5. Find the exact value (no decimals) of the volume of the solid whose base is the triangle with vertices (0, 0), (0, 10), and (5, 0) and whose cross sections taken perpendicular to the x-axis are squares. page 5

A rectangle is bounded by the x-axis, the y-axis, and the line 1.5 y y = ," , as shown in the figure. What is the maximum area of such a rectangle? O 0.8 O 1 0.5 O 1.2 O 1.25 3 -0.5 N.

A plane with the equation + volume V = 1/6 Vmin = + 12/2 = 1 (a, b, c > 0) together with the positive coordinate planes forms a tetrahedron of abc. Find the minimum value of V among all planes passing through the point P = (7,7,7). (Use symbolic notation and fractions where needed.)

9. (a) Give an equation of the sphere centered at the origin with radius 3. (b) Give an equation of a copy of the sphere from part (a), which is now centered at (4, -6, 3) and has twice the radius. (c) Give an equation of a copy of the sphere from part (a), still centered at the origin, but has twice the volume.