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Question Number 201172 Answers: 1 Comments: 0
Question Number 201166 Answers: 1 Comments: 0
Question Number 201162 Answers: 4 Comments: 0
Question Number 201152 Answers: 4 Comments: 0
$${if}\:\:\mathrm{4}^{{x}} +\mathrm{4}^{−{x}} =\mathrm{7} \\ $$$${then}\:\:\:\mathrm{8}^{{x}} +\mathrm{8}^{−{x}} =? \\ $$
Question Number 201150 Answers: 2 Comments: 0
Question Number 201149 Answers: 1 Comments: 0
Question Number 201146 Answers: 1 Comments: 4
Question Number 201144 Answers: 2 Comments: 0
$$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{45}}{\mathrm{28}}\right)^{\mathrm{6}} = \\ $$
Question Number 201140 Answers: 1 Comments: 0
$$\boldsymbol{{If}}\:\underset{−} {\boldsymbol{{R}}}=\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}\underset{−} {\boldsymbol{{i}}}−\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} \boldsymbol{{z}}\underset{−} {\boldsymbol{{j}}}+\boldsymbol{{xy}}^{\mathrm{2}} \boldsymbol{{z}}^{\mathrm{2}} \underset{−} {\boldsymbol{{k}}},\:\boldsymbol{{find}}\:\mid\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dx}}^{\mathrm{2}} }×\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dy}}^{\mathrm{2}} }\mid\:\: \\ $$$$\boldsymbol{{at}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\left(\mathrm{2},\mathrm{1},−\mathrm{2}\right) \\ $$
Question Number 201139 Answers: 1 Comments: 1
Question Number 201135 Answers: 1 Comments: 0
Question Number 201134 Answers: 0 Comments: 0
$$\: \\ $$$$\:\:\:\:\:\:{S}\::\:\:{Area}\:\:{of}\:\:\:{A}\overset{\Delta} {{B}C} \\ $$$$\:\:\:\:\:{in}\:\:\:\:{A}\overset{\Delta} {{B}C}\:\::\:\:\:\frac{{a}^{\:\mathrm{2}} }{\mathrm{4}{S}}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({cot}\left({B}\right)+{cot}\left({C}\right)\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\:\mathrm{2}} }{\mathrm{4}{S}}\:=\:\frac{\:{a}^{\:\mathrm{2}} }{\mathrm{4}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:{bc}\:{sin}\left({A}\right)\right)}=\frac{\mathrm{4}{R}^{\mathrm{2}} {sin}^{\:\mathrm{2}} \left({A}\right)}{\mathrm{8}{R}^{\:\mathrm{2}} {sin}\left({B}\right){sin}\left({C}\right){sin}\left({A}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{{sin}\:\left({A}\:\right)}{\mathrm{2}{sin}\left({B}\right){sin}\left({C}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\overset{{A}+{B}+{C}=\pi} {=}\:\:\frac{{sin}\left({B}\right){cos}\left({C}\right)+{cosBsin}\left({C}\right)}{\mathrm{2}{sin}\left({B}\right){sin}\left({C}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({cot}\left({B}\right)+{cot}\left({C}\right)\right)\:\:\:\blacksquare \\ $$$$ \\ $$
Question Number 201133 Answers: 0 Comments: 1
$$ \\ $$$$ \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{1}} ^{\:\mathrm{3}} \frac{\:\mathrm{1}}{\:\sqrt{\left({x}−\mathrm{1}\:\right)^{\mathrm{3}} }\:+\:\sqrt{\left({x}+\mathrm{1}\:\right)^{\mathrm{3}} }}\:{dx}=\:?\:\:\: \\ $$$$ \\ $$
Question Number 201112 Answers: 1 Comments: 0
Question Number 201110 Answers: 1 Comments: 0
$$\int\frac{\mathrm{1}}{\:\sqrt{\left({x}−{a}\right)^{\mathrm{3}} }+\sqrt{\left({x}+{a}\right)^{\mathrm{3}} }}{dx} \\ $$
Question Number 201108 Answers: 0 Comments: 6
Question Number 201106 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:{calculate}\:... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\left(\mathrm{2}{n}\:\right)}{\mathrm{2}^{\:{n}} .{n}}\:=\:? \\ $$$$ \\ $$
Question Number 201107 Answers: 0 Comments: 6
$${two}\:{weels},\:{those}\:{have}\:{the}\:{same}\:{materials}, \\ $$$${with}\:{radii}:\boldsymbol{{r}}_{\mathrm{1}} =\mathrm{4}\:{and}\:\boldsymbol{{r}}_{\mathrm{2}} =\mathrm{14} \\ $$$${are}\:{starting}\:{to}\:{move}\:{on}\:{a}\:{surface},{with} \\ $$$${the}\:{same}\:{velocity},{from}:\boldsymbol{{x}}=\mathrm{0}\:{to}\:\boldsymbol{{x}}=\mathrm{20}. \\ $$$${the}\:{surface}\:{has}\:{no}\:{friction}. \\ $$$${wich}\:{one}\:{arrives}\:{faster}? \\ $$$${any}\:{informations}\:{needed}? \\ $$
Question Number 201091 Answers: 1 Comments: 2
Question Number 201184 Answers: 1 Comments: 0
Question Number 201081 Answers: 4 Comments: 0
Question Number 201070 Answers: 1 Comments: 0
$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}} \\ $$$$ \\ $$$${show}\:\:{that}\:{the}\:{sequence}\:{converges}\:{and} \\ $$$${determine}\:{the}\:{limit}\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Question Number 201065 Answers: 2 Comments: 1
Question Number 201047 Answers: 0 Comments: 0
Question Number 201044 Answers: 2 Comments: 0
$$ \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \left({x}−{y}\:\right)^{\mathrm{2}} {sin}^{\:\mathrm{2}} \:\left(\:{x}+{y}\:\right){dxdy}=? \\ $$
Question Number 201041 Answers: 1 Comments: 0
$$\mathrm{4}\left(\mathrm{33}\right)\mathrm{7} \\ $$$$\mathrm{4}\left(\mathrm{24}\right)\mathrm{6} \\ $$$$\mathrm{5}\left(\:?\:\right)\mathrm{4} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\:\:\:\:\:{b}\right)\mathrm{18}\:\:\:\:\:{c}\right)\mathrm{27}\:\:\:\:\:{d}\right)\mathrm{36} \\ $$
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