Suppose that x and y vary inversely, and x = 10 when y = 8. write the function that models the inverse variation.
a. y=2/x
b. y=18/x
c. y=80/x
d. y=0.8x

c.

Step-by-step explanation:

Given:

and vary inversely.

Therefore, we can express y in terms of x as:

Where, is a constant of proportionality.

Now, at

Plug in 10 for and 8 for in the above equation and solve for .

This gives,

Therefore, the function that models the inverse variation is :

.

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: