Find the mean proportional of 8a² and (18/a⁴), where a is a positive number.

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Accepted Answer

The mean proportional between two numbers x and y is given by √(xy).

Given numbers: 8a² and 18/a⁴

Calculate the product:
8a² × (18/a⁴) = (8 × 18) × (a² / a⁴) = 144 × a^(2-4) = 144 × a^(-2) = 144 / a²

Now, mean proportional = √(144 / a²) = √144 / √(a²) = 12 / a

Since a is positive, √(a²) = a.

Therefore, the mean proportional is 12 / a.

Checking options, the correct answer is option 4: 12 / a.

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