Will give brainliest
the graph of a function passes through the point (50, 3.6), and
y x varies inversely as . find the value of y x when is 75.
a) calculate the value of k xy = .
b) write the equation that represents the inverse variation function.
c) substitute the given value into the function equation and solve to determine
the corresponding quantity.
d) check your solutions by substituting both quantities back into k xy = .

A) k = 180

B) yx = 180 is the equation of variation

C) The value of y is 2.4 when x = 75

D) The solution is right

Step-by-step explanation:

* Lets explain how to solve the problem

- Inverse variation is relationship between two variables

-  The relation expressed by an equation in which the product of

  two variables is equal to a constant

- If y varies inversely with x (y ∝ 1/x), then yx = k, where k is the

 constant of variation

* Lets solve the problem

A)

- y varies inversely with x

∵ y ∝ 1/x

∴ yx = k, where k is constant

∵ The graph of the function passes through point (50 , 3.6)

- We can find the value of k by substituting the coordinate of this

 point in the equation of variation

∵ x = 50 and y = 3.6

∴ (50)(3.6) = k

∴ k = 180

B)

- Substitute the value of k in the equation of variation

∵ yx = k

∵ k = 180

∴ yx = 180 is the equation of variation

C)

- Lets find y when x = 75

∵ yx = 180

- substitute the value of x in the equation of variation

∵ y(75) = 180

- Divide both sides by 75

∴ y = 2.4

∴ The value of y is 2.4 when x = 75

D)

- To check our solution lets substitute the value of y in the equation,

  if the left hand side has the same value of right hand side , then the

  solution is right

∵ yx = 180

∵ y = 2.4 , x = 75

∴ 2.4(75) = 180 which is the same with the right hand side

∴ The solution is right

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