MATH125: Unit 1 Individual Project
Mathematical Modeling and Problem Solving
All commonly used formulas for geometric objects are really mathematical models of the characteristics of physical objects.For example, the characteristic of the volume inside a common closed cardboard box can be modeled by the formula for the volume of a rectangular solid, V = L x W x H, where L = Length, W = Width, and H = Height of the box.A basketball, because it is a sphere, can be partially modeled by its distance from one side through the center to the other side, or diameter, by the diameter formula for a sphere, D = 2r.
Complete only ONE of the following questions.
1. (Please review Chapter 9 in the College Math text for geometric objects and their properties.)For a familiar example, the perimeter and area formulas for a rectangle are mathematical models for distance around the rectangle (perimeter) and area enclosed by the sides, respectively; P = 2L + 2W and A = L x W.For another example, the volume of a rectangular box would be:V = L x W x H, where L = Length, W = Width, and H = Height.The surface area of a rectangular box would be: SA = 2(L x W) + 2(W x H) + 2(L x H).Your problem is to obtain (or make) arectangular box with a top on it that has the smallest possible surface area and that a football and a basketball, both fully inflated,will just fit into at the same time.What could make a good model for this situation?Using Polya’stechnique for solving problems, describe and discuss the strategy, steps,and procedures you will use to solve this problem. Then, demonstrate that your solution is correct.
2. (Please review Chapter 9 in the College Math text for geometric objects and their properties; walls, windows, and ceilings are all rectangles.)The walls and ceiling in your bedroom need to be painted, and the painters’ estimates to do the work are far too expensive.You decide that you will paint the bedroom yourself.The bedroom is 14 ft. 3 in. by 16 ft., and the ceiling is 8 ft. high.The color of paint you have selected covers 75 sq.ft. per gallon, and costs $33.50 per gallon.The ceiling will be painted with a bright white ceiling paint that costs $28.50 per gallon but only covers 50 sq. ft. per gallon.There is one window in the room, and it is 3 ft. 4 in. by 5 ft. and will not be painted.The inside of the bedroom door is to be painted the same coloras the walls.Describe and discuss how you will use Polya’s problem-solving techniques to determine how much it will cost to paint this room with two coats of paint (on both walls and ceiling).Then, using your solution strategy, determine how much it will actually cost to paint your bedroom. Assuming you can paint 100 sq.ft. per hour, what will be the work time needed to paint your bedroom?(Because different paint lots of the same color may appear slightly different colors, when painting a room, you should buy all of your paint at one time and intermix the paint from at least two different cans so that the walls will all be exactly the same color.)
We value our customers and so we ensure that what we do is 100% original..
With us you are guaranteed of quality work done by our qualified experts.Your information and everything that you do with us is kept completely confidential.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read moreThe Product ordered is guaranteed to be original. Orders are checked by the most advanced anti-plagiarism software in the market to assure that the Product is 100% original. The Company has a zero tolerance policy for plagiarism.
Read moreThe Free Revision policy is a courtesy service that the Company provides to help ensure Customer’s total satisfaction with the completed Order. To receive free revision the Company requires that the Customer provide the request within fourteen (14) days from the first completion date and within a period of thirty (30) days for dissertations.
Read moreThe Company is committed to protect the privacy of the Customer and it will never resell or share any of Customer’s personal information, including credit card data, with any third party. All the online transactions are processed through the secure and reliable online payment systems.
Read moreBy placing an order with us, you agree to the service we provide. We will endear to do all that it takes to deliver a comprehensive paper as per your requirements. We also count on your cooperation to ensure that we deliver on this mandate.
Read more