Allie goes cruising on her dirt bike. She rides 2 km north, 4 km west, 13 km south, 10 km east, 1 km south and 6 km east. What was her displacement?

16.97km

Step-by-step explanation:

To get the displacement, we will use the pythagoras theorem

Sum of distances along the horizontal (east and west) is expressed as

dx = 10 - 4 + 6

dx = 6+6

dx = 12km

Sum of distances along the y;

dy = 2 - 13 - 1

dy = -11-1

dy = -12km

Find the displacement using the pythagoras theorem

D = √(12)²+(-12)²

D = √144+144

D = √288

D = 16.97km

Hence her displacement is 16.97km

8 apples are left.

step-by-step explanation:

10-2=8

10 apples

take 2

now u have 8

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}