A six-foot-tall person is standing near a street lamp that is 11 ft tall, as shown in the figure. 6 ft 11 ft d Find a function that models the length L of the person's shadow in terms of the distance d from the person to the base of the lamp. L(d) = In these problems you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the Guidelines for Modeling with Functions to help you answer these questions. Consider the following problem: A farmer has 2,000 feet of fencing and wants to fence off a rectangular field that borders a straight river. The farmer does not need a fence along the river (see the figure). x A x i What are the dimensions of the field of largest area that can be fenced? (Let x be the width of the field in feet and / be the length of the field in feet.) (a) Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field (in feet). (Round your answers to the nearest hundred feet.) X = ft ft i What are the dimensions of the field of largest area that can be fenced? (Let x be the width of the field in feet and / be the length of the field in feet.) (a) Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field (in feet). (Round your answers to the nearest hundred feet.) X = = ft ft (b) Find a function that models the area of the field in terms of one of its sides. A(x) = (c) Use your model to solve the problem, and compare with your answer to part (a). (Enter your answers in feet). x = | = ft ft Need Help? Read It A graphing device is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the Guidelines for Modeling with Functions to help you. A rancher with 550 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure). (a) Find a function A that models the total area of the four pens. (Use w to represent the width of the field.) A(w) = (b) Find the largest possible total area (in ft) of the four pens. ft 7. [-/3 Points] DETAILS SPRECALC8 2.FOM.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A graphing device is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the Guidelines for Modeling with Functions to help you. An open box with a square base of length x is to have a volume of 20 ft. (a) Find a function that models the surface area A of the box in terms of the length of one side of the base x. A(x) = (b) Find the box dimensions (in ft) that minimize the amount of material used. (Round your answers to two decimal places.) side length height ft ft Need Help? Read It A graphing device is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the Guidelines for Modeling with Functions to help you. Find the dimensions that give the largest area for the rectangle shown in the figure. y = 10-x (x, y) 0 x Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola y = 10 - x. (Round your answers to two decimal places.) height width Need Help? Read It