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goldenfox [79]
3 years ago
8

The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.

Mathematics
1 answer:
Fudgin [204]3 years ago
6 0

Given:

The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.

To find:

The combined variation equation and find y when x = 6 and z= 3.

Solution:

The variable y varies directly as x and inversely as z.

y\propto \dfrac{x}{z}

y=k\dfrac{x}{z}           ...(i)

Where, k is the constant of proportionality.

Putting x=4, y=2 and z=14, we get

2=k\dfrac{4}{14}

2=k\dfrac{2}{7}

2\times \dfrac{7}{2}=k\dfrac{2}{7}\times \dfrac{7}{2}

7=k

Putting k=7 in (i), we get

y=7\dfrac{x}{z}

Putting x=6 and z=3, we get

y=7\times \dfrac{6}{3}

y=7\times 2

y=14

Therefore, the required equation is y=7\dfrac{x}{z} and the value of y is 14 when x = 6 and z= 3.

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