that is correctly addressed arrives at
Johnclem
LSAT Master
Posts: 122
Joined: Thu Dec 31, 2015 5:43 pm
Points: 47
Hello,
For the love of God ... How is A wrong ?
This is what I did .
2) correctly addresses Mail would take longer (than 2 business days --> damaged
3) most mail arrives 3 or more business days
My prephrase was that either Most mail is getting damaged or else most mail is not correctly addressed .
Thanks
John
David Boyle
PowerScore Staff
Posts: 853
Joined: Fri Jun 07, 2013 1:25 am
Points: 743
Johnclem wrote:Hello,
For the love of God ... How is A wrong ?
This is what I did .
2) correctly addresses Mail would take longer (than 2 business days --> damaged
3) most mail arrives 3 or more business days
My prephrase was that either Most mail is getting damaged or else most mail is not correctly addressed .
Thanks
John
Hello John,
Your prephrase may be somewhat accurate, and indeed, the second part of it, "most mail is not correctly addressed", is the right answer, D. Therefore, answer A doesn't have to be true.
Hope this helps,
David
ivan
LSAT Novice
Posts: 4
Joined: Mon Sep 19, 2016 3:31 am
Points: 0
2) correcctly addressed AND 2 days damaged
3) we know that most mail 3 or more days after being sent - 2 days
I choose answer D which is a contrapositive of the 1st giagram
but I do not understand why A is incorrect. this is a repeat of the 2nd diagram:
correcctly addressed AND 2 days damaged
Thank you!
Claire Horan
PowerScore Staff
Posts: 310
Joined: Mon Apr 18, 2016 3:03 pm
Points: 237
Hello all,
As a sidenote, please be aware that when statements are limited by words like "some," "most," etc., you may not simply write the formal logic as if these words are not there. If you do, you are likely to get the problem wrong.
It follows that...
Of mail that is correctly addressed, most (more than half) does not take three or more business days.
But most mail (more than half) arrives three or more business days after being sent.
That means there must be a lot of mail that is incorrectly addressed. The "damaged in transit" part is a red herring because that we still have the fact that "nearly all mail (damaged or not) that is correctly addressed arrives at its destination within two business days of being sent. That means only a small amount of the mail that arrives late does so due to being damaged.
nikki.brar
LSAT Novice
Posts: 2
Joined: Tue Jul 11, 2017 5:22 pm
Points: 2
Diagram:
3) most mail arrives 3 + business days after being sent ( mail--(most)--> 3+days after being sent)
Ok so my thought process.. if mail is taking 3 or more days to arrive then its either damaged in transit or maybe its not correctly addressed.. I see this in answers A and D so i eliminate B,C,E..
Now to choose between A and D.
A) says a 'large proportion' of the correctly addressed mail is damaged.. where as the stimulus says NEARLY ALL correctly addressed mail arrives within 2 days and the only case that it correctly addressed mail doesnt come in 2 days is because it got damaged. so NEARLY ALL constitutes a majority.... so if a majority of correctly addressed mail arrives within 2 days, i think that less than a majority or some of the correctly addressed mail is damaged in transit. i dont know if this makes sense, but I eliminate on that basis.
D) i go with this answer because I eliminated A. but I don't really understand the reasoning.
Does this look right? Could someone help with why D is correct?
Nikki
Luke Haqq
PowerScore Staff
Posts: 183
Joined: Thu Apr 26, 2012 2:28 pm
Points: 143
Hi Nikki!
Happy to try to help with seeing why (D) is correct (glad to hear you chose the right answer!).
As I understand this one, that answer comes from what you roughly have in your first diagram--
The last sentence of the stimulus states, "Overall, however, most mail arrives three business days or more after being sent." In other words, we know its the case that ~(2 days). In most cases where mail doesn't arrive in 2 days, we know from the contrapositive, it's because it's incorrectly addressed. And that's another way of saying (D) "A large proportion of mail is incorrectly addressed."
Hope that helps!
bk1111
LSAT Master
Posts: 104
Joined: Sat Apr 22, 2017 10:11 pm
Points: 104
Luke Haqq wrote:Hi Nikki!
Happy to try to help with seeing why (D) is correct (glad to hear you chose the right answer!).
As I understand this one, that answer comes from what you roughly have in your first diagram--
The last sentence of the stimulus states, "Overall, however, most mail arrives three business days or more after being sent." In other words, we know its the case that ~(2 days). In most cases where mail doesn't arrive in 2 days, we know from the contrapositive, it's because it's incorrectly addressed. And that's another way of saying (D) "A large proportion of mail is incorrectly addressed."
Hope that helps!
Hi,
I thought we could not take a contrapositive of "most" or "some" statements. How can we use the reasoning above to logically conclude the answer as D?
LSAT2018
LSAT Master
Posts: 247
Joined: Wed Jan 10, 2018 1:11 am
Points: 248
To clarify, the correct answer (D) is a contrapositive of the first sentence?
Correctly Addressed (Most) → 2 Days
Not 2 Days (Most) → Not Correctly Addressed
3 Days or More (Most) → Not Correctly Addressed
So I take that with modifiers some/most remain unchanged in the contrapositive?
Jonathan Evans
PowerScore Staff
Posts: 681
Joined: Thu Jun 09, 2016 2:12 pm
Points: 570
Location: DFW, Texas
Hey, BK and LSAT2018,
The short answer is that you are correct, BK: you cannot make contrapositives of "some" and "most" statements (Luke has this one wrong unfortunately). There is a rather interesting exception to this rule in formal logic, but it has no bearing on this problem or on the LSAT.
If you wish to read a complete discussion of the rules of making inferences, there is an excellent in depth discussion in Chapter 13 of the Logical Reasoning Bible that helpfully covers what you need to know for the LSAT and omits extraneous information.
For the long answer, let's do a thorough analysis of this problem. I'm going to use a couple shortcuts, substituting "most" for "nearly all" for simplicity sake.
1. MailCorrectly Addressed Arrive in 2 days
2. MailCorrectly Addressed not Arrive in 2 days Damaged
3. Mail not Arrive in 2 days
Let's start by listing some safe assumptions:
Mail Arrive in 2 days OR not Arrive in 2 days
Let's now make whatever immediate inferences we can from each statement. In other words, let's see whether we know anything else from each statement by itself.
1. MailCorrectly Addressed Arrive in 2 days
from this we know that 1'. MailCorrectly Addressed not most not Arrive in 2 days.
2. MailCorrectly Addressed not Arrive in 2 days Damaged
from this we know that 2'. MailCorrectly Addressed not Damaged Arrive in 2 days
This is a conditional statement and thus has a valid contrapositive.
3. Mail not Arrive in 2 days
from this we know that 3'. Mail not most Arrive in 2 days.
Now let's make any possible additive inferences (inferences that are possible by combining more than one statement).
• Can we combine 1 and 2 to make any additive inferences? Not really anything useful. Do we know that a minority of correctly addressed mail is damaged? No, we do not. We know that MailCorrectly Addressed not Arrive in 2 days Damaged but we do not know *MailCorrectly Addressed Damaged not Arrive in 2 days. Notice this is a Mistaken Reversal™ of this conditional statement.
• Can we combine 2 and 3 to make any inferences? Clearly we cannot. The variables in these two statements are completely different, and we are unable to make any useful chains here.
• Can we combine 1 and 3 to make any inferences? Yes! We can do a couple different things here.
Mail MailCorrectly Addressed Arrive in 2 days
but Mail not Arrive in 2 days
Thus, we know that Mail MailnotCorrectly Addressed
Can we conclude that Mail MailnotCorrectly Addressed? Almost. Not quite. We can make a pretty compelling case here that since "almost all" correctly addressed mail is delivered in two days and that most mail is not delivered in two days, then the vast majority of this mail not delivered in two days is incorrectly addressed (not just damaged). Thus, as the vast majority of this group is incorrectly addressed, that would likely represent more than half of all the mail. However, there is some uncertainty because some correctly addressed mail that is damaged arrives in longer than two days.
Fortunately, the LSAT lets us off the hook here! We do know that there is some sizable quantity of mail that is incorrectly addressed. Whether this group is more than half ends up being irrelevant because that's exactly what Answer Choice (D) says! Hooray!
LSAT2018
LSAT Master
Posts: 247
Joined: Wed Jan 10, 2018 1:11 am
Points: 248
The most/large proportion is confusing! If the contrapositives for some/most do not work, how do we arrive at not correctly addressed? Can you comment on the diagrams below?
Not Two Days → Not Correctly Addressed
Mail (Most) → Not Two Days
Mail (Some) → Correctly Addressed (Most) → Two Days
Mail (Most) → Not Two Days → Not Correctly Addressed | 2,316 | 9,250 | {"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-2019-22 | latest | en | 0.945779 |
https://www.geeksforgeeks.org/dot-product-of-vectors-in-r-programming/ | 1,695,836,789,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510319.87/warc/CC-MAIN-20230927171156-20230927201156-00679.warc.gz | 879,994,486 | 37,872 | Open In App
Dot Product of Vectors in R Programming
In mathematics, the dot product or also known as the scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. Let us given two vectors A and B, and we have to find the dot product of two vectors.
Given that,
and,
where,
• i: the unit vector along the x directions
• j: the unit vector along the y directions
• k: the unit vector along the z directions
Then the dot product is calculated as:
Example:
Given two vectors A and B as,
A = 3i + 5j + 4k,
and
B = 2i + 7j + 5k
Dot Product = 3 * 2 + 5 * 7 + 4 * 5 = 6 + 35 + 20 + 61
Computing Dot Product in R
R language provides a very efficient method to calculate the dot product of two vectors. By using dot() method which is available in the geometry library one can do so.
Syntax: dot(x, y, d = NULL)
Parameters:
x: Matrix of vectors
y: Matrix of vectors
d: Dimension along which to calculate the dot product
Return: Vector with length of dth dimension
Example 1:
R
`# R Program illustrating``# dot product of two vectors` `# Import the required library``library``(geometry)` `# Taking two scalar values``a = 5``b = 7` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`
Output:
`[1] 35`
Example 2:
To determine b’s complex conjugate, we utilize the Conj() function. In our example, the Conj() function is provided by the pracma package, which we first install and load. Then, a and b, two complex numbers, are defined. The formula a1 * b1_conjugate + a2 * b2_conjugate +… is used to calculate the dot product of these two vectors, where b_conjugate is b’s complex conjugate.
R
`# Install and load the pracma package``install.packages``(``"pracma"``)``library``(pracma)``# Define two complex numbers``a <- 3 + 1i``b <- 7 + 6i``# Compute the dot product using the conjugate of b``dot_prod <- ``sum``(a * ``Conj``(b))``# Print the result``print``(dot_prod)`
Output:
`[1] 27-11i`
Example 3:
R
`# R Program illustrating``# dot product of two vectors` `# Import the required library``library``(geometry)` `# Taking two simple vectors``a = ``c``(1, 4)``b = ``c``(7, 4)` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`
Output:
`[1] 23`
Example 4:
In the following example let’s take two 2D arrays and calculate the dot product of these two. To create a 2D array in R please refer Multidimensional Array in R.
R
`# R Program illustrating``# dot product of two vectors` `# Import the required library``library``(geometry)` `# Taking two 2D array``vector1 = ``c``(2, 1)``vector2 = ``c``(0, 3)``a = ``array``(``c``(vector1, vector2), dim = ``c``(2, 2))``vector1 = ``c``(4, 2)``vector2 = ``c``(9, 3)``b = ``array``(``c``(vector1, vector2), dim = ``c``(2, 2))` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`
Output:
`[1] 10 9` | 904 | 2,909 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2023-40 | latest | en | 0.82139 |
https://www.clutchprep.com/chemistry/practice-problems/93061/a-solution-is-prepared-by-mixing-0-0300-mole-of-ch2cl2-and-0-0500-mole-of-ch2br2 | 1,611,405,794,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703537796.45/warc/CC-MAIN-20210123094754-20210123124754-00181.warc.gz | 702,838,501 | 36,276 | # Problem: A solution is prepared by mixing 0.0300 mole of CH2Cl2 and 0.0500 mole of CH2Br2 at 25°C. Assuming the solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at 25°C. At 25°C, the vapor pressures of pure CH2Cl2 and pure CH2Br2 are 133 and 11.4 torr, respectively.
###### FREE Expert Solution
Mole Fraction (X) relates the moles of each species in a mixture:
Calculate the mole fraction.
0.0300 mole of CH2Cl2
0.0500 mole of CH2Br2
XCH2Cl2 = 0.375
81% (142 ratings)
###### Problem Details
A solution is prepared by mixing 0.0300 mole of CH2Cl2 and 0.0500 mole of CH2Br2 at 25°C. Assuming the solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at 25°C. At 25°C, the vapor pressures of pure CH2Cl2 and pure CH2Br2 are 133 and 11.4 torr, respectively. | 256 | 834 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-04 | latest | en | 0.83406 |
http://clay6.com/qa/15913/if-overrightarrow-a-and-overrightarrow-b-are-unit-vectors-and-if-vectors-ov | 1,481,155,823,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542288.7/warc/CC-MAIN-20161202170902-00043-ip-10-31-129-80.ec2.internal.warc.gz | 55,168,506 | 27,317 | Browse Questions
# If $\overrightarrow a\;and\:\overrightarrow b$ are unit vectors and if vectors $\overrightarrow c=\overrightarrow a+2\overrightarrow b$ and $\overrightarrow d=5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\;and\:\overrightarrow b$ is ?
Given: $|\overrightarrow a|=|\overrightarrow b|=1$ and $\overrightarrow c\:and\:\overrightarrow d$ are $\perp$.
$\Rightarrow \overrightarrow c.\overrightarrow d=0$
$\Rightarrow(\overrightarrow a+2\overrightarrow b).(5\overrightarrow a-4\overrightarrow b)=0$
$\Rightarrow\:5|\overrightarrow a|^2-8|\overrightarrow b|^2+6\overrightarrow a.\overrightarrow b=0$
$\Rightarrow\:\overrightarrow a.\overrightarrow b=\large\frac{1}{2}$
Angle between $\overrightarrow a\:and\:\overrightarrow b$ is $cos^{-1}\bigg(\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow a||\overrightarrow b|}\bigg)$
$=cos^{-1}\large\frac{1}{2}=\frac{\pi}{3}$ | 283 | 959 | {"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} | 4.09375 | 4 | CC-MAIN-2016-50 | longest | en | 0.175582 |
https://ru.scribd.com/document/27995379/Selangor-Answer-Physics-P3-Trial-SPM-2007 | 1,566,788,424,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027330962.67/warc/CC-MAIN-20190826022215-20190826044215-00394.warc.gz | 610,129,206 | 59,641 | You are on page 1of 5
# PROGRAM PENINGKATAN PRESTASI FIZIK SPM
## JABATAN PELAJARAN SELANGOR 2007
KERTAS 3
PAPER 3
SECTION A
1
(a)(i) 1 Stating the correct manipulated variable.
Real depth // H // Volume of water
(ii) 1 Stating the correct responding variable.
Apparent depth // h
(iii) 1 Stating a correct fixed variable.
Water density / refractive index
(b) 6 Tabulating results of the experiment
1. Labels H and h are shown
2. Correct units for H and h.
3. Minimum two correct readings for h
4. All h readings are correct
5. All h readings are stated to1 decimal place.
H / cm h / cm
4.0 3.1
6.0 4.4
8.0 6.1
10.0 7.5
12.0 9.0
## (c) 5 Plotting the h against H graph
A. Responding variable,h on the y-axis and manipulated
variable, H on the x-axis.
B. Correct units for H and h shown on both axes.
C. The scales on both axes are regular not an odd scale.
D. 5 points plotted correctly (mark not given if not in table).
E. 3 points plotted correctly (mark not given if not in table).
F. Line of best fit.
G. Graph size a minumum of 5x4 (5 boxes on y-axis, 4 boxes
on x-axis).
Bil betul Skor
7 5
5-6 4
3-4 3
2 2
1 1
(d) 1 Stating the correct relationship
h is directly proportional to H // h α H
(e) 1 Stating the correct precaution
Eyes at level with readings on the meter rule (to avoid parallax
error) // Water level is determined at the bottom of the meniscus.
TOTAL 16
1
PROGRAM PENINGKATAN PRESTASI FIZIK SPM
JABATAN PELAJARAN SELANGOR 2007
KERTAS 3
h/ cm Graf h lawan H
10.0
9.0 x
8.0
x
7.0
6.0
x
5.0
x
4.0
3.0
x
2.0
1.0
H/cm
0 2 4 6 8 10 12
2
PROGRAM PENINGKATAN PRESTASI FIZIK SPM
JABATAN PELAJARAN SELANGOR 2007
KERTAS 3
2
(a)(i) 1 V is directly proportional to T // V α T
## (ii) 1 Show on graph with appropriate vertical and/or horizontal line
corresponding to 200 K.
1 37 mm3
## (b)(i) 3 1. Drawing the gradient triangle
Triangle size a minumum of 4 x 3
2. Substitution
(values from student’s triangle)
3. Jawapan dengan unit betul
0.1833 mm3 K- 1 ( Accept answers from 2 to 4 decimal places )
## (ii) 3 1. Explaining your working
2. Substitution
V = (0.1833) x 375
3. Jawapan dengan unit betul
68.74 mm3
## (c) 1 Show on graph with appropriate vertical and/or horizontal line
corresponding to 55 mm3
1 300 K
1 27 oC
JUMLAH 12
3
PROGRAM PENINGKATAN PRESTASI FIZIK SPM
JABATAN PELAJARAN SELANGOR 2007
KERTAS 3
SECTION B
Question 1
(a) 1 Making the right inference
Acceleration depends on mass
(b) 1 Building an appropriate hypothesis
The greater the mass, the greater the acceleration.
(c)(i) 1 Stating the aim of the experiment
To study the relationship between the acceleration
and mass of an object under constant force
(ii) 1 Stating the correct variables
Manipulated variable : Mass, m
Responding variable : Acceleration, a
1 Fixed variable : Force
(iii) 1 List of appropriate apparatus and material
Ruler, A.C. power supply, runway
(iv) 1 Describing set up of the apparatus
## Ticker tape Ticker timer Trolley
Elastic
Friction compensated track
a.c power
supply
## v) Stating the procedure of the experiment
Set up a friction compensated track.
Attach a ticker tape to the trolley and pass the tape
through the ticker timer.
1 Pull the 1 kg trolley down the runway with the
elastic cord kept stretched by the same amount of
force.
1 Calculate acceleration by analysing the ticker tape.
1 Repeat by adding weights to the trolley so that the
mass is 1.5 kg, 2.0 kg, 2.5 kg and 3.0 kg
Record data
Plot an a against m graph // Plot an a against 1/m
graph .
vi) 1 Tabulating data
Show table with m and a as headings
viii) 1 Analysing data **This mark may be
a a given at the last line
for procedure.
or
m 1/m
Total 12
4
PROGRAM PENINGKATAN PRESTASI FIZIK SPM
JABATAN PELAJARAN SELANGOR 2007
KERTAS 3
2
(a) 1 Making the right inference
Resistance depends on the thickness/ cross sectional area/ diameter of
the conductor //
(b) 1 Building an appropriate hypothesis
The greater the thickness/ cross sectional area/ diameter, the greater the
resistance of the conductor//
(c)(i) 1 Stating the aim of the experiment
To study the relationship between the thickness/ cross sectional area/
diameter and the resistance of the conductor.//
(ii) 1 Stating the correct variables
Manipulated variable : thickness/ cross sectional area/ diameter,A
Responding variable : Resistance, R // Potential difference, V
1 Fixed variable : Current, I // Length // Resistivity // Temperature
(iii) 1 List of appropriate apparatus and material
ammeter, voltmeter, rheostat, connecting wires, constantan
wires(s.w.g.24, s.w.g.26, s.w.g. 28, s.w.g. 30, s.w.g.32)
(iv) 1 Describing set up of the apparatus
A
V
Constantan wire
X Y
(v) Stating the procedure of the experiment
Set up the the electrical circuit as shown.
1 Connect a 50 cm constantan wire of size s.w.g.24 between terminal X
and Y.
Adjust the rheostat to get a current of I = 0.5 A on the ammeter.
Record the values of current, I and potential difference,V.
1 Calculate resistance, R of the wire, where R = V
I
1 Repeat by using 50 cm constantan wires of size s.w.g.24, s.w.g.26,
s.w.g.28, s.w.g.30 and s.w.g.32.
Record data
Plot an R against A graph
vi) 1 Tabulating data
Show table with A, I, V and R as headings
viii) 1 Analysing data
R
A or swg
Total 12 | 1,653 | 5,245 | {"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-2019-35 | latest | en | 0.585917 |
https://echo.mpiwg-berlin.mpg.de/ECHOdocuView?tocMode=figures&start=221&viewMode=text_image&ws=1.5&url=/mpiwg/online/permanent/archimedes/salus_mathe_040_en_1667&pn=1034 | 1,723,031,417,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640694449.36/warc/CC-MAIN-20240807111957-20240807141957-00502.warc.gz | 170,805,427 | 5,440 | Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
#### Table of figures
< >
[Figure 221]
[Figure 222]
[Figure 223]
[Figure 224]
[Figure 225]
[Figure 226]
[Figure 227]
[Figure 228]
[Figure 229]
[Figure 230]
[Figure 231]
[Figure 232]
[Figure 233]
[Figure 234]
[Figure 235]
[Figure 236]
[Figure 237]
[Figure 238]
[Figure 239]
[Figure 240]
[Figure 241]
[Figure 242]
[Figure 243]
[Figure 244]
[Figure 245]
[Figure 246]
[Figure 247]
[Figure 248]
[Figure 249]
[Figure 250]
< >
page |< < of 701 > >|
1
ſetled, as neceſſary
in making the Ex
periment.
NIC. In this Propoſition it is affirmed that thoſe Solid Magnitules that hap
pen to be equal in ſpecifical Gravity with the Liquid being lefeat liber
ty in the ſaid Liquid do ſo ſubmerge in the ſame, as that they lie or ap
pear not at all above the Surface of the Liquid, nor yet do they go or ſink to the
Bottom.
For ſuppoſing, on the contrary, that it were poſſible for one of
thoſe Solids being placed in the Liquid to lie in part without the
Liquid, that is above its Surface, (alwaies provided that the ſaid
Liquid be ſetled and undiſturbed,) let us imagine any Plane pro
duced thorow the Center of the Earth, thorow the Liquid, and
thorow that Solid Body: and let us imagine that the Section of the
Liquid is the Superficies A B G D, and the Section of the Solid
Body that is within it the Superſicies E Z H T, and let us ſuppoſe
the Center of the Earth to be the Point K: and let the part of the
ſaid Solid ſubmerged in the Liquid be B G H T, and let that above
be B E Z G: and let the Solid Body be ſuppoſed to be comprized in
a Pyramid that hath its Parallelogram Baſe in the upper Surface of
the Liquid, and its Summity or Vertex in the Center of the Earth:
which Pyramid let us alſo ſuppoſe to be cut or divided by the ſame
Plane in which is the Circumference A B G D, and let the Sections
of the Planes of the ſaid
Pyramid be K L and
K M: and in the Liquid
there be deſcribed a Su
perficies of another
Sphære below E Z H T,
which let be X O P;
and let this be cut by
the Superficies of the Plane: And let there be another Pyramid ta
ken or ſuppoſed equal and like to that which compriſeth the ſaid
Solid Body, and contiguous and conjunct with the ſame; and let
the Sections of its Superficies be K M and K N: and let us ſuppoſe
another Solid to be taken or imagined, of Liquor, contained in that
ſame Pyramid, which let be R S C Y, equal and like to the partial
Solid B H G T, which is immerged in the ſaid Liquid: But the
part of the Liquid which in the firſt Pyramid is under the Super
ficies X O, and that, which in the other Pyramid is under the Su
perficies O P, are equijacent or equipoſited and contiguous, but
are not preſſed equally; for that which is under the Superficies
X O is preſſed by the Solid T H E Z, and by the Liquor that is
contained between the two Spherical Superficies X O and L M
and the Planes of the Pyramid, but that which proceeds accord
ing to F O is preſſed by the Solid R S C Y, and by the Liquid | 977 | 3,022 | {"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-2024-33 | latest | en | 0.864736 |
https://www.physicsforums.com/threads/find-vemf.432178/ | 1,544,422,042,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823318.33/warc/CC-MAIN-20181210055518-20181210081018-00526.warc.gz | 997,945,208 | 12,700 | # Homework Help: Find Vemf
1. Sep 25, 2010
When a battery is connected to a 110.-ohm resistor, the current is 3.98 A. When the same battery is connected to a 400.-ohm resistor, the current is 1.11 A.
Find the emf supplied by the battery and the internal resistance of the battery.
Equations:
Vemf = i*R
I'm not sure how to approach this since you get two voltages (438.7 and 444) from the different resistors.
Should I treat these resistors like they are in the same circuit? In series or in parallel?
2. Sep 26, 2010
### collinsmark
Yes, you'll get two different voltages, by using different resistors, because there is another resistance involved that is always there: the internal resistance of the battery.
(By the way, check your math regarding the voltages you calculated.)
Not the 110 and 400 Ω resistors, no.
But the battery's internal resistance is always there, so yes, the internal resistance is within the circuit in both cases.
What do you think? (Hint: look in your textbook for "internal resistance" of a battery, and the answer should be clear.)
3. Sep 26, 2010 | 278 | 1,090 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2018-51 | latest | en | 0.929403 |
http://www.ccs.neu.edu/home/jaa/CS3800.09F/Homeworks/hw.07.html | 1,369,386,715,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368704433753/warc/CC-MAIN-20130516114033-00009-ip-10-60-113-184.ec2.internal.warc.gz | 389,945,699 | 3,283 | # CS3800 09F: Homework 07
Created: Fri 13 Nov 2009
Assigned: Fri 13 Nov 2009
Due: Mon 23 Nov 2009
## General Instructions
1. Please review the grading policy outlined in the course information page.
2. On the first page of each part of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following
Problem01020304 0506070809...
CreditRCRCRCECRC RCNARCRC...
where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not applicable" (not attempted). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.
3. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
## Specific Instructions
Note: It is quite possible to solve the questions on this assignment in many correct ways. In particular, one can reduce from many undecidable problems to show that any of the languages given below are undecidable; however, choosing the "wrong" reduction will result in a complicated solution.
In the hints that follow, I will describe particularly simple reductions that result in simle solutions. Your solutions need not follow these hints; many correct solutions reducing from different languages exist.
Each hint below corresponds to a matching problem (Hint 1 for Problem 1; Hint 2 for Problem 2, etc.)
1. Reduce from ATM. Your reduction will be similar to the reduction we used to show that REGTM was undecidable: M' will filter its inputs and take one action if the input string is "000" and another if the input string is not.
2. Again, reduce from ATM. Note that |L(M)| >= 2 means that the size of the language accepted by M must be at least two; i.e., M accepts at least two strings. In your reduction, have M' always accept one string (pick your favorite), and let it accept a second (or more)strings if and only if M accepts w.
3. Reduce from ATM. Your reduction will be similar to the reduction we used to show that REGTM was undecidable: M' will filter its inputs and take one action if the input string is of the form 0*1* and another if the input string is not. You may need to "flip" the output bit...
4. Reduce from EINTTM. Think about how you should set k and whether you should flip the output bit or not. This is perhaps the easiest problem on this assignment.
5. Again, reduce from ATM. M' should accept some particular string which is not its own reverse (pick your favorite), and it should accept all other strings if and only if M accepts w. Think about the consequences of such a reduction.
6. This problem is not a reduction in our usual sense. What you need to think about is this: How could you solve ETM using a subroutine which minimizes Turing Machines? If you could do that, then such a subroutine can't exist... So, you have to build a program which solves ETM from the subroutine which minimizes TMs. ETM questions are of the form, "Here's a TM, does it accept the empty language, i.e., no strings?" Suppose I give you a TM which accepts no stings, and you minimize it; what will it look like? Suppose I give you a TM which accepts some strings and you minimize it; what will it look like? Can you tell the difference? If so, you can solve ETM using the subroutine in question...
Describe carefully how you would solve ETM using the subroutine in question, and that in and of itself will demonstrate that the subroutine cannot exist.
## Problems
Required: 4 of the following 6 problems
Points: 25 pts per problem
1. Prove that the following language is undecidable.
L = {<M> | M is a Turing machine, and M accepts the string "000"}
2. Prove that the following language is undecidable.
L = {<M> | M is a Turing machine and |L(M)| >= 2}
3. Prove that the following language is undecidable.
L = {<M> | M is a Turing machine, and L(M) = 0*1*}
4. Prove that the following language is undecidable.
L = {<M1,M2,k> | M1 and M2 are Turing machines, and |L(M1) int L(M2)| >= k}
Here "int" is set intersection.
5. Problem 5.9
6. As we have mentioned in class, an algorithm for minimizing finite automata exists: Given as input a DFA D, the algorithm returns a DFA D' where L(D) = L(D') and D' contains as few states as possible.
Show that no such procedure for minimizing Turing Machines can exist; i.e., show that a procedure which takes as input a Turing Machine and returns as output the minimum equivalent Turing Machine cannot exist.
Hint: We have shown that ETM is undecidable. What is the smallest TM which accepts the empty language? Could you recognize such a TM if it were handed to you? Show how you could solve ETM if you had a procedure for minimizing TMs; thus, such a procedure cannot exist.
Note: This result essentially implies that one cannot write a procedure which takes as input a program and returns as output the smallest equivalent program. Such a procedure could be extremely useful, if it existed; think about the ramifications of such a procedure for the software industry.
jaa@ccs.neu.edu | 1,241 | 5,298 | {"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-2013-20 | latest | en | 0.927126 |
https://www.termpaperwarehouse.com/essay-on/Fin-515/488937 | 1,545,137,102,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376829399.59/warc/CC-MAIN-20181218123521-20181218145521-00527.warc.gz | 1,045,832,603 | 10,894 | # Fin 515
Submitted By amerghaith
Words 603
Pages 3
1. Company A has the opportunity to do any, none, or all of the projects for which the net cash flows per year are shown below. The projects are not mutually exclusive. The company has a cost of capital of 15%. Which should the company do and why? You must use at least two capital budgeting methods. Show your work. Explain your answer thoroughly. | A | B | C | 0 | -300 | -100 | -300 | 1 | 100 | -100 | 100 | 2 | 100 | 100 | 100 | 3 | 100 | 100 | 100 | 4 | 100 | 100 | 100 | 5 | 100 | 100 | 100 | 6 | 100 | 100 | -100 | 7 | -300 | -200 | 0 |
Ans. Here, we accept project B because its NPV > 0 i.e. \$29.35 and IRR>cost of capital. The IRR is 22.90% which is greater than 15%. Rest both the projects has negative NPV.
2. A project requires an initial cash outlay of \$40,000 and has expected cash inflows of \$12,000 annually for 7 years. The cost of capital is 10%. What is the project’s discounted payback period? Show your work.
Ans. 4.26 years
Year | CF | PV | CFxPV | CCF | 0 | 40000 | 1 | 40000 | 40000 | 1 | 12000 | 0.91 | 10909.09 | 29090.91 | 2 | 12000 | 0.83 | 9917.36 | 19173.55 | 3 | 12000 | 0.75 | 9015.78 | 10157.78 | 4 | 12000 | 0.68 | 8196.16 | 1961.61 | 5 | 12000 | 0.62 | 7451.06 | -5489.44 | Discounted Payback Period = 4.26 years |
3. A project requires an initial cash outlay of \$95,000 and has expected cash inflows of \$20,000 annually for 9 years. The cost of capital is 10%. What is the project’s IRR? Show your work.
Ans. IRR = 15.13%
4. A project requires an initial cash outlay of \$60,000 and has expected cash inflows of \$15,000 annually for 8 years. The cost of capital is 10%. What is the project’s payback period? Show your work.
Ans. Payback period = 4 years
5. A project requires an initial cash outlay of \$95,000 and has expected cash inflows of…...
### Similar Documents
#### Fin 515 Week 1
...Week 1 Homework Fin 515 Mini Case a. Why is corporate finance important to all managers? To help Identify and select the corporate strategies and individual projects that adds value to their firm b. Describe the organizational forms a company might have as it evolves from a start-up to a major corporation. List the advantages and disadvantages of each form. Sole Proprietor- The sole proprietor of the business can be held personally liable for the debts and obligations of the business. The risk extends to any liabilities incurred as a result of acts committed by employees of the company. A sole-proprietorship is owned by a single individual who is responsible for the long-term decisions, goals of the company and significant tax advantages. Partnership- partnership is that you don't have to register with your state and pay an often high fee, as you do to establish a corporation or limited liability company. A benefit of a partnership is that it is treated as a pass-through entity. The partnerships are allowed to pass, or file, their share of company profits and losses directly on their personal income tax return. A major disadvantage of doing business as a partnership is that all partners are liable for debts and liabilities. Corporation- the Corporation is a stand-alone entity, which means you are not liable for the assets and debts of the business. Also, the stand-alone entity also separates tax liabilities, which is another advantage. A disadvantage of a......
Words: 1349 - Pages: 6
#### Fin 515
...Week 5 - Project Jonathan Chapman jwchapman12@gmail.com October 2, 2014 Managerial Finance FIN-515-10284 DeVry University Keller Graduate School of Management Professor Hartzog Week 5 – Project 8-23 - Bauer Industries is an automobile manufacturer. Management is currently evaluating a proposal to build a plant that will manufacture lightweight trucks. Bauer plans to use a cost of capital of 12% to evaluate this project. Based on extensive research, it has prepared the following incremental free cash flow projections (in millions of dollars): | Year 0 | Years 1-9 | Year 10 | Revenues | | 100.0 | 100.0 | -Manufacturing expenses(other than depreciation) | | -35.0 | -35.0 | -Marketing expenses | | -10.0 | -10.0 | -Depreciation | | -15.0 | -15.0 | =EBIT | | 40.0 | 40.0 | -Taxes (35%) | | -14.0 | -14.0 | =Unlevered net income | | 26.0 | 26.0 | +Depreciation | | +15.0 | +15.0 | -Increases in net worth capital | | -5.0 | -5.0 | -Capital expenditures | -150.0 | | | +Continuation value | | | +12.0 | =Free cash flow | -150.0 | 36.0 | 48.0 | a. For this base-case scenario, what is the NPV of the plant to manufacture lightweight trucks? NPV=150 + 36 x 1/0.12[1-1/1.12^9] + 48/1.12^10 = \$57.3 million b. Based on input from the marketing department, Bauer is uncertain about its revenue forecast. In particular, management would like to examine the sensitivity of the NPV to the revenue assumptions.......
Words: 494 - Pages: 2
#### Fin 515 Midterm Exam Fin 515 Midterm Exam
...FIN 515 Midterm Exam FIN 515 Midterm Exam Devry - Midterm Exam http://workbank247.com/q/fin-515-midterm-exam-fin-515-midterm-exam/11200 http://workbank247.com/q/fin-515-midterm-exam-fin-515-midterm-exam/11200 CLICK below link for Answer 2015 FIN515 MANAGERIAL FINANCE MIDTERM (NOV-DEC) 1. Question : (TCO G) The firm's equity multiplier measures Question 2. Question : (TCO G) The DuPont Identity expresses the firm's ROE in terms of Question 3. Question : (TCO B) A certain investment will pay \$10,000 in 20 years. If the annual return on comparable investments is 8%, what is this investment currently worth? Show your work. Question 4. Question : (TCO B) You take out a 5 year car loan for \$20,000. The loan has a 5% annual interest rate. The payments are made monthly. What are the monthly payments? Show your work. Question 5. Question : (TCO B) Someone leases a car with the following terms: monthly payment, five year term, 5% annual interest rate, initial value of the lease is \$35,000, and value at the end of the lease is \$10,000. What are the monthly payments? Show your work. Question 6. Question : (TCO B) An accident victim has received a structured settlement. According to the terms of the agreement, the victim will receive \$10,000 per year at the end of each year for the next 15 years. Additionally, the victim will receive \$20,000 in 10 years. The victim believes they could get 7% annually on an investment they could make if they had all the money now. What would......
Words: 1098 - Pages: 5
#### Fin 515 Week 4
...A++PAPER;http://www.homeworkproviders.com/shop/fin-515-week-4/ FIN 515 WEEK 4 FIN 515 WEEK 4, Fin 515 Week 4 Weekly Problems and Midterm Exam Prob 7-2 – Prob 7-4 – Prob 7-5 –Prob 9-2 –Prob 9-4 – Prob 9-4 – Prob 9-5 – Prob 9-6 – Prob 9-7 FIN 515 Week 4 : Business Valuation and Stock Valuation - Exam 1. (TCO A) Which of the following statements is CORRECT? (Points : 10) 2. (TCO G) Which of the following statements is CORRECT? (Points : 10) 3. (TCO G) LeCompte Corp. has \$312,900 of assets, and it uses only common equity capital (zero debt). Its sales for the last year were \$620,000, and its net income after taxes was \$24,655. Stockholders recently voted in a new management team that has promised to lower costs and get the return on equity up to 15%. What profit margin would LeCompte need in order to achieve the 15% ROE, holding everything else constant? (Points : 10) 4. (TCO B) You want to buy a new sports car three years from now, and you plan to save \$4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the third deposit, three years from now? (Points : 10) 5. (TCO B) You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? Years: 0 1 2 3 4 |-----------|--------------|--------------|--------------| CFs: \$0 \$1,000 \$2,000 \$2...
Words: 394 - Pages: 2
#### Fin 515 Midterm Exam Answers
...FIN 515 Midterm Exam Answers https://hwguiders.com/downloads/fin-515-midterm-exam-answers FIN 515 Midterm Exam Answers Question 1. (TCO G) The firm’s asset turnover measures: Question 2. (TCO G) If Moon Corporation has an increase in sales, which of the following would result in no change in its EBIT margin? Question 3. (TCO B) You plan on retiring in 20 years. You currently have \$275,000 and think you will need \$1,000,000 to retire. Assuming you don’t deposit any additional money into the account, what annual return will you need to earn to meet this goal? Question 4. (TCO B) You take out a 4 year car loan for \$18,000. The loan has a 4% annual interest rate. The payments are made monthly. What are the monthly payments? Show your work. Question 5. (TCO B) You currently have \$10,000 in your retirement account. If you deposit \$500 per month and the account pays 5% interest, how much will be in the account in 10 years? Show your work. Question 6. (TCO B) You have a two children, A and B. Child A is not going to college but is working in a business to learn the ropes. Child A plans on opening a business someday. Child B is attending college. You put a certain amount of money into an account. From this account, Child B will receive \$2,000 per month for the next four years. Whatever is left at that time will go to Child A to help start the business. You want Child A to receive \$96,000 at that time. The account pays 7% annually, compounded monthly. How much money do you......
Words: 567 - Pages: 3
#### Fin 515 Midterm Exam Solution
...FIN 515 Midterm Exam Solution http://www.homework-bank.com/downloads/fin-515-midterm-exam-solution/ FIN 515 Midterm Exam Solution Question 1. (TCO G) The firm's asset turnover measures: Question 2. (TCO G) If Moon Corporation has an increase in sales, which of the following would result in no change in its EBIT margin? Question 3. (TCO B) You plan on retiring in 20 years. You currently have \$275,000 and think you will need \$1,000,000 to retire. Assuming you don’t deposit any additional money into the account, what annual return will you need to earn to meet this goal? Question 4. (TCO B) You take out a 4 year car loan for \$18,000. The loan has a 4% annual interest rate. The payments are made monthly. What are the monthly payments? Show your work. Question 5. (TCO B) You currently have \$10,000 in your retirement account. If you deposit \$500 per month and the account pays 5% interest, how much will be in the account in 10 years? Show your work. Question 6. (TCO B) You have a two children, A and B. Child A is not going to college but is working in a business to learn the ropes. Child A plans on opening a business someday. Child B is attending college. You put a certain amount of money into an account. From this account, Child B will receive \$2,000 per month for the next four years. Whatever is left at that time will go to Child A to help start the business. You want Child A to receive \$96,000 at that time. The account pays 7%......
Words: 569 - Pages: 3
#### Fin 515 Uop, Fin 515 Phoenix, Fin 515 Uophelp, Fin 515 Week 3, Fin 515 Individual Assignment , Fin 515 Learning Team Assignment, Fin 515 Product, Fin 515 a Graded , Fin 515 Summary, Fin 515 Study Guide, Fin 515
...FIN 515 UOP, FIN 515 Phoenix, FIN 515 UOPhelp, FIN 515 Week 3, FIN 515 Individual Assignment , FIN 515 Learning team Assignment, FIN 515 Product, FIN 515 A Graded , FIN 515 Summary, FIN 515 Study Guide, FIN 515 Questions , FIN 515 Answered , FIN 515 Solution, FIN 515 Final Guide, FIN 515 Final Exam, FIN 515 A++ Work, FIN 515 A Graded, FIN 515 Homework, FIN 515 help, FIN 515 week 1 DQ, FIN 515 week 2 DQ, FIN 515 week 3DQ, FIN 515 week 4 DQ, FIN 515 week 5DQ, FIN 515 week 6 DQ, FIN 515 week 1 Assignment, FIN 515 week 2 Assignment, FIN 515 week 3Assignment, FIN 515 week 4 Assignment, FIN 515 week 5 Assignment, FIN 515 All Individual and Learning Team Assignments, FIN 515 Full Course , FIN 515 Whole Class FIN 515 Entire Solution, FIN 515 University of Phoenix Learning Team Assignment, FIN 515 Checkpoint, FIN 515 All Weeks , FIN 515 Week 1-5, FIN 515 Axia College, FIN 515 online class, FIN 515 week 3DQ, FIN 515 week 4 DQ, FIN 515 week 5DQ, FIN 515 Syllabus, FIN 515 Version, FIN 515 Week 1, FIN 515 Week 2, FIN 515 Week 3, FIN 515 Week 4, FIN 515 Week 5, FIN 515 week 1 DQ, FIN 515 week 2 DQ,, FIN 515 week 2 Assignment, FIN 515 week 3Assignment, FIN 515 week 4 Assignment, FIN 515 Week 1-6, FIN 515 Assignment, FIN 515 DQs, FIN 515 Week, FIN 515 Complete Course, FIN 515 Entire Class, FIN 515 Whole Tutorial, FIN 515 Work, FIN 515 final Project, FIN 515 Material, FIN 515 tutorial, FIN 515 Complete......
Words: 408 - Pages: 2
#### Fin 515 Week 4
...FIN 515 WEEK 4 A+ Graded Tutorial Available At: http://hwsoloutions.com/?product=fin-515-week-4 Visit Our website: http://hwsoloutions.com/ Product Description PRODUCT DESCRIPTION FIN 515 WEEK 4, Fin 515 Week 4 Weekly Problems and Midterm Exam Prob 7-2 – Prob 7-4 – Prob 7-5 –Prob 9-2 –Prob 9-4 – Prob 9-4 – Prob 9-5 – Prob 9-6 – Prob 9-7 FIN 515 Week 4 : Business Valuation and Stock Valuation – Exam 1. (TCO A) Which of the following statements is CORRECT? (Points : 10) 2. (TCO G) Which of the following statements is CORRECT? (Points : 10) 3. (TCO G) LeCompte Corp. has \$312,900 of assets, and it uses only common equity capital (zero debt). Its sales for the last year were \$620,000, and its net income after taxes was \$24,655. Stockholders recently voted in a new management team that has promised to lower costs and get the return on equity up to 15%. What profit margin would LeCompte need in order to achieve the 15% ROE, holding everything else constant? (Points : 10) 4. (TCO B) You want to buy a new sports car three years from now, and you plan to save \$4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the third deposit, three years from now? (Points : 10) 5. (TCO B) You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? Years: 0......
Words: 406 - Pages: 2
#### Fin 515 Full Course Project
...FIN 515 FULL COURSE PROJECT To purchase this visit following link: http://www.activitymode.com/product/fin-515-full-course-project/ Contact us at: SUPPORT@ACTIVITYMODE.COM FIN 515 FULL COURSE PROJECT FIN 515 Full Course Project Week 5 – ProjectComplete the Problem 11-7 “New-Project Analysis” (p. 460) and detail your work in the answer to each question in a Word document named “FIN515_W5_Project_yourname.” The project is graded and worth 35 points. Submit your assignment to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/”Due Dates for Assignments & Exams” for due date information. Week 7 – Project Complete the Problem 13-10 Corporate Valuation on pages 551-552 in a Word document named “FIN515_W7_Project_yourname”. Show the details of your calculation/work in your answer to the Problem. Submit your project to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/”Due Dates for Assignments & Exams” for due date information. Activity mode aims to provide quality study notes and tutorials to the students of FIN 515 Full Course Project in order to ace their studies. FIN 515 FULL COURSE PROJECT To purchase this visit following......
Words: 885 - Pages: 4
#### Fin 515 Potential Instructors / Tutorialrank.Com
...FIN 515 Entire Courses (DEVRY) For more course tutorials visit www.tutorialrank.com Tutorial Purchased: 4 Times, Rating: A+ FIN 515 Week 1-7 All Discussion Questions (DEVRY) FIN 515 Week 1 Homework assignments (DEVRY) FIN 515 Week 2 Homework Assignment (DEVRY) FIN 515 Week 3 Homework Assignment (DEVRY) FIN 515 Week 4 Homework Assignment (DEVRY) FIN 515 Week 4 Midterm Exam (DEVRY) FIN 515 Week 5 Homework Assignment (DEVRY) FIN 515 Week 5 Project (DEVRY) FIN 515 Week 6 Homework Assignment (DEVRY) FIN 515 Week 7 Homework Assignment (DEVRY) FIN 515 Week 7 Project (DEVRY) FIN 515All Homework Assignments, DQs Midterm and Final Exam (DEVRY) -------------------------------------------------- FIN 515 Week 1 Homework assignments (DEVRY) For more course tutorials visit www.tutorialrank.com Tutorial Purchased: 2 Times, Rating: A+ Complete the following graded homework assignment in a Word document named “FIN 515_Homework1_yourname." Show the details of your calculations/work in your answer to the problems. • Mini Case (p. 45) • Problems (p. 79) o 2-6 Statement of Retained Earnings o 2-7 Corporate Tax Liability (calculate tax liability and AT income) o 2-9 Corporate After-Tax Yield (muni, corp, PS) -------------------------------------------------- FIN 515 Week 1-7 All Discussion Questions (DEVRY) For more course tutorials visit www.tutorialrank.com Tutorial Purchased: 1 Times, Rating: A+ Week 1 DQ 1 Capital Formation Week......
Words: 849 - Pages: 4
#### Fin 515 Academic Success-Snaptutorial.Com
...FIN 515 Entire Course For more classes visit www.snaptutorial.com Week 1 Homework Problems and Mini Case Week 2 Homework Assignment; Problems Week 3 Homework Assignment; Problems Week 3 Homework Problems; 5-1, 5-2, 5-6 Week 4 Homework Problems page 297, 371 Week 4 Midterm; Business Valuation and Stock Valuation Week 5 Homework Problem10-8,10-9,11-2,11-3 Week 5 Project Case 11-7-New-Project Analysis Week 6 Homework Problem12-1,13-2,13-3,13-4 Week 6 Test Correct Answers Week 7 Homework Problem 16 - 1 onward 16 – 5 Week 7 Project; The financial statements of Lioi Steel Fabricators (Problem 2 and Problem 3 Final Excel)> Week 8 Final Exam (Answers with explanation) ---------------------------------------------------------------- FIN 515 Week 1 Homework assignment For more classes visit www.snaptutorial.com Week 1 Homework Assignment Complete the following graded homework assignment in a Word document named “FIN 515_Homework1_yourname." Show the details of your calculations/work in your answer to the problems. • Mini Case (p. 45) • Problems (p. 79) o 2-6 Statement of Retained Earnings o 2-7 Corporate Tax Liability (calculate tax liability and AT income) o 2-9 Corporate After-Tax Yield (muni, corp, PS) ---------------------------------------------------------------- FIN 515 Week 1-7 All Discussion Questions For more classes visit www.snaptutorial.com Week 1 DQ 1 Capital Formation Week 1 DQ 2 Financial......
Words: 562 - Pages: 3
#### Fin 515 Full Course Project
...FIN 515 Full Course Project Purchase here http://homeworkonestop.com/FIN%20515/fin-515-full-course-project Product Description Week 5 - ProjectComplete the Problem 11-7 "New-Project Analysis" (p. 460) and detail your work in the answer to each question in a Word document named "FIN515_W5_Project_yourname." The project is graded and worth 35 points. Submit your assignment to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/"Due Dates for Assignments & Exams" for due date information. Week 7 - Project Complete the Problem 13-10 Corporate Valuation on pages 551-552 in a Word document named "FIN515_W7_Project_yourname". Show the details of your calculation/work in your answer to the Problem. Submit your project to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/"Due Dates for Assignments & Exams" for due date information. FIN 515 Full Course Project Purchase here http://homeworkonestop.com/FIN%20515/fin-515-full-course-project Product Description Week 5 - ProjectComplete the Problem 11-7 "New-Project Analysis" (p. 460) and detail your work in the answer to each question in a Word document named "FIN515_W5_Project_yourname." The project is graded and......
Words: 713 - Pages: 3
#### Fin 515 Full Course Project
...FIN 515 Full Course Project Purchase here http://homeworkonestop.com/FIN%20515/fin-515-full-course-project Product Description Week 5 - ProjectComplete the Problem 11-7 "New-Project Analysis" (p. 460) and detail your work in the answer to each question in a Word document named "FIN515_W5_Project_yourname." The project is graded and worth 35 points. Submit your assignment to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/"Due Dates for Assignments & Exams" for due date information. Week 7 - Project Complete the Problem 13-10 Corporate Valuation on pages 551-552 in a Word document named "FIN515_W7_Project_yourname". Show the details of your calculation/work in your answer to the Problem. Submit your project to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/"Due Dates for Assignments & Exams" for due date information. FIN 515 Full Course Project Purchase here http://homeworkonestop.com/FIN%20515/fin-515-full-course-project Product Description Week 5 - ProjectComplete the Problem 11-7 "New-Project Analysis" (p. 460) and detail your work in the answer to each question in a Word document named "FIN515_W5_Project_yourname." The project is graded and worth 35......
Words: 713 - Pages: 3
#### Fin 515 Full Course Project
...FIN 515 Full Course Project Purchase here http://homeworkonestop.com/FIN%20515/fin-515-full-course-project Product Description Week 5 - ProjectComplete the Problem 11-7 "New-Project Analysis" (p. 460) and detail your work in the answer to each question in a Word document named "FIN515_W5_Project_yourname." The project is graded and worth 35 points. Submit your assignment to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/"Due Dates for Assignments & Exams" for due date information. Week 7 - Project Complete the Problem 13-10 Corporate Valuation on pages 551-552 in a Word document named "FIN515_W7_Project_yourname". Show the details of your calculation/work in your answer to the Problem. Submit your project to the Dropbox located on the silver tab at the top of this page. For instructions on how to use theDropbox, read these Step-by-Step Instructions or watch this Dropbox Tutorial. See Syllabus/"Due Dates for Assignments & Exams" for due date information. FIN 515 Full Course Project Purchase here http://homeworkonestop.com/FIN%20515/fin-515-full-course-project Product Description Week 5 - ProjectComplete the Problem 11-7 "New-Project Analysis" (p. 460) and detail your work in the answer to each question in a Word document named "FIN515_W5_Project_yourname." The project is graded and worth 35......
Words: 1247 - Pages: 5
#### Fin 515 Bright Tutoring/ Fin515Dotcom
...FIN 515 Course Project 1 and 2 For more course tutorials visit www.fin515.com This Tutorial contains Week 3 Course Project (3 Sets) Week 6 Course Project (2 Sets) FIN 515 Entire Course For more course tutorials visit www.fin515.com This tutorial doesnt contain Final Exam Guide FIN 515 Week 1 DQ 1 Accounting Versus Finance FIN 515 Week 1 DQ 2 Financial Analysis FIN 515 Week 1 Quiz FIN 515 Week 1 Quiz (New) FIN 515 Week 1 Problem Set FIN 515 Week 2 DQ 1 TVM Pass-a-Problem FIN 515 Week 2 DQ 2 Assumptions of the TVM Model FIN 515 Week 2 Quiz FIN 515 Week 2 Problem Set FIN 515 Week 3 DQ 1 Examples of Capital Expenditure From Your Industry FIN 515 Week 3 DQ 2 Capital Budgeting Terms and Considerations FIN 515 Week 3 Course Project 1 (3 Papers) FIN 515 Week 3 Quiz FIN 515 Week 3 Problem Set FIN 515 Week 4 DQ 1 Market Value of a Stock Versus DDM Value FIN 515 Week 4 DQ 2 Differences in YTM of Real Life Bonds FIN 515 Week 4 Midterm FIN 515 Week 4 Problem Set FIN 515 Week 5 DQ 1 Calculating WACC for a Real Firm FIN 515 Week 5 DQ 2 Finding Stock Values for Real Stocks Using Beta and the SML FIN 515 Week 5 problem Set FIN 515 Week 5 Quiz FIN 515 Week 6 DQ 1 Examples of Real Agency Problems and How They Could Have Been Prevented FIN 515 Week 6 DQ 2 The Role of Financial Managers in Ethical Corporate Governance FIN 515 Week 6 Problem Set FIN 515 Week 6 Course Project 2 (2 Different Projects) FIN 515 Week 7 DQ 1 Industry Approaches to......
Words: 642 - Pages: 3 | 6,669 | 24,812 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2018-51 | latest | en | 0.88035 |
https://timefliesedu.com/2018/02/07/real-life-examples-of-solids-of-revolution-and-cross-sections/ | 1,685,338,137,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224644683.18/warc/CC-MAIN-20230529042138-20230529072138-00522.warc.gz | 650,589,268 | 37,261 | # Real-life Examples of Solids of Revolution and Cross-Sections
I get so much out of creating lessons. When you deeply understand a concept, you can talk about real-life situations and the math behind it. I’ve never thought about it until now, but a revolving door is a perfect example of a solid of revolution. Taking a rectangle and revolving it around a pole, creates a cylinder. What a beautiful example!
The last time I was at an AP Calculus seminar, I learned that another awesome example of a solid of revolution is a honeycomb decoration used at parties. These are perfect examples because you can see the 2-D version before it is rotated. This is exactly what we want students to know. What does the 2-D version become with you rotate it? If they can visualize that, then they get it!
Here is something fun I did in my class recently. Students cut out a shape and taped it onto a straw. Students had a blast! Some students took video!
Another concept that goes hand-in-hand with 3-D figures is the idea of cross-sections. Everytime we slice an orange, apple, or a loaf of bread, we have created a cross-section. In Algebra 2 and Pre-Calculus, we discuss cross-sections of cones. Depending on how you slice the cone, you can get a circle, an ellipse, a parabola or a hyperbola.
A great hands-on activity for cross sections is to have the students create a shape out of play-doh. Take a piece of dental floss and slice the object horizontally, vertically or even at an angle. Be sure and have them make predictions before they perform the experiment! Students with phones can take a before and after picture so that other students can see.
I enjoyed creating my Intro to 3-D Figures resource. It’s amazing how after teaching math for many years, that I can still pick up valuable insights and ideas. Math is infinite. There is no end to what you can learn! Check out both resources below. They are the same except one is a printable and the other is a digital Google Forms format!
Intro to 3-D Figures | 442 | 2,015 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2023-23 | latest | en | 0.948153 |
http://www.acemyhw.com/projects/8155/Mathematics/invertible-matrices-logical-equivalence | 1,503,304,336,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107744.5/warc/CC-MAIN-20170821080132-20170821100132-00474.warc.gz | 479,666,069 | 5,425 | # Project #8155 - Invertible matrices - logical equivalence
Write a brief essay (suggested length of 1–2 pages) in which you do the following:
Justify that the ten statements are logically equivalent to the statement “The n × n matrix A is invertible.”
(a) A is an invertible matrix.
(b) A is row equivalent to the n × n identity matrix.
(c) A has n pivot positions.
(d) The equation Ax = 0 has only the trivial solution.
(e) The equation Ax = b has at least one solution for each b in Rn
(f) The columns of A span Rn
(g) The linear transformation x Ax maps Rn onto Rn.
(h) There is an n × n matrix C such that CA = I.
(i) There is an n × n matrix D such that AD = I.
(j) The columns of A form a basis of Rn.
This does not have to be a Þ b, aÞ c, aÞ d, etc.However all statements must connect in some way.Example aÞ bÞ cÞ dÞ eÞ fÞ gÞ hÞ iÞ jÞ a.
Subject Mathematics Due By (Pacific Time) 06/22/2013 09:00 pm
TutorRating
pallavi
Chat Now!
out of 1971 reviews
amosmm
Chat Now!
out of 766 reviews
PhyzKyd
Chat Now!
out of 1164 reviews
rajdeep77
Chat Now!
out of 721 reviews
sctys
Chat Now!
out of 1600 reviews
sharadgreen
Chat Now!
out of 770 reviews
topnotcher
Chat Now!
out of 766 reviews
XXXIAO
Chat Now!
out of 680 reviews
All Rights Reserved. Copyright by AceMyHW.com - Copyright Policy | 392 | 1,319 | {"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-2017-34 | latest | en | 0.837658 |
https://discuss.leetcode.com/topic/70422/easy-understand-2-pointers-java-solution | 1,516,433,721,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084889473.61/warc/CC-MAIN-20180120063253-20180120083253-00521.warc.gz | 671,858,898 | 8,338 | # Easy Understand 2 pointers Java solution
• We keep two pointers, 1st for normal for loop to iterate through the array.
2nd is to track the position of first 0 in the array.
Keep exchanging non zero value with first 0 till the end of loop.
``````public class Solution {
public void moveZeroes(int[] nums) {
int index=-1;//index to track 1st 0 in the array
int count = 0;
for(int i=0;i<nums.length;i++){
if(index==-1&&nums[i]==0){ index = i;}//find 1st 0 for the 1st time only
if(index!=i &&nums[i]==0){count++;}//count the number consecutive 0
if(index!=-1&&i>index&&nums[i]!=0){
nums[index] = nums[i];
nums[i]=0;
index = i;
index = i-count;//need to move back 'count' times to to the position of first 0
}
}
}
}
``````
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 239 | 820 | {"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-2018-05 | latest | en | 0.7781 |
http://www.tutorsglobe.com/homework-help/physics/simple-lattices-75513.aspx | 1,553,334,311,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202781.33/warc/CC-MAIN-20190323080959-20190323102959-00017.warc.gz | 373,841,770 | 8,546 | #### Simple lattices, Physics tutorial
Introduction:
The most highly symmetrical lattices that take place naturally are the cubic structure. These are, thus, of some practical interest and as well give useful simple examples that assist in visualizing the more general cases. Around 90% of metallic crystal structure crystallizes into three (3) densely packed crystal structures vis-a-vis Body-Centered Cubic cell (BCC), Face-Centered Cubic cell (FCC) and Hexagonal Close-Packed (HCP).
Definition of Simple lattices:
The simple lattices are crystalline solids which comprise of a small group of atoms (that is, unit cells) that includes unique characteristics.
Simple lattices:
The simple lattices encompass the given elementary properties:
1) Effective number of atoms or unit cell, 'Z' that states the number of atom per primitive cell
2) Atomic radius, 'R' generally defines in terms of the lattice constant (that is, length of a side of unit cell), 'a'.
3) Nearest neighbor distance that defines the closest distance between the atomic centers.
4) Coordinate number that defines the number of nearest neighbor of the atom.
5) Atomic Packing Fraction (APF) stated as the fraction of volume in a crystal structure which is occupied through atoms.
The simple cubic lattice:
The simple cubic unit cell is a cube (that is, all sides of the similar length and all face perpendicular to one other) having an atom at each and every corner of the unit cell.
The unit cell fully explains the structure of the solid that can be regarded as an almost endless repetition of the unit cell.
Simple or primitive cubic lattice (sc or cubic-P) consists of one lattice point at the each and every corner of the unit cell. It consists of unit cell vectors a = b = c and interaxial angels α = β = γ = 90°.
The volume of the unit cell is readily computed from its shape and dimensions. This computation is specifically simple for a unit cell that is cubic. In this illustration, the atoms are in contact with each other all along the edges of the unit cell. Therefore the side of the unit cell consists of a length of 2r, where 'r' is the radius of an atom.
The simple cubic lattice consists of basis vectors a1 = ai, a2 = aj, a3 = ak and the unit cell is a simple cube. The simplest crystal based on this lattice consists of single atoms at the lattice points. Each and every atom consists of six identical nearest neighbors.
Some of the metals adopt the simple cubic structure because of inefficient use of space. The density of a crystalline solid is associated to its 'percent packing efficiency'. The packing efficiency of a simple cubic structure is only around 52%. (That is, 48% is empty space!)
% Packing Efficiency = (Volume of atoms in a unit cell/Volume of unit cell) x 100 %
Body-Centered cubic Lattice:
Body centered cubic or BCC signifies to a crystal structure in which the atoms are positioned at the corners of a cubic cell having one atom at the cell center position.
The body-centered cubic unit cell is a cube (that is, all sides of the similar length and all face perpendicular to one other) with an atom at each and every corner of the unit cell and an atom in the center of the unit cell.
The unit cell fully illustrates the structure of the solid which can be considered as an almost endless repetition of the unit cell.
The volume of the unit cell is readily computed from its shape and dimensions. This computation is particularly simple for a unit cell that is cubic. In case of the body-centered cubic unit cell, the atoms lying all along the main diagonal of the cube are in contact with one other. Therefore the diagonal of the unit cell consists of a length of 4 r, where 'r' is the radius of an atom.
Atoms, obviously, don't have well-defined bounds, and the radius of an atom is rather ambiguous. In the context of crystal structures, the diameter (2r) of an atom can be stated as the center-to-center distance between two atoms packed as tightly altogether as possible. This gives an effective radius for the atom and is at times termed as the atomic radius.
A more challenging job is to find out the number of atoms which lie in the unit cell. As illustrated above, an atom is centered on each and every corner and in the middle of the unit cell. The atom at the center of the unit cell lies entirely in the unit cell. The atoms positioned on the corners, though, exist partially within the unit cell and specifically outside the unit cell. In finding out the number of atoms within the unit cell, one should count only that part of an atom that in reality lies in the unit cell.
The density of solid is the mass of all the atoms in the unit cell divided by the volume of the unit cell.
The packing efficiency of a 'BCC' lattice is considerably higher than that of the simple cubic: 69.02%
The higher coordination number and packing efficiency signify that this lattice employs space more efficiently than the simple cubic.
The bcc lattice encompass alkali metals like Na, Li, K, Rb, Cs, magnetic metals like Cr and Fe, and refractory metals like Nb, W, Mo, Ta.
Face-Centered Cubic Lattice:
The face-centered cubic unit cell is the cube (that is, all sides of the similar length and all face perpendicular to one other) having an atom at each and every corner of the unit cell and an atom positioned in the middle of each and every face of the unit cell.
Face-centered cubic lattice (that is, fcc or cubic-F), similar to all lattices, consists of lattice points at the eight corners of the unit cell plus additional points at the centers of each face of the unit cell. It consists of unit cell vectors a = b = c and interaxial angles α = β = γ = 90°.
The unit cell fully explains the structure of the solid that can be regarded as an almost endless repetition of the unit cell.
The volume of the unit cell is readily computed from its shape and dimensions. This computation is particularly simple for a unit cell that is cubic. In case of the face-centered cubic unit cell, the atoms lying all along the diagonal of each face are in contact with one other. Therefore the diagonal of each face consists of a length of 4r, where 'r' is the radius of an atom.
Atoms, obviously, don't have well-defined bounds, and the radius of an atom is rather ambiguous. In the context of crystal structures, the diameter (2r) of an atom can be stated as the center-to-center distance among the two atoms packed as tightly together as possible. This gives an effective radius for the atom and is at time termed as the atomic radius.
A more challenging job is to find out the number of atoms which lie in the unit cell. As illustrated above, an atom is centered on each and every corner and in the middle of each face of the unit cell. None of such atoms lies fully in the unit cell. Each and every atom exists partly within the unit cell and partly outside the unit cell. In finding out the number of atoms within the unit cell, one should count only that part of an atom which in reality lies in the unit cell.
The significant characteristic of a crystal structure is the nearest distance among the atomic centers nearest-neighbor distance) and for the face-centered cubic this distance is a/√2.
The density of a solid is the mass of all the atoms in the unit cell divided by the volume of the unit cell.
FCC systems contain an APF (that is, Atomic packing factor of 0.74, the maximum packing for a system in which all the spheres contain equal diameter).
Hexagonal Close-Packed (HCP):
Assume that you are given a large number of tennis balls and asked to pack them altogether in the most efficient manner. What is the most efficient packing strategy? One could toss all the balls altogether in a box and shack the box to induce the balls to settle. The resultant packing of the balls is termed as a random closest-packed structure. Not shockingly it is not the most efficient approach to pack the tennis balls.
However there are a variety of factors which affect how atoms pack altogether in crystals, atoms usually search for the most efficient packing structure in order to maximize the intermolecular attractions. Metals give the simplest packing case, because these atoms can usually be regarded as the uniform spheres.
The two most efficient packing arrangements are the hexagonal closest-packed structure (hcp) and the cubic closest-packed structure (ccp).
In case of a hexagonal closest packed structure, the third layer consists of the similar arrangement of spheres as the first layer and covers all the tetrahedral holes. As the structure repeats itself after each and every two layers, the stacking for hcp might be illustrated as 'a-b-a-b-a-b'. The atoms in a hexagonal closest packed structure efficiently engage 74% of space whereas 26% is the empty space.
In a crystal, the atoms are arranged in a regular repeating model. The smallest repeating unit is termed as the unit cell. The whole structure can be reconstructed from the knowledge of the unit cell. The unit cell is characterized through three lengths and three angles. The quantities a and b are the lengths of the sides of the base of the cell and γ is the angle among these two sides. The quantity c is the height of the unit cell. The angles α and β illustrate the angles between the base and the vertical sides of the unit cell.
In the hexagonal closest-packed structure, a = b = 2r and c = 4(2/3)1/2 r, here r is the atomic radius of the atom. The sides of the unit cell are perpendicular to the base, therefore α = β = 90o. The base consists of a diamond (hexagonal) shape corresponding by γ = 120o.
Coordination number and APF for HCP are precisely similar as those for FCC: 12 and 0.74 correspondingly.
The hcp structure is extremely common for the elemental metals, comprising: Beryllium, Cadmium, Magnesium, Titanium, Zinc and Zirconium
Closed-packed Structures:
The arrangement in a cubic closest packing as well efficiently fills up 74% of space. Similar to the hexagonal closest packing, the second layer of spheres is positioned onto of half of the depressions of the first layer. The third layer is fully different than those first two layers and is stacked in the depressions of the second layer, therefore covering all of the octahedral holes. The spheres in the third layer are not in line with such in layer A, and the structure doesn't repeat until a fourth layer is added. The fourth layer is similar as the first layer; therefore the arrangement of layers is 'a-b-c-a-b-c'.
In crystal, the atoms are arranged in a regular repeating model. The smallest repeating unit is termed as the unit cell. The whole structure can be reconstructed from knowledge of the unit cell. The unit cell is characterized through three lengths and three angles. The quantities a and b are the lengths of the sides of the base of the cell and γ is the angle among these two sides. The quantity c is the height of the unit cell. The angles α and β illustrate the angles between the base and the vertical sides of the unit cell.
In cubic closest-packed structure, a = b = c = 2 (2)1/2 r, here r is the atomic radius of the atom. The sides of the unit cell are all mutually perpendicular, therefore α = β = γ = 90o. The unit cell for the cubic closest-packed structure is the face-centered cubic unit cell (fcc).
Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)
Expand your confidence, grow study skills and improve your grades.
Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.
Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with a tutor at www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology. Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.
Free to know our price and packages for online physics tutoring. Chat with us or submit request at info@tutorsglobe.com
2015 ©TutorsGlobe All rights reserved. TutorsGlobe Rated 4.8/5 based on 34139 reviews. | 2,640 | 12,325 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2019-13 | latest | en | 0.896166 |
https://gradebuddy.com/doc/2140905/homework-3/ | 1,586,335,965,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371810807.81/warc/CC-MAIN-20200408072713-20200408103213-00137.warc.gz | 485,749,167 | 13,312 | # UMD CMSC 250 - Homework #3 (2 pages)
Previewing page 1 of 2 page document
View Full Document
# Homework #3
Previewing page 1 of actual document.
View Full Document
View Full Document
## Homework #3
173 views
Other
Pages:
2
School:
University of Maryland, College Park
Course:
Cmsc 250 - Discrete Structures
##### Discrete Structures Documents
• 2 pages
• 2 pages
• 2 pages
• 2 pages
• 57 pages
• 12 pages
• 2 pages
• 3 pages
• 8 pages
• 4 pages
• 2 pages
• 28 pages
• 2 pages
• 6 pages
• 2 pages
• 2 pages
• 2 pages
• 4 pages
• 2 pages
• 2 pages
• 57 pages
• 2 pages
• 16 pages
• 10 pages
• 4 pages
• 2 pages
• 32 pages
• 5 pages
• 28 pages
• 4 pages
• 8 pages
• 15 pages
• 2 pages
• 8 pages
• 2 pages
• 12 pages
• 16 pages
• 2 pages
• 12 pages
• 13 pages
• 2 pages
• 12 pages
• 2 pages
• 15 pages
• 2 pages
• 2 pages
• 2 pages
• 2 pages
• 8 pages
• 3 pages
• 44 pages
• 4 pages
• 2 pages
• 2 pages
• 4 pages
• 4 pages
• 2 pages
• 2 pages
• 5 pages
• 2 pages
• 40 pages
• 14 pages
Unformatted text preview:
CMSC 250 0201 0202 Homework 3 Fall 2005 Due Wed Sept 21 at the beginning of your discussion section You must write the solutions to the problems single sided on your own lined paper with all sheets stapled together and with all answers written in sequential order or you will lose points 1 Construct a logical expression that is equivalent to the following circuit P NOT AND Q OR X OR R NOT a P NOT OR Q AND NOT X R NOT b 2 For each of the following input signals a P 1 Q 0 R 1 and b P 0 Q 0 R 1 find the output X for each of the circuits given in the figures below P Q AND NOT OR AND R P NOT Q R OR AND NOT 1 NOT 3 Convert the following numbers from one base to another a 4510 2 16 b DEAB16 2 c 11011012 10 d 51410 4 Find the following 2 0011111 110110 010011001100 11011011101 5 For each of the following let W x y mean that x has visited y where the universe of discourse for x is the set of all students in your school P for people and the universe of discourse for y is the set of all Web sites S for sites For ease of writing assume all first names are unique among the members of this domain Express each of the following statements in a simple English sentence a W Sarah www att com b x P W x www imdb org c y S W Jose y d y S W Joe y W T om y e y S z P y David W David z W y z f x P y P z S x y W x z W y z 6 Let F x y be the statement x can fool y where the universe of discourse for both is the set of all people in the world P for people Use quantifiers to express each of the following statements a Everybody can fool Fred b Evelyn can fool everybody c Everybody can fool somebody d There is no one who can fool everybody e Everyone can be fooled by somebody f No one can fool both Fred and Jerry g Nancy can fool exactly two people h There is exactly one person whom everybody can fool i No one can fool him herself j There is someone who can fool exactly one person besides himself or herself 7 Explain why x U P x f orallx U Q x is not equivalent to x U P x Q x 2
View Full Document
## Access the best Study Guides, Lecture Notes and Practice Exams
Unlocking...
Sign Up
Join to view Homework #3 and access 3M+ class-specific study document.
or
By creating an account you agree to our Privacy Policy and Terms Of Use
Already a member? | 974 | 3,336 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2020-16 | latest | en | 0.57423 |
https://number.academy/1002337 | 1,701,886,276,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100602.36/warc/CC-MAIN-20231206162528-20231206192528-00142.warc.gz | 475,518,733 | 12,264 | # Number 1002337 facts
The odd number 1,002,337 is spelled 🔊, and written in words: one million, two thousand, three hundred and thirty-seven, approximately 1.0 million. The ordinal number 1002337th is said 🔊 and written as: one million, two thousand, three hundred and thirty-seventh. The meaning of the number 1002337 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 1002337. What is 1002337 in computer science, numerology, codes and images, writing and naming in other languages
## What is 1,002,337 in other units
The decimal (Arabic) number 1002337 converted to a Roman number is (M)MMCCCXXXVII. Roman and decimal number conversions.
#### Weight conversion
1002337 kilograms (kg) = 2209752.2 pounds (lbs)
1002337 pounds (lbs) = 454657.1 kilograms (kg)
#### Length conversion
1002337 kilometers (km) equals to 622824 miles (mi).
1002337 miles (mi) equals to 1613106 kilometers (km).
1002337 meters (m) equals to 3288468 feet (ft).
1002337 feet (ft) equals 305517 meters (m).
1002337 centimeters (cm) equals to 394620.9 inches (in).
1002337 inches (in) equals to 2545936.0 centimeters (cm).
#### Temperature conversion
1002337° Fahrenheit (°F) equals to 556836.1° Celsius (°C)
1002337° Celsius (°C) equals to 1804238.6° Fahrenheit (°F)
#### Time conversion
(hours, minutes, seconds, days, weeks)
1002337 seconds equals to 1 week, 4 days, 14 hours, 25 minutes, 37 seconds
1002337 minutes equals to 2 years, 3 weeks, 3 days, 1 hour, 37 minutes
### Codes and images of the number 1002337
Number 1002337 morse code: .---- ----- ----- ..--- ...-- ...-- --...
Sign language for number 1002337:
Number 1002337 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
## Mathematics of no. 1002337
### Multiplications
#### Multiplication table of 1002337
1002337 multiplied by two equals 2004674 (1002337 x 2 = 2004674).
1002337 multiplied by three equals 3007011 (1002337 x 3 = 3007011).
1002337 multiplied by four equals 4009348 (1002337 x 4 = 4009348).
1002337 multiplied by five equals 5011685 (1002337 x 5 = 5011685).
1002337 multiplied by six equals 6014022 (1002337 x 6 = 6014022).
1002337 multiplied by seven equals 7016359 (1002337 x 7 = 7016359).
1002337 multiplied by eight equals 8018696 (1002337 x 8 = 8018696).
1002337 multiplied by nine equals 9021033 (1002337 x 9 = 9021033).
show multiplications by 6, 7, 8, 9 ...
### Fractions: decimal fraction and common fraction
#### Fraction table of 1002337
Half of 1002337 is 501168,5 (1002337 / 2 = 501168,5 = 501168 1/2).
One third of 1002337 is 334112,3333 (1002337 / 3 = 334112,3333 = 334112 1/3).
One quarter of 1002337 is 250584,25 (1002337 / 4 = 250584,25 = 250584 1/4).
One fifth of 1002337 is 200467,4 (1002337 / 5 = 200467,4 = 200467 2/5).
One sixth of 1002337 is 167056,1667 (1002337 / 6 = 167056,1667 = 167056 1/6).
One seventh of 1002337 is 143191 (1002337 / 7 = 143191).
One eighth of 1002337 is 125292,125 (1002337 / 8 = 125292,125 = 125292 1/8).
One ninth of 1002337 is 111370,7778 (1002337 / 9 = 111370,7778 = 111370 7/9).
show fractions by 6, 7, 8, 9 ...
### Calculator
1002337
#### Is Prime?
The number 1002337 is not a prime number. The closest prime numbers are 1002299, 1002341.
#### Factorization and factors (dividers)
The prime factors of 1002337 are 7 * 17 * 8423
The factors of 1002337 are 1, 7, 17, 119, 8423, 58961, 143191, 1002337.
Total factors 8.
Sum of factors 1213056 (210719).
#### Powers
The second power of 10023372 is 1.004.679.461.569.
The third power of 10023373 is 1.007.027.397.470.686.720.
#### Roots
The square root √1002337 is 1001,167818.
The cube root of 31002337 is 100,077839.
#### Logarithms
The natural logarithm of No. ln 1002337 = loge 1002337 = 13,817845.
The logarithm to base 10 of No. log10 1002337 = 6,001014.
The Napierian logarithm of No. log1/e 1002337 = -13,817845.
### Trigonometric functions
The cosine of 1002337 is 0,76323.
The sine of 1002337 is -0,646127.
The tangent of 1002337 is -0,846568.
### Properties of the number 1002337
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
## Number 1002337 in Computer Science
Code typeCode value
1002337 Number of bytes978.8KB
Unix timeUnix time 1002337 is equal to Monday Jan. 12, 1970, 2:25:37 p.m. GMT
IPv4, IPv6Number 1002337 internet address in dotted format v4 0.15.75.97, v6 ::f:4b61
1002337 Decimal = 11110100101101100001 Binary
1002337 Decimal = 1212220221121 Ternary
1002337 Decimal = 3645541 Octal
1002337 Decimal = F4B61 Hexadecimal (0xf4b61 hex)
1002337 BASE64MTAwMjMzNw==
1002337 MD58ccf743bdd22c7de8cc65ec81edf79d0
1002337 SHA256b59265f0fa4ba50e34edf5df0cc90de726bdef260a50de3f3e5f37112ba383a7
1002337 SHA3841d4616c2347db2f55ab1c48b2c3aa6997f591b4d88db9236a129d354b3bac86505ddc1362ea7be3aa934d724e8870e6e
More SHA codes related to the number 1002337 ...
If you know something interesting about the 1002337 number that you did not find on this page, do not hesitate to write us here.
## Numerology 1002337
### Character frequency in the number 1002337
Character (importance) frequency for numerology.
Character: Frequency: 1 1 0 2 2 1 3 2 7 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 1002337, the numbers 1+0+0+2+3+3+7 = 1+6 = 7 are added and the meaning of the number 7 is sought.
## № 1,002,337 in other languages
How to say or write the number one million, two thousand, three hundred and thirty-seven in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 1.002.337) un millón dos mil trescientos treinta y siete German: 🔊 (Nummer 1.002.337) eine Million zweitausenddreihundertsiebenunddreißig French: 🔊 (nombre 1 002 337) un million deux mille trois cent trente-sept Portuguese: 🔊 (número 1 002 337) um milhão e dois mil, trezentos e trinta e sete Hindi: 🔊 (संख्या 1 002 337) दस लाख, दो हज़ार, तीन सौ, सैंतीस Chinese: 🔊 (数 1 002 337) 一百万二千三百三十七 Arabian: 🔊 (عدد 1,002,337) واحد مليون و ألفان و ثلاثمائة و سبعة و ثلاثون Czech: 🔊 (číslo 1 002 337) milion dva tisíce třista třicet sedm Korean: 🔊 (번호 1,002,337) 백만 이천삼백삼십칠 Dutch: 🔊 (nummer 1 002 337) een miljoen tweeduizenddriehonderdzevenendertig Japanese: 🔊 (数 1,002,337) 百万二千三百三十七 Indonesian: 🔊 (jumlah 1.002.337) satu juta dua ribu tiga ratus tiga puluh tujuh Italian: 🔊 (numero 1 002 337) un milione e duemilatrecentotrentasette Norwegian: 🔊 (nummer 1 002 337) en million, to tusen, tre hundre og tretti-syv Polish: 🔊 (liczba 1 002 337) milion dwa tysiące trzysta trzydzieści siedem Russian: 🔊 (номер 1 002 337) один миллион две тысячи триста тридцать семь Turkish: 🔊 (numara 1,002,337) birmilyonikibinüçyüzotuzyedi Thai: 🔊 (จำนวน 1 002 337) หนึ่งล้านสองพันสามร้อยสามสิบเจ็ด Ukrainian: 🔊 (номер 1 002 337) один мільйон дві тисячі триста тридцять сім Vietnamese: 🔊 (con số 1.002.337) một triệu hai nghìn ba trăm ba mươi bảy Other languages ...
## News to email
I have read the privacy policy
## Comment
If you know something interesting about the number 1002337 or any other natural number (positive integer), please write to us here or on Facebook.
#### Comment (Maximum 2000 characters) *
The content of the comments is the opinion of the users and not of number.academy. It is not allowed to pour comments contrary to the laws, insulting, illegal or harmful to third parties. Number.academy reserves the right to remove or not publish any inappropriate comment. It also reserves the right to publish a comment on another topic. Privacy Policy.
There are no comments for this topic.
• ### How do you write the number 1002337 in words?
1002337 can be written as "one million, two thousand, three hundred and thirty-seven". | 2,719 | 7,902 | {"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-2023-50 | latest | en | 0.695047 |
https://metanumbers.com/32887 | 1,627,384,160,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153391.5/warc/CC-MAIN-20210727103626-20210727133626-00145.warc.gz | 398,635,897 | 10,833 | ## 32887
32,887 (thirty-two thousand eight hundred eighty-seven) is an odd five-digits prime number following 32886 and preceding 32888. In scientific notation, it is written as 3.2887 × 104. The sum of its digits is 28. It has a total of 1 prime factor and 2 positive divisors. There are 32,886 positive integers (up to 32887) that are relatively prime to 32887.
## Basic properties
• Is Prime? Yes
• Number parity Odd
• Number length 5
• Sum of Digits 28
• Digital Root 1
## Name
Short name 32 thousand 887 thirty-two thousand eight hundred eighty-seven
## Notation
Scientific notation 3.2887 × 104 32.887 × 103
## Prime Factorization of 32887
Prime Factorization 32887
Prime number
Distinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 32887 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 10.4008 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 32,887 is 32887. Since it has a total of 1 prime factor, 32,887 is a prime number.
## Divisors of 32887
2 divisors
Even divisors 0 2 1 1
Total Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 32888 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 16444 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 181.348 Returns the nth root of the product of n divisors H(n) 1.99994 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 32,887 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 32,887) is 32,888, the average is 16,444.
## Other Arithmetic Functions (n = 32887)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 32886 Total number of positive integers not greater than n that are coprime to n λ(n) 32886 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3526 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 32,886 positive integers (less than 32,887) that are coprime with 32,887. And there are approximately 3,526 prime numbers less than or equal to 32,887.
## Divisibility of 32887
m n mod m 2 3 4 5 6 7 8 9 1 1 3 2 1 1 7 1
32,887 is not divisible by any number less than or equal to 9.
## Classification of 32887
• Arithmetic
• Prime
• Deficient
### Expressible via specific sums
• Polite
• Non-hypotenuse
• Prime Power
• Square Free
## Base conversion (32887)
Base System Value
2 Binary 1000000001110111
3 Ternary 1200010001
4 Quaternary 20001313
5 Quinary 2023022
6 Senary 412131
8 Octal 100167
10 Decimal 32887
12 Duodecimal 17047
20 Vigesimal 4247
36 Base36 pdj
## Basic calculations (n = 32887)
### Multiplication
n×i
n×2 65774 98661 131548 164435
### Division
ni
n⁄2 16443.5 10962.3 8221.75 6577.4
### Exponentiation
ni
n2 1081554769 35569091688103 1169760718346643361 38469920744266060213207
### Nth Root
i√n
2√n 181.348 32.0387 13.4665 8.0058
## 32887 as geometric shapes
### Circle
Diameter 65774 206635 3.3978e+09
### Sphere
Volume 1.48991e+14 1.35912e+10 206635
### Square
Length = n
Perimeter 131548 1.08155e+09 46509.2
### Cube
Length = n
Surface area 6.48933e+09 3.55691e+13 56962
### Equilateral Triangle
Length = n
Perimeter 98661 4.68327e+08 28481
### Triangular Pyramid
Length = n
Surface area 1.87331e+09 4.19186e+12 26852.1
## Cryptographic Hash Functions
md5 8d2cbe9d22a199026ddcbae5f0f67ef0 f8651f1a3370db5f922f47b6cac28166241d8276 a4bfd5494dcbdb85435170641f68d0fa3e6c34e67856fef2aa6c268aa1e78aee 1681e374c83ade37af992fde0460ee85929d71dc12ec1f3e57bbf8fa7b7b937773944b1ac0b2c128646bd590ff99805e36dbcd1026f57a1af4f79fe9db8b7c35 e8f8329dc17c7252bc8170c5f046a9ae497a9833 | 1,444 | 4,148 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-31 | longest | en | 0.822032 |
https://www.edaboard.com/threads/fan-selection-for-cooling-electronics.337845/ | 1,701,624,969,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100508.42/warc/CC-MAIN-20231203161435-20231203191435-00412.warc.gz | 875,210,800 | 17,571 | Continue to Site
Fan selection for cooling electronics
Status
Not open for further replies.
nickagian
Member level 4
Hi guys,
Does anyone have experience in selecting fans for cooling electronic systems?
I have read several online guides from the various manufacturers but there is something that remains unclear to me. They all have this formula where you can calculate the minimum required air flow created by the cooling fans. This calculation is based on the total heating power of the system and a parameter called "temperature rise".
Well I don't actually understand what this "temperature rise" parameter means or how could I set a limit for it. It seems to be the allowed temperature rise inside the enclosure in comparison to the ambient temperature. But this is somewhat confusing to me. I mean, I have the system design specification that my electronics should work at a max ambient temperature of 70 degC. So what about the temperature rise?
Could anyone help in this?
Thanks,
Nikos
Hi guys,
Does anyone have experience in selecting fans for cooling electronic systems?
I have read several online guides from the various manufacturers but there is something that remains unclear to me. They all have this formula where you can calculate the minimum required air flow created by the cooling fans. This calculation is based on the total heating power of the system and a parameter called "temperature rise".
Well I don't actually understand what this "temperature rise" parameter means or how could I set a limit for it. It seems to be the allowed temperature rise inside the enclosure in comparison to the ambient temperature. But this is somewhat confusing to me. I mean, I have the system design specification that my electronics should work at a max ambient temperature of 70 degC. So what about the temperature rise?
Could anyone help in this?
Thanks,
Nikos
You can find software to design a cooling system. In many of my projects I gradually worked as follows:
1. You must know the full dissipation of your system. In my case the systems were installed in NEMA metal boxes.
If the dissipation was over 10 Watts I chose aluminum boxes, for lower power, steel was OK.
2. Use a car light bulb(s) as a power resistor, put it in the box you chose, and power it to the full dissipation you determined. Insert thermistor in the box to measure internal temperature. Locate the thermistor away from the bulb, o indicate air temperature only. Use a watch to measure time. Sit next to it all and record a table, degrees C versus time.
Plot a graph between the times taking data. The graph will show a rapid temperature rise, then going to a steady state.
Most semiconductor components and some capacitors cannot operate above 60, 85 and 100 deg.C . So check how your graph is rising. If it does not go steady above some critical temperature like 60 deg.C, you may need a fan to push the temperature down. If the graph still rises after one hour, sit and watch until it stops.
3. Get a fan and install it inside the box so the air can freely circulate. Repeat the above test and check if the plot has improved. If not or not enough, use a stronger fan. Repeat till you get a reasonable solution. Sometimes I used two small fans, better than one strong fan. Use also heat sinks on sensitive components so the circulating air cools them.
4. Once it happened to me that two fans could not give me a good inside temperature. Then I had to use an aluminum ridged block installed in NEMA box lid. Ridges on both sides allowed to dissipate more than 25 Watts inside and the inner temperature did not exceed 55 deg.C after two hours of operation. Air circulation is important.
5. if you need to dissipate a large power in a small volume, you can now use liquid coolers made for powerful computer processors. They are more costly than simple fans but offer a solution not available before say 2010.
Temperature rise is the difference between the ambient (inlet) air temperature and the outlet air temperature. Beware of internal hot spots and make an allowance for dirt and dust obstructing the air flow. Include over temperature shut down if highly stressed. Could be worth spraying the inside and out side of the cabinet matt black.
Frank
Status
Not open for further replies. | 886 | 4,295 | {"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} | 2.828125 | 3 | CC-MAIN-2023-50 | latest | en | 0.95721 |
https://www.mathhomeworkanswers.org/258430/4x-13-11?show=258475 | 1,553,071,583,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202303.66/warc/CC-MAIN-20190320064940-20190320090940-00224.warc.gz | 839,784,848 | 12,818 | Solve each inequality
4x-13<11
Add 13 to each side: 4x<24 then divide through by 4: x<6 is the answer.
by Top Rated User (614k points) | 48 | 137 | {"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-2019-13 | longest | en | 0.937217 |
https://rdrr.io/cran/geoBayes/src/R/bf.R | 1,556,138,281,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578656640.56/warc/CC-MAIN-20190424194348-20190424220348-00194.warc.gz | 529,500,760 | 17,053 | # R/bf.R In geoBayes: Analysis of Geostatistical Data using Bayes and Empirical Bayes Methods
#### Documented in bf1skel
##' Function to compute the Bayes factors from MCMC samples.
##'
##' Computes the Bayes factors using \code{method} with respect to
##' \code{reference}.
##' @title Computation of Bayes factors at the skeleton points
##' @param runs A list with outputs from the function
##' @param bfsize1 A scalar or vector of the same length as
##' \code{runs} with all integer values or all values in (0, 1]. How
##' many samples (or what proportion of the sample) to use for
##' estimating the Bayes factors at the first stage. The remaining
##' sample will be used for estimating the Bayes factors in the
##' second stage. Setting it to 1 will perform only the first stage.
##' @param method Which method to use to calculate the Bayes factors:
##' Reverse logistic or Meng-Wong.
##' @param reference Which model goes in the denominator.
##' @param transf Whether to use a transformed sample for the
##' computations. If \code{"no"} or \code{FALSE}, it doesn't. If
##' \code{"mu"} or \code{TRUE}, it uses the samples for the mean. If
##' \code{"wo"} it uses an alternative transformation. The latter
##' can be used only for the families indicated by
##' \code{.geoBayes_models$haswo}. ##' @return A list with components ##' \itemize{ ##' \item \code{logbf} A vector containing logarithm of the Bayes factors. ##' \item \code{logLik1} \code{logLik2} Matrices with the values of ##' the log-likelihood computed from the samples for each model at the ##' first and second stages. ##' \item \code{isweights} A vector with the importance sampling ##' weights for computing the Bayes factors at new points that will be ##' used at the second stage. Used internally in ##' \code{\link{bf2new}} and \code{\link{bf2optim}}. ##' \item \code{controlvar} A matrix with the control variates ##' computed at the samples that will be used in the second stage. ##' \item \code{sample2} The MCMC sample for mu or z that will be ##' used in the second stage. Used internally in ##' \code{\link{bf2new}} and \code{\link{bf2optim}}. ##' \item \code{N1}, \code{N2} Vectors containing the sample sizes ##' used in the first and second stages. ##' \item \code{distmat} Matrix of distances between locations. ##' \item \code{betm0}, \code{betQ0}, \code{ssqdf}, \code{ssqsc}, ##' \code{tsqdf}, \code{tsqsc}, \code{dispersion}, \code{response}, ##' \code{weights}, \code{modelmatrix}, \code{locations}, ##' \code{family}, \code{corrfcn}, \code{transf} Model parameters used ##' internally in. ##' \code{\link{bf2new}} and \code{\link{bf2optim}}. ##' \item \code{pnts} A list containing the skeleton points. Used ##' internally in \code{\link{bf2new}} and \code{\link{bf2optim}}. ##' } ##' @references Geyer, C. J. (1994). Estimating normalizing constants ##' and reweighting mixtures. Technical report, University of ##' Minnesota. ##' ##' Meng, X. L., & Wong, W. H. (1996). Simulating ratios of ##' normalizing constants via a simple identity: A theoretical ##' exploration. \emph{Statistica Sinica}, 6, 831-860. ##' ##' Roy, V., Evangelou, E., and Zhu, Z. (2015). Efficient estimation ##' and prediction for the Bayesian spatial generalized linear mixed ##' model with flexible link functions. \emph{Biometrics}, 72(1), 289-298. ##' @examples \dontrun{ ##' data(rhizoctonia) ##' ### Define the model ##' corrf <- "spherical" ##' kappa <- 0 ##' ssqdf <- 1 ##' ssqsc <- 1 ##' betm0 <- 0 ##' betQ0 <- .01 ##' family <- "binomial.probit" ##' ### Skeleton points ##' philist <- c(100, 140, 180) ##' omglist <- c(.5, 1) ##' parlist <- expand.grid(linkp=0, phi=philist, omg=omglist, kappa = kappa) ##' ### MCMC sizes ##' Nout <- 100 ##' Nthin <- 1 ##' Nbi <- 0 ##' ### Take MCMC samples ##' runs <- list() ##' for (i in 1:NROW(parlist)) { ##' runs[[i]] <- mcsglmm(Infected ~ 1, family, rhizoctonia, weights = Total, ##' atsample = ~ Xcoord + Ycoord, ##' Nout = Nout, Nthin = Nthin, Nbi = Nbi, ##' betm0 = betm0, betQ0 = betQ0, ##' ssqdf = ssqdf, ssqsc = ssqsc, ##' phi = parlist$phi[i], omg = parlist$omg[i], ##' linkp = parlist$linkp[i], kappa = parlist$kappa[i], ##' corrfcn = corrf, ##' corrtuning=list(phi = 0, omg = 0, kappa = 0)) ##' } ##' bf <- bf1skel(runs) ##' bf$logbf
##' }
##' @importFrom sp spDists
##' @useDynLib geoBayes bfsp_no bfsp_mu bfsp_wo bfsp_tr
##' @export
bf1skel <- function(runs, bfsize1 = 0.80, method = c("RL", "MW"),
reference = 1, transf = c("no", "mu", "wo"))
{
method <- match.arg(method)
imeth <- match(method, eval(formals()$method)) classes <- sapply(runs, class) if (any(classes != "geomcmc")) { stop ("Input runs is not a list with elements of class geomcmc.") } nruns <- length(runs) if (nruns == 0) stop ("No runs specified") reference <- as.integer(reference) if (isTRUE(reference < 1L | reference > nruns)) { stop("Argument reference does not correspond to a run in runs.") } Nout <- sapply(runs, function(x) x$MCMC$Nout) Nout1 <- getsize(bfsize1, Nout, "*") Ntot1 <- sum(Nout1) Nout2 <- Nout - Nout1 Ntot2 <- sum(Nout2) ## Check if fixed phi and omg if (!all(sapply(runs, function(x) length(x$FIXED$phi) == 1))) { stop("Each input runs must have a fixed value phi.") } if (!all(sapply(runs, function(x) length(x$FIXED$omg) == 1))) { stop("Each input runs must have a fixed value omg.") } ## Extract data and model nm_DATA <- c("response", "weights", "modelmatrix", "locations", "longlat") nm_MODEL <- c("family", "corrfcn", "betm0", "betQ0", "ssqdf", "ssqsc", "tsqdf", "tsqsc", "dispersion") DATA <- runs[[1]]$DATA[nm_DATA]
MODEL <- runs[[1]]$MODEL[nm_MODEL] if (nruns > 1) { for (i in 2:nruns) { if (!identical(runs[[i]]$DATA[nm_DATA], DATA)) {
stop("MCMC chains don't all correspond to the same data.")
}
if (!identical(runs[[i]]$MODEL[nm_MODEL], MODEL)) { stop("MCMC chains don't all correspond to the same model.") } } } y <- DATA$response
n <- as.integer(length(y))
l <- DATA$weights F <- DATA$modelmatrix
p <- NCOL(F)
loc <- DATA$locations dm <- sp::spDists(loc, longlat = DATA$longlat)
family <- MODEL$family ## ifam <- .geoBayes_family(family) corrfcn <- MODEL$corrfcn
icf <- .geoBayes_correlation(corrfcn)
betm0 <- MODEL$betm0 betQ0 <- MODEL$betQ0
ssqdf <- MODEL$ssqdf ssqsc <- MODEL$ssqsc
tsqdf <- MODEL$tsqdf tsqsc <- MODEL$tsqsc
dispersion <- MODEL$dispersion ## Choose sample getsample <- transfsample(runs, list(response = y, family = family), transf) sample <- matrix(unlist(getsample$sample), n)
itr <- getsample$itr transf <- getsample$transf
real_transf <- getsample$real_transf ifam <- getsample$ifam
## Skeleton points
phi_pnts <- as.double(sapply(runs, function(r) r$FIXED$phi))
omg_pnts <- as.double(sapply(runs, function(r) r$FIXED$omg))
nu_pnts <- as.double(sapply(runs, function(r) r$FIXED$linkp_num))
if (.geoBayes_corrfcn$needkappa[icf]) { kappa_pnts <- sapply(runs, function(r) r$FIXED$kappa) kappa_pnts <- .geoBayes_getkappa(kappa_pnts, icf) } else { kappa_pnts <- rep(0, nruns) } bfroutine <- paste0("bfsp_", real_transf) if (nruns == 1) { MCMC <- runs[[1]]$MCMC
out <- list(logbf = 1, logLik1 = MCMC$logLik[1:Ntot1], logLik2 = MCMC$logLik[-(1:Ntot1)],
isweights = rep.int(0, Ntot2),
controlvar = matrix(1, Ntot2, 1),
z = sample[[1]][, -(1:Ntot1), drop = FALSE],
N1 = Nout1, N2 = Nout2,
betm0 = betm0, betQ0 = betQ0, ssqdf = ssqdf,
ssqsc = ssqsc, tsqdf = tsqdf, tsqsc = tsqsc,
dispersion = dispersion, response = y,
weights = l, modelmatrix = F,
locations = loc, longlat = DATA$longlat, distmat = dm, family = family, referencebf = 0, corrfcn = corrfcn, transf = transf, real_transf = real_transf, itr = itr, pnts = list(nu = nu_pnts, phi = phi_pnts, omg = omg_pnts, kappa = kappa_pnts)) return(out) } ## Split the sample sel1 <- rep(rep(c(TRUE, FALSE), nruns), rbind(Nout1, Nout2)) z1 <- sample[, sel1, drop = FALSE] z2 <- sample[, !sel1, drop = FALSE] logbf <- numeric(nruns) lglk1 <- matrix(0., Ntot1, nruns) lglk2 <- matrix(0., Ntot2, nruns) zcv <- matrix(0., Ntot2, nruns) weights <- numeric(Ntot2) if (ifam == 0) { tsq <- tsqsc } else { tsq <- dispersion } RUN <- .Fortran(bfroutine, weights = weights, zcv = zcv, logbf = logbf, lglk1 = lglk1, lglk2 = lglk2, as.double(phi_pnts), as.double(omg_pnts), as.double(nu_pnts), as.double(z1), as.integer(Nout1), as.integer(Ntot1), as.double(z2), as.integer(Nout2), as.integer(Ntot2), as.double(y), as.double(l), as.double(F), as.double(dm), as.double(betm0), as.double(betQ0), as.double(ssqdf), as.double(ssqsc), max(tsqdf, 0), as.double(tsq), as.double(kappa_pnts), as.integer(icf), as.integer(n), as.integer(p), as.integer(nruns), as.integer(ifam), as.integer(imeth), as.integer(itr), PACKAGE = "geoBayes") refbf <- RUN$logbf[reference]
logbf <- RUN$logbf - refbf if (Ntot2 > 0) { weights <- RUN$weights
lglk2 <- RUN$lglk2 zcv <- RUN$zcv
} else {
weights <- lglk2 <- zcv <- NULL
}
out <- list(logbf = logbf, logLik1 = RUN\$lglk1, logLik2 = lglk2,
isweights = weights, controlvar = zcv, sample2 = z2,
N1 = Nout1, N2 = Nout2,
betm0 = betm0,
betQ0 = betQ0, ssqdf = ssqdf, ssqsc = ssqsc, tsqdf = tsqdf,
tsqsc = tsqsc, dispersion = dispersion, response = y, weights = l,
modelmatrix = F, locations = loc, distmat = dm, family = family,
corrfcn = corrfcn, transf = transf,
real_transf = real_transf, itr = itr,
pnts = list(nu = nu_pnts, phi = phi_pnts, omg = omg_pnts,
kappa = kappa_pnts))
out
}
## Try the geoBayes package in your browser
Any scripts or data that you put into this service are public.
geoBayes documentation built on Feb. 28, 2019, 5:05 p.m. | 3,173 | 9,482 | {"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} | 2.828125 | 3 | CC-MAIN-2019-18 | latest | en | 0.650757 |
https://sites.google.com/a/ocdsb.ca/ridgemontmath/grade-10/mfm2p | 1,529,332,186,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267860557.7/warc/CC-MAIN-20180618125242-20180618145242-00047.warc.gz | 714,233,980 | 10,783 | ### MFM2P Grade 10 Applied Math
Course note package: The entire course in 9 pages with worked examples.
MT: Measurement and Trigonometry
MT1. SIMILAR TRIANGLES:
use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
Tutorial Websites: Tutorial Videos : Practice Problems: Solving similar triangles: http://bit.ly/LAAjTY Similar or not? http://bit.ly/1lsadTd Similarity: http://bit.ly/1jltJPc Solving similar triangles: http://bit.ly/1mJisL4 Practice: http://bit.ly/1goUZeq Practice: http://bit.ly/1mXL7MQ Practice: http://bit.ly/1eGtKpW Practice: http://bit.ly/1k4MDcw
MT2. PYTHAGOREAN THEOREM & TRIG RATIOS:
solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
Tutorial Websites: Tutorial Videos: Practice Problems: Trig intro: http://bit.ly/1abo7Us Sine, cosine & tangent: http://bit.ly/1bML2AH Pythagorean Theorem: http://bit.ly/1dgT0SE Pythagorean Theorem proof: http://bit.ly/1ey7AKi Pythagorean Theorem interactive: http://bit.ly/1i3GM4q Trig ratios: http://bit.ly/1jiaqWR Finding missing sides & angles in right triangles: http://bit.ly/QXKPYq Using Pythagorean Theorem: http://bit.ly/1nAmKm6 Pythagorean Theorem proof: http://bit.ly/1gAWAin Trig ratios: http://bit.ly/1gItdpk Trig Practice: http://bit.ly/1iYCWwO Trig Practice: http://bit.ly/1bMLgb6 Trig practice: http://bit.ly/T7cSFJ Pythagorean Practice: http://bit.ly/1fwDupM Pythagorean Practice: http://bit.ly/1aQ0em8
MT3. SURFACE AREA & VOLUME:
solve problems involving the surface areas and volumes of three-dimensional figures, and use the imperial and metric systems of measurement.
Tutorial Websites: Tutorial Videos: Practice Problems: 3-D solids (V & SA): http://bit.ly/LACoiu Surface area: http://bit.ly/1aPYuJH Surface area of composite shapes: http://bit.ly/1bMMjYz Volume: http://bit.ly/1gAV93q Volume of cones, cylinders & spheres: http://bit.ly/1luK1Sa Volume practice: http://bit.ly/1dUxu5Y Surface area practice (rectangular prisms): http://bit.ly/1dgSJiD Surface area practice: http://bit.ly/1iYDXFb Practice area, volume & surface area: http://bit.ly/1mYp9Jy
LR: Modelling Linear Relations
LR1. SOLVING EQUATIONS:
manipulate and solve algebraic equations, as needed to solve problems;
Tutorial Websites: Tutorial Videos: Practice Problems: Solving equations: http://bit.ly/1i3ICCl Substitution: http://bit.ly/1i48lKW Solving equations: http://bit.ly/1lsd6Dh Rearranging formulas: http://bit.ly/1cGWjXr 1-step + - equation solving:http://bit.ly/T7ta1h 1-step x ÷ equation solving: http://bit.ly/1jMKGBX 2-step equation solving: http://bit.ly/1dgUmgf Word problems: http://bit.ly/T7tq0r Equations w/ variables on both sides: http://bit.ly/1lkqJjz Equation solving steps: http://bit.ly/1hOpYwO Practice rearranging equations: http://bit.ly/1abrAT1 Practice solving equations w/ algebra tiles: http://bit.ly/1bMPU8Z
LR2. CREATING GRAPHS, TABLES & EQUATIONS:
graph a line and write the equation of a line from given information;
Tutorial Websites: Tutorial Videos: Practice Problems: Linear equations: http://bit.ly/1lsdKk9 Using x- and y-intercepts: http://bit.ly/1fkjyor Slope: http://bit.ly/1cGXaYm Using slope & y-intercept: http://bit.ly/18H9EiW Creating equations: http://bit.ly/1bhjU05 Linear Regression on a graphing calculator: http://bit.ly/LY32l8 Cockroach game: http://bit.ly/1g6MfGw Distance VS Time graph game: http://davidwees.com/graphgame/ Slope: http://bit.ly/1aQ1ENB Linear relations: http://bit.ly/1ksmsei Graphing an equation: http://bit.ly/1eGzHTC y-intercept: http://bit.ly/1bhkY3V Creating an equation: http://bit.ly/1gAZeEA
LR3. SYSTEMS OF LINEAR EQUATIONS:
solve systems of two linear equations, and solve related problems that arise from realistic situations.
Tutorial Websites: Tutorial Videos: Practice Problems: Systems of linear equations: http://bit.ly/1bfD7ff Interpreting a point of intersection: http://www.showme.com/sh/?h=QRHHDXc Solving systems graphically w/ a graphing calculator: http://youtu.be/45jx68vFPjY Solving systems graphically by hand: http://bit.ly/IL8feO Solving systems by elimination: http://bit.ly/1c942yg Solving systems by substitution: http://bit.ly/1cptpdq Practice solving linear systems graphically: http://bit.ly/LAHJGK Practice elimination: http://bit.ly/1bhlT4k Practice susbstitution: http://bit.ly/1nArBn6
QR: Quadratic Relations of the Form y = ax2 + bx + c
QR1. FACTORING & EXPANDING
manipulate algebraic expressions, as needed to understand quadratic relations;
Tutorial Websites: Tutorial Videos: Practice Problems: Factoring & Expanding w/ algebra tiles: http://bit.ly/1egn4nz What the heck are algebra tiles?http://bit.ly/1lshN02 Factoring w/ algebra tiles: http://bit.ly/1gB2CiU Factoring w/ algebra tiles: http://bit.ly/1n4t9CW Factoring w/o algebra tiles: http://bit.ly/1lsi2rZ Expanding w/ algebra tiles: http://bit.ly/1aQ4SjZ Expanding w/o algebra tiles: http://bit.ly/1eoLo51 Expanding (binomial squared): http://bit.ly/1ijymXb Practicing w/ algebra tiles (click on "factor" & "expand" tabs): http://bit.ly/1bMPU8Z Factoring easier: http://bit.ly/1bMV84O Factoring harder: http://bit.ly/1fJ7qhv Expanding easier: http://bit.ly/Mo1ukR Expanding harder: http://bit.ly/1dUBeVe
Tutorial Websites: Tutorial Videos: Practice Problems: Graphing quadratics: http://bit.ly/1lsivdv Features of quadratics/parabolas: http://bit.ly/1oNeM9I Graphing quadratics: Key Features of Quadratics (use desmos to graph the equation)
solve problems by interpreting graphs of quadratic relations.
Tutorial Websites: Tutorial Videos: Practice Problems: Quadratics in real life: http://bit.ly/1egoe2g Interpreting quadratics: http://bit.ly/1fkniqd Interpreting quadratics w/ graphing calculator: http://bit.ly/1ijzcTR Interpreting Quadratics (use desmos to graph the equation) Quadratic relations problems: http://bit.ly/RVCBAb | 1,948 | 6,053 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2018-26 | longest | en | 0.392773 |
https://id.scribd.com/document/283035428/chap01-6thmath | 1,563,570,738,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526359.16/warc/CC-MAIN-20190719202605-20190719224605-00344.warc.gz | 424,228,929 | 97,240 | Anda di halaman 1dari 56
# Number, Operations,
and Statistics
Focal Point
Represent and use rational
numbers in a variety of
forms and use statistical
representations to analyze
data.
CHAPTER 1
Number Patterns and
Functions
Use letters as variables in
mathematical expressions to describe
how one quantity changes when a
related quantity changes.
Use letters to represent
unknowns in an equation.
CHAPTER 2
Statistics and Graphs
Use statistical
representations to analyze data.
20
Chabruken/Getty Images
## Math and History
People, People, and More People Have you ever looked around
you and wondered just how many people live in the United States?
How many of them live in your state? Are there more males or
females? How ethnically diverse is our nation? Well, put on your
research gear, because we are about to jump into a sea of data to
find answers to these and other related questions. Youll look at our
nations population, past and present, and make some predictions
possible.
Log on to tx.msmath1.com to begin.
21
Functions
1
Knowledge
and Skills
## Use letters as variables in
mathematical expressions
to describe how one
quantity changes when a
related quantity changes.
TEKS 6.4
Key Vocabulary
area (p. 63)
evaluate (p. 42)
function (p. 49)
variable (p. 42)
of Texas at El Paso Miners, has a seating capacity of
51,500. You can use the equation x + 21,500 = 51,500
to find what the seating capacity of the Sun Bowl
was on opening day in 1963.
five sheets of notebook paper.
1 Stack the pages, placing
the sheets of paper
3
_
inch apart.
4
the fold.
## 2 Roll up bottom edges.
All tabs should be the
same size.
## 4 Label the tabs with the
topics from the chapter.
Li*>i
>`V
-}
v*Li
*>
*i>V
i
>`
i
*
>
{"`iv"
>Li>` i
x}iL>\6>
>\V
}iL
>`
iV
*-\i
>\ >
n}iL
>
>\i>
}iL
22
## Chapter 1 Number Patterns and Functions
Kelly-Mooney Photography/CORBIS
## GET READY for Chapter 1
Diagnose Readiness You have two options for checking Prerequisite Skills.
Option 2
Take the Online Readiness Quiz at tx.msmath1.com.
Option 1
Take the Quick Quiz below. Refer to the Quick Review for help.
1. 83 + 129
2. 99 + 56
3.
67 + 42
4.
79 + 88
5.
78 + 97
6.
86 + 66
## Example 1 Find 59 + 88.
Line up the digits at the ones place.
11
## 359 and place the 1 above the tens place.
+ 88 Add the tens. Put the 4 in the tens place
447 and place the 1 above the hundreds
Subtract.
7. 43 - 7
8.
75 - 27
9.
128 - 34
10.
150 - 68
11.
102 - 76
12.
235 - 126
13.
## AGES Ariana bought three shirts
for a total of \$89. If one shirt costs
\$24 and another costs \$31, how
much did the third shirt cost?
14. 25 12
15. 18 30
16.
42 15
17.
27 34
18.
50 16
19.
47 22
20. 72 9
21. 84 6
22.
126 3
23.
146 2
24.
208 4
25.
504 8
## Example 2 Find 853 - 79.
Line up the digits at the ones place.
7 14 13 Since 9 is larger than 3, rename 3 as 13.
/
8/
5/
3 Rename the 5 in the tens place as 14
- 79 and the 8 in the hundreds place as 7.
Then subtract.
774
## Example 3 Find 15 23.
15
23
45 Multiply. 15 3 = 45
+ 300 Multiply. 15 20 = 300
345 Add. 45 + 300 = 345
Example 4 Find 318 6.
53
318 Divide in each place-value position from
6
left to right.
- 30
18
- 18 Since 18 - 18 = 0,
0 there is no remainder.
23
1-1
## A Plan for Problem Solving
Main IDEA
Solve problems using the
four-step plan.
Targeted TEKS 6.11
The student applies
to solve problems
connected to everyday
experiences, investigations in
other disciplines, and
activities in and outside of
school. (B) Use a problemsolving model that
incorporates understanding
the problem, making a plan,
carrying out the plan, and
evaluating the solution for
reasonableness. 6.13 The
student uses logical reasoning
to make conjectures and
verify conclusions. (A) Make
conjectures from patterns or
sets of examples and
TEKS 6.2(C), 6.11(C).
FUN FACTS If you lined up pennies side by side, how many would
be in one mile? Lets find out. Begin by lining up pennies in a row
until the row is 1 foot long.
in.
10
11
1.
## How many pennies are in a row that is one mile long?
(Hint: There are 5,280 feet in one mile.)
2.
find the value.
## the number of quarters in a row one mile long.
When solving math problems, it is often helpful to have an organized
problem-solving plan. The four steps below can be used to solve any
problem.
1. Explore
What facts do you know?
What do you need to find out?
Is enough information given?
Is there extra information?
2. Plan
## How do the facts relate to each other?
Plan a strategy for solving the problem.
3. Solve
## Use your plan to solve the problem.
If your plan does not work, revise it or make a
new plan.
What is the solution?
4. Check
Reasonableness In
the last step of this
plan, you check the
reasonableness of
comparing it to the
estimate.
24
12
Does the answer fit the facts given in the problem?
If not, solve the problem another way.
## Chapter 1 Number Patterns and Functions
Method of
Computation To
solve a problem,
some methods you
can choose are paper
and pencil, mental
math, a calculator, or
estimation.
## Some problems can be easily solved by adding, subtracting,
multiplying, or dividing. Key words and phrases play an important
role in deciding which operation to use.
plus
sum
total
in all
Subtraction
minus
difference
less
subtract
Multiplication
times
product
multiplied by
of
Division
divided by
quotient
## Use the Problem-Solving Plan
1 BASKETBALL Refer to the graph below. How many more threepoint field goals did Katie Smith make than Crystal Robinson?
Katie Smith
425
Crystal Robinson
Tina Thompson
Katie Smith plays for
the Detroit Shock of
the WNBA. In 2004,
she scored 432 points,
109 free throws,
field goals, and played
800 minutes.
Source: wnba.com
366
335
319
Ruthie Bolton
314
Source: WNBA
Explore
## Extra information is given in the graph. You know
the number of three-point field goals made by many
players. You need to find how many more field goals
Katie Smith made than Crystal Robinson.
Plan
## To find the difference, subtract 366 from 425. Since the
paper and pencil. Before you calculate, estimate.
Estimate 430 - 370 = 60
Solve
425 - 366 = 59
Katie Smith made 59 more three-point field goals than
Crystal Robinson.
Check
a.
## Compared to the estimate, the answer is reasonable.
Since 59 + 366 is 425, the answer is correct.
## BASKETBALL Refer to graph above. The number of three-point
goals did Mabika attempt?
## Extra Examples at tx.msmath1.com
Jerry S. Mendoza/AP/Wide World Photos
25
## 2 SWIMMING Julian is on the swim team. The table shows the
number of laps he swims in the first four days of practice. If the
pattern continues, how many laps will he swim on Friday?
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Laps
11
Explore
## You know the number of laps he swam daily. You
need to find the number of laps for Friday.
Plan
## Since an exact answer is needed and the question
contains a pattern, use mental math.
Solve
+1
11
+2
+3
## The numbers increase by 1, 2, and 3. The next number
should increase by 4. So, if Julian continues at this rate,
he will swim 11 + 4 or 15 laps.
Check
b.
## ALLOWANCE The table shows how Kaylees weekly allowance
increases based on her age. If the pattern continues, how much
allowance will Kaylee receive when she is 13 years old?
9
10
11
12
13
\$3.25
\$4.00
\$4.75
\$5.50
Age
Weekly Allowance
## Personal Tutor at tx.msmath1.com
For Exercises 1 and 2, use the four-step plan to solve each problem.
Example 1
1.
female walrus weighs about 1,835 pounds. How much less does an
2.
ANALYZE TABLES The table shows how the number of a certain bacteria
increases. At this rate, how many bacteria will there be after 2 hours?
(Hint: There are 60 minutes in one hour.)
(p. 25)
Example 2
(p. 26)
26
Time (min)
20
40
60
80
100
120
Number of Bacteria
10
20
40
80
## Chapter 1 Number Patterns and Functions
For
Exercises
3, 4
5, 6
See
Examples
1
2
For Exercises 38, use the four-step plan to solve each problem.
3.
TIME A bus departed at 11:45 A.M. It traveled 325 miles at 65 miles per
hour. How many hours did it take the bus to reach its destination?
4.
ANALYZE GRAPHS
Refer to the graph.
How many more
year-round schools
were there in
20022003 than
in 19981999?
5.
PATTERNS Complete
the pattern: 6, 11, 16,
21, , , .
## Growth of Public Year-Round
Education in the U.S.
20022003
3,181
20012002
3,011
20002001
Year
(/-%7/2+ (%,0
3,059
19992000
2,880
19981999
19971998
2,856
2,681
6.
## 2,400 2,600 2,800 3,000 3,200 3,400
SCHOOL The first
Number of Schools
five bells at Eds
Source: nayre.org
middle school ring at
8:50 A.M., 8:54 A.M.,
9:34 A.M., 9:38 A.M., and 10:18 A.M. If this pattern continues, when should
the next three bells ring?
## See pages 662, 695.
7.
MONEY The Corbetts are buying a 36-inch television for \$788. They plan
to pay in four equal payments. Find the amount of each payment.
Self-Check Quiz at
8.
SCIENCE Jupiter orbits the Sun at a rate of 8 miles per second. How far
does Jupiter travel in one day?
9.
## CHALLENGE Complete the pattern: 1, 1, 2, 6, 24, .
%842!02!#4)#%
tx.msmath1.com
H.O.T. Problems
10.
11.
*/ -!4( When using the four-step plan, explain why you
(*/
83 *5*/(
## Brandon can run one mile in
7 minutes. At this rate, how long
will it take him to run 8 miles?
A 58 min
C 54 min
B 56 min
D 15 min
13.
42 3
14.
12.
## In which corner will the circle be in
the next figure in the pattern?
F upper left
H lower left
G upper right
J lower right
(Page 658)
126 6
15.
49 7
16.
118 2
27
## Jerry S. Mendoza/AP/Wide World Photos
1-2
Prime Factors
Main IDEA
Find the prime
factorization of a
composite number.
Targeted TEKS 6.1
The student
represents and uses
rational numbers
in a variety of equivalent
forms. (D) Write prime
factorizations using
exponents.
## Any given number of squares can be arranged into one or more
different rectangles. The table shows the different rectangles that
can be made using 2, 3, or 4 squares. A 1 3 rectangle is the same
as a 3 1 rectangle.
Copy the table.
Number of
Squares
NEW Vocabulary
factor
prime number
composite number
prime factorization
Sketch of Rectangle
Formed
Dimensions of
Each Rectangle
12
13
1 4, 2 2
15
1 6, 2 3
..
.
20
1.
2.
3.
## For the numbers in which only one rectangle is formed, what do
you notice about the dimensions of the rectangle?
## When two or more numbers are multiplied, each number is called a
factor of the product.
17=7
in the Content Area
this lesson, visit
tx.msmath1.com.
28
The factors of 7
are 1 and 7.
1 6 = 6 and 2 3 = 6
The factors of 6 are 1 and 6,
and 2 and 3.
A whole number that has exactly two unique factors, 1 and the
number itself, is a prime number. A number greater than 1 with
more than two factors is a composite number.
## Identify Prime and Composite Numbers
Tell whether each number is prime, composite, or neither.
1 28
2 11
Factors of 28: 1, 2, 4, 7, 14, 28
Since 28 has more than two
factors, it is a composite
number.
Factors of 11: 1, 11
Since there are exactly two
factors, 11 is a prime number.
a.
48
b.
c.
81
## Every composite number can be expressed as a product of prime
numbers. This is called a prime factorization of the number. A
factor tree can be used to find the prime factorization of a number.
## Find Prime Factorization
3 Find the prime factorization of 54.
54
## Prime Factors When
writing the prime
factorization, it is
customary to write
the prime factors in
ascending order, that
is, from least to
greatest.
## Write the number that is
being factored at the top.
54
2 27
## Choose any pair of whole
number factors of 54.
3 18
23 9
## Continue to factor any
number that is not prime.
329
2333
## Except for the order, the
prime factors are the same.
3233
d.
34
e.
72
## Personal Tutor at tx.msmath1.com
+%9#/.#%04
Infinite Infinite means
endless.
Number
Definition
Examples
prime
## A whole number that has exactly two
factors, 1 and the number itself.
11, 13, 23
composite
two factors.
6, 10, 18
neither prime
nor composite
## 1 has only one factor.
0 has an infinite number of factors.
0, 1
29
Examples 1, 2
(p. 29)
Example 3
(p. 29)
1.
10
2.
3.
4.
61
8.
19
5.
36
9.
## GEOGRAPHY The state of South Carolina
has 46 counties. Write 46 as a product of
primes.
6.
81
7.
65
3/54(
#!2/,).!
(/-%7/2+ (%,0
For
Exercises
1021, 36,
37
2235
10.
17
11.
12.
15
13.
44
14.
23
15.
57
16.
45
17.
29
18.
56
19.
93
20.
53
21.
31
See
Examples
1, 2
3
22.
24
23.
18
24.
40
25.
75
26.
27
27.
32
28.
49
29.
25
30.
42
31.
104
32.
55
33.
77
## ANALYZE TABLES For
Exercises 3438, use the table.
34. Which speed(s) have a
prime factorization of
exactly three factors?
35.
Self-Check Quiz at
tx.msmath1.com
30
Speed (mph)
70
60
50
43
40
Animal
rabbit
giraffe
grizzly bear
elephant
squirrel
Speed (mph)
35
32
30
25
12
## Source: The World Almanac for Kids
36.
Of the cheetah, antelope, lion, coyote, and hyena, which have speeds
that are prime numbers?
37.
Of the rabbit, giraffe, grizzly bear, elephant, and squirrel, which have
speeds that are composite numbers?
38.
Name three speeds that have exactly two prime factors in common.
%842!02!#4)#%
See pages 662, 695.
## Which speed(s) have a
prime factorization whose
factors are all equal?
Animal
cheetah
antelope
lion
coyote
hyena
39.
125
40.
## Chapter 1 Number Patterns and Functions
114
41.
179
42.
291
H.O.T. Problems
43.
All odd numbers greater than or equal to 7 can be expressed as the sum
of three prime numbers. Which three prime numbers have a sum of 59?
44.
SHOPPING Amanda bought bags of snacks that each cost the same. She
spent a total of \$30. Find three possible costs per bag and the number of
bags that she could have purchased.
45.
OPEN ENDED Select two prime numbers that are greater than 50 but less
than 100.
46.
NUMBER SENSE Twin primes are two prime numbers that are consecutive
odd integers such as 3 and 5, 5 and 7, and 11 and 13. Find all of the twin
primes that are less than 100.
## CHALLENGE A counterexample is an example that shows a statement is not
true. Find a counterexample for the statement below. Explain your
reasoning.
All even numbers are composite numbers.
*/ -!4( Explain how you know a number is prime.
(*/
48.
83 *5*/(
47.
49.
51.
A 7
B 31
C 39
D 47
50.
## The volume of a rectangular prism
can be found by multiplying the
length, width, and height of the
prism. Which of the following could
be the possible dimensions of the
rectangular prism below?
F 22257
G 2357
H 2257
A 2 ft 6 ft 6 ft
J 357
B 3 ft 5 ft 7 ft
C 5 ft 5 ft 7 ft
D 3 ft 5 ft 5 ft
52.
## PATTERNS Complete the pattern: 5, 7, 10, 14, 19, .
53.
SCHOOL Each class that sells 75 tickets to the school play earns an
ice cream party. Marios class has sold 42 tickets. How many more
must they sell to earn an ice cream party? (Lesson 1-1)
54.
222
55.
55
(Lesson 1-1)
(Page 658)
56.
444
57.
10 10 10
31
1-3
## Powers and Exponents
Main IDEA
Use powers and
exponents in expressions.
## Any number can be written as a
product of prime factors.
## Targeted TEKS 6.1
The student
represents and uses
rational numbers
in a variety of equivalent
forms. (D) Write prime
factorizations using
TEKS 6.2(C).
## Fold a piece of paper in
half and make one hole
punch. Open the paper
and count the number
of holes. Copy the
table below and record
the results.
Number of
Folds
NEW Vocabulary
Number of
Holes
Prime
Factorization
1
.
.
.
5
base
exponent
power
squared
cubed
## Find the prime factorization of the number of holes and
record the results in the table.
Fold another piece of paper in half twice. Then make one
hole punch. Complete the table for two folds.
Complete the table for three, four, and five folds.
1.
2.
## How does the number of folds relate to the number of factors in
the prime factorization of the number of holes?
3.
## Write the prime factorization of the number of holes made if
you folded it eight times.
## A product of identical factors can be written using an exponent and a
base. The base is the number used as a factor. The exponent indicates
how many times the base is used as a factor.
5 factors
exponent
e
e
e
e
e
e
e
e
32 = 2 2 2 2 2 = 25
base
5 = 51.
32
## Chapter 1 Number Patterns and Functions
Horizons Companies
Powers
Words
25
32
103
## Write Powers and Products
Calculator You can
use a calculator to
evaluate powers.
To find 34, enter
4 ENTER 81.
The value of 34
is 81.
## 1 Write 3 3 3 3 using an exponent.
The base is 3. Since 3 is used as a factor four times, the exponent
is 4.
3 3 3 3 = 34
Write as a power.
2 Write 45 as a product of the same factor. Then find the value.
The base is 4. The exponent is 5. So, 4 is used as a factor five times.
45 = 4 4 4 4 4
Write 45 as a product.
= 1,024
Multiply.
## Write each product using an exponent.
a.
777
b.
10 10 10 10 10
Write each power as a product of the same factor. Then find the
value.
c.
23
d.
82
## 3 SCIENCE The approximate daytime surface temperature on the
Moon can be written as 28 degrees Fahrenheit. What is this
temperature?
28 = 2 2 2 2 2 2 2 2
Real-World Career
How Does an
Astronomer Use
Math? An astronomer
uses math to represent
great distances between
galaxies.
go to tx.msmath1.com.
= 256
Write 28 as a product.
Multiply.
e.
of 53?
f.
## TESTS A multiple choice test has 7 questions. If each question
has 4 choices, there are 47 ways the test can be answered. What
is the value of 47?
Personal Tutor at tx.msmath1.com
## Extra Examples at tx.msmath1.com
Tony Freeman/PhotoEdit
33
## Prime Factorization Using Exponents
Write the prime factorization of each number using exponents.
23
32
33
5 135
135 = 3 3 3 5
=
r
w
q
r
w
q
6 300
300 = 2 2 3 5 5
=
r
w
q
4 72
72 = 2 2 2 3 3
22 3
52
g.
Example 1
(p. 33)
Example 2
(p. 33)
Example 3
(p. 34)
34
h.
45
i.
120
## Write each product using an exponent.
1.
2222
2.
666
Write each power as a product of the same factor. Then find the value.
3.
26
5.
value of 35?
6.
## POPULATION An estimated 105 people live in Charleston, South
Carolina. About how many people live in Charleston?
(p. 33)
Examples 46
24
4.
37
7.
20
8.
48
9.
90
## (/-%7/2+ (%,0 Write each product using an exponent.
For
Exercises
1015
1623
24, 25
2633
See
Examples
1
2
3
46
10.
99
11.
8888
12.
3333333
13.
55555
14.
11 11 11
15.
777777
Write each power as a product of the same factor. Then find the value.
16.
24
17.
32
18.
54
19.
105
20.
93
21.
65
22.
81
23.
17
24.
## FOOD The number of Calories in two pancakes can be written as 73.
What whole number does 73 represent?
25.
## LANGUAGE An estimated 109 people in the world speak Mandarin
Chinese. About how many people speak this language?
26.
25
27.
56
28.
50
29.
68
30.
88
31.
98
32.
560
33.
378
34.
## FISH To find the amount of water a
cube-shaped aquarium holds, find
the cube of the measure of one side of
the aquarium. Express the amount
of water the aquarium shown holds
as a power. Then find the amount in
cubic units.
18 units
18 units
18 units
Write each power as a product of the same factor. Then find the value.
35.
seven squared
38.
## GARDENING Mrs. Locaputos garden is organized into 6 rows. Each row
contains 6 vegetable plants. How many total vegetable plants does
Mrs. Locaputo have in her garden? Write using exponents, and then
find the value.
39.
## HOBBIES A knitted scarf is made by joining 20 square blocks that are
each made up of 20 rows of 20 stitches. How many total stitches does
the scarf contain? Write using exponents, and then find the value.
40.
41.
%842!02!#4)#%
36.
eight cubed
37.
## See pages 662, 695.
Self-Check Quiz at
tx.msmath1.com
H.O.T. Problems
## Lesson 1-3 Powers and Exponents
35
42.
FIND THE ERROR Anita and Tyree are finding the value of 64. Who is
64 = 6 6 6 6
= 1,296
64 = 6 4
= 24
Anita
Tyree
## CHALLENGE For Exercises 4345,
refer to the table at the right.
43.
## Describe the pattern for the
powers of 3. Find 30.
44.
## Describe the pattern for the
powers of 5. Find 50.
45.
Powers of 5
54
34 = 81
33 = 27
32 = 9
31 = 3
30 =
= 625
104 = 10,000
53 = 125
52 = 25
103 = 1,000
102 = 100
51 =
101 =
100
50
=
## If the pattern of figures continues,
which value represents the seventh
figure in the pattern?
48.
360?
F 22 3 5 2
H 2 2 33 5
12
22
J 2 32 5
32
A 72
C 77
B 17
D 37
63
53.
## TIME Find the number of seconds in a day if there are 60 seconds
in a minute. (Lesson 1-1)
50.
36 3
55.
51.
52.
71
(Page 658)
45 5
29
(Lesson 1-2)
49.
36
(*/
83 *5*/(
G 2 3 32 5
54.
Powers of 10
## Describe the pattern for the
powers of 10. Find 101 and 100.
46.
47.
Powers of 3
56.
104 8
57.
120 6
1- 4
Order of Operations
Main IDEA
Find the value of
expressions using the
order of operations.
Targeted TEKS 6.2
subtracts, multiplies,
and divides to solve
problems and justify solutions.
(E) Use order of operations
to simplify whole number
expressions (without
exponents) in problem
solving situations.
## HEALTH The table shows
the number of Calories
burned in one minute for
two different activities.
Calories Burned
per Minute
8
10
Activity
1.
## How many Calories
would you burn by
walking for 5 minutes?
by running for 15 minutes?
2.
## Find the number of Calories a person would burn by walking
for 5 minutes and then running for 15 minutes.
3.
## What two operations did you use in Exercises 1 and 2? Explain
how to find the answer to Exercise 2 using these operations.
NEW Vocabulary
numerical expression
order of operations
## A numerical expression like 5 8 + 15 10 is a combination of
numbers and operations. The order of operations tells you which
operation to perform first so that everyone finds the same value for
an expression.
+%9#/.#%04
Order of Operations
## 1. Simplify the expressions inside grouping symbols, like parentheses.
2. Find the value of all powers.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
## Use Order of Operations
Find the value of each expression.
1 4+35
4+35
= 4 + 15
= 19
Multiply 3 and 5.
2 10 - 2 + 8
10 - 2 + 8
=8+8
= 16
a.
10 + 2 15
## Extra Examples at tx.msmath1.com
b.
16 2 4
Lesson 1-4 Order of Operations
37
## Parentheses and Exponents
Find the value of each expression.
3 20 4 + 17 (9 - 6)
20 4 + 17 (9 - 6) = 20 4 + 17 3
= 5 + 17 3
= 5 + 51
= 56
4 3 62 + 4
3 62 + 4 = 3 36 + 4
= 108 + 4
= 112
Subtract 6 from 9.
Divide 20 by 4.
Multiply 17 by 3.
Find 62.
Multiply 3 and 36.
## Find the value of each expression.
c.
25 (5 - 2) 5 - 12
d.
24 23 + 6
## 5 MOVIES Javier and four friends go to the movies. Each person
buys a movie ticket, a snack, and a soda. Write an expression for
the total cost of the trip to the movies. Then find the total cost.
Cost of Going to the Movies
Item
ticket
snack
soda
Cost (\$)
The top-grossing movie
\$377 million. The topgrossing movie of
\$437 million.
To find the total cost, write an expression and then find its value.
Words
Expression
## cost of 5 tickets plus cost of 5 snacks plus cost of 5 sodas
5 \$7
5 \$3
5 \$2
Source: movieweb.com
5 \$7 + 5 \$3 + 5 \$2
= \$35 + 5 \$3 + 5 \$2
Multiply 5 and 7.
= \$35 + \$15 + 5 \$2
Multiply 5 and 3.
## = \$35 + \$15 + \$10
Multiply 5 and 2.
= \$60
## The total cost of the trip to the movies is \$60.
e.
SHOPPING A bath and body store sells lotions for \$5, candles for
\$7, and lip balms for \$2. Write an expression for the total cost of
3 lotions, 2 candles, and 4 lip balms. Then find the total cost.
Personal Tutor at tx.msmath1.com
38
CORBIS
Examples 14
(pp. 3738)
## Find the value of each expression.
1.
9+3-5
2.
10 - 3 + 9
3.
(26 + 5) 2 - 15
4.
18 (2 + 7) 2 + 1
6.
19 - (32 + 4) + 6
5. 52
Example 5
7.
(p. 38)
+82
THEATER Tickets to a play cost \$10 for members and \$24 for nonmembers.
Write an expression to find the total cost of 4 nonmember tickets and
2 member tickets. Then find the total cost.
## (/-%7/2+ (%,0 Find the value of each expression.
For
Exercises
811
1217
1821
22, 23
See
Examples
1, 2
3
4
5
8.
8+4-3
9.
9 + 12 - 15
10.
38 - 19 + 12
11.
22 - 17 + 8
12.
7 + 9 (3 + 8)
13.
(9 + 2) 6 - 5
14.
63 (10 - 3) 3
15.
66 (6 2) + 1
16.
27 (3 + 6) 5 - 12
17.
55 11 + 7 (2 + 14)
18.
53 - 12 3
19.
26 + 62 4
20.
15 - 23 4
21.
22 2 32
22.
Texas, is \$6 for adults and \$3 for children. Write an expression to find
the total cost of 3 adult tickets and 4 childrens tickets. Then find the
total cost.
23.
MUSIC A store sells DVDs for \$20 each and CDs for \$12. Write an
expression for the total cost of 4 DVDs and 2 CDs. Then find the total
cost of these items.
## Find the value of each expression.
%842!02!#4)#%
See pages 663, 695.
Self-Check Quiz at
tx.msmath1.com
24.
8 (24 - 3) + 8
25.
12 4 + (52 - 6)
26.
9 + 43 (20 - 8) 2 + 6
27.
96 42 + (25 2) - 15 - 3
28.
## PRETZELS Alexis is making chocolate covered pretzels for 15 friends.
She has covered 3 dozen pretzels. If she wants each friend to receive
exactly 3 pretzels and have no pretzels left over, write an expression
to find how many more pretzels she should cover. Then find this
number.
its value.
29.
30.
## the cube of the quotient of 24 and 6
Lesson 1-4 Order of Operations
39
H.O.T. Problems
31.
## CHALLENGE Create an expression whose value is 10. It should contain four
numbers and two different operations.
32.
FIND THE ERROR Haley and Ryan are finding 7 - 3 + 2. Who is correct?
7-3+2=7-5
=2
7-3+2=4+2
=6
Ryan
Haley
33.
34.
35.
## */ -!4( Write a real-world problem that can be solved using
(*/
83 *5*/(
order of operations. Then solve the problem.
Arleta is 2 years younger than Josh, and Josh is 5 years older than
Marissa who is 9 years old. Which table could be used to find
Arletas age?
A
Name
Arleta
Josh
Marissa
Age (years)
9+5
9+5-2
9
Name
Arleta
Josh
Marissa
Age (years)
5
4
9
Name
Arleta
Josh
Marissa
Age (years)
2
5
9
Name
Arleta
Josh
Marissa
Age (years)
9+5-2
9+5
9
PHONE TREE Four members of a certain phone tree are each given
4 people to contact. If the phone tree is activated, the total number
of calls made is 44. How many calls is this? (Lesson 1-3)
36.
42
37.
40.
40
26 + 98
41.
75
38.
110
39.
130
42.
61 + 19
43.
54 + 6
(Page 657)
23 + 16
## (l)David Young-Wolff/PhotoEdit, (r)Tony Freeman/PhotoEdit
(Lesson 1-2)
CH
APTER
1
1.
2.
Mid-Chapter Quiz
Lessons 1-1 through 1-4
## TECHNOLOGY Roberto records the songs
and music videos listed below onto a
recordable CD that holds 700 megabytes
of data. How much storage space is left on
the CD? (Lesson 1-1)
song or video
size (MB)
song #1
35
song #2
40
song #3
37
## Write the prime factorization of each
number using exponents. (Lesson 1-3)
9.
12.
22
10.
40
11.
75
## DOGS The average annual cost of food
for a dog is about 35 dollars. What is this
cost? (Lesson 1-3)
video #1
125
video #2
140
13.
10 - 6 + 20
14.
25 (15 - 10) 2
15.
32 + 32 2
16.
12 - (43 8) + 1
17.
## TEST PRACTICE Mr. Murphy, his wife,
and 4 children, went to the county fair.
Admission to the fair was \$7.75 for
an adult and \$5.50 for a child. Arrange
the problem-solving steps below in the
correct order to find the total cost of
the tickets.
## TEST PRACTICE A principal has
144 computers for 24 classrooms. How
many computers will be in each classroom
if each classroom is to have the same
number of computers? (Lesson 1-1)
A 6
B 24
C 120
D 3,456
## Tell whether each number is prime,
composite, or neither. (Lesson 1-2)
(Lesson 1-4)
## Step K: Multiply the cost of a childs
ticket by the number of
children.
3.
57
4.
97
5.
## Step M: Multiply the cost of an adult
ticket by the number of adults.
6.
## BOOKS Can a group of 41 books be placed
onto more than one shelf so that each shelf
has the same number of books and has
more than one book per shelf? Explain
## Step N: Write down the number of
children that are going to the
county fair.
Which list shows the steps in the correct
order? (Lesson 1-4)
F N, L, M, K
## Write each power as a product of the same
factor. Then find the value. (Lesson 1-3)
7.
34
8.
63
G N, M, K, L
H K, M, N, L
J M, K, N, L
1-5
Algebra: Variables
and Expressions
Main IDEA
Evaluate algebraic
expressions.
Targeted TEKS 6.2
subtracts, multiplies,
and divides to solve
problems and justify solutions.
(C) Use multiplication and
division of whole numbers
to solve problems including
situations involving equivalent
ratios and rates. (E) Use
order of operations to
simplify whole number
expressions (without
exponents) in problem
solving situations. Also
6.11(D).
NEW Vocabulary
algebra
variable
algebraic expression
evaluate
## ART SUPPLIES A box contains
some crayons. There are also
two crayons outside of the box.
The total number of crayons is
the sum of two and some number.
The two crayons represent the
known value 2, and the box
represents the unknown value.
1.
## What does some number represent?
2.
Find the value of the expression the sum of two and some number
if some number is 14.
3.
Assume you have two boxes of crayons each with the same
number of crayons inside. Write an expression that represents
the total number of crayons in both boxes.
## Algebra is a language of symbols. One symbol that is often used is a
variable. A variable is a symbol, usually a letter, used to represent a
number. The expression 2 + n represents the sum of two and some
number.
Algebraic expressions are combinations of variables, numbers, and
at least one operation.
at least one
operation
## Any letter can be
used as a variable.
2+n
r
w
q
Variable
Everyday Use able to
change or vary, as in
variable winds
Math Use a symbol
used to represent a
number
## The letter x is often used as a variable. It is also common to use the
first letter of the value you are representing.
The variables in an expression can be replaced with any number.
Once the variables have been replaced, you can evaluate, or find the
value of, the algebraic expression.
In addition to the symbol , there are other ways to show
multiplication.
42
23
5t
st
2 times 3
5 times t
s times t
## Evaluate Algebraic Expressions
1 Evaluate 16 + b if b = 25.
16 + b = 16 + 25
Replace b with 25.
= 41
## 2 Evaluate x - y if x = 64 and y = 27.
x - y = 64 - 27
Replace x with 64 and y with 27.
= 37
Multiplication
In algebra, the
symbol is often
used to represent
multiplication, as the
symbol may be
confused with the
variable x.
## Subtract 27 from 64.
3 Evaluate 5t + 4 if t = 3.
5t + 4 = 5 3 + 4 Replace t with 3.
= 15 + 4
Multiply 5 and 3.
= 19
a. a + 8
b. a - b
c. a b
d. 2a - 5
## 4 An expression for finding the area of a triangle whose height
is 3 units longer than its base is (b + 3) b 2, where b is the
measure of the base. Find the area of such a triangle with a
base 8 units long.
B 25 units2
C 44 units2
D 88 units2
A 20 units2
You need to find the value of the expression given b = 8.
Preparing for the
Test In preparation for
the test, it is often
yourself with important
formulas or rules such
as the rules for order of
operations.
## Solve the Test Item
(b + 3) b 2 = (8 + 3) 8 2 Replace b with 8.
= 11 8 2
= 88 2
Multiply 11 and 8.
= 44
Divide 88 by 2.
The area of the triangle is 44 units2. The answer is C.
e.
## If admission to a fair is \$7 per person, and each ride ticket costs
\$2, the total cost for admission and t ride tickets is 7 + 2t. Find
the total cost for admission and 5 ride tickets.
F \$9
G \$17
H \$35
J \$45
## Personal Tutor at tx.msmath1.com
Extra Examples at tx.msmath1.com
43
Examples 13
(p. 43)
Example 4
1.
3+m
2.
z+5
3.
z-m
4.
m-2
5.
4m - 2
6.
2z + 3
7.
## TEST PRACTICE The amount of money that remains from a
\$20 dollar bill after Malina buys 4 party favors for p dollars each
is 20 - 4p. Find the amount remaining if each favor costs \$3.
(p. 43)
A \$4
C \$17
B \$8
D \$48
For
Exercises
819
2027
5153
See
Examples
1, 2
3
4
8.
m + 10
9.
n+8
10.
9-m
11.
22 - n
12.
n4
13.
12 m
14.
n3
15.
6m
16.
m+n
17.
n+m
18.
n-6
19.
m-1
20.
b-a
21.
c-b
22.
5c + 6
23.
2b + 7
24.
3a - 4
25.
4b - 10
26.
## BALLOONING Distance traveled can be found using the expression rt,
where r represents rate and t represents time. How far did a hot air
balloon travel at a rate of 15 miles per hour for 6 hours?
27.
## RACING To find the average speed of a racecar, use the expression d t,
where d represents distance and t represents time. Find the speed s of a
racecar that travels 508 miles in 4 hours.
## Evaluate each expression if a = 4, b = 15, and c = 9.
The average speed at
the 2005 Daytona 500
was 135.2 mph.
Source: nascar.com
44
CORBIS
28.
c2 + a
29.
b2 - 5c
30.
3a 4
31.
4b 5
32.
5b 2
33.
2ac
34.
35.
## What is the value of st 6r if r = 5, s = 32, and t = 45?
36.
PLANES The expression 500t can be used to find the distance traveled by
a DC10 aircraft. The variable t represents time in hours. How far can a
DC10 travel in 4 hours?
37.
4z + 8 - 6
38.
6x - 9 3
39.
15 + 9x 3
40.
7z 4 + 5x
42.
z2 - (5x)
41. y2
43.
(3z)
## GEOMETRY To find the area of a rectangle, use the
expression w, where represents the length, and
w represents the width of the rectangle. What is
the area of the rectangle shown?
7 ft
16 ft
44.
MUSIC As a member of a music club, you can order CDs for \$15 each.
The music club also charges \$5 for each shipment. The expression
15n + 5 represents the cost of n CDs. Find the total cost for ordering
3 CDs.
45.
## ANALYZE TABLES To change a temperature given in degrees Celsius to
degrees Fahrenheit, first multiply the Celsius temperature by 9. Next,
divide the answer by 5. Finally, add 32 to the result. Write an expression
that can be used to change a temperature from degrees Celsius to
degrees Fahrenheit. Then use the information in the table below to
find the difference in average temperatures in degrees Fahrenheit for
San Antonio from January to April. (Hint: Convert to degrees
Fahrenheit first.)
%842!02!#4)#%
See pages 663, 695.
Self-Check Quiz at
tx.msmath1.com
## Average Monthly Temperature
for San Antonio, Texas
Month
Temp. (C)
January
10
April
20
July
29
H.O.T. Problems
46.
## OPEN ENDED Create two algebraic expressions involving multiplication
that have the same meaning.
47.
CHALLENGE Elan and Robin each have a calculator. Elan starts at zero
and adds 3 each time. Robin starts at 100 and subtracts 7 each time.
Suppose Elan and Robin press the keys at the same time. Will their
displays ever show the same number? If so, what is the number?
48.
## SELECT A TECHNIQUE Ichiro is evaluating x2 - z, where x = 3 and z = 8.
Which of the following techniques might Ichiro use to evaluate the
expression? Justify your selection(s). Then use the technique(s) to solve
the problem.
mental math
number sense
estimation
## Lesson 1-5 Algebra: Variables and Expressions
Sandy Felsenthal/CORBIS
45
49.
Which One Doesnt Belong? Identify the expression that does not belong
with the other three. Explain your reasoning.
3+4
5x
50.
51.
ab
7x + 1
## */ -!4( Compare and contrast numerical expressions and
(*/
83 *5*/(
algebraic expressions. Use examples in your explanation.
## The expression 2r can be used to find
the diameter of a circle, where r is
the length of the radius. Find the
diameter of the compact disc.
53.
## The table shows the results of a
survey in which people were asked to
name the place they use technology
when away from home.
Where People Use Technology
Number of
Place
Responses
on vacation
57
while driving
57
outdoors
42
mall
x
gym
17
public restrooms
10
12 cm
diameter
A 3 cm
C 12 cm
B 6 cm
D 24 cm
52.
## GRIDDABLE The expression 4s can
be used to find the perimeter of a
square where s represents the length
of a side. What is the perimeter in
inches of the square below?
## Which expression represents the total
number of people who participated
in the survey?
F x - 183
H x + 183
G x + 173
J 2x + 183
26 in.
## Find the value of each expression.
55. 52
(Lesson 1-4)
54.
12 - 8 2 + 1
+ (20 2) - 7
57.
SCIENCE The distance from Earth to the Sun is close to 108 miles.
How many miles is this? (Lesson 1-3)
58.
## TESTS On a test with 62 questions, Trey missed 4 questions. How
many did he get correct? (Lesson 1-1)
59.
46
18 - 9
60.
5 + 18
## Chapter 1 Number Patterns and Functions
56.
21 (3 + 4) 3 - 8
(Page 657)
61.
14 + 7
62.
21 - 15
Explore
1- 6
Main IDEA
Illustrate functions using
technology.
Targeted TEKS 6.4
The student uses
letters as variables
in mathematical
expressions to describe how
one quantity changes when a
related quantity changes.
(A) Use tables and symbols
to represent and describe
proportional and other
relationships such as those
involving conversions,
arithmetic sequences (with a
constant rate of change),
perimeter and area.
## Graphing Calculator Lab
Function Machines
A function machine takes a value called the input and performs one or
more operations on it according to a rule to produce a new value
called the output.
3
## Another way to write the rule of a function machine is as an algebraic
expression. For the function machine above, an input value of x
produces an output value of x + 3. You can use the TI-83/84 Plus
graphing calculator to model this function machine.
## Use a graphing calculator to model a function machine for the
rule x + 3. Then use this machine to find the output values for
the input values 2, 3, 4, 9, and 12.
The graphing calculator uses X for input and Y for output values.
Enter the rule for the function into the function list. Press
to access the function list. Then press X,T,,n
3 to
enter the rule.
## Next set up a table of input and output values. Press 2nd
TblSet to display the table setup screen. Press
ENTER to highlight Indpnt: Ask. Then press
ENTER to
highlight Depend: Auto.
Graphing
Calculators
Indpnt means
independent variable
and is the input or
x-value. Depend
means dependent
variable and is the
output or y-value.
Explore 1-6 Graphing Calculator Lab: Function Machines
47
## Access the table by pressing 2nd TABLE . The calculator
will display an empty function table.
Now key in your input values, pressing ENTER after each
one.
## Use a graphing calculator to model a function machine for each
of the following rules. Use the input values 5, 6, 7, and 8 for x.
Record the inputs and their corresponding outputs in a table.
a.
x-4
b.
x+5
c.
x-2
d.
x-3
e.
x2
f.
x3
1.
## Examine the columns of inputs and outputs for Exercises ad.
What pattern do you observe in the column of inputs? What
pattern do you observe in each column of outputs?
2.
## How would each column of outputs change if the order of the
inputs was reversed to be 8, 7, 6, and 5?
3.
## Examine the columns of inputs and outputs for Exercises e and f.
What patterns do you observe in the column of outputs?
4.
## Compare the patterns you observed in Exercise 3 to the rules given
for Exercises e and f. What do you notice?
## MAKE A CONJECTURE Based on your observations from Exercises 14,
make a conjecture about the rule for each set of input and output
5.
48
Input (x)
Output (y)
6.
Input (x)
Output (y)
10
12
11
12
13
14
3
4
5
6
3
4
5
6
18
24
30
36
## Other Calculator Keystrokes at tx.msmath1.com
1- 6
Algebra: Functions
Main IDEA
Complete function tables
and find function rules.
## LIFE SCIENCE A brown bat
can eat 600 mosquitoes an hour.
## Targeted TEKS 6.4
The student uses
letters as variables
in mathematical
expressions to describe how
one quantity changes when a
related quantity changes.
(A) Use tables and symbols
to represent and describe
proportional and other
relationships such as those
involving conversions,
arithmetic sequences (with a
constant rate of change),
perimeter and area. Also
1.
## Write an expression to represent the
number of mosquitoes a brown bat can
eat in 2 hours; in 5 hours; in t hours.
## A function is a relationship that assigns exactly one output value to
one input value. The number of mosquitoes eaten (output) depends
on the number of hours (input). You can organize the input-output
values in a function table.
Input
Function Rule
Output
Number of
Hours (t)
600t
Mosquitoes
Eaten
600(1)
600
600(2)
1,200
600(3)
1,800
NEW Vocabulary
function
function table
function rule
defining the variable
## The function rule describes
the relationship between
each input and output.
## Complete a Function Table
1 The output is 4 more than the input. Complete a function table
for this relationship.
The function rule is x + 4. Add 4 to each input.
Input (x)
Output (x + 4)
Input (x)
Output (x + 4)
10
10
14
12
12
16
14
14
18
a.
Input (x)
Output (x - 2)
2
5
8
## Extra Examples at tx.msmath1.com
Joe McDonald/CORBIS
b.
Input (x)
Output (2x)
2
5
49
## Find the Rule for a Function Table
Check for
Reasonableness
rule is correct, test
more than one input
value.
## 2 Find the rule for the function table.
Study the relationship between each
Input (x) Output ()
input and output. Each output is three
2
6
times the input.
5
15
So, the function rule is 3 x, or 3x.
7
21
c.
d.
Input (x)
Output ()
16
10
Input (x)
Output ()
## When you write a function rule that represents a real-world situation,
you first choose a variable to represent the input. This is called
defining the variable.
## 3 ENTERTAINMENT A local band charges \$70 for each hour it
performs. Define a variable. Then write a function rule that
relates the total charge to the number of hours it performs.
Determine the function rule. The cost of the performance depends
on the number of hours. Let h represent the number of hours.
Words
Variable
Expression
70 h
e.
50
## SHOPPING A department store is deducting \$10 off the total
purchase for shoppers from 6 A.M. to 7 A.M. Define a variable.
Write a function rule that relates the final cost to the total
purchase amount.
Example 1
(p. 49)
Example 2
(p. 50)
Example 3
1.
For
Exercises
67
813
14, 15
See
Examples
1
2
3
Output (x + 3)
0
2
4
2.
Input (x)
Output (4x)
3
6
## Find the rule for each function table.
3.
5.
(p. 50)
(/-%7/2+ (%,0
Input (x)
1
3
5
4.
2
4
3
6
6
12
JELLY BEANS Lamar is buying jelly beans for a party. He can buy them in
bulk for \$3 a pound. Define a variable. Write a function rule that relates
the total cost of the jelly beans to the number of pounds he buys.
6.
Input (x)
Output (x - 4)
4
8
11
7.
Input (x)
Output (x 3)
## Find the rule for each function table.
8.
11.
9.
10.
10
15
10
16
20
15
22
11
35
25
34
17
12.
13.
14.
AGES Ricardo is 8 years older than his sister. Define a variable. Write a
function rule that relates Ricardos age to his sisters age.
15.
FOOD Whitney has a total of 30 cupcakes for her guests. Define a variable.
Write a function rule that relates the number of cupcakes per guest to the
number of guests.
Lesson 1-6 Algebra: Functions
51
## Find the rule for each function table.
16.
17.
4
5
18.
13
28
13
43
11
19
12
58
2
3
For Exercises 1921, define a variable and write a function rule. Then
solve each problem.
19.
MOOSE Moose can swim up to 6 miles per hour. At this rate, find the
total number of miles a moose can swim in two hours.
20.
## GREETING CARDS Kyle is buying 7 greeting cards that cost \$2 each. If he
has a coupon for \$3 off his total purchase, how much will he spend for
the greeting cards?
21.
## MUSIC An Internet company charges \$10 a year to be a member of its
music program. It also charges \$1 for each song you download. How
much will it cost if you download 46 songs in a year?
22.
FIND THE DATA Refer to the Texas Data File on pages 1619. Choose
some data and write about a real-world situation that can be described
by a function rule.
23.
## MONEY MATTERS For a school
project, Sarah and her friends
made hair scrunchies to sell for
\$3 each and friendship bracelets
to sell for \$4 each. Write a
function rule to represent the
total selling price of s scrunchies
and b bracelets. Then use the
function rule to find the price of
10 scrunchies and 12 bracelets.
24.
OPEN ENDED Create a function table. Then write a function rule. Choose
three input values and find the output values.
25.
FIND THE ERROR Nicole and Olivia are finding the function rule when
each output is 5 less than the input. Who is correct? Explain.
%842!02!#4)#%
See pages 663, 695.
Self-Check Quiz at
tx.msmath1.com
H.O.T. Problems
Function rule:
x-5
Olivia
52
Function rule:
5-x
Nicole
26.
## CHALLENGE Suppose the estimated 223 million Americans who have
jugs or bottles of coins around their homes put coins back into
circulation at a rate of \$10 a year. Create a function table showing the
amount that would be recirculated in 1, 2, and 3 years.
27.
## SELECT A TOOL Courtney is evaluating the function rule 43x - 6 for
an input of 4. Which of the following tools might Courtney use to
determine the output? Justify your selection(s). Then use the tool(s) to
solve the problem.
real objects
28.
29.
paper/pencil
graphing calculator
(*/
83 *5*/(
table.
## Which expression best represents the
y values in terms of the x values?
x
11
13
15
A 2x + 3
C 3x - 2
B x+3
D 6-x
30.
## The school store makes a profit of
\$5 for each sweatshirt sold. Which
expression best represents the profit
on 25 sweatshirts?
F 5 25
H 25 5
G 5 + 25
J 25 - 5
## Evaluate each expression if a = 3, b = 6, and c = 10.
31.
b-a
34.
FOOD A deli sells wraps for \$5 and soup for \$3 a bowl. Write and
solve an expression for the cost of 3 wraps and 2 bowls of soup.
32.
3c + a
(Lesson 1-5)
33.
bc + 12
(Lesson 1-4)
35.
AREA CODES California has 52 area codes. What is the value of 52?
(Lesson 1-3)
36.
## PREREQUISITE SKILL The table represents the
average amounts consumers spent on
back-to-school merchandise in a recent year.
How much more did consumers spend on
clothing, accessories, and shoes than on school
supplies? Use the four-step plan. (Lesson 1-1)
Back-to-School Spending
Merchandise
Amount (\$)
Clothing/Accessories
219
Electronic Equipment
101
Shoes
90
School Supplies
73
## Lesson 1-6 Algebra: Functions
53
1-7
Problem-Solving Investigation
MAIN IDEA: Solve problems by using the guess and check strategy.
Targeted TEKS 6.11 The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations
in other disciplines, and activities in and outside of school. (C) Select or develop an appropriate problem-solving strategy from a
variety of different types, including . . . guessing and checking . . . to solve a problem. Also addresses TEKS 6.11(A), 6.11(B).
e-Mail:
## YOUR MISSION: Use guess and check to solve the
problem.
THE PROBLEM: How many packages of new and used
comic books did Trent receive for his birthday?
EXPLORE
PLAN
SOLVE
CHECK
## TRENT: The comic book store sells used comic
books in packages of 5 and new comic books
in packages of 3. My sister bought me a
total of 16 comic books for my birthday.
You know that the store sells 3-book packages and 5-book packages. You need to
find the number of packages of each that were bought.
Make a guess until you find an answer that makes sense for the problem.
Number of
3-book
packages
Number of
5-book
packages
1(3) + 1(5) = 8
1(3) + 2(5) = 13
2(3) + 1(5) = 11
2(3) + 2(5) = 16
Total Number of
Comic Books
So, Trents sister bought two 3-book packages and two 5-book packages.
Two 3-book packages result in 6 books. Two 5-book packages result in 10 books.
Since 6 + 10 is 16, the answer is correct.
Explain when to use the guess and check strategy to solve a problem.
*/ -!4( Write a problem that can be solved using guess
(*/
2.
83 *5*/(
and check. Then tell the steps you would take to find the solution of
the problem.
1.
54
John Evans
Exercises 36.
3.
4.
5.
6.
9.
## MONEY Mateo has seven coins that total
\$1.50. What are the coins?
10.
pattern.
## SCIENCE Each hand in the human body
has 27 bones. There are 6 more bones in
3 fewer bones in your palm than in your
wrist. How many bones are in each part of
11.
## ORDER OF OPERATIONS Use the symbols
+, -, , or to make the following math
sentence true. Use each symbol only
once.
## NUMBERS Antonio is thinking of four
numbers from 1 through 9 whose sum is
23. Find the numbers.
MONEY A wallet contains 14 bills worth
\$150. If all of the money was in \$5 bills,
\$10 bills, and \$20 bills, how many of each
bill was in the wallet?
## Use any strategy to solve Exercises 711.
Some strategies are shown below.
3 4 6 1 = 18
## For Exercises 1214, select the appropriate
operation(s) to solve the problem.
Justify your selection(s) and solve the
problem.
12.
## JUMP-A-THON Karl is collecting money
for a jump-a-thon. His goal is to collect
\$85. So far he has collected \$10 each
from two people and \$5 each from
six people. How far away is he from
his goal?
13.
## ANALYZE TABLES How many fewer
students were on the 6th grade honor
roll in the 3rd trimester than in the
1st trimester?
G STRATEGIES
PROBLEM-SOLVIN
tep plan.
Use the four-s
eck.
Guess and ch
7.
## NUMBERS The sum of two prime numbers
is 20. Find the numbers.
## ANALYZE TABLES How much higher is
Mount Hood than Mount Marcy?
Mountain
Elevation (ft)
Mount Marcy
5,344
Mount Kea
Mount Mitchel
Mount Hood
13,796
6,684
11,239
## 6th Grade Honor Roll Students
1st Trimester
40
2nd Trimester
3rd Trimester
37
31
Source: worldatlas.com
8.
## SCHOOL Paige studied 115 spelling words
in five days. How many words did she
study each day if she studied the same
amount of words each day?
14.
## JOBS Felisa works after school at a
bicycle store. Her hourly wage is \$6.
If Felisa works 32 hours, how much does
she earn?
## Lesson 1-7 Problem-Solving Investigation: Guess and Check
55
Topic Sentences
A topic sentence is a sentence that expresses the main idea in a
paragraph. It is usually found near the beginning of the paragraph
and is followed by supporting details. Heres the beginning of a
paragraph about Mrs. Garcias math class.
Topic sentence
Mrs. Garcias math class was doing research about wild horses
living on public lands. They found that there are about 30,000
wild horses living in Nevada, 4,000 living in Wyoming, and 2,000
living in California.
However, in a word problem, the topic sentence is usually found
near the end. It is the sentence or question that tells you what you
need to find. Heres the same information, written as a word problem.
Mrs. Garcias math class was doing research about wild horses
that live on public lands. They found that there are about 30,000
wild horses living in Nevada, 4,000 living in Wyoming, and 2,000
living in California. How many more wild horses live on public
lands in Nevada than in California?
Topic sentence
## When you start to solve a word problem, follow these steps.
Step 1 Skim through the problem, looking for the topic sentence.
Step 2 Go back and read the problem more carefully, looking for the
supporting details you need to solve the problem.
Refer to pages 59 and 60. For each exercise below, write the topic
sentence. Do not solve the problem.
1.
Exercise 29
2.
Exercise 30
3.
Exercise 32
4.
Exercise 39
5.
Exercise 40
6.
Exercise 41
56
CORBIS
## Chapter 1 Number Patterns and Functions
1-8
Algebra: Equations
Main IDEA
Solve equations by using
mental math and the
guess and check strategy.
Targeted TEKS 6.11
The student applies
to solve problems
connected to everyday
experiences, investigations in
other disciplines, and activities
in and outside of school.
(C) Select or develop an
appropriate problem-solving
strategy from a variety of
different types, including
drawing a picture, looking for
a pattern, systematic
guessing and checking,
acting it out, making a table,
working a simpler problem,
or working backwards to
solve a problem. (D) Select
tools such as real objects,
manipulatives, paper/pencil,
and technology or techniques
such as mental math,
estimation, and number
sense to solve problems.
NEW Vocabulary
equation
equals sign
solve
solution
## When the amounts on each side
of a scale are equal, the scale is
balanced.
Place three centimeter
cubes and a paper bag
on one side of a scale.
Place eight centimeter cubes
on the other side of the scale.
1.
## Suppose the variable x represents the number of cubes in the
bag. What equation represents this situation?
2.
Replace the bag with centimeter cubes until the scale balances.
How many centimeter cubes did you need to balance the
scale?
Let x represent the bag. Model each sentence on a scale. Find the
number of centimeter cubes needed to balance the scale.
3.
x+1=4
4.
x+3=5
5.
x+7=8
6.
x+2=2
## An equation is a sentence that contains an equals sign, =. A few
examples are shown below.
2+7=9
10 - 6 = 4
14 = 2 7
2+x=9
4=k-6
15 m = 3
## When you replace a variable with a value that results in a true
sentence, you solve the equation. That value for the variable is the
solution of the equation.
The equation
is 2 + x = 9.
2+x=9
2+7=9
## The value for the
variable that results in
a true sentence is 7.
So, 7 is the solution.
9=9
57
## Find the Solution of an Equation
1 Is 3, 4, or 5 the solution of the equation a + 7 = 11?
Value of a
3
4
5
a + 7 11
3 + 7 = 11
10 11
4 + 7 = 11
11 = 11
5 + 7 = 11
12 11
no
yes
no
a.
## Solve an Equation Mentally
2 Solve 12 = 3h mentally.
12 = 3h
THINK 12 equals 3 times what number?
12 = 3 4 You know that 12 = 3 4.
12 = 12
The solution is 4.
b.
Solve 24 w = 8 mentally.
## 3 ANIMALS An antelope can run 49 miles per hour faster than
a squirrel. Let s represent the speed of a squirrel. Solve the
equation s + 49 = 61 mentally to find the speed of a squirrel.
Use the guess and check strategy.
and body length of a
ground squirrel can
range from 4 inches to
14 inches.
Try 10.
Try 11.
Try 12.
s + 49 = 61
?
10 + 49 = 61
59 61
s + 49 = 61
?
11 + 49 = 61
60 61
s + 49 = 61
?
12 + 49 = 61
61 = 61
c.
## ELECTIONS Mississippi has 9 fewer electoral votes than Georgia.
Let v represent Georgias number of electoral votes. Solve
15 - v = 9 to find Mississippis number of electoral votes.
Personal Tutor at tx.msmath1.com
58
Example 1
(p. 58)
Example 2
(p. 58)
Example 3
## Identify the solution of each equation from the list given.
1.
9 + w = 17; 7, 8, 9
2.
d - 11 = 5; 14, 15, 16
3.
4 = 2y; 2, 3, 4
4.
8 c = 8; 0, 1, 2
5.
x + 6 = 18
8.
## FOOD The equation b + 7 = 12 describes the number of boxes of cereal
and the number of breakfast bars in a kitchen cabinet. If b is the number
of breakfast bars, how many breakfast bars are there?
(p. 58)
(/-%7/2+ (%,0
For
Exercises
916
1728
29, 30
See
Examples
1
2
3
6.
n - 10 = 30
7.
15k = 30
## Identify the solution of each equation from the list given.
a + 15 = 23; 6, 7, 8
10.
## 29 + d = 54; 24, 25, 26
11.
35 = 45 - n; 10, 11, 12
12.
## 19 = p - 12; 29, 30, 31
13.
6w = 30; 5, 6, 7
14.
63 = 9k; 6, 7, 8
15.
36 s = 4; 9, 10, 11
16.
x 7 = 3; 20, 21, 22
9.
%842!02!#4)#%
17.
j + 7 = 13
18.
m + 4 = 17
19.
22 = 30 - m
20.
12 = 24 - y
21.
15 - b = 12
22.
25 - k = 20
23.
5m = 25
24.
10t = 90
25.
22 y = 2
26.
d3=6
27.
54 = 6b
28.
24 = 12k
29.
## MONEY The equation 45 + k = 63 represents the total cost before tax of a
pair of in-line skates for \$45 and a set of kneepads. If k is the cost of the
30.
## ANIMALS The equation b 12 = 6 describes the height of a grizzly bear,
where b is the height of the grizzly bear in inches. What is the height of
the grizzly bear in inches?
31.
RESEARCH Use the Internet or another reference source to find the only bear
species that is found in the Southern Hemisphere. What is the approximate
length and weight of this bear?
32.
## SCHOOL Last year, the number of students attending Glenwood Middle
School was 575. There are 650 students attending this year. The equation
575 + n = 650 shows the increase in the number of students from one
year to the next. Find the number of new students n.
33.
to 3? Explain.
## See pages 664, 695.
Self-Check Quiz at
tx.msmath1.com
59
H.O.T. Problems
34.
35.
## REASONING Tell whether the statement below is sometimes, always, or
never true.
Equations like a + 4 = 8 and 4 - m = 2 have exactly one solution.
CHALLENGE For Exercises 36 and 37, tell whether each statement is true or
In m + 8, the variable m can have any value.
37.
38.
## */ -!4( Create a real-world problem in which you would
(*/
83 *5*/(
solve the equation a + 12 = 30.
## The graph shows the life expectancy
of certain mammals. Which equation
can be used to find the difference d
between the number of years a blue
whale lives and the number of years a
gorilla lives?
Years
39.
36.
80
76
70
35
W Kill
Bl hal er
ue e
W
ha
le
Hu
m
an
El Af
ep ric
ha an
nt
Go
ril
la
A d + 35 = 80
90
100
80
60
40
20
0
B d - 35 = 80
C 80 + 35 = d
D d - 80 = 35
40.
## QUIZZES On a science quiz, Ivan earned 18 points. If there are 6 problems
worth 2 points each and 2 problems worth 4 points each, find the
number of problems of each type Ivan answered correctly. (Lesson 1-7)
41.
## CHORES Sophia earns a weekly allowance of \$4. Define a variable.
Write a function rule that relates the total allowance to the number
of weeks. Find the total allowance she earns in 8 weeks. (Lesson 1-6)
42.
3rst + 14
43.
45.
60
8 12
46.
(Lesson 1-5)
93s+t
44.
4 + t r 4s
(Page 658)
6 15
## Chapter 1 Number Patterns and Functions
47.
4 18
48.
5 17
Explore
1-9
Main IDEA
Use tables of data to
generate formulas.
Targeted TEKS 6.4
The student uses
letters as variables
in mathematical
expressions to describe how
one quantity changes when
a related quantity changes.
(B) Use tables of data
to generate formulas
representing relationships
involving perimeter, area,
volume of a rectangular
prism, etc.
Math Lab
Writing Formulas
The number of square units needed to cover the surface of a figure is
called its area. In this activity, you will explore how the area and side
lengths of rectangles and squares are related. You will then express
this relationship as an equation called a formula.
## On centimeter grid paper, draw, label,
and shade a rectangle with a length of
2 centimeters and a width of 3 centimeters.
2 cm
3 cm
## Count the number of squares shaded to
find the area of the rectangle. Then
record this information in a table like the one shown.
Units Area is measured in
square centimeters.
Rectangle
Length (cm)
Width (cm)
## Repeat Steps 1 and 2 for rectangles B, C, D, E, and F,
whose dimensions are shown in the table.
1.
2.
## Describe the relationship between the area of a rectangle and its
length and width in words.
3.
## MAKE A CONJECTURE What would be the area of a rectangle with
each of the following dimensions? Test your conjecture by
modeling each rectangle and counting the number of shaded
squares.
a.
4.
b.
## WRITE A FORMULA If A represents the area of a rectangle, write an
equation that describes the relationship between the rectangles
area A, length , and width w.
Explore 1-9 Math Lab: Writing Formulas
61
2 For each step below, draw new rectangles on grid paper and find
the areas. Organize the information in a table.
Using the original rectangles in Activity 1, double each
length, but keep the same width.
Using the original rectangles in Activity 1, double each
width, but keep the same length.
Using the original rectangles in Activity 1, double both the
length and width.
## ANALYZE THE RESULTS
Compare the areas you found in each step to the original areas.
Write a sentence describing how the area changed. Explain.
5.
Step 1
6.
Step 2
7.
Step 3
## On centimeter grid paper, draw, label,
and shade a square with a length of
2 centimeters.
2 cm
## Count the number of squares shaded to
find the area of the square. Record this
information in a table like the one shown.
Repeat Steps 1 and 2 for
squares B and C, whose
dimensions are shown in
the table.
Square
Side Length
(cm)
Area
(sq cm)
8.
9.
## MAKE A CONJECTURE What would be the area of a square with
side lengths of 8 centimeters? Test your conjecture.
10.
62
## WRITE A FORMULA If A represents the area of a square, write an
equation that describes the relationship between the squares
area A and side length s.
1-9
## Algebra: Area Formulas
Main IDEA
Find the areas of
rectangles and squares.
## PATTERNS Checkered patterns can often be
found on game boards and flags.
## Targeted TEKS 6.2
subtracts, multiplies,
and divides to
solve problems and justify
solutions. (C) Use
multiplication and division
of whole numbers to solve
problems including situations
involving equivalent ratios
and rates. 6.8 The student
solves application problems
involving estimation and
measurement of length,
area, time, temperature,
volume, weight, and
angles. (B) Select and use
appropriate units, tools, or
formulas to measure and to
solve problems involving
length (including perimeter),
area, time, temperature,
volume, and weight. Also
1.
NEW Vocabulary
area
formula
## Copy and complete the
table below.
Object
Squares Along
the Length
Squares Along
the Width
Squares Needed to
Cover the Surface
flag
game board
2.
What relationship exists between the length and the width, and
the number of squares needed to cover the surface?
## The area of a figure is the number of square
units needed to cover a surface. The rectangle
shown has an area of 24 square units.
4 units
6 units
## You can also use a formula to find the area of a
rectangle. A formula is an equation that shows
a relationship among certain quantities.
+%9#/.#%04
Words
24 square
units
Area of a Rectangle
## The area A of a rectangle is the
product of the length and
width w.
Model
w
Formula A = w
## Find the Area of a Rectangle
Area Units When
finding area, the units
are also multiplied.
So, area is given in
square units.
## 1 Find the area of a rectangle with length 12 feet
and width 7 feet.
A = w
Area of a rectangle
A = 12 7
A = 12 ft 7 ft
A = 84
Multiply.
A = 84 ft2
7 ft
12 ft
63
12 in.
a.
b.
6 in.
## a rectangle with a length
of 10 meters and a width
of 2 meters
## In Lesson 1-3, you wrote products as powers by using exponents.
The formula for the area of a square is also written with an exponent.
Interactive Lab tx.msmath1.com
+%9#/.#%04
Area of a Square
## The area A of a square is the
length of a side s squared.
Words
Formula A =
Model
s
s2
## Find the Area of a Square
2 Find the area of a square with side length 9 inches.
A = s2 Area of a square
A = 92
Replace s with 9.
9 in.
A = 81 Multiply.
9 in.
c.
length 5 meters
d.
## a square with side
length 7 feet
3 SPORTS Use the information at the left. What is the area of a high
school volleyball court?
The length is 60 feet, and the width is 30 feet.
A = w
Area of a rectangle
A high school volleyball
court is 60 feet long
and 30 feet wide.
A = 60 30
A = 1,800
Multiply.
Source: NFHS
e.
## SPORTS A high school basketball court measures 84 feet long
and 50 feet wide. What is the area of this court?
Personal Tutor at tx.msmath1.com
64
Example 1
(p. 63)
1.
2.
5 cm
8 ft
3 cm
15 ft
Example 2
(p. 64)
3.
4.
1 yd
4 ft
4 ft
Example 3
5.
(p. 64)
(/-%7/2+ (%,0
For
Exercises
613
1417
18, 19
See
Examples
1
2
3
1 yd
## TECHNOLOGY A television screen measures 9 inches by 12 inches. What
is the area of the viewing screen?
8 yd
6.
7.
14 ft
8.
9 in.
6 ft
4 yd
10 in.
9.
16 m
10.
25 cm
11. 17 ft
48 ft
20 cm
32 m
12.
12 inches.
13.
## What is the area of a rectangle with a length of 40 centimeters and a
width of 30 centimeters?
14.
15.
10 in.
16.
12 cm
3m
3m
17.
10 in.
12 cm
## What is the area of a square with a side length of 22 feet?
Lesson 1-9 Algebra: Area Formulas
65
18.
## SCHOOL A 3-ring binder measures 11 inches by 10 inches. What is the
area of the front cover of the binder?
19.
HOBBIES Meagan and her friends are knitting small squares to join
together to form a blanket. The side length of each square must be
7 inches. What is the area of each square?
## Find the area of each shaded region.
12 ft
20.
8 ft
21.
15 cm
22.
5m
4 ft
9 ft
5m
8 cm
11 m
15 cm
7 cm
7m
%842!02!#4)#%
23.
FIND THE DATA Refer to the Texas Data File on pages 1619. Choose
some data and write a real-world problem in which you would find the
area of a square or a rectangle.
24.
## REMODELING The Junkins are replacing the flooring in their kitchen
with ceramic tiles. They are deciding between 12-inch square tiles and
6-inch square tiles. What is the difference in the area of the two tiles
they are considering?
25.
## ANIMALS The floor spaces of two cages are
shown. The square footage of Cage 1 is
large enough for one guinea pig. For each
additional guinea pig, the cage should be
1 square foot larger. How many guinea pigs
should be kept in Cage 2?
## See pages 664, 695.
Self-Check Quiz at
tx.msmath1.com
H.O.T. Problems
1 ft
2 ft
2 ft
2 ft
26.
OPEN ENDED Draw and label a rectangle that has an area of 48 square
units.
27.
## NUMBER SENSE Give the dimensions of two different rectangles that
have the same area.
28.
FIND THE ERROR James and John are finding the area of the square with
a side of 8 feet. Who is correct? Explain your reasoning.
A = s2
A = 82
A=82
A = 16 m2
James
66
Cage 2
Cage 1
A = s2
A = 82
A=88
A = 64 m2
John
31.
29.
## CHALLENGE Suppose opposite sides of a rectangle are increased by
3 units. Would the area of the rectangle increase by 6 square units?
Use a model in your explanation.
30.
*/ -!4( Explain how to use the formula for the area of a
(*/
83 *5*/(
square. Include the formula for the area of a square in your explanation.
54 square units?
32.
A
6 units
8 units
4 units
## A family has a rectangular vegetable
garden in their backyard and planted
grass in the rest of the yard. The
rectangular backyard is 110 feet by
70 feet, and the garden is 14 feet by
6 feet. What is the area of the
backyard that is planted with
grass?
Backyard
9 units
6 ft
14 ft
70 ft
8 units
110 ft
8 units
F 360 sq ft
G 7,616 sq ft
6 units
H 7,700 sq ft
J 7,804 sq ft
9 units
33.
x + 4 = 12
34.
(Lesson 1-8)
9-m=5
36.
Input (x)
0
3
5
Output (5 + x)
35.
k - 8 = 20
(Lesson 1-6)
37.
Input (x)
2
Output (x 2)
38.
## What is the value of n3 + 5n if n = 2?
39.
SCIENCE The Milky Way galaxy is about 105 light years wide. What is
the value of 105? (Lesson 1-3)
(Lesson 1-5)
## Lesson 1-9 Algebra: Area Formulas
67
CH
APTER
Study Guide
and Review
Review from tx.msmath1.com
Key Vocabulary
algebra (p. 42)
## Be sure the following Key
Concepts are noted in your
Foldable.
Li*>i
>`V
-}
v*Li
*>
V
*i>
>` i
*i
v">
{"`i
i
>>Li>`
x}iL>\6
>\V
}iL
iV
i>`
*-\
>
>\
iL
n}
>
>\i>
}iL
Key Concepts
(Lesson 1-2)
area (p. 63)
## A prime number has exactly two factors, 1 and
the number itself.
## A composite number is a number greater than 1
with more than two factors.
## 1 has only one factor and is neither prime nor
composite. 0 has an infinite number of factors
and is neither prime nor composite.
Order of Operations
(Lesson 1-4)
## Step 1 Simplify the expression inside grouping
symbols, like parentheses.
Step 2 Find the value of all powers.
Step 3 Multiply and divide in order from left to
right.
Step 4 Add and subtract in order from left to right.
Vocabulary Check
State whether each sentence is true or
false. If false, replace the underlined word
or number to make a true sentence.
(Lesson 1-9)
1.
## The area A of a rectangle is the product of the
length and width w.
rectangle.
2.
## When two or more numbers are
multiplied, each number is called a
factor.
3.
## The base of a figure is the number of
square units needed to cover a
surface.
4.
value.
5.
## A variable is a relationship that assigns
exactly one output value to one input
value.
Area Formulas
squared.
s
s
68
## For mixed problem-solving practice,
see page 695.
Lesson-by-Lesson Review
1-1
(pp. 2427)
problem.
6.
7.
1-2
## SCHOOL Tickets to a school dance
cost \$4 each. If \$352 was collected,
how many tickets were sold?
HISTORY In the 1932 presidential
election, Franklin Roosevelt won
Hoover won 59. How many electoral
Prime Factors
44
9.
67
number.
1-3
## Explore You need to find the total
number of hours.
Plan
Multiply 2 by 10.
Solve
2 10 = 20
So, Esteban studied 20 hours.
Check Since 20 2 = 10, the answer
makes sense.
(pp. 2831)
## Tell whether each number is prime,
composite, or neither.
8.
## Example 1 Esteban studied 2 hours
each day for 10 days. How many hours
has he studied?
10.
42
13.
## CODES Cryptography uses prime
numbers to encode secure bank
account information. Suppose Sukis
bank account was encoded with the
number 273. What are the prime
number factors of this code?
11.
75
12.
96
## Example 2 Find the prime
factorization of 18.
Make a factor tree.
Write the number to be factored.
18
2 9
233
## Continue to factor any number that
is not prime until you have a row
of prime numbers.
2 3 3.
(pp. 3236)
## Write each product using an exponent.
Then find the value of the power.
14.
5555
15.
12 12 12
16.
## ANIMALS The average brain weight
in grams for a walrus is 210. Find
this value.
Example 3 Write 4 4 4 4 4 4
using an exponent. Then find the value
of the power.
The base is 4. Since 4 is a factor 6 times,
the exponent is 6.
4 4 4 4 4 4 = 46 or 4,096
69
CH
APTER
## Study Guide and Review
1-4
Order of Operations
(pp. 3740)
1-5
17.
46+23
18.
8 + 33 4
19.
10 + 15 5 - 6
20.
112 - 6 + 3 15
21.
## TRAVELING On a family trip to the
Lone Star Motorcycle Museum, Maria
counted 3 groups of motorcycles, each
with 5 motorcycles and an additional
7 lone motorcycles. Write an
expression for the number of
motorcycles Maria saw on the
freeway. Then find the number of
motorcycles she saw.
28 2 - 1 5
= 14 - 1 5
= 14 - 5
=9
22.
ab
23.
a2 b
24.
3b2 + a
25.
2a - 10
## Evaluate each expression if x = 6,
y = 8, and z = 12.
2x + 4y
27. 3z2
70
+ 4x
28.
z 3 + xy
29.
## HOME REPAIR Joe will tile a square
kitchen floor with square ceramic tile.
He knows the number of tiles needed
is equal to a2 b2, where a is the
floor length in inches and b is the
length of the tile in inches. If a = 96
and b = 8, how many tiles are
needed?
## Chapter 1 Number Patterns and Functions
Divide 28 by 2.
Multiply 1 and 5.
Subtract 5 from 14.
The value of 28 2 - 1 5 is 9.
(pp. 4246)
b = 6.
26.
## Example 4 Find the value of
28 2 - 1 5.
Example 5
Evaluate 9 - k3 if k = 2.
9 - k3 = 9 - 23 Replace k with 2.
= 9 - 8 23 = 8
=1
Subtract 8 from 9.
Example 6
and n = 5.
Evaluate 10 + mn if m = 3
10 + mn = 10 + (3)(5)
= 10 + 15
= 25
m = 3 and n = 5
Multiply 3 and 5.
## For mixed problem-solving practice,
see page 695.
1-6
Algebra: Functions
(pp. 4953)
30.
31.
32.
Input (x)
Output (x - 1)
Input (x)
Output (x + 5)
Input (x)
Output (3x)
Input (x)
Output (x 2)
10
input.
33.
function table.
x
2
8
34.
Input (x)
Output (x + 5)
14
function table.
x
13
12
18
10
12
15
35.
## TRAVEL Tina drove 60 miles per hour
to Tucson. Define a variable. Write a
function rule that relates the number
of miles traveled to the hours driven.
36.
## AGES A boy is 5 years older than his
sister. Define a variable. Write a
function rule that relates the age of
the boy to the age of his sister.
## Study the relationship between each
input and output. Divide each input by
3 to find the output.
So, the function rule is x 3.
71
CH
APTER
1
1-7
(pp. 5455)
37.
1-8
## PRODUCTION A company makes toy
cars. It sells red cars for \$2 each and
black cars for \$3 each. If the company
sold 44 cars total and made \$105,
how many red cars were sold?
38.
## NUMBERS The sum of two numbers
is 22 and their product is 117. Find
the numbers.
39.
## FISHING On a fishing trip with his
friends, Alex caught 3 more catfish
than he did trout. If the total number
of catfish and trout was 19, how
many catfish did he catch?
Algebra: Equations
40.
p+2=9
41.
20 + y = 25
42.
40 = 15 + m
43.
16 - n = 10
44.
27 = x - 3
45.
17 = 25 - h
46.
## AGE The equation 18 + p = 34
represents the sum of Pedros and
Evas ages, where p represents
Pedros age. How old is Pedro?
47.
Owens
Height
Lisas
Height
Sum of
Heights
## 60 inches 52 inches 112 inches too low
68 inches 60 inches 128 inches too high
66 inches 58 inches 124 inches
So, Owen is 66 inches tall.
Example 10 Solve x + 9 = 13
mentally.
x + 9 = 13
4 + 9 = 13
x=4
## What number plus 9 is 13?
You know that 4 + 9 is 13.
The solution is 4.
(pp. 6367)
below.
13 cm
2 cm
48.
## Make a guess. Check to see if it is
correct. Adjust the guess until it is
correct.
(pp. 5760)
1-9
## Example 9 Owen is 8 inches taller
than his sister, Lisa. If the sum of their
heights is 124 inches, how tall is
Owen?
## PAINTINGS Find the area of a painting
that measures 4 feet by 4 feet.
Example 11
Find the area of
the rectangle.
A = w
13 m
Area of a rectangle
## = 13 5 Replace with 13 and w with 5.
= 65
The area is 65 square meters.
72
5m
CH
APTER
1
1.
Practice Test
## TEST PRACTICE Justin earned \$308
by mowing lawns and raking leaves
for a total of 43 hours. He raked leaves
for 18 hours and earned \$108. Arrange
the steps below in a correct order to find
how much he earned per hour mowing
lawns.
12.
13.
## Step R: Find the number of hours Justin
spent mowing lawns.
Which list shows the steps in the correct
order?
A
B
C
D
P, Q, R
R, Q, P
Q, R, P
R, P, Q
or neither.
2.
57
5.
6.
## BIRTHDAYS Miranda told 3 friends that it
was her birthday. Each of those 3 friends
told 3 other students. By noon, 35 students
knew it was Mirandas birthday. Write this
number as a product of the same factor.
Then find the value.
3.
4.
## 1.50 + 2 12.99 + 3.50 2
(2 1.50 + 2 12.99 + 3.50) 2
2 (1.50 + 12.99 + 3.50)
(2 1.50 + 12.99) + 3.50 2
F
G
H
J
## Step P: Find the difference between \$308
and the amount Justin earned
raking leaves.
Step Q: Find the quotient of \$200 and the
number of hours Justin spent
mowing lawns.
## TEST PRACTICE Latisha and Raquel
ordered two beverages for \$1.50 each, two
dinners for \$12.99 each, and a dessert for
\$3.50. Which of the following expressions
can be used to find the amount each
should pay, not including tax?
14.
7
11
12
16
8
16
1
2
15.
## NUTRITION A medium potato has 26 grams
of carbohydrates. Define a variable. Write
a function rule that relates the amount of
carbohydrates to the number of potatoes.
16.
## MONEY Diego has \$1.30 in quarters,
dimes, and nickels. He has the same
amount of nickels as quarters, and one
more dime than nickels. How many of
each coin does he have?
31
17.
d + 9 = 14
19.
the rectangle.
18.
56 = 7k
17 ft
8 ft
7.
12 - 3 2 + 15
8.
72 23 - 4 2
9.
a + 12
10.
27 b
11.
a3 - 2b
20.
## RUGS Benito has a square rug in his dining
room. The length of each side of the rug is
42 inches. Find the area of the rug.
73
CH
APTER
Texas
Test Practice
Chapter 1
## Read each question. Then fill in the
provided by your teacher or on a sheet
of paper.
1.
2.
## \$3.50 for each additional hour that the
roller blades are rented. Which equation
can be used to find, c, the cost in dollars of
the rental for h hours?
## At a large middle school, there are 18
22 students in each homeroom. About
how many sixth-grade students attend the
middle school?
A 250
C 400
B 325
D 650
A c = 4h + 3.5
B c = 3.5 - 4h
C c = 3.5(h + 4)
D c = 3.5h + 4
5. Mr. Weiss started painting the kitchen at
## 8:45 A.M. and finished painting at 12:00 P.M.
About how many hours elapsed between
the time he started painting and the time
he finished painting the kitchen?
## Samantha drives 585 miles to reach her
vacation spot. Her total drive time is nine
hours. How would you find Samanthas
average speed for the trip?
F 2h
## F Add Samanthas total miles driven to
her total drive time.
G 3h
## G Subtract Samanthas total drive time
from the total miles driven.
J 5h
## H Multiply Samanthas total miles driven
by the total drive time.
H 4h
A 33 52
## J Divide Samanthas total miles driven
by her total drive time.
3.
## GRIDDABLE Lynette is painting a 15-foot
by 10-foot rectangular wall that has a
9-foot by 5-foot rectangular window at
its center. How many square feet wall
does she need to paint?
B 27
C 23 32 5
D 3 2 5 72
7. Jeremy was asked to find two integers that
## have a difference of 3 and a sum of 71. He
said that the integers were 39 and 36. Why
not 3.
FT
FT
FT
FT
8.
74
## GRIDDABLE What is the value of
45 (7 + 2) - 1?
for the Texas Test
For test-taking strategies and more practice,
see pages TX1TX23.
## length of each side of the garden was
8 feet. Find the area of the garden.
## of meatball subs sold each day.
A 16 ft2
B 32 ft2
C 64
Number of
Meatball Subs Sold
40
25
30
45
65
70
50
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
ft2
D 80 ft2
## Question 9 Review any terms and
formulas that you have learned before
you take the test.
that week?
F 150 subs
G 200 subs
H 300 subs
## over 4 consecutive years.
J 350 subs
Mollys Age, x
(years)
2
3
4
5
Maxs Age, y
(years)
5
6
7
8
Pre-AP
13. The table shows how much Kyle has
four weeks.
## Which expression best represents Maxs age
in terms of Mollys age?
F y+3
H x+3
G 3x
J 3y
Week
1
2
3
4
5
## computer paper every 5 working days.
About how many boxes of computer paper
does Jack use in 36 working days?
Amount
(\$)
2
3
5
9
17
A 8
C 21
## a. If this pattern continues, how much can
Kyle expect to earn in the sixth week?
B 15
D 108
## NEED EXTRA HELP?
If You Missed Question...
10
11
Go to Lesson...
1-1
1-1
1-9
1-5
1-1
1-3
1-1
1-4
1-9
1-6
12
1
13
1
75 | 24,075 | 78,455 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2019-30 | latest | en | 0.845419 |
https://www.exactlywhatistime.com/days-before-date/july-20/13-days | 1,701,836,710,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100583.13/warc/CC-MAIN-20231206031946-20231206061946-00773.warc.gz | 813,568,623 | 5,649 | # What date is 13 days before Saturday July 20, 2024?
## Calculating 13 days before Saturday July 20, 2024 by hand
This page helps you figure out the date that is 13 days before Saturday July 20, 2024. We've made a calculator to find the date before a certain number of days before a specific date. In this example, we want to know the date 13 days before Saturday July 20, 2024.
Trying to do this in your head can be really hard and take a long time. An easier way is to use a calendar, either a paper one or an app on your phone or computer, to look at the days before the date you're interested in. But the best and quickest way to find the answer is by using our days before specific date calculator, which you can find here.
If you want to change the question on this page, you have two choices: you can change the URL in your browser's address bar, or go to our days before specific date calculator to type in a new question. Remember, figuring out these types of calculations in your head can be really tough, so we made this calculator to help make it much easier for you.
## Sunday July 07, 2024 Stats
• Day of the week: Sunday
• Month: July
• Day of the year: 189
## Counting 13 days backward from Saturday July 20, 2024
Counting backward from today, Sunday July 07, 2024 is 13 before now using our current calendar. 13 days is equivalent to:
13 days is also 312 hours. Sunday July 07, 2024 is 51% of the year completed.
## Within 13 days there are 312 hours, 18720 minutes, or 1123200 seconds
Sunday Sunday July 07, 2024 is day number 189 of the year. At that time, we will be 51% through 2024.
## In 13 days, the Average Person Spent...
• 2792.4 hours Sleeping
• 371.28 hours Eating and drinking
• 608.4 hours Household activities
• 180.96 hours Housework
• 199.68 hours Food preparation and cleanup
• 62.4 hours Lawn and garden care
• 1092.0 hours Working and work-related activities
• 1004.64 hours Working
• 1644.24 hours Leisure and sports
• 892.32 hours Watching television
## Famous Sporting and Music Events on July 07
• 1970 Actress Shelley Duvall (21) weds Bernard Sampson
• 1990 Wimbledon Women's Tennis: Martina Navratilova wins her record 9th Wimbledon singles title beating American Zina Garrison 6-4, 6-1 | 596 | 2,245 | {"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} | 3.359375 | 3 | CC-MAIN-2023-50 | latest | en | 0.930576 |
http://slideplayer.com/slide/1732750/ | 1,544,507,165,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823565.27/warc/CC-MAIN-20181211040413-20181211061913-00155.warc.gz | 269,986,922 | 31,770 | # Aula 4 Mecânica dos Fluidos Sandro R. Lautenschlager
## Presentation on theme: "Aula 4 Mecânica dos Fluidos Sandro R. Lautenschlager"— Presentation transcript:
Aula 4 Mecânica dos Fluidos Sandro R. Lautenschlager
2-Estática do fluido
Exemplos Aceleração linear a Represa Cilindro rotativo
Fluid Mechanics Overview
Gas Liquids Statics Dynamics , Flows Water, Oils, Alcohols, etc. Stability Air, He, Ar, N2, etc. Buoyancy Pressure Compressible/ Incompressible Laminar/ Turbulent Surface Tension Steady/Unsteady Compressibility Density Viscosity Vapor Pressure Viscous/Inviscid
Fluid Statics By definition, the fluid is at rest.
Or, no there is no relative motion between adjacent particles. No shearing forces is placed on the fluid. There are only pressure forces, and no shear. Results in relatively “simple” analysis Generally look for the pressure variation in the fluid
Pressure at a Point: Pascal’s Law
Pressure is the normal force per unit area at a given point acting on a given plane within a fluid mass of interest. Blaise Pascal ( ) How does the pressure at a point vary with orientation of the plane passing through the point? Pressure Forces F.B.D. Gravity Force Wedged Shaped Fluid Mass p is average pressure in the x, y, and z direction. Ps is the average pressure on the surface q is the plane inclination is the length is each coordinate direction, x, y, z ds is the length of the plane g is the specific weight V = (1/2dydz)*dx
Pressure at a Point: Pascal’s Law
For simplicity in our Free Body Diagram, the x-pressure forces cancel and do not need to be shown. Thus to arrive at our solution we balance only the the y and z forces: Rigid body motion in the y-direction Pressure Force in the y-direction on the y-face Pressure Force on the plane in the y-direction Pressure Force in the z-direction on the z-face Pressure Force in the plane in the z-direction Rigid body motion in the z-direction Weight of the Wedge Now, we can simplify each equation in each direction, noting that dy and dz can be rewritten in terms of ds:
Pressure at a Point: Pascal’s Law
Substituting and rewriting the equations of motion, we obtain: Math Now, noting that we are really interested at point only, we let dy and dz go to zero: Pascal’s Law: the pressure at a point in a fluid at rest, or in motion, is independent of the direction as long as there are no shearing stresses present.
Pressure at a Point: Pascal’s Law
p1dxds p2dxds psdxds ps = p1 = p2 Note: In dynamic system subject to shear, the normal stress representing the pressure in the fluid is not necessarily the same in all directions. In such a case the pressure is taken as the average of the three directions.
Pressure Field Equations
How does the pressure vary in a fluid or from point to point when no shear stresses are present? Consider a Small Fluid Element Surface Forces p is pressure is specific weight Taylor Series Body Forces V = dydzdx For simplicity the x-direction surface forces are not shown
Considerando a pressão num ponto Usando a regra da cadeia
Hydrostatic Condition: a = 0
ax=ay=az=0 This leads to the conclusion that for liquids or gases at rest, the Pressure gradient in the vertical direction at any point in fluid depends only on the specific weight of the fluid at that point. The pressure does not depend on x or y. Hydrostatic Equation
Hydrostatic Condition: Physical Implications
Pressure changes with elevation Pressure does not change in the horizontal x-y plane The pressure gradient in the vertical direction is negative The pressure decreases as we move upward in a fluid at rest Pressure in a liquid does not change due to the shape of the container Specific Weight g does not have to be constant in a fluid at rest Air and other gases will likely have a varying g Thus, fluids could be incompressible or compressible statically
Hydrostatic Condition: Incompressible Fluids
The specific weight changes either through r, density or g, gravity. The change in g is negligible, and for liquids r does not vary appreciable, thus most liquids will be considered incompressible. Starting with the Hydrostatic Equation: We can immediately integrate since g is a constant: where the subscripts 1 and 2 refer two different vertical levels as in the schematic.
Hydrostatic Condition: Incompressible Fluids
As in the schematic, noting the definition of h = z2 –z1: Linear Variation with Depth h is known as the pressure head. The type of pressure distribution is known as a hydrostatic distribution. The pressure must increase with depth to hold up the fluid above it, and h is the depth measured from the location of p2. The equation for the pressure head is the following: Physically, it is the height of the column of fluid of a specific weight, needed to give the pressure difference p1 – p2.
Hydrostatic Condition: Incompressible Fluids
If we are working exclusively with a liquid, then there is a free surface at the liquid-gas interface. For most applications, the pressure exerted at the surface is atmospheric pressure, po. Then the equation is written as follows: The Pressure in a homogenous, incompressible fluid at rest depends on the depth of the fluid relative to some reference and is not influenced by the shape of the container. Lines of constant Pressure p = po h1 p = p1 p = p2 For p2 = p = gh + po For p1 = p = gh1 + po
Hydrostatic Application: Transmission of Fluid Pressure
Mechanical advantage can be gained with equality of pressures A small force applied at the small piston is used to develop a large force at the large piston. This is the principle between hydraulic jacks, lifts, presses, and hydraulic controls Mechanical force is applied through jacks action or compressed air for example
Hydrostatic Condition: Compressible Fluids
Gases such as air, oxygen and nitrogen are thought of as compressible, so we must consider the variation of density in the hydrostatic equation: Note: g = rg and not a constant, then Thus, R is the Gas Constant T is the temperature r is the density By the Ideal gas law: Then, For Isothermal Conditions, T is constant, To:
Hydrostatic Condition: U.S. Standard Atmosphere
Idealized Representation of the Mid-Latitude Atmosphere Standard Atmosphere is used in the design of aircraft, missiles and spacecraft. Stratosphere: Isothermal, T = To Troposphere: Linear Variation, T = Ta - bz
Hydrostatic Condition: U.S. Standard Atmosphere
Starting from, Now, for the Troposphere, Temperature is not constant: b is known as the lapse rate, K/m, and Ta is the temperature at sea level, K. Substitute for temperature and Integrate: pa is the pressure at sea level, kPa, R is the gas constant, J/kg.K
Pressure Distribution in the Atmosphere
Measurement of Pressure
Absolute Pressure: Pressure measured relative to a perfect vacuum Gage Pressure: Pressure measured relative to local atmospheric pressure A gage pressure of zero corresponds to a pressure that is at local atmospheric pressure. Absolute pressure is always positive Gage pressure can be either negative or positive Negative gage pressure is known as a vacuum or suction Standard units of Pressure are psi, psia, kPa, kPa (absolute) Pressure could also be measured in terms of the height of a fluid in a column Units in terms of fluid column height are mm Hg, inches of Hg, m or inches of H20,etc Example: Local Atmospheric Pressure is 14.7 psi, and I measure a 20 psia (“a” is for absolute). What is the gage pressure? The gage pressure is 20 psia – 14.7 psi = 5.3 psi If I measure 10 psia, then the gage pressure is -4.7 psi, or is a “vacuum”.
Measurement of Pressure: Schematic
+ - + +
Measurement of Pressure: Barometers
The first mercury barometer was constructed in by Torricelli. He showed that the height of mercury in a column was 1/14 that of a water barometer, due to the fact that mercury is 14 times more dense that water. He also noticed that level of mercury varied from day to day due to weather changes, and that at the top of the column there is a vacuum. Evangelista Torricelli ( ) Torricelli’s Sketch Schematic: Animation of Experiment: Note, often pvapor is very small, and patm is 14.7 psi, thus:
Measurement of Pressure: Manometry
Manometry is a standard technique for measuring pressure using liquid columns in vertical or include tubes. The devices used in this manner are known as manometers. The operation of three types of manometers will be discussed today: The Piezometer Tube The U-Tube Manometer The Inclined Tube Manometer The fundamental equation for manometers since they involve columns of fluid at rest is the following: h is positive moving downward, and negative moving upward, that is pressure in columns of fluid decrease with gains in height, and increase with gain in depth.
Measurement of Pressure: Piezometer Tube
po Disadvantages: 1)The pressure in the container has to be greater than atmospheric pressure. 2) Pressure must be relatively small to maintain a small column of fluid. 3) The measurement of pressure must be of a liquid. Move Up the Tube Closed End “Container” pA (abs) Moving from left to right: pA(abs) - g1h1 = po Rearranging: Gage Pressure Then in terms of gage pressure, the equation for a Piezometer Tube: Note: pA = p1 because they are at the same level
Measurement of Pressure: U-Tube Manometer
Note: in the same fluid we can “jump” across from 2 to 3 as they are at the same level, and thus must have the same pressure. The fluid in the U-tube is known as the gage fluid. The gage fluid type depends on the application, i.e. pressures attained, and whether the fluid measured is a gas or liquid. Closed End “Container” pA Since, one end is open we can work entirely in gage pressure: Moving from left to right: pA + g1h1 - g2h2 = 0 Then the equation for the pressure in the container is the following: If the fluid in the container is a gas, then the fluid 1 terms can be ignored:
Measurement of Pressure: U-Tube Manometer
Measuring a Pressure Differential Closed End “Container” pB Final notes: 1)Common gage fluids are Hg and Water, some oils, and must be immiscible. 2)Temp. must be considered in very accurate measurements, as the gage fluid properties can change. 3) Capillarity can play a role, but in many cases each meniscus will cancel. Closed End “Container” pA Moving from left to right: pA + g1h1 - g2h2 - g3h3 = pB Then the equation for the pressure difference in the container is the following:
Measurement of Pressure: Inclined-Tube Manometer
This type of manometer is used to measure small pressure changes. pB pA h2 q h2 l2 Moving from left to right: pA + g1h1 - g2h2 - g3h3 = pB Substituting for h2: Rearranging to Obtain the Difference: If the pressure difference is between gases: Thus, for the length of the tube we can measure a greater pressure differential.
Similar presentations | 2,519 | 10,805 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2018-51 | latest | en | 0.836464 |
https://www.airmilescalculator.com/distance/hel-to-kao/ | 1,716,251,900,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058342.37/warc/CC-MAIN-20240520234822-20240521024822-00599.warc.gz | 573,836,099 | 32,606 | # How far is Kuusamo from Helsinki?
The distance between Helsinki (Helsinki Airport) and Kuusamo (Kuusamo Airport) is 415 miles / 667 kilometers / 360 nautical miles.
The driving distance from Helsinki (HEL) to Kuusamo (KAO) is 500 miles / 804 kilometers, and travel time by car is about 10 hours 23 minutes.
415
Miles
667
Kilometers
360
Nautical miles
1 h 17 min
## Distance from Helsinki to Kuusamo
There are several ways to calculate the distance from Helsinki to Kuusamo. Here are two standard methods:
Vincenty's formula (applied above)
• 414.712 miles
• 667.414 kilometers
• 360.375 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet.
Haversine formula
• 413.654 miles
• 665.712 kilometers
• 359.456 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Helsinki to Kuusamo?
The estimated flight time from Helsinki Airport to Kuusamo Airport is 1 hour and 17 minutes.
## Flight carbon footprint between Helsinki Airport (HEL) and Kuusamo Airport (KAO)
On average, flying from Helsinki to Kuusamo generates about 86 kg of CO2 per passenger, and 86 kilograms equals 190 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Helsinki to Kuusamo
See the map of the shortest flight path between Helsinki Airport (HEL) and Kuusamo Airport (KAO).
## Airport information
Origin Helsinki Airport
City: Helsinki
Country: Finland
IATA Code: HEL
ICAO Code: EFHK
Coordinates: 60°19′1″N, 24°57′47″E
Destination Kuusamo Airport
City: Kuusamo
Country: Finland
IATA Code: KAO
ICAO Code: EFKS
Coordinates: 65°59′15″N, 29°14′21″E | 492 | 1,903 | {"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-2024-22 | latest | en | 0.802728 |
https://www.scribd.com/document/361520358/Ratio-Analysis | 1,568,987,962,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514574039.24/warc/CC-MAIN-20190920134548-20190920160548-00260.warc.gz | 987,709,070 | 72,365 | You are on page 1of 19
# 14-09-2017
## Financial Statements Analysis
1
14-09-2017
FINANCIAL STATEMENTS
ANALYSIS
Ratio Analysis
Ratio Analysis
Ratio Analysis
## Ratio analysis is a widely used tool of financial analysis. It
is defined as the systematic use of ratio to interpret the
financial statements so that the strengths and
weaknesses of a firm as well as its historical
performance and current financial
condition can be determined.
2
14-09-2017
Basis of Comparison
1) Trend Analysis involves comparison of a firm over a
period of time, that is, present ratios are compared with
past ratios for the same firm. It indicates the direction of
change in the performance improvement, deterioration
or constancy over the years.
## 2) Interfirm Comparison involves comparing the ratios of a
firm with those of others in the same lines of business or
for the industry as a whole. It reflects the firms
performance in relation to its competitors.
Types of Ratios
Integrated
Growth Ratios
Analysis Ratios
3
14-09-2017
## Net Working Capital
Net working capital is a measure of liquidity calculated by
subtracting current liabilities from current assets.
## Table 1: Net Working Capital (Rs. In Lakh)
Particulars Company A Company B
Total current assets Rs 180 Rs 30
Total current liabilities 120 10
NWC 60 20
Table 2: Change in Net Working Capital (Rs. in Lakh)
Particulars Company A Company B
Current assets Rs 150 Rs 300
Current liabilities 75 200
NWC 75 100
Liquidity Ratios
## Liquidity ratios measure the ability
of a firm to meet its short-term
obligations
4
14-09-2017
Current Ratio
Current Ratio is a measure of liquidity calculated dividing
the current assets by the current liabilities
Current Assets
Current Ratio =
Current Liabilities
(Rs. in Lakh) (Rs. in Lakh)
Particulars Firm A Firm B
Current Assets Rs 180 Rs 30
Current Liabilities Rs 120 Rs 10
Current Ratio = 3:2 (1.5:1) 3:1
Acid-Test Ratio
The quick or acid test ratio takes into consideration
the differences in the liquidity of the
components of current assets
Quick Assets
Acid-test Ratio =
Current Liabilities
## Quick Assets = Current assets Stock
Pre-paid expenses
5
14-09-2017
## Example 1: Acid-Test Ratio
(Rs. in Lakh)
Cash Rs 20
Debtors 20
Inventory 120
Total current assets 160
Total current liabilities 80
(1) Current Ratio 2:1
(2) Acid-test Ratio 0.5 : 1
## Supplementary Ratios for
Liquidity
Inventory Turnover
Debtors Turnover Ratio
Ratio
6
14-09-2017
## Inventory Turnover Ratio
The ratio indicates how fast inventory is sold. A high ratio is good
from the viewpoint of liquidity and vice versa. A low ratio
would signify that inventory does not sell fast and stays
on the shelf or in the warehouse for a long time.
## Cost of goods sold
Inventory turnover ratio =
Average inventory
## The average inventory refers to the simple average of the opening
and closing inventory.
## Example 2: Inventory Turnover Ratio
A firm has sold goods worth Rs 300 lakh with a gross profit margin of
20 per cent. The stock at the beginning and the end of the year
was Rs 35 lakh and Rs 45 lakh respectively. What is the
inventory turnover ratio?
## Inventory (Rs 300 Rs 60) 6 (times
= =
turnover ratio (Rs 35 + Rs 45) 2 per year)
Inventory 12 months
= = 2 months
holding period Inventory turnover ratio, (6)
7
14-09-2017
## Debtors Turnover Ratio
The ratio measures how rapidly receivables are collected. A high
ratio is indicative of shorter time-lag between credit sales and
cash collection. A low ratio shows that debts are not
being collected rapidly.
## Net credit sales
Debtors turnover ratio =
Average debtors
## Net credit sales consist of gross credit sales minus
returns, if any, from customers.
## Average debtors is the simple average of debtors (including
bills receivable) at the beginning and at the end of year.
## Example 3: Debtors Turnover Ratio
A firm has made credit sales of Rs 240 lakh during the year. The
outstanding amount of debtors at the beginning and at the end
of the year respectively was Rs 27.5 lakh and Rs 32.5 lakh.
Determine the debtors turnover ratio.
## Debtors Rs 240 8 (times
= =
turnover ratio (Rs 27.5 + Rs 32.5) 2 per year)
## Debtors 12 Months 1.5
= =
collection period Debtors turnover ratio, (8) Months
8
14-09-2017
## Creditors Turnover Ratio
A low turnover ratio reflects liberal credit terms granted by
suppliers, while a high ratio shows that accounts are to be settled
rapidly. The creditors turnover ratio is an important tool of
analysis as a firm can reduce its requirement of current assets by
relying on suppliers credit.
## Creditors turnover Net credit purchases
=
ratio Average creditors
Net credit purchases = Gross credit purchases - Returns to
suppliers.
## Average creditors = Average of creditors (including bills payable)
outstanding at the beginning and at the end of the year.
## The firm in previous Examples has made credit purchases of Rs 180
lakh. The amount payable to the creditors at the beginning
and at the end of the year is Rs 42.5 lakh and Rs 47.5 lakh
respectively. Find out the creditors turnover ratio.
## Creditors (Rs 180) 4 (times
= =
turnover ratio (Rs 42.5 Rs 47.5) 2 per year)
Creditors 12 months
= = 3 months
payment period Creditors turnover ratio, (4)
9
14-09-2017
## The summing up of the three turnover ratios (known as a cash cycle)
has a bearing on the liquidity of a firm. The cash cycle captures
the interrelationship of sales, collections from debtors
and payment to creditors.
## The combined effect of the three turnover ratios
is summarised below:
## Inventory holding period 2 months
Add: Debtors collection period + 1.5 months
Less: Creditors payment period 3 months
0.5 months
As a rule, the shorter is the cash cycle, the better are the liquidity
ratios as measured above and vice versa.
## Defensive interval ratio is the ratio between quick
assets and projected daily cash requirement.
## Defensive- Liquid assets
=
interval ratio Projected daily cash requirement
## Projected daily Projected cash operating expenditure
=
cash requirement Number of days in a year (365)
10
14-09-2017
## Leverage Capital Structure Ratio
There are two aspects of the long-term solvency of a firm:
(i) Ability to repay the principal when due, and
(ii) Regular payment of the interest .
Capital structure or leverage ratios throw light on the
long-term solvency of a firm.
## Accordingly, there are two different types of leverage ratios.
First type: These ratios are Second type: These ratios are
computed from the balance computed from the Income
sheet Statement
(a) Debt-equity ratio (a) Interest coverage ratio
(b) Debt-assets ratio (b) Dividend coverage ratio
(c) Equity-assets ratio
I. Debt-equity ratio
Debt-equity ratio measures the ratio of long-term or total
debt to shareholders equity.
## Debt-equity ratio measures
Totalthe ratio of long-
Debt
Debt-equity ratiode3bt
term or total = to shareholders equity
Shareholders equity
If the D/E ratio is high, the owners are putting up relatively less
money of their own. It is danger signal for the lenders and
creditors. If the project should fail financially, the
creditors would lose heavily.
A low D/E ratio has just the opposite implications. To the creditors, a
relatively high stake of the owners implies sufficient safety
margin and substantial protection against
shrinkage in assets.
11
14-09-2017
## For the company also, the servicing of debt is less
burdensome and consequently its credit standing
is not adversely affected, its operational flexibility
is not jeopardised and it will be able to
## The disadvantage of low debt-equity ratio is that
the shareholders of the firm are deprived
of the benefits of trading on equity
or leverage.
Trading on equity (leverage) is the use of borrowed funds in
## Trading on Equity (Amount in Rs thousand)
Particular A B C D
(a) Total assets 1,000 1,000 1,000 1,000
Financing pattern:
Equity capital 1,000 800 600 200
15% Debt 200 400 800
(b)Operating profit (EBIT) 300 300 300 300
Less: Interest 30 60 120
Earnings before taxes 300 270 240 180
Less: Taxes (0.35) 105 94.5 84 63
Earnings after taxes 195 175.5 156 117
Return on equity (per cent) 19.5 21.9 26 58.5
12
14-09-2017
## II. Debt to Total Capital
The relationship between creditors funds and
owners capital can also be expressed using
Debt to total capital ratio.
Total debt
Debt to total capital ratio =
Permanent capital
Long-term debt.
## III. Debt to total assets ratio
Total debt
Debt to total assets ratio =
Total assets
Proprietary Ratio
Proprietary ratio indicates the extent to which assets
are financed by owners funds.
Proprietary funds
Proprietary ratio = X 100
Total assets
## Capital Gearing Ratio
Capital gearing ratio is used to know the relationship between equity
funds (net worth) and fixed income bearing funds (Preference
shares, debentures and other borrowed funds.
13
14-09-2017
Coverage Ratio
Interest Coverage Ratio
Interest Coverage Ratio measures the firms ability to make
contractual interest payments.
## EBIT (Earning before interest and taxes)
Interest coverage ratio =
Interest
## Dividend Coverage Ratio
Dividend Coverage Ratio measures the firms ability to pay dividend
on preference share which carry a stated rate of return.
## EAT (Earning after taxes)
Dividend coverage ratio =
Preference dividend
Profitability Ratio
Profitability ratios can be computed either from
sales or investment.
## Profitability Ratios Profitability Ratios
Related to Sales Related to Investments
(i) Profit Margin (i) Return on Investments
Equity
14
14-09-2017
Profit Margin
## Gross profit margin measures the percentage of each sales
rupee remaining after the firm has paid for its goods.
X 100
Sales
## Net Profit Margin
Net profit margin measures the percentage of each sales rupee
remaining after all costs and expense including interest
and taxes have been deducted.
## Earning before interest and taxes
i. Operating Profit Ratio =
Net sales
## Earnings before taxes
ii. Pre-tax Profit Ratio =
Net sales
## Earning after interest and taxes
iii. Net Profit Ratio = Net sales
15
14-09-2017
## Example 7: From the following information of a firm,
determine (i) Gross profit margin and (ii) Net profit
margin. (Amount in Rs Lakh)
1. Sales Rs 200
2. Cost of goods sold 100
3. Other operating expenses 50
Rs 100
(1) Gross profit margin = = 50 per cent
Rs 200
Rs 50
(2) Net profit margin = = 25 per cent
Rs 200
Expenses Ratio
Cost of goods sold
i. Cost of goods sold = X 100
Net sales
ii. Operating expenses = X 100
Net sales
iii. Administrative expenses = X 100
Net sales
Selling expenses
iv. Selling expenses ratio = X 100
Net sales
Cost of goods sold + Operating expenses
v. Operating ratio = X 100
Net sales
Financial expenses
vi. Financial expenses = X 100
Net sales
16
14-09-2017
Return on Investment
Return on Investments measures the overall effectiveness
of management in generating profits with
its available assets.
## i. Return on Assets (ROA)
EBIT
ROA =
Average total assets
## ii. Return on Capital Employed (ROCE)
EBIT
ROCE =
Average total capital employed
## Return on Shareholders Equity
Return on shareholders equity measures the return on the
owners (both preference and equity shareholders )
investment in the firm.
## Return on total shareholders equity =
Net profit after taxes
X 100
Average total shareholders equity
## Return on ordinary shareholders equity (Net worth) =
Net profit after taxes Preference dividend
X 100
Average ordinary shareholders equity
17
14-09-2017
Efficiency Ratio
Activity ratios measure the speed with which various
accounts/assets are converted into sales or cash.
Inventory turnover measures the efficiency of various types
of inventories.
## i. Inventory Turnover Cost
measures theof goods sold
activity/liquidity of
Inventory Turnover Ratio =
Average
inventory of a firm; the speed with whichinventory
inventory is sold
## i. Inventory Turnover Cost
measures theofactivity/liquidity
raw materials usedof
Raw materials turnover =
inventory of a firm; the speed with which
Average inventory
raw material is sold
inventory
## i. Inventory Turnover measuresCost of goods manufactured
the activity/liquidity of
Work-in-progress turnover =
Average
inventory of a firm; the speed work-in-progress
with which inventory isinventory
sold
## Debtors Turnover Ratio
Liquidity of a firms receivables can be examined
in two ways.
i. Credit sales
i. Inventory Turnover
Debtors turnover = measures the activity/liquidity of inventory of
a firm; the speed with
Average
whichdebtors
inventory
+ Average
is sold bills receivable (B/R)
## Months (days) in a year
2. Average collection period =
Debtors turnover
Months (days)
i. Inventory Turnover in a year
measures (x) (Average Debtors
the activity/liquidity + Average
of inventory of a(B/R)
Alternatively =
Total credit
firm; the speed with which inventory is sold sales
## Ageing Schedule enables analysis to identify
slow paying debtors.
18
14-09-2017
## Assets Turnover Ratio
Assets turnover indicates the efficiency with which firm
uses all its assets to generate sales.
## i. Cost of goods sold of inventory of
i. Inventory Turnover
Total assets measures
turnover = the activity/liquidity
a firm; the speed with which inventory
Average total
is sold
assets
Cost of goods sold
ii. Fixed assets turnover =
Average fixed assets
Cost of goods sold
i. Inventory
iii. Turnover
Capital turnover = measuresAverage
the activity/liquidity of inventory of
a firm; the speed with which inventory iscapital
sold employed
Cost of goods sold
iv. Current assets turnover =
Average current assets
## i. Cost of goods sold
v. Inventory Turnover
Working capital measures
turnover = the activity/liquidity of inventory of
Net working
a firm; the speed with which inventory capital
is sold
## 2) Return on equity funds = (EAT Preference dividend)/Average ordinary
shareholders equity (net worth).
## 3) Earnings per share (EPS) = Net profit available to equity shareholders
(EAT Dp)/Number of equity shares outstanding (N).
## 4) Dividends per share (DPS) = Dividend paid to ordinary
shareholders/Number of ordinary shares outstanding (N).
## 9) Book value per share = Ordinary shareholders equity/Number of equity
shares outstanding.
19 | 3,530 | 14,335 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2019-39 | latest | en | 0.879558 |
faq.sparckco.com | 1,726,614,880,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.53/warc/CC-MAIN-20240917204739-20240917234739-00655.warc.gz | 222,700,383 | 13,295 | # Calculating Absenteeism Costs and Projected Savings
## Here's a high level overview of how to calculate absenteeism costs and projected savings.
The second section to cover in the executive meeting is absenteeism. The most important thing to highlight in this section is that an increase in engagement can reduce the number of “sick days” which increases productivity and saves them money. She wanted to know how?
Well, engaged employees take an average of 2.7 sick days per year while disengaged employees double that with an average of 6.2 sick days. This is important because when someone takes a “sick day," you are paying for their time off while losing their productivity. Lost time and money is never desirable!
Luckily, increased engagement saves about 37% in absenteeism costs by converting those disengaged employees into more committed and engaged individuals who won’t take as many “sick days.” This shift creates an opportunity to save money and increase productivity by keeping your employees excited about their work and invested in the organization.
For the example above, the total absenteeism costs calculated by the Sparck Engagement Calculator was \$1,079,183. In other words, if Stark Industries increased engagement, they can save an average of 37% in absenteeism costs, which is just shy of \$400,000. These savings are realized because increased engagement will reduce the number of sick days by converting disengaged employees into more enthusiastic and committed team members. This transition will increase productivity and save the department money.
### The Formulas
Though this is a multiple step process, at a high level, we are able to calculate the total absenteeism costs of \$1,079,183 and the projected savings of \$399,298 using these formulas:
• Estimated Absenteeism Costs: Total Absenteeism Costs for Engaged Employees + Total Absenteeism Costs for Disengaged Employees
• Projected Absenteeism Savings: Total Absenteeism Costs x 37%
### Estimated Absenteeism Costs
Starting with Estimated Absenteeism Costs, the number of average “sick days” taken by engaged employees compared to disengaged employees is the most important area to take into account. We use researched backed numbers of 2.7 average sick days for engaged employees and 6.2 average sick days for disengaged employees.
Once we identify the costs for each, we add them together to get the total projected absenteeism costs for on an annual basis.
The Estimated Absenteeism Costs of \$1,079,183 is broken down this way:
• \$723,525 (engaged employees)
• \$355,660 (disengaged employees)
To understand how we got \$723,525 in total absenteeism costs for engaged employees and \$355,660 for disengaged employees, here’s what it comes down to...
First, when an employee takes a sick day, a company loses productivity and money because they are still paying for that time even though no work is being done. In order to measure these two areas to get the total absenteeism costs, we have to see how much productivity and money is lost for each type of employee.
• Lost Productivity: We are able to calculate how much productivity the division is losing by looking at the average Revenue per Employee. This measures the average financial output of each employee. We need this number to uncover how much productivity is lost when an employee takes a sick day.
• Lost Money: We then need to get an estimate of how much money is lost by looking at the Average Salary. These are dollars that are being spent for hours that aren’t being worked. After all, their employees have sick time so they are still being compensated even though they aren’t in the office.
Secondly, we need to calculate absenteeism costs for engaged employees separately from disengaged employees because because absenteeism costs vary drastically due to the amount of sick days they take. Engaged employees take an average of 2.7 days and disengaged employees take 6.2 days a year.
Here's the formula for Absenteeism Costs:
Lost Productivity Lost Money (Avg. Revenue Per Employee x Avg. Sick Days) + (Avg. Salary x Avg. Sick Days) = Absenteeism Cost
This calculation figures out the cost for a single engaged employee and a single disengaged employee, so you also have to know many employees in the division are engaged and disengaged to determine the total absenteeism costs for each group.
If you've never done an engagement survey before, you may not know how many of your employees were engaged or disengaged. According to Gallup, 17% of the workforce is disengaged, so it serves as a credible benchmark and this number is set as a default in the Sparck Calculator17% of 290 employees is 49, which means we have have 49 disengaged employees and 241 engaged employees.
Gallup found a historic drop in engagement levels as of June 2020, but for data purposes, we still recommend using the benchmark of 17% disengaged employees. We're in a very unique time right now.
### High Level Overview of Absenteeism Costs and Savings
Because absenteeism calculations are far more complex than our revenue calculation, we broke it down into three different parts:
Engaged Employees: To determine the absenteeism costs for engaged employees, we multiply 241 (83% of 290) employees by the individual absenteeism cost for an engaged employee to get the total engaged employee absenteeism costs of \$723,525.
Disengaged Employees: To determine the absenteeism costs for disengaged employees, we can multiply the individual absenteeism cost for a disengaged employee by 49 (17% of 290) employees to get the total cost of \$355,660.
Total Absenteeism Costs + Projected Savings: We add the two total costs together (\$355,660 and \$723,525), which gets us to the total absenteeism costs of \$1,079,183 on the ROI Analysis. Then, to uncover the potential savings, we simply multiply this total cost by 37%. | 1,278 | 5,894 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-38 | latest | en | 0.939999 |
https://thebacktoschoolblog.com/2022/10/halloween-subtraction-game/ | 1,680,388,663,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296950363.89/warc/CC-MAIN-20230401221921-20230402011921-00130.warc.gz | 610,152,550 | 14,824 | Saturday April 1, 2023
Latest:
131 total views
Kids can’t help but be a little distracted as we get closer and closer to Halloween. If you’re looking for a way to tap into that Halloween enthusiasm AND get a little learning in, then treat your kids to some Halloween fun this spooky season with this fun math game, Roll and Cover Halloween Subtraction. This printable Halloween Roll and Cover Subtraction game is a hands-on way for pre-k and kindergarten students to model subtraction problems with real materials. It can be used as part of a math center, small group lesson, or as an option for early finishers.
###### GET A FULL WEEK OF HALLOWEEN THEME ACTIVITIES IN OUR PRINTABLE PRESCHOOL LESSON PLANS
This Halloween roll and cover subtraction activity is an easy way to add some fun Halloween theme activities to your math centers, take-home math practice, or just a fun way to celebrate Halloween while working on math skills.
If you use manipulatives like small pom poms, mini erasers, or other manipulates to cover the numbers as you play, you can use this set over and over again. You could also use sheet protectors and dry erase markers.
We chose these adorable spider rings that we’ve used in other Halloween math activities.
## How to Play
• Roll two dice.
• Subtract the other number.
• Cover the difference.
This printable set also includes an optional work mat to help your little ones work through the various math problems.
By asking children to first identify the greater number they are also getting additional number sense practice along the way.
### GET THE FREE PRINTABLE HALLOWEEN SUBTRACTION ROLL AND COVER
Complete the form below to request your freebie.
### GET A FULL SET OF HALLOWEEN THEME ACTIVITIES
Watch this short video to see just a few examples of the types of activities and printables included in this set:
The 132-page Halloween Lesson Plan Set includes hands-on activities and these additional printables:
1) -at Word Family Bat Game (in color and b/w)
2) Candy Corn Science Experiment Recording Sheet (in color and b/w)
3) Candy Corn Uppercase, Lowercase, and Beginning Sound Picture Puzzles for Letters C, A, N, D, Y, H, O and R (in color and b/w)
4) Candy Corn Counting Cards 1-10 (in color and b/w)
5) Halloween Costume Syllable Sorting Activity (in color and b/w)
6) Haunted House Colors Board Game-3 variations to work on color recognition or color word recognition (in color and b/w)
7) “Look at the Costumes” Emergent Reader-3 variations
8) 0-35 Halloween Number Cards (in color and b/w)
9) Halloween Roll and Graph Math Game (in color and b/w)
10) Halloween Picture-Word Cards (in color and b/w)
11) Build a Jack-o-Lantern Pumpkin Mats and Shape Pieces
12) My Jack-o-Lantern Recording Sheets-2 variations, one to focus on shape recognition and one to focus on writing
13) Spider Number Mats and Ways to Show Numbers 0-10
Also available on Teachers Pay Teachers.
## MORE HALLOWEEN LESSON PLAN SETS
### News
Setting aside your legal obligation to refer students to Child Protective Services if you suspect abuse or neglect, there… | 708 | 3,107 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2023-14 | latest | en | 0.867076 |
https://www.studypool.com/discuss/270836/help-in-solving-algebra-word-problem-4?free | 1,506,456,889,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818696681.94/warc/CC-MAIN-20170926193955-20170926213955-00132.warc.gz | 851,794,165 | 14,399 | Time remaining:
##### Help in solving algebra word problem
label Algebra
account_circle Unassigned
schedule 0 Hours
account_balance_wallet \$5
If a 221-mile trip took 8 1/2 gallons of gas, how many miles can be driven with a full tank of 20 gallons?
Sep 26th, 2017
=[221-mile/8 1/2 gallons]x20 gallons
=520 miles
Nov 5th, 2014
...
Sep 26th, 2017
...
Sep 26th, 2017
Sep 26th, 2017
check_circle | 131 | 399 | {"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-2017-39 | latest | en | 0.879253 |
https://www.chemicalforums.com/index.php?topic=103011.0 | 1,585,698,174,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370504930.16/warc/CC-MAIN-20200331212647-20200401002647-00448.warc.gz | 873,457,124 | 8,747 | March 31, 2020, 07:42:54 PM
Forum Rules: Read This Before Posting
### Topic: 2 solutions mixed (Read 465 times)
0 Members and 1 Guest are viewing this topic.
#### Helly
• Full Member
• Posts: 143
• Mole Snacks: +0/-2
##### 2 solutions mixed
« on: February 11, 2020, 11:33:21 AM »
3.6 gram glucose in 500 gram water mixed with 4.75 gram MgCl2 in 1000 gram water. (Kd = 0.52 °C/m. and Kf = 1.86 °C/m.) whats the temperature after mixing?
i think that the glucose solution will increased in temperature and the MgCl2 solution will decrease in temperature, until they both reached equilibrium temperature.
Q = mcΔT
m = molal
but i dont know how to find ΔT
#### mjc123
• Chemist
• Sr. Member
• Posts: 1737
• Mole Snacks: +242/-11
##### Re: 2 solutions mixed
« Reply #1 on: February 11, 2020, 12:45:08 PM »
What's the temperature before mixing? Without knowing that you're stuck. Are they at different temperatures before mixing?
Why do you quote Kd and Kf? Are they relevant? (Does the question give you them as red herrings?)
m means molal in Kd = 0.52°C/m, but it does not mean molal in Q = mcΔT. What does it mean?
There is not enough information to answer the question. Can you quote the whole question?
#### Helly
• Full Member
• Posts: 143
• Mole Snacks: +0/-2
##### Re: 2 solutions mixed
« Reply #2 on: February 11, 2020, 12:56:38 PM »
Thats the all information.. yes i think i need the early temperature..
Delta T = kb molal i
Or delta T = kf . Molal . I
#### mjc123
• Chemist
• Sr. Member
• Posts: 1737
• Mole Snacks: +242/-11
##### Re: 2 solutions mixed
« Reply #3 on: February 12, 2020, 04:37:28 AM »
Quote
Delta T = kb molal i
Or delta T = kf . Molal . I
That's irrelevant unless you're considering the change in the melting or boiling point. What you're asking for is the temperature change on mixing - something quite different. (And still without enough information to determine it.)
#### MNIO
• Regular Member
• Posts: 67
• Mole Snacks: +8/-0
##### Re: 2 solutions mixed
« Reply #4 on: February 12, 2020, 04:59:16 PM »
can you copy and paste the exact problem? here's why I ask
dTfp = Kf * m * i is an estimate of FREEZING POINT of solutions
dTbp = Kb * m * i is an estimate of BOILING POINT of solutions
where i is related to the formula of the salts
m is related to the mass of salts AND mass of H2O
essentially you're given the information you need to calculate fp and bp of the resulting solutions
************
the way you asked the question "what is the TEMPERATURE after mixing" is a different problem entirely and is way beyond the scope of a high school chemistry homework problem.
#### Helly
• Full Member
• Posts: 143
• Mole Snacks: +0/-2
##### Re: 2 solutions mixed
« Reply #5 on: March 11, 2020, 12:35:48 PM »
The question was
3.6 gram glucose in 500 gram water mixed with 4.75 gram MgCl2 in 1000 gram water. (Kd = 0.52 °C/m. and Kf = 1.86 °C/m.) whats the temperature after mixing?
What formula do i use? What information was lacking?
#### AWK
• Retired Staff
• Sr. Member
• Posts: 7124
• Mole Snacks: +502/-84
• Gender:
##### Re: 2 solutions mixed
« Reply #6 on: March 11, 2020, 01:02:55 PM »
Probably problem concern the elevation of boiling point and the depression of freezing point after mixing.
AWK
#### alfred0809
• Very New Member
• Posts: 1
• Mole Snacks: +0/-0
##### Re: 2 solutions mixed
« Reply #7 on: March 12, 2020, 01:48:51 AM »
What are some colorless/clear solutions that when mixed will precipitate into something colourful that primary school students would enjoy.
#### mjc123
• Chemist
• Sr. Member
• Posts: 1737
• Mole Snacks: +242/-11
##### Re: 2 solutions mixed
« Reply #8 on: March 12, 2020, 06:35:00 AM »
If you've got a new question, start a new thread, don't hijack someone else's. | 1,151 | 3,765 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2020-16 | longest | en | 0.87134 |
https://www.toprankers.com/exams/sbi-po-mains-exam-analysis-4th-june-2017/ | 1,603,381,543,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107879673.14/warc/CC-MAIN-20201022141106-20201022171106-00299.warc.gz | 924,116,065 | 24,057 | SBI PO Mains Exam analysis 4th June 2017
SBI PO Mains Exam Analysis 2017 – Complete Question Paper Review, Questions Asked, Cut off, Difficulty level of SBI PO Mains today analysis
SBI PO Mains Exam Analysis 2017 : How was your paper( 4th June)
SBI PO Questions Asked on 4th June 2017
Every student is looking for questions asked in SBI PO Mains held on 4th June 2017. We have received tons of requests for an article on SBI PO mains 2017 questions asked. So, we bring you some of the questions asked in SBI PO mains 2017 exam.
SBI PO Mains 2017 Questions Asked: Section- wise
Let us take a look at all the sections one by one-
SBI PO Mains Questions Asked: Reasoning-
• Linear Arrangement –
1Q – All people facing south in a row
1Q – People were sitting in 2 separate rows. Distance between the rows was given.
1Q – Some people were in a small box and some in a big box (square). People in the small box faced inside and people in the big box faced outside.
1Q – 8 people facing north.
• Puzzles – one question based on photo frames & shelves
• Coding Decoding- Number format
• Input Output – 3 questions based on new format
SBI PO Mains Questions Asked : DI (Quant)-
• Pie Chart– 1 set – based on boats and streams. Two pie charts were provided, one was for upstream distance and another was for downstream distance. A table was provided for stream speed.
• 5 questions from data sufficiency
• Missing DI – 2 sets. One set was based on Profit & Loss – Discount.
The other set was based on Time and Work.
• Caselet DI – One set from this topic was asked.
• 5 questions were asked from mathematical inequality
• Geometry – 2 Questions were asked from geometry
1- 1 parallel line & 1 intersecting line.
2 – A quadrilateral inside a rectangle (with one pair of opposite sides of quadrilateral on the length side of rectangle, their lengths were given). Given area of quadrilateral is half of the area of rectangle.
• No questions were asked from series.
SBI PO Mains Analysis 4 June 2017
SBI PO Mains Questions Asked: General Awareness-
• What is the total agricultural credit target as per the budget?– 10 lakh crore
• Who is the chairman of Indian FIFA Committee? – Justice Mukul Mudgal
• What does “P” in APBS stand for?- Payment
• Indian government has approved the Electronic Development Fund with corpus of – Rs.6381
• Who is the highest women wicket taker? – Jhulan Goswami
• The Cheque Truncation issue comes under __________ act – Section 6B of Negotiable Instruments Act 1881
• The initial promoter stake for first 5 years for small banks should not be less than _________ – 40%
• ___________ is a company`s liquidity financial metric- Working Capital
• The Global Financial Integrity Black Money Inflow in India is _________ – USD 770 Bn
• As per reports of SIPRI in the year 2016, the total expenditure of India`s Military Expenditure was– USD 56 Bn
• Who is the head of the committee of IBBI? – MS Sahoo
SBI PO Mains Questions Asked: Reasoning: English-
• Reading Comprehension- 1 question based on German Economy, Decision making by an employee.
• Error Spotting- questions were asked on spotting errors in phrases
SBI PO Mains 2017 Questions Asked- Descriptive Test
Essay Writing-
1. a) An essay on Travelling is better than watching movies and documentary.
b) An essay on Why Technology’s being in power is a menace?
c) An essay on the effects of social media and its consequences on our population.
Letter Writing-
1. a) A letter to the branch manager of your bank regarding Non Credit of amount deposited in ATM
b) A letter to the editor expressing your concern over impact of irrelevant news through social media.
c) A letter to your sibling giving them advise related to stress and anxiety (or) write to an author thanking for publishing a book on ‘fighting depression’.
SBI PO Exam Shift Timings:
SBI PO Mains Exam Date Shift Timings 04th June 2017(Sunday) Shift 01- 09am onwards Shift 02- 12:30pm onwards
SBI PO Mains exam pattern:
The SBI PO Mains 2017 will be in two parts Objective Test 200 marks and Descriptive Test of 50 marks.
Objective Test: The objective test will contain 155 questionnaire for 200 marks and will have a time duration of 3 hours. The Objective test will have multiple choice questions.
Section No. of Questions Marks Duration Reasoning & Computer Aptitude 45 60 60 minutes Data Analysis & Interpretation 35 60 45 minutes General Awareness about Economy/ Banking 40 40 35 minutes English Language 35 40 40 minutes TOTAL 155 200 3 hours
Descriptive Test: The Descriptive paper will have 50 marks and candidates will have a time of 30 minutes time duration. The test is aimed at studying your letter writing and essay writing skills. Only those students who have scored good cutoff in the objective tests will be eligible for writing the descriptive tests.
Lakhs of students are appearing for the examination. The vacancies available for SBI PO is 2313. It remains one of the most envied jobs in the country. The exam is being conducted in 2 shifts.
SBI PO Exam Shift Timings:
The shift timings of the Mains examination is given below:
Shift Timings Shift 1 9.00 Am onwards Shift 2 12.30 PM onwards
There will be four sections in the exam:
1. Reasoning & Computer Aptitude
2. Data Analysis & Interpretation
3. General Awareness about Economy/ Banking
4. English Language
Some Exam Day Tips for SBI PO Mains:
• You have to solve 200 questions in 120 minutes for objective paper.
• Don’t waste too much time on any particular question.
• Use rough sheet provided for the calculation.
• Assign time to each question (i.e. 1 minute) and stick to it.
• Drop the questions that you think will take a lot of your time
• Attempt a good number of questions to be able to clear sectional and overall cut off marks
• Do not stress too much.
We request all students and candidates to share their experiences on the exam conducted today in the comments section below. How was your Exam?
SBI PO MAINS EXAM ANALYSIS 2017(Good Attempts)
SECTIONS GOOD ATTEMPTS
English Language 16-18
Reasoning & Computer Aptitude 20-22
Data Analysis and Interpretation 9-12
General Awareness 27-30
Total 75-78
Note: Good attempts is based on our readers review
DESCRITIVE TEST – SBI PO MAINS 2017:
This section was of 50 marks with a time limit of 30 minutes.
Letter Writing (150 words)
a) Write a letter to your branch manager as you’ve deposited some amount but it is still not credited into your account
b) Write a letter to editor expressing your concern over impact of irrelevant news through socia media
c) Write a letter to your sibling giving them advise related to stress and anxiety.
Essay Writing (150 words)
a) Write an essay on the positive and negative impact of technology.
b) Write an essay on effect of social media and its consequences on our population.
SBI PO Mains Exam Analysis 4th June 2017
As per Our Readers Review The SBI PO Mains exam 2017 was ‘Difficult’ as termed by most of you!
• Data Analysis & Interpretation was (Moderate-Difficult) Level.
• ENGLISH LANGUAGE Section of SBI PO Mains Exam 2017 was (Difficult).
• The Reasoning and Computer Aptitude Paper was ( Difficult ) as per last years SBI PO Mains exam
• GENERAL AWARENESS Section of SBI PO Mains exam 2017 was quite (Easy- Moderate) Level
SBI PO Mains Exam Analysis 2017 : How was your exam ?
Please comment below how was your SBI PO Mains 2017 exam. You can also provide valuable feed about the exam held on 4th June (All Shifts)
• Pattern
• Tips -section wise and overall
• Difficulty level – section wise and overall
• Any issues faced
• Good Attempts – section wise and overall
Your comments will help us in improving the quality of study materials and mock tests.
Stay tuned for more updates for SBI PO Exam Analysis 2017.
Best Wishes from TopRankers! | 1,931 | 7,816 | {"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-2020-45 | latest | en | 0.970281 |
https://www.coursehero.com/file/5455449/hw4/ | 1,495,855,006,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608765.79/warc/CC-MAIN-20170527021224-20170527041224-00050.warc.gz | 1,097,895,756 | 44,002 | # hw4 - ME 210B Homework 4 Due 1 Consider the Runge-Kutta...
This preview shows page 1. Sign up to view the full content.
ME 210B Homework # 4 Due February 18, 2009 1. Consider the Runge-Kutta method defined by 3 - 3 6 | 1 4 3 - 2 3 12 3+ 3 6 | 3+2 3 12 1 4 | 1 2 1 2 (a) (1 point) Write the formula which corresponds to this Runge- Kutta matrix (b) (2 points) Using the order conditions from the book, verify that the method is order 4 (Hint: read Section 4.3 very carefully, in- cluding the examples). 2. (3 points) Write the following in Runge-Kutta matrix form, and find its order via Taylor expansion: y n + 2 3 = y n + h 3 [ f ( y n + 2 3 ) + f ( y n )] y n +1 = y n + h 4 [3 f ( y n + 2 3 ) + f ( y n )] 3. (3 points) It has been argued that displaying absolute stability regions
This is the end of the preview. Sign up to access the rest of the document.
## This note was uploaded on 07/08/2009 for the course ME 210B taught by Professor Linda during the Spring '09 term at UCSB.
Ask a homework question - tutors are online | 347 | 1,033 | {"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} | 3.15625 | 3 | CC-MAIN-2017-22 | longest | en | 0.900044 |
https://elteoremadecuales.com/appell-humbert-theorem/?lang=fr | 1,680,301,028,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949689.58/warc/CC-MAIN-20230331210803-20230401000803-00542.warc.gz | 271,181,610 | 19,270 | # Théorème d'Appell-Humbert
En mathématiques, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety. It was proved for 2-dimensional tori by Appell (1891) and Humbert (1893), and in general by Lefschetz (1921)
# Théorème d'Appell-Humbert
Dans mathématiques, la Théorème d'Appell-Humbert describes the line bundles on a complex torus or complex abelian variety.
It was proved for 2-dimensional tori by Appell (1891) et Humbert (1893), and in general by Lefschetz (1921)
Índice
## Déclaration[]
Supposer que
$"{displaystyle$
is a complex torus given by
$"{displaystyle$displaystyle V/Lambda }
$"{displaystyle$
is a lattice in a complex vector space
$"{displaystyle$
. Si
$"{displaystyle$
is a Hermitian form on
$"{displaystyle$
whose imaginary part
$"{displaystyle$
is integral on
$"{displaystyle$displaystyle Lambda times Lambda }
, et
$"{displaystyle$
is a map from
$"{displaystyle$
to the unit circle
$"{displaystyle$zin mathbb {C} :|z|=1}}
, called a semi-character, tel que
$"{displaystyle$u+v)=e^{ipi E(tu,v)}alpha (tu)alpha (v) }
alors
$"{displaystyle$pi H(z,tu)+H(tu,tu)pi /2} }
est un 1-cocycle de
$"{displaystyle$
defining a line bundle on
$"{displaystyle$
. For the trivial Hermitian form, this just reduces to a character. Note that the space of character morphisms is isomorphic with a real torus
$"{displaystyle$Hom}}_{textbf {Ab}}(Lambda ,tu(1))cong mathbb {R} ^{2n}/mathbb {Z} ^{2n}}
si
$"{displaystyle$displaystyle Lambda cong mathbb {Z} ^{2n}}
since any such character factors through
$"{displaystyle$
composed with the exponential map. C'est-à-dire, a character is a map of the form
$"{displaystyle$pi ilangle l^{*},-hochet )}
for some covector
$"{displaystyle$displaystyle l^{*}in V^{*}}
. The periodicity of
$"{displaystyle$pi if(X))}
for a linear
$"{displaystyle$
gives the isomorphism of the character group with the real torus given above. En réalité, this torus can be equipped with a complex structure, giving the dual complex torus.
Explicitement, a line bundle on
$"{displaystyle$displaystyle T=V/Lambda }
may be constructed by descent from a line bundle on
$"{displaystyle$
(which is necessarily trivial) et un descent data, namely a compatible collection of isomorphisms
$"{displaystyle$displaystyle u^{*}{mathématique {O}}_{V}à {mathématique {O}}_{V}}
, one for each
$"{displaystyle$displaystyle uin U}
. Such isomorphisms may be presented as nonvanishing holomorphic functions on
$"{displaystyle$
, and for each
$"{displaystyle$
the expression above is a corresponding holomorphic function.
The Appell–Humbert theorem (Mumford 2008) says that every line bundle on
$"{displaystyle$
can be constructed like this for a unique choice of
$"{displaystyle$
et
$"{displaystyle$
satisfying the conditions above.
## Ample line bundles[]
Lefschetz proved that the line bundle
$"{displaystyle$
, associated to the Hermitian form
$"{displaystyle$
is ample if and only if
$"{displaystyle$
is positive definite, and in this case
$"{displaystyle$
is very ample. A consequence is that the complex torus is algebraic if and only if there is a positive definite Hermitian form whose imaginary part is integral on
$"{displaystyle$displaystyle Lambda times Lambda }
## Références[]
• Appell, P. (1891), "Sur les functiones périodiques de deux variables", Journal de Mathématiques Pures et Appliquées, Série IV, 7: 157–219
• Humbert, g. (1893), "Théorie générale des surfaces hyperelliptiques", Journal de Mathématiques Pures et Appliquées, Série IV, 9: 29–170, 361–475
• Lefschetz, Solomon (1921), "On Certain Numerical Invariants of Algebraic Varieties with Application to Abelian Varieties", Transactions de l'American Mathematical Society, Providence, R.I.: Société mathématique américaine, 22 (3): 327–406, est ce que je:10.2307/1988897, ISSN 0002-9947, JSTOR 1988897
• Lefschetz, Solomon (1921), "On Certain Numerical Invariants of Algebraic Varieties with Application to Abelian Varieties", Transactions de l'American Mathematical Society, Providence, R.I.: Société mathématique américaine, 22 (4): 407–482, est ce que je:10.2307/1988964, ISSN 0002-9947, JSTOR 1988964
• Mumford, David (2008) [1970], Variétés abéliennes, Institut Tata d'études de recherche fondamentale en mathématiques, vol. 5, Providence, R.I.: Société mathématique américaine, ISBN 978-81-85931-86-9, M 0282985, OCLC 138290
Si vous voulez connaître d'autres articles similaires à Théorème d'Appell-Humbert vous pouvez visiter la catégorie Variétés abéliennes.
Monter
Nous utilisons nos propres cookies et ceux de tiers pour améliorer l'expérience utilisateur Plus d'informations | 1,374 | 4,696 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 36, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2023-14 | latest | en | 0.51403 |
https://www.daytodaygk.com/ibps-clerk-express-2015-quantitative-aptitute-day-three/ | 1,685,944,904,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224651325.38/warc/CC-MAIN-20230605053432-20230605083432-00756.warc.gz | 788,124,488 | 16,851 | # Quantitative Aptitude Quiz – 7
Dear Friends,
This is the Third day of our IBPS Clerk Express. We heart fully thank you all for the participation. Don’t miss our GK Discussion tonight at 09:00 pm.
1. The perimeter of a square is twice that of a rectangle. If the perimeter of the square is 72 cm and the length of the rectangle is 12 cm, what is the difference between the breadth of the rectangle and the side of the square?
1) 9 cm 2) 12 cm 3) 18 cm 4) 3 cm 5) None of these
4a=4(l+b)
72=4(12+b)
b=6
then side of square=72/4=18 ,
a-b=18-6=12cm
2. Find the average of the following set of scores.
253, 124, 255, 534, 836, 375, 101, 443, 760
1) 427 2) 413 3) 441 4) 490 5) None of these
3. The monthly salary of Ajay is 1/4th of his father.Ajay’s brother salary is 2/5 th of his father salary and Ajay’s brother paying 12800 for study loan which is 1/4th of his salary. The savings and expenses ratio of Ajay is 3:5. How does Ajay save each month?
1) 12,000 2)12,500 3)12,800 4)13,000 5)None of these
1/4 th of Ajay=father and 2/3 rd of Ajay’s brother= father
then Ajay’s brother 1/4th salary =12800 then total salary =12800×4=51,200
then father salary= 51200/2 *5=128000
Ajay’s salary= 128000/4=32000
thrfre his savings=32000/8 *3=12,000Rs
Q(4-9) Study the following pie-charts carefully and answer the questions given below:
The pie-charts shows the number of students appearing for the university exam and selected by the university.
4. What is the difference between the number of students selected from engineering and number of students selected from others discipline?
1) 207 2)184 3)315 4)295 5)267
5) For which discipline is the difference between the number of students appeared to selected is minimum?
1) Agriculture 2)Management 3)Science 4)Others 5)Commerce
6) The total number of candidates appearing from Science and others discipline was what percent of the number of candidates appearing from engineering and commerce discipline?
1)117% 2)108% 3)140.63% 4)129.33% 5)None of theses
7) What is the total number of candidates selected from Science and Management together?
1)2505 2)2065 3)3056 4)2722 5)2852
8) What was the ratio of the number of students appearing in Management discipline to the number of students selected from Engineering discipline?
1) 19:17 2)187:184 3)23:21 4)105:97 5)None of these
9. The number of students selected in commerce and management together is what percent of the number of students appearing in Science and Agriculture discipline?
1)24.39% 2)32.33% 3)25.64% 4)31.74% 5)36.21%
10. A bag contains 5 red balls,6 yellow balls and 3 green balls.If two balls are picked at random what is the probability that either both are red or both are green in the colour?
1)3/7 2)2/7 3)1/7 4)4/7 5)3/14
either red or green=5C2 + 3C2
probability=5C2 + 3C2/ 14C2 = 1/7
11. 19 30 44 67 117 ?
1)348 2)448 3)248 4)548 5)258
12. 7 9 18 46 111 ?
1) 245 2)235 3)265 4)257 5)237
7 +(1³+1)=9
9+ (2³+1)=18 …and so on
13. 7 24 58 109 ? 262
1)183 2)189 3)177 4)187 5)None of these
+17, +34,+51,….
14.19 20 16 25 9 ?
1)32 2)33 3)34 4)35 5)36
+1², -2², +3², -4²……
15. 7.4 9.2 11.4 14 17 ?
1)19.8 2)22.6 3)23 4)21 5)20.4
+1.8, +2.2,+2.6, +3, +3.4, ….
THANK YOU FRIENDS
Don’t Forget to Share Your Marks in the comment section!!!
Come back @ 12:00 pm for Reasoning Quiz | 1,263 | 3,567 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2023-23 | latest | en | 0.857343 |
https://fivethirtyeight.com/features/state-pegs-coleman-lead-at-172-votes/ | 1,527,413,696,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794868239.93/warc/CC-MAIN-20180527091644-20180527111644-00087.warc.gz | 522,688,103 | 28,198 | [UPDATED] State Pegs Coleman Lead at 172 Votes; Challenges Increase for Fourth Straight Day
UPDATED at 9:50 PM with technical mumbo-jumbo.
The nightly, 8 PM update from the Minnesota Secretary of State now shows Norm Coleman with a nominal lead of 172 votes over Al Franken. According to the state’s accounting, Franken has gained 43 votes on Coleman since the recount process began. However, the high number of challenges on both sides probably obscures any true movement in the vote counts.
Indeed, whereas as of midday, it appeared that the Coleman campaign was challenging significantly more ballots than Franken, Franken has fully caught up with Coleman’s rate of challenges in the 8 PM count, with both campaigns challenging record-setting numbers of ballots. The Franken campaign’s challenge rate in ballots counted today was 18.3 per 10,000 votes; Coleman’s was 18.2 per 10,000 votes. The rates of challenged ballots have been increasing by an aggregate of about 50 percent per day over each day of the recount process.
TECHNICAL UPDATE: Different versions of the projection technique that we unveiled yesterday continue to peg Franken as a slight favorite. I am going to list four different versions here — this will get technical:
‘Gross’ models evaluate each candidate’s results individually, e.g. how much Franken gains in the absolute count. ‘Net’ models evaluate how much Franken gains relative to Coleman, without worrying about the absolute count. ‘Simple’ models include a maximum of three variables (plus a constant term): Franken’s share of the two-way vote in that precinct, the frequency of challenges initiated by Coleman, and the frequency of challenges initiated by Franken. ‘Complex’ models account for two-way and three-way interactions (where statistically significant) between these independent variables. The regression is weighted based on the square root of the number of votes tabulated in that precinct. Variables are dropped if not statistically significant at the 95 percent certianty level.
Type Depth Franken Coleman Net Result
Gross Simple +473 +138 Franken +335 Franken +120
Gross Complex +368 +17 Franken +351 Franken +136
Net Simple -- -- Franken +336 Franken +121
Net Complex -- -- Franken +263 Franken +48
The various versions of the model project a Franken win by between 48 and 136 votes once all ballots are re-counted and all challenges are resolved. However — disclaimer! — the margins of error on these regressions are HIGH, e.g. at least +/- 200 votes to achieve a 95 percent certainty level. The point is not really to project a precise margin of victory (or defeat) for Franken but to suggest Franken probably has made more progress in the recount than is implied by the state’s in-progress totals and may in fact be the favorite to win it.
…and actually, there’s a (relatively) simpler way to get at the same result. Taking a simple regression of Franken’s challenge rate on Coleman’s net total and vice versa, the models suggest that Franken is losing about .87 votes for every Coleman challenge, whereas Coleman is losing .74 votes for every Franken challenge. That would imply that about 87% of Coleman’s challenges are to Franken votes that were initially ruled legal, and that 74% of Franken’s challenges are to Coleman votes that were initially ruled legal. Challenges of this type result in a temporary deduction to the opposing candidate’s total until the challenges are resolved.
Given each candidate’s present number of challenges, this would suggest that Coleman has succeeded in (temporarily) deducting 1,211 from Franken’s total by challenging legal ballots, whereas Franken has succeeded in deducting 1,033 votes from Coleman’s total — a gap of 178 votes. If all such challenges are rejected, Franken would presently have a lead of 6 ballots, and presumably would be on pace to make up additional ground as the final 26 percent of ballots are counted.
The key intuition is that, although the candidates have issued almost exactly the same number of challenges, Coleman is almost certainly making more of the type of challenge — challenging ballots initially ruled to be legal — that result in a deduction to the opponent’s total. Conversely, Franken is probably appealing the local election official’s decision more frequently on ballots ruled to be undervotes — but this type of challenge has no immediate impact on the state’s reported totals. This has nothing to do with which campaign’s challenges are more frivolous or not — it’s just that much of Coleman’s apparent lead is an artifact of the way that the state keeps score of different types of challenges.
EDIT: Well, let me qualify the above finding some more. Whether or not you arrive at the result I describe above — that a higher percentage of Coleman’s challenges are to legal Franken ballots — depends heavily on whether and how you’re weighting the regression to account for precinct size. I suspect this is because both campaigns’ standards for challenging ballots have changed (i.e. loosened) with each subsequent day of the recount, and also with each subsequent day of the recount, we have tended to move into larger precincts. So, sprinkle in additional ‘probablys’ and ‘maybes’ as needed. This is confusing stuff.
EDIT #2: Another complication is that it appears as though types of challenges in a given precinct are also a function of the favorability of that precinct for Al Franken. In strong Coleman precincts, almost all of the challenges appear to involve legal ballots that the campaigns are trying to get thrown out. In strong Franken precincts, on the other hand, a more sizable percentage of the action appears to involve undervotes that were not counted initially.
Nate Silver is the founder and editor in chief of FiveThirtyEight.
Filed under | 1,178 | 5,827 | {"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-2018-22 | longest | en | 0.937945 |
https://gmatclub.com/forum/sc-gmat-redundant-words-notes-104492.html | 1,627,537,297,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153816.3/warc/CC-MAIN-20210729043158-20210729073158-00159.warc.gz | 284,387,862 | 156,677 | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 28 Jul 2021, 21:41
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
SORT BY:
Tags:
### Show Tags Hide Tags
Intern
Joined: 20 Jul 2010
Posts: 27
##### Most Helpful Community Reply
Manhattan Prep Instructor
Joined: 22 Sep 2010
Posts: 166
Schools:MBA, Thunderbird School of Global Management / BA, Wesleyan University
##### General Discussion
Manager
Joined: 16 Jul 2010
Posts: 63
Manager
Joined: 08 Jul 2008
Posts: 56
Manager
Joined: 02 Oct 2010
Posts: 70
Intern
Joined: 20 Jul 2010
Posts: 27
Director
Joined: 17 Mar 2014
Posts: 621
VP
Joined: 12 Dec 2016
Posts: 1263
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
VP
Joined: 12 Dec 2016
Posts: 1263
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Senior Manager
Joined: 09 Mar 2017
Posts: 438
Location: India
Concentration: Marketing, Organizational Behavior
WE:Information Technology (Computer Software)
VP
Joined: 12 Dec 2016
Posts: 1263
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Retired Moderator
Joined: 10 Oct 2016
Status:Long way to go!
Posts: 1265
Location: Viet Nam
Senior Manager
Joined: 09 Mar 2017
Posts: 438
Location: India
Concentration: Marketing, Organizational Behavior
WE:Information Technology (Computer Software)
Intern
Joined: 06 Mar 2020
Posts: 38
Non-Human User
Joined: 01 Oct 2013
Posts: 11027
Moderators:
GMAT Club Verbal Expert
4685 posts
GMAT Club Verbal Expert
242 posts
GMAT Club team member
9639 posts
SC Moderator
1203 posts
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne | 621 | 2,066 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-31 | latest | en | 0.833334 |
http://www.nelson.com/mathfocus/grade3/quizzes/ch03/ch03_9.htm | 1,582,929,365,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875147647.2/warc/CC-MAIN-20200228200903-20200228230903-00307.warc.gz | 213,373,667 | 6,020 | Name: Lesson 9 - Estimating Sums and Differences
1.
What ten is close to 57?
a. 60 b. 50 c. 55
2.
What ten is close to 32?
a. 50 b. 40 c. 30
3.
What ten is close to 86?
a. 90 b. 100 c. 80
4.
What ten is close to 65?
a. 60 b. 70 c. 50
5.
Use tens to find a number that is close to the sum 36 + 41.
a. 30 + 40 = 70 b. 40 + 40 = 80 c. 40 + 50 = 90
6.
Use tens to find a number that is close to the sum 53 + 24.
a. 50 + 20 = 70 b. 50 + 30 = 80 c. 60 + 30 = 90
7.
Use tens to find a number that is close to the sum 78 + 38.
a. 70 + 40 = 110 b. 80 + 30 = 110 c. 80 + 40 = 120
8.
Use tens to find a number that is close to the difference 52 - 17.
a. 50 - 10 = 40 b. 50 - 20 = 30 c. 60 - 20 = 40
9.
Use tens to find a number that is close to the difference 71 - 44.
a. 70 - 40 = 30 b. 70 - 50 = 20 c. 80 - 40 = 40
10.
Use tens to find a number that is close to the difference 97 - 56.
a. 90 - 60 = 30 b. 100 - 60 = 40 c. 100 - 50 = 50 | 412 | 959 | {"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} | 4.3125 | 4 | CC-MAIN-2020-10 | latest | en | 0.647477 |
https://web2.0calc.com/questions/imaginary-numbers-precalc | 1,643,273,876,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305242.48/warc/CC-MAIN-20220127072916-20220127102916-00168.warc.gz | 642,417,280 | 7,586 | +0
# Imaginary Numbers Precalc
0
70
13
+437
Compute $$\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}}$$.
Here's what I tried to do:
For the first imaginary number, (1-i)^10, I simplified it down to -2^5 * i. The next two imaginary numbers I tried to simplify using DeMoivre's Theorem. But I got stuck on simplifying them down to make it easy to divide. A little help?
Dec 17, 2021
#1
-1
The complex number works out to 4.
Dec 17, 2021
#2
+115924
+1
You need to check each step of this answer as I likely made one or more carelsee errors.
Redone on a later post with the careless error removed.
https://web2.0calc.com/questions/imaginary-numbers-precalc/edit-2#r12
$$\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}}\\~\\ =\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(1+i\sqrt 3)^{10}}\times \frac{(1-i\sqrt 3)^{10}}{(1-i\sqrt 3)^{10}}\\~\\ =\frac{[(1-i)(1-i\sqrt 3)]^{10}(\sqrt 3 + i)^5}{[(1+i\sqrt 3)(1-i\sqrt 3)]^{10}}\\~\\ =\frac{[[(1-\sqrt3)-(1+\sqrt3)i]^{2}]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\ =\frac{[4i]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\ =\frac{[i]^5(\sqrt 3 + i)^5}{4^{5}}\\~\\ =\frac{i(\sqrt 3 + i)^5}{4^{5}}\\~\\ =\frac{i(16(\sqrt3+i)}{4^{5}}\\~\\ =\frac{i(\sqrt3+i)}{4^3}\\~\\ =\frac{-1+\sqrt3i}{64}\\~\\$$
Latex:
\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}}\\~\\
=\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(1+i\sqrt 3)^{10}}\times \frac{(1-i\sqrt 3)^{10}}{(1-i\sqrt 3)^{10}}\\~\\
=\frac{[(1-i)(1-i\sqrt 3)]^{10}(\sqrt 3 + i)^5}{[(1+i\sqrt 3)(1-i\sqrt 3)]^{10}}\\~\\
=\frac{[[(1-\sqrt3)-(1+\sqrt3)i]^{2}]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\
=\frac{[4i]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\
=\frac{[i]^5(\sqrt 3 + i)^5}{4^{5}}\\~\\
=\frac{i(\sqrt 3 + i)^5}{4^{5}}\\~\\
=\frac{i(16(\sqrt3+i)}{4^{5}}\\~\\
=\frac{i(\sqrt3+i)}{4^3}\\~\\
=\frac{-1+\sqrt3i}{64}\\~\\
Dec 17, 2021
edited by Melody Dec 18, 2021
#3
+437
0
Oh I forgot to say that it should work out to be a real number. So I think there were a few errors.
MobiusLoops Dec 17, 2021
edited by MobiusLoops Dec 17, 2021
#4
+115924
+2
I expect there were a number of trivial errors.
However, there is nothing wrong with my logic.
I am quite sure you are able to use my logic and find the errors.
You asked for a little help. You did not ask to be given a full copiable answer!
Melody Dec 17, 2021
edited by Melody Dec 17, 2021
#5
+437
0
You're right. I'm gonna try to do it lol :D
MobiusLoops Dec 18, 2021
#6
+437
0
Ok I found out how to do it!
We have to convert the complex numbers into cos + i * sin!
It makes so much sense now lol
MobiusLoops Dec 18, 2021
#7
+115924
+1
That would be an alternate way of doing it. My method (minus careless errors) also works.
Melody Dec 18, 2021
#8
+437
0
Well thanks Melody for pointing me in the right direction :)
MobiusLoops Dec 18, 2021
#9
+115924
+1
Why don't you display your solution.
I expect it is an easier method.
Melody Dec 18, 2021
#10
+437
+2
Ok! There are two important formulas! Euler's formula and de Moivre's theorem. Here are links to them:
Euler's Formula: https://www.math.columbia.edu/~woit/eulerformula.pdf
de Moivre's theorem: https://byjus.com/jee/de-moviers-theorem/
$$\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}}$$
First, you find the modulus for each complex number. You get the modulus by taking the coefficients of the real and the imaginary parts. An example from this problem would be | 1-i | = $$\sqrt{(1^2)+(-1^2)} = \sqrt2$$ and $$\sqrt2$$ would be the modulus.
I would think the people reading this question would be taking precalc, so I'll assume they know how to use these formulas correctly. If not, go read the articles posted above.
Solution:
$$\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}} =$$
$$\frac{ (\sqrt{2} )^{10} \left( \cos (-\frac{\pi}4) + i \sin(-\frac{\pi}4) \right)^{10} \cdot 2^5 \left( \cos\frac\pi 6 + i \sin\frac\pi 6 \right)^5}{2^{10}\left( \cos\frac{4\pi}3 + i \sin \frac{4\pi}3 \right)^{10}} =$$
If you don't know how we got this $$\uparrow$$, basically, we found the modulus, then took the coefficients, and found the angle that matches the cos and sin values.
$$\frac{ 2^{10} \left( \cos (-\frac{5\pi}2) + i \sin (-\frac{5\pi}2) \right)\left( \cos\frac{5\pi}6 + i \sin \frac{5\pi}6 \right)}{ 2^{10} \left( \cos\frac{40\pi}3 + i \sin\frac{40\pi}3 \right) } =$$
Here we used de Moivre's theorem. Go look at the article for an explanation.
$$\frac{ \cos (-\frac{5\pi}3) + i \sin (-\frac{5\pi}3) }{ \cos(\frac{40\pi}3) + i\sin(\frac{40\pi}3) } =$$
We simplified to get this.
$$\cos (-15\pi) + i\sin (-15\pi) = -1$$
Final Solution!!! :D
MobiusLoops Dec 18, 2021
#11
+115924
+1
Thanks MobiusLoops
Melody Dec 18, 2021
#12
+115924
+1
Just to prove my point, I have redone it without any errors.
$$\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}}\\~\\ =\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(1+i\sqrt 3)^{10}}\times \frac{(1-i\sqrt 3)^{10}}{(1-i\sqrt 3)^{10}}\\~\\ =\frac{[(1-i)(1-i\sqrt 3)]^{10}(\sqrt 3 + i)^5}{[(1+i\sqrt 3)(1-i\sqrt 3)]^{10}}\\~\\ =\frac{[[(1-\sqrt3)-(1+\sqrt3)i]^{2}]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\ \text{no errors to here}\\~\\ =\frac{[-4\sqrt3+4i]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\ =\frac{(-4)^5[\sqrt3-i]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\ =\frac{-(4)^5[(\sqrt3-i)(\sqrt 3 + i)]^5}{4^{10}}\\~\\ =\frac{-[3+1]^5}{4^{5}}\\~\\ =-1$$
LaTex:
\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(-1-i\sqrt 3)^{10}}\\~\\
=\frac{(1-i)^{10}(\sqrt 3 + i)^5}{(1+i\sqrt 3)^{10}}\times \frac{(1-i\sqrt 3)^{10}}{(1-i\sqrt 3)^{10}}\\~\\
=\frac{[(1-i)(1-i\sqrt 3)]^{10}(\sqrt 3 + i)^5}{[(1+i\sqrt 3)(1-i\sqrt 3)]^{10}}\\~\\
=\frac{[[(1-\sqrt3)-(1+\sqrt3)i]^{2}]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\
\text{no errors to here}\\~\\
=\frac{[-4\sqrt3+4i]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\
=\frac{(-4)^5[\sqrt3-i]^5(\sqrt 3 + i)^5}{4^{10}}\\~\\
=\frac{-(4)^5[(\sqrt3-i)(\sqrt 3 + i)]^5}{4^{10}}\\~\\
=\frac{-[3+1]^5}{4^{5}}\\~\\
=-1
Melody Dec 18, 2021
#13
+437
0
Cool!
MobiusLoops Dec 18, 2021 | 2,536 | 5,889 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2022-05 | longest | en | 0.681016 |
https://brainmass.com/statistics/hypothesis-testing/testing-of-hypothesis-463903 | 1,544,705,977,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376824822.41/warc/CC-MAIN-20181213123823-20181213145323-00329.warc.gz | 552,161,762 | 19,239 | Explore BrainMass
Share
# Testing of Hypothesis
This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!
On Friday, Wall Street traders were anxiously awaiting the federal government's release of numbers on the January increase in nonfarm payrolls. The early consensus estimate among economists was for a growth of 250,000 new jobs (CNBC, February 3, 2006). However, a sample of 20 economists taken Thursday afternoon provided a sample mean of 266,000 with a sample standard deviation of 24,000. Financial analysts often call such a sample mean, based on late-breaking news, the "whisper number". Treat the "consensus estimate" as the population mean. Conduct a hypothesis test to determine whether the whisper number justifies a conclusion of a statistically significant increase in the consensus estimate of economists. Use ? = .01 as the level of significance.
https://brainmass.com/statistics/hypothesis-testing/testing-of-hypothesis-463903
#### Solution Summary
The solution explains a testing of hypothesis problem from financial economics.
\$2.19
## Testing Hypothesis at 0.05 Level
Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.
Treatment 1 Treatment 2 Treatment 3
8 3 3
11 2 4
10 1 5
3 4
2
A. State the null hypothesis and the alternate hypothesis.
B. What is the decision rule?
C. Compute SST, SSE, SS total.
D. Complete an ANOVA table.
E. State your decision regarding the null hypothesis.
F. If Ho is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95% level of confidence.
View Full Posting Details | 385 | 1,687 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2018-51 | longest | en | 0.910631 |
https://www.teachstarter.com/us/teaching-resource/perimeter-formula-for-2-d-shapes-poster/ | 1,713,507,692,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817289.27/warc/CC-MAIN-20240419043820-20240419073820-00701.warc.gz | 916,442,998 | 74,044 | teaching resource
# Perimeter Anchor Chart
• Updated: 13 Oct 2023
Use this perimeter anchor chart to teach students how to find the perimeter of shapes such as squares, rectangles, triangles, hexagons and parallelograms.
• Non-Editable: PDF
• Pages: 1 Page
Tag #TeachStarter on Instagram for a chance to be featured!
teaching resource
# Perimeter Anchor Chart
• Updated: 13 Oct 2023
Use this perimeter anchor chart to teach students how to find the perimeter of shapes such as squares, rectangles, triangles, hexagons and parallelograms.
• Non-Editable: PDF
• Pages: 1 Page
Use this perimeter anchor chart to teach students how to find the perimeter of shapes such as squares, rectangles, triangles, hexagons and parallelograms.
## Find the Perimeter of Shapes with Our Perimeter Anchor Chart
Are your students struggling to grasp the concept of finding the perimeter of various 2D shapes? Look no further than Teach Starter’s Perimeter Anchor Chart! With this comprehensive and easy-to-understand teaching tool, you’ll be able to help your students understand how to find the perimeter of shapes in no time!
Our perimeter anchor chart has been designed by our experienced teacher team to guide your students through the fundamentals of finding the perimeter of different shapes. It serves as a valuable resource in the classroom to facilitate learning and retention of these key perimeter processes.
The features of this Perimeter Anchor Chart include:
• A definition of perimeter (the distance around a 2D shape)
• Visuals of a square, rectangle, triangle, hexagon, parallelogram and a compound shape
• Perimeter formulas for each of the six shapes
This perimeter anchor chart explaining how to find the perimeter of shapes downloads as a full-color or black-and-white PDF. Why not display the color version of the perimeter anchor chart on your math bulletin board, then provide the students with a copy of the black-and-white version to paste into their notebooks.
This anchor chart is a must-have teaching resource when it comes to teaching your students about how to find the perimeter of shapes!
## How Can This Perimeter Anchor Chart Help Students?
This teaching resource can help your students master the skill of finding the perimeter of shapes in the following ways:
1. Simplified Learning – Our anchor chart simplifies the often complex concept of finding perimeter. It breaks it down into manageable steps, making it easier for students to understand and remember.
2. Visual Learning – The combination of clear visuals and concise explanations allows students to engage in visual learning, which is a powerful method for retention and comprehension.
3. Easy Reference – Whether it’s during class, homework or studying for an assessment, the Perimeter Anchor Chart serves as a quick and reliable reference tool for students. They can independently reference it whenever they need help.
Use the download button above to access the color or black-and-white PDF.
You may wish to enlarge this poster to enhance readability for display purposes.
## More Resources on How to Find Perimeter
Teach Starter has more great resources to save you time when teaching the perimeter of shapes to your class. Click below for some more curriculum-aligned, teacher-created activities!
### teaching resource
#### Interactive Perimeter Puzzle
Play this perimeter game with your class so they can practice calculating the perimeter of a variety of 2D shapes.
### teaching resource
#### Perimeter with Missing Sides – Word Problems Worksheet
Use this perimeter with missing sides worksheet when exploring the concept of perimeter in your math lessons.
### teaching resource
#### Draw the Perimeter Worksheet
Get students to draw a figure with a given perimeter with this perimeter of rectangles worksheet. | 761 | 3,839 | {"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-2024-18 | latest | en | 0.878787 |
https://bitbucket.org/jpellerin/jinja2-main/src/2c008226281a/tests/test_tests.py | 1,435,677,108,000,000,000 | text/html | crawl-data/CC-MAIN-2015-27/segments/1435375093974.67/warc/CC-MAIN-20150627031813-00279-ip-10-179-60-89.ec2.internal.warc.gz | 833,481,714 | 16,591 | # jinja2-main / tests / test_tests.py
``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94``` ```# -*- coding: utf-8 -*- """ unit test for the test functions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ :copyright: (c) 2009 by the Jinja Team. :license: BSD, see LICENSE for more details. """ from jinja2 import Environment, Markup env = Environment() DEFINED = '''{{ missing is defined }}|{{ true is defined }}''' EVEN = '''{{ 1 is even }}|{{ 2 is even }}''' LOWER = '''{{ "foo" is lower }}|{{ "FOO" is lower }}''' ODD = '''{{ 1 is odd }}|{{ 2 is odd }}''' SEQUENCE = '''{{ [1, 2, 3] is sequence }}|\ {{ "foo" is sequence }}|\ {{ 42 is sequence }}''' UPPER = '''{{ "FOO" is upper }}|{{ "foo" is upper }}''' SAMEAS = '''{{ foo is sameas false }}|{{ 0 is sameas false }}''' NOPARENFORARG1 = '''{{ foo is sameas none }}''' TYPECHECKS = '''\ {{ 42 is undefined }} {{ 42 is defined }} {{ 42 is none }} {{ none is none }} {{ 42 is number }} {{ 42 is string }} {{ "foo" is string }} {{ "foo" is sequence }} {{ [1] is sequence }} {{ range is callable }} {{ 42 is callable }} {{ range(5) is iterable }}''' def test_defined(): tmpl = env.from_string(DEFINED) assert tmpl.render() == 'False|True' def test_even(): tmpl = env.from_string(EVEN) assert tmpl.render() == 'False|True' def test_odd(): tmpl = env.from_string(ODD) assert tmpl.render() == 'True|False' def test_lower(): tmpl = env.from_string(LOWER) assert tmpl.render() == 'True|False' def test_typechecks(): tmpl = env.from_string(TYPECHECKS) assert tmpl.render() == '' def test_sequence(): tmpl = env.from_string(SEQUENCE) assert tmpl.render() == 'True|True|False' def test_upper(): tmpl = env.from_string(UPPER) assert tmpl.render() == 'True|False' def test_sameas(): tmpl = env.from_string(SAMEAS) assert tmpl.render(foo=False) == 'True|False' def test_typechecks(): tmpl = env.from_string(TYPECHECKS) assert tmpl.render() == ( 'False\nTrue\nFalse\nTrue\nTrue\nFalse\n' 'True\nTrue\nTrue\nTrue\nFalse\nTrue' ) def test_no_paren_for_arg1(): tmpl = env.from_string(NOPARENFORARG1) assert tmpl.render(foo=None) == 'True' def test_escaped(): env = Environment(autoescape=True) tmpl = env.from_string('{{ x is escaped }}|{{ y is escaped }}') assert tmpl.render(x='foo', y=Markup('foo')) == 'False|True' ``` | 817 | 2,468 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2015-27 | latest | en | 0.480179 |
http://www.minyanville.com/businessmarkets/articles/9/16/2003/id/2419 | 1,537,433,249,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267156423.25/warc/CC-MAIN-20180920081624-20180920101624-00032.warc.gz | 378,468,765 | 17,027 | Sorry!! The article you are trying to read is not available now.
# Calculus
By
PRINT
I have in the past discussed the importance of calculus in option pricing. I have gone into some detail in the following few pages (with the help of an excerpt from "A Mathematical Universe" by William Dunham) for those of you interested in a better understanding of how it works. For those of you who don't care, stop reading now!
There are two types of calculus: integral calculus is concerned with the area under curves (on a graph), while differential calculus deals with the slopes of curves, which defines rate of change. The latter is what traders are concerned with and what I will discuss.
Graphs describe the relationship between one variable and another. The following graph depicts a straight line in a coordinate plane: it shows how the variables x and y vary to each other. It illustrates that if x increases by a certain number of units, y will increase by a certain number of units. The number of units of y for a certain number of units of x depends on the steepness of the line or its slope.
The slope of a line is defined as the change in y per unit change in x (the rate of change of a unit of y per unit of x); a line tells us that this rate of change is constant. If the world were a totally linear place (if planes never changed speed or acceleration), we could graph (describe) all relationships with lines.
But the world is not such a simple place. Markets go up and down at different rates and planes change their speed and acceleration: the real world exhibits non-linear behavior manifest as curves on a graph. Differential calculus was developed as a set of rules that determines the slope of a curve (rate of change) at any coordinate on the curve. Specifically, calculus determines the slope of the tangent line at that coordinate.
Consider the following graph of a parabola. It may represent the speed of a plane (y) over time (x). The speed is changing, defined as acceleration. As the curve declines the plane is slowing down, at the bottom of the curve its speed is constant, and as the curve inclines it is accelerating. The change in acceleration of the plane at any time (x) is measured by the slope of the tangent line at any point on the curve. As the slope of the tangent at any point increases or decreases, so does the rate of acceleration. At the bottom of the parabola where the slope of the tangent is zero, there is no acceleration and the plane is traveling at a constant velocity.
At point (3, 4) where we have drawn the tangent line, imagine the plane splits in two. Plane A is traveling per the parabola, but Plane B stays on the tangent. Plane A begins accelerating at a faster and faster rate (as the slope of the tangent line increases), while Plane B continues to accelerate at a constant rate. So how do we determine the slope of the tangent? Leibniz in the late 17th century probably spent years in trial and error to give us an ingenious short cut. In order to calculate the slope of the tangent, all we need are two points. But at x =3 we only have one point (3, 4). Consider Leibniz' clever solution in the following graph.
We can calculate another point B on the parabola for x =4 (4, 7) and then draw a line called a secant to point A (3, 4) creating line AB. We then calculate the slope of AB as shown in the graph to be 3. But we can get closer to the slope of the tangent at (3, 4) by successively using secants with x coordinates closer and closer to point A. Secant AC has a slope of 2.50 while secant AD has a slope of 2.10. If we kept doing this we would get a slope approaching 2 as the secants become better and better approximations of the actual tangent.
What Leibniz did was streamline this process of approximations that allows us to quickly find the slope of any tangent on the parabola. This requires a more general and algebraic approach as illustrated in the following graph.
If we are trying to determine the slope of the tangent at P, we first consider the point Q with an x coordinate x +h (h is a small unspecified amount). By using x +h as the x coordinate, the y coordinate for Q then becomes:
a(x + h)^2 + b(x + h) + c =
a(x^2 + 2xh + h^2) + b(x + h) + c =
ax^2 + 2axh + ah^2 + bx + bh + c
So Q is the point (x + h, ax^2 + 2axh + ah^2 + bx + bh + c). Point P is (x, ax^2 + bx + c).
To find the slope of this secant we plug these two points into our slope formula:
Slope PQ = y2-y1 = (ax^2 + 2axh + ah^2 + bx + bh + c) - (ax^2 + bx + c)
x2-x1 (x + h) - x
= ax^2 + 2axh + ah^2 + bx +bh + c - ax^2 - bx -c
x + h -x
= 2axh + ah^2 + bh = h(2ax + ah +b)
h h
= 2ax + ah +b
As we move the secants closer to the tangent, h approaches zero; so the ah variable can just be dropped and we get for the slope of the tangent: 2ax + b.
If we apply this formula to the actual parabola y = x^2 - 4x +7 at x =3, where a = 1 and b = -4 (c does not matter), we get 2(1)(3) + (-4) = 2.
The slope of the tangent to a curve is the limit of the slopes of the secants as h goes to zero. This limit is called the derivative and the process of finding it is called differentiation.
< Previous
• 1
Next >
No positions in stocks mentioned.
The information on this website solely reflects the analysis of or opinion about the performance of securities and financial markets by the writers whose articles appear on the site. The views expressed by the writers are not necessarily the views of Minyanville Media, Inc. or members of its management. Nothing contained on the website is intended to constitute a recommendation or advice addressed to an individual investor or category of investors to purchase, sell or hold any security, or to take any action with respect to the prospective movement of the securities markets or to solicit the purchase or sale of any security. Any investment decisions must be made by the reader either individually or in consultation with his or her investment professional. Minyanville writers and staff may trade or hold positions in securities that are discussed in articles appearing on the website. Writers of articles are required to disclose whether they have a position in any stock or fund discussed in an article, but are not permitted to disclose the size or direction of the position. Nothing on this website is intended to solicit business of any kind for a writer's business or fund. Minyanville management and staff as well as contributing writers will not respond to emails or other communications requesting investment advice. | 1,554 | 6,537 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2018-39 | latest | en | 0.956955 |
https://stats.stackexchange.com/questions/527110/how-to-calculate-average-importance-of-factors-attributes-correctly-in-conjoi/539624 | 1,719,064,566,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862396.85/warc/CC-MAIN-20240622112740-20240622142740-00323.warc.gz | 478,068,400 | 39,962 | # How to calculate average importance of factors (attributes) correctly in "conjoint" package (R)?
First, load conjoint package:
library(conjoint)
Then, I load chocolate data:
data(chocolate)
#cprof (profiles - cards)
#cpref (preferences - stack shape)
#cprefm (preferences - unstack shape)
#clevn (levels into attributes)
#csimp (simulation importance matrix)
ShowAllUtilities(x = cprof, y = cpref, z = clevn, y.type = "score")
Consider this part of the output:
[1] "Part worths (utilities) of levels (model parameters for whole sample):"
levnms utls
1 intercept 8,6849
2 milk -1,0891
3 walnut -0,7328
4 delicaties -0,9224
5 dark 2,7443
6 low -0,5709
7 average 0,1188
8 high 0,4521
9 paperback -0,0287
10 hardback 0,0287
11 light -0,1686
12 middle 0,1734
13 heavy -0,0048
14 little -0,6466
15 much 0,6466
I calculate the average importance of utilities manually:
First, kind attribute:
2 milk -1,0891
3 walnut -0,7328
4 delicaties -0,9224
5 dark 2,7443
2,7443 - (-1,0891) = 3,8334
Price:
6 low -0,5709
7 average 0,1188
8 high 0,4521
0,4521 - (-0,5709) = 1,0230
Packing:
9 paperback -0,0287
10 hardback 0,0287
0,0287 - (-0,0287) = 0,0574
Weight:
11 light -0,1686
12 middle 0,1734
13 heavy -0,0048
0,1734 - (-0,1686) = 0,3420
Calories:
14 little -0,6466
15 much 0,6466
0,6466 - (-0,6466) = 1,2932
Where the sum is 6,5490
And calculate the average importances for each attribute:
First, kind attribute importance:
3,8334/6,5490 = 0,5853*100 = 58,53
Price
1,0230/6,5490 = 0,1562*100 = 15,62
Packing:
0,0574/6,5490 = 0,0088*100 = 0,8765
Weight:
0,3420/6,5490 = 0,0522*100 = 5,22
Calories:
1,2932/6,5490 = 0,1975*100 = 19,74
But, the output Average importance of factors (attributes) is:
56,79 16,42 5,43 10,61 10,75
Sum of average importance: 100
What is the explanation for this inaccuracy?
Can you improve your answer, please. There are several mistakes, such as in the first attribute calculation. Also, what is y,type = "score" supposed to be?
Usually you should be able to calculate importance the way you did. But it seems the part worths are displayed in a non-standard way. I am not familiar with the conjoint package, so I do not no why, but there is probably a good reason for it.
Anyway, running normal regression:
library(conjoint)
data(chocolate)
pref <- pivot_longer(cprefm, 1:16, names_to = "profile", values_to = "rating")
cprof <- t(apply(cprof, 1, as.factor))
pref2 <- cbind(pref, cprof)
summary(lm(rating ~ kind + price + packing + weight + calorie, data = pref2))
Gives:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.68487 0.12648 68.667 < 2e-16 ***
kind1 -1.08908 0.19815 -5.496 4.62e-08 ***
kind2 -0.73276 0.19815 -3.698 0.000226 ***
kind3 -0.92241 0.19815 -4.655 3.55e-06 ***
price1 -0.57088 0.15254 -3.743 0.000190 ***
price2 0.11877 0.17887 0.664 0.506777
packing1 -0.02874 0.11440 -0.251 0.801714
weight1 -0.16858 0.15254 -1.105 0.269272
weight2 0.17337 0.17887 0.969 0.332575
calorie1 -0.64655 0.11440 -5.652 1.93e-08 ***
Coefficients look the same, but this time they are correct. If there is an intercept, then the missing attribute level is the base line. This means it has a value of 0. So kind4 should be 0, but in your case it is 2.7443.
When using radiant, the correct result is displayed (kind4 is 0):
library(radiant)
summary(conjoint(pref2, rvar = "rating",
evar = c("kind", "price", "packing", "weight", "calorie")))
Conjoint part-worths:
Attributes Levels PW
kind 1 -1.089
kind 2 -0.733
kind 3 -0.922
kind 4 0.000
price 1 -0.571
price 2 0.119
price 3 0.000
packing 1 -0.029
packing 2 0.000
weight 1 -0.169
weight 2 0.173
weight 3 0.000
calorie 1 -0.647
calorie 2 0.000
Base utility ~ 8.685
And the importance weights are different to yours and to the conjoint package:
Conjoint importance weights:
Attributes IW
kind 0.390
price 0.247
packing 0.010
weight 0.122
calorie 0.231
I do not really know why the conjoint package gives a different result. Still, the lm-approach should be correct.
Note that there many different ways to standardize in conjoint analysis. So it is hard to say what is going on here. I guess the program developer/maintainer knows best, so you can contact him (info from CRAN): Tomasz Bartlomowicz [email protected] | 1,613 | 4,697 | {"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} | 3.015625 | 3 | CC-MAIN-2024-26 | latest | en | 0.50074 |
http://mathhelpforum.com/advanced-applied-math/190928-solving-convolution-equation-two-solutions-one-correct-print.html | 1,529,580,331,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864139.22/warc/CC-MAIN-20180621094633-20180621114633-00176.warc.gz | 202,819,708 | 2,654 | # Solving a convolution equation: two solutions, which one is correct?
• Oct 21st 2011, 12:46 AM
MatNorge
Solving a convolution equation: two solutions, which one is correct?
Hi All,
Here is my problem:
Considering the following equation,
Ur(t)*G(t)=A
- Ur(t) is what we are looking for and is =0 for all t<0
- * is a convolution
- G(t) = 1/Q1 + (P1/Q2-1/Q1)exp(-Q1.t/Q2) for t>=0 (Q1, Q2 and P1 are constants) and G(t)=0 for all t<0
- A is a constant
I derived a solution using the Laplace Transform and also found a way to get a solution through a derivation in the time domain using the Stieltjes integrals . Both derivations are in the .doc attached
The issue is that the two solutions are different and I don't know why...
Which one is correct if any?(Wondering)
Thanks for your help or ideas,
MatNorge | 237 | 816 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2018-26 | latest | en | 0.935478 |
https://blogs.glowscotland.org.uk/glowblogs/rpotteruodep/2018/10/18/would-you-chance-it-all/ | 1,656,695,968,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103943339.53/warc/CC-MAIN-20220701155803-20220701185803-00077.warc.gz | 183,628,426 | 17,174 | # Would You Chance it All?
How often do you take a chance? The answer would be every day. Every day we take a chance, whether it be crossing the road, going to the gym or simply choosing to watch the TV. We cannot predict the potential outcome of doing something, yet, without even thinking, we create the factors that are influenced by our decisions. Something of which has lead us to be where we are to this day.
Before this module began, I remembered learning about probability in high school. I was never intrigued by the prospect of learning about probability. However, after the lecture about this I have felt that I can relate chance and probability to my personal experiences and highlight to pupils the basic maths behind this, whilst making it enjoyable to learn about. Inter-connectedness is a concept of Liping MA’s that can be used between maths and our everyday lives (Ma 2010). By interconnecting our experiences with the subject of probability, basic mathematical skills can be integrated into our everyday experiences, something which I believe is important when obtain fundamental maths skills.
Probability is “the likelihood or chance that something may happen” (Turner, n.d. p5) and can be worked out by:
Probability of something happening = The number of ways it can happen – over – the total number of outcomes
For example, when rolling a dice there are 6 possible outcomes. However, if I were to only try and role a 5, the possibility of this would be 1 in 6. In many cases people try to predict the possible outcome, however as we have discovered in maths, it is not as simple as this.
Gambling has a profound and direct link to probability and chance. By taking this chance it can be the profit or the lost to some people’s bank balances. Those who are serious gamblers are costing the government £1.2 billion a year (IPPR, 2016). This is not only impacting the economy but can also cause extreme debt for some people, and a break down in relationships and mental health. This is why some people try to predict casino games and influence the outcome, in the hope they can solve the problem (Aasved, 2004).
There are aspects of gambling which are linked to multiple perspectives. This is about having a variety of different ways to reach an answer. For example, there are variety of meals you can have in a restaurant. Say for example there were 2 choices for a starter, 3 for main meal and 3 for dessert, you have to list of different meals that you can possibly have. Therefore, there are many different combinations and to figure this out multiple perspective is important.
Gambling is something which relies on randomness and probability (Turner, n.d). When discussing this in our lecture, we all thought that surely humans can create randomness effectively? Wrong! We wrote our predictions of either heads or tails, if we were to flip our coin 30 times. I thought I would try and mix it up a bit, put heads 4 times in a row, a couple tails etc, but the answers truly baffled me. It ended up being completely 50/50. Even when I was trying to be as random as possible. The results were similar on a larger scale of our class, with the majority of people being one or two off the other. When actually flipping a coin, my results were 21 heads and 9 tails, and this varied around the lecture room. Therefore, as humans, we THINK we are being random, however nothing is quite that simple and we actually try to create logic results rather than random. I remember when conducting my answers, I thought I had to put a head and not another tails because 4 tails in a row was being silly, yet the physical experiment proved this to happen with heads.
Using a coin is a simple way of introducing probability and chance to children, as there are only two outcomes. If they have the basic skills and understanding of what a half or 50% means then probability can quickly follow behind. This aids their longitudinal development, as they have the basic skills prior to probability and therefore they can build on this to have a deepened understanding of problem solving and the possibilities of finding the answer. It also helps them in more complex scenarios, for in class work and future work, if they were working in a restaurant for example. Therefore, multiple perspective, basic skills and longitudinal coherence, all key skills in profound fundamental maths (Ma, 2010) can be shadowed through everyday maths.
It is important that we recognise that gambling can possibly be predicted. However, slot machines and casinos profit more from us than we would ever earn back (unless you’re the 1 in 45057474 to win big on the lottery! (Lottoland, 2016)). Slot machines are to us, a quick and easy way to win money back. Charles Fey, developed the Liberty Bell machine in 1895, which has 3 reels and 5 symbols. This machine in particular pays out 50% of the time with an average of 75% pay-back. Therefore, although you seem to ‘win’ more, you are in fact, losing more!
Stefan Mandel, 1964, applied to buy every combination to the Romanian lottery. He followed this up by doing this with the Virginia state lottery. The video below highlights the result of this.
In conclusion, probability and chance is something that we use every day. Some people take this for granted and some take it to extremes. However, we have the ability to use multiple perspectives to figure out possible outcomes, which can be used in our daily lives and in maths in primary school. Yet, probability on a gambling scale, as seen in the video, can be on a completely different scale to our everyday probability. I believe that Liping MA’s principles are important here and they are concepts that I will look at deleloping in future placements and my teaching career.
References:
Aasved, M. (2004) The Biology of Gambling. Springfiled: Charles C Thomas.
LottoLand. (2018). The Probability of Winning the Lottery. Available: https://www.lottoland.co.uk/magazine/the-probability-of-winning-the-lottery-.html. (Accessed on: 17th October 2018)
Ma, L. (2010) Knowing and Teaching Elementary Mathematics (Anniversary Ed.) New York: Routledge.
Slot Machine History (2010). Who is Charles Fey? Available: http://slotmachineshistory.com/charles-fey.htm. (Assessed on: 15th October 2018)
The Progressive Policy Think Tank. (2016). Cards on the table: The Cost to Government Associated with People Who Are Problem Gamblers in Britain. Available: https://www.ippr.org/publications/cards-on-the-table. (Accessed on: 16th October 2018)
Tuner, N. (no date) Probability, Random Events, and the Mathematics of Gambling
Wherbert, P. (2010). Stefan Mandel (online video) Available: https://www.youtube.com/watch?v=4TqFp0efLK0 (Accessed on: 16th October 2018) | 1,490 | 6,750 | {"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-2022-27 | latest | en | 0.971673 |
https://en.over-blog.com/An_introduction_to_calculus-1228321782-art400943.html | 1,653,679,115,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662675072.99/warc/CC-MAIN-20220527174336-20220527204336-00113.warc.gz | 272,409,189 | 10,510 | Not yet registered? Create a OverBlog!
# An introduction to calculus
Calculus has a reputation as being an impossibly complex and esoteric branch of mathematics. The truth though, is that calculus is simply an advanced form of algebra and geometry that anyone with a solid grounding in those two disciplines can understand. Below is a basic overview of what calculus is and a few examples of its real world applications in real life.
Anyone who has taken a basic geometry course will be familiar with the formula used to find the slope of a line - the rise divided by the run (height by distance). This works perfectly for a straight line. If the line is curved though, all that the formula will give you is the average slope. To find the exact slope at any point along the line, it is necessary to use calculus. Determining the slope of the curve In simple terms, this is done by simply magnifying the section of the curve whose slope is to be determined until it is a straight line and then use the basic 'rise over run' equation to determine the slope. If this process is repeated infinitely, this can provide the exact slope of the curve at every point.
Application of calculus in real life situations The same process can be used to determine the length of an irregular line between two points or the area and/or volume of an irregular shape.
Some real world applications of this would be in determining the length of cable needed by the electric company if it were stringing above ground lines from one point to another, or the amount of material needed to construct a hot air balloon.
Other common areas in which calculus is used include computers, cell phones, aviation. and economics or business studies and projections.
### Same category articles Maths
If you are looking to further your mathematical knowledge from the comfort of your own home (and without the use of boring textbooks), then academic games may be the solution. Learn more about the best online mathematical games and where to find them. | 394 | 2,019 | {"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} | 3.46875 | 3 | CC-MAIN-2022-21 | latest | en | 0.943457 |
https://userforum.dhsprogram.com/index.php?t=msg&th=1361&goto=12989 | 1,597,339,039,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439739048.46/warc/CC-MAIN-20200813161908-20200813191908-00063.warc.gz | 524,703,415 | 9,265 | The DHS Program User Forum
Discussions regarding The DHS Program data and results
Home » Topics » Fertility » Wanted Total Fertility Rate in DHS
Wanted Total Fertility Rate in DHS Thu, 19 June 2014 09:14
AbdoulM Messages: 2Registered: June 2014 Member
Hello!
I am working on fertility using the DHS data from several african countries
The Total Fertility Rate (TFR) values I computed are exactely the same as in the DHS reports
But when computing the Wanted TFR, the values are not matching the ones published in the reports
The method consist in excluding the unwanted births before using the Schoumaker's stata software module (tfr2)
Find below how I made it
Please help me understand where the differences come from
Thanks,
I use the definition of "wantedness" as given in the "Guide to DHS Statistics" (Page 87, Updated Sept. 2006)
Let's remind that:
*b3_ is the date of birth in CMC;
*b5_ is the survival status (1 or 0);
*b7_ is the age at death, mounth imputed;
*v613 is the ideal number of children.
A birth is considered wanted if the number of living children at the time of conception of the child i (NLC_i) is less than the ideal number of children (INC), that is: i is wanted if NLC_i < INC
The time of conception for a child i is: dconcep_i = b3_i - 9
A preceding child (let's say j) is considered living at the time of conception of the child i if:
**C1) j is born before the date of conception of i, That is: b3_j < dconcep_i
**C2) j is living at the time of the survey, That is: b5_j==1
**C3) OR j died at or before the date of conception of i, That is: b3_j + b7_j <= dconcep_i
According to these conditions, I create a dummy variable (G) as:
For every child j preceding i,
*G_ij =1 if {C1 AND (C2 OR C3)}
*If no, G_ij=0
The number of living children at the time of conception of i is computed as NLC_i = Sum(G_ij) over j.
For every i, we can now compare NLC_i with the INC
*If NLC_i < INC, then i is wanted
*If no, i is not wanted
I then recode every b3_i (i=1 to 6) as: recode b3_i (0/21600=0) if NLC_i > INC
This is supposed to exclude all the unwanted births when computing the TFR (with the Schoumaker's tfr2)
I am aware that the missing values in Stata can distort the resluts, so I write the commands accordingly.
Find attached the do-file, it may help understanding the process
Regards,
AbdoulM
University of Geneva
• Attachment: Wanted_TFR.do
(Size: 25.97KB, Downloaded 614 times)
Re: Wanted Total Fertility Rate in DHS [message #2466 is a reply to message #2448] Tue, 24 June 2014 14:32
Liz-DHS Messages: 1515Registered: February 2013 Senior Member
Dear User,
We are currently researching your post and will get back to you as soon as we can.
Thank you!
Re: Wanted Total Fertility Rate in DHS [message #2467 is a reply to message #2448] Tue, 24 June 2014 15:05
Liz-DHS Messages: 1515Registered: February 2013 Senior Member
Dear User,
Here is a response from one of our technical experts,Dr. Shea Rutstein:
Here is the STATA instruction given:
A preceding child (let's say j) is considered living at the time of conception of the child i if:
**C1) j is born before the date of conception of i, That is: b3_j < dconcep_i
**C2) j is living at the time of the survey, That is: b5_j==1
**C3) OR j died at or before the date of conception of i, That is: b3_j + b7_j <= dconcep_i
But a child who died at or before conception of the next child is dead at the time of conception.
The correct code should be
**C3) OR j died after the date of conception of i, That is: b3_j + b7_j > dconcep_i
Shea
Re: Wanted Total Fertility Rate in DHS [message #2474 is a reply to message #2467] Tue, 24 June 2014 18:23
AbdoulM Messages: 2Registered: June 2014 Member
Liz, Shea,
Thank you very much for this effective answer!
Regards,
AbdoulM
Re: Wanted Total Fertility Rate in DHS [message #12989 is a reply to message #2448] Thu, 31 August 2017 10:05
Mercysh Messages: 35Registered: April 2014 Member
Do you mind to share your do file for TFR, I see your results are comparable to those published in DHS reports.
Mercy
Re: Wanted Total Fertility Rate in DHS [message #12995 is a reply to message #12989] Mon, 04 September 2017 09:20
Maurel Messages: 1Registered: September 2017 Location: Cameroon Member
Hello!
I am working on the impact of socioeconomic status on fertility trends desired and achieved among Cameroonian women using the DHS surveys of 2004 and 2011. I used the Moumouni's do file to make the corrections as suggested above but I still do not get the same results as DHS. could someone help me find the problem?
thank you!
Re: Wanted Total Fertility Rate in DHS [message #13032 is a reply to message #12995] Sun, 10 September 2017 13:18
Liz-DHS Messages: 1515Registered: February 2013 Senior Member
Dear User,
I think to get any real assistance, you would need to post your code. Other users may be able to look at it and help you troubleshoot. In addition you may want to read the paper by Bruno Schoumaker which may help. It is titled "A Stata module for computing fertility rates and TFRs from birth histories: tfr2"
https://www.demographic-research.org/volumes/vol28/38/
Thank you!
[Updated on: Sun, 10 September 2017 13:18]
Report message to a moderator
Re: Wanted Total Fertility Rate in DHS [message #14943 is a reply to message #2474] Fri, 18 May 2018 01:42
ashwini Messages: 3Registered: May 2018 Member
Hello,
I wanted to compute the Wanted Fertility rate and followed the instruction and the method posted by the one of the user but results are not matching with the report.
Can I get help on this?
These are the steps followed-
A preceding child (let's say j) is considered living at the time of conception of the child i if:
**C1) j is born before the date of conception of i, That is: b3_j < dconcep_i
**C2) j is living at the time of the survey, That is: b5_j==1
**C3) OR j died at or before the date of conception of i, That is: b3_j + b7_j <= dconcep_i
But a child who died at or before conception of the next child is dead at the time of conception.
The correct code should be
**C3) OR j died after the date of conception of i, That is: b3_j + b7_j > dconcep_i
Thank you.
Re: Wanted Total Fertility Rate in DHS [message #15025 is a reply to message #14943] Fri, 25 May 2018 14:58
Liz-DHS Messages: 1515Registered: February 2013 Senior Member
A response from Dr. Shea Rutstein:
Quote:
Our code for the wanted TFR table is
for ch in REC21_EDT do { Births }
birth = B3;
if birth in lowcm:higcm then
agegroup = int( (birth-V011)/60 ) - 2; { Age group at birth }
if agegroup in 1:7 then
chi = 0;
do i = soccurs( REC21 ) while i > ch by (-1)
if B5(i) = 1 then
chi = chi + 1
else
deathm = B7(i);
if !special( B6(i) ) & int( B6(i)/100 ) = 3 then { if age at death in years }
deathm = B7(i) + 6; { assume death occur in the middle }
endif;
if B3(i) + deathm >= B3 - 9 then
chi = chi + 1;
endif
;
endif;
enddo;
if V613 in 0:90 & chi < V613 then
colt606 = 1;
xtab( t606b, rweight )
endif;
colt606 = 2;
xtab( t606b, rweight );
endif;
endif;
enddo;
Note the highlighted section:
It says add the age at death of a dead child to the date of birth of that child to get the date of death. If that sum (the date of death) is equal to or greater than the date of birth of the next child minus nine months (date of conception) then the child was living at the time of conception. The number of the living children is then compared with the desired number of children and, if less, then the next child was wanted. If the same or higher than the desired number, then the next child was not wanted at that time. The division into wanted-unwanted is done for all children born in the time period for the fertility rates.
So the user is correct except for children who died in the same month as the conception. These children are considered as living at the time of conception since the dates of conception and dates of death are a little fuzzy due to only being precise as to month.
I looked up the Guide to DHS Statistics which needs to be corrected on page 90:
It says:
1. Wantedness--A birth is considered wanted if the number of living children at the time of conception of the birth is less than the ideal number of children as reported by the respondent. For the calculation of the time of conception, nine months are subtracted from the date of birth. A preceding child is considered living at the time of conception if it was born before the date of conception and a) is living at the time of the survey or b) died at or before the date of conception (calculations based on century-month codes). The date of death of preceding children who died is calculated by adding the age at death in months to the child's birth date in century-month code. If a child's age at death is reported in years, then the child is assumed to have died at ages 6 months higher than the number of years (30 months for children who died at 2 years of age, 42 months for children who died at 3 years of age, etc.).
The highlighted word should be "after" instead of "before". The Guide needs to be corrected. The CSPRO program is OK.
Re: Wanted Total Fertility Rate in DHS [message #16648 is a reply to message #15025] Tue, 12 February 2019 01:26
ashwini Messages: 3Registered: May 2018 Member
Hello,
Can I get the stata do file for wanted fertility rate?
I have followed the steps but still figures are not matching the report.
Request you to kindly give the stata commands for calculating Wanted fertility rate.
Thank you.
Previous Topic: ASFR :Further Analysis using NDHS, 2011 Next Topic: Preceding birth interval (variable b11), birth spacing
Goto Forum:
Current Time: Thu Aug 13 13:17:08 Eastern Daylight Time 2020 | 2,634 | 9,665 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2020-34 | latest | en | 0.888781 |
https://photography.tutsplus.com/courses/a-photographers-guide-to-light/lessons/direct-reflection | 1,653,432,653,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662577259.70/warc/CC-MAIN-20220524203438-20220524233438-00648.warc.gz | 528,885,004 | 17,910 | Unlimited AE and Premiere Pro templates, videos & more! Unlimited asset downloads! From \$16.50/m
FREELessons:11Length:1 hour
• Overview
• Transcript
# 4.2 Direct Reflection
In this lesson you will learn about direct reflections and see how they work in lighting and photography.
## 5.Conclusion1 lesson, 01:46
### 4.2 Direct Reflection
In this lesson, you will learn about direct reflections and see how they work in lighting and photography. According to the wiki, direct reflection, also known as specular reflection, is the mirror like reflection of a light from a surface in which the light from a single incoming direction is reflected into a single outgoing direction. The word specular is sometimes used to described the brightest part of a highlight. It's also used to describe highlights created from hard lights. Specular means having the properties of a mirror. So, sometimes these usages are correct and other times they're just nonsense. To make things clear, I am going to use the term direct reflection instead of specular reflection. This direct reflection behavior is described by the law of reflection which essentially states that the angle of incidence equals the angle of reflection. Let's check out an example. So in this demo, I have my green laser, a mirror, and a protractor that's printed out on a piece of paper. The light that's coming from the laser to the mirror is called the incident light and the light that's leaving the mirror is called the reflected light. If you imagine a line being drawn perpendicular to the surface of the mirror, right around this 90 degree mark. This is called the normal line. The normal line divides the angle between the incident light and the reflected light into two equal angles. The angle between the incident light and the normal is knows as the angle of incidence. The angle between the reflected light and the normal is known as the angle of reflection. And you can see, no matter where I put the laser, these two angles always equal each other. In this example, I'm shooting a hard drive platter here in a room with only one light source. And in the first two photos here, you can see that the hard drive platter looks black. That is until the camera is positioned right in line so I can see the reflection of the light source in the hard drive platter. Now, the interesting thing here is that the light source that's being reflected in the hard drive platter appears almost as bright as the light source itself. I say almost as bright because mirrors aren't perfect and they don't reflect all of the light. There's always going to be a little bit of light that's lost to absorption. But essentially, the light source in the reflection is as bright as the light source itself. And this would seem to break the inverse square law because if I pulled this mirror back 30 more feet. The reflection of the light source would still be as bright as the light source itself even though it's at a much greater distance. But, you see the thing that changes is the size of the reflection. Even though the light source appears to be as bright in the reflection because the actual reflection is larger, it's reflecting more light. So if I move this light to half the distance, it's going to reflect four times as much light. Exactly what the inverse square law says that it will. This leads us to an important concept when dealing with objects that have a lot of direct reflection. When you are trying to photograph an object that has a lot of direct reflection, you need to think more about positioning the lights in objects to reflect back to the camera. In other words, you don't think about how to light the object as much as you think about how to get the reflection of the light which is pretty much the only thing that you're going to see back to the camera. This leads us to the idea of the family of angles. I learned about the idea of the family of angles in a book called Light, Science, and Magic, an Introduction to Photographic Lighting. This is a fantastic book which I highly recommend. The concept is fairly simple, if you are shooting an object with a lot of direct reflection, there is a range of angles that produce this direct reflection. Anything outside this family of angles is not something that your camera can see. This is an important concept to understand because it will help you determine where to position your lights. Because of the law of reflection, you can fairly easily determine where the family of angles is located with respect to the camera. If you are shooting a mirror-like object and you want to see a direct reflection of your light source in the mirror, you need to use a light source large enough to fill the family of angles. If you don't wanna see a direct reflection of the light in the mirror, we need to position the camera and the light so that the light is not located in the family of angles. So now that you've learned about diffuse and direct reflection, it's time to look at polarized reflections, which is coming up next.
Back to the top | 1,044 | 5,062 | {"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} | 3.15625 | 3 | CC-MAIN-2022-21 | latest | en | 0.945489 |
http://www.hulver.com/scoop/tag/fermat | 1,534,727,486,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221215487.79/warc/CC-MAIN-20180820003554-20180820023554-00209.warc.gz | 507,247,172 | 5,266 | Halving sums of squares
By Alan Crowe (Thu Apr 23, 2009 at 05:10:28 PM EST) fermat (all tags)
My previous diary entry concerned multiplying the sums of squares. Now I try to go the other way, factoring sums of squares. Since this is harder I make little progress, but make an interesting detour to visit the quarter-square multiplier.
(1042 words in story) Full Story
Sums of squares
By Alan Crowe (Fri Apr 17, 2009 at 03:10:33 PM EST) fermat (all tags)
Some numbers can be written as the sum of two squares. For example 113=7²+8² and 205=14²+3².
If we multiply 113×205=23165 is the result a sum of squares? Yes, 23165=146²+43², but why? 146 and 43 seem unrelated to any of 3,7,8,14.
(2 comments, 386 words in story) Full Story | 224 | 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} | 3.4375 | 3 | CC-MAIN-2018-34 | longest | en | 0.839689 |
http://acko.net/blog/taming-complex-numbers-in-grapher-app/ | 1,429,362,692,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1429246634333.17/warc/CC-MAIN-20150417045714-00283-ip-10-235-10-82.ec2.internal.warc.gz | 2,688,902 | 5,182 | Taming complex numbers in Grapher.app
Of all the free extras that Mac OS X has, Grapher has to be one of the coolest. This little app, hidden away in the `Applications/Utilities` folder, is a powerful graphing tool for mathematical equations and data sets.
As you might expect from Apple, it typesets symbolic math beautifully and produces smooth, anti-aliased graphs. But this isn't just a little tech demo to showcase some of OS X's technologies: Grapher's features blow away your crusty old TI-83, and it comes with its own set of surprises. For example, not only can you save graphs as PDF or EPS, but it can export animations and even doubles as a LaTeX formula editor.
In fact, it does so much that its main weakness is the documentation, which only covers the very basics. The best way to learn Grapher is to look at the handful of included examples, although it might take you a while to find out how to replicate them from scratch.
The other day I needed to quickly graph a couple of things involving complex numbers, and it seemed that Grapher was doing some very freaky shit. Either that, or my math was really rusty. It turned out I'm not as stupid as I thought, and there are some weird caveats with using complex numbers in Grapher. Oddly, there is very little information online about it, so I figured for future reference, I should document the workarounds I discovered.
Let's dive in. Fuck MS Paint, I've got math to do.
Refresher
To type formulas into Grapher, you can use the symbol palette, available in the Window menu, or type away using various keyboard shortcuts:
• Type `^` for exponents, `_` for indices, `/` for fractions. Grapher understands exponents and other notations, for example the Bessel functions `Jn(x)`.
• Use the arrow keys to move around the equation: in and out of parentheses, exponents, fractions, etc. Pay attention to the cursor to see where you're typing.
• Type out greek letter names for the symbols: `alpha`, `omega`, `pi`.
• Common mathematical constants work: `e`, `π`, `i`.
• The very useful 'Copy LaTeX expression' command is hidden away in the editor's right-click menu.
Using complex numbers
At first sight, complex numbers 'just work'. Using `i` as the imaginary unit, you can use numbers like `1 + 2i` or plot graphs like `y=eix`. You can use the `Re()` and `Im()` operators to explicitly extract the real or imaginary part of a complex number and use `abs()` and `arg()` to extract the modulus and argument. If an expression's result is complex, Grapher will only plot the real part.
This last bit is where things get tricky, because this silent casting of complex numbers to reals also sometimes happens in intermediate values.
Silent truncation
Let's plot a complex parametric curve directly using formulas of the form `x + iy=...`. As an example, let's look at this:
These equations are using Euler's formula `ei·x = cos x + i·sin x` to plot a half circle each. The only difference between the two formulas is that the second one is passing its value through the (useless) function `f(t)`.
Now if we replace `ei·x` with `1/ei·x = e–i·x = cos x – i·sin x` and change `f(t)` to `1/t`, all that should happen is that the graph is mirrored vertically. Instead, this happens:
The blue circle segment is drawn as a broken horizontal line. What's happening is that Grapher is treating the definition `f(t) = 1/t` as if it said `f(t) = 1/Re(t)`. In other words, it is truncating the complex input of `f(t)` to a real number.
To fix this, you need to replace the variable `t` with `complex(t)`. This `complex()` function is listed in the built-in definitions list in the Help menu, but lacks any documentation. With this fix applied, the graph will plot as expected:
Further tests reveal that `complex(t)` is in fact equivalent to writing out `Re(t) + i·Im(t)`, thus manually recomposing the complex number from its own real and imaginary parts. If it weren't for the existence of the `complex()` helper, one might consider this issue a bug. The way it is now, it seems this behaviour is somewhat intentional.
Moral of the story: wrap all your function inputs in `complex()` to avoid nasty surprises.
Broken built-ins
Another annoying issue is that certain built-in functions don't handle complex inputs. To show this, you can try plotting `y=sinh(–i2·x)`. Mathematically, this is equivalent to plotting `y=sinh(x)` directly. However the presence of the imaginary unit causes the plot to fail.
As a workaround, you need to define your own functions using known formulas and incorporating the `complex()` fix.
For example, you might define:
```fixsinh(x) = (ecomplex(x) – e-complex(x))/ 2 fixcosh(x) = (ecomplex(x) + e-complex(x))/ 2```
Other built-ins are trickier. For example, ` Γ(z)` needs replacing, but mathematically it is defined as an improper integral. Unfortunately, Grapher's integrator doesn't seem to handle the definition for `Γ(z)` at all — though it's supposed to do improper integrals.
When using built-in definitions, always verify that you're getting the results you need with a simple example.
Math porn
To round this off, here's an example where I use these tricks to plot a Kaiser sampling window and its frequency response:
Happy graphing!
This article contains graphics made with WebGL, which your browser does not seem to support.
Try Google Chrome or Mozilla Firefox. × | 1,259 | 5,378 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2015-18 | longest | en | 0.945074 |
https://www.sawaal.com/numbers-questions-and-answers/a-teacher-multiplies-987-by-a-certain-number-and-obtains-556781-as-her-answer-if-in-the-answer-both-_11121 | 1,537,565,681,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267157569.48/warc/CC-MAIN-20180921210113-20180921230513-00001.warc.gz | 849,497,472 | 15,496 | 5
Q:
# A teacher multiplies 987 by a certain number and obtains 556781 as her answer. If in the answer, both 6 and 7 are wrong but the other digits are correct, then the correct answer will be
A) 553681 B) 555181 C) 556581 D) 555681
Explanation:
Given number is 987 = 3 x 7 x 47.
So, required number must be divisible by each one of 3, 7, 47.
None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7.
Q:
7, 16, 36, 78, 144, ?
which number come in place of question mark
A) 168 B) 196 C) 222 D) 256
Explanation:
0 106
Q:
Which of the following is a rational number?
A) 0.241 B) 1.732 C) 4 D) All of the above
Explanation:
Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.
Every integer is a rational number since Q can be 1.
Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.
Hence, 4 is a rational number in the given options.
1 330
Q:
Which expression is equivalent to $i233$?
A) i B) 1 C) -i D) -1
Explanation:
We know that,
3 887
Q:
The product of a number and its multiplicative inverse is
A) 1 B) 0 C) -1 D) Infinity
Explanation:
The mutiplicative inverse of a number is nothing but a reciprocal of a number.
Now, the product of a number and its multiplicative inverse is always equal to 1.
For example :
Let the number be 15
Multiplicative inverse of 15 = 1/15
The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.
2 634
Q:
25 divided by 7
A) 3.571 B) 35.71 C) 0.351 D) 0.0357
Explanation:
Here we have 25 divided by 7.
25 will not go directly in 7
Hence, we get the result in decimals.
25/7 = 3.571.
3 601
Q:
Which of the following is not a prime number?
A) 5 B) 11 C) 21 D) 37
Explanation:
A prime number is a whole number greater than 1 whose only factors are 1 and itself.
Factors of 5 are 1, 5
Factors of 11 are 1, 11
Factors of 21 are 1, 3, 7, 21
Factors of 37 are 1, 37.
Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.
2 429
Q:
What are the Multiples of 4?
The Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 upto 40. Mutiples of 4 means which can be divided by 4 leaving remainder '0'.
Common Multiples of 4 & 6 are 12, 24, 36, 48, 60 upto 60.
963
Q:
The sum of three consecutive odd numbers is 93. What is the middle number?
A) 31 B) 33 C) 29 D) 27
Explanation:
Let the three consecutive odd numbers be x, x+2, x+4
Then,
x + x + 2 + x + 4 = 93
=> 3x + 6 = 93
=> 3x = 87
=> x = 29 => 29, 31, 33 are three consecutive odd numbers.
Therefore, the middle number is 31. | 904 | 2,730 | {"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": 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-2018-39 | latest | en | 0.888552 |
https://web2.0calc.com/questions/discounts-math-problem | 1,580,207,207,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251778168.77/warc/CC-MAIN-20200128091916-20200128121916-00334.warc.gz | 702,728,508 | 5,855 | +0
# Discounts math problem
0
48
1
An item is regularly priced at \$59.It is on sale for 45% off the regular price.
Dec 11, 2019
#1
+1
The regular price is 59\$ , It gets reduced 45%
so we can write:
100%-45%=55% (Current price here we want to find it)
59\$: x = y
x=59*45/100=26.55\$
59-26.55=32.45\$ Current cost that's what the price it is on sale right now, you would save 26.55 dollars!
Dec 11, 2019 | 149 | 423 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2020-05 | longest | en | 0.911651 |
https://math.stackexchange.com/questions/3748878/is-analytical-solution-available-for-this-pde | 1,620,527,701,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988953.13/warc/CC-MAIN-20210509002206-20210509032206-00581.warc.gz | 420,771,772 | 37,301 | Is analytical solution available for this PDE?
I been trying to solve the below PDE analytically for awhile now but with no success, perhaps someone here can help me with it. $$\frac{\partial w(x,t)}{\partial t}= \frac{\partial}{\partial x} \bigg(\beta \exp (-g(x)) \frac{\partial}{\partial x} \big\{ w(x,t) \exp(g(x)) \big\} \bigg)$$
And the boundary and initial conditions: (1) $$w(x,0)=m$$ and (2) $$w(0,t)=n, w(L,t)=p$$.
Is analytical solution possible here?
• Are $m$, $n$, and $p$ numbers or functions? – Josh B. Jul 7 '20 at 17:43
• They are constants – Lucas Derck Jul 7 '20 at 17:43
• This is the one-dimensional heat equation with Dirichlet conditions, right? – SimpleProgrammer Jul 7 '20 at 17:54
• @SimpleProgrammer, in principle Yes! – Lucas Derck Jul 7 '20 at 17:57
If you write $$w(x,t) = v(x,t) \exp(-g(t))$$, the PDE becomes
$$\dfrac{\partial v}{\partial t} = \beta\dfrac{\partial^2 v}{\partial x^2} - \beta g'(x) \dfrac{\partial v}{\partial x}$$ This has separation-of-variables solutions $$v(x,t) = X(x) T(t)$$ where $$c$$ is an arbitrary constant and $$T'(t) = c \beta T(t), \ X''(x) = c X(x) + g'(x) X'(x)$$ In general I think the equation for $$X$$ can't be solved in closed form, but can be reduced to a first-order nonlinear equation: if $$X(x) = \exp(u(x))$$, $$u'' + (u')^2 = g'(x) u'(x) - c$$ which is a first-order nonlinear equation for $$u'(x)$$. | 472 | 1,381 | {"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": 12, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-21 | longest | en | 0.84631 |
http://www.sz-wholesale.com/Search-Result/Owl-Writing-Pad/ | 1,519,029,905,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812556.20/warc/CC-MAIN-20180219072328-20180219092328-00287.warc.gz | 560,007,883 | 9,044 | Welecom to Sz-wholesale.com
» »
# Wholesale Owl Writing Pad
#### 3 items found in wholesale Owl Writing Pad
[Total 1 Pages,3 Products] pages 1
• ### What to Look For in Wholesale Promo Flash Drives
Also called a thumb drive, USB drive, and pen drive, flash drives are the most portable and removable storage device that can be plugged into a USB port of a laptop or personal computer. These drives have gradually replaced the existence and function of the floppy disk, CDs, and now, DVDs. These drives are even capable of storing large amount of data and are a lot more reliable and handy in keeping any data safe. Once the drive is unplugged from the computer, the files can be accessed anytime at the owner's disposal. These items are also effective when it comes to advertisement. Wholesale Promo Flash Drives are gaining more popularity and preference than ever before in the corporate and business world. However, you cannot just buy any kind of drive, especially on wholesale. So for you to be safe when choosing the right kind of Wholesale Promo Flash Drives, here are some useful guides. When looking for the types of
• ### Buy Wholesale Promotional Armani Suits from China, How to Calculate Sea Freight?
International ocean shipping is a practice used to trade goods all over the world. Items are packed into shipping containers and loaded onto a vessel before traveling across the sea to an arrival port. Large machinery and project material that is too large to fit into ocean containers are known as break-bulk and travels uncovered, aboard vessels. Calculating sea freight is the process that determines a shipment's mass, which is used to rate the cost of either an LCL (less than container-load) or a break-bulk shipment. Instructions LCL shipments 1. For LCL shipments, Measure the length, width, and height of your cargo (in inches). Calculate the volume of your cargo using the formula: Length x Width x Height = Volume (in cubic inches). 2. Create the denominator by multiplying 12 x 12 x 12. There are 12 inches in a foot: (12 x 12 x 12) = 1,728 cubic inches. 3. Divide the volume by 1,728 to get your cubic footage volume: Volume / 1,728 = cubic feet. 4. Multiply by 0.0283168466 to | 494 | 2,213 | {"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-2018-09 | latest | en | 0.923694 |
https://www.askiitians.com/forums/Trigonometry/23/16430/trigonometry-ratios.htm | 1,701,551,820,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100452.79/warc/CC-MAIN-20231202203800-20231202233800-00176.warc.gz | 736,366,244 | 43,566 | # eliminate(thita) from the equations atan(thita)+bcot2(thita)=c and acot(thita)-btan2(thita)=c
148 Points
13 years ago
Dear ravi
atanθ+bcot2θ=c ........1 acotθ-btan2θ=c ..........2
subtract equation
a(cotθ -tanθ)=b(cot2θ+tan2θ)
a cos2θ/cosθsinθ = b/cos2θ sin2θ
2a/tan2θ = 2b/sin4θ
sin4θ /tan2θ =b/a
2tan2θ/(1+tan22θ).tan2θ =b/a
let T =tan2θ
2T/(1+T2)T =b/a
T2 =(2a-b)/b ....................3
and from the equation 1 and 2
c-b/T =atanθ
c+bT =acotθ
multiply
(c-b/T)(c+bT) =a2
c2 -b2 +bc(T-1/T) =a2
c2 -b2 +bc(T2-1)/T =a2
put the value of T
c2 -b2 +bc(2a-2b)/b .√b/(√2a-b) =a2
2c(a-b)√b =(a2+b2-c2)√(2a-b)
Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed solution very quickly.
All the best.
Regards, | 365 | 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} | 4.09375 | 4 | CC-MAIN-2023-50 | latest | en | 0.655828 |
https://www.gamblegeeks.com/easy-guide-for-newbies-to-play-roulette/ | 1,702,312,744,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679515260.97/warc/CC-MAIN-20231211143258-20231211173258-00536.warc.gz | 846,129,210 | 32,564 | Home ROULETTE How To Play Roulette? Easy Guide For Newbies
# How To Play Roulette? Easy Guide For Newbies
Many think that playing roulette is just choosing a number and waiting for the ball to land on it, but there are different types of roulette wheels and countless strategies that you can use to try to get interesting prizes.
## Easy guide for newbies to roulette
In this article you will find all the details to become a great roulette player. You will not only learn how to play roulette, but you will learn about the different types that exist and the most common strategies in this mythical casino game.
## Types of roulettes
The types or varieties of roulette arise from different locations where it is played in a different way from roulette. For this reason, the names they receive guide us very well regarding their origin. We can divide the types of roulettes into 2: European roulette and American roulette .
Although it is true that French roulette, which is a variety of European roulette, has also gained importance over time.
### How to play American roulette?
Now, we are going to see how to play American roulette, which, as its name suggests, comes from the United States , and has some specifications that make it a very recognizable type of roulette:
• It is a roulette that has 38 boxes, among which we find double 0, 0 and the numbers between 1 and 36.
• If the ball ends in 0, the simple bets are lost.
### How to play European roulette or French roulette?
Both are the same type of roulette, they have 37 numbers from 0 to 36, but with an internal section and an external one, where you can make different bets that will cover 18 numbers. In it you will have the option to make a foul or pass, even or odd and red or black.
### How to play French roulette?
French roulette is a variant of European roulette, as we have already mentioned. This maintains the European roulette format with 37 numbers with a single green zero.
The big difference with the European one is in the possibility of outside bets and the respective combinations of these both at the top and at the bottom of the table.
## Strategies for playing roulette
We are going to see some of the best-known strategies to play roulette.
• Martingale: it is one of the best known and used strategies. It consists of betting a unit: if it is correct, it is maintained; if you lose, it doubles until you get it right and you start over from scratch.
• Fibonacci: This strategy, whose name comes from the mathematician who discovered it, deals with the following: you start by betting 1, if you win you keep it and if you lose, you bet triple, then five times, then x8, then x13, then x21, x34, x55, x89, etc. you have to follow the sequence of numbers that this mathematician discovered. It is an aggressive strategy and for which it will be necessary to have a good initial amount.
• D’Alembert: it is a progressive method that consists of betting a greater amount when we lose and less when we win. Based on a bet of five euros, if we lose we will bet ten on the next play; if we lose again, fifteen, etc. When we win, we will reduce five euros; if we win again, we reduce another five, etc. It is a more conservative strategy than the previous one.
• Labouchere: Strategy based on the curious game style of a British aristocrat. For this strategy you will need a profit target, for example 20, and create a sequence that adds up to the same amount that you have set as your goal: 2 – 3 – 2 – 4 – 3 – 2 – 3 – 1.
But, in addition to these famous strategies, there are other ways to bet on roulette following formulas. The most experienced players usually play the neighbors of 0 (22, 18, 29, 7, 28, 12, 35, 3, 26, 32, 15, 19, 4, 21, 2 and 25), the ‘ orphans ‘ ( 1, 20, 14, 31, 9, 17, 34 and 6) or the ‘ cylinder third ‘ numbers (33, 16, 24, 5, 10, 23, 8, 30, 11, 36, 13 and 27).
Gamble Geekshttps://www.gamblegeeks.com
We here at Gamble geeks provide the latest information and news that are related to the Gaming industry. | 976 | 4,030 | {"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} | 2.625 | 3 | CC-MAIN-2023-50 | longest | en | 0.943432 |
https://www.artlembo.com/post/a-poor-man-s-parallel-processor-for-gis | 1,720,860,298,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514493.69/warc/CC-MAIN-20240713083241-20240713113241-00712.warc.gz | 519,120,829 | 201,418 | top of page
Search
# A Poor Man’s Parallel Processor for GIS
In addition to SQL, I also am interested in processing large volumes of spatial data. One of the newest rages in “big data” is Hadoop. According to Wikipedia:
Apache Hadoop is an open-source software framework written in Java for distributed storage and distributed processing of very large data sets on computer clusters built from commodity hardware.
One way this is implemented is a programming model called MapReduce. Don’t get too excited, it doesn’t have anything to do with maps or GIS – but, it is very clever and powerful for certain types of problems. The concept is if you have a really large dataset, you divide and conquer that dataset in a number of steps. For example, say we wanted to know all the people with the name “John” in the phonebook, and say we had 26 computers in a cluster – we might solve this by:
1. Use each computer (1-26) to find all the “Johns” for the first letter in the last name (A-Z). That way, you have effectively broken the problem into 26 smaller units.
2. Once each computer has counted up the number of Johns, you have reduced the dataset (hence, MapReduce) to 26 variables.
3. Now, count up the total of the 26 variables.
That is an oversimplified version of course, but it helps to illustrate what we want to do. I understand that the University of Minnesota has created a set of functions called SpatialHadoop. I want to test this over the summer, but for now I decided to create my own poor man’s version using PostGRES.
The Problem
I have 37 million points, and 240 polygons. For each point, I want to find out what polygon the point is in. Easy enough. However, the data size is prohibiting. After running the process for days in ArcGIS, Manifold, QGIS, and PostGRES, the process either did not finish, or just crashed the computer. Our traditional ways do doing this just wasn’t working.
I figured that if I could somehow replicate the MapReduce problem, we might be in business.
The Solution
I decided to try and solve this problem with PostGRES and PostGIS. My initial test was to work with 1 million records. If it worked, I would try scaling it up to 37 million.
Now, PostGRES is not a multithreaded application. Meaning, if you have 8 CPUs on your computer, PostGRES is only going to run in one CPU. But, if you run 5 instances of PostGRES, each will run in its own thread on a CPU.
Therefore, I created an SQL script that performed the spatial containment query on a portion of the data and wrote the results to a table. For instance, this query will INSERT the point ID and polygon ID into a table for each point contained in the polygon:
```INSERT INTO testtable
SELECT points.pointid, polygons."ID_2"
FROM
points , polygons
WHERE st_contains(polygons.geometry,points.geometry)
AND points.pointid BETWEEN 15000000 and 15100000```
The above query effectively performs the containment query on only 100,000 records. I then ran the query in 5 different threads, each evaluating a 100,000 chunk of points. So, the BETWEEN clause was changed to 15200001 AND 15300000, and so on. Therefore, the 5 separate threads processed all 500,000 records, 100,000 (1/5th of the data) records at a time.
The Results
I noticed a couple of interesting things: the change in speed and the utilization of the CPU.
Speed
It turns out that running multiple instances of the SQL statements completes the job faster than only running one instance. For example, running the above query on 500,000 records
```INSERT INTO testtable
SELECT points.pointid, polygons."ID_2"
FROM
points , polygons
WHERE st_contains(polygons.geometry,points.geometry)
AND points.pointid BETWEEN 15000000 and 15500000```
completes in 365 seconds.
But, running 5 instances of the query takes 130 seconds!!!
CPU Usage
As expected, the CPU usage when one instance of PostGRES was running showed that only a single CPU was firing at its maximum. However, when I ran the five instances, you can see that many more of the CPUs were firing.
Early Conclusion
This showed me that we can actually maximize the thread use with PostGRES for completing a computationally intensive spatial task by breaking the problem into different chunks.
The main bottleneck was inserting into the table. As you can see from the figure above, the execution time increased in each window, with a maximum of 358 seconds – I don’t believe that the data was running serially, but rather the INSERT portion of the query had to wait it’s turn to update the table.
Where to go next
I’m not ready to tackle the 37 million points just yet. I want to see if there are some ways to speed this up even more. In my next post, I will use an UPDATE statement instead of the INSERT statement to see if there are any differences in speed. After that, I want to try some other tasks, like determining how many points are in the polygons. This will allow us to run the query in five threads, obtaining 5 result tables, and then running a final query to add up the results of the five tables. The question on my mind is what scenarios give us the best opportunities to parallelize our work activities.
If this looks promising, I have 24 computers in my lab, and if I use 5 threads for each computer, that gives me 120 threads to run the query. | 1,277 | 5,331 | {"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-2024-30 | latest | en | 0.941799 |
https://short-question.com/what-are-the-colors-of-pool-balls/ | 1,716,487,119,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058653.47/warc/CC-MAIN-20240523173456-20240523203456-00706.warc.gz | 462,957,753 | 42,938 | Short-Question
Practical answers to complex questions
What are the colors of pool balls?
What are the colors of pool balls?
The majority of the balls are red, and there is a small selection of colored balls and the cue ball. Generally, Snooker uses 15 red balls, alongside 6 colored balls. These colored balls can vary, but they are typically yellow, blue, pink, green, brown, and black. The cue ball, as always, is white.
How many colors are there on a pool table?
The six colours (a term referring to all balls except the white and the reds) are placed on their own spots.
What are the numbers and colors of pool balls?
Balls that are numbered one through eight are one solid color, except for a small circle with the number in it.
• The one ball is yellow;
• two is blue;
• three is red;
• four is purple;
• five is orange;
• six is green;
• seven is burgundy;
• and the eight ball, as most people know, is black.
Why are pool balls different colors?
Sets for American snooker are typically 21⁄8 in (54.0 mm), with numbered colour balls. The set of eight colours used for snooker balls (including white) are thought to be derived from croquet, which uses the same set of colors. Snooker was invented in 1884 by British Army officers stationed in India.
What order do pool balls go in?
Sit the triangle rack on the table and place the balls numbered 1 through 9 within the triangle. Position the balls in random order split among five rows so that the balls form a diamond; the first and fifth row will have one ball, the second and fourth rows will have two balls and the third row has three balls.
What is the best Colour for a pool table?
Blue, green, and red are typical pool table felt colors, but don’t be afraid to branch out. If you don’t want to go too wild, stick to neutral tones. Remember that whatever chalk you use will show up less if it is the same color as the felt. If you have a preference for blue chalk, stick to blue felt.
What is the standard color for the one ball in billiards?
yellow
Pool
1 solid yellow
13 orange stripe
14 green stripe
15 maroon stripe
cue ball , white or off-white (sometimes with one or more spots)
What Colour is the number 9-ball in pool?
The cue ball , which is usually a solid shade of white (but may be spotted in some tournaments), is struck to hit the other balls on the table. The remaining balls are numbered 1 through 9, each a distinct color, with the 9-ball being striped yellow and white. | 576 | 2,469 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2024-22 | latest | en | 0.962173 |
https://pressbooks.nscc.ca/aviationelecronics/chapter/16-1-introduction-to-analog-to-digital-to-analog-conversion/ | 1,723,433,664,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641028735.71/warc/CC-MAIN-20240812030550-20240812060550-00801.warc.gz | 369,230,262 | 24,258 | # 16.1 Introduction to Analog to Digital to Analog Conversion
Up to now, all of the circuits you have studied in this book were analog circuits. That is, the input waveforms were time-continuous and had infinite resolution along the time and amplitude axes. That is, you could discern increasingly smaller and finer changes as you examined a particular section. No matter whether the circuit was a simple amplifier, function synthesizer, integrator, filter, or what have you, the analog nature of the signal was always true. Fundamentally, the universe is analog in nature (at least as far as we can tell – until someone discovers a quantum time particle). Our only real deviation from the pure analog system was the use of the comparator. Although the input to the comparator was analog, the output was decidedly digital; its output was either a logic high (+ππ ππ‘) or a logic low (βππ ππ‘) . You can think of the comparator’s output as having very low resolution, as only two states are possible. The comparator’s output is still time-continuous in that a logic transition can occur at any time. This is in contrast to a pure digital system where transitions are time-discrete. This means that logic levels can only change at specific times, usually controlled by some form of master clock. A purely digital system then, is the antithesis of a pure analog system. An analog system is time-continuous and has infinite amplitude resolution. A digital system is time-discrete and has finite amplitude resolution (two states in our example).
As you have no doubt noticed in your parallel work, digital systems have certain advantages and benefits relative to analog systems. These advantages include noise immunity, storage capability, and available numeric processing power. It makes sense, then, that a combination of analog and digital systems could offer the best of both worlds. This chapter examines the processes of converting analog signals into a digital format and turning digital words into an analog signal. A few representative examples of processing the signal in the digital domain are presented as well. Some examples with which you might already be familiar include the stereo compact disk (CD) and the digital storage oscilloscope. We will break down this topic into two broad sections: analog-to-digital conversion (AD) and digital-to-analog conversion (DA). Since many AD systems require digital-to-analog converters, we will examine DA systems first.
Given enough time, an analog circuit may be designed and manufactured for virtually any application. Why, then, would anyone desire to work in the digital domain? Perhaps the major reason for working in the digital domain is the flexibility it offers. Once signals are represented in a digital form, they may be manipulated by various means, including software programs. You have probably discovered that replicating a computer program is far easier than replicating an analog circuit. What’s more, a program is much easier to update and customize than a hardware circuit. Because of this, it is possible to manipulate a signal in many different ways with the same digital/computer hardware; all that needs to be altered is the manipulation instructions (i.e., the program). The analog circuit, in contrast, needs to be re-wired, and extra components need to be added or old portions removed. This can be far more costly and time-intensive than just updating software. By working in the digital domain, processing circuits do not exist per se; rather, a generic IC such as a CPU is used to create a βvirtual circuitβ. With a certain amount of intelligence in the system design, the virtual circuit may be able to alter its own performance in order to precisely adapt to various signals. This all boils down to the fact that a digital scheme may offer much greater flexibility for involved tasks and allows a streamlined, generic hardware solution for complex applications. Because of this attribute, the digital solution may wind up being significantly less expensive than its analog counterpart.
When an analog signal is transferred to the digital domain, it is represented as a series of numbers (usually, high/low binary logic levels). One nice property of this representation is that it is exactly repeatable. In other words, an infinite number of copies of the data may be generated, and no distortions or deviations from the original will appear. The last copy will be identical to the first. Compare this to a simple analog copy. For example, if you were to record a song with a cassette recorder and then make a copy of the tape, the second-generation copy would suffer from increased noise and distortion. A copy of the second copy would produce even worse results. Every time the signal is copied, some corruption occurs. It is for this reason that early long distance telephone calls were of such low quality. Modern communications systems employ digital techniques that allow much higher quality, even if one person is in New York and the other is in Australia, halfway around the planet.
Besides being a desirable mathematical attribute, repeatability also lends itself to the problem of long term storage. A storage medium for a binary signal only needs to resolve two levels, whereas the analog medium needs to resolve very fine changes in signal strength. As you might guess, deterioration of the analog medium is a serious problem and results in information loss. The digital medium can theoretically survive a much higher level of deterioration without information loss. In a computerized system, data may be stored in a variety of formats including RAM (Random Access Memory) and magnetic tape or disk. For playback only (i.e., read only), data may be stored in ROM (Read Only Memory) or laser disk formats (such as DVD or audio CD).
As always, the benefits of the digital scheme arrive with specific disadvantages. First, for simpler applications, the cost of the digital approach is very high and cannot be justified. Second, the process of converting a signal between the analog and digital domains is an inexact one. Some information about the signal will be lost during the conversion. This is because the digital representation has finite resolution. This means that only signal changes larger than a certain minimum size (the resolution step size) are discernable, and therefore, some form of round-off error is inevitable. This characteristic helps determine the range of allowable signals, from the smallest detectable signal to the maximum signal before overload occurs. Third, analog systems are inherently faster than digital systems. Analog solutions can process input signals at much higher frequencies than digital schemes. Also, analog systems work in real-time, whereas digital systems might not. Digital systems can only perform in real-time if the input signal is not a very high frequency, if the processing task is not overly complex, or if specialized processing circuits are added. Not all applications require real-time performance, so this limitation is not always a problem. Also, because we can expect computing power to get less and less expensive in the coming years, cost-effective digital processing will undoubtedly expand into new areas. | 1,419 | 7,292 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2024-33 | latest | en | 0.958631 |
https://www.teacherspayteachers.com/Product/First-Grade-Math-MEGA-BUNDLE-Print-and-Go-2531512 | 1,487,542,287,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170253.67/warc/CC-MAIN-20170219104610-00561-ip-10-171-10-108.ec2.internal.warc.gz | 903,271,303 | 26,016 | # First Grade Math - MEGA BUNDLE - Print and Go
Subjects
Resource Types
Product Rating
3.9
File Type
Compressed Zip File
How to unzip files.
65.41 MB | 210 pages
### PRODUCT DESCRIPTION
PRINT & GO! Geometry BUNDLE
Ten pages of practice for each of the 21 standards/skills for first graders!
Use as homework, morning work, mini-assessments, and in-class work. These pages aren't crammed with fancy fonts and clipart - they are designed with the first grader in mind!
The following resources are included in this MEGA BUNDLE:
Geometry
1.G.1 - Shapes and Their Attributes
1.G.2 - Composite Shapes
1.G.3 - Decomposing Shapes
Operations and Algebraic Thinking
1.OA.1 - Addition and Subtraction Word Problems
1.OA.3 - Associative and Commutative Property
1.OA.5 - Relating Counting to Addition and Subtraction
1.OA.6 - Adding and Subtracting Fluently
1.OA.7 - True or False and The Equal Sign
1.OA.8 – Missing Numbers in Equations
Measurement and Data
1.MD.1 – Ordering Objects by Length
1.MD.2 – Measuring Length of Objects
1.MD.3 – Telling Time (Nearest hour and half hour)
1.MD.4 – Data and Graphing
Numbers and Operations in Base 10
1.NBT.1 - Counting to 120
1.NBT.2 - Tens and Ones
1.NBT.3 - Comparing Numbers
1.NBT.5 - Ten More, Ten Less
1.NBT.6 - Subtract Multiples of 10
•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
CONNECT WITH ME!
Cupcakes & Curriculum on TPT
Cupcakes & Curriculum on Instagram
Cupcakes & Curriculum Blog
•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
Total Pages
210
N/A
Teaching Duration
Lifelong Tool
### Average Ratings
4.0
Overall Quality:
3.9
Accuracy:
4.0
Practicality:
4.0
Thoroughness:
4.0
Creativity:
4.0
Clarity:
3.9
Total:
10 ratings
\$25.00
List Price: \$52.50
You Save: \$27.50
User Rating: 4.0/4.0
(3,146 Followers)
\$25.00
List Price: \$52.50
You Save: \$27.50
Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. | 685 | 1,986 | {"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} | 3.265625 | 3 | CC-MAIN-2017-09 | longest | en | 0.631177 |
https://www.coursehero.com/file/6602642/1290-Mechanics-Homework-Mechanics-of-Materials-Solution/ | 1,524,590,231,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946807.67/warc/CC-MAIN-20180424154911-20180424174911-00343.warc.gz | 782,642,446 | 25,792 | {[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
1290_Mechanics Homework Mechanics of Materials Solution
# 1290_Mechanics Homework Mechanics of Materials Solution -...
This preview shows page 1. Sign up to view the full content.
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: 10.115 A steel tube of 80-mm outer diameter is to carry a 93—kN load P with an eccentricity of 20 mm. The tubes available for use are made with wall thiclmesses in increments of 3 mm from 6 mm to 15 mm. Using the allowable-stress method, determine the lightest tube that can be used. Assume E= 200 GPa, are 250 MPa. SOLUTION PROBLEM 10.1 1 5 80—mm outer : diameter 3 37 726; 0.536: 27.24 6 3'4 IS‘lS 0.451 24.25 5! 31 2007 LZSS 2523! I? 2‘2 2544 LSQS 21L“ 25 3063 1.704 23.59 Sleefi : E: 200000 MP4 C 4331”“: :" (223“)2125cs - l. _ _2______ 2 _ Le/r‘ _ Try z-sm 7' 255,—7-[06 - 86. ?2< C; 0mm 12.5. :- f-t‘iwfielfl—éCQQfin )‘ = 1.335 6“, .- 4.1 ‘ 'L—‘ENY’J 5;;th %(O_GQI'IT] = 100-? MPa _ —3 31; + Plea = 3:21:3‘ *gfiilo3z(§%;£9;%jiflfi_l = 104.2 MPa. > 10011 MP4 (“0+ dreamed ) loll. Z ( [00.51 l(2oo7slo" 3= 20‘3de w. = 2073 Mm?" Appmxlmul‘t veal-Arse? are“ .. La 2 {7‘ w t=12mm 7rm= 40.I2<CL \$37; = 0.7172 Es. = Lesa 6..., = 93 3 MP“ Pe _ M+ ‘l3kl0‘)(20v{05)(‘fouo ’) ____ H 3% + 3-9 ' zssswo-b {.528 Mo“ 85° a" < ”‘3 M9“ USE t "I '2 MM ...
View Full Document
{[ snackBarMessage ]} | 617 | 1,420 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2018-17 | latest | en | 0.529438 |
https://www.coursehero.com/file/6646308/Differential-Equations-Lecture-Work-Solutions-69/ | 1,519,519,264,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891816068.93/warc/CC-MAIN-20180224231522-20180225011522-00699.warc.gz | 819,437,493 | 79,276 | {[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
Differential Equations Lecture Work Solutions 69
# Differential Equations Lecture Work Solutions 69 - 8a 1 1...
This preview shows page 1. Sign up to view the full content.
8a. u rr + 1 r u r + 1 r 2 u θθ =0 u ( a, θ )= f ( θ ) u ( b, θ )= g ( θ ) r 2 R 0 + rR 0 λR =0 Θ 0 + λ Θ=0 Θ(0) = Θ(2 π ) Θ 0 (0) = Θ 0 (2 π ) The eigenvalues and eigenfunctions can be found in the summary of chapter 4 λ 0 =0 Θ 0 =1 fo r n =0 λ n = n 2 Θ n =co s and sin for n =1 , 2 ,... Use these eigenvalues in the R equation and we get the following solutions: R 0 = A 0 + B 0 ln rn =0 R n = A n r n + B n r n n =1 , 2 ,... Since r = 0 is outside the domain and r is Fnite, we have no reason to throw away any of the 4 parameters A 0 ,A n ,B 0 ,B n . Thus the solution u ( r, θ )=( A 0 + B 0 ln r ) | {z } R 0 · 1 |{z} Θ 0 · a 0 + X n =1 ( A n r n + B n r n ) | {z } R n ( a n cos + b n sin ) |
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
Ask a homework question - tutors are online | 401 | 1,074 | {"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 | 0.689284 |
http://www.studystack.com/flashcard-1736281 | 1,477,454,913,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720615.90/warc/CC-MAIN-20161020183840-00022-ip-10-171-6-4.ec2.internal.warc.gz | 712,916,681 | 17,157 | or
or
taken
why
Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.
Enter the email address associated with your account, and we'll email you a link to reset your password.
Don't know (0)
Know (0)
remaining cards (0)
Save
0:01
Flashcards Matching Hangman Crossword Type In Quiz Test StudyStack Study Table Bug Match Hungry Bug Unscramble Chopped Targets
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
# operations w integer
(6-(-10))/(4/(-2)= -8
(2+1)x6/(-9)= -2
9-(10/(-2)-5)= 9
(-1)cubedx(8-(-2)= -10
5+(-7)-(-3)+2= 3
(-10)x(-1)-(-8)/4= 12
-3+6+(-9)= -6
(-5)x(-1)-(-1)= 6
(-1) to the power of (-2)x(-8)= -1
8/2-(-3)= 7
4x(-1)squared= 4
7x(-12)-48= -132
(-15)+3+12-(-6)= 6
(34+(-46)0-5x(-11)= 43
(-144)-(36x(-2))= -72
3.2x(-10) to the power of 4= 32,000
0.5x6-3= 0
20.8/(-1.3)x(14.8+17.2)= -512
10.8+(-6)squared-1.2x2.1= 44.28
8x(-1)+(-3)squared= 1
(-2)+10 to the power of 1/1= -1.9
(-8) to the power of 9x1-(-9)= 1.8
(-1)x2/1x(-6)= 12
(7+4)x(18-(-6)x(-3))= 0
(-3)-15x(-4)= 57
(7+4)x(18-6x(-3))= 396
Created by: syddj123 | 533 | 1,242 | {"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-2016-44 | latest | en | 0.674308 |
https://nrich.maths.org/public/leg.php?code=72&cl=2&cldcmpid=2555 | 1,454,974,572,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701154682.35/warc/CC-MAIN-20160205193914-00167-ip-10-236-182-209.ec2.internal.warc.gz | 779,581,593 | 10,153 | # Search by Topic
#### Resources tagged with Generalising similar to Can You Find a Perfect Number?:
Filter by: Content type:
Stage:
Challenge level:
### Division Rules
##### Stage: 2 Challenge Level:
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
### Repeaters
##### Stage: 3 Challenge Level:
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
### What Numbers Can We Make Now?
##### Stage: 3 and 4 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
### Elevenses
##### Stage: 3 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
### Special Sums and Products
##### Stage: 3 Challenge Level:
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
### Three Dice
##### Stage: 2 Challenge Level:
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
### Crossings
##### Stage: 2 Challenge Level:
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
### Got it for Two
##### Stage: 2 Challenge Level:
Got It game for an adult and child. How can you play so that you know you will always win?
### GOT IT Now
##### Stage: 2 and 3 Challenge Level:
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
### Number Tracks
##### Stage: 2 Challenge Level:
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
### Round and Round the Circle
##### Stage: 2 Challenge Level:
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
### One O Five
##### Stage: 3 Challenge Level:
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
### Calendar Calculations
##### Stage: 2 Challenge Level:
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
### What Numbers Can We Make?
##### Stage: 3 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
### Summing Consecutive Numbers
##### Stage: 3 Challenge Level:
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
### Broken Toaster
##### Stage: 2 Short Challenge Level:
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
### Sums and Differences 1
##### Stage: 2 Challenge Level:
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
### More Magic Potting Sheds
##### Stage: 3 Challenge Level:
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
### Mini-max
##### Stage: 3 Challenge Level:
Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .
### Journeys in Numberland
##### Stage: 2 Challenge Level:
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
### Three Times Seven
##### Stage: 3 Challenge Level:
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
### Magic Constants
##### Stage: 2 Challenge Level:
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
### Hidden Squares
##### Stage: 3 Challenge Level:
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
### Doplication
##### Stage: 2 Challenge Level:
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
### Button-up Some More
##### Stage: 2 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
### Reverse to Order
##### Stage: 3 Challenge Level:
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
### Take Three from Five
##### Stage: 3 and 4 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
### Tiling
##### Stage: 2 Challenge Level:
An investigation that gives you the opportunity to make and justify predictions.
### Sums and Differences 2
##### Stage: 2 Challenge Level:
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
##### Stage: 3 Challenge Level:
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
### Sum Equals Product
##### Stage: 3 Challenge Level:
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
### Christmas Chocolates
##### Stage: 3 Challenge Level:
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
### Strike it Out
##### Stage: 1 and 2 Challenge Level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
### Mystic Rose
##### Stage: 3 Challenge Level:
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
### Handshakes
##### Stage: 3 Challenge Level:
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
### Go Forth and Generalise
##### Stage: 3
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
### Arithmagons
##### Stage: 3 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
### Consecutive Negative Numbers
##### Stage: 3 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
### Number Differences
##### Stage: 2 Challenge Level:
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
### Domino Numbers
##### Stage: 2 Challenge Level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
### Cubes Within Cubes Revisited
##### Stage: 3 Challenge Level:
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
### Multiplication Square
##### Stage: 3 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
### Got It
##### Stage: 2 and 3 Challenge Level:
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
### Magic Vs
##### Stage: 2 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
### Sliding Puzzle
##### Stage: 1, 2, 3 and 4 Challenge Level:
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
### Picturing Triangle Numbers
##### Stage: 3 Challenge Level:
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
### Tourism
##### Stage: 3 Challenge Level:
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
### Searching for Mean(ing)
##### Stage: 3 Challenge Level:
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
### Number Pyramids
##### Stage: 3 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
### Games Related to Nim
##### Stage: 1, 2, 3 and 4
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. | 2,288 | 9,764 | {"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} | 4.15625 | 4 | CC-MAIN-2016-07 | longest | en | 0.875117 |
http://spotidoc.com/doc/1605284/chapter-21-electric-potential | 1,540,236,037,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583515375.86/warc/CC-MAIN-20181022180558-20181022202058-00416.warc.gz | 345,070,713 | 9,973 | # Chapter 21 Electric Potential
```Chapter 21
Electric Potential
Topics:
•
•
•
•
Conservation of energy
Work and Delta PE
Electric potential energy
Electric potential
Sample question:
Shown is the electric potential measured on the surface of a patient.
This potential is caused by electrical signals originating in the beating
heart. Why does the potential have this pattern, and what do these
measurements tell us about the heart s condition?
Slide 21-1
What to do to do well in this class
A. Focus on key physics concepts
• May seem like basics but will help you solve even complex
problems
• Focus on principle rather than recipes
• Need to have a functional understanding of key concepts
• Express key equations as sentences
• Know where they come from and what they mean
• Know how and when to apply them
• Know which equations are general and which are special cases
• Must know when not to apply special cases
• Look at a problem after a good physics diagram and maybe a
good physical diagram and know what key physics concepts apply
in that problem
• Memorize key concepts so you can look at a problem, say that s
Newton 2, and know the associated equation in a snap
Slide 21-16
What to do to do well in this class
A. Focus on key physics concepts
• How to do this
• When you look at problems, mentally group problems by
the physics rather than the physical situation
• After each class or at least each week, create a notesheet
to organize a structure of the new key concepts for each
chapter and note how they fit in with previous key concepts
• Use the note sheet to do homework problems (a) do as
many homework problems as you can just using this
sheet. (b) then go to your notes and the textbook for your
missing pieces
• Use flash cards to memorize key concepts - include the
concept description, relevant equations, diagrams, and
what types of problems benefit from using that concept
• Pay close attention to examples done in class and note the
physics and assume/observes in each example and how
these are used
Slide 21-16
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Types of Energy
Conservation of Energy Equation (key concept)
Slide 21-16
Chapter 21 Key Ideas (Physics 151)
Dot Product
Method for multiplying two vectors to get a scalar
Definition of Work
Work is how forces add energy to or take away energy from a
system. It is the effect of a force applied over a displacement.
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Definition of Work
!
! ! !
Work!!W = F!i!!r = F !r cos "
Where ! = angle between the vectors
Work- Energy Theorem (only valid when particle model applies)
Wnet = !KE
Work done by a conservative force (Fg, Fs, & Fe)
Wg = !"PEg Also work done by conservative force
is path independent
Conservation of Energy Equation
KEi +
!
PEi + " Esys = KE f +
different !types
!
PE f + "Eth
different !types
Slide 21-16
Energy Bar Graph Sample
Energy Bar Chart Example 1
Energy Bar Chart Example II
Energy Bar Chart Example III
Review of Work
!
! ! !
Definition of Work: Work!!W = F!i!!r = F !r cos "
where ! = angle between the vectors
• Calculate the work done in moving each ball from y = 0 meters to y = 5 meters
• Calculate the work per kg for moving each ball from y = 0 m to 5 m
• Calculate the change in gravitational potential energy per kg for moving each
ball from = 0 m to 5 m
• Calculate the speed each ball would have as it reached the ground if released
from 5 meters above the ground
Slide 21-16
Electric Potential Energy
Slide 21-9
Electric Potential Energy
Case A - Book starts & stops at rest
WNet = !EK = 0J
Whand + Wg = 0 ! Whand = "Wg = #Eg
Case C - Charge at rest at A and B
WNet = !EK = 0J
Whand + We = 0 ! Whand = "We = #Ee
Slide 21-9
Electric potential energy: A qualitative analysis
• A positively charged
cannonball is held near
another fixed positively
charged object in the
barrel of the cannon. • Some type of energy must
decrease if gravitational
and kinetic energies
increase in this process.
Chapter 21 Key Equations (2)
Key Energy Equations from Physics 152
q1q2
PEe = k
r12
Electric Potential Energy for 2 point charges
(zero potential energy when charges an infinite distance apart)
D Potential Energy for a uniform infinite plate
!
!
%
!PEe = "We = " & Fe # !r cos \$ '( = " ( q E ) !r cos \$
For one plate, zero potential energy is at infinity
For two plates, zero potential energy is at one plate or
inbetween the two plates
Electric Potential V and Change in Electric Potential => Delta V
Slide 21-16
Graphing the electric potential energy versus distance
• Because of the 1/r dependence, the electric potential
energy approaches positive infinity when the
separation approaches zero, and it becomes less
positive and approaches zero as like charges are
moved far apart.
Example: Electric Potential Energy
A cart on a track has a large, positive charge and is located between
two sheets of charge. Initially at rest at point A, the cart moves
from A to C.
a. Draw qualitative force diagrams for
the cart at positions A, B and C.
b. Draw qualitative energy bar charts
for the cart when it is at each position
A, B and C. List the objects that
c. How would your force and energy diagrams change (if at all) if the sheet to
the right were also positively charged?
Slide 21-16
Changes in Electric Potential Energy - Delta PEe
For each situation below, identify which arrangement (final or initial) has more
electrical potential energy within the system of charges and their field.
Initial (A)
Final (B)
(a)
Greatest Delta PEe
(b)
(c)
(d)
Hydrogen Atom
Slide 21-16
Changes in Electric Potential Energy – Delta PEe
For each situation below, identify which arrangement (final or initial) has more
electrical potential energy within the system of charges and their field.
Initial (A)
Final (B)
(e)
(f)
Greatest Delta PEe
(g)
Slide 21-16
Changes in Electric Potential Energy – Delta PEe
Is the change ∆PEe of a + charged particle positive, negative,
or zero as it moves from i to f?
(a) Positive (b) Negative (c) Zero (d) Can t tell
Slide 21-11
Electric Potential Model Worksheet 2: Energy and Potential in Uniform Fields
"
Rank the change in gravitational potential energy for the following lettered objects in the
Earth s gravitational field.
a. . most _______ _________ ________ ________ _______ _______ ________
b. Explain your ranking, stating why each is greater than, less than, or equal to its
neighbors.
c. Where is the energy stored? What gains or loses energy as the masses move from one
place to another?
Slide 21-16
Electric Potential Energy Example Problem
The electric field between two
charged plates is uniform with a
strength of 4 N/C.
a. Draw several electric field lines in the
region between the plates.
b. Determine the change in electrical
potential energy in moving a positive
4 microCoulomb charge from A to B.
c. Determine the change in electrical potential energy in moving a
negative 12 microCoulomb charge from A to B.
Slide 21-16
Gravitational Potential Energy: Example Problem 2
A spacecraft is launched away from earth
a. Draw several gravitational field lines
in the region around Earth.
b. Determine the change in
gravitational potential energy when
the spacecraft moves from A to B,
where A is 10 million miles from
Earth and B is 30 million miles from
Earth.
Slide 21-16
Electric Potential Energy: Example Problem 3
A small charge moves farther from a
positive source charge.
a. Draw several electric field lines in the region
around the source charge.
b. Determine the change in electrical potential
energy in moving a positive 4 nC charge
from A to B, where A is 3 cm from the source
charge and B is 10 cm away.
c. Determine the change in electrical potential
energy in moving a negative 4 nC charge
from A to B.
Slide 21-16
Electric Potential
U elec = qV; V = U elec / q
<= Replace
before using
Slide 21-10
Chapter 21 Key Equations (3)
Electric Potential is the Electric Potential Energy per Charge
V=
PEe
!!
qtest
!V =
!PEe
W
=" e
qtest
qtest
Electric Potential increases as you approach positive source
charges and decreases as you approach negative source
charges (source charges are the charges generating the electric
field)
A line where Delta V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and Delta PEe= 0 J)
Slide 21-16
Electric Potential and E-Field for Three Important Cases
For a point charge
q
1 q
V=K =
r 4!" 0 r
For very large charged plates, must use
!
!
!
!
!
! !
!PEe
We
Fe !i!!r
qtest E!i!!r
!
!V =
="
="
="
= " E!i!!r = " E !r cos #
qtest
qtest
qtest
qtest
Slide 21-25
Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
Slide 21-14
Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
Slide 21-14
Example
A proton has a speed of 3.5 x 105 m/s at a point where the
electrical potential is 600 V. It moves through a point where the
electric potential is 1000 V. What is its speed at this second point?
Slide 21-16
Slide 21-15
Chapter 22
Current and Resistance
Topics:
• Current
• Conservation of current
• Batteries
• Resistance and resistivity
• Simple circuits
Sample question:
How can the measurement of an electric current passed through a
person s body allow a determination of the percentage body fat?
Slide 22-1
Properties of a Current
Slide 22-8
Brainstorm: what is used up when current flows?
(Penguin Racetrack Demo)
Slide 21-1
Definition of a Current
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If
the red x still appears, you may have to delete the image and then insert it again.
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
Slide 22-9
Simple Circuits
The current is determined by
the potential difference and
the resistance of the wire:
∆V
_____
chem
I =
R
Slide 22-13
Slide 22-3
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still
appears, you may have to delete the image and then insert it again.
Slide 22-4
Batteries
The potential difference
between the terminals of a
battery, often called the
terminal voltage, is the
battery s emf.
Wchem
!Vbat =
=e
q
Slide 22-20
Series and Parallel
Slide 21-1
Resistivity
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your
computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
The resistance of a wire
depends on its dimensions
and the resistivity of its
material:
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer,
and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your
computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
Slide 22-22
Kirchhoff s Laws
Slide 23-11
The V field
• Can we describe electric fields using the
concepts of work and energy? • To do so, we need to describe the electric
field not as a force-related E field, but as an
energy-related field.
Electric potential due to a single charged object
Finding the electric potential energy when the V field is known
• If we know the electric potential at a specific
location, we can rearrange the definition of the V
field to determine the electric potential energy:
The superposition principle and the V field
due to multiple charges
• where Q , Q , Q , … are the source charges
1
2
3
(including their signs) creating the field and r1, r2, r3,
… are the distances between the source charges
and the location where we are determining the V
field.
• So Electric Potentials (V) add just like Electric Potential Energies
Quantitative Example
• Suppose that the heart's dipole charges −Q and +Q are separated
by distance d. Write an expression for the V field due to both
charges at point A, a distance d to the right of the +Q charge.
1. Simplify and diagram.
2. Represent mathematically.
Finding the electric potential energy when the V field is known
• If we know the electric potential at a specific
location, we can rearrange the definition of the V
field to determine the electric potential energy:
Potential difference – Delta V
• The value of the electric potential depends
on the choice of zero level, so we often use
the difference in electric potential between
two points.
Particles in a potential difference
• A positively charged object accelerates from
regions of higher electric potential toward
regions of lower potential (like an object
falling to lower elevation in Earth's
gravitational field).
• A negatively charged particle tends to do the
opposite, accelerating from regions of lower
``` | 3,368 | 13,493 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2018-43 | latest | en | 0.934024 |
https://eaglesrewind.com/2013/10/16/not-all-points-are-created-equal-part-2/?replytocom=2004 | 1,656,738,146,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103984681.57/warc/CC-MAIN-20220702040603-20220702070603-00455.warc.gz | 278,714,603 | 31,931 | # Not All Points Are Created Equal: Part 2
I want to start looking at this in smaller chunks, which will hopefully be a little clearer. First, some overall major takeaways:
– E = R ((60 – T) / 60) + C, the formula, for reference.
– Large underdogs should be extremely aggressive early in games, when R (relative strength) is at its largest.
Underdogs should attempt to use as much of the clock as possible. This is more “conventional” and something I didn’t talk about last week, but it’s a logical extension of what I was talking about. If you have two very mismatched teams, and make them play 100 games, it’s almost certain that the “better” team will win more than it will lose. The larger the sample, the more likely it is to reflect that actual “relative strength”. By using up a clock, the underdog is limiting the sample size “# of plays” from which the relative strength advantage can play out. Using our formula, by bleeding the clock, underdogs are attacking the R value indirectly, using T, instead of going at R itself (scoring points).
– During the game, strategic decisions should incorporate an objective view of how the rest of the game is likely to play out. For large underdogs, this means they should expect to be outscored, and therefore need to be aggressive in scoring points.
Favorites Strategy
I didn’t discuss how this effects the strategy of the Favorite. In the most simple reading, it can be assumed that the Favorite should be more “conservative”. Going back to our Broncos vs. Jaguars example, 3 points is a lot more valuable to Denver than it is to Jacksonville (hence “not all points are equal”). Therefore, given the same FG opportunity as the one we gave Jacksonville (expected points for FG and going for it are equal, purely a risk/reward play), it should elect the LOW risk option (the FG).
That’s because, as I explained above, at any time T, the favorite can expect to outplay the underdog over the rest of the game, i.e. the R value is advantagous. As time goes on, this becomes less of a factor (T declining ultimately takes the R half of the equation to 0).
In general, I agree with this. Large favorites should be content to take whatever points they can get, early in the game.
However, there is a slight wrinkle, one that will appeal to the more aggressive fans. Let’s go back to our graphic for a moment. Here is the range of outcomes at the start of the game:
As you can see/remember, if we assume a “random walk” from there, Denver should expect to win a very large percentage of the time. There is a case to be made for being aggressive, though, and hopefully you can see it.
It goes back to when I explained that you can actually “win” the game before the game is over. Assume the same EP-Neutral opportunity above, but this time imagine that gaining 7 points is enough to shift the range of outcomes (yellow shade) entirely above the X-Axis. Would you go for it or kick? Probably go for it, right? After all, if you have a chance to “win the game”, with relatively low risk (still have a heavy advantage if you don’t convert), you should do it.
Obviously, I have to note that this is a purely theoretical situation. During the game, it’s not possible to know EXACTLY where the range of expected outcomes lies. Therefore, we can’t be sure of where the line between 100% win and 99% win is, even if some of us see that final 1% as extremely valuable.
Still, it implies that there are some situations, even if they are hard to identify, where the Favorite should also be aggressive. In general, though, it should take the lower risk strategic options, because it does NOT want to significantly shift R (outside of the specific scenario I just outlined).
Random Walk
I don’t think I made a big enough point of this model in the post last week. There are two ways to view the game, ex-ante, and I think one of them is much better than the other.
1) This is the normal model. Teams start on even ground (Score tied 0 – 0) and we “expect” the course of play to naturally favor one team (the favorite) over the other (the underdog). During actual play, we project that the difference in skill will gradually manifest itself in the score, and ultimately mean victory for the Favorite. That’s the usual way of thinking about it.
What I’ve done is to flip that around a bit.
2) Teams start on UNEVEN ground (R value), and from there we expect a random series of events to occur, though they will be within a range of possible outcomes. This certainly isn’t the “natural” way of thinking about things, but it appeals to me for one very big reason. Can you guess what that is?
I like it because it forces us to accept and recognize the large role of luck and chance in the outcome of the game. Future human events are inherently unpredictable, right? So how do we reconcile that with the first option I outlined above (the normal model)? Isn’t it explicitly forcing us to predict that which is, by its very nature, unpredictable?
The result of this is that we get ridiculous explanations for unexpected outcomes of games. For example, take the Giants-Patriots SB (Helmet Catch). The Patriots were heavy favorites, and yet lost a close game. Why?
– Is it because Eli Manning is just REALLY clutch?
– Is it because the Patriots “choked”?
– Is it because the Giants have more “heart”? or “wanted it more”?
Of course not, those are all ridiculous explanations, and yet they’re a natural outgrowth of the way we normally think of games (option 1).
Now let’s look at the “Random Walk / Ex-Ante Relative Strength” model (the name needs work). Here’s the picture again, just imagine a Patriots logo instead of the Broncos and a Giants logo instead of the Jaguars.
Suddenly there’s no explanation needed for the outcome of the game. Just look at the picture; you can see there’s a section of the yellow shaded area below the X-Axis. If we assume that at time T=60, all future game events will take a random path through the yellow area, then it’s obvious that SOME of those infinite paths will end up in the area below the X-Axis. It just so happens that THIS PARTICULAR run was among those.
Now there’s also obviously some unpredictability in deriving a value for R. It’s very difficult to know just how good each team is and how they match up against each other. However, I’d argue that all of the necessary information for getting an accurate R value is theoretically knowable. Compare that the Normal Model. It requires us to predict future events, which is NOT POSSIBLE, even in theory.
The upshot of the “Random Walk” is that it forces people to confront a lack of “control”. It basically boils the game down to a lottery. That sucks some of the fun out of it, but that doesn’t mean its a less accurate model of analysis.
Similar to last time, I’m going to cut this off prematurely for the sake of time and clarity. Hopefully you’re still with me.
## 8 thoughts on “Not All Points Are Created Equal: Part 2”
1. Could be a fun exercise to try and calculate an absolute value of R for each team based on whichever stats over whichever sample you think most relevant such that delta-R would be the relative strength for a given game. Obviously it’s unlikely to be particularly accurate, but it could be fun to have a go.
• Im considering it, though can’t decide whether its better to use the gambling spreads or something like FO’s DVOAs. Maybe a combination of both.
On Thu, Oct 17, 2013 at 8:16 AM, Eagles Rewind
• I’d be inclined to do a DVOA kind of thing, given that no matter how much we want to assume Vegas is an efficient market, it almost certainly isn’t.
2. It seems like there are some incentives working at cross-purposes here. On one hand, it pays for the underdog to be aggressive, which means taking some shots and increasing the risk for 3 (or even 4) and outs. On the other hand, it pays for the underdog to suck up the clock.
I wonder if there’s some way to resolve this seeming tension?
3. Another example of an underdog team playing to lose with their conservatism on Thursday night.
4th and Goal at the Seattle 4 yard line, Cardinals kick a field goal down 18 points at the top of the 4th Quarter. Yikes.
4. > E = R ((60 – T) / 60) + C, the formula, for reference.
If we have to look up what the letters mean, from the other article is it really that useful as a reference? There’s plenty of space to write things out long hand. The formula could be a bit clearer anyway:
The Expected Margin = (Relative Strength) * (Time Remaining) + The Current Margin
> Large underdogs should be extremely aggressive early in games, when R (relative
> strength) is at its largest.
An implicit assumption for your model is that the relative strength is constant, so the notion that R is at its largest at the beginning of the game is nonsense. (The “R ((60 – T) / 60)” term is at its largest at the beginning of the game, but the expected margin of victory may not be, and the win probability certainly won’t be.)
Sure, underdogs should be aggressive early in the game, but, if the game plays out as expected, they should be aggressive throughout the entire game. If the game slips away from them, the underdogs should become more risk tolerant, and if they manage to do better than expected, the underdogs should be more risk averse.
> … Going back to our Broncos vs. Jaguars example, 3 points is a lot more valuable to Denver > than it is to Jacksonville …
Winning a football game is a zero-sum proposition. Therefore any event (including scoring) will have equal and opposite value for the teams.
Denver should be more willing to kick field goals, not because the points are more valuable to them than to Jacksonville, but because Denver is ‘virtually ahead’ and thus prefers the relative certainty of the field goal.
> – Underdogs should attempt to use as much of the clock as possible.
The analysis requires some more sophisticated math, and is proabably outside the scope of this discussion, but in a random walk model luck needs time to have an impact, so the underdogs really only want to burn clock early in the game, or if they get unexpectedly lucky. (That should make sense: in a typical NFL mismatch, at some time in the game the favorite will get a comfortable margin, and then start running the clock, while the underdog is under time pressure.) Since a certain small win is better than a likely large one, in more extreme cases, the favorite may actually be the team that wants to burn clock early.
> After all, if you have a chance to “win the game”, with relatively low risk (still have a heavy
> advantage if you don’t convert), you should do it.
If the situation is that low in risk, you’re going to be chosing between two or three (maybe even four) different ways to ‘win the game’.
• This part was incorrect:
> Since a certain small win is better than a likely large one, in more extreme
> cases, the favorite may actually be the team that wants to burn clock early.
As long as the game is tied – like it is at the beginning of the game – the underdog is happy to eat up clock. | 2,583 | 11,138 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2022-27 | latest | en | 0.948036 |
https://bumpercarfilms.com/qa/what-is-the-difference-between-force-and-average-force.html | 1,618,200,095,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038066568.16/warc/CC-MAIN-20210412023359-20210412053359-00036.warc.gz | 272,927,651 | 8,223 | # What Is The Difference Between Force And Average Force?
## What is the difference between average force and net force?
Newton’s second law is defined such that the net force on an object at any moment is equal to the product of its mass and acceleration, or →Fnet=m→a.
There is an average force over a given period of time, and there is a net force on an object in an instant..
## How do u calculate force?
The force (F) required to move an object of mass (m) with an acceleration (a) is given by the formula F = m x a. So, force = mass multiplied by acceleration.
## What is Newton’s third law sometimes called?
Newton’s third law: If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A. … We sometimes refer to this law loosely as action-reaction, where the force exerted is the action and the force experienced as a consequence is the reaction.
## What is the formula for calculating speed?
The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time.
## Is Average force the same as impulse?
Key terms. Product of the average force exerted on an object and the time interval during which the force is exerted. Impulse is equal to the change in momentum ( Δ p \Delta p Δp ) and is sometimes represented with the symbol J.
## What net force is needed for a 1500 kg car?
We assume the acceleration is constant, so we can use the kinematic equations, Eqs. 2-11, to calculate it. vo= 100 km/h FIGURE 4-6 Example 4-3. The net force required is then SF = ma = (1500 kg)(-7.1 m/s) = -1.1 X 10^N.
## What is impulse equal to?
The impulse experienced by the object equals the change in momentum of the object. In equation form, F • t = m • Δ v. In a collision, objects experience an impulse; the impulse causes and is equal to the change in momentum.
## Can forces be negative?
Forces can be positive or negative. Actually, forces which are aimed to the right are usually called positive forces. And forces which are aimed to the left are usually said to be in a negative direction.
## How do you calculate stopping force?
The stopping force Fb is directly proportional to the speed of the car and it can be expressed by the relation:Fb=kv. Inserting it into the equation (2) we obtain:ma=−kv. We express the acceleration as a change of the speed in time:mdvdt=−kv. The speed v(t):Aug 4, 2016
## What is the average net force?
The average force is the force exerted by some object moving at some defined rate of speed i.e. velocity for a defined period of time. … Therefore, the average force is equal to the mass of the body multiplied by the average velocity of the object over the defined time.
## What is Net Force formula?
FNet = Fa + Fg. Where, … When a force is applied to the body, not only is the applied force acting, there are many other forces like gravitational force Fg, frictional force Ff and the normal force that balances the other force. Therefore, the net force formula is given by, FNet = Fa + Fg + Ff + FN.
## How do you calculate work?
Work can be calculated with the equation: Work = Force × Distance. The SI unit for work is the joule (J), or Newton • meter (N • m). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.
## How much force is a Kilonewton?
One kilonewton, 1 kN, is equivalent to 102.0 kgf, or about 100 kg of load under Earth gravity. 1 kN = 102 kg × 9.81 m/s2. So for example, a platform that shows it is rated at 321 kilonewtons (72,000 lbf), will safely support a 32,100 kilograms (70,800 lb) load.
## What force is required to accelerate a body?
∴F=6kgms2=6 Newton. =6N. Therefore, Force required to accelerate the body is 6N. (answer). | 956 | 3,820 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2021-17 | latest | en | 0.930078 |
https://www.philosophy-science-humanities-controversies.com/listview-details.php?id=746770&a=t&first_name=J.&author=Bigelow&concept=Set%20Theory | 1,527,286,201,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867220.74/warc/CC-MAIN-20180525215613-20180525235613-00353.warc.gz | 797,807,850 | 4,872 | # Philosophy Lexicon of Arguments
Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle.
_____________
Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.
Author Item Summary Meta data
I 363
Set theory/Bigelow/Pargetter: is a child of the union of arithmetics and geometry. Descartes has done some preliminary work, the meta language was invented in the coordinate system.
---
I 364
It allows us to expand the correlation between points in the coordinate system, a line corresponds to a set of number pairs, etc.
Equations: many such quantities can be adequately described by equations.
Example: set of points on a circle line
(x - a)2 + (y - b)² = c².
for fixed numbers a, b and c. This corresponds to a unique set and this is unambiguously equivalent to an equation.
---
I 365
Set theory/Bigelow/Pargetter: reduces not only geometry to numbers and sets, but also numbers to sets. This cleared pure mathematics from empirical concerns.
Modal Realism/Bigelow/Pargetter: pro: for each logically consistent universal, there will be possibilia that instantiate it.
Instantiation/Bigelow/Pargetter: guaranteed by logical consistency.
Platonism/modal realism/Bigelow/Pargetter: our platonism is determined by the fact that we allow actualized uninstantiated universals. ((s) Not instantiated in the actual world).
N.B.: then we do not need set theory to guarantee instantiations of geometric proportions a priori. They can be studied whether or not they are instantiated in the real world.
---
I 366
Set theory/Bigelow/Pargetter: nevertheless, we say that there are sets of numbers that correspond to possible objects. One and the same geometric figure corresponds to an infinite number of different sets of pairs of numbers. ((s) The figure can be moved in the coordinate system).
These different sets of number pairs have something in common, even if they do not have two pairs of numbers in common: a universal.
Sets/Bigelow/Pargetter: they exist whether or not one detects them.
Universals/Bigelow/Pargetter: also exist, e.g. if you discover that two equations are in the same relation to pairs of numbers: they have the same extension.
_____________
Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990
> Counter arguments against Bigelow
> Counter arguments in relation to Set Theory
> Export as BibTeX Datei
Ed. Martin Schulz, access date 2018-05-26 | 734 | 3,332 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2018-22 | latest | en | 0.914669 |
https://intecexpo.com/faqs/why-every-integer-is-a-whole-number/ | 1,669,744,893,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710710.91/warc/CC-MAIN-20221129164449-20221129194449-00524.warc.gz | 381,050,699 | 7,611 | # Why Every Integer Is a Whole Number?
August 16, 2022
Each integer starts at 0 and can be either positive or negative. But integers start at 0 up to positive numbers, so integers cannot be negative. So it would be wrong to say that every integer is an integer.
## Why is every integer number is a whole number?
Any integer is not an integer . Therefore the given statement is wrong. So the correct answer is “WRONG”. Note: an integer can be positive or negative, while whole numbers are only positive.
## Is every integer a whole number?
All integers are integers. All integers are integers.
## Which statement is true every integer is a whole number?
Summary: The statement “Every natural number is an integer” is true, the statements “Every integer is an integer” and “Every rational number is an integer” are false.
## What is called whole number?
Integers are the numbers without fractions and it is a collection of positive integers and zero. It is represented by the symbol “W” and the numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ……………}. Zero as a whole represents nothing or a null value.
## Why zero is a whole number?
All integers are the part of integers that starts with zero and ends at infinity. Since we know that integers are the numbers that can be created by adding and subtracting ones. Suppose if we add 1+1, we get 2, which is an integer. Therefore, 0 is an integer.
## Is every integer a natural number?
Therefore, any integer is not a natural number.
## Is every integer is a rational number?
So we can conclude that every integer can be written in terms of a rational number, which has the form of p/q. ∴ The given statement is true. Every integer is a rational number.
## What is every integer?
Answer: Every integer is a rational number. The statement is true. An integer is a number with no decimal or fractional part from the set of negative and positive numbers, including zero.
## What is the difference between whole number and integer?
Integers are all natural numbers including 0, e.g. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart, e.g. … -4, -3, -2, -1, 0.1, 2, 3, 4,… where a and b are both integers.
## Is a whole number True or False give reason?
Question. Each integer starts at 0 and can be either positive or negative. But integers start at 0 up to positive numbers, so integers cannot be negative. So it would be wrong to say that every integer is an integer. Therefore any integer is not an integer.. | 596 | 2,499 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2022-49 | latest | en | 0.903206 |
https://www.edplace.com/worksheet_info/maths/keystage2/year6/topic/940/2060/geometry:-whats-the-angle | 1,723,059,221,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640707024.37/warc/CC-MAIN-20240807174317-20240807204317-00878.warc.gz | 585,752,545 | 12,616 | # Use a Variety of Rules to Find the Missing Angle
In this worksheet, students will answer a variety of angle-based questions.
Key stage: KS 2
Curriculum topic: Geometry: Properties of Shapes
Curriculum subtopic: Compare Shape Properties
Popular topics: Angles worksheets, Geometry worksheets
Difficulty level:
#### Worksheet Overview
What can you remember about angle rules?
You might not recall them all, but there are probably some that you already know.
Here are the most important ones to remember:
right angle is 90º
The angles inside a triangle add up to 180º
The angles around a point add up to 360º
straight line angle is 180º
These other ones involve remembering some names too!
An acute angle is less than 90º
Easy to remember because 'a cute' kitten is very small!
An obtuse angle is between 90º and 180º
A reflex angle is between 180º and 360º
How many of those did you already know?
Let's have a go at applying some of these rules in the questions that follow.
You can look back at this page by clicking the red help button on the right of the screen at any point.
### What is EdPlace?
We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.
Get started | 336 | 1,505 | {"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-2024-33 | latest | en | 0.910514 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.