Problem 1: If xxx varies directly as yyy and x=35x = 35x=35 when y=7y = 7y=7, what is the value of yyy when x=25x = 25x=25?<\/h3>\n\n\n\n
Step 1:<\/strong> Since xxx varies directly as yyy, we can write the equation of variation as:x=kyx = kyx=ky<\/p>\n\n\n\n where kkk is the constant of proportionality.<\/p>\n\n\n\n Step 2:<\/strong> Use the given values x=35x = 35x=35 and y=7y = 7y=7 to find kkk.35=k\u00d7735 = k \\times 735=k\u00d77<\/p>\n\n\n\n Divide both sides by 7:k=357=5k = \\frac{35}{7} = 5k=735\u200b=5<\/p>\n\n\n\n Step 3:<\/strong> Now that we know k=5k = 5k=5, we can write the equation of variation as:x=5yx = 5yx=5y<\/p>\n\n\n\n Step 4:<\/strong> To find yyy when x=25x = 25x=25, substitute x=25x = 25x=25 into the equation:25=5y25 = 5y25=5y<\/p>\n\n\n\n Divide both sides by 5:y=255=5y = \\frac{25}{5} = 5y=525\u200b=5<\/p>\n\n\n\n Answer for Problem 1:<\/strong> The value of yyy is 5.<\/p>\n\n\n\n Step 1:<\/strong> Since yyy varies inversely as xxx, we can write the equation of variation as:y=kxy = \\frac{k}{x}y=xk\u200b<\/p>\n\n\n\n where kkk is the constant of proportionality.<\/p>\n\n\n\n Step 2:<\/strong> Use the given values y=3y = 3y=3 and x=4x = 4x=4 to find kkk.3=k43 = \\frac{k}{4}3=4k\u200b<\/p>\n\n\n\n Multiply both sides by 4:k=3\u00d74=12k = 3 \\times 4 = 12k=3\u00d74=12<\/p>\n\n\n\n Step 3:<\/strong> Now that we know k=12k = 12k=12, we can write the equation of variation as:y=12xy = \\frac{12}{x}y=x12\u200b<\/p>\n\n\n\n Step 4:<\/strong> To find yyy when x=6x = 6x=6, substitute x=6x = 6x=6 into the equation:y=126=2y = \\frac{12}{6} = 2y=612\u200b=2<\/p>\n\n\n\n Answer for Problem 2:<\/strong> The value of yyy is 2.<\/p>\n\n\n\n Step 1:<\/strong> Since zzz varies jointly as xxx and yyy, the equation of variation is:z=kxyz = kxyz=kxy<\/p>\n\n\n\n where kkk is the constant of proportionality.<\/p>\n\n\n\n Step 2:<\/strong> Use the given values z=3z = 3z=3, x=3x = 3x=3, and y=15y = 15y=15 to find kkk.3=k\u00d73\u00d7153 = k \\times 3 \\times 153=k\u00d73\u00d715<\/p>\n\n\n\n Simplify the right-hand side:3=k\u00d7453 = k \\times 453=k\u00d745<\/p>\n\n\n\n Now, divide both sides by 45:k=345=115k = \\frac{3}{45} = \\frac{1}{15}k=453\u200b=151\u200b<\/p>\n\n\n\n Step 3:<\/strong> Now that we know k=115k = \\frac{1}{15}k=151\u200b, the equation of variation becomes:z=115xyz = \\frac{1}{15}xyz=151\u200bxy<\/p>\n\n\n\n Step 4:<\/strong> To find zzz for any values of xxx and yyy, simply substitute the values of xxx and yyy into the equation. For example, if x=4x = 4x=4 and y=10y = 10y=10:z=115\u00d74\u00d710=4015=83z = \\frac{1}{15} \\times 4 \\times 10 = \\frac{40}{15} = \\frac{8}{3}z=151\u200b\u00d74\u00d710=1540\u200b=38\u200b<\/p>\n\n\n\n Answer for Problem 3:<\/strong> The equation of variation is z=115xyz = \\frac{1}{15}xyz=151\u200bxy, and for x=4x = 4x=4 and y=10y = 10y=10, z=83z = \\frac{8}{3}z=38\u200b.<\/p>\n\n\n\n TASK 3 Direction: Solve for the indicated variable in each of the following: Example: If x varies directly as y and x = 12 when y = 2, what is the value of y when x = 24? Solution: Since x varies directly as y, then the equation of variation is in the form x […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-257501","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257501","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=257501"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257501\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nProblem 2: If yyy varies inversely as xxx and y=3y = 3y=3 when x=4x = 4x=4, find yyy when x=6x = 6x=6.<\/h3>\n\n\n\n
\n\n\n\nProblem 3: zzz varies jointly as xxx and yyy. If z=3z = 3z=3 when x=3x = 3x=3 and y=15y = 15y=15, find the equation of variation and use it to find zzz for given values of xxx and yyy.<\/h3>\n\n\n\n
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