Question Number 203327 by mr W last updated on 16/Jan/24 Answered by ajfour last updated on 16/Jan/24 Commented by ajfour last updated on 16/Jan/24 $${What}\:{would}\:{r}\:{be}\:{in}\:{this}\:{case}?…
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Question Number 203321 by SonGoku last updated on 16/Jan/24 $$\mathrm{Help}-\mathrm{me}! \\ $$$$\: \\ $$$$\mathrm{Observe}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{below}\:\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{widthof}\:\mathrm{a}\:\mathrm{lake}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{following}\:\mathrm{data}: \\ $$$$\: \\ $$$$\left(\mathrm{AB}\right)\mathrm{m};\:\hat {\mathrm{C}}\:=\:\mathrm{39}°\mathrm{52}'\mathrm{12}'' \\ $$$$\left(\mathrm{BC}\:−\:\mathrm{257}.\mathrm{5}\right)\mathrm{m};\:\hat {\mathrm{A}}\:=\:\mathrm{97}°\mathrm{7}'\mathrm{56}'' \\ $$$$\left(\mathrm{CA}\:−\:\mathrm{30}\right)\mathrm{m};\:\hat {\mathrm{B}}\:=\:\mathrm{42}°\mathrm{59}'\mathrm{52}''…
Question Number 203319 by ajfour last updated on 16/Jan/24 Commented by mr W last updated on 16/Jan/24 $$\mathrm{4}\:{equal}\:{spheres}\:{inside}\:{a}\:{regular} \\ $$$${tetrahedron}\:{with}\:{edge}\:{length}\:{a}? \\ $$ Commented by ajfour…
Question Number 203329 by Calculusboy last updated on 16/Jan/24 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{ranges}}\:\boldsymbol{{of}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{which}}\: \\ $$$$\boldsymbol{{series}}\:\boldsymbol{{convergent}}\:\boldsymbol{{or}}\:\boldsymbol{{divergent}} \\ $$$$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(\boldsymbol{{n}}+\mathrm{1}\right)}{\boldsymbol{{n}}^{\mathrm{3}} }\boldsymbol{{x}}^{\boldsymbol{{n}}} \\ $$ Answered by Mathspace last updated on…
Question Number 203313 by CrispyXYZ last updated on 16/Jan/24 $${a}_{{n}+\mathrm{1}} ={a}_{{n}} ^{\mathrm{2}} +\mathrm{2}{a}_{{n}} −\mathrm{2},\:{a}_{\mathrm{1}} =\mathrm{3}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\Sigma\:\frac{\mathrm{1}}{{a}_{{n}} +\mathrm{2}}\:\leqslant\:\frac{\mathrm{3}}{\mathrm{10}}. \\ $$ Answered by witcher3 last updated…
Question Number 203330 by Calculusboy last updated on 16/Jan/24 Answered by MM42 last updated on 16/Jan/24 $$={lim}_{{x}\rightarrow\mathrm{1}} \:\frac{{sin}\left({x}−\mathrm{1}\right)}{\left({x}−\mathrm{1}\right)}\:×\frac{\mathrm{1}}{{x}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\:\:\checkmark \\ $$ Commented by Calculusboy last updated…
Question Number 203308 by talminator2856792 last updated on 15/Jan/24 $$\:\:\mathrm{my}\:\mathrm{iq}\:\mathrm{is}\:\mathrm{not}\:\mathrm{good}\:\mathrm{enough}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{mathematician}.\:\: \\ $$$$\:\:\mathrm{i}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{what}\:\mathrm{to}\:\mathrm{do}\:\mathrm{with}\:\mathrm{my}\:\mathrm{life}\:\mathrm{now}.\:\: \\ $$$$\:\:\mathrm{what}\:\mathrm{is}\:\mathrm{there}\:\mathrm{for}\:\mathrm{me}.\:\: \\ $$ Answered by behi834171 last updated on 16/Jan/24 $${hi} \\…
Question Number 203309 by hardmath last updated on 15/Jan/24 $$\mathrm{If}\:\:\:\mathrm{z}_{\mathrm{1}} =\:\mathrm{3}\:+\:\mathrm{3}\sqrt{\mathrm{3}}\:\boldsymbol{\mathrm{i}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}_{\mathrm{2}} =\:-\mathrm{1}\:−\:\sqrt{\mathrm{3}}\:\boldsymbol{\mathrm{i}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{z}_{\mathrm{1}} ^{\:\mathrm{3}} }{\mathrm{z}_{\mathrm{2}} ^{\:\mathrm{6}} }\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated…
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