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S: Math in our own world by Makaila l. and Cassidy Y.

FC: Math in Our Own World

1: Index Chocolate Dream 2-3 Olympic Records 4-7 Weather Underground 8-9 Mathematical Harmony 10-13 Here's Your Change 14-15 Coaster Crazy 16-19 Math Mind 20-22 Sites 23

2: Measurement chocolate fudge ingredients: 2 cups (400 grams) granulated white sugar 2 squares (2 oz)(60 grams) unsweetened chocolate, chopped 2 tablespoons of light corn syrup 2/3 cup (160 ml) 1/2 and 1/2 (or light cream) 2 tablespoons (28 grams) unsalted butter, cut into pieces 1/8 teaspoon of salt 1 teaspoon of pure vanilla extract Instructions: Grease the bottom and sides of an 8 x 8 x 2 inch (20 x 20 x 5 cm) pan with about 1 tablespoon (14 grams) of room temperature unsalted butter. Set aside In a heavy 2 1/2 - 3 quart saucepan, place the sugar, chocolate, light corn syrup, and half-and-half Cover the pan with a lid for about 2-3 minutes boil the mixture gently (adjust the heat as necessary) until the temperature reaches the soft ball stage of 236 degrees F(113 degrees C).

3: From the 2 tablespoons of butter on top of the fudge. Allow the fudge to cool to lukewarm (110 degrees F) (38 - 43 degrees C). Store and serve at room temperature. Makes one 8 x 8 inch (20 x 20 cm) pan of fudge. If you cut the recipe in half, how many brownies would it make?

4: Olympic Records Including updates from Sydney 2000 , from Schinias 2004, & from Beijing 2008 Men: Single Skull (x1) : Xeno Mueller (SUI) Atalnta1996 6.44.85 Double Skull (x2) : Rossano Galtarossa, Alessio Sartori (ITA) Schinias (SF) 2004 6.11.49 Quadruple Skull (x4) : Chris Morgan, James McRae, Brendan Long, Daniel Noonan (AUS) Beijing (heat) 5:36.20 Coxless Pair (2-) : Steven Redgrave, Matthew Pinsent (GBR) Atlanta 1996 6.20.09 Coxless (4-) : Jochen Urban, Sebastian Thormann, Philipp Studer, Burnd Heidicker (GER) Schinias 2004 (FB) 5:48.52

5: Eight (8+) Jason Read, Wyatt Allen, Chris Ahrens, Joseph Hansen, Matt Deakin, Dan Beery, Beau Hoopman, Bryan Volpenhein, Pete Cipollone (USA) : Schinias 2004 (heat) 5:19.85 Women : Single Scull (x1) : Katrin Rutchow-Stomporowski (GER) : Schinias 2004 7:18.12 Double Skull (x2): Kerstin Koeppen, Kathrin Boron (GER) : Banvoles 1992 6.49.00 Quadruple Skull (x4) : Tang Bin, Jin ziwei, Xi Aihua, Zhang Yangvang (CHN) Inger Pors, Ulla hansen, Sarah Lauritzen, Dorthe Pedersen, (DEN) : Beijing 2008 (heat) 6:11.83 Coxless Pair (2-) : Megan Still, Kate Slatter (AUS) : Atlanta 1996 7:01.39

6: Eight (8+) : Kate Johnson, Samantha Magee, Megan Dirkmaat, Alison Cox, Caryn Davies, Laurel Korholz, Anna Mickelson, Lianne Nelson, Mary Whipple (USA) : Schinias 2004 (heat) 5:56.55 Lightweight : Lightweight Men : Double Scull (x2) : Zac Purchase, Mark Hunter (GBR) Zac Purchase, Mark Hunter (GBR) : Beijing (final) Beijing 2008 (heat) 6:10.99, 6:13.69 Coxless Four (4-) : Thomas Ebert, Morten Joergensen, Mads Christian Kruse Andersen, Eskild Balschmidt Ebbesen (DEN) : Beiging 2008 (final) 5:47.76, 5:50.12 Lightweight Women : double skull (2x) : Sally Newmarch, Amber Halliday (AUS) : Schinias 2004 (heat) 6:49.90

7: how much faster was Kerstin Koeppen than Katrin Rutchhow?

8: WeatherUnderground Place Temperature Humidity Pressure Conditions Wind updated Bullhead City 62.6 F 25%29.56 in ClearSE at 5.8 mph 9:04 AM MST Casa Grande 41.9 F 37%30.14 in ClearSSW at 2.0 mph 9:09 AM MST Phoenix 48.7 F 39%30.29 in Mostly CloudyCalm10:14 AM MST Prescott 37.9 F 29%30.12 in ClearNorth at 3.0 mph 10:14 AM MST Flagstaff 40.6 F 39%23.51 in ClearCalm10:17 AM MST Grand Canyon 33.1 F 54%30.33 in ClearENE at 5.0 mph 9:09 AM MST

9: Glendale 46 F 46%30.14 in (Rising) ClearNorth at 4 mph 8:47 AM MST Mesa 52.9 F 25%30.14 in ClearNNE at 12.0 mph 9:08 AM MST Page 36.7 F 51%30.36 in ClearNW at 5.0 mph 9:09 AM MST Kingman 38.9 F 60%30.30 in ClearCalm9:09 AM MST how much warmer was Phoenix than Prescott?

10: Mathematical Harmony oIt is a remarkable(!) coincidence that 27/12 is very close to 3/2. Why? Harmony occurs in music when two pitches vibrate at frequencies in small integer ratios. For instance, the notes of middle C and high C sound good together (concordant) because the latter has TWICE the frequency of the former. Middle C and the G above it sound good together because the frequencies of G and C are in a 3:2 ratio. Well, almost! In the 16th century the popular method for tuning a piano was to a just-toned scale. What this means is that harmonies with the fundamental note (tonic) of the scale were pure; i.e., the frequency ratios were pure integer ratios. But because of this, shifting the melody to other keys would make the music sound different (and bad) because the harmonies in other keys were impure!So, the equal-tempered scale (in common use today), popularized by Bach, sets out to "even out" the badness by making the frequency ratios the same between all 12 notes of the chromatic scale (the white and the black keys on a piano).So, the equal-tempered scale (in common use today), popularized by Bach, sets out to "even out" the badness by making the frequency ratios the same between all 12 notes of the chromatic scale (the white and the black keys on a piano).

11: But because of this, shifting the melody to other keys would make the music sound different (and bad) because the harmonies in other keys were impure!So, the equal-tempered scale (in common use today), popularized by Bach, sets out to "even out" the badness by making the frequency ratios the same between all 12 notes of the chromatic scale (the white and the black keys on a piano).Harmonies shifted to other keys would sound exactly the same, although a really good ear might be able to tell that the harmonies in the equal-tempered scale are not quite pure. So to divide the ratio 2:1 from high C to middle C into 12 equal parts, we need to make the ratios between successive note frequencies 21/12:1. The startling fact that 27/12 is very close to 3/2 ensures that the interval between C and G, which are 7 notes apart in the chromatic scale, sounds "almost" pure! Most people cannot tell the difference!What a harmonious coincidence! The Math Behind the Fact: It is possible that our octave might be divided into something other than 12 equal parts if the above coincidence were not true! It is worth noting that on a stringed instrument, a player has complete control over the frequency of notes.

12: So she can produce pure harmonies. Very good string players will actually play A-sharp and B-flat differently. Sometimes they don't even realize they are doing it--- they just do what their ear tells them. Playing pure harmonies on stringed instruments also means that the same note will sound different depending on the key the music is played in; for instance, notes based on 'C' will produce slightly different frequencies than those based on 'A' There are a lot of interesting connections of mathematics with music. Take courses in music theory to learn more!

14: Here's Your Change Get as much money in your piggy bank as possible, by figuring out the correct change.Figure out how many of each bill or coin that you expect to get back when you pay for something. For example, if something costs $3.75 and you pay with a five dollar bill, you would expect back one quarter and one dollar bill. If you get the answer correct, the amount of change is added to your piggy bank. If you get the answer wrong, the correct amount of change is subtracted from your piggy bank. The more money you get in your piggy bank, the harder the questions will get. To begin the game, choose a difficulty level, then choose a currency by clicking the country's flag: Easy (amounts less than $1.00) Medium (amounts less than $5.00) Hard (amounts less than $100.00) Super Brain (big spenders) Example: If the Amount of Sale is $0.65 and the Amount Paid is $0.80, the correct change is $0.15. To get it right, you would put a 1 in the $0.10 box and a 1 in the $0.05 box. You may also click once

15: on the $0.10 coin and once on the $0.05 coin. You may also click once on the $0.10 coin and once on the $0.05 coin. Like this : Amount of Sale: $0.69 Amount Paid: $0.75 You CLICK a nickel and a penny. go to to play the game.

16: Coaster Crazy Activity 1 Energy Equation While there’s a ton of math involved in roller coasters — it’s nearly 100-percent math from start to finish — one of the hardest things to understand is how they work. Engineer Walt Davis illustrates an equation for roller coaster energy and energy loss. To see how it works, and hear him describe it, just click on the button or the words. Here is Mr. Davis' equation and an explanation of the formula; also see the animation. P.E. + K.E. = T.E. P.E. = Potential Energy K.E. = Kinetic Energy T.E. = Total Energy The Coaster looses energy to friction. There are three types of friction: wind, rolling friction, and braking.

17: “Almost everything that happens on a coaster can be described by a very simple mathematical formula. In terms of energy, the formula is simply this: potential energy plus kinetic energy equals total energy. If you understand what happens in that formula all the details of it, you can design a coaster." “If we start with the energy input device on a coaster, that’s the motor. The motor puts energy into it as the coaster goes up the first hill, where we are at our peak of potential energy point on the coaster. And then as we move up and down the hills and trade height for speed, we wind up with a kinetic energy component, and this is a two-way street. Potential goes to kinetic and kinetic can come back to potential as you’re going up and down hills and going faster and slower."“At the same time that’s going on, you also have a one-way street out here, where you’re losing some of this energy all the time to friction. And there are three kinds of friction that affect a coaster. We have wind, we have rolling friction, and we have the brakes. The brakes take out any extra energy left over at the end of the ride.

18: This is the part that everybody experiences, and this is the fun part of the coaster, the trade off back and forth between potential and kinetic. A coaster designer, a coaster engineer, has to be very interested in what happens at this point -- the motor -- and this point — the energy loss due to friction — because this tells how long and how high your coaster can be.” if the potential energy is 42.6 and the kenetic energy is 13.8 what is the total energy?

20: Math Mind Back to "Here's Your Change" Boys VS. Girls How much money did the customer get? Here's your info: amount of sale : $ .70 amount paid : $ 1.00 amount of tax : $.20 amount of sale :$ 1.25 amount paid : $ 2.50 amount of tax : $ .95 amount of sale : $ 2.22 amount paid :$ 3.42 amount of tax : $ .43 amount of sale :$ 3.74 amount paid :$ 5.57 amount of tax : $ .31

22: Answers number 1 is $ .10 number 2 is $ .30 number 3 is $ .77 number 4 is $ 1.52

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