Question Number 6843 by Tawakalitu. last updated on 30/Jul/16 $$\mathrm{2}^{\mathrm{10}} \:+\:\mathrm{3}^{\mathrm{20}} \:+\:\mathrm{4}^{\mathrm{30}} \:+\:\mathrm{5}^{\mathrm{40}} \:+\:\mathrm{6}^{\mathrm{50}} \:\:\left({mod}\:\mathrm{7}\right)\:=\:? \\ $$ Commented by prakash jain last updated on 31/Jul/16…
Question Number 6841 by Tawakalitu. last updated on 30/Jul/16 $${Integrate}:\:\:{x}\:{sec}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right) \\ $$$$ \\ $$ Commented by Tawakalitu. last updated on 30/Jul/16 $${I}\:{have}\:{solve}\:{this}\:{one}.\:{i}\:{got}\:…\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:{tan}\left({x}^{\mathrm{2}} \right)\:+\:{C}…
Question Number 6838 by Tawakalitu. last updated on 30/Jul/16 $${Find}\:{the}\:{value}\:{of}\:{x} \\ $$$$\mathrm{4}^{{x}} \:=\:\frac{\mathrm{243}}{{x}} \\ $$ Commented by Yozzii last updated on 31/Jul/16 $$\mathrm{4}^{{x}} =\frac{\mathrm{243}}{{x}} \\…
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Question Number 6834 by nburiburu last updated on 30/Jul/16 $${a}\in\mathbb{Z},\:\left(\mathrm{2}{a}^{\mathrm{3}} +\mathrm{3}{a}^{\mathrm{2}} −\mathrm{3}{a}+\mathrm{7}\::\:{a}^{\mathrm{2}} +{a}−\mathrm{2}\right)\neq\mathrm{1}\:\Leftrightarrow\:{a}=\mathrm{3}{k}+\mathrm{1},\:{k}\in\mathbb{Z} \\ $$ Commented by Yozzii last updated on 30/Jul/16 $${All}\:{integers}\:{can}\:{be}\:{written}\:{in}\:{one} \\ $$$${of}\:{the}\:{following}\:{forms}\:{since}…
Question Number 137907 by peter frank last updated on 08/Apr/21 Answered by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{1}+{lnx}}{{x}}{dx}=\int_{\mathrm{1}} ^{{e}} \left(\frac{\mathrm{1}}{{x}}+\frac{{lnx}}{{x}}\right){dx} \\ $$$$=\left[{lnx}+\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{2}}\right]_{\mathrm{1}}…
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Question Number 6832 by Tawakalitu. last updated on 30/Jul/16 $${What}\:{remainder}\:{does}\:\mathrm{3}^{\mathrm{6}{n}} \:−\:\mathrm{2}^{\mathrm{6}{n}} \:\:{leave}\:{when}\:{divided}\:{by}\:\mathrm{35}\:{for}\: \\ $$$${any}\:{value}\:{of}\:{n}\: \\ $$ Commented by Yozzii last updated on 30/Jul/16 $$\mathrm{3}^{\mathrm{6}{n}} −\mathrm{2}^{\mathrm{6}{n}}…
Question Number 6831 by Tawakalitu. last updated on 30/Jul/16 $${Find}\:{the}\:\mathrm{100}{th}\:{digits}\:{of}\:{this}\:{sum}\: \\ $$$$\mathrm{1}\:+\:\mathrm{50}\:+\:\mathrm{50}^{\mathrm{2}} \:+\:…..\:+\:\mathrm{50}^{\mathrm{999}} \\ $$ Commented by prakash jain last updated on 31/Jul/16 $$\mathrm{How}\:\mathrm{did}\:\mathrm{you}\:\mathrm{get} \\…
Question Number 6830 by Rasheed Soomro last updated on 30/Jul/16 $${A},\:{B},\:{and}\:{C}\:{are}\:{three}\:{non}-{collinear}\:{points}\:{such} \\ $$$${that}\:\mid{AB}\mid={c}\:,\:\mid{BC}\mid={a}\:\:{and}\:\:\mid{CA}\mid={b}. \\ $$$${What}\:{will}\:{be}\:{the}\:{condition}\:{for}\:{a}\:{point}\:{D}\:{to}\:{be} \\ $$$${concircle}\:{with}\:{A},\:{B}\:\:{and}\:{C}\:{when}\:{all}\:{the}\:{four} \\ $$$${points}\:{belong}\:{to}\:{same}\:{plane}? \\ $$ Terms of Service Privacy…