{"id":3182,"date":"2025-08-15T22:30:04","date_gmt":"2025-08-15T22:30:04","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3182"},"modified":"2025-09-18T19:01:41","modified_gmt":"2025-09-18T19:01:41","slug":"systems-of-nonlinear-equations-and-inequalities-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/systems-of-nonlinear-equations-and-inequalities-apply-it\/","title":{"raw":"Systems of Nonlinear Equations and Inequalities: Apply It","rendered":"Systems of Nonlinear Equations and Inequalities: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Solve a system of nonlinear equations.<\/li>\r\n \t<li>Graph a system of nonlinear inequalities.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p class=\"whitespace-normal break-words\">TechComm Solutions is designing a satellite communication network for a rural mountain region. They need to strategically place satellite dishes to ensure optimal coverage while working within terrain constraints and signal strength requirements. The engineering team must determine exact intersection points where coverage areas meet.<\/p>\r\n\r\n<h3 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">The Network Design Challenge<\/h3>\r\n<p class=\"whitespace-normal break-words\">The engineering team is working with two primary satellite dishes that will provide overlapping coverage:<\/p>\r\n\r\n<ul>\r\n \t<li class=\"whitespace-normal break-words\">Dish A: Creates a circular coverage area described by [latex]x^2 + y^2 = 25[\/latex] (radius of 5 km)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Dish B: Positioned to create coverage following [latex]y = x^2 - 4[\/latex] (parabolic pattern)<\/li>\r\n<\/ul>\r\n<p class=\"whitespace-normal break-words\">The team needs to find where these coverage areas intersect to place relay towers at the optimal connection points.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312324[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Solve a system of nonlinear equations.<\/li>\n<li>Graph a system of nonlinear inequalities.<\/li>\n<\/ul>\n<\/section>\n<p class=\"whitespace-normal break-words\">TechComm Solutions is designing a satellite communication network for a rural mountain region. They need to strategically place satellite dishes to ensure optimal coverage while working within terrain constraints and signal strength requirements. The engineering team must determine exact intersection points where coverage areas meet.<\/p>\n<h3 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">The Network Design Challenge<\/h3>\n<p class=\"whitespace-normal break-words\">The engineering team is working with two primary satellite dishes that will provide overlapping coverage:<\/p>\n<ul>\n<li class=\"whitespace-normal break-words\">Dish A: Creates a circular coverage area described by [latex]x^2 + y^2 = 25[\/latex] (radius of 5 km)<\/li>\n<li class=\"whitespace-normal break-words\">Dish B: Positioned to create coverage following [latex]y = x^2 - 4[\/latex] (parabolic pattern)<\/li>\n<\/ul>\n<p class=\"whitespace-normal break-words\">The team needs to find where these coverage areas intersect to place relay towers at the optimal connection points.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312324\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312324&theme=lumen&iframe_resize_id=ohm312324&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":67,"menu_order":25,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":131,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3182"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3182\/revisions"}],"predecessor-version":[{"id":4116,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3182\/revisions\/4116"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/131"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3182\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3182"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3182"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3182"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}