Answer:
- k = 2; y = 2·x·z
- x = 10; k = 2
- y = 192; y = 4·x·z
- z = 2; k = 3
- x = 48/9; k = 3/4
Explanation:
When we say "y varies jointly as x and z", we mean that y is proportional to x with some constant of proportionality, and also y is proportional to z with some constant of proportionality. The joint variation means that each "constant" of proportionality will depend on the other variable:
y = k·x·z
This can be solved for the different variables:
k = y/(x·z)
x = y/(k·z)
z = y/(k·x)
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a)
k = y/(x·z) = 30/(3·5) = 2; the equation is y = 2·x·z
b)
k = 2 (read from the equation); x = y/(k·z) = 80/(2·4) = 10
c)
y = k·x·z = 4·6·8 = 192; the equation is y = 4·x·z
d)
k = 3 (read from the equation); z = y/(k·x) = 60/(3·10) = 2
e)
k = 3/4 (read from the equation); x = y/(k·z) = 48/(3/4·12) = 48/9