Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be
, the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
![f'(p) = -0.02\cdot p +9](https://tex.z-dn.net/?f=f%27%28p%29%20%3D%20-0.02%5Ccdot%20p%20%2B9)
Let equalize the resulting expression to zero and solve afterwards:
![-0.02\cdot p + 9 = 0](https://tex.z-dn.net/?f=-0.02%5Ccdot%20p%20%2B%209%20%3D%200)
![p = 450](https://tex.z-dn.net/?f=p%20%3D%20450)
Second Derivative Test
![f''(p) = -0.02](https://tex.z-dn.net/?f=f%27%27%28p%29%20%3D%20-0.02)
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
![f(450) = -0.01\cdot (450)^{2}+9\cdot (450)](https://tex.z-dn.net/?f=f%28450%29%20%3D%20-0.01%5Ccdot%20%28450%29%5E%7B2%7D%2B9%5Ccdot%20%28450%29)
![f(450) =2025](https://tex.z-dn.net/?f=f%28450%29%20%3D2025)
The maximum sustainable yield is 202500 swordfishes.
The displacement between t = 0 and t = 3 is 45 meters, so the correct option is d.
<h3>
How to find the displacement?</h3>
The displacement is defined as the difference between the final position and the initial position.
The initial position is what we get when we evaluate in t = 0.
s = 0^3 -18*0^2+60*0 = 0
The initial position is 0 meters.
The initial position is what we get when we evaluate in t = 3.
s = 3^3 -18*3^2+60*3 = 45
The final position is 45 meters.
Then the displacement is:
D = 45m - 0m = 45m
The correct option is d.
If you want to learn more about displacements:
brainly.com/question/4931057
#SPJ1
One batch = 3 3/4 + 1 5/8
one batch = 3 6/8 + 1 5/8
one batch = 4 11/8
one batch = 5 3/8 pound of flour
One week = 86 pound
86 ÷ 5 3/8 = 86 ÷ 43/8
86 ÷ 5 3/8 = 86 x 8/43
86 ÷ 5 3/8 =16
She makes 16 batches of pasta
We can put both in an equation, when we do, x=6
:)
Answer:
![\Delta C=-5t^2-250](https://tex.z-dn.net/?f=%5CDelta%20C%3D-5t%5E2-250)
Step-by-step explanation:
Given:
The average cost of a computer in the year 2000 is given as:
![C=-5t^2+750](https://tex.z-dn.net/?f=C%3D-5t%5E2%2B750)
The average cost of a computer in the year 2008 is given as:
![C=-10t^2+500](https://tex.z-dn.net/?f=C%3D-10t%5E2%2B500)
Now, the difference in average cost between the years 2008 and 2000 can be calculated by subtracting the average cost in 2000 from the average cost in 2008.
Framing in equation form, we get:
Difference in average cost (ΔC) is given as:
![\Delta C=C_{2008}-C_{2000}\\\\\Delta C= (-10t^2+500)-(-5t^2+750)\\\\\textrm{Distributing the megative sign inside the second polynomial, we get:}\\\\\Delta C=-10t^2+500+5t^2-750\\\\\textrm{Grouping like terms, we get}\\\\\Delta C=(-10t^2+5t^2)+(500-750)\\\\\Delta C=-5t^2-250](https://tex.z-dn.net/?f=%5CDelta%20C%3DC_%7B2008%7D-C_%7B2000%7D%5C%5C%5C%5C%5CDelta%20C%3D%20%28-10t%5E2%2B500%29-%28-5t%5E2%2B750%29%5C%5C%5C%5C%5Ctextrm%7BDistributing%20the%20megative%20sign%20inside%20the%20second%20polynomial%2C%20we%20get%3A%7D%5C%5C%5C%5C%5CDelta%20C%3D-10t%5E2%2B500%2B5t%5E2-750%5C%5C%5C%5C%5Ctextrm%7BGrouping%20like%20terms%2C%20we%20get%7D%5C%5C%5C%5C%5CDelta%20C%3D%28-10t%5E2%2B5t%5E2%29%2B%28500-750%29%5C%5C%5C%5C%5CDelta%20C%3D-5t%5E2-250)
Therefore, the difference in the costs for a computer between 2008 and 2000 is ![\Delta C=-5t^2-250](https://tex.z-dn.net/?f=%5CDelta%20C%3D-5t%5E2-250)