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))
not sure how much she bought, but all you’d have to do is multiply the cost of salmon fillets ($8.30) times the amount she bought.
Example: if Mrs. Patrolia bought 3 pounds it would be $8.30 x 3.
Answer:
base side = 20cm
height = 40 cm
minimum cost = $7200
Step-by-step explanation:
Let x (cm) be the base side and h (cm) be the height of the box. Since the volume of the box must be 16000 cubic cm, we have:
The areas of the top and bottom is
And so their cost is:
The areas of the sides is
And so their cost is:
We can substitute into the equation above to get
So the total cost of the bases and the sides:
This is the function we would want to minimize. We can start by taking the 1st derivative, and set it to 0
So the height would be
So the minimum total cost would be
Answer:
x≤3 or x>10
Step-by-step explanation:
x≤3 because the dot is a solid dot at 3 and pointing backward toward numbers less than 3.
x>10 because the dot is an open circle pointing toward numbers greater than 10.
Ben can type 510 words in ten minutes.
153 words/3 minutes = 153/3
= 153 words ÷ 3 / 3 min ÷ 3
= 51 words / 1 min
51 x 10 (minutes) = 510.