Evaluate. Math problem 7th grade.
1 answer:
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Let 
. Then 
and 
are two fundamental, linearly independent solution that satisfy
Note that
, so that 
. Adding 
doesn't change this, since 
.
So if we suppose
then substituting
would give
To make sure everything cancels out, multiply the second degree term by
, so that
Then if
, we get
as desired. So one possible ODE would be
(See "Euler-Cauchy equation" for more info)
Note that
So if we suppose
then substituting
To make sure everything cancels out, multiply the second degree term by
Then if
as desired. So one possible ODE would be
(See "Euler-Cauchy equation" for more info)
For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be: centimeters.
Likewise, from the same theorem we have:
