Jacks father drives to work in 30 minutes while driivng at his usual speed. When traffic is bad, he drives 30 miles per hour slower and the trip takes one hour longer. How far is Jack's father's work from home

The distance of Jack's father's work from home is 22.5 miles.

Step-by-step explanation:

Given;

time it takes Jacks father at usual speed, t = 30 minutes = 0.5 hour

Jacks father speed when traffic is bad, = 30 mph slower

let the usual speed = v

let the distance of Jack's father's work from home = y

When traffic is normal;

When traffic is bad;

Solve equation (1) and (2) together;

Therefore, the distance of Jack's father's work from home is 22.5 miles.

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}

answer: 177/8

step-by-step explanation: