Yvette encoded a secret phrase using matrix multiplication. Using A = 1.B = 2. C = 3, and so on, she multiplied the clear text

code for each letter by the matrix Cu

t

to get a matrix that ventes

to get a matrix that represents the encoded text. The matrix representing the

2

4873114 30 136 78 35

encoded text is

(21 32 50 1358 35 15

decode the text

What is the secret phrase? Determine the location of spaces after you

O FIND THE PRODUCT

O FIND THE INVERSE

O FINE IS THE PIANO

O FINE IS A WARM DAY

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}

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

~just a girl in love with shawn mendes

step-by-step explanation:

d

step-by-step explanation:

i used the pitagoras theoreme