Read: Desperately Seeking Mathematical Truth 1) Explain the roles of axioms, theorems, conjectures, and proofs in relation to mathematical truth/certainty.
2) Identify two reasons why mathematical knowledge may not be true with absolute certainty in all cases.

As oil prices rose during 2006, demand for alternative fuels increased. ethanol, one alternative feul, is made from corn. according to an article in the wall street journal the price of tortillas which are made from corn also rose during 2006. the price spike in tortillas is part of the ripple effect from the ethanol boom. draw demand and supply graph for corn market and use it to show the effect on this market of an increase demand for an ethanol. be sure to indicate the equilibrium price and quantity before and after the increase in demand for ethanol.

Which statement best describes the development of ideas in "sonnet 91"? the quatrains build ideas off of one another, and the couplet conveys a new idea. the quatrains contradict one another, and the couplet resolves their disagreement. the couplet agrees with the idea in the first quatrain but contradicts the others. the couplet builds off of the idea of the third quatrain but contradicts the others.

Of all the attributes essential to a respected man or woman or to a respected nation, the predominant characteristic is self-discipline. laws cannot be made compelling people to suppress their desire for power or position. no method of legislating such wisdom exists. as free people, we must face a choice between two types of discipline. one is the self-discipline that is still open to us—the kind that free people and free nations exercise when they select the executives, lawmakers, and judges who will govern them and assure their protection and well-being. the second is a cold-blooded, ill-intentioned, form of discipline that may be thrust upon us by strangers—the discipline of force, terrorism, suspicion, and intimidation—the discipline used in totalitarian regimes.does every sentence following the first in some way support the theme?