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
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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.
Hi there!
To solve, we must use the following trig identity:
sin(u - v) = sin(u)cos(v) - sin(v)cos(u)
We can rewrite the left hand side of the equation as:
Split the fraction:
First fraction reduces to 1:
Simpify each with common arguments:
Answer:
a) P) 0.25 = 1/4 both
b) P) 0.75 = 3/4 one
c) P) 0.25 = 1/4 none
Step-by-step explanation:
4 routes to D + H
6 routes to H + S
= D H S
4 | 6
- 2 | -3
= 2 | 3 = route 1 = 2/4 and route 2 = 3/6
= 1/2 route 1 and 1/2 route 2
Answer a ) = 1/2 x 1/2 = 0.25 = 1/4 = 0.25 probability
Answer b) = 1- (1/2 x 1/2) = 1- 0.25 = 3/4 = 0.75 probability
Answer c) = 1/2 x 1/2 = 0.25 = 1/4 = 0.25 probability
A straight line is 180°. 180°-135°=55°, so x=55°, which is an acute angle because it is less than 90°.
