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sammy [17]
3 years ago
8

Find a whole number x in x/113 so that the ratio is a good estimate for pi

Mathematics
1 answer:
NISA [10]3 years ago
4 0
So the initial question is x / 113 = 3.14 (we're keeping it a smaller decimal for now)

What you should do first is multiply both sides by 113

Your answer should be x = 354.82

Round this up to x = 355. <-- This is why we only used 3.14 at the start

Now check your work:
x / 113 = ?
355 / 113 = 3.14159265358979... which essentially is pi
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lbvjy [14]

Step-by-step explanation:

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Substituting x^2=a, given bi-quadratic equation reduces in the form of following quadratic equation:

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Let us factorize the above quadratic equation:

a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\

Since square root of a negative number cannot be found, so:

x \neq \pm \sqrt{-100}\\

CASE\: (2)\:\\When\: a =5 \implies x^2 =5\\\therefore x=\pm \sqrt{5}\\

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