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2 years ago

14

Which of the following explains the relationship between angles c and d

1 answer:

Paladinen [302]2 years ago

4 0

Where’s the picture, if you had a picture i could help you :)

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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

NISA [10]

A=-26/11 —> you will solve for a by simplifying both sides of the equation, then isolating the variable.

4 0

3 years ago

Patrick is keeping track of how far he jogs each morning.

katrin2010 [14]

Answer:

21:50

Step-by-step explanation:

We need to find the ratio of 420 m to 1 km.

We know that,

1 km = 1000 m

So,

The ratio becomes,

$\dfrac{420\ m}{1\ km}=\dfrac{420\ m}{1000\ m}\\\\=\dfrac{42\ m}{100\ m}\\\\=\dfrac{21}{50}$

So, the required ratio is 21:50.

5 0

3 years ago

What % of $30,000 = $15,000

sammy [17]

15,000/30,000
0.50
50%

Hope this helps!

5 0

3 years ago

Simplify 3^8 ÷ 3^2 <br> A. 3^4<br> B. 3^10<br> C. 3^6<br> D. 3^6

olga_2 [115]

Answer: 3^6 so D or C

Step-by-step explanation:

When dividing two squares, you minus the number

3 0

2 years ago

Read 2 more answers