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:
36
Step-by-step explanation:
because square of term on LHS = square of term on RHS
if 5 - 3y = 6
then (5 - 3y)² = 36
Answer:
150 ft. x 400 ft. = 60,000
Step-by-step explanation:
<span>Simplifying
3x + 10 = 5x + 22
Reorder the terms:
10 + 3x = 5x + 22
Reorder the terms:
10 + 3x = 22 + 5x
Solving
10 + 3x = 22 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
10 + 3x + -5x = 22 + 5x + -5x
Combine like terms: 3x + -5x = -2x
10 + -2x = 22 + 5x + -5x
Combine like terms: 5x + -5x = 0
10 + -2x = 22 + 0
10 + -2x = 22
Add '-10' to each side of the equation.
10 + -10 + -2x = 22 + -10
Combine like terms: 10 + -10 = 0
0 + -2x = 22 + -10
-2x = 22 + -10
Combine like terms: 22 + -10 = 12
-2x = 12
Divide each side by '-2'.
x = -6
Simplifying
x = -6</span>
Answer:
∠D = 13°
Step-by-step explanation:
∠A and ∠D are vertical angles and thus are congruent, hence
x - 2 = - 3x + 58 ( add 3x to both sides )
4x - 2 = 58 ( add 2 to both sides )
4x = 60 ( divide both sides by 4 )
x = 15
∠D = x - 2 = 15 - 2 = 13°
