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Question Number 134097 Answers: 2 Comments: 0
$$\mathrm{In}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD}\:,\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{APQ}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{it}.\:\mathrm{AP}=\mathrm{4}\:\mathrm{cm}, \\ $$$$\mathrm{PQ}=\mathrm{3}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{AQ}=\mathrm{5}\:\mathrm{cm}.\:\mathrm{Point} \\ $$$$\mathrm{P}\:\mathrm{is}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:\mathrm{BC}\:\mathrm{and}\:\mathrm{point}\:\mathrm{Q} \\ $$$$\mathrm{is}\:\mathrm{on}\:\mathrm{side}\:\mathrm{CD}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{square}\:\mathrm{ABCD}. \\ $$
Question Number 132230 Answers: 1 Comments: 0
$$ \\ $$$$ \\ $$$$\boldsymbol{{S}}=\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{+\infty} {\sum}}\left(\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} −\mathrm{1}}}−\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} +\mathrm{1}}}\right) \\ $$$$\boldsymbol{{S}}\:={l}\:{or}\:\boldsymbol{{S}}=\infty\:\:??? \\ $$
Question Number 131847 Answers: 1 Comments: 0
$$\:\boldsymbol{{Let}}\:\left(\boldsymbol{\Omega},\digamma,\boldsymbol{{P}}\right)\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{probalistics}}\:\boldsymbol{{space}}\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}},\: \\ $$$$\boldsymbol{{A}},\boldsymbol{{B}}\in\digamma \\ $$$$\boldsymbol{{if}}\:\left(\boldsymbol{{P}}\left(\boldsymbol{{A}}\mid\boldsymbol{{B}}\right)\leqslant{P}\left(\boldsymbol{{A}}\right)\:\boldsymbol{{and}}\:\boldsymbol{{P}}\left(\boldsymbol{{B}}\mid\boldsymbol{{A}}\right)\ll\boldsymbol{{P}}\left({B}\right)\right) \\ $$$${t}\boldsymbol{{h}}{en}\:\boldsymbol{{P}}\left({A}\mid\overset{\_} {\boldsymbol{{B}}}\right)\geqslant\boldsymbol{{P}}\left(\boldsymbol{{A}}\right) \\ $$$$ \\ $$
Question Number 131590 Answers: 2 Comments: 0
$$\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\boldsymbol{{U}}_{\boldsymbol{{n}}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\boldsymbol{{x}}+\boldsymbol{{x}}^{\mathrm{2}} +....+\boldsymbol{{x}}^{\boldsymbol{{n}}} }\: \\ $$$$\boldsymbol{{converges}}!! \\ $$
Question Number 131465 Answers: 1 Comments: 0
$${Let}\:{a},{b}\:{and}\:{c}\:{be}\:{three}\:{positive}\:{real}\:{numbers} \\ $$$$.\:{Prove}\:{that}\:{a}+{b}+{c}\:\leqslant\:\frac{{a}^{\mathrm{2}} +{bc}}{{b}+{c}}+\frac{{b}^{\mathrm{2}} +{ca}}{{c}+{a}}+\frac{{c}^{\mathrm{2}} +{ab}}{{a}+{b}} \\ $$
Question Number 127382 Answers: 1 Comments: 0
Question Number 125593 Answers: 2 Comments: 0
Question Number 125491 Answers: 1 Comments: 1
Question Number 125444 Answers: 1 Comments: 1
Question Number 125337 Answers: 1 Comments: 1
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Question Number 125108 Answers: 0 Comments: 3
Question Number 125084 Answers: 1 Comments: 3
Question Number 125021 Answers: 1 Comments: 0
Question Number 124821 Answers: 1 Comments: 2
Question Number 124743 Answers: 1 Comments: 1
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Question Number 124189 Answers: 0 Comments: 5
Question Number 124117 Answers: 0 Comments: 0
Question Number 123738 Answers: 1 Comments: 1
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Question Number 123528 Answers: 1 Comments: 1
Question Number 123507 Answers: 0 Comments: 6
Question Number 123489 Answers: 1 Comments: 0
Question Number 123302 Answers: 2 Comments: 0
Question Number 123212 Answers: 1 Comments: 1
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