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Question Number 197589 Answers: 1 Comments: 0
$${how}\:{many}\:{natural}\:{numbers}\:{with}\:\mathrm{4} \\ $$$${different}\:{digits}\:{are}\:{divisible}\:{by}\:\mathrm{3}? \\ $$
Question Number 197169 Answers: 2 Comments: 0
$$\mathrm{7}{x}+\mathrm{4}{y}=\mathrm{2} \\ $$
Question Number 197155 Answers: 1 Comments: 0
$$\:{A}\:{bullet}\:{of}\:{mass}\:\mathrm{180}{g}\:{is}\:{fired}\: \\ $$$$\:{horizontally}\:{into}\:{a}\:{fixed}\:{wooden}\: \\ $$$$\:{block}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{24}{m}/{s}.\:{if}\:{the}\: \\ $$$${bullet}\:{is}\:{brought}\:{to}\:{rest}\:{in}\:\mathrm{0}.\mathrm{4}{sec}\:{by}\:{a} \\ $$$${constant}\:{resistance},\:{calculate}\:{the} \\ $$$${distance}\:{moved}\:{by}\:{the}\:{bullet}\:{in}\:{the} \\ $$$${wood} \\ $$
Question Number 197147 Answers: 2 Comments: 0
Question Number 197146 Answers: 1 Comments: 0
$$\mathrm{Find}:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}\left(\mathrm{x}\right)}{\Psi\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:? \\ $$
Question Number 197133 Answers: 1 Comments: 0
Question Number 197132 Answers: 1 Comments: 1
$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{\mathrm{ln}\left(\mathrm{t}+\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}{\mathrm{t}}\right)^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$
Question Number 197129 Answers: 2 Comments: 0
Question Number 197128 Answers: 1 Comments: 1
Question Number 197125 Answers: 1 Comments: 1
Question Number 197113 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{{ln}\left({t}+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)}{{t}}\right){dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$
Question Number 197112 Answers: 2 Comments: 0
Question Number 197111 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\cancel{ } \\ $$
Question Number 197110 Answers: 1 Comments: 0
Question Number 197104 Answers: 0 Comments: 3
Question Number 197099 Answers: 2 Comments: 0
$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{cos}{t}\right)}{\mathrm{sin}{t}}\:\mathrm{d}{t}=??? \\ $$
Question Number 197095 Answers: 1 Comments: 0
Question Number 197094 Answers: 1 Comments: 0
Question Number 197089 Answers: 2 Comments: 0
$$\mathrm{Simplify}\:\left(\frac{\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}}{\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{i}}\right)^{\mathrm{10}} \\ $$
Question Number 197081 Answers: 0 Comments: 5
Question Number 197073 Answers: 1 Comments: 0
Question Number 197072 Answers: 2 Comments: 0
$$\mathrm{tan123}=\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{tan167}=? \\ $$
Question Number 197064 Answers: 2 Comments: 0
Question Number 197063 Answers: 1 Comments: 0
Question Number 197060 Answers: 1 Comments: 1
$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$
Question Number 197057 Answers: 3 Comments: 2
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