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ANEK [815]
3 years ago
11

Find the equation of the line that passes through point A (1,7) and B (-3, -1)

Mathematics
1 answer:
amid [387]3 years ago
6 0

Answer:

The equation of the line is 2 x - y + 5 = 0.

Step-by-step explanation:

Here the given points are A( 1, 7) & B( -3, - 1) -

Equation of a line whose points are given such that

( x_{1}, y_{1} ) & ( x_{2}, y_{2} )-

 y - y_{1}  = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }   ( x - x_{1}  )

i.e. <em> y - 7= \frac{- 1 - 7}{ -3-1}  ( x- 1)</em>

<em>       y - 7 =  \frac{- 8}{- 4} ( x -1)</em>

<em>       y - 7 =  2 ( x - 1) </em>

<em>       y - 7  =   2  x - 2</em>

<em>       2 x - y + 5 = 0</em>

Hence the equation of the required line whose passes trough the points ( 1, 7) & ( -3, -1)  is 2 x - y  + 5 = 0.

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Determine the astm grain size number if 33 grains per square inch are measured at a magnification of 270×
strojnjashka [21]
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
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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
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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
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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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