Answer:
- number of multiplies is n!
- n=10, 3.6 ms
- n=15, 21.8 min
- n=20, 77.09 yr
- n=25, 4.9×10^8 yr
Step-by-step explanation:
Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...
mpy[n] = n·mp[n-1]
mpy[2] = 2
So, ...
mpy[n] = n! . . . n ≥ 2
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If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...
10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10
Then the larger matrices take ...
n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min
n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years
n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years
_____
For the shorter time periods (less than 100 years), we use 365.25 days per year.
For the longer time periods (more than 400 years), we use 365.2425 days per year.
Answer:
2+2=4+3=7+6=13+8=16+5=21+9=30-8=22+4=26
Answer:
Step-by-step explanation:
21 hits / 45 at bats
7/15
<u>Answer:</u>
x + y ≥ 26 + 15
5x + 8y ≥ 250 (see below)
Step-by-step explanation:
First, write an equation to represent the total cost to wash cars:
$5x = cost for cars
Then, write another for trucks:
$8y = cost for trucks
If the question is saying that they will wash at least 26 cars and 15 trucks, that means they could wash more. This means that we'll need an inequality:
This inequality represents that the total number of cars and trucks they wash will be at least—which means that it is equal to or greater than—than the amount given:
x + y ≥ 26 + 15
Any equation or inequality with two unknowns is not solvable, meaning we need a system of equations:
If they make at least $250, that means that we need to combine the costs of the cars and trucks to make an inequality:
5x + 8y ≥ 250
Now you have your system of equations:
x + y ≥ 26 + 15
5x + 8y ≥ 250
