1.)(a) CPU 1 has speed of 2.6 GH (steps per second) and runs a program which needs 10.9 T steps.
(b) CPU 2 has speed of 2.2 GH and runs program which needs 7.3 T steps.
---How long does it take for CPU 1 and CPU 2 to finish the work? (Show all work!)
2.)How many more more 4 letter words can you invent with 4 possible letters as opposed with 2 letters.(Show all work!)
Assuming each step takes one cycle (Hertz), 1(a) takes
10.9t/2.6G seconds
=10.9*10^12/(2.6*10^9)
=4192 s
Calculate similarly for 1(b).
2.
Assume the number of distinct letters = n, then n! n-letter words can be formed.
Difference = 4!-2! words
(I assume you make 2-letter words with the two letters, the question is not very clear.).
JAAAAAAAAAAAAAAAVAAAAAAAAAAA
1.) To determine how long it takes for CPU 1 and CPU 2 to finish the work, we need to divide the total number of steps needed by the speed of each CPU.
(a) CPU 1:
Total steps needed = 10.9 T
Speed of CPU 1 = 2.6 GH
To convert 10.9 T to steps:
1 T = 1 trillion steps
10.9 T = 10.9 trillion steps
To calculate the time:
Time = Total steps / Speed
Time taken by CPU 1 = 10.9 T steps / 2.6 GH = (10.9 * 10^12) steps / (2.6 * 10^9) steps/second
Simplifying:
Time taken by CPU 1 = (10.9 / 2.6) * (10^12 / 10^9) seconds = 4.192 * 10^3 seconds
(b) CPU 2:
Total steps needed = 7.3 T
Speed of CPU 2 = 2.2 GH
To convert 7.3 T to steps:
7.3 T = 7.3 trillion steps
To calculate the time:
Time = Total steps / Speed
Time taken by CPU 2 = 7.3 T steps / 2.2 GH = (7.3 * 10^12) steps / (2.2 * 10^9) steps/second
Simplifying:
Time taken by CPU 2 = (7.3 / 2.2) * (10^12 / 10^9) seconds = 3.32 * 10^3 seconds
Therefore, CPU 1 takes approximately 4.192 * 10^3 seconds to finish the work, and CPU 2 takes approximately 3.32 * 10^3 seconds to finish the work.
2.) To find out how many more 4-letter words can be invented with 4 possible letters compared to 2 possible letters, we need to calculate the number of combinations in each case.
(a) With 2 possible letters:
In this case, we can have a combination of 2 letters at a time, and there are 4 possible letters.
To calculate the number of combinations, we use the formula for combination (nCr):
Number of combinations = n! / (r! * (n - r)!)
Number of combinations with 2 possible letters:
Number of combinations = 4! / (2! * (4 - 2)!)
= 4! / (2! * 2!)
= (4 * 3 * 2 * 1) / ((2 * 1) * (2 * 1))
= 24 / 4
= 6
(b) With 4 possible letters:
In this case, we can have a combination of 4 letters at a time, and there are also 4 possible letters.
Number of combinations with 4 possible letters:
Number of combinations = 4! / (4! * (4 - 4)!)
= 4! / (4! * 0!)
= (4 * 3 * 2 * 1) / (4 * 3 * 2 * 1)
= 24 / 24
= 1
Therefore, the number of more 4-letter words that can be invented with 4 possible letters compared to 2 letters is 1.