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How many vertices does a square pyramid have

Square Pyramid Vertices

What is a vertex?
A vertex is a corner.

The picture above has a square pyramid looked at from the top, directly up front, and from an angle.

Using the picture above, it is clear that a square pyramid has 5 corners, or vertices.

Other fun facts
A face : is a side of a shape
An edge : is a border

A square pyramid also has five faces and 8 edges.

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September 2nd 2010 @ 15:37

Posted By: Caren Chan - Category: No Category

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How to Simplify Square Roots

Square roots like to hurt students by being unneedingly complicated. At least simplifying them is a simple enough task.

Simplifying square roots with only numbers in them.

They key is to factorize it into as many squares as possible.

Common squares are: 4, 9, 16, and 25.

Square root is represented with V

V(236) = V(4 * 59) - First you write into factors
V(236) = 2V(* 59) - Second you take out squares. 2^2 = 4, so 4 becomes 2 when taken out

59 is actually a prime number. If you didn't know that, it's easy enough to "guess". Try dividing a number by 2,3,5,7, 11, and 13. Chances are if it can't be divided by those, then it's probably prime.

Let's try another example.

V252 - It's even, let's try 4.
V252 = V(4 * 63) - 56 has digits that add up to 9 so it's divisible by 3, let's try 9.
V252 = V(4 * 9 * 7) - 7 is prime and the others are squares. You're done factoring.
V252 = 2 * 3 * V(7) = 6V7

If you're unsure of squares, you can always do a full prime factorization.
V252 - it's even let's try 2
V252 = V(2 * 126)
V252 = V(2 * 2 * 63)
V252 = V(2 * 2 * 3 * 21)
V252 = V(2 * 2 * 3 * 3 * 7).
Notice there are 2 2's and 2 3's?
So if you don't like dealing with squares, you can instead pair off factors. Same thing, but it makes it harder to accidentally write down the wrong number.
V252 =V([2 * 2 ]* [3 * 3] * 7).
V252 = 2 * 3V 7 = 6V7

Simplifying square roots with negative numbers in them.
Same as with regular numbers or expressions, but you put an i.

So see how we established that V252 = 6V7? What about V-252? Well it's 6iV7. You just take that negative sign and put it out in front as an i

Simplifying square roots with variables.
Divide the exponent of the variable by 2. Whatever it divides by becomes the front. Whatever remains (1) is left in.
V(x^2) = x because 2/2 = 1
V(x ^ 4) = 2x because 4/2 = 2
V(x ^ 6) = 3x because 6/2 = 3

Vx= Vx because 1/2 = 0 remainder 1
V(x^3) = xVx because 3/2 = 1 remainder 1
V(x^5) = x^2 Vx because 5/2 = 2 remainder 1

What about negative exponents?
V(x^-2) = x^-1
V(x^-3) = x^-1 √ x^-1

If you have a multiplication of both numbers and variables, treat them as normal
V(4x^2 y ^ 3) = 2xyVy

What about division?
If you see 4/9, don't think of it as 4 divided by 9. Think of it as 4 * 1/9
V(4 * (1/9)) is obviously 2* (1/3) or 2/3

Because 1/9 is nothing more than 1/3 squared. It's the same principle as negative exponents (since a division is nothing more than a negative exponent)

And if there are - and plus signs?
Then you have a whole new can of worms. You CANNOT treat them separately
V(4 plus 9) is not the same as [V(4*9) = 2*3 = 6]. Sadly when you see a plus or - sign, you will to perform the operation first, then hope you can still simplify.

V(4 plus x) cannot be simplified
V( (4 plus x) ^2 simplifies to (4 plus x). Why? Well remember you can take out expressions if they have exponents.
V (4 plus x)^3 = (4 plus x)V(4 plus x) same principle applies to odd exponents as well
V (2 plus (4 - x)^2) You cannot take the 4 plus x out there because it is attached to that 2. It's an all or nothing hope. In that case you'd have to actually multiply out the square, add the two, and hope the result is also a square. It isn't.

Picture Credit: Wikimedia Commons by Yves Baelde

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September 2nd 2010 @ 13:22

Posted By: Caren Chan - Category: No Category

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Snickers Candy Questions

I want one now...

Who invented the snickers candy bar?
If you wondered who makes snickers candy bars, the Mars company invented the candy bar. The Mars company obviously also makes Mars and was founded by Frank Mars.

Where was the snickers candy bar invented
In the 1930's. Obviously, it's good candy to remain so popular for this long.

Where are snickers candy bars manufactured
Snickers candy bars are manufactured in Mars factories. These are located in the US.

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September 2nd 2010 @ 02:03

Posted By: Caren Chan - Category: No Category

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