(a)
To calculate : The coordinates of the points at
The point
Given information :
The roof of the St .Louis Science Center has a hyperbolic cross section with the dimensions shown in the figure. A coordinate grid is overlaid on the diagram with its origin at, the center of the narrowest part of the roof.
Calculation :
Observe the given figure. Since the origin is at
Divide
The
Let us determine the coordinates of
Divide
The
(b)
To determine : An equation that models the cross section using the coordinates of the points at
The equation that models the cross section is
Given information :
The roof of the St.Louis Science Center has a hyperbolic cross section with the dimensions shown in the figure. A coordinate grid is overlaid on the diagram with its origin at, the center of the narrowest part of the roof.
Explanation :
From part (a), we get the coordinates of
The standard equation of a hyperbola with its center at the origin and the transverse axis horizontal is
Put
Put
Therefore, the equation that models the cross section is
(c)
To calculate : The total height
The height of the roof is
Given information :
The roof of the St.Louis Science Center has a hyperbolic cross section with the dimensions shown in the figure. A coordinate grid is overlaid on the diagram with its origin at, the center of the narrowest part of the roof.
Calculation :
Label the figure as below:
Find the coordinates of the point
Let
The coordinates of
Put
Take square root of both the sides.
Therefore, the height of the roof is
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education