Aprism whose base is a 9-sided polygon is intersected by a plane. in which case could the cross section be a 10-sided polygon?

when the plane makes a narrow angle with the base.

Step-by-step explanation:

Given: A prism with a Nonagon as base.

To find: When a cross section be a Decagon.

Nonagon is a polygon with 9 sides

Decagon is a polygon with 10 sides.

1). when a cross section is taken parallel to the base, the cross section will be Nonagon .i.e., it will be a 9 sided polygon.

2).when a  cross section is taken perpendicular to the base, the cross section will be a rectangle.

3). when a slant cross section is taken .i.e., one with any angle other than 90° or 180° to the base. It will be a 10-sided polygon.

99

step-by-step explanation:

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}