Solve the following Math (PreCalculus) problem and show your work, please. PLEASE MAKE SURE TO DO THE STEPS CORRECTLY AND FIND THE RIGHT ANSWER. Circle or Box the anwer.

Problem 1- An open box with a square base is to have a volume of 108 cubic inches. Could you find the dimensions of the box that will have minimum surface area? Let x= length of the side of the base. Identify the primary and secondary equations.

Show work for each one and please give me the correct answer. Circle or box the answer.

Problem 2- Use the Intermediate Value Theorem to show that there exists a root(zero) between x=0.001 and x=0.1 for f(x)=x^3-100x+2. SOLVE FOR THE ROOT.

Problem 3- A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t)=-4.9t^2+229t+234.

a. Find the maximum height the rocket attains. Round your answer to four decimal places.

b. How long does the rocket take to reach maximum height. Round your answer to four decimal places.