By Expressing diagonals as vectors, and using the definition of the .pdf

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By Expressing diagonals as vectors, and using the definition of the dot product, find the smaller angle between any two diagonals of a cube, where each diagonal connects diametrically opposite corners and passes through the center of the cube. Solution vectors of diagonal will be from (0,0,0) to (a,a,a) d1 = ai +aj + ak from( a,0,0) to (0,a,a) d2 = -ai + aj + ak cos = d1 . d2 / { |d1| |d2| } d1.d2 = -a^2 + a^2 + a^2 =a^2 |d1| = 3 a |d2| = 3 a cos = a^2 /3 a^2 = 1/3 = cos-1(1/3).

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$By Expressing diagonals as vectors, and using the definition of the dot product, find the smaller angle between any two diagonals of a cube, where each diagonal connects diametrically opposite corners and passes through the center of the cube. Solution vectors of diagonal will be from (0,0,0) to (a,a,a) d1 = ai +aj + ak from( a,0,0) to (0,a,a) d2 = -ai + aj + ak cos = d1 . d2 / { |d1| |d2| } d1.d2 = -a^2 + a^2 + a^2 =a^2 |d1| = 3 a |d2| = 3 a cos = a^2 /3 a^2 = 1/3 = cos-1(1/3)$

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Business Law In the following situations, two parties claim the same goods. Discuss who is most likely to prevail in each circumstance. Explain the basis for your response. (a) Olan steals Phil Solution O stolen the television of P and sells it to Q. In a sale, the title of ownership transfers from seller to buyer. As the seller stolen the television, he will have no ownership on that and eventually the buyer will not get any ownership. The ownership is still with its owner, P. So P has right to demand for return S is in the business of selling television sets. The sale of television is a part of the course of business. So T gets the title and R cannot demand it back. The merchant S can be made liable for the television..

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Business Law Class MSA CH.05 Criminal Law (2) set 10 William Parks, a special agent of the U.S. Customs Service, was investigating allegations that Bet-Air, Inc. (a seller of spare aviation parts and supplies) had supplied restricted military parts to Iran. Parks entered Bet-Air\'s property and removed a bag of shredded documents from a garbage dumpster. The dumpster was located near the Bet-Air offices in a parking area reserved for the firm\'s employees. To reach the dumpster, Parks had to travel 40 yards on a private paved road. No signs indicated that the road was private. In later judicial proceedings, Parks testified that at the time he traveled on the road, he did not know he was on Bet-Air\'s property. When reconstructed, some of the previously shredded documents contained information seemingly relevant to the investigation. Parks used the shredded documents and the information they revealed as the basis for obtaining a warrant to search the Bet-Air premises. In executing the search warrant, Parks and other law enforcement officers seized numerous documents and Bet- Air records. A federal grand jury indicted Bet-Air\'s chairman, Terence Hall, and other defendants on various counts related to the alleged supplying of restricted military parts to Iran. Contending that the Fourth Amendment had been violated, Hall filed a motion asking the court to suppress (i.e., exclude) all evidence derived from the warrantless search of the dumpster and all evidence seized during the search of the Bet-Air premises (the search pursuant to the warrant). The federal district court denied Hall\'s motion. Following a jury trial, Hall was convicted on all counts and sentenced to prison. He appealed, again arguing that the Fourth Amendment was violated. How did the appellate court rule? Was there a Fourth Amendment violation? Solution Answer:Hatchett, Circuit Judge In California v. Greenwood (1988), the Supreme Court held that a warrantless search and seizure of garbage left in a plastic bag on the curb in front of, but outside the curtilage of, a private house did not violate the Fourth Amendment. The Court held that such a search would only violate the Fourth Amendment if the persons discarding the garbage manifested a subjective expectation of privacy in their garbage that society accepts as objectively reasonable. The Court concluded that Greenwood had exposed his garbage to the public sufficiently to render his subjective expectation of privacy objectively unreasonable. Hall points to the fact that Parks obtained documents that were shredded, then placed inside a green garbage bag, which was in turn placed inside a garbage dumpster. We believe that the manner in which Bet-Air disposed of its garbage serves only to demonstrate that Bet-Air manifested a subjective expectation of privacy in its discarded garbage. Whether Parks\'s actions were proscribed by the Fourth Amendment, however, turns on whether society is prepared to accept Bet-Air\'s subjective e.

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