SOLUTION: an open box is to be constructed from a piece of cardboard 15 inches by 25 inches by cutting squares of length x from each corner and folding up the sides. Express the volume of t

Algebra ->  Volume -> SOLUTION: an open box is to be constructed from a piece of cardboard 15 inches by 25 inches by cutting squares of length x from each corner and folding up the sides. Express the volume of t      Log On


   

Question 30504: an open box is to be constructed from a piece of cardboard 15 inches by 25 inches by cutting squares of length x from each corner and folding up the sides. Express the volume of the box as a function of x. what is the domain v?
Answer by venugopalramana(3286) About Me  (Show Source):
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an open box is to be constructed from a piece of cardboard 15 inches by 25 inches by cutting squares of length x from each corner and folding up the sides. Express the volume of the box as a function of x. what is the domain v?
WHEN WE CUT X LONG PIECES ON ALL 4 SIDES THE CARD BOARD WILL GET REDUCED BY
X+X=2X...ALONG LENGTH AND...X+X=2X.....ALONG WIDTH
SO OPEN BOX LENGTH = 25-2X AND WIDTH = 15-2X..AND HEIGHT =X ...SO VOLUME V IS GIVEN BY LEMGTH*WIDTH*HEIGHT
V=(25-2X)(15-2X)X...DOMAIN OF V IS GIVEN BY THE FACT THAT LENGTH OR WIDTH CAN NOT BE NEGATIVE...CRITICAL VALUE BEING WIDTH WE GET ....
15-2X>0...OR....15>2X...OR....7.5>X....OR X<7.5