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.
Step-by-step explanation:
the answer is in the picture above
Answer:
Hence, the correct option is;
They are parallel because they have the same slope of -2
Step-by-step explanation:
Here we have;
AB falls on the line 6x + 3y = 9..........................(1)
CD falls on the line 4x + 2y = 8..........................(2)
Therefore, for equation (1),
3y = 9 - 6x which gives;
y = -2x + 3
for equation (2),
2y = 8 - 4x which gives;
y = -2x + 4
The equation of a straight line is y = m·x + c
Where:
m = Slope
c = Intercept
Hence, since, by comparison to the equation of a straight line, both lines have the same slope of -2, but different intercept, we have that both lines are parallel
Hence, the correct option is;
They are parallel because they have the same slope of -2.
Answer:
He'll pay $110.25
Step-by-step explanation:
To find the area, we divide the shape into two parts at approximately the middle line. The top shape is a trapezoid of base length 7 feet and height 6 feet, while the bottom shape is a parallelogram with one side equal to 4 feet.
Area of trapezoid = (7 + 4)/2 x 6
Area of trapezoid = 33 sq ft
Area of parallelogram = 4 x 4
Area of parallelogram = 16 sq ft
Total area = 49 sq ft
Cost = 2.25 x 49
Cost = $110.25
Answer:
30 miles apart.
Step-by-step explanation:
The scale for the map is 1 inch represents a distance of 10 miles.
That is 1 inch : 10 miles.
We want to find the number of miles two towns are apart, if they are 3 miles apart on the map.
We just have to multiply each term in the ratio by 10 to get:
3 inches: 30 miles
Therefore the two towns will be 30 miles apart.