cube of the following numbers : 4 2/3 please give answer in steps
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Answer:
Step-by-step explanation:
The question says there are three numbers but with a specific ratio. What that means is that once we pick one of the numbers, the other two are known to us through the ratios. We can therefore replace all 3 of the numbers with a single variable:
2
:
3
:
4
⇒
2
x
:
3
x
:
4
x
Now, no matter what we choose for
x
we get the three numbers in the ratios specified. We are also told the sum of the cubes of these three numbers which we can write:
(
2
x
)
3
+
(
3
x
)
3
+
(
4
x
)
3
=
0.334125
distributing the powers across the factors using
(
a
⋅
b
)
c
=
a
c
b
c
we get:
8
x
3
+
27
x
3
+
64
x
3
=
99
x
3
=
0.334125
x
3
=
0.334125
99
=
0.003375
x
=
3
√
0.003375
=
0.15
So the 3 numbers are:
2
⋅
0.15
,
3
⋅
0.15
,
4
⋅
0.15
⇒
0.3
,
0.45
,
0.6