Machines x and y work at their respective constant rates. how many more hours does it take machine y, working alone, to fill a production order of a certain size than it takes machine x, working alone?
1. machine x and y, working together, fill a production order of this size in two thirds the time that machine x does.2. machine y, working alone, fills a production order of this size in twice the time that machine x, working alone, does.

1)

2)

Step-by-step explanation:

1) X=production rate of X (units/hour)

Y=production rate of Y (units/hour)

C=order (units)

t=working time (hour)

Combining:

In time:

Difference of time:

2)

Difference of time:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )