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3 years ago

NEED HELP FAST WILL MARK BRAINLIEST

Mathematics

1 answer:

Tju [1.3M]3 years ago

6 0

Pretty sure the answer is 18

3^2+3^2=9+9=18 (with a square root)

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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 $\phi(9) = 6$ .

Now,

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

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

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

so that

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

7 0

2 years ago

Please help me ASAP!!!! It is greatly appreciated!!! Will mark as Brainliest!!!!

Karo-lina-s [1.5K]

Answer: 5/4

Step-by-step explanation:

6 0

3 years ago

The measure of angle M is_degrees.

jasenka [17]

Answer:

m=37

Step-by-step explanation:

The 2 angles are complementary, or add to 90 degrees. Wee know this because of the little square in the corner that indicates a right angle, which is equal to 90 degrees.

m+53=90

Solve for m by getting m by itself. To do this, subtract 53 from both sides to "reverse" the addition being done to m.

m+53-53=90-53

The 53s on the left cancel, and we are left with:

m=37

3 0

3 years ago

Read 2 more answers

Please help!! Thanks

Troyanec [42]

X=3

X/-3 = -1 ,Leave X by itself so multiply by -3 on both sides.

X = -1*-3

X = 3, negative times negative equals positive.

6 0