Question 1058213: z varies directly as x^3 and inversely as y^3.
If z = 184 when x = 10 and y = 6,
find z if x = 9 and y = 3.
(Round off your answer to the nearest hundredth.)
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! z varies directly as x^3 and inversely as y^3.
If z = 184 when x = 10 and y = 6,
find z if x = 9 and y = 3.
(Round off your answer to the nearest hundredth.)
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 z.
There is one "directly" variable, x³
There is one "inversely" variable, y³
Substituting
x³
z = k·----
y³
Substituting the complete set of data,
where ALL the variables are given:
z=184, x=10, y=6
10³
184 = k·-----
6³
1000
184 = k·-----
216
Reduce 1000/216 to 125/27
125
184 = k·-----
27
Solve for k. Multiply through by 27
4968 = k·125
4968
---- = k
125
Now substitute k = 4968/125 into:
x³
z = k·----
y³
which gives:
4968 x³
z = ----·----
125 y³
Now substitute the second set of data,
and solve for the missing letter z
Substitute x=9 and y=3 into
4968 x³
z = ----·----
125 y³
4968 9³
z = ----·----
125 3³
We grab the calculator and get
z = 1073.088
Round to the nearest hundredth:
z = 1073.09
Edwin
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