Brian will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $44 and costs an additional $0.10 per mile driven. The second plan has an initial fee of $49 and costs an additional $0.08 per mile driven. For what amount of driving do the two plans cost the same? _ miles
What is the cost when two plans cost the same? $_

250 miles

69 dollars

Step-by-step explanation:

Plan 1

44+.10m

Plan 2

49 +.08m

Set the two plans equal

44+.10m = 49 +.08m

Subtract .08m from each side

44+.10m - .08m = 49 +.08m-.08m

44+.02m = 49

Subtract 44 from each side

44 +.02m-44 = 49-44

.02m = 5

Divide each side by .02

.02m/.02 = 5/.02

m = 250

The cost is 44 +.10(250)

                  44 +25

                    69

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}