Question

The volume, V, in cubic centimeters, of a block of wood that a sculptor uses to carve to carve a wolf can be modeled by V(x) = 9x + 3x2- 120x, where x represents the thickness of the block, in centimeters. What maximum thickness of wolf can be carved from a block of wood with volume 1332 cm3?

Answer 1

The maximum thickness of the block that can be carved to form a wolf with a volume of 1332 cm³ is approximately 7.556 cm.

Step-by-step explanation:

The maximum thickness of the block that can be carved to form a wolf with a volume of 1332 cm3 can be found by setting the given volume equation equal to 1332 and solving for x:

9x + 3x2 - 120x = 1332

Combining like terms and rearranging the equation, we get:

3x2 - 111x - 1332 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = (-b ± sqrt(b2 - 4ac)) / 2a

Substituting the values of a, b, and c into the formula, we get:

x = (-(-111) ± sqrt((-111)2 - 4(3)(-1332))) / (2(3))

Simplifying further, we get:

x = (111 ± sqrt(12321 + 15984)) / 6

x = (111 ± sqrt(28305)) / 6

Since we are looking for the maximum thickness, we take the positive root:

x = (111 + sqrt(28305)) / 6

Using a calculator, we find that the maximum thickness of the block that can be carved is approximately 7.556 cm.