Equal area question

mikesown

1. The problem statement, all variables and given/known data
"Find a horizontal line y=k that divides the area between y=x^2 and y=9 into two parts"

2. Relevant equations

3. 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.

christianjb

Find the two areas as a function of k.

mikesown

Quote by christianjb

Find the two areas as a function of k.

Can you elaborate more on that? I'm not quite sure what you mean.

christianjb

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)

Hurkyl

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.

HallsofIvy

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?

Similar discussions for: Equal area question
Thread	Forum	Replies
question about equal torques	Introductory Physics Homework	1
MIPS32 (ASM) greater than or equal too, pseudo instruction question	Engineering, Comp Sci, & Technology Homework	0
surface area of a cube with the length of each edge equal to x+1	General Math	5
Equal areas in equal times	Calculus & Beyond Homework	3
quick question. Do they equal?	Introductory Physics Homework	6

mikesown	Equal area question 1. The problem statement, all variables and given/known data "Find a horizontal line y=k that divides the area between y=x^2 and y=9 into two parts" 2. Relevant equations 3. 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.

christianjb	Equal area question 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)

Hurkyl Recognitions: Gold Member Science Advisor Staff Emeritus	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.

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	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?