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Question-155212

Question Number 155212 by ajfour last updated on 27/Sep/21 Commented by mr W last updated on 27/Sep/21 $$\mathrm{cos}\:\theta=\frac{{p}}{\mathrm{1}}\:\Rightarrow\mathrm{cos}\:\theta={p} \\ $$$$\frac{{c}}{\mathrm{sin}\:\theta}={p}\:\mathrm{sin}\:\theta\:\Rightarrow\mathrm{sin}^{\mathrm{2}} \:\theta=\frac{{c}}{{p}} \\ $$$$\frac{{c}}{{p}}+{p}^{\mathrm{2}} =\mathrm{1} \\…

Prove-that-r-1-2n-1-1-r-1-0-1-x-r-1-x-2n-r-dx-0-1-1-x-2n-x-2n-1-x-2n-1-x-2n-1-dx-

Question Number 24142 by Tinkutara last updated on 13/Nov/17 $${Prove}\:{that} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{{r}} \left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}−{r}} {dx}\right) \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left[\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}} +{x}^{\mathrm{2}{n}} −\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}+\mathrm{1}}…

Solve-for-positive-integers-abcd-abc-a-1-b-1-c-1-

Question Number 155204 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}: \\ $$$$\mathrm{abcd}\:+\:\mathrm{abc}\:=\:\left(\mathrm{a}+\mathrm{1}\right)\left(\mathrm{b}+\mathrm{1}\right)\left(\mathrm{c}+\mathrm{1}\right) \\ $$ Answered by MJS_new last updated on 27/Sep/21 $${a}\leqslant{b}\leqslant{c} \\ $$$$\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{for}\:{a}\:{b}\:{c}\:{d}\:\mathrm{are} \\…

0-ln-x-e-x-e-x-dx-

Question Number 155207 by mathdanisur last updated on 26/Sep/21 $$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by mindispower last updated on 27/Sep/21 $$\Omega={f}'\left(\mathrm{0}\right),{f}'\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…

what-is-the-first-three-smallest-positive-integer-that-leaves-a-reminder-of-1-when-divided-by-3-and-5-qnd-7-

Question Number 89668 by Mr.Panoply last updated on 18/Apr/20 $${what}\:{is}\:{the}\:{first}\:{three}\:{smallest}\:{positive}\: \\ $$$${integer}\:{that}\:{leaves}\:{a}\:{reminder}\:{of}\:\mathrm{1}.\:{when} \\ $$$${divided}\:{by}\:\mathrm{3}\:{and}\:\mathrm{5}\:{qnd}\:\mathrm{7}? \\ $$ Commented by mr W last updated on 18/Apr/20 $${lcm}\left(\mathrm{3},\mathrm{5},\mathrm{7}\right)=\mathrm{3}×\mathrm{5}×\mathrm{7}=\mathrm{105}…

Determine-all-positive-integers-a-b-c-d-x-y-z-t-and-a-b-c-d-which-satisfy-a-b-c-td-b-c-d-xa-c-d-a-yb-d-a-b-zc-

Question Number 155206 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d};\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}\:\:\mathrm{and}\:\:\mathrm{a}\neq\mathrm{b}\neq\mathrm{c}\neq\mathrm{d} \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{td}\:; \\ $$$$\mathrm{b}+\mathrm{c}+\mathrm{d}=\mathrm{xa}\:;\:\mathrm{c}+\mathrm{d}+\mathrm{a}=\mathrm{yb}\:;\:\mathrm{d}+\mathrm{a}+\mathrm{b}=\mathrm{zc} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-155203

Question Number 155203 by nadovic last updated on 26/Sep/21 Answered by TheHoneyCat last updated on 29/Sep/21 $$\mathrm{let}\:\mathrm{O}\:\mathrm{be}\:\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{a}\:\mathrm{vertice}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle} \\ $$$$\mathrm{let}\:\theta\:\mathrm{be}\:\mathrm{an}\:\mathrm{angle}\:\left(\mathrm{in}\:\mathrm{radian}\right)\:\mathrm{between}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{axis}\:\left(\mathrm{O}{z}\:\mathrm{or}\:\mathrm{O}{y}\right)\:\mathrm{and}\:\mathrm{the}\:\left(\mathrm{OA}\right)\:\mathrm{line} \\ $$$$…

Given-that-sin-A-1-2-and-sin-C-3-2-without-u-using-calculator-solve-a-tan-A-C-b-cos-A-C-

Question Number 89662 by 974342176 last updated on 18/Apr/20 $${Given}\:{that}\:\mathrm{sin}\:{A}=\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:\mathrm{sin}\:{C}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:{without}\:{u} \\ $$$${using}\:{calculator}\:{solve} \\ $$$$\left.{a}\right)\:\mathrm{tan}\:\left({A}+{C}\right) \\ $$$$\left.{b}\right)\:{cos}\left({A}−{C}\right) \\ $$ Answered by TANMAY PANACEA. last updated on…