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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 = 120i i2 + i + 9 where i is the light intensity (measured in thousands of foot-candles). for what light intensity is p a maximum?

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The given function is:

P = 120 i / (i^2 + i + 9)

or

P = 120 i (i^2 + i + 9)^-1

The maxima point is obtained by taking the 1st
derivative of the function then equating dP / di = 0:

dP / di = 120 (i^2
+ i + 9)^-1 + (-1) 120 i (i^2 + i + 9)^-2 (2i + 1)

setting dP / di =0 and multiplying whole equation by (i^2
+ i + 9)^2:

0 = 120 (i^2 + i + 9) – 120i (2i + 1)

Dividing further by 120 will yield:

i^2 + i + 9 – 2i^2 – i = 0

-i^2 + 9 =0

i^2 = 9

i = 3      (ANSWER)

Therefore P is a maximum when i = 3

Checking:

P = 120 * 3 / (3^2 + 3 + 9)

P = 17.14

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If a Killer whale is feeding at the fourth trophic level, how much phytoplankton mass is required to add each gram of new mass to the whale? Assume that 10% of the energy at one trophic level is transferred to the next level. a. 1000 grams b. 100 grams c. 500 grams d. 1 gram

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The correct answer is option C, that is, 30 minutes.  

It is essential to get a good night sleep for good mental, physical, and emotional health. It is as essential as consuming a healthy diet and doing enough exercise. It has been found that about half of the adults do not shut their eyes, with many admitting that they lie awake at night fretting about their worries.  

Thus, to tackle the situation, one should be preparing to go to sleep before 30 minutes of light out. One needs to put the body and brain in the right state where sleep can take place easily.  

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Which of the following is a major group of Protista? algae phytoplankton protozoa all of the above

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Which of the following is a major group of Protista? algae phytoplankton protozoa all of the above

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