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:53
Step-by-step explanation:
Answer:4,500
Step-by-step explanation:
720 multiple by 25 gives you 18,000 then you find 25% of 18,000 by multiplying 18,000 times 25/100 which gives you 4,500. Or you can find 25%of 25 then multiple the answer by 720
Thanks for including the graph!
Okay, so -
From examining the graph, we can see that for every minute the number of words increases by 40.
Now, since the x axis (the horizontal thingy kabob at the bottom) is time, and the y axis (the vertical thingy kabob) is the number of words - we can conclude that the answer is B!
Just remember that the value of the y axis is dependent on the value of the x axis. Also, note that x almost always represents time!
