Neighborhoods of functions (problem)

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In summary, the owner of a pizza parlor is concerned about the area of a medium size pizza, which has a 14-inch diameter. They do not want the area to exceed 176 square inches or be less than 132 square inches. Using 22/7 as an approximation for pi, the equation to represent this is 132 <= (22/7 * r^2) <= 176, where r is the radius of the pizza. The tolerance in this case refers to the acceptable range of variation for the diameter of the pizza to still meet these area requirements.
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konartist
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I need help on neighborhoods of functions:

38. The owner of a pizza parlor says money is lost on a medium size pizza, which has a 14-inch diameter, if its area exceeds 176 square inches. Customers complain if the area is less than 132 square inches. What tolerance is allowed for the diameter? use 22/7 as an approximation for pi.

This is what I've got:
[tex]176<(22/7 \times 7^2)< 132[/tex]
What exactly does it mean by tolerance and I know that I'm missing a variable but I'm not sure where the variable goes.
 
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  • #2
you don't want the area to be more than 176 square inches because you'll lose money and you don't want it to be less than 132 because the customers will complain

132<=22/7 * 7^2 <= 176

I think by tolerence they mean how much can the diameter vary or change from 7 inches so that the area of the pizza is still within these limits
 
  • #3
ahhh I see now
so:
[tex]132<22/7 \times r^2<176[/tex]

so just solve for r I think.
thanks buzz that made more sense.
 

FAQ: Neighborhoods of functions (problem)

What are "neighborhoods of functions"?

Neighborhoods of functions refer to a set of similar functions that are defined in a specific region or neighborhood of a given point. These functions may have similar properties or behaviors in that particular region.

What is the importance of studying neighborhoods of functions?

Studying neighborhoods of functions allows us to gain a deeper understanding of the local behavior of functions and how they change within a specific region. This knowledge can be applied in various fields such as physics, engineering, and economics to make accurate predictions and solve real-world problems.

How are neighborhoods of functions related to calculus?

Calculus is a branch of mathematics that deals with change and motion. The concept of neighborhoods of functions is closely related to calculus because it involves studying the behavior of functions as they vary within a specific region or neighborhood. Calculus provides the tools and techniques to analyze and understand this behavior.

Can neighborhoods of functions be visualized?

Yes, neighborhoods of functions can be visualized using graphs and diagrams. By plotting the functions within a specific region, we can see how they behave and identify any similarities or differences between them. This visual representation can help in understanding the functions and their relationships better.

How are neighborhoods of functions used in real-life applications?

Neighborhoods of functions have various real-life applications, such as predicting stock market trends, optimizing production processes, and determining optimal routes for transportation. By studying the local behavior of functions in a given region, we can make more accurate predictions and decisions in these and other fields.

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