Mrs. Brown hosts an yearly art contest keeps a record of the number of entries each year.
1 answer:
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Answer: The average velocity of the object over the time interval [3,6] is 20.
Step-by-step explanation:
Since we have given that
s(3) = 156
s(6) = 216
We need to find the average velocity over the time interval [3,6].
So, average velocity becomes
Hence, the average velocity of the object over the time interval [3,6] is 20.
Answer:
The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Step-by-step explanation:
Let , for
.
represents the temperature of the water, measured in degrees Celsius, and
is the number of salmon swimming upstream to spawn, dimensionless.
We compute the first and second derivatives of the function:
(Eq. 1)
(Eq. 2)
Then we equalize (Eq. 1) to zero and solve for :
And all roots are found by Quadratic Formula:
,
Only the first root is inside the given interval of the function. Hence, the correct answer is:
Now we evaluate the second derivative at given result. That is:
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.