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-y varies inversely with x. If y = 3 and k (the constant of variation) = 33, what is x?

Round to the nearest whole number, if necessary.


-y varies inversely with x. When y = 11, x = 5.2. What is the value of k, the constant of inverse variation?

Round to the nearest tenth, if necessary.


-y varies inversely with x, and k (the constant of variation) = 72. What is the value of y when x = 7.8?

Round to the nearest tenth, if necessary.

Respuesta :

Louli

Answer:

Part a .............> x = 11

Part b .............> k = 57.2

Part c .............> y = 9.2

Explanation:

The three problems deal with inverse variation between two variables

An inverse variation relation between two variables means that when one of the variables increases, the other will decrease (and vice versa)

Mathematically, an inverse variation relation is represented as follows:

[tex]y = \frac{k}{x}[/tex]

where x and y are the two variables and k is the constant of variation

Now, let's check the givens:

Part a:

We are given that y = 3 and k = 33

Substitute in the original relation and solve for x as follows:

[tex]y = \frac{k}{x}\\ \\3 = \frac{33}{x}\\ \\x=\frac{33}{3}=11[/tex]

Part b:

We are given that y = 11 and x = 5.2

Substitute in the original relation and solve for k as follows:

[tex]y=\frac{k}{x}\\ \\11=\frac{k}{5.2}\\ \\k=11*5.2=57.2[/tex]

Part c:

We are given that x=7.8 and k=72

Substitute in the original relation and solve for y as follows:

[tex]y=\frac{k}{x}=\frac{72}{7.8}=9.2[/tex] to the nearest tenth

Hope this helps :)

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