Question

Domain of a polynomial. Application question(measurement). So it's a 2 part question but I believe I have the first part done. The second part is asking what would be a suitable domain and I have no idea. None of them look right. haha. So some help would be greatly appreciated! Thank you.

Answer 1

9. B. 30.0 cm³

10. D. 0 < x < 5

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