
In Problems 79-84, use the following discussion. The formula can be used to approximate the number of hours of daylight D when the declination of the Sun is at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, must be expressed in radians.
Approximate the number of hours of daylight in Honolulu, Hawaii ( north latitude), for the following dates:
(a) Summer solstice
(b) Vernal equinox
(c) July 4

To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight in Honolulu, Hawaii ( north latitude), for the following dates:
a. Summer solstice .
Answer to Problem 71AYU
Solution:
a. hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
a. Summer solstice north latitude .
Formula used:
Calculation:
a. Summer solstice north latitude .
Convert degree into radians.
hours.

To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight in Honolulu, Hawaii ( north latitude), for the following dates:
b. Vernal equinox .
Answer to Problem 71AYU
Solution:
b. hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
b. Vernal equinox ; north latitude .
Formula used:
Calculation:
b. Vernal equinox ; north latitude .
Convert degree into radians.
hours.

To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight in Honolulu, Hawaii ( north latitude), for the following dates:
c. July 4 .
Answer to Problem 71AYU
Solution:
c. hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
c. July 4 north latitude .
Formula used:
Calculation:
c. July 4 north latitude .
Convert degree into radians.
hours.
Chapter 7 Solutions
Precalculus
Additional Math Textbook Solutions
Elementary Statistics
College Algebra with Modeling & Visualization (5th Edition)
Algebra and Trigonometry (6th Edition)
Elementary Statistics (13th Edition)
Introductory Statistics
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
- Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?arrow_forward1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).arrow_forwardDoes the series converge or divergearrow_forward
- Suppose that a particle moves along a straight line with velocity v (t) = 62t, where 0 < t <3 (v(t) in meters per second, t in seconds). Find the displacement d (t) at time t and the displacement up to t = 3. d(t) ds = ["v (s) da = { The displacement up to t = 3 is d(3)- meters.arrow_forwardLet f (x) = x², a 3, and b = = 4. Answer exactly. a. Find the average value fave of f between a and b. fave b. Find a point c where f (c) = fave. Enter only one of the possible values for c. c=arrow_forwardplease do Q3arrow_forward
- Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.) (a) In(0.75) (b) In(24) (c) In(18) 1 (d) In ≈ 2 72arrow_forwardFind the indefinite integral. (Remember the constant of integration.) √tan(8x) tan(8x) sec²(8x) dxarrow_forwardFind the indefinite integral by making a change of variables. (Remember the constant of integration.) √(x+4) 4)√6-x dxarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





