Siddharth D.

Graduate Computer Engineering Student at NYU

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Organic Chemistry

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Question:

What is the difference between an Alkane, Alkene and Alkyne?

Siddharth D.

Answer:

The simple difference between them is that the hydrocarbons with single bonds are Alkanes, those with a double bond are Alkenes and the hydrocarbons that have a triple bond are Alkynes.

Set Theory

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Question:

Suppose Walter’s online music store conducts a customer survey to determine the preferences of its customers. Customers are asked what type of music they like. They may choose from the following categories: Pop (P), Jazz (J), Classical (C), and none of the above (N). Of 100 customers some of the results are as follows: 44 like Classical 27 like all three 15 like only Pop 10 like Jazz and Classical, but not Pop How many like Classical but not Jazz?

Siddharth D.

Answer:

This can be solved easily as follows: There are n(C) = 44 total that like Classical, and n(C ∩ J) = 27 + 10 = 37 that like both Jazz and Classical, so 44 − 37 = 7 like Classical but not Jazz.

Algebra

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Question:

Solving quadratic equations can be done in various ways: For eg: Given the problem Solve x2 + bx + c = 0, find a number that completes the square of x^2 + bx to get to an equivalent equation of the form Solve (x - d)^2 = f, that can be solved as in the above example.

Siddharth D.

Answer:

Here is how we can solve it: Solve x^2 - 2x - 6 = 0. x^2 - 2x = 6 Rewrite equation x^2 - 2x + 1 = 6 + 1 Add square of ½ coefficient of x term to both sides (this is the completing the square step) (x - 1)2 = 7 Factor left hand side into it's perfect square x - 1 = ± Square root property x = 1 ± Solve for x x = 1 + x = 1 - Two solutions This is called the 'Solving by Completing the square' method.

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