Skills and Applications
Electrical Network Applying Kirchhoff’s Laws to the electrical network in the figure, the currents
Find the currents.
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Chapter 7 Solutions
Precalculus (MindTap Course List)
- Electricity By using Kirchhoffs Laws, it can be shown that the currents I1, I2 and I3 that pass through the three branches of the circuit in the figure satisfy the given linear system. Solve the system to find I1, I2 and I3. {I1+I2I3=016I18I2=48I2+4I3=5arrow_forwardCircuit Analysis: Consider the circuit shown in the figure. The currents I1, I2, and I3 (in amperes) are the solution of the system 4I1+8I3=22I2+8I3=6I1+I2I3=0. Use Cramer’s Rule to find the three currents.arrow_forwardNutrition A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 32 units of niacin and 22000 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.12 unit of niacin and 100 units of retinol per gram. Food B contains 0.20 unit of niacin and 50 units of retinol per gram. How many gram of each food does she feed this group of rats each day?arrow_forward
- Nutrition A researcher performs an experiment to test a hypothesis is that involves the nutrients niacin and retinol. She feeds one group of laboratory rats daily of diet of precisely 32units of niacin and 22,000units of retinol. She uses two types of commercial foods. Food A contains 0.12unit of niacin and 100units of retinol per gram. Food B contains 0.20unit of niacin and 50units units of retinol per gram. How many grams of each does she feed this group of rats each day?arrow_forwardThink About It Consider the system of equations ax+by=cdx+ey=f (a) Find values for a,b,c,d,e and f so that the system has one distinct solution. (There is more than one correct answer.) (b) Explain how to solve the system in part (a) by the method of substitution and graphically. (c) Write a brief paragraph describing any advantages of the method of substitution over the graphical method of solving a system of equations.arrow_forwardAPPLICATIONS The Arch of a BridgeThe opening of a railway bridge over a roadway is in the shape of a parabola. A surveyor measures the heights of the three points on the bridge, as shown in the figure. He wishes to find an equation of the form y=ax2+bx+c to model the shape of the arch. a Use the surveyed points to set up a system of linear equations for the unknown coefficients a, b and c. b Solve the system using Cramers Rule.arrow_forward
- Mathematical Modeling: A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. ( x and y are measured in feet.) (a) Use a system of equations to find the equation of the parabola y=ax2+bx+c that passes through the three points. Solve the system using matrices. (b) Use a graphing utility to graph the parabola. (c) Graphically approximate the maximum height of the ball and the point at which the ball struck the ground. (d) Analytically find the maximum height of the ball and the point at which the ball struck the ground. (e) Compare your results from parts (c) and (d).arrow_forwardSolving a system of equations Solve the system, or shoe that it has no solution. If the system has infinitely many solutions, express them in the ordered pair form given in Example 6. {0.2x0.2y=1.80.3x+0.5y=3.3}arrow_forwardNetwork Analysis Water is flowing through a network of pipes in thousands of cubic meters per hour, as shown in figure. a Solve this system for the water flow represented by xii=1,2,...,7. b Find the water flow when x1=x2=100. c Find the water flow when x6=x7=0. d Find the water flow when x5=1000 and x6=0.arrow_forward
- Network Analysis The figure shows the flow of traffic in vehicles per hour through a network of streets. a Solve this system for xi,i=1,2,...,5. b Find the traffic flow when x2=200 and x3=50. c Find the traffic flow when x2=150 and x3=0.arrow_forwardPlanting Crops A farmer is considering two plans of crop rotation on his 100-acre farm. Plan A: Plant tomatoes every season. Plan B: Alternate between soybeans and tomatoes each season. The revenue from tomatoes is $1600 an acre, and the revenue from soybeans is $1200 an acre. Tomatoes require fertilizing the land, which costs about $300 an acre. Soybeans do not require fertilizer; moreover, they add nitrogen to the soil so tomatoes can be planted the following season without fertilizing. (a) Find a formula for the profit if Plan A is used for n years. (b) Find a formula for the profit if Plan B is used for 2n years (starting with soybeans). (c) If the farmer intends to plant these crops for 10 years, which plan is more profitable?arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning