Thanksgiving Turkeys

Math on November 9th, 2009 Comments Off

math tutor turkey
Problem

You have five Turkeys. If you weigh them in every possible combination of 2, the weights are 16, 18, 19, 20, 21, 22, 23, 24, 26, and 27 kg. What are the individual weights?

Solution

Come back next week for the solution.

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SAT Vocabulary

Math on November 8th, 2009 Comments Off

Problem

Odysseus was the most _____ of all Greek Kings. Many tales tell of how his cunning won the day.

(a) primeval
(b) fastidious
(c) archetypal
(d) adroit
(e) punctual

Solution

Come back next week for the solution!

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Sentence Correction

English on October 22nd, 2009 Comments Off

Problem

Identify, name, and correct the error in the following sentence.

“Before I got on the Subway, I had realized that I had forgotten my wallet,” whined Jon, who was on the verge of tears.

Solution

This is an error of verb agreement. The verb realize does not need the past perfect tense, but rather the perfect. It should read “…I realized that I had forgotten my wallet,…”

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Interconnected Pendulums

Math on October 20th, 2009 Comments Off

Phoenix Math Tutoring-pendulums
Problem

The bobs of two pendulums are connected by a spring. When one is moved by an angle (theta) theta and released, what is the resulting motion? Do they eventually have the same energy?

For physics students, let the pendulums length=L, point mass=M, and spring constant=K. Find the equations of motion for both pendulums.

Solution

This is by far the most complicated problem that has ever been on problem of the week. Feel good if you were able to solve part of it. You likely wont be able to take the solution this far until college Physics. If you have a more intuitive solution, please add it to the comments.

For beginners, you’d do well to recognize that the energy will never be equally distributed between the two pendulums. It will be periodic, with one pendulum having all the energy at certain times and the other having none, and then switched.

For advanced students, the Lagrangian (kinetic energy minus potential energy) is given by:

physics tutoring equ1-1

where

physics tutoring equ1-2

The solution to the problem is then path which minimizes the Lagrangian, or the particular solution to the differential equation:

physics tutoring equ1-3

where q is a generalized coordinate.  For anyone who would like an additional challenge, solve this equation and graph some results in MATLAB or your favorite mathematical language.  Small angle assumptions may be used.  This will be the Problem of the Week this week.  Good luck.

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SAT Vocab

English on October 16th, 2009 Comments Off

Problem

Choose the best word to complete the following sentence:

The students _____ the food in the cafeteria, saying that it was the best-tasting school lunch in the citiy.

(A) vilified
(B) extolled
(C) squandered
(D) carped
(E) railed at

Solution

The answer is (B) Extolled, which means to lift up or praise highly.

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Missing Numbers

Math on October 12th, 2009 Comments Off

Problem

Solve this simple arithmetic by replacing each # sign with a different digit, 1-9, using each digit only once. ## represents a two-digit number.

##
x #
—–
## + ## = ##

Solution

When filled in correctly, the equation is:

17
x 4
—–
68 + 25 = 93

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SAT English- Grammar

Math on October 9th, 2009 Comments Off

Problem

Find, name, and correct the error in the sentence below:

Everyone has their own idea about parenting; it’s a hot topic.

Solution

This sentence has a pronoun error. Everyone is a singular subject, thus the pronoun their should be his or her.

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Triple Duel

Math on October 5th, 2009 Comments Off

Phoenix Math Tutoring Cowboy Problem

Three Cowboys Arden, Begley, and Corry compete in a duel. Arden and Begley are both sure shots (they hit their targets 100 percent of the time) while Corry only hits his target 50% of the time. Everybody has perfect knowledge (knows everybody’s percents, knows that everbody knows everybody’s pecents, knows everybody knows that everybody knows everybody’s percents, etc…).

They draw lots to determine the shooting order. Who has the best chance of survival?

Solution

Even though Corry has only a 50 percent chance of hitting his opponent, he actually has the best chance of surviving, at 50 percent. When drawing lots there are three situations that may arise:

  • A shoots first: he will shoot B, and then C will have a 50% chance. A/C have a 50/50 split.
  • B shoots first: same as above. B/C have a 50/50 split.
  • C shoots first: C misses intentionally. Depending on who shoots second, A or B shoots the other, and then C has a 50 percent chance.  Thus A/B/C is 25/25/50.

Overall A has a 25% chance of survival, B has a 25% chance, and C has a 50% chance.

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SAT English- Sentence Correction

English on October 2nd, 2009 Comments Off

Problem

Identify, name, and correct the error in the following sentence.

Carl, please pick me up from the airport quick so we arrive at the baseball game on time.

Solution
The word quick modifies the verb pick up, so it should be an adverb. The sentence should read “Carl, please pick me up from the airport quickly so we arrive at the baseball game on time.”

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Penny Problem

Math on September 28th, 2009 Comments Off

Phoenix Tutoring PenniesProblem

You are given ten pennies arranged like this picture. Move three of them so that the arrow in the opposite direction.

Solution

Take the top penny and move it to a new row, in the center, under the bottom row into the following configuration:

x       x

x        x       x

x       x       x       x

x

Number the rows from top to bottom: 1, 2, 3, and 4. Now take the two outside pennies from row 3 (which has 4 pennies) leaving two, and move them to the outsides of row 1.

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