Mathematics+activity

Hi///// I'm Gabriella. today I want tell you about mathematics. It is powerful sbject. we could not live without math. we need math in everything. that's why we have to study math.

I want to tell you some math problem. if you solve everything... maybe,maybe U R genius. now~ let's go to the question.

1**.you have the land.and you are going to sale it.**
 * but you have to use the rope.it is 120 m long.\ **
 * cost of the land is $3000 for each m^2(it means square) **
 * now to earn the most money, you have to make the biggest shape. **
 * make your own shape(using the rope) and find out how much does it cost. **

Do you think you solved the proublem? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Did U think it was very easy one? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">well... what shape did you made? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">square!!!

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">..... is not the answer. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">the answer is a circle. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">now do you know why? you aren't? then I will explain it to you. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">when the shape is square, the biggest shape that you can make is this. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">each side of this square is 30m long. and its volume is 900m^2.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">but when the shape is circle.(π=3.14159,R=radius) <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">**the circumference=2πR**=120m <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">2x3.14159xR=120 <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">R=120/(2X3.14159) <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">=19.0986093029326(I'll suppose this 19) <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">=3.14159x19x19 <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">=1134.11399m^2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">see? circle's volume is much bigger than square's. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">now money. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">1134.11399x3000=$3,402,341.97
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">volume=πR^2(square) **

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">so the answer is <span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 190%;">circle <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">,$3,402,341.97( <span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 190%;">$3,402,341 <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">)


 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">2.The Roald Dahl activity. its thick is 1mm. **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">There is one sheet of paper.when you fold it once, it will be 2mm thick. **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">and when you fold it again(twice) it will be 4mm thick. **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">when you fold it 3 times, it will be 8mm. **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">when you fold it 4 times, it will be 16mm. **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">now the problem is... **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">when you fold it 50times, how thick it will be? **

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Did you solve this question? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">it is harder than the first one. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">now I'll tell you how to solve it.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">let's suppose. how many times did you fold=x <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">and how thick this sheet is(mm)=y <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">method is 'y=2^x' <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">(now let me cheack this method. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">when x =3. y=2^3=8. okey. this method is correct.)

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">so. problem is this,"when x=50, what's y? " <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">substitute 50 in x. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">y=2^50=2x2x2x2x2x2x2x2x2x2x2x2.......................................................x2x2x2x2x2x2x2x2(50times) <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">= 1125899906842624mm <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">it's about <span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 170%;">112,589,907km <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">thick. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">amazing ehe? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">but you know what? any paper in the world can fold only 7 times. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">not more than that. if you cannot believe, maybe you can try to fold it more than 7:D