Please help me write a 2 column proof AB parallel to DC ; BC parallel to AE prove BC/EA = BD/EB
1 answer:
Answer and Step-by-step explanation:
Since it is given that
AB || DC
BC || AE
Based on this we can conclude that
If AB || DC
So we can say
∠ABE ≅ ∠CDB
This indicates that the alternate interior angles are congruent i.e its angle and sides are equal
Now
If BC || AE
So we can say
∠CBD ≅ ∠BEA
This indicates that the alternate interior angles are congruent i.e its angle and sides are equal
Now
ΔAEB is same as ΔCBD
This indicates that in one triangle two angles are same to another two angles so both triangles are similar to each other i.e this is a AA Similarity Postulate
Finally we proof
As the same sides are proportional to each other
We compared both based on interior angles
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Answer:
Step-by-step explanation:
The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:
A differential equation of the form:
Will have a characteristic equation of the form:
Where solutions are the roots from which the general solution can be found.
For real roots the solution is given by:
For real repeated roots the solution is given by:
For complex roots the solution is given by:
Where:
Let's find the solution for using the previous information:
The characteristic equation is:
So, the roots are given by:
Therefore, the solution is:
As you can see, is the same solution provided by the problem.
Moving on, let's find the derivative of in order to find the constants
and
:
Evaluating the initial conditions:
And
Now we have found the value of the constants, the solution of the second-order IVP is: