Discov ' ' ery Actwtty 1: Keeping Bruin Out Suppose YOU Want to 1 Your ne' 3 p am a TeCtan ular- hitch thhggzgrs: crazly dog, 13min althoizhpgxiigiaibli garden' but you need to protect it from cure y You ha 5 ep In apen his owners ft erim Ve not seen ' 0 en forget to 1;ardere1tI-of Your garden With 18 meters oftxkhiriofg escape: yet,but plan on "10103ng the With dimensmns that will produce the maidrridrrf'aiiiztdrrrt Coaise Your goal is to build a area. a. Draw ' a picture of your garden labeling the length x and the width y. W I/Vzata'm Lg Uf) D'hgtrfiu use the formula for perime for the Perimeter P and then iso ven below. Substitute ter of a rectangle gi de of the equation. b. To develop an equation, late y on one si the 18 meters of fencing Perimeter = 2 - length + 2 width P = 23; + 2y ation by substituting the expression for y, found in part b, in the area 0. ' iven below. equauon g Area = length width A = x y d To better understand the rectangular dimensions that Will give maximum area, complete the followmg table with the aid of a graphing calculator. Hint: Enter the equations for width and area found in parts b and 0, into your calculator, and then build the table. {tama}; 'e. Describe any patterns you observe in the table from part d. M f. If the length and Width must be counting numbers, then what dimensions produce a maximum area for the garden and what is that area. Explain. ---------------------------.--------------------- Mf fix-- Mf g. Use the data in the table in part d to graph the area equation from part c. Be sure to label each axis and give the graph a title.h' Verify the dime ' with an area Of 2131an (length' x and Wldfl}, y) that are needed to build a rectangular garden quare meters, by substltutmg 20 for A in the equation obtained in part c. Solve this uadr . , inc" axz + gx + jicofquauon by faCtOrmg. Hmt: First put the equation in standard form, L Can you build a garden with an area greater than 20 square meters? Use the table feature of a gaphing calculator to complete the following table. If the length and Width can be any real numbers, then What dimensions produce a maximum area for the garden and what is that area. Explain. j. f-H-f "/ // If the length. Also, what type of h. Explain why the area of a rectangular garden is a function of function is this? '/'/--.--------------- /,--------------------- jr Mf"- @ WE} (Sm? W domain of the area function? at Wernemeficat range ofth'e area function