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:
its the second one
Step-by-step explanation:
Answer: option c
Step-by-step explanation: with a two-tailed hypothesis she can find the way to go deep on the study, she will be able to increase the statistical power. She will be able to separate in specifics groups.
Table:
y = x²
can also be written as: f(x) = x²
Plug in each x value and calculate the output:
f(-4) = (-4)² = 16
f(-3) = (-3)² = 9
f(-2) = 4
f(-1) = 1
f(-
) = 
f(0) = 0
f() =
f(1) = 1
f(2) = 4
f(3) = 9
f(4) = 16
Answers:
a) graph shown in picture
b) vertex is at (0, 0)
