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andrezito [222]
3 years ago
15

Solve for x 2|x-6|+14=38

Mathematics
1 answer:
ale4655 [162]3 years ago
4 0

Answer:

x=18   x=-6

Step-by-step explanation:

2|x-6|+14=38

The first step is to isolate the absolute value

Subtract 14 from each side

2|x-6|+14-14=38-14

2|x-6|=24

Divide by 2 on each side

2/2|x-6|=24/2

|x-6| = 12

Now we can seperate the absolute value into two parts, the positive and the negative

x-6 =12          x-6 = -12

Add 6 to each side

x-6+6 =12+6     x-6+6 = -12+6

x=18                    x= -6

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Determine the astm grain size number if 33 grains per square inch are measured at a magnification of 270×
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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.
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