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:
The ratio of the circumference to its diameter.
the proportion can be written this way
Circumference / diameter = pi / 1
2.25 for the first mile. That leaves 4.2 miles.
4 * 0.1 = 0.4
0.15 * 4 = $6.00
0.15 * 2 = 0.3
$6.30 + $2.25 = $8.55
$10.00 - $8.55 = $1.45
The driver's tip was $1.45.
Answer: a = 2,315.5
Step-by-step explanation:
a = 2πrh+2πr²
a = 2π(9)(32) + 2π9²
a = 2π x 288 + 2π x 81
a = 1809.6 + 508.9
a = 2,315.5
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