6. Z varies inversely as d^3. If z = 3 when d = 2, find z when d is 4

Z = 0.375

Step-by-step explanation:

Z varies inversely as d ^ 3

so Z ∝ 1 / d ^ 3

To convert proportionality to equality,

Z ∝ 1 / d ^ 3,

Z = k / d ^ 3,

K is proportionality constant,

First we find k by putting values Z = 3 and d = 2,

Z = k / d ^ 3,

=> k = Z d ^ 3,

=> k = 3 (2) ^ 3,

=> k = 3 x 8,

So value of k is 24

Now find Z by putting values

k = 24 and d = 4

Z = k / d ^ 3,

Z = 24 / (4) ^ 3

Z = 24 / 64

Z = 0.375