Adam plans a diet for his dog, louie. louie consumes between 510 and 540 calories per day. if louie eats 1 1/2 servings of dog food each day, how many treats can louie have? dog food 320 calories per serving treats 10 calories per treat write and solve a compound inequality to represent this situation. let x represent the number of treats louie can have each day.

The compound inequality is

Step-by-step explanation:

Let

x -----> represent the number of treats Louie can have each day

step 1

Find the number of calories for 1 1/2 serving of dog

1 1/2=1.5

one serving is 320 calories

so

1.5*320=480 calories

step 2

Find the compound inequality

The compound inequality is

Divide in two inequalities

------> inequality A

-----> inequality B

therefore

The compound inequality is equal to

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}