Electrical Network Applying Kirchhoff’s Laws to the electrical network in the figure, the currents
Find the currents.
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College Algebra
- 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_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_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_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_forwardThe Arch of a Bridge The opening of a railway bridge over a roadway is in the shape of a parabola. A surveyor measures the heights of 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. Use the surveyed points to set up a system of linear equations for the unknown coefficients a, b, and c. Solve the system using Cramer’s 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_forwardElimination method Use the elimination method to fins all solutions of the system of equations. {3x2y2=11x2+42=8}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
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