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regent47.docx - NAME MATH125 Unit 1 Submission Assignment...

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NAME: MATH125: Unit 1 Submission Assignment Answer Form Mathematical Modeling and Problem Solving ALL questions below regarding SENDING A PACKAGE and PAINTING A BEDROOM must be answered. Show ALL step-by-step calculations, round all of your final answers correctly, and include the units of measurement . Upload this modified Answer Form to the intellipath Unit 1 Submission lesson. Make sure you submit your work in a modified MS Word document; handwritten work will not be accepted . If you need assistance, please contact your course instructor. All commonly used formulas for geometric objects are really mathematical models of the characteristics of physical objects. For example, a basketball, because it is a sphere, can be partially modeled by its distance from one side through the center (radius, r ) and then to the other side by the diameter formula for a sphere: D = 2 r . For familiar two-dimensional variables length, L , and width, W , the perimeter and area formulas for a rectangle are mathematical models for distance around the rectangle (perimeter, P ) and the region enclosed by the sides (area, A ), respectively: P = 2L + 2W and A = L x W Along with another variable, height, H, a three-dimensional rectangular prism’s volume and surface area can be measured. For example, the formulas for a common closed cardboard box’s inside space (volume, V ) and outside covering (surface area, SA ) are respectively: V = L x W x H and SA = 2(L x W) + 2(W x H) + 2(L x H) For this Submission Assignment follow Polya’s principles to solve your problems, and include the following: Explain your interpretation of what the problem is about. Develop and write down a strategy for solving this problem; show the steps in the correct order for your attempted solution. Did your strategy actually solve the problem? How do you know? Suppose your solution did not solve the problem—what would be your next action? SENDING A PACKAGE Your goal is to construct a rectangular box with a top on it that has the smallest possible surface area in which a football and a basketball, both fully inflated, will just fit into at the same time. Pictured below, the football measures 6.5 inches high and 11.55 inches long, while the basketball is 9.55 inches high:
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1. What box dimensions make a good model for this situation? All quantities are inside-of-the-box measurements. First, position the football and basketball side-by-side. Then, slide the basketball so that it is even with one point of the football. Now, measurements can be made that will give the minimum width across both objects. That will be the minimum width of the box with the smallest surface area. Using the following diagrams, first find the exact LENGTH and HEIGHT. Do not round:
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ANSWERS Length 11.55 inches Height 9.55 inches Explain your answer here: (4 points) I have taken the maximum length the two objects, first one is 11.55 inches and the second is 9.5 inches. So length should be 11.55 inches because it is greater. Next for height we use same process. First ball has height 6.5 inches and second ball has 9.55 inches. Since 9.55 is greater, so height should be 9.55inches.
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  • Summer '17
  • momanyi
  • Statistics, inches, square feet, step-by-step calculations

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