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crimeas [40]
2 years ago
6

Any number raised to the zero power always equals

Mathematics
2 answers:
Otrada [13]2 years ago
7 0
Always equals 1. Always!
KonstantinChe [14]2 years ago
3 0
And it is 1. Can't really explain sorry ~JZ HOPE IT HELPS
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What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{130}$ and $n^{-1}\pmod{231}$ are both defined?
olasank [31]

First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.

We have

130 = 2 • 5 • 13

231 = 3 • 7 • 11

so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.

To verify the claim, we try to solve the system of congruences

\begin{cases} 17x \equiv 1 \pmod{130} \\ 17y \equiv 1 \pmod{231} \end{cases}

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:

130 = 7 • 17 + 11

17 = 1 • 11 + 6

11 = 1 • 6 + 5

6 = 1 • 5 + 1

⇒   1 = 23 • 17 - 3 • 130

Then

23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)

so that x = 23.

Repeat for 231 and 17:

231 = 13 • 17 + 10

17 = 1 • 10 + 7

10 = 1 • 7 + 3

7 = 2 • 3 + 1

⇒   1 = 68 • 17 - 5 • 231

Then

68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)

so that y = 68.

3 0
2 years ago
PLEASE HELP! this is a 4 part problem but here is the first part!! :(
dimulka [17.4K]

Answer:

HI SORRY IM, SPEAK SPANISH... FROMN COLOMBIA

Step-by-step explanation:

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8 0
3 years ago
The distance from Clarion to DuBois is 2 1/2 inches on the map. the actual distance is 40 miles. The distance from DuBois to Rid
lisov135 [29]
Hello!

You have to find how many miles is 1 inch on the map

We can do this by doing 40 / 2 1/2 = 16

16 miles is equal to one inch

So we multiply this by 1 1/2

16 * 1 1/2 = 24

The answer is 24 miles

Hope this helps!
4 0
3 years ago
A 1.4 m tall child is standing next to a flagpole. The child's shadow is 1.2 m long. At the same time, the shadow of the flagpol
andreyandreev [35.5K]

Answer:

The flag pole is 9 feet tall.

Step-by-step explanation:


5 0
2 years ago
A ball bounces back 0.6 of its height on every bounce. If a ball is dropped 200 feet, how high does it bounce the fifth bounce?
MissTica

It is asking you to slice off 40% of the bounce height in each subsequent bounce.


So you start with full height 1, that's n = 0 bounces. Then after n = 1 bounce the new height is .6. After the second bounce, n = 2, the height becomes .6 X .6 = .36. And after n = 3, we have .6 X .6 X .6 = .216


So by induction we see that h(n = 5) = .6^n = .6^5 = 0.07776 = .078 of its original height or H = .078*200 = 15.6 ft. after five bounces. ANS. 16.0 if rounded to the nearest tenth

:)


4 0
3 years ago
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