8.9
The equation for the grain size is expressed as the equality:
Nm(M/100)^2 = 2^(n-1)
where
Nm = number of grains per square inch at magnification M.
M = Magnification
n = ASTM grain size number
Let's solve for n, then substitute the known values and calculate.
Nm(M/100)^2 = 2^(n-1)
log(Nm(M/100)^2) = log(2^(n-1))
log(Nm) + 2*log(M/100) = (n-1) * log(2)
(log(Nm) + 2*log(M/100))/log(2) = n-1
(log(Nm) + 2*log(M/100))/log(2) + 1 = n
(log(33) + 2*log(270/100))/log(2) + 1 = n
(1.51851394 + 2*0.431363764)/0.301029996 + 1 = n
(1.51851394 + 0.862727528)/0.301029996 + 1 = n
2.381241468/0.301029996 + 1 = n
7.910312934 + 1 = n
8.910312934 = n
So the ASTM grain size number is 8.9
If you want to calculate the number of grains per square inch, you'd use the
same formula with M equal to 1. So:
Nm(M/100)^2 = 2^(n-1)
Nm(1/100)^2 = 2^(8.9-1)
Nm(1/10000) = 2^7.9
Nm(1/10000) = 238.8564458
Nm = 2388564.458
Or about 2,400,000 grains per square inch.
Answer:
n = -1
Step-by-step explanation:
Guess your question is to find n
Given:
-6 + 3n = -9
-6 + 3n = -9
Add 6 to both sides
-6 + 6 + 3n = -9 + 6
3n = -3
Divide both sides by 3
n = -3 / 3
= -1
n = -1
Check:
-6 + 3n = -9
-6 + 3(-1) = -9
-6 - 3 = -9
- 9 = - 9
The team gained a total of 3 yards. That is because they first gained 8 (0 + 8), then lost 3 (8 - 3).
As a decimal .375 as a percentage it would be 37.5
Answer:
Irrational
rational
Step-by-step explanation:
