LINKING concepts... For Individual or Group Explorations Designing a Race Track An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track. a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section. b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track. c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track. d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
LINKING concepts... For Individual or Group Explorations Designing a Race Track An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track. a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section. b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track. c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track. d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
Solution Summary: The author calculates the dimensions of xandy in the figure that will maximize the area of the rectangular center section.
An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track.
a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section.
b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track.
c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track.
d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
PRIMERA EVALUACIÓN SUMATIVA
10. Determina la medida de los ángulos in-
teriores coloreados en cada poligono.
⚫ Octágono regular
A
11. Calcula es número de lados qu
poligono regular, si la medida
quiera de sus ángulos internos
• a=156°
A= (-2x+80
2
156 180-
360
0 = 24-360
360=24°
• a = 162°
1620-180-360
6=18-360
360=19
2=360=
18
12. Calcula las medida
ternos del cuadrilá
B
X+5
x+10
A
X+X+
Sx+6
5x=3
x=30
0
лаб
• Cuadrilátero
120°
110°
• α = 166° 40'
200=180-360
0 =
26-360
360=20
ひ=360
20
18 J
60°
⚫a=169° 42' 51.43"
169.4143180-340
0 = 10.29 54-360
360 10.2857
2=360
10.2857
@Sa
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