{"id":4782,"date":"2022-09-02T15:24:55","date_gmt":"2022-09-02T13:24:55","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-a-delka-obrazce-priklad-1\/"},"modified":"2022-09-02T15:24:55","modified_gmt":"2022-09-02T13:24:55","slug":"obsah-a-delka-obrazce-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-a-delka-obrazce-priklad-1\/","title":{"rendered":"Obsah a d\u00e9lka obrazce &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Obrazec je tvo\u0159en z 9 dla\u017edic situovan\u00fdch do tvaru p\u00edsmene &#8220;L&#8221;. Dla\u017edice jsou nat\u011bsno vedle sebe a zv\u011bt\u0161uj\u00ed se. Rozm\u011bry ka\u017ed\u00fdch 2 sousedn\u00edch dla\u017edic jsou v pom\u011bru 1:2. D\u00e9lka cel\u00e9ho obrazce z 9 dla\u017edic je ozna\u010dena jako <em><strong>d<\/strong><\/em>.&nbsp;<\/p>\n<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone  wp-image-4781\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/obrazec-300x156.png\" alt=\"\" width=\"527\" height=\"274\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/obrazec-300x156.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/obrazec-300x156.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/obrazec.png 586w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Ka\u017edou dla\u017edici m\u016f\u017eete rozd\u011blit na t\u0159i \u010dtverce o stejn\u00e9 velikosti. Prvn\u00ed dla\u017edice je nejmen\u0161\u00ed. Jej\u00ed obsah je <em><strong>3 mm\u00b2<\/strong><\/em> (ka\u017ed\u00fd \u010dtverec <em><strong>1 mm x 1 mm<\/strong><\/em>, tedy <em><strong>3 x 1 mm\u00b2<\/strong><\/em>).<br \/>&nbsp; <br \/><strong>V obrazci (z 9 dla\u017edic) ur\u010dete:<\/strong><br \/><strong>a) obsah plochy 5. nejmen\u0161\u00ed dla\u017edice (v mm \u010dtvere\u010dn\u00edch)<\/strong><br \/><strong>b) d\u00e9lku d cel\u00e9ho obrazce (v mm)<\/strong><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p><em>a) Obsah plochy 5. nejmen\u0161\u00ed dla\u017edice<\/em><\/p>\n<p>1) Ze zad\u00e1n\u00ed jsme schopni vy\u010d\u00edst obsah dla\u017edic<br \/>$$ob_{1} = 3$$<br \/>$$ob_{2} = 12$$<br \/>$$ob_{3}=48$$<br \/>jedn\u00e1 se o geometrickou posloupnost, kde q = 4<br \/>2) <strong>Nyn\u00ed m\u016f\u017eeme vypo\u010d\u00edtat obsah p\u00e1t\u00e9 dla\u017edice<\/strong><br \/>$$ob_{5}=ob_{1}\\cdot q^{4}$$<br \/>$$ob_{5}=3\\cdot 4^{4}$$<br \/>$$ob_{5}=768 cm^{2}$$<\/p>\n<p><em>b) D\u00e9lku d cel\u00e9ho obrazce<\/em><br \/>1) Nyn\u00ed se pod\u00edvejme na to, co v\u00edme o d\u00e9lce dla\u017edic<br \/>Prvn\u00ed dla\u017edice $$a_{1}&nbsp;= 2$$<br \/>Druh\u00e1 dla\u017edice $$a_{2} = 4$$<br \/>T\u0159et\u00ed dla\u017edice $$a_{3} = 8$$<br \/>(jedn\u00e1 se o geometrickou posloupnost, kde q = 2)<br \/>4) <strong>D\u00e9lka cel\u00e9ho obrazce slo\u017een\u00e9ho z dev\u00edti obrazc\u016f<\/strong><br \/>$$s_{n}=a_{1} \\frac{a^{n} &#8211; 1}{q &#8211; 1}$$<br \/>$$s_{9}=\\frac{2^{9} &#8211; 1}{2 &#8211; 1}$$<br \/>$$s_{9} = 1 022 mm$$<\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 6-8 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n<p><br data-mce-bogus=\"1\"><\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4782","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Obsah a d\u00e9lka obrazce - p\u0159\u00edklad 1 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-a-delka-obrazce-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Obsah a d\u00e9lka obrazce - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Obrazec je tvo\u0159en z 9 dla\u017edic situovan\u00fdch do tvaru p\u00edsmene &#8220;L&#8221;. Dla\u017edice jsou nat\u011bsno vedle sebe a zv\u011bt\u0161uj\u00ed se. Rozm\u011bry ka\u017ed\u00fdch 2 sousedn\u00edch dla\u017edic jsou v pom\u011bru 1:2. D\u00e9lka cel\u00e9ho obrazce z 9 dla\u017edic je ozna\u010dena jako d.&nbsp; Ka\u017edou dla\u017edici m\u016f\u017eete rozd\u011blit na t\u0159i \u010dtverce o stejn\u00e9 velikosti. Prvn\u00ed dla\u017edice je nejmen\u0161\u00ed. Jej\u00ed obsah ... 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