2. alex drew a scale drawing of an auditorium. he used the scale 3 inches = 2 feet. if the stage is 30 inches in the drawing, how wide is the actual stage? enter your answer with units.

3. mei is on a biking tour of europe. while looking at a map of the tour route, she notices that the next two stops are 9 centimeters apart. what is the actual distance between the next two stops if the scale of the map is 3 centimeters = 8 kilometers? enter your answer with units.

4. bella is river rafting in lewis county. the starting and ending points of the trip are 4 inches apart on a map of the river. in real life, these two points are 36 miles away from each other. what is the scale of the map?
1 inch : miles

5. brett made a scale drawing of an italian restaurant. the restaurant's kitchen is 3 centimeters long in the drawing. the actual kitchen is 21 meters long. what scale did brett use for the drawing?
1 centimeter : meters

2. The scale is 3 inches = 2 feet.

Divide total inches by 3, then multiply by 2:

30 / 3 = 10

10*2 = 20 feet.

3. Divide the 9cm by 3cm, then multiply by 8 km

9/3 = 3

3*8 = 24 kilometers.

4. Divide real distance by distance on map:

36 / 4 = 9

1 inch = 9 miles

5. Divide real dimension by the drawing dimension:

21 meters / 3 centimeters = 7

1 cm = 7 meters

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 2/54

step-by-step explanation: