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:
c. 25
Step-by-step explanation:
100/12 = 8.3
8.3 × 3 = 24.9
rounded up is 25
Answer:
13. 5 minutes
Step-by-step explanation:
This is a simple proportion problem. Make two fractions where one item is always on the top and the other on the bottom.
Now, cross multiply (multiply the two numbers diagonal from each other and divide the diagonal with the x value)
576 x 3 = 1, 728
1, 728 / 128 = 13.5
Answer:
3
Step-by-step explanation:
x = 3
<u>Solution</u> :
Let, the number be A
Given, A/2 + 12 = 6
⇒ (A + 24)/2 = 6
⇒ A + 24 = 12
⇒ A = 12 - 24
⇒ A = - 12
∴ the required number is (- 12). (Ans.)
