The maximum number of fish is going to be p(9) = 200
The information given doesnt work. If she bought each nephew a gift at the lowest price of 14 dollars each, she would still pay $126 (9 x 14)
Some given information must be wrong. She must either have less nephews or have spent more money.
Answer:
The complete solution is
Step-by-step explanation:
Given differential equation is
3y"- 8y' - 3y =4
The trial solution is
![y = e^{mx}](https://tex.z-dn.net/?f=y%20%3D%20e%5E%7Bmx%7D)
Differentiating with respect to x
![y'= me^{mx}](https://tex.z-dn.net/?f=y%27%3D%20me%5E%7Bmx%7D)
Again differentiating with respect to x
![y''= m ^2 e^{mx}](https://tex.z-dn.net/?f=y%27%27%3D%20m%20%5E2%20e%5E%7Bmx%7D)
Putting the value of y, y' and y'' in left side of the differential equation
![3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0](https://tex.z-dn.net/?f=3m%5E2e%5E%7Bmx%7D-8m%20e%5E%7Bmx%7D-%203e%5E%7Bmx%7D%3D0)
![\Rightarrow 3m^2-8m-3=0](https://tex.z-dn.net/?f=%5CRightarrow%203m%5E2-8m-3%3D0)
The auxiliary equation is
![3m^2-8m-3=0](https://tex.z-dn.net/?f=3m%5E2-8m-3%3D0)
![\Rightarrow 3m^2 -9m+m-3m=0](https://tex.z-dn.net/?f=%5CRightarrow%203m%5E2%20-9m%2Bm-3m%3D0)
![\Rightarrow 3m(m-3)+1(m-3)=0](https://tex.z-dn.net/?f=%5CRightarrow%203m%28m-3%29%2B1%28m-3%29%3D0)
![\Rightarrow (3m+1)(m-3)=0](https://tex.z-dn.net/?f=%5CRightarrow%20%283m%2B1%29%28m-3%29%3D0)
The complementary function is
![y= Ae^{3x}+Be^{-\frac13 x}](https://tex.z-dn.net/?f=y%3D%20Ae%5E%7B3x%7D%2BBe%5E%7B-%5Cfrac13%20x%7D)
y''= D², y' = D
The given differential equation is
(3D²-8D-3D)y =4
⇒(3D+1)(D-3)y =4
Since the linear operation is
L(D) ≡ (3D+1)(D-3)
For particular integral
![y_p=\frac 1{(3D+1)(D-3)} .4](https://tex.z-dn.net/?f=y_p%3D%5Cfrac%201%7B%283D%2B1%29%28D-3%29%7D%20.4)
[since
]
[ replace D by 0 , since L(0)≠0]
![=-\frac43](https://tex.z-dn.net/?f=%3D-%5Cfrac43)
The complete solution is
y= C.F+P.I
![\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43](https://tex.z-dn.net/?f=%5Ctherefore%20y%3D%20Ae%5E%7B3x%7D%2BBe%5E%7B-%5Cfrac13%20x%7D-%5Cfrac43)
The length of the prism is 15 feet.
Step-by-step explanation:
Step 1:
The volume of a rectangular prism is the product of its length, its width, and its height.
The volume of a rectangular prism = ![(length)(width)(height).](https://tex.z-dn.net/?f=%28length%29%28width%29%28height%29.)
Assume the length of this prism is
feet, the width of the prism is 9 feet and the height is 8 feet.
The volume of the prism is given as 1,080 cubic feet.
Step 2:
The volume of a rectangular prism = ![(length)(width)(height).](https://tex.z-dn.net/?f=%28length%29%28width%29%28height%29.)
![1080=(l)(9)(8) = 72l,](https://tex.z-dn.net/?f=1080%3D%28l%29%289%29%288%29%20%3D%2072l%2C)
![l = \frac{1080}{72} = 15.](https://tex.z-dn.net/?f=l%20%3D%20%5Cfrac%7B1080%7D%7B72%7D%20%20%3D%2015.)
So the length of the rectangular prism is 15 feet.
The slope of g(x) would be 5-2/1-0=3
they have the same slope