A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks, the sheet is only 1.25 meters thick. Let y represent the ice sheet's thickness ( in meters) after x weeks. Complete the equation for the relationship between the thickness and number of weeks.
Answer:
y = 2 - 0.25x
Step-by-step explanation:
From the question, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet reduced to 1.25 meters
Hence, the difference in the thickness in 3 weeks is calculated as:
2m - 1.25m = 0.75m
The amount of changes that occurred in 3 weeks is given as:
= 0.75/3 = 0.25 meters,
We are told that, the ice is melting with the constant rate.
Therefore, the equation for the relationship between the thickness and number of weeks is given as:
y = 2 - 0.25x
Answer:
f (g(x)) = 12x + 8
g(f(x)) = 12x + 48
Step-by-step explanation:
These are composition of functions.
(Unless I am reading your notation wrong) Are the functions multiplying eachother? Is the F actually a lower case f ?
Simply do some substitutions.
f (g(x)) = 2 ( 6x) + 8 = 12x + 8
g (f (x) ) = 6 (2x + 8) = 12x + 48
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.
Answer:
1. a 2. b 3. can't see 4.c 5. b c e
Step-by-step explanation: