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:
Step-by-step explanation:
<u>We can't multiply.</u>
<u>We got to count up by 12's for each 1/2 hour.</u>
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168.
<u>Simplified:</u>
- 24, 48, 72, 96, 120, 144, 168.
<u>Estimate:</u>
- 12 = 1/2 hour
- 24 = 1 hour
- 36 = 1 1/2 hours
- 48 = 2 hours
- 60 = 2 1/2 hours
- 72 = 3 hours
- 84 = 3 1/2 hours
- 96 = 4 hours
- 108 = 4 1/2 hours
- 120 = 5 hours.
- 132 = 5 1/2 hours
- 144 = 6 hours
- 156 = 6 1/2 hours
- 168 = 7 hours.
Answer is 168.
Answer:
2 is scalene
3 is right
4 is right
5 is equalatirel
6 is scalene
7 is isocoles
8 is equalatirel
9 is right
Step-by-step explanation:
