{"id":1953,"date":"2016-11-02T22:49:24","date_gmt":"2016-11-02T22:49:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=1953"},"modified":"2017-04-04T19:27:51","modified_gmt":"2017-04-04T19:27:51","slug":"summary-variation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/summary-variation\/","title":{"raw":"Summary: Variation","rendered":"Summary: Variation"},"content":{"raw":"<section id=\"fs-id1165137898092\" class=\"key-equations\" data-depth=\"1\">\r\n<h1 data-type=\"title\">Key Equations<\/h1>\r\n<table id=\"eip-id1165133094986\" summary=\"..\">\r\n<tbody>\r\n<tr>\r\n<td data-valign=\"middle\" data-align=\"left\">Direct variation<\/td>\r\n<td>[latex]y=k{x}^{n},k\\text{ is a nonzero constant}\\\\[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-valign=\"middle\" data-align=\"left\">Inverse variation<\/td>\r\n<td>[latex]y=\\frac{k}{{x}^{n}},k\\text{ is a nonzero constant}\\\\[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><section id=\"fs-id1165137419773\" class=\"key-concepts\" data-depth=\"1\">\r\n<h1 data-type=\"title\">Key Concepts<\/h1>\r\n<ul id=\"fs-id1165137723142\">\r\n \t<li>A relationship where one quantity is a constant multiplied by another quantity is called direct variation.<\/li>\r\n \t<li>Two variables that are directly proportional to one another will have a constant ratio.<\/li>\r\n \t<li>A relationship where one quantity is a constant divided by another quantity is called inverse variation.<\/li>\r\n \t<li>Two variables that are inversely proportional to one another will have a constant multiple.<\/li>\r\n \t<li>In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.<\/li>\r\n<\/ul>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1165137735724\" class=\"definition\">\r\n \t<dt><strong>constant of variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137735729\">the non-zero value <em>k<\/em>\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137762202\" class=\"definition\">\r\n \t<dt><strong>direct variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137762208\">the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137462046\" class=\"definition\">\r\n \t<dt><strong>inverse variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137462052\">the relationship between two variables in which the product of the variables is a constant<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135501040\" class=\"definition\">\r\n \t<dt><strong>inversely proportional<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137874542\">a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137874546\" class=\"definition\">\r\n \t<dt><strong>joint variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135696715\">a relationship where a variable varies directly or inversely with multiple variables<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135696718\" class=\"definition\">\r\n \t<dt><strong>varies directly<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137432955\">a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137432958\" class=\"definition\">\r\n \t<dt><strong>varies inversely<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135439853\">a relationship where one quantity is a constant divided by the other quantity<\/dd>\r\n<\/dl>\r\n<\/section>","rendered":"<section id=\"fs-id1165137898092\" class=\"key-equations\" data-depth=\"1\">\n<h1 data-type=\"title\">Key Equations<\/h1>\n<table id=\"eip-id1165133094986\" summary=\"..\">\n<tbody>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Direct variation<\/td>\n<td>[latex]y=k{x}^{n},k\\text{ is a nonzero constant}\\\\[\/latex].<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Inverse variation<\/td>\n<td>[latex]y=\\frac{k}{{x}^{n}},k\\text{ is a nonzero constant}\\\\[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165137419773\" class=\"key-concepts\" data-depth=\"1\">\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1165137723142\">\n<li>A relationship where one quantity is a constant multiplied by another quantity is called direct variation.<\/li>\n<li>Two variables that are directly proportional to one another will have a constant ratio.<\/li>\n<li>A relationship where one quantity is a constant divided by another quantity is called inverse variation.<\/li>\n<li>Two variables that are inversely proportional to one another will have a constant multiple.<\/li>\n<li>In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137735724\" class=\"definition\">\n<dt><strong>constant of variation<\/strong><\/dt>\n<dd id=\"fs-id1165137735729\">the non-zero value <em>k<\/em>\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137762202\" class=\"definition\">\n<dt><strong>direct variation<\/strong><\/dt>\n<dd id=\"fs-id1165137762208\">the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137462046\" class=\"definition\">\n<dt><strong>inverse variation<\/strong><\/dt>\n<dd id=\"fs-id1165137462052\">the relationship between two variables in which the product of the variables is a constant<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135501040\" class=\"definition\">\n<dt><strong>inversely proportional<\/strong><\/dt>\n<dd id=\"fs-id1165137874542\">a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137874546\" class=\"definition\">\n<dt><strong>joint variation<\/strong><\/dt>\n<dd id=\"fs-id1165135696715\">a relationship where a variable varies directly or inversely with multiple variables<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135696718\" class=\"definition\">\n<dt><strong>varies directly<\/strong><\/dt>\n<dd id=\"fs-id1165137432955\">a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137432958\" class=\"definition\">\n<dt><strong>varies inversely<\/strong><\/dt>\n<dd id=\"fs-id1165135439853\">a relationship where one quantity is a constant divided by the other quantity<\/dd>\n<\/dl>\n<\/section>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1953\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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