## Wednesday, June 8, 2011

### June Vacation Chap 9.2 RATE (L1) Rate in Everyday Situation

What's defined in Wikipedia: Rate (mathematics)
In mathematics, a rate is a ratio between two measurements, often with different units.[1]. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity. The most common type of rate is "per unit time", such as speed, heart rate and flux. Rates that have a non-time denominator include exchange rates, literacy rates and electric flux.

When we describe the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.

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Rate is commonly used in our daily life. Here are some examples:

40 km/h - 40 kilometres per hour
30 steps/min - 30 steps in per minute
2 l/hour - 2 litres per hour
67 words/min - 60 words per 1 min
80 m/week - 80 metres per week
25km/l - 25 kilometres per 1 litre
\$90/m³ - \$90 per cubic metre

Think of 2 real life situations in which we use the concept of rate to describe useful information.

Here is an example:
The Singapore Flyer rotates at the rate of 0.24 m/s or 0.76 km/h

1. 1) A plane would need to travel at least 1236km/h to break the sound barrier.
(Reference : WolframAlpha, Link is too huge)

2) An iPhone 4 screen would have a density of 326 pixels per inch (ppi)
(Reference : http://www.apple.com/iphone/features/retina-display.html)

2. 1)Sound travels at 340.29m/s.

3. 1) The equator of the earth is moving at 1675km/h
(http://www.universetoday.com/26623/how-fast-does-the-earth-rotate/)

2) Cyclist Miguel Indurain had a resting heart rate of 29 beats/min

(http://en.wikipedia.org/wiki/Heart_rate)

4. Abortion,rates in the USA is 29.3/1,000 women aged 15-44.
http://www.rhrealitycheck.org/blog/2010/03/01/abortion-women-color-bigger-picture

Every year, 8.37/1000 people will die

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

5. 1) Light travels at a rate of 299,792,458m/s
(http://en.wikipedia.org/wiki/Speed_of_light)

2) The fastest car, Bugatti Veyron Super Sport , travels at a rate of 431km/h
(http://www.fastestcar.net/)

6. 1) The death rate in Singapore is 4.95 deaths per 1,000 citizens
(http://www.indexmundi.com/singapore/death_rate.html)

2) The birth rate in Singapore is 8.5 births per 1,000 citizens
(http://www.indexmundi.com/singapore/birth_rate.html)

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8. 1) The average pedestrian walking speed is 1.2 m per second or 1.2m/s
(reference too long)
2) The cost of gold in singapore dollars (SGD) is \$1884.53 per 1 ounce
(reference: http://coinmill.com/XAU_calculator.html)

9. 1) The average number of trees cut down per year is 3-6 billion trees/ year
http://understory.ran.org/2008/04/22/how-many-trees-are-cut-down-every-year/

2)The orbital speed of the Earth averages about 29.8 km/s (107000 km/h)
http://en.wikipedia.org/wiki/Earth

10. 1) The fastest typer in the world is Stella Pajunas-Garnand, who can type 216 words per minute.
(Reference: http://en.wikipedia.org/wiki/Words_per_minute)

2) The average daily traffic of the Golden Gate Bridge is 118,000.
(Reference: http://en.wikipedia.org/wiki/Golden_gate_bridge)

11. 1)light travels at 299792km/s

2)platinum cost SGD\$85.89 per gram
reference:wolfram alpha

12. 1) around 70,000 people die in the world per day

2) 267 people are born per min

13. 1) We can use rate to calculate the fuel efficiency of a vehicle.
eg. car=> 10 liters/km (normal roads)
=> 15 liters/km (freeway)
2) We can use rate to calculate how many people have gone to a tourist attraction per x hours/minutes

14. 1) The current exchange rate for 1 SGD to EUR is 0.564066

(Reference: http://www.xe.com/ucc/convert/?Amount=1&From=SGD&To=EUR)

2) The current exchange rate for 1 SGD to AUD is 0.765877

(Reference: http://www.xe.com/ucc/convert/?Amount=1&From=SGD&To=AUD)

15. 1) Growth rate in Singapore population annually is 1.8%

(Taken from: http://www.singstat.gov.sg/stats/keyind.html)

2) Average walking speed is 5km/h

(Taken from: http://en.wikipedia.org/wiki/Walking)

16. 1)the rate of 1 singapore dollar to 1 US dollar is 0.809247.
(taken from:http://www.xe.com/ucc/convert/?Amount=1&From=SGD&To=USD)
2)the rate of 1 singapore dollar to 1 euro is 0.567852.
(http://www.xe.com/ucc/convert/?Amount=1&From=SGD&To=EUR)

17. 1) Most airliners reach takeoff speed at around 150-180 mph

2)a heart would beat between 60 and 100 beats per minute

18. 1) one singapore dollar is 5.22560597 Chinese Yuan
(got from news)

2)1 singapore dollar is 0.505332749 British Pound
(from the news)

19. Charles O&#39;Rourke6/26/2011 08:12:00 PM

1)A person drinks approximately 5 cups of water per day
(Observation)
2)1100 people are born in china every day

20. 1) 5 million dogs are abandoned each year.
2)By year 2040, its is estimated that 80 million people will die per year.

21. A baby is aborted every 24secs in the world
155000 people die everyday