According to the formula F = (9\/5)C + 32, if the temperature in degrees Fahrenheit (F) increases by 27, by how much does the temperature in degrees Celsius (C) increase?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine how much the temperature in degrees Celsius (C) increases when the temperature in degrees Fahrenheit (F) increases by 27, we can analyze the given formula:<\/p>\n\n\n\n [ This equation expresses Fahrenheit as a linear function of Celsius. Rearranging to express Celsius in terms of Fahrenheit:<\/p>\n\n\n\n [ The relationship between changes in Fahrenheit ((\\Delta F)) and Celsius ((\\Delta C)) can be determined by differentiating (F = \\left(\\frac{9}{5}\\right)C + 32) with respect to (C):<\/p>\n\n\n\n [ This indicates that a change of 1 degree Celsius corresponds to a change of ( \\frac{9}{5} ) degrees Fahrenheit. Thus, the change in Celsius for a given change in Fahrenheit is:<\/p>\n\n\n\n [ Given that (\\Delta F = 27), the corresponding change in Celsius is:<\/p>\n\n\n\n [ When the temperature in Fahrenheit increases by 27 degrees, the temperature in Celsius increases by 15 degrees<\/strong>.<\/p>\n\n\n\n The formula (F = \\left(\\frac{9}{5}\\right)C + 32) defines the conversion between Celsius and Fahrenheit scales. The (\\frac{9}{5}) factor shows that Fahrenheit changes faster than Celsius due to differing scale intervals. Specifically, a 1-degree change in Celsius corresponds to a (\\frac{9}{5})-degree change in Fahrenheit.<\/p>\n\n\n\n When considering an increase in Fahrenheit, the corresponding change in Celsius can be calculated by dividing the Fahrenheit change by (\\frac{9}{5}), which is equivalent to multiplying by (\\frac{5}{9}). This is because the scales are proportional but have different intervals.<\/p>\n\n\n\n In this problem, the increase of 27 degrees Fahrenheit is scaled back to Celsius using the factor (\\frac{5}{9}), resulting in an increase of 15 degrees Celsius. This proportional relationship demonstrates the difference in granularity between the two temperature scales and ensures precise conversions for any temperature change.<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" According to the formula F = (9\/5)C + 32, if the temperature in degrees Fahrenheit (F) increases by 27, by how much does the temperature in degrees Celsius (C) increase? The Correct Answer and Explanation is : To determine how much the temperature in degrees Celsius (C) increases when the temperature in degrees Fahrenheit (F) […]<\/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-183777","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183777","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=183777"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183777\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
F = \\left(\\frac{9}{5}\\right)C + 32
]<\/p>\n\n\n\n
C = \\frac{5}{9}(F – 32)
]<\/p>\n\n\n\nStep 1: Relationship Between Changes in F and C<\/h3>\n\n\n\n
\\frac{dF}{dC} = \\frac{9}{5}
]<\/p>\n\n\n\n
\\Delta C = \\frac{\\Delta F}{\\frac{9}{5}} = \\Delta F \\cdot \\frac{5}{9}
]<\/p>\n\n\n\nStep 2: Plugging in the Change in Fahrenheit<\/h3>\n\n\n\n
\\Delta C = 27 \\cdot \\frac{5}{9} = 15
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n