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Virty [35]
3 years ago
12

For the following right triangle, find the side length. Round your answer to the nearest hundredth

Mathematics
2 answers:
Mars2501 [29]3 years ago
5 0

Answer:

9.75

Step-by-step explanation:

To do this problem, use the Pythagorean Theorem, a^2 + b^2 = c^2. Right now, you have that a = 7 and c = 12, so it would be

7^2 + b^2 = 12^2\\49 + b^2 = 144\\b^2 = 95\\b = \sqrt{95}

Rounding to the nearest hundredth, you get: 9.75

IRINA_888 [86]3 years ago
4 0

Answer:9.75

Step-by-step explanation:12x12 =144 and 7x7= 49 subtract 144-49 and get 95 the square root of 95 is approximately 9.747 rounded to the nearest hundredths place is 9.75

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4 0
3 years ago
WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"
Feliz [49]

Recall Euler's theorem: if \gcd(a,n) = 1, then

a^{\phi(n)} \equiv 1 \pmod n

where \phi is Euler's totient function.

We have \gcd(9,32) = 1 - in fact, \gcd(9,32^k)=1 for any k\in\Bbb N since 9=3^2 and 32=2^5 share no common divisors - as well as \phi(9) = 6.

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37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} =  32\cdot\left(32^{(\cdots)}\right)^6

where the c_i are positive integer coefficients from the binomial expansion. By Euler's theorem,

\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9

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32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9

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