Answer:
1-51
2-18
3-123
4-39
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
So angle 2 and angle 4 have a relationship that is called same-side interior or consecutive interior angles. The name there depends what class you are in but they mean the same thing.
If you have the transversal goes through parallel lines, then same-side interior angles will add up to 180 degrees.
So you are trying to solve the following equation for x:
angle2+angle4=180
2x+10+4x+80=180
Combine like terms:
6x+90=180
Subtract 90 on both sides:
6x =90
Divide both sides by 6:
x =90/6
Simplify:
x =15
15 is x so that the lines are parallel
I think it is
(-infinity, infinity)
Answer:
dy/dt = y ( 3 - y )
Step-by-step explanation:
Given data:
Determine an autonomous differential equation with the following properties
y = 0 and Y = 3
y' > 0 for 0 < y < 3
y' < 0 for -∞ < y < 0 and 3 < y < ∞
considering an autonomous differential equation
dy/dt = y ( 3 - y )
y = 0 and 3 represents equilibrium solutions
if 0 < y < 3 then y ( 3 - y ) > 0 for 0 < y < 3
hence : dy / dt = y' > 0 for 0 < y < 3
y ( 3 - y ) < 0 for -∞ < y < 0 and 3 < y < ∞
hence : dy / dt = y' < 0 for -∞ < y < 0 and 3 < y < ∞
this shows that the autonomous differential equation satisfies every condition hence the autonomous differential equation is :
dy/dt = y ( 3 - y )
