Question Number 203351 by Mingma last updated on 17/Jan/24 Answered by witcher3 last updated on 17/Jan/24 $$\mathrm{x}\in\mathrm{E}\cap\mathrm{F}\Leftrightarrow\left(\mathrm{x}\in\mathrm{E}\:\&\mathrm{x}\in\mathrm{F}\right) \\ $$$$\Leftrightarrow\left(\mathrm{x}\in\mathbb{N}\:\&\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{15\&}\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\right) \\ $$$$\mathrm{x}\in\mathbb{N}\Rightarrow\mathrm{x}\geqslant\mathrm{0}\:\Rightarrow\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\Rightarrow\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\geqslant\mathrm{1} \\ $$$$\Leftrightarrow\left\{\mathrm{x}\in\mathbb{N};\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{15},\:\mathrm{x}+\mathrm{1}\mid\mathrm{2}\right\},\mathrm{x}=\left\{\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9},\mathrm{11},\mathrm{13},\mathrm{15}\right\} \\ $$…
Question Number 203374 by otchereabdullai@gmail.com last updated on 17/Jan/24 Answered by Calculusboy last updated on 18/Jan/24 $$\boldsymbol{{Solution}}:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}\:\:\:\left(\boldsymbol{{by}}\:\boldsymbol{{using}}\:\boldsymbol{{algebraic}}\:\boldsymbol{{methods}}\right) \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}×\frac{\mathrm{5}\boldsymbol{{x}}}{\mathrm{5}\boldsymbol{{x}}}=\frac{\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}×\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{5}\boldsymbol{{x}}} \\ $$$$\boldsymbol{{NB}}:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tanax}}}{\boldsymbol{{x}}}=\mathrm{1}\:\:\boldsymbol{{then}}\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}}…
Question Number 203375 by a.lgnaoui last updated on 17/Jan/24 $$\:\mathrm{valeur}\:\boldsymbol{\mathrm{x}}? \\ $$$$\left(\measuredangle\mathrm{ECA}\:\:=\mathrm{90}\right) \\ $$ Commented by mr W last updated on 18/Jan/24 $$\mathrm{17}\:\mathrm{sin}\:\mathrm{5}{x}+\mathrm{17}\:\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\mathrm{13} \\ $$$$\mathrm{sin}\:\mathrm{5}{x}+\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\frac{\mathrm{13}}{\mathrm{17}}…
Question Number 203370 by mr W last updated on 17/Jan/24 Commented by mr W last updated on 17/Jan/24 $${Q}\mathrm{203319} \\ $$ Answered by mr W…
Question Number 203367 by mr W last updated on 17/Jan/24 $${if}\:\boldsymbol{{a}}+\boldsymbol{{b}}=\mathrm{198},\:{what}\:{is}\:{the}\:{largest} \\ $$$$\boldsymbol{{integer}}\:{root}\:{which}\:{the}\:{equation} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{ax}}+\boldsymbol{{b}}=\mathrm{0}\:{may}\:{have}? \\ $$ Answered by ajfour last updated on 18/Jan/24…
Question Number 203325 by depressiveshrek last updated on 16/Jan/24 $$\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{2}{x}\right)+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)=\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by esmaeil last updated on 16/Jan/24 $${sin}^{\mathrm{2}} {x}+\left(\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} {x}\overset{\mathrm{2}}…
Question Number 203327 by mr W last updated on 16/Jan/24 Answered by ajfour last updated on 16/Jan/24 Commented by ajfour last updated on 16/Jan/24 $${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…