Neighborhoods of functions (problem)

  • Thread starter Thread starter konartist
  • Start date Start date
  • Tags Tags
    Functions
Click For Summary
SUMMARY

The discussion centers on calculating the tolerance for the diameter of a medium-sized pizza, specifically a 14-inch diameter pizza, based on area constraints. The owner of the pizza parlor incurs losses if the area exceeds 176 square inches and faces customer complaints if the area falls below 132 square inches. The area is calculated using the formula A = πr², with π approximated as 22/7. The final equation established is 132 < (22/7) * r² < 176, where r represents the radius of the pizza.

PREREQUISITES
  • Understanding of the area formula for circles (A = πr²)
  • Basic algebra skills for solving inequalities
  • Knowledge of the concept of tolerance in measurements
  • Familiarity with the approximation of π as 22/7
NEXT STEPS
  • Calculate the radius limits using the inequalities 132 < (22/7) * r² < 176
  • Explore the concept of tolerance in manufacturing and its applications
  • Learn about the implications of area calculations in business decisions
  • Investigate the geometric properties of circles and their relevance in real-world scenarios
USEFUL FOR

Mathematicians, business owners in the food industry, and students studying geometry or optimization will benefit from this discussion.

konartist
Messages
47
Reaction score
0
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.
 
Physics news on Phys.org
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
 
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.
 

Similar threads

Replies
11
Views
3K
Replies
2
Views
1K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
7
Views
5K
Replies
10
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K