Question

Given z varies jointly as x and y, use the given values to find an equation that relates x, y, and z.

x = 3, y = 8, and z = 54

Answer 1

To find the relation between x, y, and z, use the joint variation equation z = kxy. With given values x = 3, y = 8, and z = 54, we solve for the constant k and obtain the final equation z = 2.25xy.

Step-by-step explanation:

The question asks to find an equation relating x, y, and z when z varies jointly as x and y. Given the values x = 3, y = 8, and z = 54, we can establish the joint variation equation which can be written as z = kxy, where k is the constant of variation. To find k, we insert the given values:

54 = k · 3 · 8

Now, we solve for k:

k = 54 / (3 · 8) = 54 / 24 = 2.25

Once we have found k, we can write the final equation that relates x, y, and z:

z = 2.25xy.

Answer 2

z = 2.25xy

Step-by-step explanation:

Given z varies jointly as x and y then the equation relating them is

z = kxy ← k is the constant of variation

To find k use the condition x = 3, y = 8 and z = 54 , then

54 = k × 3 × 8 = 24k ( divide both sides by 24 )

`(54)/(24)` = k = 2.25

z = 2.25xy ← equation of variation