{"id":1229,"date":"2025-09-07T17:51:19","date_gmt":"2025-09-07T10:51:19","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=1229"},"modified":"2025-09-11T03:24:12","modified_gmt":"2025-09-10T20:24:12","slug":"problem-solving-open-box","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/problem-solving-open-box\/","title":{"rendered":"Problem Solving: The Open Box Problem"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/pemecahan-masalah-kotak-terbuka\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">How can you make the largest possible open box from a flat rectangular card? In this problem, squares of equal size are cut from each corner, and the sides are folded up to form a box without a lid. By changing the size of the squares, the box&#8217;s volume changes too. Explore the card, the box, and the graph to see how the dimensions are connected and to figure out which box gives the maximum volume.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull has-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<h3 class=\"has-text-align-center\">Open Box Problem<\/h3>\n\n\n\n<p>Drag the black point on the card to change the value of <em>x<\/em> and see how the box changes. Can you find the size that makes the box the biggest?<\/p>\n\n\n\n<div class=\"wp-block-columns alignfull\">\n<div class=\"wp-block-column\">\n<div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 380px; height: 380px;\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 380px; height: 380px;\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<div id=\"calculator3\" class=\"aligncenter size-full\" style=\"width: 380px; height: 380px;\"><\/div>\n\n<script>\n  var calculator1 = Desmos.GraphingCalculator(document.getElementById('calculator1'), {\n    expressions: false,\n    settingsMenu: false,\n\ttrace: false\n  });\n  var calculator2 = Desmos.Calculator3D(document.getElementById('calculator2'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator3 = Desmos.GraphingCalculator(document.getElementById('calculator3'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n\n  var state1 = {\n    \"version\": 11,\n    \"randomSeed\": \"187168d2547d55092576325e6f16459d\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -15,\n            \"ymin\": -15,\n            \"xmax\": 15,\n            \"ymax\": 15\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"xAxisStep\": 2,\n        \"yAxisStep\": 2,\n        \"xAxisNumbers\": false,\n        \"yAxisNumbers\": false,\n        \"polarNumbers\": false,\n\t\t\"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-15\",\n            \"xmax\": \"15\",\n            \"ymin\": \"-15\",\n            \"ymax\": \"15\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Ukuran\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x_{0}=2\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"8\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"7\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"p_{0}=24\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"30\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"8\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"l_{0}=16\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"30\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"5\",\n                \"title\": \"Titik-titik penting\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"6\",\n                \"folderId\": \"5\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"A_{1}=\\\\left(\\\\frac{1}{2}p_{0},\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`A_1`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"12\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"B_{1}=\\\\left(\\\\frac{1}{2}p_{0}-x_{0},\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`B_1`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"16\",\n                \"folderId\": \"5\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"C_{1}=\\\\left(\\\\frac{1}{2}p_{0},\\\\frac{1}{2}l_{0}-x_{0}\\\\right)\",\n                \"label\": \"`C_1`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"5\",\n                \"color\": \"#388c46\",\n                \"latex\": \"D_{1}=\\\\left(\\\\frac{1}{2}p_{0}-x_{0},\\\\frac{1}{2}l_{0}-x_{0}\\\\right)\",\n                \"label\": \"`D_1`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"9\",\n                \"folderId\": \"5\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"A_{2}=\\\\left(-\\\\frac{1}{2}p_{0},\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`A_2`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"13\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"B_{2}=\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`B_2`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"17\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{2}=\\\\left(-\\\\frac{1}{2}p_{0},\\\\frac{1}{2}l_{0}-x_{0}\\\\right)\",\n                \"label\": \"`C_2`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"21\",\n                \"folderId\": \"5\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"D_{2}=\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},\\\\frac{1}{2}l_{0}-x_{0}\\\\right)\",\n                \"label\": \"`D_2`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"10\",\n                \"folderId\": \"5\",\n                \"color\": \"#388c46\",\n                \"latex\": \"A_{3}=\\\\left(-\\\\frac{1}{2}p_{0},-\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`A_3`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"5\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"B_{3}=\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},-\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`B_3`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"18\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"C_{3}=\\\\left(-\\\\frac{1}{2}p_{0},-\\\\frac{1}{2}l_{0}+x_{0}\\\\right)\",\n                \"label\": \"`C_3`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"22\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"D_{3}=\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},-\\\\frac{1}{2}l_{0}+x_{0}\\\\right)\",\n                \"label\": \"`D_3`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"5\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"A_{4}=\\\\left(\\\\frac{1}{2}p_{0},-\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`A_4`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"15\",\n                \"folderId\": \"5\",\n                \"color\": \"#388c46\",\n                \"latex\": \"B_{4}=\\\\left(\\\\frac{1}{2}p_{0}-x_{0},-\\\\frac{1}{2}l_{0}\\\\right)\",\n                \"label\": \"`B_4`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"19\",\n                \"folderId\": \"5\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"C_{4}=\\\\left(\\\\frac{1}{2}p_{0},-\\\\frac{1}{2}l_{0}+x_{0}\\\\right)\",\n                \"label\": \"`C_4`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"23\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"D_{4}=\\\\left(\\\\frac{1}{2}p_{0}-x_{0},-\\\\frac{1}{2}l_{0}+x_{0}\\\\right)\",\n                \"label\": \"`D_4`\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"25\",\n                \"title\": \"Jaring-jaring balok\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"32\",\n                \"folderId\": \"25\",\n                \"text\": \"Dasar:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"26\",\n                \"folderId\": \"25\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{1},D_{2},D_{3},D_{4}\\\\right)\",\n                \"lines\": false,\n                \"fillOpacity\": \".6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"44\",\n                \"folderId\": \"25\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{1},D_{2},D_{3},D_{4}\\\\right)\",\n                \"fill\": false,\n                \"lines\": true,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \".6\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"34\",\n                \"folderId\": \"25\",\n                \"text\": \"Atas:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"27\",\n                \"folderId\": \"25\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{1},B_{1},B_{2},D_{2}\\\\right)\",\n                \"lines\": false\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"45\",\n                \"folderId\": \"25\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{1},B_{1},B_{2},D_{2}\\\\right)\",\n                \"fill\": false,\n                \"lines\": true,\n                \"colorLatex\": \"w_{putih}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"36\",\n                \"folderId\": \"25\",\n                \"text\": \"Kiri:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"28\",\n                \"folderId\": \"25\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{2},C_{2},C_{3},D_{3}\\\\right)\",\n                \"lines\": false\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"46\",\n                \"folderId\": \"25\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{2},C_{2},C_{3},D_{3}\\\\right)\",\n                \"fill\": false,\n                \"lines\": true,\n                \"colorLatex\": \"w_{putih}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"38\",\n                \"folderId\": \"25\",\n                \"text\": \"Bawah:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"29\",\n                \"folderId\": \"25\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{4},D_{3},B_{3},B_{4}\\\\right)\",\n                \"lines\": false\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"47\",\n                \"folderId\": \"25\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{4},D_{3},B_{3},B_{4}\\\\right)\",\n                \"fill\": false,\n                \"lines\": true,\n                \"colorLatex\": \"w_{putih}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"40\",\n                \"folderId\": \"25\",\n                \"text\": \"Kanan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"30\",\n                \"folderId\": \"25\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{4},C_{4},C_{1},D_{1}\\\\right)\",\n                \"lines\": false\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"48\",\n                \"folderId\": \"25\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(D_{4},C_{4},C_{1},D_{1}\\\\right)\",\n                \"fill\": false,\n                \"lines\": true,\n                \"colorLatex\": \"w_{putih}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"53\",\n                \"folderId\": \"25\",\n                \"text\": \"Bingkai\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"25\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(A_{1},A_{2},A_{3},A_{4}\\\\right)\",\n                \"fill\": false,\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"72\",\n                \"title\": \"Ukuran\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"74\",\n                \"folderId\": \"72\",\n                \"text\": \"Panjang:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"80\",\n                \"folderId\": \"72\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,-\\\\frac{1}{2}l_{0}\\\\left\\\\{K=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`p=${p_{0}}`\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"84\",\n                \"folderId\": \"72\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,-\\\\frac{1}{2}l_{0}\\\\left\\\\{K=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": 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\"type\": \"expression\",\n                \"id\": \"85\",\n                \"folderId\": \"72\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-\\\\frac{1}{2}p_{0},0\\\\left\\\\{K=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`l`\",\n                \"hidden\": true,\n                \"labelOrientation\": \"above\",\n                \"labelSize\": \".9\",\n                \"labelAngle\": \"\\\\frac{\\\\pi}{2}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"78\",\n                \"folderId\": \"72\",\n                \"text\": \"Potongan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"82\",\n                \"folderId\": \"72\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t,\\\\frac{1}{2}l_{0}+.5\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}\",\n                    \"max\": \"-\\\\frac{1}{2}p_{0}+x_{0}\"\n                },\n                \"lineWidth\": \"1.5\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}\",\n                    \"max\": \"-\\\\frac{1}{2}p_{0}+x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"83\",\n                \"folderId\": \"72\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{-\\\\frac{1}{2}p_{0}-\\\\frac{1}{2}p_{0}+x_{0}}{2},\\\\frac{1}{2}l_{0}+.5\\\\left\\\\{K=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`x=${x_{0}}`\",\n                \"hidden\": true,\n                \"labelOrientation\": \"above\",\n                \"labelSize\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"86\",\n                \"folderId\": \"72\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{-\\\\frac{1}{2}p_{0}-\\\\frac{1}{2}p_{0}+x_{0}}{2},\\\\frac{1}{2}l_{0}+.5\\\\left\\\\{K=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`x`\",\n                \"hidden\": true,\n                \"labelOrientation\": \"above\",\n                \"labelSize\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"50\",\n                \"title\": \"Dragger\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"51\",\n                \"folderId\": \"50\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},\\\\frac{1}{2}l_{0}-x_{0}\\\\right)\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"56\",\n                \"title\": \"Tombol\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"67\",\n                \"folderId\": \"56\",\n                \"text\": \"Kontrol:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"68\",\n                \"folderId\": \"56\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"K=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"65\",\n                \"folderId\": \"56\",\n                \"text\": \"Ukuran tombol:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"57\",\n                \"folderId\": \"56\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"T_{1}=\\\\left(14.5,14.5\\\\right)\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"58\",\n                \"folderId\": \"56\",\n                \"color\": \"#388c46\",\n                \"latex\": \"p_{t}=12\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"59\",\n                \"folderId\": \"56\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"l_{t}=2.5\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"61\",\n                \"folderId\": \"56\",\n                \"text\": \"Tampilkan\/sembunyikan ukuran\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"56\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(T_{1},\\\\left(T_{1}.x-p_{t},T_{1}.y\\\\right),\\\\left(T_{1}.x-p_{t},T_{1}.y-l_{t}\\\\right),\\\\left(T_{1}.x,T_{1}.y-l_{t}\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"63\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(T_{1},\\\\left(T_{1}.x-p_{t},T_{1}.y\\\\right),\\\\left(T_{1}.x-p_{t},T_{1}.y-l_{t}\\\\right),\\\\left(T_{1}.x,T_{1}.y-l_{t}\\\\right)\\\\right)\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"K\\\\to1-K\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"69\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{T_{1}.x-p_{t}+T_{1}.x}{2},\\\\frac{T_{1}.y-l_{t}+T_{1}.y}{2}\\\\left\\\\{K=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Show size\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"70\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{T_{1}.x-p_{t}+T_{1}.x}{2},\\\\frac{T_{1}.y-l_{t}+T_{1}.y}{2}\\\\left\\\\{K=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Hide size\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"42\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"43\",\n                \"folderId\": \"42\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  var state2 = {\n    \"version\": 11,\n    \"randomSeed\": \"35819a4c3f523aeb4a466929e243ef4a\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -13,\n            \"ymin\": -13,\n            \"zmin\": -5,\n            \"xmax\": 13,\n            \"ymax\": 13,\n            \"zmax\": 21\n        },\n        \"userLockedViewport\": true,\n        \"threeDMode\": true,\n        \"worldRotation3D\": [\n            -0.5132799671593365,\n            -0.8314696123025455,\n            -0.21260752369181402,\n            0.7681777567114165,\n            -0.555570233019602,\n            0.3181896451432086,\n            -0.3826834323650898,\n            0,\n            0.9238795325112867\n        ],\n        \"showAxis3D\": false,\n        \"product\": \"graphing-3d\",\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-13\",\n            \"xmax\": \"13\",\n            \"ymin\": \"-13\",\n            \"ymax\": \"13\",\n            \"zmin\": \"-5\",\n            \"zmax\": \"21\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Diketahui\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"p_{0}=24\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"4\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"l_{0}=16\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"5\",\n                \"folderId\": \"2\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x_{0}=2\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"8\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"8\",\n                \"title\": \"Balok\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"46\",\n                \"folderId\": \"8\",\n                \"text\": \"Dasar:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"44\",\n                \"folderId\": \"8\",\n                \"color\": \"#aaaaaa\",\n                \"latex\": \"z=0\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"11\",\n                \"folderId\": \"8\",\n                \"text\": \"Bawah:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"9\",\n                \"folderId\": \"8\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"z=0\\\\left\\\\{-\\\\frac{1}{2}p_{0}+x_{0}\\\\le x\\\\le\\\\frac{1}{2}p_{0}-x_{0}\\\\right\\\\}\\\\left\\\\{-\\\\frac{1}{2}l_{0}+x_{0}\\\\le y\\\\le\\\\frac{1}{2}l_{0}-x_{0}\\\\right\\\\}\",\n                \"lines\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"27\",\n                \"folderId\": \"8\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},t,0\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"31\",\n                \"folderId\": \"8\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(\\\\frac{1}{2}p_{0}-x_{0},t,0\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"32\",\n                \"folderId\": \"8\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(t,\\\\frac{1}{2}l_{0}-x_{0},0\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"33\",\n                \"folderId\": \"8\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(t,-\\\\frac{1}{2}l_{0}+x_{0},0\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"13\",\n                \"folderId\": \"8\",\n                \"text\": \"Belakang:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"8\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"y=\\\\frac{1}{2}l_{0}-x_{0}\\\\left\\\\{-\\\\frac{1}{2}p_{0}+x_{0}\\\\le x\\\\le\\\\frac{1}{2}p_{0}-x_{0}\\\\right\\\\}\\\\left\\\\{0\\\\le z\\\\le x_{0}\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"16\",\n                \"folderId\": \"8\",\n                \"text\": \"Kiri:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"17\",\n                \"folderId\": \"8\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x=-\\\\frac{1}{2}p_{0}+x_{0}\\\\left\\\\{-\\\\frac{1}{2}l_{0}+x_{0}\\\\le y\\\\le\\\\frac{1}{2}l_{0}-x_{0}\\\\right\\\\}\\\\left\\\\{0\\\\le z\\\\le x_{0}\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"39\",\n                \"folderId\": \"8\",\n                \"text\": \"Garis vertikal:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"40\",\n                \"folderId\": \"8\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},-\\\\frac{1}{2}l_{0}+x_{0},t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"41\",\n                \"folderId\": \"8\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(\\\\frac{1}{2}p_{0}-x_{0},-\\\\frac{1}{2}l_{0}+x_{0},t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"42\",\n                \"folderId\": \"8\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(\\\\frac{1}{2}p_{0}-x_{0},\\\\frac{1}{2}l_{0}-x_{0},t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"43\",\n                \"folderId\": \"8\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},\\\\frac{1}{2}l_{0}-x_{0},t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"19\",\n                \"folderId\": \"8\",\n                \"text\": \"Kanan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"8\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x=\\\\frac{1}{2}p_{0}-x_{0}\\\\left\\\\{-\\\\frac{1}{2}l_{0}+x_{0}\\\\le y\\\\le\\\\frac{1}{2}l_{0}-x_{0}\\\\right\\\\}\\\\left\\\\{0\\\\le z\\\\le x_{0}\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"23\",\n                \"folderId\": \"8\",\n                \"text\": \"Depan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"24\",\n                \"folderId\": \"8\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"y=-\\\\frac{1}{2}l_{0}+x_{0}\\\\left\\\\{-\\\\frac{1}{2}p_{0}+x_{0}\\\\le x\\\\le\\\\frac{1}{2}p_{0}-x_{0}\\\\right\\\\}\\\\left\\\\{0\\\\le z\\\\le x_{0}\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"26\",\n                \"title\": \"Bingkai\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"34\",\n                \"folderId\": \"26\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(-\\\\frac{1}{2}p_{0}+x_{0},t,x_{0}\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"35\",\n                \"folderId\": \"26\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(\\\\frac{1}{2}p_{0}-x_{0},t,x_{0}\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}l_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}l_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"37\",\n                \"folderId\": \"26\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(t,\\\\frac{1}{2}l_{0}-x_{0},x_{0}\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"36\",\n                \"folderId\": \"26\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(t,-\\\\frac{1}{2}l_{0}+x_{0},x_{0}\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \".8\",\n                \"domain\": {\n                    \"min\": \"-\\\\frac{1}{2}p_{0}+x_{0}\",\n                    \"max\": \"\\\\frac{1}{2}p_{0}-x_{0}\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"29\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"30\",\n                \"folderId\": \"29\",\n                \"color\": \"#c74440\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrate3dLineWidthZero\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n  \n  var state3 = {\n    \"version\": 11,\n    \"randomSeed\": \"1b26a1475da3e9d9280c0a7b80ac80bf\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -2,\n            \"ymin\": -100,\n            \"xmax\": 10,\n            \"ymax\": 700\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"xAxisStep\": 1,\n        \"yAxisStep\": 50,\n        \"xAxisNumbers\": false,\n        \"yAxisNumbers\": false,\n        \"polarNumbers\": false,\n        \"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-2\",\n            \"xmax\": \"10\",\n            \"ymin\": \"-100\",\n            \"ymax\": \"700\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Diketahui\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"p_{0}=24\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"4\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"l_{0}=16\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x_{0}=6\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"\\\\frac{1}{2}\\\\min\\\\left(p_{0},l_{0}\\\\right)\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"69\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"K=1\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"6\",\n                \"title\": \"Model\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"7\",\n                \"folderId\": \"6\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"V\\\\left(x\\\\right)=\\\\left(p_{0}-2x\\\\right)\\\\left(l_{0}-2x\\\\right)x\\\\left\\\\{0\\\\le x\\\\le\\\\frac{1}{2}\\\\min\\\\left(p_{0},l_{0}\\\\right)\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"56\",\n                \"title\": \"Bidang koordinat\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"57\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t,0\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"0\",\n                    \"max\": \"15\"\n                },\n                \"lineWidth\": \"1.5\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"15\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"58\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"1000\"\n                },\n                \"lineWidth\": \"1.5\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"1000\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"60\",\n                \"folderId\": \"56\",\n                \"text\": \"Tik x:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"61\",\n                \"folderId\": \"56\",\n                \"color\": \"#388c46\",\n                \"latex\": \"t_{ikX}=\\\\left[0,2.5,5,7.5\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{ikX},t\\\\right)\\\\left\\\\{K=1\\\\right\\\\}\",\n                \"parametricDomain\": {\n                    \"min\": \"-10\",\n                    \"max\": \"0\"\n                },\n                \"lineWidth\": \"1\",\n                \"domain\": {\n                    \"min\": \"-10\",\n                    \"max\": \"0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"63\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{ikX},-5\\\\left\\\\{K=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${t_{ikX}}\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"65\",\n                \"folderId\": \"56\",\n                \"text\": \"Tik y:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"56\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"t_{ikY}=\\\\left[200,400,600\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"67\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t,t_{ikY}\\\\right)\\\\left\\\\{K=1\\\\right\\\\}\",\n                \"parametricDomain\": {\n                    \"min\": \"-.1\",\n                    \"max\": \"0\"\n                },\n                \"lineWidth\": \"1\",\n                \"domain\": {\n                    \"min\": \"-.1\",\n                    \"max\": \"0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"68\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-.05,t_{ikY}\\\\left\\\\{K=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${t_{ikY}}\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"71\",\n                \"folderId\": \"56\",\n                \"text\": \"Titik asal:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"72\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-.1,-5\\\\right)\\\\left\\\\{K=0\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"0\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below_left\",\n                \"labelSize\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"74\",\n                \"folderId\": \"56\",\n                \"text\": \"Judul sumbu:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"75\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(9.75,-50\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`x`\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"76\",\n                \"folderId\": \"56\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-1.25,675\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Volume\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelAngle\": \"\\\\frac{\\\\pi}{2}\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"9\",\n                \"title\": \"Bantuan koordinat\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"15\",\n                \"folderId\": \"9\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t,V\\\\left(x_{0}\\\\right)\\\\right)\",\n                \"lineStyle\": \"DASHED\",\n                \"parametricDomain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                },\n                \"lineWidth\": \"1\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"16\",\n                \"folderId\": \"9\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(x_{0},t\\\\right)\",\n                \"lineStyle\": \"DASHED\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"V\\\\left(x_{0}\\\\right)\"\n                },\n                \"lineWidth\": \"1\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"V\\\\left(x_{0}\\\\right)\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"14\",\n                \"folderId\": \"9\",\n                \"text\": \"Ruas-ruas garis pada sumbu:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"10\",\n                \"folderId\": \"9\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(t,0\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                },\n                \"lineOpacity\": \".6\",\n                \"lineWidth\": \"5\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"x_{0}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"12\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(0,t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"V\\\\left(x_{0}\\\\right)\"\n                },\n                \"lineOpacity\": \".6\",\n                \"lineWidth\": \"5\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"V\\\\left(x_{0}\\\\right)\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"21\",\n                \"title\": \"Jejak-jejak titik\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"22\",\n                \"folderId\": \"21\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"h_{apus}=A_{daftar}\\\\to\\\\left[\\\\left(0,0\\\\right)\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"23\",\n                \"folderId\": \"21\",\n                \"color\": \"#c74440\",\n                \"latex\": \"A_{daftar}=\\\\left[\\\\left(0,0\\\\right)\\\\right]\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"24\",\n                \"folderId\": \"21\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"i_{nList}\\\\left(L_{ist},P\\\\right)=\\\\left\\\\{\\\\operatorname{total}\\\\left(\\\\sum_{n=\\\\left[1...\\\\operatorname{length}\\\\left(L_{ist}\\\\right)\\\\right]}^{\\\\left[1...\\\\operatorname{length}\\\\left(L_{ist}\\\\right)\\\\right]}\\\\left\\\\{P.x=L_{ist}\\\\left[n\\\\right].x:\\\\left\\\\{P.y=L_{ist}\\\\left[n\\\\right].y:1,0\\\\right\\\\},0\\\\right\\\\}\\\\right)\\\\ge1:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"21\",\n                \"color\": \"#388c46\",\n                \"latex\": \"t_{ambah}=\\\\left\\\\{i_{nList}\\\\left(A_{daftar},A\\\\right)=0:A_{daftar}\\\\to\\\\operatorname{join}\\\\left(A_{daftar},A\\\\right)\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"26\",\n                \"folderId\": \"21\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"A_{tampil}=A_{daftar}\\\\left[2...\\\\operatorname{length}\\\\left(A_{daftar}\\\\right)\\\\right]\\\\left\\\\{\\\\operatorname{length}\\\\left(A_{daftar}\\\\right)>1\\\\right\\\\}\",\n                \"pointOpacity\": \".9\",\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"21\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{A}=\\\\operatorname{length}\\\\left(A_{daftar}.x\\\\right)\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"18\",\n                \"title\": \"Titik\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"19\",\n                \"folderId\": \"18\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"A=\\\\left(x_{0},V\\\\left(x_{0}\\\\right)\\\\right)\",\n                \"dragMode\": \"NONE\",\n                \"pointOutline\": true,\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"28\",\n                \"title\": \"Tombol\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"30\",\n                \"folderId\": \"28\",\n                \"text\": \"Kontrol:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"31\",\n                \"folderId\": \"28\",\n                \"color\": \"#388c46\",\n                \"latex\": \"r_{ekam}=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"36\",\n                \"folderId\": \"28\",\n                \"text\": \"Margin tombol:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"37\",\n                \"folderId\": \"28\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"m_{x}=0.25\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"39\",\n                \"folderId\": \"28\",\n                \"color\": \"#c74440\",\n                \"latex\": \"m_{y}=12.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"38\",\n                \"folderId\": \"28\",\n                \"color\": \"#000000\",\n                \"latex\": \"T_{1}=\\\\left(10-m_{x},700-m_{y}\\\\right)\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"33\",\n                \"folderId\": \"28\",\n                \"text\": \"Rekam jejak\/berhenti rekam\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"40\",\n                \"folderId\": \"28\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"p_{1}=3.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"41\",\n                \"folderId\": \"28\",\n                \"color\": \"#388c46\",\n                \"latex\": \"l_{1}=62.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"34\",\n                \"folderId\": \"28\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(T_{1},\\\\left(T_{1}.x-p_{1},T_{1}.y\\\\right),\\\\left(T_{1}.x-p_{1},T_{1}.y-l_{1}\\\\right),\\\\left(T_{1}.x,T_{1}.y-l_{1}\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"45\",\n                \"folderId\": \"28\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(T_{1},\\\\left(T_{1}.x-p_{1},T_{1}.y\\\\right),\\\\left(T_{1}.x-p_{1},T_{1}.y-l_{1}\\\\right),\\\\left(T_{1}.x,T_{1}.y-l_{1}\\\\right)\\\\right)\",\n                \"lines\": true,\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"r_{ekam}\\\\to1-r_{ekam}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"46\",\n                \"folderId\": \"28\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(T_{1}.x-\\\\frac{1}{2}p_{1},T_{1}.y-\\\\frac{1}{2}l_{1}\\\\left\\\\{r_{ekam}=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Record trace\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n         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\"expression\",\n                \"id\": \"50\",\n                \"folderId\": \"28\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(T_{1}.x-p_{1}-m_{x},T_{1}.y\\\\right),\\\\left(T_{1}.x-p_{1}-m_{x}-p_{2},T_{1}.y\\\\right),\\\\left(T_{1}.x-p_{1}-m_{x}-p_{2},T_{1}.y-l_{1}\\\\right),\\\\left(T_{1}.x-p_{1}-m_{x},T_{1}.y-l_{1}\\\\right)\\\\right)\\\\left\\\\{L_{A}\\\\ge2\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"52\",\n                \"folderId\": \"28\",\n                \"color\": \"#000000\",\n                \"latex\": 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\"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"43\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"44\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            }\n        ],\n        \"ticker\": {\n            \"handlerLatex\": \"\\\\left\\\\{r_{ekam}=1:t_{ambah}\\\\right\\\\}\",\n            \"playing\": true,\n            \"open\": true\n        }\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n  calculator3.setState(state3);\n\n  \/\/ Source\n  var x0Helper = calculator1.HelperExpression({ latex: 'x_{0}' });\n  var kHelper = calculator1.HelperExpression({ latex: 'K' });\n\n  \/\/ Sink\n  x0Helper.observe('numericValue', function() {\n    var value = x0Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '5', latex: `x_{0}=${value}` });\n\t  calculator3.setExpression({ id: '11', latex: `x_{0}=${value}` });\n    }\n  });\n  kHelper.observe('numericValue', function() {\n    var value = kHelper.numericValue;\n    if (!isNaN(value)) {\n      calculator3.setExpression({ id: '69', latex: `K=${value}` });\n    }\n  });\n\n<\/script>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more 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href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Polyhedron\">Polyhedron<\/a><\/li>\n<li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Rectangular+Prism\">Rectangular Prism<\/a><\/li>\n<li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Net\">Net<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>An interactive learning resource that illustrates how cutting equal squares from a rectangular card and folding the sides creates an open box, with the relationship between cut size and volume shown dynamically through a box model and a graph.<\/p>\n","protected":false},"author":1,"featured_media":1250,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"advanced_seo_description":"","spay_email":""},"jetpack_shortlink":"https:\/\/wp.me\/P93lma-jP","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1229"}],"collection":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/comments?post=1229"}],"version-history":[{"count":16,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1229\/revisions"}],"predecessor-version":[{"id":1376,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1229\/revisions\/1376"}],"up":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1140"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media\/1250"}],"wp:attachment":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media?parent=1229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}