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If-b-c-x-c-a-y-a-b-z-0-then-prove-that-b-c-y-z-c-a-z-x-a-b-x-y-

Question Number 216270 by MATHEMATICSAM last updated on 02/Feb/25 $$\mathrm{If}\:\left({b}\:−\:{c}\right){x}\:+\:\left({c}\:−\:{a}\right){y}\:+\:\left({a}\:−\:{b}\right){z}\:=\:\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{b}\:−\:{c}}{{y}\:−\:{z}}\:=\:\frac{{c}\:−\:{a}}{{z}\:−\:{x}}\:=\:\frac{{a}\:−\:{b}}{{x}\:−\:{y}}\:. \\ $$ Answered by Rasheed.Sindhi last updated on 02/Feb/25 $$\mathrm{If}\:\left({b}\:−\:{c}\right){x}\:+\:\left({c}\:−\:{a}\right){y}\:+\:\left({a}\:−\:{b}\right){z}\:=\:\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{b}\:−\:{c}}{{y}\:−\:{z}}\:=\:\frac{{c}\:−\:{a}}{{z}\:−\:{x}}\:=\:\frac{{a}\:−\:{b}}{{x}\:−\:{y}}\:. \\…

Prove-0-pi-2-d-0-pi-2-f-sin-cos-sin-d-pi-2-0-1-f-x-dx-

Question Number 216281 by MrGaster last updated on 02/Feb/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {d}\phi\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\theta\:\mathrm{cos}\:\theta\right)\mathrm{sin}\theta\:{d}\theta=\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$ Commented by mr W last updated on…

prove-that-n-1-cos-n-n-1-1-2-1-3-1-n-is-convergent-

Question Number 216274 by mnjuly1970 last updated on 02/Feb/25 $$ \\ $$$$\:\:\:{prove}\:{that}\:: \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{cos}\left(\:{n}\:\right)}{{n}}\:\left(\:\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:…+\frac{\mathrm{1}}{\:\sqrt{{n}}}\:\right) \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:{is}\:\:\:{convergent}. \\ $$$$ \\…

If-x-is-a-positive-acute-angle-and-sinx-sin-2-x-sin-3-x-1-then-find-minimum-value-of-cot-2-x-

Question Number 216253 by MATHEMATICSAM last updated on 01/Feb/25 $$\mathrm{If}\:{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{acute}\:\mathrm{angle}\:\mathrm{and} \\ $$$$\mathrm{sin}{x}\:+\:\mathrm{sin}^{\mathrm{2}} {x}\:+\:\mathrm{sin}^{\mathrm{3}} {x}\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cot}^{\mathrm{2}} {x}. \\ $$ Commented by Frix last updated on…

Find-the-smallest-value-of-the-expression-a-b-c-d-b-c-d-a-c-d-a-b-d-a-b-c-a-b-c-d-N-

Question Number 216251 by Abdullahrussell last updated on 01/Feb/25 $${Find}\:{the}\:{smallest}\:{value}\:{of}\:{the}\:{expression} \\ $$$$\:\lfloor\frac{{a}+{b}+{c}}{{d}}\rfloor+\lfloor\frac{{b}+{c}+{d}}{{a}}\rfloor+\lfloor\frac{{c}+{d}+{a}}{{b}}\rfloor+\lfloor\frac{{d}+{a}+{b}}{{c}}\rfloor \\ $$$$\:\:\left({a},{b},{c},{d}\right)\in{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-216245

Question Number 216245 by Tawa11 last updated on 01/Feb/25 Commented by Tawa11 last updated on 01/Feb/25 $$\mathrm{I}\:\mathrm{can}\:\mathrm{use}\:\mathrm{cosine}\:\mathrm{rule}. \\ $$$$\mathrm{But}\:\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{see}\:\mathrm{if}\:\mathrm{there}\:\mathrm{is} \\ $$$$\mathrm{better}\:\mathrm{approach}. \\ $$ Commented by…