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Rectangular prism A is defined as such: Length is twice as long as width, and half as long as height. A rectangular prism B has one extra unit in each dimension as A. The difference in the volume of prism B and twice the volume of prism A, plus one, is one 8th of the total volume of prism A. What are the exact dimesions of both prisms A and B? Can this be solved? Please explain how you got the answer.
Rectangular prism A is defined as such: Length is twice as long as width, and half as long as height. A rectangular prism B has one extra unit in each dimension as A. The difference in the volume of prism B and twice the volume of prism A, plus one, is one 8th of the total volume of prism A. What are the exact dimesions of both prisms A and B? Can this be solved? Please explain how you got the answer.
so we have a prism of length 2w, width of w, and height of 4w.
prism B has length of (2w+1),width of w+1, and hieght of 4w+1
so the difference of B-2A+1=A/8
(2w+1)(w+1)(4w+1)-16w^3+1=w^3
(8w^2+3w+1)(w+1)-17w^3+1=0
8w^3+11w^2+3w+2-17w^3=0
-9w^3+11w^2+6w+2=0
solving for w gives you:
w=(11+cuberoot(6191-27sqrt(21486))+cuberoot(6191+27sqrt(21486)))/27=1.6934 and with 2 other complex roots.
so the dimensions as follows.
sorry, not this time. You will probably kill me If I worded this wrong, But I am almost sure I didn't. Feel free to try again.:)
i am a hyperactive member now lol i changed my answer btw (look in the original post i made a slight mistake with algebra the first time now i changed it) everything seems to be right. maybe i just couldn't understand ur wording correctly. Kalkewl8ter will be here soon and i am sure she would give u a correct solution