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:
a. 2.6(0.12)
Step-by-step explanation:
Check all of the other answers: b. c. and d. are variations of equations that equal to 2.912. 2.6(0.12) is not the correct equation because it equals to 0.312. The kitten‘s weight must increase, so that is the incorrect equation.
Answer:
Step-by-step explanation:
3x^2 + 2x^2 - 5x + 7x + 6 - 9
5x^2 + 2x - 3
Answer:
Blank above the 3: 9
Blanks underneath the 593: 540
Blanks underneath the line: 53
Blank by the "R": 53
Step-by-step explanation:
Simply divide.
Answer:
Step-by-step explanation:
y = 4x + 1
Slope of line = 4
Slope of perpendicular to line = -¼
Point-slope equation for line of slope -¼ that passes through (12, -7):
y+7= -¼(x-12)
