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)
Answer:
3 one
Step-by-step explanation:
Answer:
![\frac{100 meters}{x seconds} = \frac{200 meters}{22.4 seconds}](https://tex.z-dn.net/?f=%5Cfrac%7B100%20meters%7D%7Bx%20seconds%7D%20%20%3D%20%5Cfrac%7B200%20meters%7D%7B22.4%20seconds%7D)
Step-by-step explanation:
8x=90
90/8= 11.25
x= 11.25
Perímetro del rectángulo = 74 pulgadas
Deje que el ancho del rectángulo sea 'x'.
Entonces, la longitud de este rectángulo = x + 5
We know that :
![\color{hotpink}\tt \: Perímetro \: del \: rectángulo =\color{plum} 2 × (l + b)](https://tex.z-dn.net/?f=%5Ccolor%7Bhotpink%7D%5Ctt%20%5C%3A%20Per%C3%ADmetro%20%20%5C%3A%20del%20%5C%3A%20%20rect%C3%A1ngulo%20%3D%5Ccolor%7Bplum%7D%202%20%C3%97%20%28l%20%2B%20b%29%20)
Lo que significa :
![=\tt 2(x + x + 5) = 74](https://tex.z-dn.net/?f=%20%3D%5Ctt%202%28x%20%2B%20x%20%2B%205%29%20%3D%2074)
![=\tt 2(2x + 5) = 74](https://tex.z-dn.net/?f=%20%3D%5Ctt%202%282x%20%2B%205%29%20%3D%2074)
![=\tt 4x +10 = 74](https://tex.z-dn.net/?f=%20%3D%5Ctt%204x%20%2B10%20%3D%2074%20)
![=\tt 4x = 74 - 10](https://tex.z-dn.net/?f=%20%3D%5Ctt%204x%20%3D%2074%20-%2010)
![=\tt 4x = 64](https://tex.z-dn.net/?f=%20%3D%5Ctt%204x%20%3D%2064)
![=\tt x = \frac{64}{4}](https://tex.z-dn.net/?f=%20%3D%5Ctt%20x%20%3D%20%20%5Cfrac%7B64%7D%7B4%7D%20)
![\color{plum} =\tt x = 16](https://tex.z-dn.net/?f=%5Ccolor%7Bplum%7D%20%3D%5Ctt%20x%20%3D%2016)
Por lo tanto, el ancho de este rectángulo = 16 pulgadas
Entonces, la longitud de este rectángulo :
![=\tt x + 5](https://tex.z-dn.net/?f=%20%3D%5Ctt%20x%20%2B%205)
![= \tt16 + 5](https://tex.z-dn.net/?f=%20%3D%20%5Ctt16%20%2B%205)
![\color{plum} =\tt 21 \: pulgadas](https://tex.z-dn.net/?f=%5Ccolor%7Bplum%7D%20%3D%5Ctt%2021%20%5C%3A%20pulgadas)
La longitud de este rectángulo = 21 pulgadas
<h2>Por lo tanto :</h2>
● Longitud del rectángulo = <em>21 pulgadas</em>
● Ancho del rectángulo = <em>16 pulgadas</em>