What are the missing reasons in the two-column proof?

Reasons:

1. Because, MO cuts Angle PMN in two equal parts.

2.As ∠PMN is cut in to equal parts thus:

∠PMN = ∠NMO + ∠PMO, where these two parts (∠NMO, ∠PMO) are equal.

3. Both are the same, common you can say..

4. Because, MO cuts Angle PON in two equal parts.

5. As ∠PON is cut in to equal parts thus:

∠PON = ∠NOM + ∠POM, where these two parts (∠NOM , ∠POM) are equal.

6. From the above statements, we have:

= ∠NMO + ∠PMO (Proved)

= ∠NOM + ∠POM (Proved)

= MO = MO (Proved)

Thus, ∆PMO ≅ ∆NMO, by AAS rule

As simpoool as that!

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

the answer is 62.8 cubic units