{"id":909,"date":"2025-12-05T13:22:10","date_gmt":"2025-12-05T12:22:10","guid":{"rendered":"https:\/\/mymatma.pl\/?p=909"},"modified":"2025-12-08T17:11:27","modified_gmt":"2025-12-08T16:11:27","slug":"zadanie-33","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=909","title":{"rendered":"Zadanie 33"},"content":{"rendered":"\n<p><strong>zadanie 18 \u2013 sierpie\u0144 2025 (1 pkt)<\/strong><\/p>\n\n\n\n<p>Trzywyrazowy ci\u0105g (\u221a5,1,x) jest arytmetyczny. Trzywyrazowy ci\u0105g (\u221a5,1,y) jest geometryczny. Liczby x oraz y spe\u0142niaj\u0105 warunki:<\/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=\"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\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\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\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\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_69e228101f2a7\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e228101f2a7\"\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 B.\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_69e228101f2b1\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e228101f2b1\"\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<!DOCTYPE html>\n<html lang=\"pl\">\n<head>\n    <meta charset=\"UTF-8\">\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n<\/head>\n<body>\n    <p>Dany jest trzywyrazowy ci\u0105g arytmetyczny (\u221a5, 1, x) i trzywyrazowy ci\u0105g geometryczny (\u221a5, 1, y).<\/p>\n\n    <p>Wybierz prawdziwe warunki dla x i y:<\/p>\n    <ul>\n        <li>a) x<0 i y<0<\/li>\n        <li>b) x<0 i y>0<\/li>\n        <li>c) x>0 i y<0<\/li>\n        <li>d) x>0 i y>0<\/li>\n    <\/ul>\n\n    <div>\n        <p>Krok 1: Wyznaczamy x z ci\u0105gu arytmetycznego:<\/p>\n        <p>x &#8211; 1 = 1 &#8211; \u221a5 \u2192 x = 2 &#8211; \u221a5<\/p>\n        <p>Obliczamy przybli\u017cenie: \u221a5 \u2248 2.236 \u2192 x \u2248 2 &#8211; 2.236 = -0.236 &lt; 0<\/p>\n\n        <p>Krok 2: Wyznaczamy y z ci\u0105gu geometrycznego:<\/p>\n        <p>(1)\u00b2 = \u221a5 \u22c5 y \u2192 y = 1 \/ \u221a5 \u2248 0.447 &gt; 0<\/p>\n\n        <p><strong>Wniosek:<\/strong> x &lt; 0 i y &gt; 0<\/p>\n        <p>Zatem poprawna odpowied\u017a to <strong>b)<\/strong><\/p>\n    <\/div>\n<\/body>\n<\/html>\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 18 \u2013 sierpie\u0144 2025 (1 pkt) Trzywyrazowy ci\u0105g (\u221a5,1,x) jest arytmetyczny. Trzywyrazowy ci\u0105g (\u221a5,1,y) jest geometryczny. Liczby x oraz y spe\u0142niaj\u0105 warunki:<\/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":[31,50,115,81,83],"tags":[29,51,112],"class_list":["post-909","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-sierpien-2025","category-trzy-kolejne-wyrazy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-sierpien-2025","tag-trzy-kolejne-wyrazy-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 18 \u2013 sierpie\u0144 2025 (1 pkt) Trzywyrazowy ci\u0105g (\u221a5,1,x) jest arytmetyczny. Trzywyrazowy ci\u0105g (\u221a5,1,y) jest geometryczny. Liczby x oraz y spe\u0142niaj\u0105 warunki:","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/909","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=909"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/909\/revisions"}],"predecessor-version":[{"id":927,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/909\/revisions\/927"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}