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Math Homework Help

Right Foot Forward

published on November 20th, 2007 . by Vanaja

A short man takes three steps to a tall man’s two steps. They both start out on the left foot. How many steps do they have to take before they are both are stepping out on the right foot together?

Ans:

Very simple. biggrin

A Puzzle In Paradox

published on November 1st, 2007 . by Vanaja
Thirteen teachers are in Paradox, a math conference. When they arrive at the Enigma Hotel to check in, they are told that only 12 rooms are available. Since their school had made reservations for 13 rooms, the teachers are a bit upset that they will have to find another place to stay. As they are preparing to leave and find another hotel, the manager comes out and asks if there is a problem. When she hears of their situation she assures them that the Enigma Hotel has enough space to accommodate each teacher in his or her own room. She takes two of the teachers to room #1 and promises to come back in a few minutes and take one of them to another room. She takes the third teacher to room #2, the fourth teacher to room #3, the fifth teacher to room #4 and so on, taking the twelfth teacher to room #11. She then returns to room #1 and escorts the extra teacher waiting there to room #12. All of the teachers are now happily settled in their own rooms.

Is this possible? Why or why not? question

O.K Here is the solution.

Actually, it is not possible. When the manager is putting the 12 th teacher in #11, the 13 th teacher is still waiting there and he or she must go to the #12 room. So, all the rooms are now occupied and in the first room there are two teachers and the teacher waiting there can not go to the #13 room.

Just Relax

published on October 31st, 2007 . by Vanaja

We have been discussing about serious math topics and problems for a long time. We also need some rest from that. So today we can have some math jockes.
Here we go.

Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don’t need the sun!

Q: How does one insult a mathematician?
A: You say: “Your brain is smaller than any eps1ilin >0!”

Q: How does a mathematician induce good behavior in her children?
A: `I’ve told you n times, I’ve told you n+1 times…’

Q: Why do mathematicians often confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25.

Q: What does a mathematician present to his fiancee when he wants to propose?
A: A polynomial ring!

Two math students, a boy and his girlfriend, are going to a fair. They are in line to ride the ferries
The boy says: “It’s a sin for those people to keep us waiting like this!”
The girl replies: “No - it’s a cosin, silly!!!”

HAPPY HALLOWEEN! twisted

Mathematics Of Ice To Aid Global Warming Forecasts

published on September 21st, 2007 . by Vanaja

University of Utah mathematicians have arrived at a new understanding of how salt-saturated ocean water flows through sea ice — a discovery that promises to improve forecasts of how global warming will affect polar icepacks.

In the current issue of the journal Geophysical Research Letters, math Professor Ken Golden and colleagues show that brine moving up or down through floating sea ice follows “universal transport properties.”
“It means that almost the exact same formulas describing how water flows through sedimentary rocks in the Earth’s crust apply to brine flow in sea ice, even though the microstructural details of the rocks are quite different from sea ice,” says Golden, who currently is on an Australian research ship in Antarctica.

(University of Utah mathematician Ken Golden stands in front of sea ice melt ponds in the Arctic near Barrow, Alaska. His research on sea ice’s permeability to salt water promises to help improve forecasts of the effects of global warming. )


The study suggests similar porous materials — including ice on other worlds, such as Jupiter’s icy ocean-covered moon Europa — should follow the same rules, he adds.
Golden has made several trips to Antarctica and the Arctic for his studies.

The American Geophysical Union, which publishes the journal carrying Golden’s study, says sea ice is important because it is both “an indicator and regulator of climate change; its thinning and retreat show the effects of climate warming, and its presence greatly reduces solar heating of the polar oceans.”

“Sea ice also is a primary habitat for microbial communities, sustaining marine food webs,” the group adds. “The permeability of sea ice and its ability to transport brine are important to many problems in geophysics and biology, yet remain poorly understood.”

The AGU says Golden’s study presents “a unified picture of sea ice permeability,” and how that permeability to brine flow varies with the temperature and salinity of the ice.

Icy math and climate change

“One of the most important aspects of the polar sea ice packs is the role they play in Earth’s albedo — whether Earth absorbs or reflects incoming solar radiation,” says Golden. “White sea ice reflects; the ocean absorbs. In the late spring, melt ponds [atop the ice] critically affect the albedo of the polar ice packs. The drainage of these melt ponds is again largely controlled by the permeability of the ice.”

The Intergovernmental Panel on Climate Change’s predictions “that the summer Arctic ice pack may disappear sometime during 2050-2100 depend in part on these types of considerations,” he adds. “Now that we have a much firmer understanding of how permeability depends on the variables of sea ice, namely temperature and salinity, our results can help to provide more realistic representations of sea ice in global climate models, helping to hone the predictions for world climate and the effects of warming.”

The results “can also help in understanding how polar ecosystems respond to climate change,” Golden says. “Biological processes in the polar regions depend on brine flow through sea ice. For example, the rich food webs in the polar oceans are based on algae and bacteria living in the ice, and their nutrient intake is controlled by brine flow.”

“In the Antarctic, ice formed from flooding of ice surfaces is an important component of the ice pack, and this formation is dependent on brine flow,” he adds. “Brine drainage out of sea ice and the subsequent formation of Antarctic bottom water is an important part of the world’s oceans.”
Golden says the formulas that describe brine flow through sea ice and groundwater flow through sediments arose from abstract solid-state physics models used to describe atomic-scale phenomena in metals.

“These formulas exhibit universality, meaning that the end result doesn’t depend on the details of the model or system, only on the dimension of the system,” he says. “While large classes of abstract models obey this principle, real materials often do not. So it is surprising that a complex, real material like sea ice actually obeys these formulas.”

To conduct the study, Golden and colleagues analyzed sea ice and “modeled” or simulated its behavior mathematically, and also made field and laboratory measurements of sea ice, including using X-rays to make CT-scan images of how the microscopic pore structure of ice varies with temperature.

Golden conducted the study with University of Utah colleagues Amy Heaton, a chemistry graduate student, and Jingyi Zhu, an associate professor of mathematics. Other co-authors are from the University of Alaska Fairbanks.

Courtesy: Science Daily.

Mathematical Signs

published on September 15th, 2007 . by Vanaja

If you look at any mathematics book written before 1500’s, it will be very hard to understand.The Hindu -Arabic numerals familiar to us may have been used. Every thing else was different. The signs and symbols that make up the rest of the language of mathematics as we study it today had not yet been invented.

The sign and sign for subtraction first appeared in 1489 in a German arithmetic handbook. They may have been borrowed from signs used by merchants to mark certain packages . A +was marked on packages with too much of whatever the package contained, while a - meant too little.

The sign for multiplication was invented by an Englishman William Oughtredin 1631.

The sign for division was invented earlier by a German mathematician Johann Heinrich Rahn.

The = for “equals” was invented by the English mathematician Robert Recorde in 1557.


A cricket problem

published on September 9th, 2007 . by Vanaja

A group consists of 50 students. Out of these 20 are girls .There are 10 Australian students. Out of 50 students, 25 students like cricket.
What is the probability of selecting an Australian girl who likes cricket?

Hint:

Probability of selecting a girl= 20/50
Probability of selecting an Australian student = 10/50
Probability of a student like cricket=25/50

Therefore the the probability of selecting an Australian girl who likes cricket= (20/50 )(10/50)(25/50) = 1/25 =0.25

Net Problem

published on August 29th, 2007 . by Vanaja

The following is the net representation of a cube.

How will you place the letters L, A, F on the figure so that it should spell LEAF around the sides of the cube?


A football problem

published on August 21st, 2007 . by Vanaja

At a football championship 600 tickets were sold .
Child ticket cost $2 each and adult ticket cost $5 each. The total money collected for the game was $1650.

Find the number of tickets sold in each category.
Hint:
Let x be number of children and y be number of adults.
x+y = 600
2x+5y= 1650
==>x= 450, y=150

What is statistics?

published on August 9th, 2007 . by Vanaja

The word statistics conveys many meanings to people. to some it is another form of mathematics and for some other it suggests charts, graphs and tables which they find in newspapers and many other such things.

The study of statistics involves methods of refining numerical and non-numerical information into useful forms. In addition to meaning data, statitics also refers to a subject just as mathematics or physics. In this sense statistics is a body ofmethods of obtainining and analysing in order to make decisions on them.

Math Problem Solving Techniques

published on June 17th, 2007 . by Vanaja

Life is an arena of problems. L.A Averill has said,”The only worthwhile life is a life which contains its problems; to live without any longings and ambitions is to live only half way”. A human child has to meet and solve problems as he grows-problems which present in his physical surroundings, his intellectual associations and in his social contacts. These problems grow in number and complexity as he or she grows older and older. His success in life is in large measuredetermined by the individual’s capasity and competence to solve them.

Mathematics is a subject of problems.Stydying mathematics is different from studying other subjects. Math is learned by doing problems. Efficiency and ability in solving problems is a guarantee for success in learning this subject.

  1. The first and most important step in solving a problem is to understand the problem.Read the problem clearly and grasp its meaning. Superficial or careless reading does not pay in mathematics. Be sure that you understand clearly what is given and what you are expected to find or prove. Keep these things in mind throughout your work.
  2. Take sufficient time to think.
  3. Plan thoroughly before you start.I dentify which skills and techniques you have learned can be applied to solve the problem at hand.

READ MORE…….

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