Question Number 140961 by iloveisrael last updated on 14/May/21 $$\:\underset{\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\:\frac{\mathrm{ln}\:\left({x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{{x}}\:{dx}\:=?\: \\ $$ Answered by qaz last updated on 14/May/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 75426 by otchereabdullai@gmail.com last updated on 10/Dec/19 $$\mathrm{A}\:\mathrm{boy}\:\mathrm{has}\:\mathrm{to}\:\mathrm{cover}\:\:\mathrm{4km}\:\:\mathrm{to}\: \\ $$$$\mathrm{catch}\:\mathrm{a}\:\mathrm{bus}.\:\mathrm{He}\:\mathrm{walks}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{distance}\:\mathrm{as}\:\mathrm{3km}/\mathrm{h}\:\mathrm{and}\:\mathrm{run}\:\mathrm{the}\:\mathrm{rest}\:\mathrm{at} \\ $$$$\mathrm{5km}/\mathrm{h}\:\mathrm{if}\:\mathrm{he}\:\mathrm{takes}\:\mathrm{1hour}\:\mathrm{to}\:\mathrm{complete}\: \\ $$$$\mathrm{the}\:\mathrm{distance}.\:\mathrm{For}\:\mathrm{how}\:\mathrm{many}\:\mathrm{kilometres} \\ $$$$\mathrm{does}\:\mathrm{he}\:\mathrm{walk} \\ $$ Answered by MJS…
Question Number 9890 by konen last updated on 12/Jan/17 $$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{16}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{25}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{36}}\right)…\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3600}}\right)=? \\ $$ Answered by nume1114 last updated on 12/Jan/17 $$\:\:\:\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{16}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{25}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{36}}\right)…\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3600}}\right) \\ $$$$=\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{2}} }\right)…\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{60}^{\mathrm{2}}…
Question Number 140956 by mnjuly1970 last updated on 14/May/21 $$\:\:\:\:\:\:\:\:\:\:…..{advanced}……{calculus}….. \\ $$$$\:\:\:\:\:{prove}\:{that}: \\ $$$$\:\:\boldsymbol{\phi}:=\:\int_{−\infty} ^{\:\infty} \frac{{sin}^{\mathrm{4}} \left({x}\right).{cos}^{\mathrm{4}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{16}} \\ $$$$\:\:{m}.{n} \\ $$ Answered by…
Question Number 140959 by loveineq last updated on 14/May/21 $$\mathrm{Let}\:{a},{b}\:\geqslant\:\mathrm{0}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\centerdot\frac{\left(\mathrm{2}+{a}\right)\left(\mathrm{2}+{b}\right)}{\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{b}\right)}\:\geqslant\:\frac{\mathrm{4}−{a}−{b}}{\mathrm{4}+{a}+{b}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by MJS_new last updated on 14/May/21 $$\mathrm{this}\:\mathrm{is}\:\mathrm{easy} \\…
Question Number 140958 by mathmax by abdo last updated on 14/May/21 $$\mathrm{find}\:\mathrm{e}^{\begin{pmatrix}{−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75421 by peter frank last updated on 10/Dec/19 $${If}\:{p}\:{is}\:{a}\:{point}\:{in}\:{the}\:{base} \\ $$$${AB}\:{of}\:\:{a}\:\:{triangle}\:\:{ABC} \\ $$$${such}\:{that}\:{AP}\:\::{PB}={P}:{Q} \\ $$$${prove}\:{that} \\ $$$$\left({p}+{q}\right)\mathrm{cot}\:\theta={q}\mathrm{cot}\:{A}−{p}\mathrm{cot}\:{B} \\ $$ Commented by som(math1967) last…
Question Number 9884 by Joel575 last updated on 12/Jan/17 $$\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{2}} \:+\:\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{9}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$ Answered by sandy_suhendra last updated on 12/Jan/17 $$\left(\mathrm{x}^{\mathrm{2}}…
Question Number 9883 by Joel575 last updated on 12/Jan/17 $$\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{2}} \:+\:\mathrm{7}\left({x}^{\mathrm{2}} −\mathrm{6}{x}\right)\:+\:\mathrm{19}\:=\:\mathrm{0} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9880 by sandipkd@ last updated on 12/Jan/17 Answered by bansal22luvi@gmail.com last updated on 12/Jan/17 $${let}\:{the}\:{radius}\:{of}\:{smallest}\:{circle}\:{be}\:{r} \\ $$$${CO}=\left(\mathrm{2}−{x}\right) \\ $$$${C}_{\mathrm{1}} {O}=\left(\mathrm{1}+{x}\right) \\ $$$${C}_{\mathrm{1}} {C}=\mathrm{1}…