An open-top box is to be constructed from a 6-in by 10-in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume of the box as a function of x. V(x) = (b) For what values of a does the formula from part (a) make sense in the context of the problem? < x < (c) Using technology, graph the volume function and use it to estimate the maximum volume of the box. NOTE: Round your answers to two decimal places. The maximum volume is approximately V= It is attained when x is approximately
An open-top box is to be constructed from a 6-in by 10-in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume of the box as a function of x. V(x) = (b) For what values of a does the formula from part (a) make sense in the context of the problem? < x < (c) Using technology, graph the volume function and use it to estimate the maximum volume of the box. NOTE: Round your answers to two decimal places. The maximum volume is approximately V= It is attained when x is approximately
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
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Transcribed Image Text:An open-top box is to be constructed from a 6-in by 10-in
rectangular sheet of tin by cutting out squares of equal size at
each corner, then folding up the resulting flaps. Let x denote the
length of the side of each cut-out square. Assume negligible thickness.
(a) Find a formula for the volume of the box as a function of x.
V(x) =
(b) For what values of a does the formula from part (a) make sense
in the context of the problem?
< x
(c) Using technology, graph the volume function and use it to
estimate the maximum volume of the box.
NOTE: Round your answers to two decimal places.
The maximum volume is approximately V=
It is attained when x is approximately
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