# DeShawn ran 40.7 miles less than Mark (m) last week. DeShawn ran 9.3 miles. How many miles did Markrun? Do not include spaces in your

###### Question:

## Answers

Try a or d, hope that

geometric series converge the common ratio r has magnitude less than one.

[tex]|r| < 1[/tex]

which is equivalent to

[tex]-1 < r < 1[/tex]

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

[tex]s = \dfrac{a}{1 -r}[/tex]

where a is the first term.

[tex]s = \dfrac{100}{1 - 1/2} = 200[/tex]

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}

[tex]|x| < \frac 1 2 \sqrt[3]{2}[/tex]

[tex]Could someone solve these with work?[/tex]the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )

[tex]Geometry question to find the radius[/tex]4, -4 is the other point it would pass through