Can anyone give a Thrall explain ERATOSTHENES’ SIEVE
1 answer:
Answer:
See below
Step-by-step explanation:
The sieve of Eratosthenes is a stepwise method for finding all prime numbers up to a given number n.
Assume that you want to find all the prime numbers between 1 and 100.
Step 1.
Create a square grid with numbers from 1 to 100.
You will be finding numbers in the grid that are composite (not prime) and discarding them. The remaining numbers are the primes.
Step 2.
<em>Mark 1</em>, because it is not a prime.
Step 3.
2 is prime. Mark all <em>multiples of 2</em>, starting from 4 (green in the image below).
Step 4.
3 is prime. Mark all <em>multiples of 3</em>, starting from 9 (blue)
Step 5.
4 is composite, so, <em>mark all multiples of 5</em>, starting from 25 (orange).
Step 6.
6 is composite, so, <em>mark all multiples of 7</em>, starting from 49 (purple).
Step 7.
8, 9, and 10 are composite, and 11² > 100, so we can <em>stop</em>.
All the unmarked numbers are the prime numbers between 1 and 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
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Answer:
The new graph has a steeper slope and a y-intercept of 8.
Step-by-step explanation:
From Analytical Geometry, we define a straight line by following first order polynomial (linear function):
(1)
Where:
- Independent variable.
- Dependent variable.
- y-Intercept.
- Slope.
And the slope represents the change in dependent variable () divided by the change in independent variable (
). That is:
If and
, then the new line is steeper with respect to the original line.
Let , its slope and y-intercept are 5 and 0, respectively. If slope is changed into 9 and y-intercept becomes 8, then the new graph has a steeper slope and a y-intercept of 8.