Light Intensity The intensity of illumination I from a lightvaries inversely as the square of the distance d from thelight.(a) Write this statement as an equation.(b) Determine the constant of proportionality if it is knownthat a lamp has an intensity of 1000 candles at a dis-tance of 8 m.(c) What is the intensity of this lamp at a distance of 20 m?

To write the equation for light intensity.

Answered: Light Intensity The intensity of…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.CR: Chapter Review

Problem 113E

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Loudness of Sound The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. (a) Write an equation that expresses this variation. (b) Find the constant of proportionality if a person 10 ft. from a lawn mower experiences a sound level of 70 dB . (c) If the distance in part (b) is doubled, by what factor is the loudness changed? (d) If the distance in part (b) is cut in half, by what factor is the loudness changed?
Power from a Windmill The power P that can be obtained from a windmill is directly proportional to the cube of the wind speed s. (a)Write an equation that expresses this variation. (b) Find the constant of proportionality for a windmill that produces 96 watts of power when the wind is blowing at 20 mi/h. (c) How much power will this windmill produce if the wind speed increases to 30 mi/h?
Keplers Third Law Keplers Third Law of planetary motion states that the square of the period T of a planet the time it takes for the planet to make a complete revolution about the sun is directly proportional to the cube of its average distance d from the sun. a Express Keplers Third Law as an equation. b Find the constant of proportionality by using the fact that for our planet the period is about 365 days and the average distance is about 93 million miles. c The planet Neptune is about 2.79109 mi from the sun. Find the period of Neptune.
A Jet of Water The power P of a jet of water is jointly proportional to the cross-sectional area A of the jet and to the cube of the velocity v. a Write an equation that expresses this variation. b If the velocity is doubled and the cross-sectional area is halved, by what factor is the power changed? c If the velocity is halved and the cross-sectional area is tripled, by what factor is the power changed?
Kepler’s Third Law Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time it takes fur the planet to make a complete resolution about the sun) is directly proportional to the cube of its average distance d from the sun. (a) Express Kepler’s Third Law as an equation. (b) Find the constant of proportionality by using the Fact that for our planet the period is about 365 days and the average distance is about 93 million miles (c) The planet Neptune is about 2.79109 mi from the sun. Find the period of Neptune.
Energy The power P produced by a wind turbine is directly proportional to the cube of the wind speed S. A wind speed of 27 miles per hour produces a power output of 750 kilowatts. Find the output for a wind speed of 40 miles per hour.
Skidding in a Curve A car is traveling on a curve that forms a circular arc. The force F needed to keep the car from skidding is jointly proportional to the weight w of the car and the square of its speed s and is inversely proportional to the radius r of the curve. a Write an equation that expresses this variation. b A car weighing 1600 lb travels around a curve at 60 mi/h. The next car to round this curve weighs 2500 lb and requires the same force as the first car to keep from skidding. How fast is the second car traveling?
Equations of Proportionality Write an equation that expresses the statement. y is proportional to x and inversely proportional to t.

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