{"id":"cb_question_bank:c231b5bc-9dcf-4b98-9fd6-770121adba60","source_id":"cb_question_bank","source_item_id":"c231b5bc-9dcf-4b98-9fd6-770121adba60","external_id":null,"ibn":"04588-DC","question_id":"2f958af9","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"v squared equals, the fraction with numerator L T, and denominator m The formula above expresses the square of the speed v of a wave moving along a string in terms of tension T , mass m , and length L of the string. What is T in terms of m , v , and L ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"standalone_statement style:1 \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d16640d710b726665197307386e0f15afa3c5c5fca1e355c53517f013751e2de\" alt=\"v squared equals, the fraction with numerator L T, and denominator m\"></span></span>\n          </p><p class=\"stem_paragraph \">The formula above expresses the square of the speed&nbsp;<span class=\"italic\">v</span> of a wave moving along a string in terms of tension&nbsp;<span class=\"italic\">T</span>, mass&nbsp;<span class=\"italic\">m</span>, and length&nbsp;<span class=\"italic\">L</span> of the string. What is <span class=\"italic\">T</span> in terms of <span class=\"italic\">m</span>, <span class=\"italic\">v</span>, and <span class=\"italic\">L</span> ?</p><p></p>\n","rationale_html":"<p>Choice A is correct. To write the formula as <span class=\"italic\">T</span> in terms of <span class=\"italic\">m, v,</span> and <span class=\"italic\">L </span>means to isolate <span class=\"italic\">T</span> on one side of the equation. First, multiply both sides of the equation by <span class=\"italic\">m</span>, which gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/003a78190f372eae9be0f2f2445a66976e6053436a624fd094be1ec245317788\" alt=\"m v squared, equals the fraction with numerator m L T, and denominator m\"></span>, which simplifies to <span class=\"italic\">mv</span><sup>2 </sup>= <span class=\"italic\">LT</span>. Next, divide both sides of the equation by <span class=\"italic\">L</span>, which gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b1ddfcb26fceff5921d9ac750e858ca7cbc15c9c23d22e6bf3d14d90af37f3e\" alt=\"the fraction with numerator m v squared, and denominator L, equals the fraction with numerator L T, and denominator L\"></span>, which simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7bc16279ca49e88e934a2e6fff6d708d38475ccc2d45549805f8254e523e455\" alt=\"T equals the fraction with numerator m v squared, and denominator L\"></span>.</p><p>Choices B, C, and D are incorrect and may be the result of incorrectly applying operations to each side of the equation.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7bc16279ca49e88e934a2e6fff6d708d38475ccc2d45549805f8254e523e455\" alt=\"T equals, the fraction with numerator m v squared, and denominator L\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e4aa2fb7865f4f92046ff84d0270e99fdd5b57968cb3695924448c838fc8ed1c\" alt=\"T equals, the fraction with numerator m, and denominator v squared L, end fraction\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a9d9ff621ef649e56f0da4418c9153ca9c6fd71777cbe0b136cfb1d7d6d5e00a\" alt=\"T equals, the fraction with numerator m L, and denominator v squared, end fraction\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b37c9ecbee9f15f12895c4a4fd92be368520ab7148789c828093e6da4ceb9956\" alt=\"T equals, the fraction with numerator L, and denominator m v squared, end fraction\"></span></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}