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:
356.53
Step-by-step explanation:
Calculate the semicircle and square areas separately. For the semicircle, A = πr²/2, so 100.53
And for the square, A = a², so 256
Hope this helps
<span>First we define Charlene's the average time, which is (8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6 = 8.5. Normal time is 8.5/1.1 = 7.7. Charlene is faster than normal.</span>
Answer:
False
Step-by-step explanation:
Counterexample:
If i = 2, then the answer will be 16 and not 1.
He should choose the second option because he will be paid more money, with the percentage he expects.
Hope this helps!
