Answer:
<u>x = 3 y y = 2</u>
Step-by-step explanation:
a) Metodo de reduccion:
Para aplicar este metodo debemos multiplcar por 3 la ecuacion 2 y sumarlas.

*3

-------sumamos las ecuacioens--------


Ahora, remplazamos x en la ecuacion 2.


b) Igualacion
Debemos despejar x en ambas y luego igualarlas


Igualando:




Ahora, remplazamos y en la ecuacion 2.



c) Sustitucion
Despejamos x de la primero ecuacion y lo remplazamos en dos.


Multiplicamos por 4


Remplazando en 1.



Answer:
![x(t) = e ^{-3t} [-cos (4t) - \frac{3}{4}sin (4t)]](https://tex.z-dn.net/?f=x%28t%29%20%3D%20e%20%5E%7B-3t%7D%20%5B-cos%20%284t%29%20-%20%5Cfrac%7B3%7D%7B4%7Dsin%20%284t%29%5D)
Step-by-step explanation:
A force of 5 pounds stretches a spring 1 foot.
This implies that, the string constant (K) = 5 lbs? ft
Mass (m) = 
= 
The damping force 
The negativity of the damping force is due to the fact that it opposes the motion.
Then the force due to the spring is :
where;
x = the mass distance from the equilibrium point.
Total Force F = 
⇒ F = -1.2v - 5.0 x
⇒ mx = -1.2v - 5.0 x
where v = x' and a = x"
Hence, the equation becomes mx" = -1.2x' - 5.0 x
⇒
= 0
⇒ 
The auxiliary equation is can be written as:

⇒ r = 
r = 
r =
OR 
Now,the general equation of motion is :


Initial Conditions are:
x(0) = -1 and x' (0) = 0
x(0) = -1
⇒ -1 = 
x' (0) =0 ⇒ 0 = -3(-1) + (4
)
⇒
= 
Thus:
![x(t) = e ^{-3t} [-cos (4t) - \frac{3}{4}sin (4t)]](https://tex.z-dn.net/?f=x%28t%29%20%3D%20e%20%5E%7B-3t%7D%20%5B-cos%20%284t%29%20-%20%5Cfrac%7B3%7D%7B4%7Dsin%20%284t%29%5D)
Answer:62
Step-by-step explanation:
<span>To calculate the total miles he is allowed we must setup an expression for total cost of the car per day. Cost = 43.09 + .04x where x is the number of miles driven. To find out the number of miles driven with $100, we plug in $100 for cost and solve for x. Doing this we get 100 = 43.09 + .04x, where .04x = 56.91 and solving for x we get x=1422.75 or 1422 miles. In this case we do not round up since adding an additional mile would put us over the $100 budget. Answer = 1422 miles.</span>