Answer:
The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).
Step-by-step explanation:
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If you add them all together, you'd get 157. Then you divide by 7 and you'd get 31.4
Answer:
Interest = A - P = 1015 - 1000 = $15
Step-by-step explanation:
Answer:
a.![w(t)=-12e^{2t}](https://tex.z-dn.net/?f=w%28t%29%3D-12e%5E%7B2t%7D)
b.![y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}](https://tex.z-dn.net/?f=%20y%28t%29%3D-%5Cfrac%7B9%7D%7B2%7De%5E%7B7t%7D-%5Cfrac%7B5%7D%7B2%7De%5E%7B-5t%7D)
Step-by-step explanation:
We have a differential equation
y''-2 y'-35 y=0
Auxillary equation
![(D^2-2D-35)=0](https://tex.z-dn.net/?f=%28D%5E2-2D-35%29%3D0)
By factorization method we are finding the solution
![D^2-7D+5D-35=0](https://tex.z-dn.net/?f=D%5E2-7D%2B5D-35%3D0)
![(D-7)(D+5)=0](https://tex.z-dn.net/?f=%28D-7%29%28D%2B5%29%3D0)
Substitute each factor equal to zero
D-7=0 and D+5=0
D=7 and D=-5
Therefore ,
General solution is
![y(x)=C_1e^{7t}+C_2e^{-5t}](https://tex.z-dn.net/?f=y%28x%29%3DC_1e%5E%7B7t%7D%2BC_2e%5E%7B-5t%7D)
Let ![y_1=e^{7t} \;and \;y_2=e^{-5t}](https://tex.z-dn.net/?f=y_1%3De%5E%7B7t%7D%20%5C%3Band%20%5C%3By_2%3De%5E%7B-5t%7D)
We have to find Wronskian
![w(t)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}](https://tex.z-dn.net/?f=w%28t%29%3D%5Cbegin%7Bvmatrix%7Dy_1%26y_2%5C%5Cy%27_1%26y%27_2%5Cend%7Bvmatrix%7D)
Substitute values then we get
![w(t)=\begin{vmatrix}e^{7t}&e^{-5t}\\7e^{7t}&-5e^{-5t}\end{vmatrix}](https://tex.z-dn.net/?f=w%28t%29%3D%5Cbegin%7Bvmatrix%7De%5E%7B7t%7D%26e%5E%7B-5t%7D%5C%5C7e%5E%7B7t%7D%26-5e%5E%7B-5t%7D%5Cend%7Bvmatrix%7D)
![w(t)=-5e^{7t}\cdot e^{-5t}-7e^{7t}\cdot e^{-5t}=-5e^{7t-5t}-7e^[7t-5t}](https://tex.z-dn.net/?f=w%28t%29%3D-5e%5E%7B7t%7D%5Ccdot%20e%5E%7B-5t%7D-7e%5E%7B7t%7D%5Ccdot%20e%5E%7B-5t%7D%3D-5e%5E%7B7t-5t%7D-7e%5E%5B7t-5t%7D)
![w(t)=-5e^{2t}-7e^{2t}=-12e^{2t}](https://tex.z-dn.net/?f=w%28t%29%3D-5e%5E%7B2t%7D-7e%5E%7B2t%7D%3D-12e%5E%7B2t%7D)
a.![w(t)=-12e^{2t}](https://tex.z-dn.net/?f=w%28t%29%3D-12e%5E%7B2t%7D)
We are given that y(0)=-7 and y'(0)=23
Substitute the value in general solution the we get
![y(0)=C_1+C_2](https://tex.z-dn.net/?f=y%280%29%3DC_1%2BC_2)
....(equation I)
![y'(t)=7C_1e^{7t}-5C_2e^{-5t}](https://tex.z-dn.net/?f=y%27%28t%29%3D7C_1e%5E%7B7t%7D-5C_2e%5E%7B-5t%7D)
![y'(0)=7C_1-5C_2](https://tex.z-dn.net/?f=y%27%280%29%3D7C_1-5C_2)
......(equation II)
Equation I is multiply by 5 then we subtract equation II from equation I
Using elimination method we eliminate![C_1](https://tex.z-dn.net/?f=%20C_1)
Then we get ![C_2=-\frac{5}{2}](https://tex.z-dn.net/?f=C_2%3D-%5Cfrac%7B5%7D%7B2%7D)
Substitute the value of
in I equation then we get
![C_1-\frac{5}{2}=-7](https://tex.z-dn.net/?f=%20C_1-%5Cfrac%7B5%7D%7B2%7D%3D-7)
![C_1=-7+\frac{5}{2}=\frac{-14+5}{2}=-\frac{9}{2}](https://tex.z-dn.net/?f=%20C_1%3D-7%2B%5Cfrac%7B5%7D%7B2%7D%3D%5Cfrac%7B-14%2B5%7D%7B2%7D%3D-%5Cfrac%7B9%7D%7B2%7D)
Hence, the general solution is
b.![y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}](https://tex.z-dn.net/?f=%20y%28t%29%3D-%5Cfrac%7B9%7D%7B2%7De%5E%7B7t%7D-%5Cfrac%7B5%7D%7B2%7De%5E%7B-5t%7D)
Answer: im not really sure but is it 605
Step-by-step explanation:
11•11•15/3