Are (7 comma negative 3 comma negative 9 comma 2 )and (14 comma negative 6 comma negative 18 comma 4 )homogeneous coordinates for the same point in set of real numbers R cubed? Why or why not?

Step-by-step explanation:

The given points are (7, -3, -9, 2) and (14, -6, -18, 4).

If we multiply the first coordinate with the common factor 2, then we will get the coordinates of the second point. Hence, as per the definition of homogeneouos point, the given coordinates are homogeneous coordinates of same point.

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}

sine

step-by-step explanation: