Gizmos answers Vocabulary: base unit, cancel, conversion factor, dimensional analysis, metric system, prefix, scientific notation Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Sara lives in Toronto, Canada, while her cousin Michael lives in Detroit, Michigan. They like to compare how fast they are growing up. Sara tells Michael she is 160 centimeters tall, while Michael says he is 60 inches tall. If there are 2.54 centimeters in an inch, who is taller

Sara is taller than Michael

Step-by-step explanation:

From the question, Sara tells Michael she is 160 centimeters tall, that is

Sara's height is 160 centimeters.

and Michael says he is 60 inches tall, that is

Michael's height is 60 inches.

To determine who is taller among Sarah and Michael, we will have to compare their heights in the same unit.

Lets compare the heights in centimeters,

Sara's height is in centimeters, then

We will have to convert Michael's height from inches to centimeters

From the question, If there are 2.54 centimeters in an inch, that is

1 inch = 2.54 centimeters

Then 60 inches = 60 × 2.54 centimeters

= 152.4 centimeters

Hence, Michael's height in centimeters is 152.4 centimeters

Since Sara is 160 centimeters tall, then Sara is taller than Michael.

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}