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lukranit [14]
3 years ago
5

Please answer offering a lot of points and give brainliest pleaseeeee

Physics
1 answer:
asambeis [7]3 years ago
3 0

23 is the right answer.

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The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 9
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Answer:

At light intensity I = 3, is P a maximum

Explanation:

Given:

P=\frac{90I}{I^2+I+9}

now differentiating the above equation with respect to Intensity 'I' we get

\frac{dp}{dI}=\frac{(I^2+I+9).\frac{d(90I)}{dI}-90I.\frac{d((I^2+I+9)}{dI}}{(I^2+I+9)^2}

or

\frac{dp}{dI}=\frac{(I^2+I+9).90-90I.(2I+1)}{(I^2+I+9)^2}

or

\frac{dp}{dI}=\frac{90I^2+90I+810)-(180I^2+90I)}{(I^2+I+9)^2}

or

\frac{dp}{dI}=\frac{-90I^2+810)}{(I^2+I+9)^2}

Now for the maxima \frac{dP}{dI}=0

thus,

0=\frac{-90I^2+810)}{(I^2+I+9)^2}

or

-90I^2+810=0

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I^2=\frac{810}{90}

or

I^2=9

or

I = 3

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at I = 3

P=\frac{90\times3}{3^2+3+9}

or

P=\frac{270}{21}

or

P=12.85

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3 years ago
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