Answer:
9. B. 30.0 cm³
10. D. 0 < x < 5
Step-by-step explanation:
9. A graphing calculator is useful for finding zeros and extrema of cubics. Mine shows the maximum value of the volume function to be 30.0 cm³.
You can expand the function to
... V = x³ -12x² +35x
and differentiate to find the value of x that gives maximum volume.
... 3x² -24x +35 = 0
... x = (24-√(24² -4(3)(35)))/(2(3)) = 4 - √(4 1/3) ≈ 1.91833 . . . . by the quadratic formula
Putting this value into the volume formula gives
.. V ≈ (1.91833)(3.08167)(5.08167) ≈ 30.04 . . . . cm³
10. All dimensions must be non-negative, so you must have
- x > 0
- 5 - x > 0 . . . . . x < 5
- 7 - x > 0 . . . . . x < 7 . . . (the previous condition is more restrictive)
Hence the appropriate choice is ...
... D. 0 < x < 5
