Simplified form : 17y + 7
Answer:
Some.
Terms that include a number and a letter are expressions.
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:
19.44
Step-by-step explanation:
We have the following information:
3 red balls, 5 green balls, and 1 yellow ball
In total there are 3 + 5 + 1 = 9 balls.
We calculate the probability of each:
Network: 3/9
Green: 5/9
Yellow: 1/9
Each one corresponds a price in profit or losses:
Network: 4
Green: -3
Yellow: 10
So in total it would be the sum of the multiplication of the probability and the price and then multiply everything by 25:
(4 * 3/9 + -3 * 5/9 + 10 * 1/9) * 25 = (0.777) * 25
= 19.44
U have a dashed line...meaning there is no equal sign in the problem.....it goes thru the origin (0,0)...meaning the y int is 0....u have a slope of 3/4
so ur inequality is : y = 3/4x <==
