{"id":28200,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/if-x2y225-and-dydt6-how-do-you-find-dxdt-when-y4"},"modified":"2017-08-12T07:11:27","modified_gmt":"2017-08-12T07:11:27","slug":"if-x2y225-and-dydt6-how-do-you-find-dxdt-when-y4","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/if-x2y225-and-dydt6-how-do-you-find-dxdt-when-y4\/","title":{"rendered":"If ##x^2+y^2=25## and ##dy\/dt=6##, how do you find ##dx\/dt## when ##y=4## ?"},"content":{"rendered":"<p>There are two values depending on the point.<\/p>\n<p>##{dx}\/{dt}={(-8 &#8221; at &#8221; (3,4)),(8 &#8221; at &#8220;(-3,4)):}##<\/p>\n<p>Let us look at some details.<\/p>\n<p>First, let us find the values of ##x##.<\/p>\n<p>By plugging in ##y=4## into ##x^2+y^2=25##,<\/p>\n<p>##x^2+16=25 Rightarrow x^2=9 Rightarrow x=pm3##<\/p>\n<p>Now, let us find some derivatives. <\/p>\n<p>By differentiating with respect to ##t##,<\/p>\n<p>##d\/{dt}(x^2+y^2)=d\/{dt}(25) Rightarrow 2x{dx}\/{dt}+2y{dy}\/{dt}=0##<\/p>\n<p>by dividing by ##2x##,<\/p>\n<p>##Rightarrow {dx}\/{dx}+y\/x{dy}\/{dt}=0##<\/p>\n<p>by subtracting ##y\/x{dy}\/{dt}##,<\/p>\n<p>##Rightarrow {dx}\/{dt}=-y\/x{dy}\/{dt}##<\/p>\n<p>Since ##y=4##, ##x=pm3##, and ##{dy}\/{dt}=6##,<\/p>\n<p>##{dx}\/{dt}=-{4}\/{pm3}(6)=pm8##<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are two values depending on the point. ##{dx}\/{dt}={(-8 &#8221; at &#8221; (3,4)),(8 &#8221; at &#8220;(-3,4)):}## Let us look at some details. First, let us find the values of ##x##. By plugging in ##y=4## into ##x^2+y^2=25##, ##x^2+16=25 Rightarrow x^2=9 Rightarrow <a href=\"https:\/\/www.benedictsol.com\/blogs\/if-x2y225-and-dydt6-how-do-you-find-dxdt-when-y4\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-28200","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=28200"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28200\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=28200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=28200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=28200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}