1. The Mathematics of Records Ralph Bell ED 325 November 7, 2011
2. Record SpeedsO A standard vinyl record has a speed of 33 revolutions per minute (rpm). If you were listening to a song that is 7 minutes and 4 seconds, the record would spin 233.2 times during the song.33 x 7 = 23133/60 = .55 (record turns per second).55 x 4 = 2.2231 + 2.2 = 233.2
3. Record SpeedsO A single is released on a smaller vinyl record that turns at a speed of 45rpm. If you were to listen to the same 7 min 4 sec song, the record would spin 318 times.45 x 7 = 31545/60 = .75.75 x 4 = 3315 + 3 = 318
4. Record Circumference O A standard vinyl record has a diameter of 12in. Therefore the circumference of any standard record is 33.70 inches. 3.14 x 12 = 33.70 A single vinyl record has a diameter of 7in. Therefore the circumference of any single is 22 inches 3.14 x 7 = 22NCTM geometry: findthe distance betweenpoints alonghorizontal and verticallines
5. Record WeightO Records are weighted in grams. Up until the 21st century, records were 125 grams. Nowadays any new or re-released album weights 180 grams. This means records are 55 grams heavier.O 180 – 125 = 55 1 pound = 453.59237 grams 1 gram = 0.00220462262 pounds 180 grams = 0.396832 poundsNCTM measurement = understand the need for measuring withstandard units and become familiar with standard units in thecustomary and metric systems
6. Average Side LengthO Unlike a cd both sides of a record are played. These are referred to as side a and side b. To calculate the average side length of a Beatles album one must add up multiple side lengths and divide by the number of sides. Below are side a lengths for the Beatles first 5 albums. To add seconds divide the number of seconds by 60 and add the decimal to the number of minutes17:05+15:35+16:28+16:31+17:1917.08+15.58+16.46+16.52+17.37= 82.9682.96/5=16.592.592 X 60 = 36Average Side Length = 16 minutes 36 secondsNCTM data analysis and probability: propose and justifyconclusions and predictions that are based on data and designstudies to further investigate the conclusions or predictions
7. Average Song LengthO To calculate the average song length on a side add up the length of the songs and divide by the number of songs. The Beatles album Revolver has 7 songs on the first side.2:39+2:08+3:02+3:01+2:26+2:40+2:372.65+2.13+3.03+3.02+2.43+2.66+2.62=18.5518.55/7=2.65.65 x 60 = 39Average Song Length = 2 minutes 39 secondsNCTM number and operations: work flexibly with fractions,decimals, and percents to solve problems
8. Record SalesO In the year 2001 180,000 records were bought. In the year 2010 223,000 records were bought. This is an increase of 23.89% over 9 years.223,000 – 180,000 = 43,00043,000/180,000 = 0.23890.2389 x 100 = 23.89
9. Record PricesO For various reasons records are more expensive than cd’s. If you wanted to buy the Grateful Dead album American Beauty, it would cost $10.99 on cd and $24.98 on vinyl. The vinyl record costs $13.99 more.24.98 – 10.99 = 13.99The percent increase in price is 127%13.99/10.99 = 1.271.27 x 100 = 127
10. Record PricesO Double albums are even more expensive compared to cd’s. The Bob Dylan album Blonde on Blonde would also cost $10.99 on cd but the vinyl would cost $31.97. The vinyl record costs $20.98 more.31.97 – 10.99 = 20.98The percent increase in price is 190%20.98/10.99 = 1.901.90 x 100 = 190%
11. Valuable RecordsO In 2009 a copy of the Beatles album Yesterday and Today sold for $39,000 at auction. The average price for an album in 1966 (year album came out) was $5.99. This means the value of the record increased by 650985.14%39,000 – 5.99 = 38,994.0138994.01/5.99 = 6509.85146509.8514 x 100 = 650985.14
12. Changing The NeedleO You should change the needle on your record player after listening to 1,000 hours of music. If the average record length is 50 minutes, you can listen to 1,200 records before you have to change the needle.1000 x 60 = 60,00060,000/50 = 1,200
13. Record StoresO In 2003 there were about 6,000 record stores in America. Today there are about 1,884. In the past 8 years 4,116 record stores have closed.6,000 – 1,884 = 4,116This is a decrease of 68.6%4,116/6000 = 0.6860.686 x 100 = 68.6
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