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
__
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.
First, find the 40% discount.
40% of 195 is 78
195 x 0.40 = 78
Subtract that from 195
195 - 78 = 117
Now, find 66 2/3% of 117, since it is an additional reduction after the original discount.
2/3 = 0.667, so 66 2/3% is 66.667%
117 x 0.66667 = 78.00039
And subtract that from 117
117 - 78.00039 = 38.99961, which in dollars would be $38.99. (hundredths, etc. of a cent are usually just dropped; no rounding involved.)
The discount price would then be $38.99
Answer:
a)3,6,9,12,15,18,24 b)7,14,21,28,35,52,49,56
a)16 b)40 c)24 d)36
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
![\sqrt[3]{216}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216%7D)
= ![\sqrt[3]{8}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D)
· ![\sqrt[3]{27}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D)
= ![\sqrt[3]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%7D)
³ · ![\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%7D)
³ = 2 x 3 = 6
24:48 which can be simplified to 1:2
