Answer:
Answer=C
Step-by-step explanation:
Answer:
x = 40
Step-by-step explanation:
The angles add to 180 degrees
30+110 +x = 180
Combine like terms
140 +x = 180
Subtract 140 from each side
140+x-140 =180-140
x = 40
The sixth graders collected $250 of their $300 goal. The seventh graders collected $250 of thier $450 goal.
Sixth Graders:
$250 / $300
Reduce: $25 / $30 = 5/6
Seventh Graders:
$250 / $450
Reduce: $25 / $45 = 5/9
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take

, so that

and we're left with the ODE linear in

:

Now suppose

has a power series expansion



Then the ODE can be written as


![\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%5Cge2%7D%5Cbigg%5Bn%28n-1%29a_n-%28n-1%29a_%7Bn-1%7D%5Cbigg%5Dx%5E%7Bn-2%7D%3D0)
All the coefficients of the series vanish, and setting

in the power series forms for

and

tell us that

and

, so we get the recurrence

We can solve explicitly for

quite easily:

and so on. Continuing in this way we end up with

so that the solution to the ODE is

We also require the solution to satisfy

, which we can do easily by adding and subtracting a constant as needed:
Hopefully try is works. Took me a few hrs to figure it out but I think I got it