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:
x= -3
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable x.
Answer:
48 Plants
Step-by-step explanation:
3 per packet
42 / 14 = 3
3 x 16 = 48
48 Plants
Hope this helped!
Answer: Option C.
Step-by-step explanation:
The volume of a sphere can be calculated with this formula:
Where "r" is the radius.
You can observe in the figure that the value of the radius of this sphere is:
Then you can substitute this radius into the formula .
Therefore, the volume of the sphere shown in the figure is:
Answer:
Step-by-step explanation:
Don't use 0 as a substitute for θ. 0 is always 0.
cosθ = -5/(2√15)
secθ = 1/cosθ = -2√15/5
