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:
Value of x will be 0.1515
Step-by-step explanation:
We have given the equation 
We have top fond the value of x using exponent and logarithmic property
So
Taking log both side
x = 0.1515
if there were 100 questions then 76 were correct, and 24 incorrect, you can simplify and rearrange the fraction depending on how many questions there were,
Answer:
a = 3
Step-by-step explanation:
Factor both expressions
x² - x - 6
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)
The factors are - 3 and + 2 , since
- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus
x² - x - 6 = (x - 3)(x + 2)
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x² + 3x - 18
consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)
The factors are + 6 and - 3 , since
6 × - 3 = - 18 and 6 - 3 = + 3 , thus
x² + 3x - 18 = (x + 6)(x - 3)
Both expressions have a common factor of (x - 3)
Compare with (x - a ), then a = 3
