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V125BC [204]
3 years ago
15

Determine the vertical asymptote for the rational function f(x) = x-4 over 3x +2

Mathematics
1 answer:
Ghella [55]3 years ago
8 0

Answer:  (b) x = -2/3

<u>Step-by-step explanation:</u>

The vertical asymptote is the restriction on x.

The denominator cannot be equal to zero so that it the restriction.

Set the denominator equal to zero and solve for x to find the asymptote.

3x + 2 = 0

3x       = -2

 x       = -2/3

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A peach orchard owner wants to maximize the amount of peaches produced by her orchard.
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Answer:

  a) Y(x) = {900, x≤30; 900-40(x-30), x>30}

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Step-by-step explanation:

a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.

\displaystyle Y(x)=\left\{\begin{array}{lcl}900&\text{for}&x\le 30\\900-40(x-30)&\text{for}&x>30\end{array}\right.

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b) The yield per acre is the product of the number of trees and the yield per tree:

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c) The derivative is ...

\displaystyle\frac{dT}{dx}=\left \{\begin{array}{lcl}900&\text{for}&x\le 30\\2100-80x& \text{for}&x>30\end{array}\right.

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The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.

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