Quiz 2 - Common Maxima and Minima Problems

The problems in this quiz are common optimization problems in engineering lincesure examinations. The allotted time is 30 minutes for you to solve all ten problems. This is to simulate the 100 items board examination given for 5 hours.

All of the problems here can be solved without the aid of differentiation if you know the exact variable relationships for maximum and minimum quantity. Example is, if you are required to inscribed the largest rectangle in a given a circle, differentiation will lead you to a square.



If you already know that it is a square, then you don't need to do the differentiation. Go directly in solving the square for faster solution. All of the problems here can be done in this way, that is, if you know the variable relationship of the situation. If not, then you can still do the differentiation to solve the problem.

The 10 problems you are going to answer are taken from a pool of problems in growing numbers. We are constantly adding problems in here, if you take this quiz again chances are, you will encounter different sets of problems.

Note that you are only given up to 3 times to take this quiz. So fire your best shots and good luck.

Quiz 1 - Basic Algebra

There are 10 problems in this quiz taken randomly from a pool of 100 problems. If you are able to finish this quiz and will take it again, chances are, you will encounter different problems. Unfinished quiz is internally saved, it will resume where you leave with the same set of problems the next time you run the quiz. The system however will delete any incomplete quiz after 10 days.

This quiz is designed for 30 minutes, you are given three minutes per problem although most of the problems can be answered in less than a minute. The total time allotted for this quiz is 40 minutes, the ten minutes allowance is for the loading of each problem. We assume each problem will load in one minute, we understand that the number is too conservative.

The topics in this quiz are as follows: logarithm, inequality, absolute value, radicals, factoring, determinants, worded problems, polynomials, variations, complex numbers, partial fractions, complex fractions, quadratic equations, progressions, sequence, and other topics in Algebra. You may not encounter all the topics as you are given only 10 items per quiz.

You can take this quiz as many times as you want, and hopefully you will encounter all the 100 problems from the pool where the 10 problems are randomly generated. All of your finished quizzes are stored under your account and you can access it any time you want.

You need to login in order to take this quiz. Good luck and enjoy!

Problem 863 | Deflection by Three-Moment Equation

Problem 863
For the beam shown in Fig. P-863, determine the value of EIδ midway between the supports and at the left end.




At midway between the supports
$\delta = \dfrac{1066.67}{EI} ~ \text{ upward}$

At the left end
$\delta = \dfrac{16,000}{EI} ~ \text{ downward}$


For the complete solution using the three moment equation, see it here: http://www.mathalino.com/reviewer/strength-materials/problem-863-deflect...

The Polar Coordinate System

In Polar Coordinate System, the references are a fixed point and a fixed line. The fixed point is called the pole and the fixed line is called the polar axis. The location of a point is expressed according to its distance from the pole and its angle from the polar axis. The distance is denoted by r and the angle by θ.