Substituting this into the other ODE gives
Since , it follows that . The ODE in has characteristic equation
with roots , admitting the characteristic solution
From the initial conditions we get
So we have
Take the derivative and multiply it by -1/4 to get the solution for :
Answer:
144
Step-by-step explanation:
PEMDAS
(12)^2
144
Answer:
∠3 is 70°
Step-by-step explanation:
∠1 is 50° since it is across from another 50° angle
and then you use the equation x+25+2x+50=180 to find x
x then equals 35°
you then use the alternate interior angle theorem to say that ∠3 is 2x, or 70°
Check out the attached image. I drew what I think your book is showing. The figure on the left is triangle ABC without any extended segments. The figure on the right has segment AB extended shown in red. This forms the exterior angle x
The rule that connects x, y and z together is the remote interior angle theorem. It says that adding two interior angles is going to be equal to the exterior angle that is not touching either interior angle. The "remote" part means "far away" so just think of the two angles that are furthest way or not touching the exterior angle in question.
In terms of algebra, the rule is
x+y = z