x varies directly as y and inversely as the square of z. If x=10 when y=8 and
z=2, find x when y=12 and z=3.
Formula:
"directly" variable (or product of "jointly" variables)
(if no directly or jointly variables, write 1 here)
"Varying" quantity = k·---------------------------------------------------------
"inversely" variable (or product of "inversely variables")
(If no inversely variable(s), write 1 here)
The "varying" quantity is x.
There is one "directly" variable, y
There is one "inversely" variable, z²
Substituting
y
x = k·----
z²
Substituting the complete set of data,
where ALL the variables are given:
x=10, y=8, z=2
8
10 = k·----
2²
Solve for k
8
10 = k·---
4
10 = k·2
10 = 2k
5 = k
Now substitute k = 5 into:
y
x = k·----
z²
which gives:
y
x = 5·----
z²
Now substitute the second set of data,
and solve for the missing letter x
Substitute y=12 and z=3 into
y
x = 5·----
z²
12
x = 5·----
3²
12
x = 5·----
9
3 divides into 9 to give 3 and into 12 to give 4:
4
12
x = 5·----
9
3
4
x = 5·---
3
20
x = ----
3
x = 6
Edwin
