Question 1
A function is the mathematical way of describing a relationship between two sets of variables. In usual notation, the set of the independent variables x, is called the domain and the set of the dependent variables y is termed the range.
Most commonly encountered functions are
The linear function y = x, the quadratic function y = x2, the cubic function
y = x3, the exponential function y = ex, the logarithmic function y = log(x), and periodic functions such as y = cos x, y = sin x, the set of the variable quantity x is the domain, and the set of the corresponding values of the variable y constitutes the range.
Below I reproduce (courtesy of the mathsisfun website,
www.mathsisfun.com/sets/functions-common.html), in descending order,
the linear, quadratic,
cubic, logarithmic,
the sine, and the exponential functions graphs.
Question 2
Carbon dating is the method whereby the age of very old objects is estimated.
The method consists of measuring the current radioactivity of the specimen due to its unstable (and rare) carbon isotope 14C content and comparing it with the average background radioactivity of the atmosphere. (Willard Libby 1947). The specimen must contain remains of a plant. So long as the plant was alive its radioactivity due to the intake of CO2 from the atmosphere was equal to the radioactivity of the atmosphere however when it died, the amount of 14C in it began to fall due to the radioactive decay of this element into nitrogen (14N). The half-life of 14C, defined by T_(1/2)=(ln(2))/λ, can be measured experimentally and is found to have the value 1.808 ×〖10〗^11 seconds. The above expression results from the fact that nuclear decay, and therefore the radioactivity of a radioactive...
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... mount Everest at 8863 m from the surface of the Earth, and using the known values of the weighted molar masses of oxygen and nitrogen, the gravitational acceleration constant, the gas constant, and assuming a temperature of 273 K (or 0 degrees Celsius), (Calter and Calter, 2011.) we obtain a pressure of about 0.034 mega pascal which is equivalent to 0.33 atmosphere which is a third of what we have at sea level.
References
1 P. Calter and M. Calter, Technical Mathematics, 6th ed. Jonh Wiley and Sons, 2011.
2 The Wolfram Functions Site,
www.functions.wolfram.com.
3 D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, John Wiley and Sons, 2005 (chapter 44).
4 Willard Libby – Noble Lecture: Radiocarbon Dating,
www.nobelprize.org/nobel_prizes/chemistry.
5 P. Schmidt and F. Ayers, Schaum’s Outline of College Mathematics, McGraw-Hill Companies, 2010.
4. Identify the layer of the Earth in the diagram to the right which makes up 70% of the Earth’s mass and is mostly solid but capable of flow, causing changes in the Earth’s surface. (S6E5a)
Ever since people knew it was possible to reach the summits of Mount Everest about 4,000 people have attempted to climb it and a one in four ratio of people have died from doing so. “Once Everest was determined to be the highest summit on earth, it was only a matter of time before people decided that Everest needed to be climbed” (Krakauer 13). The very first person to reach the summits of Mount Everest was in 1953 also ever since then about seven percent out of every 4,000
Potassium-40 (40K) is a radioactive material that decays into argon-40 (40Ar). The half-life of a sample of 40K is 1.3 billion years. Rocks containing 40K have been around since the formation of the earth, and 40Ar gas has been accumulating in those rocks since the earth formed. However, when rocks are heated by volcanic action, all the 40Ar leaves the rock when the gases escape. Create a scenario and discuss, based on your knowledge of half-life, the value of potassium-argon dating to geologists.
5. Collected Papers, Charles Hartshorne and Paul Weiss, (edd.) (Cambridge: The Belknap Press of Harvard University Press, 1960). Volume and page number, respectively, noted in the text.
An exponential equation is a type of transcendental equation, or equation that can be solved for one factor in terms of another. An exponential function f with base a is denoted by f (x) = ax, where a is greater than 0, a can not equal 1, and x is any real number. The base 1 is excluded because 1 to any power yields 1. For example, 1 to the fourth power is 1×1×1×1, which equals 1. That is a constant function which is not exponential, so 1 is not allowed to be the base of an exponential equation. Otherwise, the base of a can be any number that is greater than 0 and isn’t 1, and x can be any real number. The equation for the parent function of an exponential functions follows as so:
Boccaccio, Giovanni. Decameron. Ed. Charles Singleton. Trans. John Payne. Berkeley: U of California P, 1982.
In the graph, it shows the law of demand; as the price increase there is a decrease in the quan...
A change in quantity supplied is just a movement from one point to another in the supply curve. In opposite, the cause of a change in supply is a change in one the determinants of supply that shifts the curve either to the left or the right. These determinants are the resource prices, technology, taxes and subsidies, producer expectations, and number of sellers. An equilibrium price is required to produce an equilibrium quantity and a price below that amount is referred as quantity supplied of zero no firms that are entering that particular business. If the coefficient of price is greater than zero, as the price of the output goes up, firms wants to produce more of that output. As the price of the output goes up it becomes more appealing for the firms to shift resources into the production of that output. Therefore, the slope of a supply curve is the change in price divided by the change in quantity. The constant in this equation is something less (negative number always) than zero because it requires strictly a positive...
Fowler, Michael. “Modern Physics.” Lecture. Mass and Energy. 1 Mar. 2008. Web. 13 Oct. 2013.
Kirkpatrick, Larry D. and Gerald F. Wheeler. Physics: A World View, 4th ed. Orlando, FL. Harcourt College Publishers: 2001. p- 365-71
Radiocarbon dating is used to tell how old something is. When some normal carbon gets hit by the rays of the sun it turns into carbon 14. Plants absorb this radioactive carbon in the form of carbon dioxide. Animals receive this carbon from eating the plants. When the organism is dead it loses the carbon 14. Scientists can tell how old something is based on the amount of carbon 14 in a dead object. Carbon dating is accurate if the amount of carbon 14 in the atmosphere has remained the same throughout time. The second is if carbon 14 has always decayed at the same
H. Young, & R. Geller, Sears & Zemansky's College Physics, 8th ed., (Pearson Education Inc., San Francisco, 2007), pp. 422-426, 428, 430-431.
slope. I think that out of all the variables, this is the one which is
2) Fundamentals of Physics Extended: Fifth Edition. David Hanley, Robert Resnick, Jearl Walker. Published by John Wiley & Sons, Inc, New York, Chichester, Brisbane, Toronto, Singapore. 1997.
Serway, Raymond A, and Robert J Beichner. Physics: For Scientists and Engineers. United States of