solve using python

You are building a bookshelf for a family member who is very particular about aesthetics. The shelf will hold books that will be arranged from left to right increasing in size, as shown in the diagram: You are asked to use a composite to construct the shelf, which has the following characteristics and dimensions E= Young's modulus (psi)=3.667 L= length of bookshelf (inches) =75.0 I= second moment of area (inches 4)=3.00104 You recognize this is a problem of a uniform beam with a linearly increasing distributed load, which means you can calculate the deflection of the beam, y, based on the equation for an elastic curve: Deflection, y, as a function of position along beam: y=120EILw0(x5+2L2x3L4x) you determine the load will be: W0=load(lb/inch)=1.75 Part A. Your family member knows it is likely there will be some sagging somewhere in the middle of the shelf (ie deflection, y ), and asks you where along the shelf the maximum sagging will occur. You know that the maximum deflection occurs where dy/dx=0, and you are interested in where it falls somewhere between the two ends of the shelf. Where along the beam will this point fall? Report the position along the beam, with the same number of significant figures as used to report the length. Show your work (can be in a separate file, be sure to explain your steps clearly -a graph can be helpful). Part B. You want to reassure your family member that the sagging will not be drastic-you decide to use the deflection equation to report a predicted maximum deflection of the shelf. (Report to the same decimal place as your answer in part A, and report the units) Part C. You build the shelf, and load it with books ordered as requested. Out of curiosity you measure the max deflection and find it is 1.5 inches. If you consider this the true value of deflection, what is your true percent relative error? What might be some factors contributing to any difference between your calculation and observed value? (describe at least 2)