Answer:
Step-by-step explanation:
? whats the question
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer:
x : -3
Step-by-step explanation:
1) 15x-3(3x + 4) = 6 (distribute -3 to the numbers on the inside of parentheses)
2) 15x - 9x - 12 =6 (combine like terms 15x-9x = 6x)
3) -6x - 12 = 6 (add twelve to both sides, add the 12 to cancel out the 12)
4) -6x = 18 (divide the -6 on both sides)
5) x = -3
Lets create both equations and :
f(x) = 5x^2 + 1
linear binomial form: x - 4
according to the remainder theorem, x - 4 is a divisor of f(x) if and only if f(4) = 0
f(4) = 5*16 + 1 = 81
hence x - 4 is not a divisor of f(x)
Hello, thanks for using Brainly!
We are solving 6x6-4+9.
We will do three steps in this case.
First is 6x6, 6x6 is 30.
So now we must keep in our head we have 30 as our first number.
Now, let's -4 from 30. 30-4 is 26.
We just did step 2. Boom!
So, we have 26 as our second number. Let's do our third step.
If we have 26, we need to add 9 to that. To quickly find that we know that 26+10 is 36. That is adding ten, we need 9 so minus 1 from 36 we get 35.
Our final answer is 35.
