The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function A(x)= 4x sqrt(1-x)^2)Where x represents the length in feet, of half the base of the beam.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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I assume that the problem requests to calculate the cross-sectional area of a beam since the formula A(x) expresses the area of a beam with respect to x(the length, in feet, of half the base of the beam).

Hence, the length of half of the base of the beam may take different values.

Considering one half of a foot the length of half of the base of the beam and substituting `1/2`  for x in the formula of area yields:

`A(1/2) = 4*(1/2)*sqrt(1 - (1/2)^2)`

`` `A(1/2) = 2sqrt(1 - 1/4)`

Bringing the terms under the square root to the same denominator yields:

`A(1/2) = 2sqrt((4 - 1)/4) =gt A(1/2) = 2sqrt3/2 =gt A(1/2) = sqrt3`

Hence, evaluating the cross-sectional area of the beam yields:`A(1/2) = sqrt3 ` quare feet. 

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