Calculating Mean Absolute Deviation
2 answers:
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Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
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<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
This is the isosceles right triangle, the diagonal of a square, the thing that so upset the Pythagoreans. The two sides and diagonal of a square are in ratio so we get
We could have also gotten this using Trig:
Or by recognizing u=v because remaining angle is 45 so this must be isosceles so
9514 1404 393
Answer:
C. 0.98
Step-by-step explanation:
The attached graph shows the constraints. The feasible solution space is the doubly-shaded area in the first quadrant. The negative coefficients on x and y suggest that the objective function will be maximized when x and y are minimized. The solution space vertex that does that is ...
(x, y, Y) = (6, 4, 0.98)
