Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to three decimal places.)
y = x, y = 8, x = 0
a = _____.

So to find the boundary that split the equation into 2 equal areas, the boundary must lie somewhere between the 2 place to want to split up. In other word, a is the end boundaries of the first integral and the starting boundary of the second integral.

Since the two area must equal to each other, set the two integral equal to each other and solve for a.

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-03-21T10:10:58+01:00

The value of a for which x=a will divide the enclosed area into two equal areas will be 2.43.

Let us say x=a divides the region into two equal areas.

From the attached diagram,

Point D≡(a,8)

Point E≡(a, a)

The length of DE will be 8-a.

As we know that triangles ADE and ABO will be similar

So, [tex]\frac{areaADE}{areaABO} = (\frac{DE}{BO}) ^{2}[/tex]

[tex]\frac{1}{2} = (\frac{a-8}{8}) ^{2}[/tex]

[tex]a^2-16a+32 = 0[/tex]

a =13.66(Not Possible)

a= 2.34

Therefore, The value of a for which x=a will divide the enclosed area into two equal areas will be 2.43.

To get more about the similarity of triangles visit:

https://brainly.com/question/8430622

Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to three decimal places.) y = x, y = 8, x = 0 a = _____.

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Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to three decimal places.)
y = x, y = 8, x = 0
a = _____.