Title: Math Portfolio

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 Subject: History Author: Jennifer S Date: January 22, 2017 Level: University Grade: Length: 4 / 1034 No of views: 0 Essay rating: good 0, average 0, bad 0 (total score: 0)

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The function is y=x2. As mentioned above the parameters are between x=a and x=b. Here a=0 and b=1. The graph of the function- [pic] y=xn where n=2. The Area of the shaded region or area B was found to be 0.3333333333 units2. Area A = 1- Area B = 1- 0.33333333 = 0.6666666666 units2 Mathematically the area can also be found by the following- Area A can be found by the formula- [pic] Area B can be found by the formula- [pic] Total Area = 1 unit2 Area B = [pic] = [pic] Area A = [pic] = [pic] Ratio of area A : area B [pic] : [pic] = 2 : 1(satisfies the conjecture n:1) Now I will investigate the ratios of area A and B with other natural numbers...

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The parameters will stay the same a=0 and b=1. The ratios when n =3 The graph of y=x3 [pic] Y=xn where n=3. The Area of the shaded region or area B was found to be 0.25 units2. Area A = 1- Area B = 1- 0.25 = 0.75 units2 Mathematically the area can also be found by the following- Total area = 1unit2 Area B = [pic] = [pic] Area A = [pic] = [pic] Ratio of area A : area B [pic] : [pic] = 3 : 1(satisfies the conjecture n:1) Now I will investigate the ratio of the areas for n being a rational number...

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