Question

-y varies inversely with x. If y = 8 and k (the constant of variation) = 19, what is x?

Round to the nearest thousandth, if necessary.


-y varies inversely with x, and k (the constant of variation) = 23. What is the value of y when x = 7?

Round to the nearest tenth, if necessary.


-y varies inversely with x. When y = 6.7, x = 1. What is the value of k, the constant of inverse variation?

Round to the nearest tenth, if necessary.

Answer 1

Part 1)
`x=2.375`

Part 2)
`y=3.3`

Part 3)
`k=6.7`

Explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

Part 1) y varies inversely with x. If y = 8 and k (the constant of variation) = 19, what is x?

we know that

`y*x=k`

substitute the given values and solve for x

`8*x=19`

`x=19/8`

`x=2.375`

Part 2) y varies inversely with x, and k (the constant of variation) = 23. What is the value of y when x = 7?

we know that

`y*x=k`

substitute the given values and solve for y

`y*7=23`

`y=23/7`

`y=3.3`

Part 3) y varies inversely with x. When y = 6.7, x = 1. What is the value of k, the constant of inverse variation?

we know that

`y*x=k`

substitute the given values and solve for k

`6.7*1=k`

`k=6.7`