A straight street of fixed width a metres on the horizontal ground is bounded on its parallel sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The intensity of light at point R at ground level on the street is proportional to the angle 0, in radians, where 0= ZPRQ as shown in the diagram. 10 m 9 m a m It is given that x is the distance of R from the base of the wall of height 10 metres. (i) Find an exact expression for 0 in terms of x, a and n. de (ii) Show that dr 10 9. Find, in terms of a, the value of x when the 100+x? (a-x) +81 intensity of light at R is maximum. (iii) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5 ms. Given that a = 20, find the rate of change of 0 at the instant when R is at the midpoint of the street. Give your answer correct to 4 significant figures. 10 tan 9. or 0 = tan [() 0 3 п - tan -1 -1 -1 a – x + tan 10 -1 X (ii) x = 10a – 3/10(a² +1), а - х 9 (iii) –0.0001381]
A straight street of fixed width a metres on the horizontal ground is bounded on its parallel sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The intensity of light at point R at ground level on the street is proportional to the angle 0, in radians, where 0= ZPRQ as shown in the diagram. 10 m 9 m a m It is given that x is the distance of R from the base of the wall of height 10 metres. (i) Find an exact expression for 0 in terms of x, a and n. de (ii) Show that dr 10 9. Find, in terms of a, the value of x when the 100+x? (a-x) +81 intensity of light at R is maximum. (iii) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5 ms. Given that a = 20, find the rate of change of 0 at the instant when R is at the midpoint of the street. Give your answer correct to 4 significant figures. 10 tan 9. or 0 = tan [() 0 3 п - tan -1 -1 -1 a – x + tan 10 -1 X (ii) x = 10a – 3/10(a² +1), а - х 9 (iii) –0.0001381]
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 14E: A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral...
Related questions
Concept explainers
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
Question
Full solution pls for the whole question. Answers can be found below.
![A straight street of fixed width a metres on the horizontal ground is bounded on its parallel
sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The
intensity of light at point R at ground level on the street is proportional to the angle 0, in
radians, where 0 = ZPRQ as shown in the diagram.
10 m
9 m
R
am
It is given that x is the distance of R from the base of the wall of height 10 metres.
(i)
Find an exact expression for 0 in terms of x, a and T .
de
Show that
10
9.
(ii)
dr 100+x2 (a-x) +81
Find, in terms of a, the value of x when the
intensity of light at R is maximum.
(111) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5
ms. Given that a =
20, find the rate of change of 0 at the instant when R is at the midpoint
of the street. Give your answer correct to 4 significant figures.
10
[(1) 0 =
-1
T – tan
-1
tan
9
or 0 = tan
-1 a– x
+ tan
10
10a – 3/10(a² +1),
(ii) х %3D
а - х
9.
(iii) –0.0001381]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F902f5c45-8106-4c05-84fa-6818a38e7876%2F9f96dfff-b126-4273-b846-782e45fa03d6%2Ffj3tv4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A straight street of fixed width a metres on the horizontal ground is bounded on its parallel
sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The
intensity of light at point R at ground level on the street is proportional to the angle 0, in
radians, where 0 = ZPRQ as shown in the diagram.
10 m
9 m
R
am
It is given that x is the distance of R from the base of the wall of height 10 metres.
(i)
Find an exact expression for 0 in terms of x, a and T .
de
Show that
10
9.
(ii)
dr 100+x2 (a-x) +81
Find, in terms of a, the value of x when the
intensity of light at R is maximum.
(111) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5
ms. Given that a =
20, find the rate of change of 0 at the instant when R is at the midpoint
of the street. Give your answer correct to 4 significant figures.
10
[(1) 0 =
-1
T – tan
-1
tan
9
or 0 = tan
-1 a– x
+ tan
10
10a – 3/10(a² +1),
(ii) х %3D
а - х
9.
(iii) –0.0001381]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math 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,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning