<h2>
Answer:</h2>
<u>The equivalent expression is </u><u> (2 / x ^ 3) * sqrt (2)</u>
<h2>
Step-by-step explanation:</h2>
We have sqrt 8 / x ^ 6
Rewriting the expression:
=sqrt (8 / x ^ 6)
=sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))
=(2 / (x * x * x)) sqrt (2)
= (2 / x ^ 3) * sqrt (2)
We get finally
(2 / x ^ 3) * sqrt (2)
<h3>Problem Solution</h3>
Assuming the spool is a cylinder and the circumference we're winding around is that of a circle with the given area, we can write the relation between circumference and area as
... C = 2√(πA)
10 times the circumference is then
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
<h3>Formula Derivation</h3>
The usual formulas for circumference and area are
... C = 2πr
... A = πr²
If we multiply the area formula by π and take the square root, we get
... πA = (πr)²
... √(πA) = πr
Multiplying this by 2 gives circumference.
... C = 2√(πA) = 2πr
Answer:
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Step-by-step explanation:
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