{"id":6866,"date":"2014-04-30T16:30:53","date_gmt":"2014-04-30T16:30:53","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6866"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-direct-inverse-joint-and-combined-variation","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-direct-inverse-joint-and-combined-variation\/","title":{"rendered":"Math Review of Direct, Inverse, Joint, and Combined Variation"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Equations that describe the relationship between two variables in a sentence express the variation between those variables.\u00a0 Examples of types of variation include direct, inverse, joint, and combined variation.<\/p>\n

What Is Direct Variation?<\/strong><\/p>\n

In direct variation, as one variable is multiplied by a constant and increases, another variable (the quotient) also increases.\u00a0 Suppose Jane works at McDonald\u2019s and is paid $9.35 per hour.\u00a0 Her total wages vary directly with the amount of hours she works.\u00a0 If she works 1 hour, her gross wages (before taxes) are $9.35, and if she works 2 hours her gross wages are $18.70.\u00a0 If she works 8 hours, her wages are $74.80.\u00a0 If the hours she works are plotted on the x axis against her wages on the y axis, the resulting line is a straight line showing direct variation.<\/p>\n

What Is Inverse Variation?<\/strong><\/p>\n

Inverse variation is a relationship between variables so that as one variable decreases the other variable increases.\u00a0 The equations expressing inverse variation take the form xy = k, where k is a constant, as well as y = k\/x..\u00a0 For example, the current c varies inversely with the resistance in ohms r.\u00a0 When the current is 40 amps, the resistance is 12 ohms.\u00a0 When the current is 24 amps, the resistance is 20 ohms.\u00a0 If the current is plotted on the x axis, and the resistance is plotted on the y axis, the graph is in 2 separate curves called a hyperbola.<\/p>\n

What Is Joint Variation?<\/strong><\/p>\n

Joint variation is a relationship between three variables, where one variable varies directly as the product of two or more variables.\u00a0 The relationship between distance, rate, and time in motion problems is a good example of joint variation.\u00a0 Suppose the rate is 60 miles per hour, and the time is 2 hours.\u00a0 The distance is 120 miles.\u00a0 Similarly, if the rate is 70 miles an hour and the time is 3 hours, the distance is 120 miles.<\/p>\n

What Is Combined Variation?<\/strong><\/p>\n

Joint variation is a more complex relationship between three variables, where one variable varies directly as one variable and inversely as another.\u00a0 The equations expressing combined variation take the form x = ky\/z.\u00a0 The force of attraction F of a body varies directly as its mass m times a constant k and inversely as the square of the distance d between the bodies.\u00a0 The equation is F = km\/d2<\/sup>, so if F equals 100 Newtons, m equals 8kg, and d equals 5 meters, then the equation is 100 = 8k\/25.\u00a0 Suppose the mass is 10 kg and the distance is 15 meters.\u00a0 Then F will equal 13 8\/9 Newtons.<\/p>\n

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Overview: Equations that describe the relationship between two variables in a sentence express the variation between those variables.\u00a0 Examples of types of variation include direct, inverse, joint, and combined variation. What Is Direct Variation? In direct variation, as one variable is multiplied by a constant and increases, another variable (the quotient) also increases.\u00a0 Suppose Jane […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2658,2655,2656,2657],"class_list":["post-6866","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-combined-variation","tag-direct-variation","tag-inverse-variation","tag-joint-variation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6866","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6866"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6866\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6866"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6866"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}