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 =

a≈2.343

Step-by-step explanation:

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Integrating an equation from boundary x₀ to x₁ gives you the area underneath that boundary.

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.

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15