arctan(x)=(85)/((150/2-(65/4)))

{ "query": { "display": "$$\\arctan\\left(x\\right)=\\frac{85}{\\left(\\frac{150}{2}-\\left(\\frac{65}{4}\\right)\\right)}$$", "symbolab_question": "EQUATION#\\arctan(x)=\\frac{85}{(\\frac{150}{2}-(\\frac{65}{4}))}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=\\tan(\\frac{68}{47})", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\arctan\\left(x\\right)=\\frac{85}{\\left(\\frac{150}{2}-\\left(\\frac{65}{4}\\right)\\right)}{\\quad:\\quad}x=\\tan\\left(\\frac{68}{47}\\right)$$", "input": "\\arctan\\left(x\\right)=\\frac{85}{\\left(\\frac{150}{2}-\\left(\\frac{65}{4}\\right)\\right)}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{85}{\\frac{150}{2}-\\frac{65}{4}}:{\\quad}\\frac{68}{47}$$", "input": "\\frac{85}{\\frac{150}{2}-\\frac{65}{4}}", "steps": [ { "type": "step", "primary": "Divide the numbers: $$\\frac{150}{2}=75$$", "result": "=\\frac{85}{75-\\frac{65}{4}}" }, { "type": "interim", "title": "Join $$75-\\frac{65}{4}:{\\quad}\\frac{235}{4}$$", "input": "75-\\frac{65}{4}", "result": "=\\frac{85}{\\frac{235}{4}}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$75=\\frac{75\\cdot\\:4}{4}$$", "result": "=\\frac{75\\cdot\\:4}{4}-\\frac{65}{4}" }, { "type": "step", "primary": "Since the denominators are equal, combine the fractions: $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{75\\cdot\\:4-65}{4}" }, { "type": "interim", "title": "$$75\\cdot\\:4-65=235$$", "input": "75\\cdot\\:4-65", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$75\\cdot\\:4=300$$", "result": "=300-65" }, { "type": "step", "primary": "Subtract the numbers: $$300-65=235$$", "result": "=235" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7L+wiZMwa3cjwxJrj63Jhry061ljBSPJeENOw2efoSWu7r6j58Ks80TtVMGKFpIfh0hsfpm4hvWwLMHYl2vAKa7inKlnYhxfdJwOEL4PL7miwiNrEngO+NNvZ9sqNu+2V" } }, { "type": "step", "result": "=\\frac{235}{4}" } ], "meta": { "interimType": "Algebraic Manipulation Join Concise Title 1Eq" } }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{\\frac{b}{c}}=\\frac{a\\cdot\\:c}{b}$$", "result": "=\\frac{85\\cdot\\:4}{235}" }, { "type": "step", "primary": "Multiply the numbers: $$85\\cdot\\:4=340$$", "result": "=\\frac{340}{235}" }, { "type": "step", "primary": "Cancel the common factor: $$5$$", "result": "=\\frac{68}{47}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7zCUJ4XXTRi2LFnGEExvOpZTXbpjMmEj5pzgsir6fVDGFPN0hTTOJ9BInhthgCS+LzRqDxPUzBN6vjj5oJL9kUMasmD28Tv1MiAivE8KNNos4/icn8GXbA33bUDa0q2xSixpjZyz1hn/Tx95aZo6CSLr37QlEGOE6UHFQm3Ya7V+yclbpcpmI7HkP2GkS9SOJ3vsiyHepYKj0VcG64szx7bCI2sSeA74029n2yo277ZU=" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\arctan\\left(x\\right)=\\frac{68}{47}", "result": "x=\\tan\\left(\\frac{68}{47}\\right)", "steps": [ { "type": "step", "primary": "$$\\arctan\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\tan\\left(a\\right)$$", "result": "x=\\tan\\left(\\frac{68}{47}\\right)" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\arctan(x)-\\frac{85}{(\\frac{150}{2}-(\\frac{65}{4}))}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }