# Mathematics in Context: Building Formulas: Algebra by Encycbrita

By Encycbrita

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Explain. A rule for building an exit ramp states that the vertical distance of the ramp must be no more than one-eighth of the horizontal distance. 3. a. Which of the following ramps fits this rule? i. iii. ii. 5 meter 2 meters 1 meter b. Write the rule for an exit ramp in mathematical language. 4. Design a staircase for a public building with a total height of 3 m. The staircase should take up as little floor space as possible (that is, it should have the smallest possible depth measurement). Make sure it fits the rule for a public building and the rule 2R ؉ T ‫ ؍‬63.

B. How do the surface areas of the cans compare? Be prepared to explain your answer without making calculations. 17. Suppose one can has double the diameter of another can. a. Do you think the amount of liquid that fits in the larger can will double? Give mathematical reasons to support your answer. b. What can you tell about the surface area of the larger can compared to that of the original can? Section D: Formulas and Geometry 39 D Formulas and Geometry Pyramids Nicolas, an artist, makes clocks in the shape of a pyramid by pouring plastic into a mold.

Sample formulas: The Number of Orange Tiles is the Patio Number times itself. Number of Orange Tiles ‫ ؍‬Patio Number ؋ Patio Number G‫؍‬P؋P G ‫ ؍‬P2 c. Discuss your formula with a classmate. You can find many equivalent formulas. W ‫( ؍‬P ؉ 2) ؉ (P ؉ 2) ؉ P ؉ P W ‫ ؍‬2(P ؉ 2) ؉ 2P W ‫ ؍‬4 ؉ 4P W ‫ ؍‬4(P ؉ 1) W ‫ ؍‬4(P ؉ 2) ؊ 4 W ‫( ؍‬P ؉ 2) ؋ (P ؉ 2) ؊ (P ؋ P) d. You can find the answer by extending the table or by using the formulas you found. Number of Orange Tiles in Patio Number 10 is 100.