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iren [92.7K]
2 years ago
15

Printing signs costs $28 for the design plates plus $2 per sign. Which equation correctly describes the cost, c, of s signs?

Mathematics
1 answer:
Dmitriy789 [7]2 years ago
8 0

Answer:

Step-by-step explanation:

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The number of salmon swimming upstream to spawn is approximated by the following function:
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Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

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Let S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965, for 6 \leq x \leq 20. x represents the temperature of the water, measured in degrees Celsius, and S is the number of salmon swimming upstream to spawn, dimensionless.

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Then we equalize (Eq. 1) to zero and solve for x:

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And all roots are found by Quadratic Formula:

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Only the first root is inside the given interval of the function. Hence, the correct answer is:

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Now we evaluate the second derivative at given result. That is:

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S''(12.305) = -69.83

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

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