{"id":28204,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/the-altitude-of-a-triangle-is-increasing-at-a-rate-of-1-5-cmmin-while-the-area-of-the-triangle-is-increasing-at-a-rate-of-5-square-cmmin-at-what-rate-is-the-base-of-the-triangle-changing-when-the-a"},"modified":"2017-08-12T07:11:32","modified_gmt":"2017-08-12T07:11:32","slug":"the-altitude-of-a-triangle-is-increasing-at-a-rate-of-1-5-cmmin-while-the-area-of-the-triangle-is-increasing-at-a-rate-of-5-square-cmmin-at-what-rate-is-the-base-of-the-triangle-changing-when-the-a","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/the-altitude-of-a-triangle-is-increasing-at-a-rate-of-1-5-cmmin-while-the-area-of-the-triangle-is-increasing-at-a-rate-of-5-square-cmmin-at-what-rate-is-the-base-of-the-triangle-changing-when-the-a\/","title":{"rendered":"The altitude of a triangle is increasing at a rate of 1.5 cm\/min while the area of the triangle is increasing at a rate of 5 square cm\/min. At what rate is the base of the triangle changing when the altitude is 9 cm and the area is 81 square cm?"},"content":{"rendered":"

This is a related rates (of change) type problem.<\/p>\n

The variables of interest are ##a## = altitude ##A## = area and, since the area of a triangle is ##A=1\/2ba##, we need ##b## = base.<\/p>\n

The given rates of change are in units per minute, so the (invisible) independent variable is ##t## = time in minutes.<\/p>\n

We are given: ##(da)\/dt = 3\/2## cm\/min<\/p>\n

##(dA)\/dt = 5## cm##””^2##\/min<\/p>\n

And we are asked to find ##(db)\/dt## when ##a = 9## cm and ##A = 81##cm##””^2##<\/p>\n

##A=1\/2ba##, differentiating with respect to ##t##, we get:<\/p>\n

##d\/dt(A)=d\/dt(1\/2ba)##.<\/p>\n

We’ll need the on the right.<\/p>\n

##(dA)\/dt = 1\/2 (db)\/dt a + 1\/2b (da)\/dt##<\/p>\n

We were given every value except ##(db)\/dt## (which we are trying to find) and ##b##. Using the formula for area and the given values of ##a## and ##A##, we can see that ##b=18##cm.<\/p>\n

Substituting:<\/p>\n

##5= 1\/2 (db)\/dt (9)+1\/2(18)3\/2## <\/p>\n

Solve for ##(db)\/dt = -17\/9##cm\/min.<\/p>\n

The base is decreasing at ##17\/9## cm\/min.<\/p>\n","protected":false},"excerpt":{"rendered":"

This is a related rates (of change) type problem. The variables of interest are ##a## = altitude ##A## = area and, since the area of a triangle is ##A=1\/2ba##, we need ##b## = base. The given rates of change are Read More …<\/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-28204","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28204","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=28204"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28204\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=28204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=28204"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=28204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}