Asked by Alexa
An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.
Answers
Answered by
Steve
if the squares are of side x, then
v = x(12-2x)^2 = 4x^3-48x^2+144x
dv/dx = 12x^2 - 96x + 144
= 12(x-2)(x-6)
so, v has a max at x=2.
v = x(12-2x)^2 = 4x^3-48x^2+144x
dv/dx = 12x^2 - 96x + 144
= 12(x-2)(x-6)
so, v has a max at x=2.
Answered by
Alexa
Thank you sir.
Answered by
Joey
A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with
side length x from each corner and folding up the sides.
a. Find a formula for the volume of the box in terms of x
b. Find the value for x that will maximize the volume of the box. Round to 2 decimal places if needed.
side length x from each corner and folding up the sides.
a. Find a formula for the volume of the box in terms of x
b. Find the value for x that will maximize the volume of the box. Round to 2 decimal places if needed.
Answered by
Kana
v=(13-2x)(11-2x).x
dV/dx= 3x^2-96x+143
use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a
ans x=2.26
dV/dx= 3x^2-96x+143
use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a
ans x=2.26
Answered by
Kana
v=(13-2x)(11-2x).x
dV/dx= 3x^2-96x+143
use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a
ans x=1.98
sorry for the previous ans
dV/dx= 3x^2-96x+143
use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a
ans x=1.98
sorry for the previous ans
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