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.
The hypotenuse is the square root of 58.
a^2+b^2=c^2
7^2+3^2=c^2
49+9=c^2
58=c^2
c= square root of 58
R = x(A+B)
distribute
R=Ax+Bx
subtract Ax from each side
R-Ax=Bx
divideby x
(R-Ax)/x =B
Choice C
.0091 rounded to the nearest hundredths is .01.
I don't know how to use as a bar diagram, but all I know is the solution is 30 students in the class. 8/10=24, so 10/10=x, since (10/10)/(8/10)= 5/4, then you multiply 24 by 5/4 to get 30 students as your answer.
Hope I'm a brainliest for this question!
