QUICK QUESTION: Minimizing Restrictions

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In summary, the problem is asking for the dimensions of a box with a square base and no top that minimizes the amount of material used, given that the volume must be 10,000cm^3 and the smallest dimension is 5cm. The equations used are V=x^2y and SA=x^2+4xy, with y=10,000/x^2. The final solution is x=27.1 and y=13.6, with the limitation that x must be greater than or equal to 5.
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banfill_89
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Homework Statement



Question: a box with a square base and no top must have a volume of 10,000cm^3. if the smallest dimensions in any direction is 5cm, the determine the dimensions of the box that minimize the amount of material used.

Homework Equations



V=x^2&y
SA=x^2+4xy
(isolate for y using given volume in V equation to obtain y=10,000/x^2)

The Attempt at a Solution



SA=x^2+4x(10,000/x^2)

when solved...x=27.1
y= 13.6I have an answer on what the dimensions are, but what do i use as my limitations besides what my x values are. I know i have to use x>or=5...for some reason i can never figure these limitations/restrictions out...
 
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  • #2
"must have a volume of 10,000cm^3" Sounds like a restriction to me.
 

1. How can minimizing restrictions benefit scientific research?

Minimizing restrictions can benefit scientific research by allowing for more flexibility and exploration in designing experiments. It can also lead to more diverse and inclusive samples, which can improve the generalizability of research findings.

2. What types of restrictions can hinder scientific progress?

Restrictions such as limited funding, ethical guidelines, and regulations can hinder scientific progress by limiting the scope and feasibility of research projects. Restrictions can also come from societal or cultural norms that limit the types of questions that can be asked or the methods that can be used.

3. How can researchers balance minimizing restrictions with ethical considerations?

Researchers can balance minimizing restrictions with ethical considerations by carefully evaluating the potential risks and benefits of their research. They can also consult with ethical review boards and follow established guidelines and protocols to ensure that their research is conducted in an ethical and responsible manner.

4. Can minimizing restrictions lead to biased results?

Minimizing restrictions does not necessarily lead to biased results, but it can increase the potential for bias if not carefully considered. It is important for researchers to be aware of their own biases and to actively work towards minimizing them in their research design and interpretation of results.

5. How can the scientific community as a whole work towards minimizing restrictions?

The scientific community can work towards minimizing restrictions by advocating for more flexible and inclusive research practices, promoting diversity and inclusivity in research teams and participants, and addressing systemic barriers that may limit access to resources and opportunities for certain groups of researchers.

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