Find Equal Area Between y=x^2 and y=9

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Homework Help Overview

The problem involves finding a horizontal line y=k that divides the area between the curves y=x^2 and y=9 into two equal parts. The context is centered around area calculations in calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss finding the areas as functions of k and the implications of the variable k on area calculations. There are attempts to derive expressions for the areas A1 and A2 based on k.

Discussion Status

Participants are exploring different methods to express the areas in relation to k and are questioning how to compute these areas effectively. Some guidance has been offered regarding the computation of areas, but no consensus has been reached on the specific approach to take.

Contextual Notes

There is mention of the total area being 36, with the goal of finding k such that each area is equal to 18. The discussion includes various interpretations of how to set up the area calculations based on the curves involved.

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Homework Statement


"Find a horizontal line y=k that divides the area between y=x^2 and y=9 into two parts"


Homework Equations





The Attempt at a Solution


Found intersection at (-3,9), (3,9)
Found total area to be 36, half(the area needed for each portion) to be 18. Don't know where to go from here.
 
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Find the two areas as a function of k.
 
christianjb said:
Find the two areas as a function of k.

Can you elaborate more on that? I'm not quite sure what you mean.
 
y=k divides the total area into two parts, A1=A1(k) and A2=A2(k). You need to find an expression for each area as a function of k and then find the value of k for which A1(k)=A2(k)
 
Don't be intimidated by the variable k -- the fact it's there changes nothing. You know how to compute areas, so compute the area of one of the portions.
 
What is the area of the region bounded by y= k, y= 9 and y= x2? For what value of k is that 18?

Even simpler: What is the area of the region bounded by y= 0, y= k and y= x2? For what value of k is that 18?
 

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