# Tutor profile: Brian B.

## Questions

### Subject: SAT

Consider these two SAT questions. 1 is from a no calculator math section, and 2 is from a language section. 1) The equation below shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? $$C=\frac{5}{9}(F-32)$$ I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $$\frac{5}{9}$$ degree Celsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of $$\frac{5}{9}$$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I only B) II only C) III only D) I and II only 2) Read the following passage. Afterwards, select the edit which improves the section written in parenthesis. If the section is already written in the most correct way, choose "NO CHANGE". Ulysses S. Grant: An Unusual Leader On March 10th, 1864, President Abraham Lincoln signed a brief document officially promoting then-Major General Ulysses S. Grant to the rank of Lieutenant General of the U.S. Army, tasking the future president with the job (of being the leader of all the Union troops) against the Confederate Army. A) NO CHANGE B) of leading all of the troops that were union C) of leading all union troops D) of Union leader for all of the troops

1) D is the most correct answer. This can be reached one of two ways. Mathematically, the formula can be treated like the equation of a line: $$y=mx+b$$ If the $$\frac{5}{9}$$ is multiplied through the parentheses, the formula becomes: $$C=\frac{5}{9}F-\frac{5}{9}(32)$$ The last term $$\frac{5}{9}(32)$$ is a constant. Since we're only looking at how this formula changes with different inputs, it can be ignored. The Formula then becomes: $$C=\frac{5}{9}F$$ The slope of this line is $$\frac{5}{9}$$. That means that for every 1 degree increase of F, C increases by $$\frac{5}{9}$$. That means statement I is TRUE. Similarly, if 1 is input as C's value, you can solve for F to get $$\frac{9}{5}$$ which is the decimal 1.8. This means statement II is TRUE. Here we can already see D is the answer. In the real SAT setting, since time is short, you would want to stop here and move on to the next question. For the sake of learning though, let's see why statement III is FALSE. If you plug in $$\frac{5}{9}$$ for F, you find that C works out to be $$\frac{25}{81}$$. Since $$\frac{25}{81}$$ is not 1, the statement is FALSE. If you saw this question and the linear equations did not seem obvious, don't panic! The problem can also be solved with a little bit of logic. Logical and systematic approaches to problems are key to high scores on the Math portions of the SAT. While not every problem can be solved this way, it's usually a good strategy when an answer or tactic isn't immediately apparent. Sometimes it will even be faster to solve the problem this way than the intended solution! And even if approaching a problem logically doesn't leave you with one answer, it can often eliminate 1 or 2 answers which might help you make an educated guess at the answer. To solve this problem logically, follow through with each statement. Statement 1 reads: I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $$\frac{5}{9}$$ degree Celsius. We can perform a quick experiment to test this statement and see what a 1 degree increase of F would do. First plug in 0 for F. The resulting C value is $$\frac{160}{9}$$. Next plug in 1 for F. The resulting C value is $$\frac{165}{9}$$. Since the rule given by statement 1 is shown here, we can conclude from our experiment that statement 1 is true! Statement 2 reads: II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. We can perform a similar experiment here. When 0 is plugged in for C, F can be solved to get 32. You could also use some knowledge from science class to intuit that 32 degrees Fahrenheit is the same as 0 degrees Celsius. Next plug in 1 for C. F comes out to be 33.8, thus proving that statement 2 is true! Like last time, you'd want to stop here and answer D on the real test, but for the sake of the exercise, let's look at statement 3 logically. Statement 3 reads: III. A temperature increase of $$\frac{5}{9}$$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. We know from experiment 1 that if we plug in 0 for F, we'll get $$\frac{160}{9}$$ out. So, let's see what happens when we plug in $$\frac{5}{9}$$ for F. C comes out as $$\frac{-1415}{9}$$ which is not equal to 1, so statement 3 is false! This confirms that the answer is D. 2) Choice C is the most correct way of writing that phrase. The original version is overly wordy and confusing to read, so A is definitely wrong. Choices B and D are also both wordy and redundant. Choice C says the information that needs to be said in the most concise and elegant way, so it is most correct. These editing questions can get tricky. A good strategy is to very quietly read the segments to yourself, or even just move your lips as if you're saying the words. Our brains are a lot better at picking up strange grammar when we speak or hear it than when we read it.

### Subject: Mechanical Engineering

Explain what the Carnot Cycle is and describe its stages. What is Carnot Efficiency and how is it calculated?

The Carnot Cycle is a theoretical Thermodynamic Cycle which postulates the most efficient engine allowed by the laws of Thermodynamics; if the cycle is reversed, it demonstrates the most efficient refrigeration system allowed. The efficiency of the Carnot Cycle can never be achieved by a real engine or refrigeration system--it is purely theoretical. A Carnot engine consists of two heat reservoirs with starting temperatures $$T_H$$ and $$T_C$$, simply, Hot and Cold. These reservoirs are infinitely large and thus are unaffected by a single cycle. The cycle is reversible and thus does not generate entropy, meaning entropy is conserved. An The Carnot Cycle has four distinct stages: 1) Isothermal expansion of the working fluid at temperature $$T_H$$. The expanding gas does work to move the piston of the engine, and entropy increases. 2) Isentropic expansion of the working fluid. The gas continues to do work and expand, thus losing internal energy. At the end of stage 2, the temperature drops to $$T_C$$. 3) Isothermal compression of the working fluid at temperature $$T_C$$. The surroundings do work on the gas, retracting the piston, and removing heat from the system. This decreases the system's entropy by the same magnitude it increased in Stage 1. 4) Adiabatic compression of the working fluid. The piston further compresses the gas, increasing its internal energy and temperature to reach $$T_H$$. By the end of this stage, the working fluid is in the same state it was at in Stage 1. Carnot Efficiency is the theoretical efficiency of a Carnot Cycle. It is calculated using the formula: $$ \frac{T_H-T_C}{T_H} $$ This value is usually expressed as a percentage rather than a decimal.

### Subject: Film and Theater

Using Freytag's Pyramid, analyze the dramatic structure of Sophocles's Oedipus Rex.

According to Freytag's Pyramid, the classical dramatic structure can be broken down into 7 basic steps: Exposition, Inciting Incident, Rising Action, Complication, Climax, Reversal, Falling Action, Resolution, and Denouement. In the case of Oedipus Rex, the exposition we're given states that Thebes is in crisis because of a plague ravaging the city. The start of this plague coincided with the rise of Thebes's new king, Oedipus, who took the throne after defeating the monstrous Sphinx who was terrorizing the city. We learn that Oedipus and Jocasta, his wife and queen of Thebes, have sent their brother, Creon, to the Oracle at Delphi in search of answers about the mysterious plague. The inciting incident occurs once Creon returns to Thebes with chilling news from the Orcacle. He claims that the plague is divine punishment from the gods for letting the murderer of Thebes' previous king, Laius, go unpunished. Oedipus vows to discover who the murder is and bring him to justice; this is what leads us into the Rising Action of the play. Oedipus sends for the blind prophet Tiresias, a wise elder of Thebes, to help shed light on the situation. At first, Tiresias refuses to tell Oedipus what he knows, claiming Oedipus will greatly regret the knowledge. After Oedipus threatens to charge Tiresias with complacency in Laius's murder, Tiresias reluctantly informs Oedipus that he himself is the murderer. Oedipus is in disbelief of this claim and accuses Tiresias of conspiring with Creon to dethrone him. Outraged, Tiresias storms away with the puzzling decree that the murderer is a native citizen of Thebes who is father and brother to his own children, and son and husband to his own mother. Oedipus then summons Creon accusing him of treason; he's stopped short of sentencing him to death by Jocasta and the Chorus. Jocasta then attempts to comfort Oedipus by telling him of when she and her previous husband, Laius, had been given false information by an oracle. The prophecy they were given claimed that Laius would be killed by his own son. Jocasta concludes this must not have been true since it's thought Laius was killed by bandits on the crossroads to Delphi. In addition, Laius had tasked Jocasta with killing their firstborn son as to assure the prophecy would not come true. Upon hearing this story, Oedipus starts to develop a harrowing theory. On his way to Thebes, Oedipus had killed a man over a dispute about their chariots. He begins to fear that that man may have been Laius. In hopes to disprove himself, Oedipus calls for a Shepherd who'd claimed witness to the murder. Before the Shepherd arrives, a Messenger comes to tell Oedipus the news that his father, Polybus, had died. This moment is what initiates the play's Complication. Relieved by this news, Oedipus initially believes Tiresias's claims to be false. Things begin to darken, however, once the Messenger reveals he used to be a shepherd. The Messenger claims that once, another shepherd had placed a baby in his care. The Messenger had passed this baby on to Polybus to raise as his own. Oedipus then learns from the Chorus that the shepherd who gave the Messenger the baby is the Shepherd who had witnessed Laius's murder. Jocasta now realizes the truth and begs Oedipus to stop his search. He refuses and Jocasta manically flees into the palace. The Shepherd arrives and he too begs Oedipus to stop his search, but once he's threatened with execution, the Shepherd states that Jocasta had tasked him with abandoning her baby on top of a mountain, as she didn't have the heart to carry out the murder herself. The Shepherd reveals that he too could not commit the act and, instead, gave the child to another shepherd, the Messenger. With this, the Shepherd confirms everything foretold in both prophecies. This is the climax of the play. In the gruesome Reversal, Jocasta hangs herself out of grief. Upon seeing her body, Oedipus takes the golden pins from her dress and gouges his eyes out with them. This begins the play's falling action. Oedipus addresses the people of Thebes and announces that he will keep to his word and punish Laius's murderer. In doing so, Oedipus exiles himself from the city. As he leaves, Oedipus tasks Creon with taking up the throne, and raising Oedipus's daughters, Antigone and Ismene. This is the play's true denouement, and it ends with Creon upholding Oedipus's request as the Chorus recites a final warning to the audience.

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