{"id":774,"date":"2026-05-05T05:04:14","date_gmt":"2026-05-05T05:04:14","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc\/"},"modified":"2026-05-05T07:39:07","modified_gmt":"2026-05-05T07:39:07","slug":"23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc\/","title":{"rendered":"23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c"},"content":{"rendered":"<p><strong>23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/strong> l\u00e0 tuy\u1ec3n t\u1eadp c\u00e1c b\u00e0i to\u00e1n t\u1ed1i \u01b0u th\u1ef1c ti\u1ec5n \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft b\u1eb1ng \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m. C\u00e1c b\u00e0i to\u00e1n \u0111a d\u1ea1ng, phong ph\u00fa, t\u1eeb y h\u1ecdc, k\u1ef9 thu\u1eadt, kinh t\u1ebf \u0111\u1ebfn v\u1eadt l\u00fd v\u00e0 h\u00f3a h\u1ecdc, gi\u00fap ng\u01b0\u1eddi h\u1ecdc th\u1ea5y r\u00f5 t\u1ea7m quan tr\u1ecdng v\u00e0 t\u00ednh \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m trong \u0111\u1eddi s\u1ed1ng. H\u00e3y c\u00f9ng <a href=\"https:\/\/tailieuonthi.edu.vn\/\" rel=\"noopener\" target=\"_blank\"><strong>T\u00e0i Li\u1ec7u \u00d4n Thi<\/strong><\/a> tham kh\u1ea3o t\u00e0i li\u1ec7u \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 t\u1ed1i \u01b0u trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/p>\n<h2><strong>N\u1ed9i dung 23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/strong><\/h2>\n<p>T\u00e0i li\u1ec7u<strong> 23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/strong> \u0111\u01b0\u1ee3c chia th\u00e0nh c\u00e1c ph\u1ea7n ch\u00ednh:<\/p>\n<ul>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 1:<\/strong> V\u1eadn d\u1ee5ng \u0111\u1ea1o h\u00e0m \u0111\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n t\u1ed1i \u01b0u th\u1ef1c ti\u1ec5n<\/li>\n<li><strong>Ch\u1ee7 \u0111\u1ec1 2: <\/strong>V\u1eadn d\u1ee5ng \u0111\u1ea1o h\u00e0m \u0111\u1ec3 gi\u1ea3i quy\u1ebft m\u1ed9t s\u1ed1 b\u00e0i to\u00e1n t\u1ed1i \u01b0u trong kinh t\u1ebf<\/li>\n<li><strong>B\u00e0i t\u1eadp:<\/strong> Bao g\u1ed3m 23 b\u00e0i t\u1eadp th\u1ef1c t\u1ebf \u0111i\u1ec3n h\u00ecnh, minh h\u1ecda c\u00e1c \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m trong nhi\u1ec1u l\u0129nh v\u1ef1c:<\/li>\n<\/ul>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp n\u1eb1m trong b\u1ed9 <a href=\"https:\/\/tailieuonthi.edu.vn\/lop-12\/toan-12\/\" rel=\"noopener\" target=\"_blank\"><strong>t\u00e0i li\u1ec7u to\u00e1n 12<\/strong><\/a> n\u00e0y:<\/p>\n<p><strong>C\u00e2u 1 [EMPIRE TEAM]:<\/strong> B\u1ea1n H\u00e0 c\u00f3 m\u1ed9t t\u1ea5m b\u00eca h\u00ecnh vu\u00f4ng c\u1ea1nh $60 \\text{ cm}$ (H\u00ecnh 1). B\u1ea1n mu\u1ed1n l\u00e0m m\u1ed9t c\u00e1i h\u1ed9p \u0111\u1ef1ng \u0111\u1ed3 c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt m\u00e0 c\u00f3 th\u1ec3 \u0111\u1ec3 \u0111\u01b0\u1ee3c v\u00e0o m\u1ed9t ng\u0103n gi\u00e1 s\u00e1ch c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh b\u1eb1ng $37 \\text{ cm}$, chi\u1ec1u cao b\u1eb1ng $28 \\text{ cm}$. B\u1ea1n c\u1eaft b\u1ed1n g\u00f3c c\u1ee7a t\u1ea5m b\u00eca \u0111\u00f3 b\u1ed1n h\u00ecnh vu\u00f4ng b\u1eb1ng nhau, m\u1ed7i h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh b\u1eb1ng $r$ (cm), r\u1ed3i g\u1ea5p l\u1ea1i th\u00e0nh m\u1ed9t c\u00e1i h\u1ed9p kh\u00f4ng n\u1eafp (H\u00ecnh 2). T\u00ecm s\u1ed1 nguy\u00ean d\u01b0\u01a1ng $r$ \u0111\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c c\u00e1i h\u1ed9p \u0111\u1ef1ng \u0111\u1ed3 c\u00f3 th\u1ec3 t\u00edch l\u1edbn nh\u1ea5t.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter size-full wp-image-4292\" decoding=\"async\" height=\"160\" sizes=\"auto, (max-width: 485px) 100vw, 485px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc-1.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc-1.jpg 485w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc-1-300x99.jpg 300w\" width=\"485\"\/><\/p>\n<p><strong>C\u00e2u 2 [EMPIRE TEAM]:<\/strong> H\u00ecnh v\u1ebd minh h\u1ecda m\u1ed9t m\u00e0n h\u00ecnh $BC$ c\u00f3 chi\u1ec1u cao $1,4 \\text{ m}$ \u0111\u01b0\u1ee3c \u0111\u1eb7t th\u1eb3ng \u0111\u1ee9ng v\u00e0 m\u00e9p d\u01b0\u1edbi c\u1ee7a m\u00e0n h\u00ecnh c\u00e1ch m\u1eb7t \u0111\u1ea5t m\u1ed9t kho\u1ea3ng $BA = 1,8 \\text{ m}$. M\u1ed9t chi\u1ebfc \u0111\u00e8n quan s\u00e1t m\u00e0n h\u00ecnh \u0111\u01b0\u1ee3c \u0111\u1eb7t \u1edf v\u1ecb tr\u00ed $O$ tr\u00ean m\u1eb7t \u0111\u1ea5t. H\u00e3y t\u00ednh kho\u1ea3ng c\u00e1ch $AO$ sao cho g\u00f3c quan s\u00e1t $\\widehat{BOC}$ l\u00e0 l\u1edbn nh\u1ea5t.<\/p>\n<p><img loading=\"lazy\" alt=\"\" class=\"aligncenter size-full wp-image-4293\" decoding=\"async\" height=\"167\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" src=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc-2.jpg\" srcset=\"https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc-2.jpg 346w, https:\/\/tailieuonthi.edu.vn\/wp-content\/uploads\/2025\/07\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc-2-300x145.jpg 300w\" width=\"346\"\/><\/p>\n<p><strong>C\u00e2u 3 [EMPIRE TEAM]:<\/strong> Khi nu\u00f4i c\u00e1 th\u00ed nghi\u1ec7m trong h\u1ed3, m\u1ed9t nh\u00e0 sinh v\u1eadt h\u1ecdc th\u1ea5y r\u1eb1ng: N\u1ebfu tr\u00ean m\u1ed7i \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t h\u1ed3 c\u00f3 $n$ con c\u00e1 th\u00ec trung b\u00ecnh m\u1ed7i con c\u00e1 sau m\u1ed9t v\u1ee5 thu ho\u1ea1ch c\u00e2n n\u1eb7ng: $P(n) = 480 \u2013 20n$ (gam). H\u1ecfi ph\u1ea3i th\u1ea3 bao nhi\u00eau c\u00e1 tr\u00ean m\u1ed9t \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t h\u1ed3 \u0111\u1ec3 sau m\u1ed9t v\u1ee5 thu ho\u1ea1ch \u0111\u01b0\u1ee3c nhi\u1ec1u c\u00e1 nh\u1ea5t?<\/p>\n<p><strong>C\u00e2u 4 [EMPIRE TEAM]:<\/strong> M\u1ed9t con c\u00e1 h\u1ed3i b\u01a1i ng\u01b0\u1ee3c d\u00f2ng \u0111\u1ec3 v\u01b0\u1ee3t m\u1ed9t kho\u1ea3ng c\u00e1ch l\u00e0 $300 \\text{ km}$. V\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $6 \\text{ km\/h}$. N\u1ebfu v\u1eadn t\u1ed1c b\u01a1i c\u1ee7a c\u00e1 khi n\u01b0\u1edbc \u0111\u1ee9ng y\u00ean l\u00e0 $v$ (km\/h) th\u00ec n\u0103ng l\u01b0\u1ee3ng ti\u00eau hao c\u1ee7a c\u00e1 trong $t$ gi\u1edd \u0111\u01b0\u1ee3c cho b\u1edfi c\u00f4ng th\u1ee9c: $E(v) = cv^3t$ trong \u0111\u00f3 $c$ l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1, $E$ \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng jun. T\u00ecm v\u1eadn t\u1ed1c b\u01a1i c\u1ee7a c\u00e1 khi n\u01b0\u1edbc \u0111\u1ee9ng y\u00ean \u0111\u1ec3 n\u0103ng l\u01b0\u1ee3ng ti\u00eau hao l\u00e0 \u00edt nh\u1ea5t.<\/p>\n<p><strong>C\u00e2u 5 [EMPIRE TEAM]:<\/strong> M\u1ed9t nh\u00e0 m\u00e1y s\u1ea3n xu\u1ea5t xe \u0111\u1ea1p cho th\u1ecb tr\u01b0\u1eddng ch\u00e2u \u00c2u theo \u0111\u01a1n gi\u00e1 $120 \\text{ euro}$. Chi ph\u00ed m\u1ed7i ng\u00e0y c\u1ee7a nh\u00e0 m\u00e1y \u0111\u01b0\u1ee3c cho b\u1edfi h\u00e0m s\u1ed1:<\/p>\n<p>$K(x) = 0,02x^3 \u2013 3x^2 + 172x + 2400$.<\/p>\n<p>trong \u0111\u00f3 $x$ l\u00e0 s\u1ed1 l\u01b0\u1ee3ng xe \u0111\u1ea1p s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c trong ng\u00e0y h\u00f4m \u0111\u00f3. M\u1ed7i ng\u00e0y c\u00f3 th\u1ec3 s\u1ea3n xu\u1ea5t t\u1ed1i \u0111a 130 xe \u0111\u1ea1p. Gi\u1ea3 s\u1eed s\u1ed1 xe \u0111\u1ea1p s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c trong m\u1ed7i ng\u00e0y \u0111\u1ec1u \u0111\u01b0\u1ee3c b\u00e1n h\u1ebft v\u00e0o cu\u1ed1i ng\u00e0y \u0111\u00f3. G\u1ecdi $G(x)$ l\u00e0 h\u00e0m s\u1ed1 bi\u1ec3u di\u1ec5n l\u1ee3i nhu\u1eadn h\u00e0ng ng\u00e0y c\u1ee7a nh\u00e0 m\u00e1y.<\/p>\n<p>1. V\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $G(x)$ tr\u00ean \u0111o\u1ea1n $[0; 140]$.<br \/>\n2. S\u1ed1 l\u01b0\u1ee3ng xe m\u1ed7i ng\u00e0y c\u1ea7n s\u1ea3n xu\u1ea5t l\u00e0 bao nhi\u00eau chi\u1ebfc \u0111\u1ec3 nh\u00e0 m\u00e1y c\u00f3 l\u00e3i?<br \/>\n3. S\u1ed1 l\u01b0\u1ee3ng xe m\u1ed7i ng\u00e0y c\u1ea7n s\u1ea3n xu\u1ea5t l\u00e0 bao nhi\u00eau chi\u1ebfc \u0111\u1ec3 nh\u00e0 m\u00e1y c\u00f3 l\u1ee3i nhu\u1eadn l\u1edbn nh\u1ea5t?<br \/>\n4. Gi\u1ea3 s\u1eed nh\u00e0 m\u00e1y quy\u1ebft \u0111\u1ecbnh t\u1eadn d\u1ee5ng t\u1ed1i \u0111a c\u00f4ng su\u1ea5t s\u1ea3n xu\u1ea5t 130 xe \u0111\u1ea1p m\u1ed7i ng\u00e0y. Nh\u00e0 m\u00e1y ph\u1ea3i ch\u1ecdn \u0111\u01a1n gi\u00e1 l\u00e0 bao nhi\u00eau \u0111\u1ec3 c\u00f3 l\u00e3i?<\/p>\n<h2><strong>T\u1ea3i 23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/strong><\/h2>\n<p>H\u00e3y t\u1ea3i ngay t\u00e0i li\u1ec7u <a href=\"https:\/\/tailieuonthi.edu.vn\/23-bai-toan-thuc-te-dien-hinh-thay-do-van-duc\/\" rel=\"noopener\" target=\"_blank\"><strong>23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/strong><\/a> \u0111\u1ec3 luy\u1ec7n t\u1eadp v\u00e0 n\u00e2ng cao kh\u1ea3 n\u0103ng \u1ee9ng d\u1ee5ng to\u00e1n h\u1ecdc c\u1ee7a b\u1ea1n!<\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/drive.google.com\/file\/d\/1NuN0hiOy0BqjPOxECF0Wvwfep2Kxqs6i\/view\" rel=\"nofollow noopener\" target=\"_blank\">T\u1ea3i 23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/a><\/p>\n<p><a class=\"custom-button\" href=\"https:\/\/www.facebook.com\/share\/v\/16j374Ytdd\/\" rel=\"nofollow noopener\" target=\"_blank\">Live ch\u1eefa 23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>23 b\u00e0i to\u00e1n Th\u1ef1c T\u1ebf \u0111i\u1ec3n h\u00ecnh Th\u1ea7y \u0110\u1ed7 V\u0103n \u0110\u1ee9c l\u00e0 tuy\u1ec3n t\u1eadp c\u00e1c b\u00e0i to\u00e1n t\u1ed1i \u01b0u th\u1ef1c ti\u1ec5n \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft b\u1eb1ng \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m. C\u00e1c b\u00e0i to\u00e1n \u0111a d\u1ea1ng, phong ph\u00fa, t\u1eeb y h\u1ecdc, k\u1ef9 thu\u1eadt, kinh t\u1ebf \u0111\u1ebfn v\u1eadt l\u00fd v\u00e0 h\u00f3a h\u1ecdc, gi\u00fap ng\u01b0\u1eddi h\u1ecdc th\u1ea5y r\u00f5 [&#8230;]\n","protected":false},"author":1,"featured_media":1972,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[52,34,10],"class_list":["post-774","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-toan-12","tag-empire-team","tag-thay-do-van-duc","tag-toan-12"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/774","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=774"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/774\/revisions"}],"predecessor-version":[{"id":1973,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/774\/revisions\/1973"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1972"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=774"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=774"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}