Answer:
3x
Step-by-step explanation:
So the ornament is $16.00-3/4% off=15.88
-3/4%=0.12 So, $16.00-0.12=15.88
The ornament costs $15.88.
Answer:
![y" + 2y' + 2y = 0](https://tex.z-dn.net/?f=y%22%20%2B%202y%27%20%2B%202y%20%3D%200)
Step-by-step explanation:
Given
![y=c_1e^{-x}cosx+c_2e^{-x}sinx](https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B-x%7Dcosx%2Bc_2e%5E%7B-x%7Dsinx)
Required
Determine a homogeneous linear differential equation
Rewrite the expression as:
![y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)](https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B%5Calpha%20x%7Dcos%28%5Cbeta%20x%29%2Bc_2e%5E%7B%5Calpha%20x%7Dsin%28%5Cbeta%20x%29)
Where
and ![\beta = 1](https://tex.z-dn.net/?f=%5Cbeta%20%3D%201)
For a homogeneous linear differential equation, the repeated value m is given as:
![m = \alpha \± \beta i](https://tex.z-dn.net/?f=m%20%3D%20%5Calpha%20%5C%C2%B1%20%5Cbeta%20i)
Substitute values for
and ![\beta](https://tex.z-dn.net/?f=%5Cbeta)
![m = -1 \± 1*i](https://tex.z-dn.net/?f=m%20%3D%20-1%20%5C%C2%B1%201%2Ai)
![m = -1 \± i](https://tex.z-dn.net/?f=m%20%3D%20-1%20%5C%C2%B1%20i)
Add 1 to both sides
![m +1= 1 -1 \± i](https://tex.z-dn.net/?f=m%20%2B1%3D%201%20-1%20%5C%C2%B1%20i)
![m +1= \± i](https://tex.z-dn.net/?f=m%20%2B1%3D%20%5C%C2%B1%20i)
Square both sides
![(m +1)^2= (\± i)^2](https://tex.z-dn.net/?f=%28m%20%2B1%29%5E2%3D%20%28%5C%C2%B1%20i%29%5E2)
![m^2 + m + m + 1 = i^2](https://tex.z-dn.net/?f=m%5E2%20%2B%20m%20%2B%20m%20%2B%201%20%3D%20i%5E2)
![m^2 + 2m + 1 = i^2](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%201%20%3D%20i%5E2)
In complex numbers:
![i^2 = -1](https://tex.z-dn.net/?f=i%5E2%20%3D%20-1)
So, the expression becomes:
![m^2 + 2m + 1 = -1](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%201%20%3D%20-1)
Add 1 to both sides
![m^2 + 2m + 1 +1= -1+1](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%201%20%2B1%3D%20-1%2B1)
![m^2 + 2m + 2= 0](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%202%3D%200)
This corresponds to the homogeneous linear differential equation
![y" + 2y' + 2y = 0](https://tex.z-dn.net/?f=y%22%20%2B%202y%27%20%2B%202y%20%3D%200)
F(x)=x^3+2
we see the power is odd
the ends go in opsoite directions
we know that if the leadind coefient (number in front of highest power term) is positive, then odd powered polynomials go from bottom left to top right
and for even ones, it goes both up
for negative, odd ones go from top left to bottom right
for even, both go down
we gots
f(x)=1x^3+2
positive and odd, so it goes from bottom left to top right
as x approaches negative inifnity, y approaches negaitve infinity
as x approaches infinity, y approaches infinity
Answer:
a = 70 km/h - 20 km/h / 0.008 h = 50 km/h / 0.008 h = 6250 km/h²