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Folio MT 2010

# Folio MT 2010

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07/04/2010

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TitleContents Page1. Introduction
History, moral, aesthetical values, others
2. Objectives
2.1To form 3 different functions of the curve of the concrete structure.2.2To find the area of the concrete structure to be painted2.3To estimate the cost of concrete in difference structures.2.4Determine which structure has the minimum cost.2.5Determine the structure to be chosen based on cost and other aspects.2.6To observe the relation between k and area to be painted2.7To express the area to be painted, A in terms of k and the value of Awhen k approaches the value of 4.2.8To predict the shape of A when k approaches the value of 4.
3. Problem Solving
a) Based on different points of reference, there are three different functions canbe written:1.General form:f(x) = -ax
2
- 0.5(-0.5) = -a(2)
2
- 0.5 a = 0.125Hence, f(x) = -0.125 x
2
– 0.5
(0, -0.5)O

y2-2(2, -1)-1

2.General form:f(x) = -a (x - b)
2
+ cf(x) = -a (x - 2)
2
- 0.5 -1 = -a (0 2)
2
- 0.5a = 0.125Hence, f(x) = -0.125(x -2)
2
– 0.53.General form:f(x) = -a (x + b)
2
+ cf(x) = -a (x + 2)
2
- 0.5 -1 = -a (0 + 2)
2
- 0.5a = 0.125Hence, f(x) = -0.125(x +2)
2
– 0.5
(2, -0.5)O

xy4O-12-1(-2, -0.5)

xy-4O-2

2-2
b) The area to be painted:Area =
dx
x
5.025.0
222
∫
=
x x
5.03125.0
3
=
)2(5.0 3)8(125.0 )2(5.0 3)8(125.0
=
+
131131
=
31
1 -
31
- 1=
38
= - 2.667 = 2.667 meter
2
.
(0, -0.5)O

xy2-2(2, -1)-1
y = -0.125 x
2
– 0.5
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