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A company produces a cardboard box in the shape of a cube. The surface area of the box is represented by S=6x2, where x is the edge length of the box. Find the inverse by solving for x without switching the variables.

User Koobz
by
7.9k points

2 Answers

4 votes

Answer:

√2

Step-by-step explanation:

Before answering this question I must tell the following formulas:

Volume of Cube = S3

Surface Area of Cube = 6S2

If S = 6x2, then the value of x must be √2. In this way the original equation would have been S = 6 x (√2) 2 which would give the value S = 6x2.

User Kirancodify
by
8.7k points
3 votes

Answer:

x =
\sqrt{(S)/(6) } or
( (S)/(6) )^{(1)/(2) }

Step-by-step explanation:

The cardboard box is in the shape of a cube. The surface area of the box is given by:

S = 6
x^(2)

To find the inverse, we have to solve for x. To solve for x means we will make x the subject of the equation above

Divide both the right and left hand side by 6, we have:

6
x^(2) ÷ 6 = S ÷ 6 ⇒
x^(2) =
(S)/(6)


x^(2) =
(S)/(6)

Take the square root for both the right and left hand side, we have:


\sqrt{x^(2) } =
\sqrt{(S)/(6)} ⇒ x =
\sqrt{(S)/(6)}

x =
\sqrt{(S)/(6) } or
( (S)/(6) )^{(1)/(2) }

Therefore, x is equivalent to the square root of (S/6)

User Alexyichu
by
7.9k points

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