一道英文数学题,求具体步骤An open cardboard box is to be make by cutting small squares of side x cm from each of the four corners of a larger square of card of side 10 cm, and folding along the dashed lines, as shown in the diagram. Find t
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一道英文数学题,求具体步骤An open cardboard box is to be make by cutting small squares of side x cm from each of the four corners of a larger square of card of side 10 cm, and folding along the dashed lines, as shown in the diagram. Find t
一道英文数学题,求具体步骤
An open cardboard box is to be make by cutting small squares of side x cm from each of the four corners of a larger square of card of side 10 cm, and folding along the dashed lines, as shown in the diagram. Find the value of x such that the box has a maximum volume, and state the value of that maximum volume.
（图片请大家自行想象,因为我实在是不会加图
一道英文数学题,求具体步骤An open cardboard box is to be make by cutting small squares of side x cm from each of the four corners of a larger square of card of side 10 cm, and folding along the dashed lines, as shown in the diagram. Find t
Answer:
Because,It's volume=(10-2X)*(10-2X)*X
So,According to the inequality: Cube roots of ( abc)《(a+b+c)/3
or : abc《[(a+b+c)/3]³
When, and only when a=b=c ,Take equals
(10-2X)*(10-2X)*X= (10-2X)*(10-2X)*4X/4《[(10-2X+10-2X+4X)/3]³/4=(20/3)³/4
So, (10-2X)*(10-2X)*X《2000/27
When (10-2X)=(10-2X)=4X
Solution of： X=5/3
So ,When X=5/3
The volume of the petitions cubes maximum is Vmax=2000/27
(Inspection: ( 10-2*5/3)²*5/3=(5/3)*(20/3)²=2000/27)
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