Chapter 4.1 Marginal Functions in Economics
___________ Cost: Suppose that C ( x ) describes the cost function for producing x number of a certain product. Then the ___________ cost is the derivative of the cost function, C ( x) , and measures the rate of ________ of the cost function ______________ the number of units ______________. Note 1: The marginal cost for a particular value of x is the ___________ cost of one __________ unit of production. ___________ Revenue Function: R( x) px xf ( x) , where p f ( x) is the unit ________ function and x the __________ of units sold. Note 2: The unit price function comes from solving the ___________ equation in x and p for ____. ___________ Revenue: Suppose that R( x ) describes the revenue function for selling x number of a certain product. Then the ___________ revenue is the derivative of the revenue function, R( x) , and measures the rate of ________ of the revenue function ______________ the number of units ______________.

2

Note 3: R( x)

d xf ( x) dx

.

Note 4: The marginal revenue for a particular value of x is the ___________ revenue of one __________ unit sold. ___________ Profit: Suppose that P( x ) describes the profit function for producing and selling x number of a certain product. Then the ___________ profit is the derivative of the profit function, P( x) , and measures the rate of ________ of the profit function ______________ the number of units ______________ and ______________. Note 5: The marginal profit for a particular value of x is the ___________ profit of one ___________ unit of production. ___________ Cost Function: Suppose C ( x ) is a total cost function. Then the ___________ cost function, denoted by C ( x ) , is C ( x) Note 6: C ( x ) is read C bar of x. Note 7: Similarly, ___________ revenue and ___________ profit are defined. .

3

___________ Average Cost: Suppose that C ( x ) describes the cost function for producing x number of a certain product....

...1
Class X Mathematics Chapter 2: Polynomials Chapter Notes Top Definitions 1. A polynomial p(x) in one variable x is an algebraic expression in x of the form p(x) = anxn an1xn1 an 2 xn 2 ........ a2 x2 a1x a0 , where (i) a0 , a1, a2......an are constants (ii)x is a variable (iii) a0 , a1, a2......an are respectively the coefficients of xi. (iv) Each of anxn an1xn1, an 2 xn 2 ,........a2 x 2 , a1x, a0 , with an 0, is called a term of a polynomial. 2. 3. 4. The highest exponent of the variable in a polynomial is called the degree of the polynomial. A polynomial of degree one is called a linear polynomial. It is of the form ax + b. Examples: x-2, 4y+89, 3x-z. A polynomial of degree two is called a quadratic polynomial. It is of the form ax2 + bx + c. where a, b, c are real numbers and a 0 Examples: x2-2x+5, x2-3x etc. A polynomial of degree 3 is called a cubic polynomial and has the general form ax3 + bx2 + c x +d. For example: x3 2 x 2 2 x 5 etc. A real number k is said to be the zero of the polynomial p(x) if p (k) = 0.
5.
6.
Top Concepts: 1. 2. 3. 4. The graph of a polynomial p(x) of degree n can intersects or touch the x axis at atmost n points. A polynomial of degree n has at most n distinct real zeroes. The zero of the polynomial p(x) satisfies the equation p(x) = 0. For any linear polynomial ax+b, zero of the polynomial will be given by the expression (-b/a).
2
5. 6. 7. 8. 9. 10. The number of...

...block to overcome its state of inertia. A body travelling on an inclined plane due to its weight has an angle of repose, wherein it has a uniform sliding motion. There is no acceleration taking place when the block slides uniformly. No matter what vertical height or horizontal distance is used, the angle of repose will remain the same. The tangent of the angle of repose is always equal to the coefficient of friction of the block.
Coefficient of friction denoted by μ is determined the formula μ=FN f=Friction force, N=normal force. The value of μ has no units since it only serves as a factor between F and N. In order to obtain a constant value for the μ, one has to consider state of equilibrium for the object being experimented. We also took note of the fact that 0 < u < 1.
In cases which there is an angle of repose, all forces involved are being translated with accordance to the surface’s inclination. The weight will now have components that contribute to the sliding of the object. If we have the angle of repose as θ, the components of W contributed to the object in sliding motion are Wsinθ, parallel to the surface and Wcosθ, perpendicular to the surface. Since the system is in equilibrium, Wsinθ is also equaled by the frictional force, while Wcosθ is also equaled by the normal force. In determining μ, it would be μ=FN=WsinθWcosθ=tanθ. Since the θ for the value of μ is also the θ of inclination, therefore in correlation, we can relate μ as equal to the...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...pp. 737-738. Please note that entries must be alphabetized and that the first line of each entry should be flush with the margin, but all successive lines should be indented 5 spaces. This is called a “hanging indent.”
Assignment: Write an essay about a concept that interests you and that you want to study further. When you have a good understanding of the concept, explain it to your readers, using definition, comparison and contrast, cause and effect and/or any other appropriate rhetorical strategies, considering carefully what your readers already know about the topic and how your essay might add to what they know. Be sure to support your explanation with specific facts and examples.
You are required to cite at least seven (7) sources. Two (2) of these may be approved websites and four (4) must be articles originally published in a reputable magazine, newspaper or peer-edited journal. Use the library’s online databases to find such articles. A handout posted on Bb under Content explains how to do this, and we will have a day in the computer lab, or classroom, where I walk you through the process. Please note that, without an individual exception approved by me, you may use no more than two (2) books. All information taken from your sources must be properly documented, using MLA style parenthetical citations along with a Works cited page. SMG, Ch. 27 shows you how to do this. If you have questions at any stage of the process,...

...CHAPTER 15
SS13
Beginning of class
Homemade leverage / arbitrage exercise:
Maverick Corp. has expected earnings of 10 million per year forever and a market value of 100 million dollars. Maverick Corp. has no debt and pays no corporate taxes. Cord Corp. has 10 million per year expected earnings forever. As with Maverick Corp., Cord Corp pays no taxes and expects to continue forever. Cord Corp. has 40 million (market value) in debt outstanding with a 10% return on debt. The equity in Cord Corp has a market value of 80 million dollars. Markets are efficient, the probability of default on debt is zero. Assume that in the stock market no trader is allowed to own more than 40% of the equity of any one corporation. Please describe how you could make arbitrage profits (what must you do) and what your maximum personal gain in wealth would be (profits).
NOTE 40+80 = 120>100
Value of the levered firm > value of the unlevered firm
Arbitrage argument says buy low sell high, sell levered portfolio/buy the unlevered portfolio
(Strategy #2)- “sell short the levered firm (overpriced so we sell the stock short)
Annual interest of r on debt instrument BL for payment of (.10 X 40 million) = 4,000,000
Individual sells short 40% of firm’s stock
Initial Investment Expected cash flow to investor
-{.4(VL – BL)} = {.4(120-40)} -{.4(earnings – r x BL)}=.
=-{.4(80)}=-32 -{.4(10-4)}= -2.4...

...17-19 (“Isn’t it . . . nothing?”)
primarily serves to
(A) reveal the scientific community’s limited
understanding of Noctiluca
(B) imply that some research on luminescence
is flawed
(C) suggest that an adaptation serves no biological
purpose
(D) note an apparent drawback to luminescence
in Noctiluca
(E) indicate that luminescence can serve a variety
of functions
-6-
a hypothesis is most likely accurate
a prediction will probably prove fruitless
a theory is likely to be rejected
an event will probably occur
an observation is likely to be understood
24. A “submarine recharging its batteries at the surface”
(line 71) is most analogous to a
23. The luminescence of Malacosteus (line 50) differs
from that of other species in that it
(A)
(B)
(C)
(D)
(E)
(A)
(B)
(C)
(D)
(E)
is only possible in deep water
temporarily startles other animals
is more obvious near the surface of the ocean
is most likely visible only to a Malacosteus
often protects Malacosteus from its predators
crab temporarily outside of its protective shell
shark continually foraging for food in the ocean
koala living in captivity in a zoo
bat emitting sounds to track an insect
goose flying south for the winter
NOTE: The reading passages in this test are brief excerpts
or adaptations of excerpts from the published material. The ideas
contained in them do not necessarily represent the opinions of
the College Board or Educational...

...Operations Management textbook notes
CHAPTER 1
* Services are deeds, processes and performances. Interactions between customers and service employees and physical resources.
* Roles of services in economy: financial services, manufacturing, distribution services, personal services, government, business, infrastructure
* Services are not peripheral activities but rather an integral part of society
* Stage of economic Activity:
1) Quinary- extending human potential (health, education , research)
2) Quaternary- trade and commerce (transportation, com, finance, govt)
3) Teritary- domestic services- restaurants, hotels, laundry
4) Secondary- manufacturing, processing
5) Primary- agriculture, mining
* Clark Fisher Hypothesis: classification of economies by noting the activity of the majority of the workforce.
* PREINDUSTRIAL SOCIETY: productivity is low and bears little evidence of technology. Social life revolves around the extended household, a lot unemployment. Tradition , routine, authority
* INDUSTRIAL SOCIETY: production of goods, make more with less. Life is machine paced. Standard of living measured by Quantity of good. Bureaucracy and hierarchy
* POST INDUSTRIAL: quality of life, services such as health ,education and recreation. Information is key source.
* The consumer service experience is adding value by engaging and connecting with the customer in a personal and memorable way....

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