Recall that
So we have
So either .
Since , we expect , so we take the negative square root. Then
This then means we have
C=2.50+2m
This is your standard y=mx+b equation. 2.50 is your y intercept or starting point. 2m is the slop of the line. 2 on the x axis for every 1 on the y axis.
Answer:
=4sqrt(10)
Step-by-step explanation:
The geometric mean of two numbers is sqrt(a*b) where a and b are the two numbers
geometric mean = sqrt(8*20)
=sqrt(160)
= sqrt(16*10)
We know that sqrt(ab) = sqrt(a) sqrt(b)
=sqrt(16) sqrt(10)
=4sqrt(10)
I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal