Saturday, September 4th, 2010

If you have a function called ƒ, let’s call its inverse ƒ^{–1} (i.e. ƒ^{–1} is the inverse function of ƒ).

By definition, the property of ƒ^{–1} is that if ƒ(a)=b, then ƒ^{–1}(b)=a. Wikipedia (http://en.wikipedia.org/wiki/Inverse_function) has a good example:

A function ƒ and its inverse ƒ^{–1}. Because ƒ maps a to 3, the inverse ƒ^{–1 } maps 3 back to a. In mathematics, if ƒ is a function from a set A to a set B, then an inverse function for ƒ is a function from B to A, with the property that a round trip from A to B to A (or from B to A to B) returns each element of the initial set to itself.

Monday, July 19th, 2010

### Solution:

You can simply 12 – ( x + 3 ) +10 by rearranging the terms:

- 12 –x -3 +10
- 19-x

Saturday, July 17th, 2010

### Here’s how you solve this type of question:

- Start with an equation like 3x + 5y = 15
- Move 3x to the other side, so 5y = 15 – 3x
- Divide both sides by 5, so y = 3 – x
- Another way of writing this is y = -.6x + 3, or y=mx = b, where m=-0.6 and b = 3
- If m = -0.6, that means that the slope =-0.6

Saturday, July 17th, 2010

### Solution:

This is a well known “trick question”. It’s simply a series of squares with the digits reversed:

1^{2} = 1 => 1

2^{2} = 4 => 4

3^{2} = 9 => 9

4^{2} = 16 => 61

5^{2} = 25 => 52

6^{2} = 36 => 63

7^{2} = 49 => 94

8^{2} = 64 => 46

9^{2} = 81 => 18

Saturday, July 17th, 2010

### Here’s how you solve this type of question:

- The base of the 3D rectangle is in the shape of a 2D rectangle.
- Multiply the length of this 2D rectangle by its width to let the area

Saturday, July 17th, 2010

### Solution:

**The arithmetic mean is the average.**

http://en.wikipedia.org/wiki/Arithmetic_mean

Saturday, July 17th, 2010

### Solution:

Volume of wood is 72*54*48 = 186,624 cmcube; the mass would be 186,624 * 0.9 = 167,961.6 g.

Friday, July 16th, 2010

### Solution:

**If we let the age of the father be “F”, and the age of the son be “S”, then we know the following:**

**1. F = 3 x S**

2. F+S=40

**Therefore, F=3x(40-F)…so 4F=120. **

**Therefore, F=30 and S=10.**