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Level(2)\n## TitleText1('Calculus: Early Transcendentals')\n## AuthorText1('Rogawski')\n## EditionText1('1')\n## Section1('11.1')\n## Problem1('30')\n## KEYWORDS('polar coordinates')\n\nDOCUMENT();        # This should be the first executable line in the problem.\n\nloadMacros(\n    \"PGstandard.pl\",\n    \"MathObjects.pl\",\n    \"PGML.pl\",\n);\n\nTEXT(beginproblem());\n\nContext(\"Numeric\")-\u003evariables-\u003eadd(y=\u003e\"Real\",t=\u003e\"Real\");\n$a = random(2,9);\ndo {$b = random(1,9);} until ($b != $a);\n$r = random(2,5);\n$rr = $r**2;\n$y = Formula(\"$b-$r*sin(t)\");\n\nBEGIN_PGML\nThe circle\n\n\u003e\u003e [``(x - [$a])^2 + (y - [$b])^2 = [$rr]``] \u003c\u003c\n\ncan be drawn with parametric equations.\nAssuming the circle is traced clockwise as the parameter increases and\n\n\u003e\u003e [``x(t) = [$a] + [$r] \\cos t``], \u003c\u003c\n\nthen \n\n\u003e\u003e [``y(t) = ``] [__]{$y}. \u003c\u003c\n\nEND_PGML\n\nENDDOCUMENT();\n","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"637fc5c158ed1a0004e9bde0","part_id":"5a134a64c04210000413c91a","description":null,"points":1.0,"automatic_manual_credit":true,"accessible":false,"answer":"1-3*sin(t)","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(1-3\\sin\\!\\left(t\\right)\\)"}],"interactive_html":"\n\u003cdiv class=\"PGML\"\u003e\nThe circle\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{(x - 9)^2 + (y - 1)^2 = 9}\\)\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\ncan be drawn with parametric equations.\nAssuming the circle is traced clockwise as the parameter increases and\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{x(t) = 9 + 3 \\cos t}\\),\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nthen \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{y(t) = }\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n.\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\nThe circle\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{(x - 9)^2 + (y - 1)^2 = 9}\\)\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\ncan be drawn with parametric equations.\nAssuming the circle is traced clockwise as the parameter increases and\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{x(t) = 9 + 3 \\cos t}\\),\n\u003c/div\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nthen \n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv style=\"text-align:center; margin:0\"\u003e\n\\(\\displaystyle{y(t) = }\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n.\n\u003c/div\u003e\n\u003cdiv 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v3"}},"image":{"identifier":"calculus-4.jpg","size":92521,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6cb0717758b325775b77fe/calculus-4.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c6cb0717758b325775b77fe/thumb_calculus-4.jpg"},"related_products":[{"id":"5c533d7d78811e0e5904234d","name":"OpenStax Calculus Volume 1","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5c58eabf4a8e21002b802892","name":"Active Calculus (Boelkins)","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5c6c7c0e7758b300165b7b6e","name":"OpenStax Calculus Volume 2","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5c735527c6e851001a2555ad","name":"APEX Calculus (Hartman)","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5f16ff9e4a1e8d1366b8f2b1","name":"Active Calculus Multivariable 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Surfaces"},{"id":"602519c99c19cc000461f1f3","name":"2.7 Cylindrical and Spherical Coordinates"},{"id":"602519c99c19cc000461f1f4","name":"3.1 Vector-Valued Functions and Space Curves"},{"id":"602519c99c19cc000461f1f5","name":"3.2 Calculus of Vector-Valued Functions"},{"id":"602519c99c19cc000461f1f6","name":"3.3 Arc Length and Curvature"},{"id":"602519c99c19cc000461f1f7","name":"3.4 Motion in Space"},{"id":"602519c99c19cc000461f1f8","name":"4.1 Introduction to Multivariable Functions"},{"id":"602519ca9c19cc000461f1f9","name":"4.2 Limits and Continuity"},{"id":"602519ca9c19cc000461f1fa","name":"4.3 Partial Derivatives"},{"id":"602519ca9c19cc000461f1fb","name":"4.4 Tangent Planes and Linear Approximations"},{"id":"602519ca9c19cc000461f1fc","name":"4.5 The Multivariable Chain Rule"},{"id":"602519ca9c19cc000461f1fd","name":"4.6 Directional Derivatives and the Gradient"},{"id":"602519ca9c19cc000461f1fe","name":"4.7 Maxima/Minima Problems"},{"id":"602519ca9c19cc000461f1ff","name":"4.8 Lagrange Multipliers"},{"id":"602519ca9c19cc000461f200","name":"5.1 Double Integrals over Rectangular Regions"},{"id":"602519ca9c19cc000461f201","name":"5.2 Double Integrals over General Regions"},{"id":"602519cb9c19cc000461f202","name":"5.3 Double Integration in Polar Coordinates"},{"id":"602519cb9c19cc000461f203","name":"5.4 Triple Integrals"},{"id":"602519cb9c19cc000461f204","name":"5.5 Triple Integrals in Cylindrical and Spherical Coordinates"},{"id":"602519cb9c19cc000461f205","name":"5.6 Calculating Centers of Mass and Moments of Inertia"},{"id":"602519cb9c19cc000461f206","name":"5.7 Change of Variables in Multiple Integrals"},{"id":"602519cb9c19cc000461f207","name":"6.1 Vector Fields"},{"id":"602519cb9c19cc000461f208","name":"6.2 Line Integrals"},{"id":"602519cb9c19cc000461f209","name":"6.3 Conservative Vector Fields"},{"id":"602519cb9c19cc000461f20a","name":"6.4 Flow, Flux, Green's Theorem"},{"id":"602519cc9c19cc000461f20b","name":"6.5 Divergence and Curl"},{"id":"602519cc9c19cc000461f20c","name":"6.6 Surface Integrals"},{"id":"602519cc9c19cc000461f20d","name":"6.7 Stokes' Theorem"},{"id":"602519cc9c19cc000461f20e","name":"6.8 The Divergence Theorem"},{"id":"602519cc9c19cc000461f20f","name":"7.1 Second-Order Linear Equations"},{"id":"602519cc9c19cc000461f210","name":"7.2 Nonhomogeneous Linear Equations"},{"id":"602519cc9c19cc000461f211","name":"7.3 Applications"},{"id":"602519cd9c19cc000461f212","name":"7.4 Series Solutions of Differential Equations"}]}}