Solving a Hard Math Question: Volume of Concentrated Orange Juice

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Homework Help Overview

The problem involves calculating the volume of concentrated orange juice and determining how many glasses can be filled with the prepared juice after adding water. The context includes algebraic expressions for volume and dimensions of the glasses.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the volume of the orange juice concentrate and the impact of adding water. There is a mention of needing to account for the height of the glasses when calculating the number of glasses that can be filled.

Discussion Status

Some participants have offered insights into the relationship between the volumes of the concentrate and the water. There is recognition of potential confusion in the problem's wording, and a clarification about the nature of the result being a function of x rather than a constant.

Contextual Notes

Participants note the complexity of the problem and the need for careful interpretation of the question's wording, particularly regarding the volume relationships and the dimensions of the glasses.

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in my opinion, i find this question really hard.

-the volume of a can of concentrated orange juice is represented by the following expression:
[tex](8x^3-54x+54)\pi[/tex]cm^3
the juice is prepared by emptying the concentrate into a large container and by adding 3 cans of the same volume of water. after a good stir, the juice is poured into glasses measuring 9 cm in height and whose radius is (2x-3) cm. Use a simplified algebraic expression to represent the number of glasses that can be filled up to 1 cm from the rim.

i've drawn my diagrams i just don't know where to start. any help would be apreciated...
thanks in advance
 
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The volume of the large container is 4*volume of oj concentrate

you would then divide that by the volume of the glass (-1 cm of height)
 
o i see wat the question ment when it said "3 cans of water of the same volume" AS THE CONCENTRATE, its really badly written... thanks tho
 
btw, you won't find a constant number, you will find a function of x
 

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