{"id":736,"date":"2025-12-04T10:03:18","date_gmt":"2025-12-04T09:03:18","guid":{"rendered":"http:\/\/mymatma.pl\/?p=736"},"modified":"2025-12-05T11:37:18","modified_gmt":"2025-12-05T10:37:18","slug":"zadanie-13","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=736","title":{"rendered":"Zadanie 13"},"content":{"rendered":"\n<p><strong>zadanie 15.2 \u2013 czerwiec 2023 (0 pkt lub 1 pkt)<\/strong><br>Liczby m(2,5) , m(4,5) , m(6,5) w podanej kolejno\u015bci tworz\u0105 ci\u0105g geometryczny. Oblicz iloraz tego ci\u0105gu. Zapisz obliczenia. Przyznaj sobie samodzielnie punkty, zgodnie z proponowan\u0105 punktacj\u0105 <strong>(0 pkt lub 1 pkt)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22a654d4c7\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22a654d4c7\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \nPrawid\u0142owa odpowied\u017a to q=\u221a(0,6)\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22a654d4d3\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22a654d4d3\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<div>\n  <h2>Wyja\u015bnienie<\/h2>\n  <p><strong>Krok 1. Obliczenie warto\u015bci m(2,5) oraz m(4,5)<\/strong><\/p>\n  <p>Do wyznaczenia ilorazu ci\u0105gu potrzebujemy znajomo\u015bci dw\u00f3ch wyraz\u00f3w ci\u0105gu. Obliczmy zatem warto\u015bci:<\/p>\n  <ul>\n    <li><code>m(2,5) = m\u2080 \u00b7 (0,6)^0,25\u00b72,5 = m\u2080 \u00b7 (0,6)^0,625<\/code><\/li>\n    <li><code>m(4,5) = m\u2080 \u00b7 (0,6)^0,25\u00b74,5 = m\u2080 \u00b7 (0,6)^1,125<\/code><\/li>\n  <\/ul>\n\n  <p><strong>Krok 2. Obliczenie ilorazu ci\u0105gu geometrycznego<\/strong><\/p>\n  <p>Znaj\u0105c dwa s\u0105siednie wyrazy ci\u0105gu geometrycznego, mo\u017cemy obliczy\u0107 iloraz:<\/p>\n  <p>\n    <code>q = m(4,5) \/ m(2,5)<\/code><br>\n    <code>q = (m\u2080 \u00b7 (0,6)^1,125) \/ (m\u2080 \u00b7 (0,6)^0,625)<\/code><br>\n    <code>q = (0,6)^1,125 \/ (0,6)^0,625<\/code><br>\n    <code>q = (0,6)^(1,125 \u2212 0,625)<\/code><br>\n    <code>q = (0,6)^0,5<\/code><br>\n    <code>q = \u221a0,6<\/code>\n  <\/p>\n\n  <p><strong>Iloraz ci\u0105gu geometrycznego: q = \u221a0,6<\/strong><\/p>\n<\/div>\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 15.2 \u2013 czerwiec 2023 (0 pkt lub 1 pkt)Liczby m(2,5) , m(4,5) , m(6,5) w podanej kolejno\u015bci tworz\u0105 ci\u0105g geometryczny. Oblicz iloraz tego ci\u0105gu. Zapisz obliczenia. Przyznaj sobie samodzielnie punkty, zgodnie z proponowan\u0105 punktacj\u0105 (0 pkt lub 1 pkt)<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"_uag_custom_page_level_css":"","_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31,56,49,81,83],"tags":[29,55,52],"class_list":["post-736","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-czerwiec-2023","category-iloraz-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-czerwiec-2023","tag-iloraz-ciagu"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"kubio-fullhd":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"adminmymatma","author_link":"https:\/\/mymatma.pl\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"zadanie 15.2 \u2013 czerwiec 2023 (0 pkt lub 1 pkt)Liczby m(2,5) , m(4,5) , m(6,5) w podanej kolejno\u015bci tworz\u0105 ci\u0105g geometryczny. Oblicz iloraz tego ci\u0105gu. Zapisz obliczenia. Przyznaj sobie samodzielnie punkty, zgodnie z proponowan\u0105 punktacj\u0105 (0 pkt lub 1 pkt)","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/736","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=736"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/736\/revisions"}],"predecessor-version":[{"id":737,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/736\/revisions\/737"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}