If z varies directly as x and inversely as y, and z = 8 when x = 12 and y = 3, the value of the constant of proportionality is what number?

Question

If z varies directly as x and inversely as y, and z = 8 when x = 12 and y = 3, the value of the constant of proportionality is what number?

2 Answers

Impact of this question

76293 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-13T08:02:55

$k = 2$ $k=2$

Explanation:

when z varies directly proportional to x means a division

$c = \frac{z}{x}$ $c=z/x$ where c is a constant of proportionality

when z varies inversely proportional to x it means a product

$z y = c$ $zy=c$

now with both

$k = \frac{z y}{x}$ $k=(zy)/x$

$z = 8; x = 12 and y = 3$ $z=8; x=12 and y=3$

$k = \frac{8.3}{12}$ $k=(8.3)/12$

$k = 2$ $k=2$

Answer 2 · 2017-11-13T08:57:47

$k = 2$ $k=2$

Explanation:

$the initial statement is z \propto \frac{x}{y}$ $"the initial statement is "zpropx/y$

$to convert to an equation multiply by k the constant$ $"to convert to an equation multiply by k the constant"$
$of variation$ $"of variation"$

$\Rightarrow z = k \times \frac{x}{y} = \frac{k x}{y}$ $rArrz=kxx x/y=(kx)/y$

$to find k use the given condition$ $"to find k use the given condition"$

$z = 8 when x = 12 and y = 3$ $z=8" when "x=12" and "y=3$

$z = \frac{k x}{y} \Rightarrow k = \frac{y z}{x} = \frac{3 \times 8}{12} = \frac{24}{12} = 2$ $z=(kx)/yrArrk=(yz)/x=(3xx8)/12=24/12=2$

Science

Math

Humanities

... and beyond

If z varies directly as x and inversely as y, and z = 8 when x = 12 and y = 3, the value of the constant of proportionality is what number?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question