Laser Beams A concert stage has a parabolic roof. The front edge of the roof is defined by the equation h(x) = -x² + 8, where x is the horizontal distance from %3D the centre and h is the height, both in metres. A vertical lighting tower is built at x = 9. Coloured laser lights are installed at various intervals going up the tower. The beams of light are to shine on the front edge of the roof, with their paths defined by the following equations. Blue: 6x + 8y – 73 = 0 Green: x + 2y – 17 = 0 Orange: x + y – 10 = 0 Red: 2x + 8y – 67 = 0 a) Sketch the graph of h(x). b) Determine the coordinates of any point(s) of intersection of each laser beam with the edge of the roof. c) All but one of these laser beams share a common property. Describe the property. d) Determine the height of each light source on the tower. e) Determine an equation for the path of a fifth laser beam that is to be tangent to the edge of the roof at the vertex. Where should this light source be located on the tower? f) Consider the one laser light that does not share the common property. Keeping the location of the light source fixed, determine a new equation for the path of the laser light so that it now shares the common property. Where does it intersect the edge of the roof?
Laser Beams A concert stage has a parabolic roof. The front edge of the roof is defined by the equation h(x) = -x² + 8, where x is the horizontal distance from %3D the centre and h is the height, both in metres. A vertical lighting tower is built at x = 9. Coloured laser lights are installed at various intervals going up the tower. The beams of light are to shine on the front edge of the roof, with their paths defined by the following equations. Blue: 6x + 8y – 73 = 0 Green: x + 2y – 17 = 0 Orange: x + y – 10 = 0 Red: 2x + 8y – 67 = 0 a) Sketch the graph of h(x). b) Determine the coordinates of any point(s) of intersection of each laser beam with the edge of the roof. c) All but one of these laser beams share a common property. Describe the property. d) Determine the height of each light source on the tower. e) Determine an equation for the path of a fifth laser beam that is to be tangent to the edge of the roof at the vertex. Where should this light source be located on the tower? f) Consider the one laser light that does not share the common property. Keeping the location of the light source fixed, determine a new equation for the path of the laser light so that it now shares the common property. Where does it intersect the edge of the roof?
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Topic Video
Question
I need a answer for question E
Transcribed Image Text:Laser Beams
A concert stage has a parabolic roof. The front edge of the roof is defined
by the equation h(x) = -x² + 8, where x is the horizontal distance from
%3D
the centre and h is the height, both in metres. A vertical lighting tower is
built at x = 9. Coloured laser lights are installed at various intervals going
up the tower. The beams of light are to shine on the front edge of the roof,
with their paths defined by the following equations.
Blue: 6x + 8y – 73 = 0
Green: x + 2y – 17 = 0
Orange: x + y – 10 = 0
Red: 2x + 8y – 67 = 0
%3D
a) Sketch the graph of h(x).
b) Determine the coordinates of any point(s) of intersection of each laser
beam with the edge of the roof.
c) All but one of these laser beams share a common property. Describe the
property.
d) Determine the height of each light source on the tower.
e) Determine an equation for the path of a fifth laser beam that is to be
tangent to the edge of the roof at the vertex. Where should this light
source be located on the tower?
f) Consider the one laser light that does not share the common property.
Keeping the location of the light source fixed, determine a new equation
for the path of the laser light so that it now shares the common property.
Where does it intersect the edge of the roof?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning