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.
Equivalent system, equivalent systema of equations
15f -8f+ 13= 55
⇒ 7f+ 13= 55
⇒ 7f= 55- 13
⇒ 7f= 42
⇒ f= 42/7
⇒ f=6
Final answer: f=6~
Answer:
<u>X</u> <u>Y</u> <u>(</u><u>X,</u><u>Y)</u>
-4 14. (-4,14)
-3 12. (-3,12)
-2 10. (-2,10)
-1 8. (-1,8)
0 6 (0,6)
1 4. (1,4)
2 2. (2,2)
Hmm... Let's see..
Alrighty: $400= 100% (the whole amount of money). 1% of that money= 400/100. If $400 invests once in one year, that is... 424 dollars.
Anyone out there who is looking for monthly payment, you invest 400 dollars with interest, the answer is 4934.22
Hope that helps ya!
