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Question Number 177931 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{the}\:\mathrm{principle}\:\mathrm{of}\: \\ $$$$\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}.\mathrm{4}.\mathrm{7}+\mathrm{2}.\mathrm{5}.\mathrm{8}+\mathrm{3}.\mathrm{6}.\mathrm{9}+...\mathrm{n}\left(\mathrm{n}+\mathrm{3}\right)\left(\mathrm{n}+\mathrm{6}\right) \\ $$$$=\frac{\mathrm{n}}{\mathrm{4}}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{6}\right)\left(\mathrm{n}+\mathrm{7}\right) \\ $$
Question Number 177930 Answers: 2 Comments: 0
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{LCM}\: \\ $$$$\mathrm{14a}^{\mathrm{2}} \mathrm{b}^{\mathrm{3}} \mathrm{c}^{\mathrm{4}} ,\mathrm{20ab}^{\mathrm{4}} \mathrm{c}^{\mathrm{4}} \:\mathrm{and} \\ $$$$\:\mathrm{35a}^{\mathrm{5}} \mathrm{b}^{\mathrm{3}} \mathrm{c} \\ $$
Question Number 177929 Answers: 1 Comments: 0
$$\mathrm{Find}\:\mathrm{LCM}\: \\ $$$$\mathrm{3y}+\mathrm{12},\mathrm{y}^{\mathrm{2}} −\mathrm{16}\:\mathrm{and}\:\mathrm{y}^{\mathrm{4}} −\mathrm{64y} \\ $$
Question Number 177928 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\left[\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}} +\mathrm{3y}}\right]\boldsymbol{\div}\left[\frac{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} −\mathrm{3xy}}{\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}} }\right]×\left[\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }\right]=\mathrm{xy} \\ $$
Question Number 177922 Answers: 1 Comments: 0
Question Number 177913 Answers: 0 Comments: 0
$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{if}}\:\:\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} =\int\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:\:\:\boldsymbol{\mathrm{and}}\:\: \\ $$$$\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} \:=\:−\frac{\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{cosx}}\:}{\boldsymbol{\mathrm{n}}}\:+\frac{\boldsymbol{\mathrm{sin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+\mathrm{f}\left(\mathrm{n}\right)\mathrm{I}_{\mathrm{n}−\mathrm{2}} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{f}\left(\mathrm{n}\right)\:=\:? \\ $$
Question Number 177914 Answers: 2 Comments: 0
$$\left(\mathrm{1}\right)\:\:\:\:\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{4}{sin}\mathrm{13}\:{cos}\mathrm{13}}=? \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$
Question Number 177910 Answers: 2 Comments: 0
Question Number 177906 Answers: 1 Comments: 0
$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{5}}\right)\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{5}}\right)}{\mathrm{sin}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$
Question Number 177900 Answers: 1 Comments: 0
Question Number 177890 Answers: 0 Comments: 2
Question Number 177886 Answers: 1 Comments: 1
Question Number 177884 Answers: 1 Comments: 0
Question Number 177880 Answers: 1 Comments: 0
Question Number 177875 Answers: 0 Comments: 1
Question Number 177873 Answers: 2 Comments: 0
$${solve}\:{for}\:{x}\in\mathbb{R} \\ $$$$\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+{x}}}}}}={x} \\ $$
Question Number 177870 Answers: 0 Comments: 0
Question Number 177867 Answers: 1 Comments: 0
Question Number 177866 Answers: 2 Comments: 0
Question Number 177865 Answers: 2 Comments: 0
Question Number 177859 Answers: 1 Comments: 0
Question Number 177856 Answers: 1 Comments: 0
$${p}\left({x}\right)+{p}\left({x}−\mathrm{1}\right)=\mathrm{2}{x}+\mathrm{4} \\ $$$${p}\left({x}\right)=? \\ $$
Question Number 177848 Answers: 2 Comments: 3
Question Number 177835 Answers: 1 Comments: 0
Question Number 177832 Answers: 1 Comments: 0
Question Number 177828 Answers: 0 Comments: 0
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