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# Mostly IT blog

Created on Thu Jul 28, 2011 6:03 am with 15 blog posts
My blog is just a rundown of what I have learnt recently in IT related things. Or it could include other things from time to time.

more inspirational quotes in Main with 1 comments on Wed Apr 04, 2012 6:43 am
Inspirational quotes in Main with 5 comments on Wed Apr 04, 2012 6:01 am
Self-study update in Maths with 3 comments on Tue Dec 06, 2011 5:33 am
Well I haven't forgotten my resolve to re-learn my maths skills.

I have been working on linear equations for a bit. i haven't been able to put anything up on it because it is somewhat more difficult than the arithmetic I revised. And more important in many ways.

Turning worded problems into equations has been challenging and is probably one of the most important maths improvements I can do right now to improving my programming ability. After I get through this chapter, I will continue to practise this particular aspect of maths. I am however enjoying it immensely and feel I am progressing infinatley, albeit slowly.

My programming learning is slower again, but have been looking into try/except/raise but need to go and use them in programs to feel confident.

Over the past bit of time, my maths has overtaken my programming, next week I need to get a bit further in the programming side.
Proportion in Maths with 0 comments on Tue Nov 22, 2011 11:25 pm
"The statement of equality of two ratios is called a proportion."

Find an unknown ratio with a proportion

Eg. If x:4 = 7:12

Make them fractions
make them simple as possible
solve for x
(if x on left, multiply both sides by denominator under x. if x on right, multiply both sides by denominator on opposite and x)

Eg. x:4 = 7:12
x/4 = 7/12
4 * x/4 = 4 * 7/12
x = 28/12
x = 2 and 4/12
x = 2 and 1/3

Eg. If 4: x = 16:20
4/x = 16/20
4/x = 4/5
5x * 4/x = 5x * 4/5
20 = 4x
5 = x

Mean Proportion

"If a: x = x:b, then x is called a mean proportion of a and b."

Make them fractions.
Solve for x

Eg. find a mean proportion of 1 and 2.
1: x = x:2
1/x = x/2
2x * 1/x = 2x * x/2
2 = x^2
plus or minus sqrt.2 = x

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Real Life Application

Gears and belts

tD/tF = rF/rD

That means:

number of teeth on the driver wheel divided by number of teeth on the follower wheel
is equal to
the number of revolutions on the follower wheel divided by the number of revs on the driver wheel.

Note: that they are inverse...

On a belt it is measured, not by teeth, but by the diametre of the wheels. Essentially though, it is the same formula.

dD/dF = rF/rD

Therefore, if you know how many teeth there are, you can figure out how many revolutions by using mean proportion.
Ratio in Maths with 0 comments on Tue Nov 22, 2011 9:36 am
"A ratio is a comparison between two like quantities in the same units."

Simplest form ratios

A ratio, such as a:b can be reduced similarly like fractions, using a lowest common denominator approach.

Eg.
2:4 is the same as
1:2

The example ratios 2:4 and 1:2 are also known as equivalent ratios because they really are the same. See also Proportion.

Finding a ratio between quantities

change into same units, then
put lower one on the left
find the simplest

Eg.
300mls and 1.5litres goes to
300mls and 1500 litres
300:1500
3:15
1:5

Dividing a quantity into ratios

If you are given a ratio and a total, you can work out the ratio amounts thus:
Divide the total by the parts to find 1 part
Times the ratio amount by 1 part.

Eg.
20m total, 2:3
2+3=5
20/5=4
4*2 is 8:4*3 is 12
8 metres, 12 metres.

If you are given a ratio and one part:
Divide value by the ratio amount, gives you multiplying factor
Times factor by other ratio amount, now you know value of both sides