Concept explainers
Amperage, Wattage, and Voltage Amperage is a measure of the amount of electricity that is moving through a circuit, whereas voltage is a measure of the force pushing the electricity. The wattage W consumed by an electrical device can be determined by calculating the product of the amperage I and voltage V. (Source: Wilcox. G. and C. Hesselberth, Electricity for Engineering Technology, Allyn & Bacon.)
(a) A household circuit has voltage
V = 163 sin 120πt
when an incandescent light bulb is turned on with amperage
I = 1.23 sin 120πt.
Graph the wattage W — VI consumed by the light bulb in the window [0.0.05] by [ -50. 300].
(b) Determine the maximum and minimum wattages used by the light bulb.
(c) Use identities to determine values for a. c. and w so that W — a cos(wt) + c.
(d) Check by graphing both expressions for W on the same coordinate axes.
(e) Use the graph to estimate the average wattage used by the light. For how many watts (to the nearest integer) would this incandescent light bulb be rated?
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
TRIGONOMETRY MSU CUSTOM W/MML
- Market supply The following table shows the quantity S of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price P, in dollars per bushel. S = quantity of wheat P = price 1.0 1.35 1.5 2.40 2.0 3.45 2.5 4.50 In economics, it is customary to plot S on the horizontal axis and P on the vertical axis, so we will think of S as a variable and of P as a function of S. a. Show that these data can be modeled by a linear function, and find its formula. b. Make a graph of the linear formula you found in part a. This is called the market supply curve. c. Explain why the market supply curve should be increasing. Hint: Think about what should happen when the price increases. d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of 3.90 per bushel?arrow_forwardLean Body Weight in Females This is a continuation of Exercise 24. The text cited in Exercise 24 gives a more complex method of calculating lean body weight for young adult females: L=19.81+0.73W+21.2R-0.88A-1.39H+2.43F Here L is the lean body weight in pounds, W is the weight in pounds, R is wrist diameter, A is the abdominal circumference in inches, H is hip circumference if inches, and F is forearm circumference in inches. According to this formula, what is the approximate lean body weight of a young adult female who weighs 132 pounds and has wrist diameter of 2 inches, abdominal circumference of 27 inches, hip circumference of 37 inches and forearm circumference of 7 inches? What is the weight of her body fat? What is her body fat percent? Lean Body Weight in Males A persons lean body weight L is the amount that he or she would weigh if all body fat were marginally to disappear. One text gives the equation that practitioners can use most feasibly in the field to predict lean body weight in young males. The equation is L=98.42+1.08W-4.14A Here L is the lean body weight in pounds, W is the weight in pounds and A is the abdominal circumference in inches. Find the approximate lean body weight of a young adult male who weighs 188 pounds and has an abdominal circumference of 35 inches. What is the weight of his body fat? What is his body fat percent?arrow_forwardSpeed of Sound in the North Atlantic The speed of sound in ocean water is 1148.94meterspersecond, provided that the ocean water has a salinity of 35 35partsperthousand, the temperature it 0degreesCelsius, and the measurement is taken at the surface. If any one of these three factors varies, the speed of sound also changes. Different oceans often differ in salinity. In the North Atlantic Central Water the main body of water for the northern half of the Atlantic Ocean, the salinity can be determined from the temperature, so the speed of sound depends only on temperature and depth. A simplified polynomial formula for velocity in this body of water is V=1447.733+4.7713T0.05435T2+0.0002374T3+0.0163D+1.675107D27.1391013TD3 Here V is the speed of sound in meters per second, T is the water temperature in degrees Celsius, and D is depth in meters. This formula is valid for depths up to 8000 meters and for temperatures between 0 and 30 degrees Celsius. a. What type of polynomial is V as a function of T alone? Of D alone? b. For a fixed depth of 1000meters, write the formula for V in terms of T alone. c. Graph V as a function of T for the fixed depth of 1000meters. d. What is the concavity of the graph from part c? What does this imply about the speed of sound at that depth as temperature increases?arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage