Concept explainers
Electrical Trades The electrical resistance of a given length of wire is inversely proportional to the square of the diameter of the wire:
If a certain length of wire with a diameter of 34.852 mils has a resistance of 8.125 ohms, what is the resistance of the same length of the same composition wire with a diameter of 45.507 mils?
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
- Music The fundamental frequency (in hertz) of a piano string is directly proportional to the square root of its tension and inversely proportional to its length and the square root of its mass density. A string has a frequency of 100 hertz. Find the frequency of a string with each property. (a) Four times the tension (b) Twice the length (c) Four times the tension and twice the lengtharrow_forwardElectrical resistance The resistance of a wire varies directly as the length of the wire and inversely as the square of its diameter. A 1000-foot length of wire, 0.05 inch in diameter, has a resistance of 200 ohms. What would be the resistance of a 1500-foot length of wire that is 0.08 inch in diameter.arrow_forwardApplications Set up and solve the required proportion. Heat dissipation The power, in watts, dissipated as heat in a resistor varies directly with the square of the voltage and inversely with the resistance. If 20 volts are placed across a 20-ohm resistor, it will dissipate 20 watts. What voltage across a 10-ohm resistor will dissipate 40 watts?arrow_forward
- Automobile collisions The energy dissipated in an auto mobile collision varies directly with the square of the speed. By what factor does the energy increase in a 50-mph collision compared with a 20-mph collision?arrow_forwardEnergy 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.arrow_forwardSkidding 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?arrow_forward
- Ecology The diameter of the largest particle that a stream can move is approximately directly proportional to the square of the velocity of the stream. When the velocity is 14 mile per hour, the stream can move coarse sand particles about 0.02 inch in diameter. Approximate the velocity required to carry particles 0.12 inch in diameter.arrow_forwardLoudness 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?arrow_forwardBeam Load The maximum load that a horizontal beam can safely support varies jointly as the width of the beam and the square of its depth and inversely as the length of the beam. Determine how each change affects the beam’s maximum load. (a) Doubling the width (b) Doubling the depth (c) Halving the length (d) Halving the width and doubling the lengtharrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning