Marlin and his brother are going to Antonio, TX next week. They figure that they will drive 792 miles round trip. If their car g
2 answers:
You might be interested in
Answer:
(a)Therefore the volume of the box is 361.19 cubic ft.
(b)Therefore the volume of the box is 361.19 cubic ft.
Step-by-step explanation:
Given that,
Squares with sides length x are cut out from of each corner of a rectangular piece of cardboard measuring 23 ft and 13 ft.
Now the length of the box is =(23-2x) ft
The width of the box is =(13-2x) ft
The height of the box is= x
The volume of the box is = Length×width×Height
=(23-2x)(13-2x)x cubic ft
= 299x-72x²+4x³ cubic ft
Let,
V=299x-72x²+4x³
Differentiating with respect to x
V'= 299-144x+12x²
Again differentiating with respect to x
V''= -144+24x
To find the maximum volume, we set V'=0
∴299-144x+12x²=0
Applying quadratic formula , here a=12,b= -144 and c=299
For x= 9.33 , the width of the box will negative which is impossible.
So, x= 2.67
So, at x=2.67, the volume of the box will be maximum.
Therefore the volume of the box is
=(299x-72x²+4x³) cubic ft
=361.19 cubic ft
(b)
The value of s will same with the value of x
so the volume of the box also remains same.
Therefore the volume of the box is 361.19 cubic ft