Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 16x2 + 9y2 = 144. cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

In the - plane, the base has equation(s)

which is to say, the distance (parallel to the -axis) between the top and the bottom of the ellipse is

so that at any given , the cross-section has a hypotenuse whose length is .

The cross-section is an isosceles right triangle, which means the legs occur with the hypotenuse in a ratio of 1 to , so that the legs have length . Then the area of each cross-section is

Then the volume of this solid is

27

step-by-step explanation:

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x