Respuesta :
Complete Question
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!
Answer:
(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)f(1.3)-f(0.2)
(d) f(5.6)-f(5.5)
Step-by-step explanation:
Let the Length of the paper =l (in inches)
Let the Width of the paper =w (in inches)
Let the length of the cutout square = x (in inches)
- Base Length of the Box = l-2x
- Base Width of the box =w-2x
- Height of the box =x
Volume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]
(a)When the cutout length is 0.2 inches.
x=0.2
Volume of the box (in cubic inches) ,
[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)When the cutout length is 01.3 inches.
x=1.3
Volume of the box (in cubic inches) ,
[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)If the cutout length increases from 0.2 inches to 1.3 inches.
Change In volume (in cubic inches):
[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]
(d)If the cutout length increases from 5.5 inches to 5.6 inches.
Change In volume (in cubic inches):
[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]
