Question Number 209246 by Erico last updated on 05/Jul/24 $$\mathrm{Find}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{t}+\mathrm{e}^{\mathrm{f}\left(\mathrm{t}\right)} } \\ $$ Answered by mr W last updated on 06/Jul/24 $${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}}…
Question Number 208862 by THORR last updated on 25/Jun/24 $${x}=\:{b}^{\mathrm{2}} \: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 207864 by efronzo1 last updated on 29/May/24 $$\:\:\:\:\:\underbrace{\:} \\ $$ Answered by Rasheed.Sindhi last updated on 29/May/24 $$\mathrm{2}^{\mathrm{5}{m}} \centerdot\mathrm{5}^{\mathrm{2}{n}} \centerdot{k}=\mathrm{2020}^{\mathrm{2020}} =\left(\mathrm{2}^{\mathrm{2}} .\mathrm{5}.\mathrm{101}\right)^{\mathrm{2020}} \\…
Question Number 207372 by sniper237 last updated on 12/May/24 $$\mathrm{2}\:{students}\:{are}\:{passing}\: \\ $$$${a}\:{test}\:{of}\:\:{n}\:{questions}\:{with} \\ $$$${the}\:{same}\:{chance}\:{to}\:{find}\:{each}\:{one} \\ $$$${Show}\:\:{the}\:{chance}\:{that}\:{they}\:{both} \\ $$$$\:{don}'{t}\:{find}\:{a}\:{same}\:{question}\:{is}\:\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$ Commented by A5T last updated…
Question Number 204141 by Tawa11 last updated on 06/Feb/24 Answered by AST last updated on 07/Feb/24 $${A}_{\mathrm{3}} \cap{A}_{−\mathrm{3}} =\left(−\infty,−\mathrm{3}\right]=\cap_{{i}=−\mathrm{3}} ^{\mathrm{3}} \\ $$ Commented by Tawa11…
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Question Number 203634 by cortano12 last updated on 24/Jan/24 $$\:\:\: \\ $$ Answered by Frix last updated on 24/Jan/24 $$\frac{\mathrm{2}^{{n}^{\mathrm{2}} } −\mathrm{1}}{\mathrm{2}^{{n}} −\mathrm{1}}\approx\mathrm{2}^{{n}^{\mathrm{2}} −{n}} \:\Rightarrow\:{k}=\mathrm{271}…
Question Number 203490 by cortano12 last updated on 20/Jan/24 $$\:\:\:\:\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×…×\mathrm{2005}\:=\:…\:\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$ Answered by AST last updated on 20/Jan/24 $${x}=\mathrm{1}×\mathrm{3}×\mathrm{5}…×\mathrm{2005}\equiv\mathrm{0}\left({mod}\:\mathrm{125}\right) \\ $$$${x}\equiv\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}\right)^{\mathrm{250}} ×\mathrm{1}×\mathrm{3}×\mathrm{5}\left({mod}\:\mathrm{8}\right)\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right) \\ $$$${x}=\mathrm{125}{q}\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{q}\equiv\mathrm{15}\left({mod}\:\mathrm{8}\right)\Rightarrow{q}\equiv\mathrm{3}\left({mod}\:\mathrm{8}\right)…
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Question Number 200284 by depressiveshrek last updated on 16/Nov/23 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{set}\:{A}\:\mathrm{containing}\:{n} \\ $$$$\mathrm{elements},\:\mid\mathcal{P}\left({A}\right)\mid=\mathrm{2}^{{n}} . \\ $$ Answered by AST last updated on 16/Nov/23 $${C}_{\mathrm{0}} ^{{n}} +^{{n}}…