Question
You are given a new rectangular sheet that measures 20 by 30 ; what would the equation be for
the volume of the boxes you could make by cutting out squares of size
What would the domain of this new function be?
the volume of the boxes you could make by cutting out squares of size
What would the domain of this new function be?
Ask by Herrera Powers. in the United States
Oct 01,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The volume equation is
Solution
To find the volume of the boxes created by cutting out squares of size
-
Determine the dimensions of the box after cutting out the squares:
- After cutting out squares of size
from each corner, the new dimensions of the box will be: - Length:
(since we cut from both ends of the length) - Width:
(since we cut from both ends of the width)
- Length:
- The height of the box will be
(the size of the squares cut out).
- After cutting out squares of size
-
Write the volume equation:
The volumeof the box can be expressed as: Therefore, the equation for the volumeis: -
Determine the domain of the function:
The variablemust satisfy certain conditions: -
must be greater than 0 (since we are cutting out squares). -
must be greater than 0, which gives: -
must also be greater than 0, which gives:
The more restrictive condition is. -
Combining these conditions, the domain of the function
In interval notation, the domain is:
Thus, the volume equation is
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