Question

Find b such that the line y = b divides the region bounded by the graphs of the two equations into two regions of equal area. Round your answer to three decimal places.

Answer 1

To find b such that the line y = b divides the region bounded by the two equations into two regions of equal area, we can calculate the area under the curve
`y = x^2 - 1` and set it equal to the area of a triangle formed by certain points. Solving the equation, we find two possible values for
`b: ±sqrt(3)`.

Step-by-step explanation:

To find b such that the line
`y = b` divides the region bounded by the two equations into two regions of equal area, we need to find the area under the curve
`y = x^2 - 1`. We can do this by calculating the area of the right triangle formed by the points (0, -1), (0, b), and
`(b^2 - 1, b)`. The area of a triangle is given by
`A = 1/2 * base * height`, so we can set up the equation
`(1/2) * (b^2 - 1) * b = (1/2) * b * (b - (-1))`. Solving this equation, we find
`b = ±sqrt(3)` or approximately
`±1.732`.