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.) y = 81 − x2, y = 0

Answer 1

To 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, we need to integrate the equation y = 81 - x^2 and solve for b.

Step-by-step explanation:

To 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, we need to find the x-values where the area under the curve y = 81 - x^2 is equal to half the area under the x-axis (y = 0).

To do this, we can integrate the equation y = 81 - x^2 from the x-values where the curve intersects the x-axis, which are -9 and 9. Setting the integral equal to half the area under the x-axis, we can solve for b.

By setting up and solving the integral, we find that b = 54.