The height of the box rounded to the nearest tenth of a centimeter is 35.7 centimeters.
Darnisha has to find the value of z for V(z) = 72,500.
V (a) = 4x³-520x² +1,2002
=> 4z³-520z² +1,2002 = 72,500
=> z³-130z² + 3000.5 = 18125
Multiply both sides of the equation by 4
=> 4z³-520z² +12002 = 72,500
=> z³-130z² + 3000.5 = 18125
=> z³-130z² + 3000.5 - 18125 = 0
=> z³-130z² - 15124.5 = 0
Use a graphing calculator to solve z³-130z² - 15124.5 = 0
z ≈ 35.74
The height of the box rounded to the nearest tenth of a centimeter is 35.7 centimeters.
So the answer is 35.7