Question Number 209872 by Frix last updated on 24/Jul/24 $$\mathrm{Solve}\:\mathrm{for}\:{x}\in\mathbb{R}: \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}=\sqrt{{x}+\mathrm{1}} \\ $$ Answered by Ghisom last updated on 24/Jul/24 $${x}={t}+\mathrm{1} \\…
Question Number 209889 by Tawa11 last updated on 24/Jul/24 Answered by som(math1967) last updated on 25/Jul/24 $${let}\:{PQ}={QS}={QR}={x} \\ $$$${cos}\angle{PQS}=\frac{{x}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{12}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} }=\frac{{x}^{\mathrm{2}} −\mathrm{72}}{{x}^{\mathrm{2}} }…
Question Number 209852 by hardmath last updated on 23/Jul/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{arctan}\:\left(\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} }\right)\:=\:? \\ $$ Answered by mr W last updated on 24/Jul/24 $$\frac{\mathrm{2}}{{n}^{\mathrm{2}} }=\frac{\left({n}+\mathrm{1}\right)−\left({n}−\mathrm{1}\right)}{\mathrm{1}+\left({n}+\mathrm{1}\right)\left({n}−\mathrm{1}\right)}…
Question Number 209853 by peter frank last updated on 23/Jul/24 Commented by mr W last updated on 23/Jul/24 $${the}\:{iron}\:{rod}\:{must}\:{be}\:{of}\:{a}\:{length}\:{of} \\ $$$$\mathrm{44482}\:{cm}! \\ $$ Answered by…
Question Number 209837 by lmcp1203 last updated on 23/Jul/24 $$ \\ $$$${if}\:{the}\:{series}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{converges}\:{to}\:{k}\:.\:\:{find}\:\:{the}\:{convergence}\:{value}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by mr W last…
Question Number 209838 by malwan last updated on 23/Jul/24 $${If}\:{sin}\:{x}\:+\:{cos}\:{x}\:+\:{tan}\:{x}\:+\:{cot}\:{x}\:+ \\ $$$${sec}\:{x}\:+\:{csc}\:{x}\:=\:\mathrm{7}\:,\:{find}\:{sin}\mathrm{2}{x}? \\ $$ Answered by mahdipoor last updated on 23/Jul/24 $$=\frac{{s}^{\mathrm{2}} {c}+{c}^{\mathrm{2}} {s}+{s}^{\mathrm{2}} +{c}^{\mathrm{2}}…
Question Number 209860 by lmcp1203 last updated on 23/Jul/24 $$ \\ $$$$\mathrm{Magnitude}\:\mathrm{A}\:\mathrm{varies}\:\mathrm{proportionally}\:\mathrm{with}\:\left(\mathrm{B}\:\mathrm{squared}\:+\:\mathrm{4}\right)\:\mathrm{and}\:\mathrm{magnitude}\:\mathrm{B}\:\mathrm{varies}\:\mathrm{proportionally}\:\mathrm{with} \\ $$$$\left({t}\mathrm{he}\:\mathrm{root}\:\mathrm{of}\:\mathrm{C}\right)\:−\:\mathrm{5}.\:\mathrm{Also}\:\mathrm{when}\:\mathrm{A}\:\mathrm{is}\:\mathrm{16}\:,\:\mathrm{B}\:\mathrm{is}\:\mathrm{12}\:\mathrm{and}\:\mathrm{C}\:\mathrm{takes}\:\mathrm{the}\:\mathrm{value}\:\mathrm{81}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{that}\:\mathrm{A}\:\mathrm{takes} \\ $$$$\mathrm{wh}{e}\mathrm{n}\:\mathrm{C}\:\mathrm{is}\:\mathrm{49}.\:\:\:{help}\:\:{me}.\:{please}.\:{thanks} \\ $$ Answered by mr W last updated on…
Question Number 209845 by peter frank last updated on 23/Jul/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 209846 by peter frank last updated on 23/Jul/24 Answered by mr W last updated on 23/Jul/24 $${the}\:{result}\:{is}\:{too}\:{large}. \\ $$$$\mathrm{20}×\left(\mathrm{15}−\mathrm{10}\right)×\mathrm{12}×\mathrm{10}^{−\mathrm{6}} =\mathrm{0}.\mathrm{0012}{m} \\ $$$$=\mathrm{1}.\mathrm{2}\:{mm} \\…
Question Number 209847 by SonGoku last updated on 23/Jul/24 Answered by mr W last updated on 23/Jul/24 $${depth}\:={h} \\ $$$${h}=\sqrt{\mathrm{23}^{\mathrm{2}} −\left(\frac{\mathrm{53}−\mathrm{41}}{\mathrm{2}}\right)^{\mathrm{2}} }=\sqrt{\mathrm{493}}=\mathrm{22}.\mathrm{20}{m} \\ $$$${cross}\:{section}\:{area}\:={A} \\…