42% of the body voted = 11960
Total student body = 11960/42% = 28476.19 = 28476 students
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.
If the total age of both April and Amy are 53
And Amy is 9 years younger than april.
Then to solve for Amy's age you would subtract 9 from 53 and divide by 2
which equals 22
Since amy is 9 years younger than April, then April's age is Amy's age 22 + 9 which gives you 31
April's age is 31 and Amy's age is 22
1. Vertex: f(x)=x^2+2x+3
=> a=1 b=2
=> x=-2/2*1 => x=-2/2
=> x=-1
=> (-1,2)
2. Axis of symmetry: x=-1
