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 would be greatly appreciated! you.

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

Hence the appropriate choice is ...

... D. 0 < x < 5

  about 5.6 days

step-by-step explanation:

we can fill the given information into the decay equation and solve for the value of t at which half the sample remains.

the half-life is about 5.6 days.