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30. An open-top box is to be made by cutting small congruent squares from the corners of a 12 inch by 12 inch sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible

Respuesta :

profereyes12122

Answer:

Squares should measure 2 inches per side ensures maximum box volume

Step-by-step explanation:

[tex](12-2x)^{2} =144-48x+4x^{2}[/tex]

[tex]V=x(144-48x+4x^{2} )=144x-48x^{2} +4x^{3}[/tex]

[tex]V'=144-96x+12x^{2}[/tex] = [tex](x-6)(x-2)[/tex]

[tex]x_{1} =6[/tex]

[tex]x_{2} =2[/tex]  this is de right value

Hope this helps