lucas211 wrote:The variable x is inversely proportional to the square of the variable y. If y is divided by 3a, then x is multiplied by which of the following:
a) 1/9a
b) 1/(9a^2)
c) 1/3a
d) 9a
e) 9a^2
a and b are INVERSELY PROPORTIONAL if their product is always THE SAME:
ab = k, where k is a constant.
The variable x is inversely proportional to the square of the variable y.
Since x and y² are inversely proportional, we get:
xy² = k, where k is a constant.
Let x� = 1 and y� = 6.
Plugging x� = 1 and y� = 6 into (x�)(y�)² = k, we get:
(x�)(y�)² = (1)(6²) = 36, implying that k=36.
If y is divided by 3a, then x is multiplied by which of the following?
Let a=2.
Dividing y� by 3a, we get;
y₂ = y�/3a = 6/(3*2) = 1.
Plugging y₂ = 1 and k=36 into (x₂)(y₂)² = k, we get:
(x₂)(1²) = 36
xâ‚‚ = 36.
Since x� = 1 and x₂ = 36, the value of x is multiplied by 36. This is our target.
Now plug a=2 into the answer choices to see which yields our target of 36.
Only
E works:
9a² = (9)(2²) = 36.
The correct answer is
E.
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