作业帮A display case is in the shape of a rectangular box with a square base.Suppose the volume is 21 cubic ft and it costs $1 per square ft.to build the glass top and $0.50 per sq.ft.to build the sides and base.If x is the length of one side of the base,w
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A display case is in the shape of a rectangular box with a square base.Suppose the volume is 21 cubic ft and it costs $1 per square ft.to build the glass top and $0.50 per sq.ft.to build the sides and base.If x is the length of one side of the base,w
A display case is in the shape of a rectangular box with a square base.Suppose the volume is 21 cubic ft and it costs $1 per square ft.to build the glass top and $0.50 per sq.ft.to build the sides and base.If x is the length of one side of the base,what value should x have to minimize the cost?Round your answer to two decimal places.
A display case is in the shape of a rectangular box with a square base.Suppose the volume is 21 cubic ft and it costs $1 per square ft.to build the glass top and $0.50 per sq.ft.to build the sides and base.If x is the length of one side of the base,w
题目看得懂么?
换成数学语言就是一个长方体,底是正方形,面积为21,顶部费用为每单位1,侧面和底部费用为每单位0.5,现设底部长度为x,求x,使费用最低（结果保留两位小数）.
底部正方形变长为x,设长方体高为h,则x²h=21,即h=21/x²
费用C=0.5*（x²+4xh）+1*x²=1.5x²+2xh=1.5x²+42/x
求导,得C‘=3x-42/x² C’=0,得x=14的三次方根
x （0,14的三次方根） 14的三次方根 14的三次方根
C‘ - 0 +
C ↓ ↑
即x=14的三次方根时,C取得最小值
即x=2.41时,费用最低,大约为23.24
都是英语吗？？？
假设我们要做一个长方体的陈列框，陈列框的底为正方形。假设陈列框的容积为21立方尺，玻璃顶的造价为每平方尺1美刀，周围边框和底边的造价为每平方尺0.5美刀，求成本最低时底边长x（精确到小数点后2位）。
底边长x，因此高为21/(x^2)。陈列框的造价为1 * x^2 + 0.5 * 5 * x * 21/(x^2) = x^2 + 105/2x
多项式最小时x = 2.97尺...
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假设我们要做一个长方体的陈列框，陈列框的底为正方形。假设陈列框的容积为21立方尺，玻璃顶的造价为每平方尺1美刀，周围边框和底边的造价为每平方尺0.5美刀，求成本最低时底边长x（精确到小数点后2位）。
底边长x，因此高为21/(x^2)。陈列框的造价为1 * x^2 + 0.5 * 5 * x * 21/(x^2) = x^2 + 105/2x
多项式最小时x = 2.97尺
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由题可知当底面变长为x时，其高度为h=21/(x*x)。
则造价y=(h*x*4+x*x)*0.5+x*x*1.0
=42/x+1.5*x*x
则有y'=-42/(x*x)+3x
令y’=0，解得x*x*x=14
易知x*x*x=14时y取最小值
此时y=9/2*根号14
自己想