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-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.

Respuesta :

calculista

Answer:

Part 1) [tex]x=2.375[/tex]

Part 2) [tex]y=3.3[/tex]

Part 3) [tex]k=6.7[/tex]

Step-by-step explanation:

we know that

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

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

we know that

[tex]y*x=k[/tex]

substitute the given values and solve for x

[tex]8*x=19[/tex]

[tex]x=19/8[/tex]

[tex]x=2.375[/tex]

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

[tex]y*x=k[/tex]

substitute the given values and solve for y

[tex]y*7=23[/tex]

[tex]y=23/7[/tex]

[tex]y=3.3[/tex]

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

[tex]y*x=k[/tex]

substitute the given values and solve for k

[tex]6.7*1=k[/tex]

[tex]k=6.7[/tex]

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