1.5 horas para realizar un afinamiento; 0,2 horas para limpiar la bateria; 0,75 horas para cambiar el aceite y el filtro del motor; 1,45 horas para cambiar y alinear luces; y 1,3 horas para reparar el sistema de aire acondicionado. por hora de trabajo cobra 32,8 soles; ? cuánto cuesta la reparación del automóvil?

Step-by-step explanation:

The question in English

1.5 hours for tuning; 0.2 hours for cleaning the battery; 0.75 hours for changing the oil and engine filter; 1.45 hours for changing and aligning lights; and 1.3 hours for repairing the air conditioning system. The hourly rate is 32.8 soles; how much does it cost to repair the car?

step 1

Sum the hours to repair the car

step 2

Find the cost

Multiply the total hours by

so

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}