Answer:
4
Step-by-step explanation:
-2x- 4 + 5x = 8
Collect like terms
-2x + 5x = 8 +4( when a variable crosses over equality sign it becomes either negative or positive depending on the sign)
3x = 12
Divide via by coefficient of x
X = 12/3
= 4
The volume of the prism given its dimensions is equal to 160 cubic units.
<h3>What is the volume of the
prism?</h3>
The given prism is made up of two prisms. The volume of the prism is the volume of the two shapes.
- One of the prisms have the dimensions: 4 x 4 x 5.
Volume = 80
- The other prism has the dimensions: 8 x 2 x 5.
Volume = 80
Volume of the prism = 80 x 2 = 160 cubic units.
To learn more about rectangular prisms, please check: brainly.com/question/8890358
Answer:
i think 42
Step-by-step explanation:
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.
