How to Calculate Engraving Costs for Pewter Mugs: An Engraving Promotion Guide

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SUMMARY

The discussion focuses on calculating engraving costs for pewter mugs during a promotional offer. The base price of the mug is $35, with the first six letters of engraving included for free. Each additional letter incurs a charge of $0.20. A piecewise function is required to model the total price based on the number of engraved letters, specifically defined for values of x representing the number of letters.

PREREQUISITES
  • Understanding of piecewise functions in mathematics
  • Basic knowledge of algebraic expressions and inequalities
  • Familiarity with absolute value functions
  • Ability to apply mathematical transformations and coordinate systems
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  • Research how to construct piecewise functions in algebra
  • Learn about absolute value functions and their applications
  • Study the principles of promotional pricing strategies
  • Explore mathematical modeling techniques for real-world scenarios
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High school students, mathematics educators, and anyone involved in pricing strategies or promotional offers in retail settings.

uyenchristine
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We need help on piecewise function...

A gift shop sells pewter mugs for $35. They are currenly running an engraving promotion. The first six letter are free. Each additional letter cost $0.20. Write the piecewise model that gives the price of the mug with x engraved letter..

PLease help we need it immediately...:cry:
 
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How about the piecewise function? That's basically what we need. =)
 
Oh! Thank you!
 
can you help us with another problem,please
 
the largest pyramid included in the first wonder of the world is Khufu. IT stands 450 feet tall and its base is 755 feet long. Imagine that a coordinate plane is placed over side of the pyramid. In the coordinate plane, each unit represent one foot and the origin is at the center of the pyramid base. Write an abolute value function for the outline of the pyramid...please help
 
uyenchristine said:
the largest pyramid included in the first wonder of the world is Khufu. IT stands 450 feet tall and its base is 755 feet long. Imagine that a coordinate plane is placed over side of the pyramid. In the coordinate plane, each unit represent one foot and the origin is at the center of the pyramid base. Write an abolute value function for the outline of the pyramid...please help
In the case you describe, the square base can be defined by the set of two inequalities
\left\{ \begin{gathered}<br /> \left| x \right| = 755/2,\;\left| y \right| \leqslant 755/2 \hfill \\<br /> \left| x \right| \leqslant 755/2,\;\left| y \right| = 755/2 \hfill \\ <br /> \end{gathered} \right\}

Since the problem does not specify an orientation for the base (only that its center be the origin), any rotational transformation (about the origin) on the square described by the two inequalities can serve as an answer.

For example, another possible solution is
\left| {x + y} \right| = \left| {x - y} \right| = 755/\sqrt 2
where \left| x \right|,\left| y \right| \leqslant 755/\sqrt 2
 
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oh!
 
could u put into a simplified way?
 
cause we are high school students:wink:
 
  • #10
Which part do you find difficult?
 
  • #11
everything. can you explain to us why it's that answer?
 
  • #12
uyenchristine said:
A gift shop sells pewter mugs for $35. They are currenly running an engraving promotion. The first six letter are free. Each additional letter cost $0.20. Write the piecewise model that gives the price of the mug with x engraved letter..

PLease help we need it immediately...:cry:
Don’t worry about the piece wise function part yet. Figure out a formula that will give you the price of each mug for letters 6 and beyond. Then figure out an equation for letters 5 and less.
 

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