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