Answer:
2.19
Step-by-step explanation:
Answer:
1. 32
2. 24
3. 
4. 
5. 15
6. 
Step-by-step explanation:
1. 4÷ 
2. 6÷
3.
÷4=
4.
÷4=
5. 5÷
6.
÷5=
If a,b, and c are prime numbers, do (a*b) and c have a common factor that is greater than 1
(1) a,b, and c are all different prime numbers
(2) c≠2
1. Let's assume values of 1,3 and 5 to a, b, and c respectively
a b = 1*3 = 3
3 and 5 do not have any common factor aside 1
Let's assume values of 1,3 and 2 to a,b and c respectively
a *b = 1*3 = 3
3 and 2 does not have a common factor aside 1
2. c
2
Let's assume values of 2,7 and 3 to a b and c response
a * b = 2 *7 = 14
14 and 3 does not have a common factor aside 1
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Answer:
This is easy -- it's just a list of steps. At this level, the problems are pretty simple.
Let's just do one, then I'll write out the list of steps for you.
Find the inverse of f( x ) = -( 1 / 3 )x + 1
STEP 1: Stick a "y" in for the "f(x)" guy:
y = -( 1 / 3 )x + 1
STEP 2: Switch the x and y
( because every (x, y) has a (y, x) partner! ):
x = -( 1 / 3 )y + 1
STEP 3: Solve for y:
x = -( 1 / 3 )y + 1 ... multiply by 3 to ditch the fraction ... 3x = -y + 3 ... ditch the +3 ... subtract 3 from both sides ... 3x - 3 = -y ... multiply by -1 ... -3x + 3 = y ... y = -3x + 3
STEP 4: Stick in the inverse notation, f^( -1 )( x )
f^( -1 )( x ) = -3x + 3
Step-by-step explanation:
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.