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# Tutor profile: Brian B.

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Brian B.
Knowledgeable Mechanical Engineer and Accomplished Theatre Artist
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## Questions

### Subject:SAT

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Question:

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

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Brian B.

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

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Question:

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

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Brian B.

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

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Question:

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

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Brian B.

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