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Category: Arithmetic

If-x-y-z-then-prove-the-following-inequality-x-2-2-y-2-2-z-2-2-9-xy-yz-xz-

Question Number 120847 by Jamshidbek2311 last updated on 03/Nov/20 $${If}\:{x},{y},{z}\:\:{then}\:{prove}\:{the}\:{following} \\ $$$${inequality} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({y}^{\mathrm{2}} +\mathrm{2}\right)\left({z}^{\mathrm{2}} +\mathrm{2}\right)=\mathrm{9}\left({xy}+{yz}+{xz}\right) \\ $$ Commented by Jamshidbek2311 last updated on…

QUIZ-If-the-sum-of-the-numbers-1-to-100-can-be-calculated-with-Carl-Gauss-s-method-then-How-do-we-calculate-the-sum-of-the-numbers-starting-from-2-and-going-up-to-100-by-twos-in-an-easy-way-with-the

Question Number 186348 by test1234 last updated on 03/Feb/23 $$\mathrm{Q}{UIZ}: \\ $$$${If}\:{the}\:{sum}\:{of}\:{the}\:{numbers}\:\mathrm{1}\:{to}\:\mathrm{100}\:{can} \\ $$$${be}\:{calculated}\:{with}\:{Carl}\:{Gauss}'{s}\:{method}, \\ $$$${then}\:{How}\:{do}\:{we}\:{calculate}\:{the}\:{sum}\:{of}\:{the} \\ $$$${numbers}\:{starting}\:{from}\:\mathrm{2}\:{and}\:{going}\:{up}\:{to} \\ $$$$\mathrm{100}\:{by}\:{twos}\:{in}\:{an}\:{easy}\:{way}\:{with}\:{the}\:{same} \\ $$$${method}? \\ $$$${Or}\:\mathrm{2}+\mathrm{4}+\mathrm{6}+\mathrm{8}+\mathrm{10}+…+\mathrm{100}=? \\…

0-dx-x-1-x-2-n-

Question Number 120654 by peter frank last updated on 01/Nov/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\left[\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right]^{\mathrm{n}} } \\ $$ Answered by mindispower last updated on 01/Nov/20 $${x}={sh}\left({t}\right),{n}>\mathrm{1}…

Question-120560

Question Number 120560 by peter frank last updated on 01/Nov/20 Answered by mathmax by abdo last updated on 01/Nov/20 $$\mathrm{I}=\int\:\:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:\Rightarrow\mathrm{I}\:=\int\:\:\frac{\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{2}}}{\mathrm{1}+\frac{\mathrm{1}+\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{2}}}\mathrm{dx}\:=\int\:\:\frac{\mathrm{2}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{3}+\mathrm{cos}\left(\mathrm{2x}\right)}\mathrm{dx} \\ $$$$=_{\mathrm{tanx}=\mathrm{t}} \:\:\:\:\int\:\:\frac{\mathrm{2}−\frac{\mathrm{1}−\mathrm{t}^{\mathrm{2}}…

It-takes-Musa-3-days-to-buid-a-room-while-it-takes-John-4-days-How-many-days-will-it-takes-both-of-them-

Question Number 120502 by Engr_Jidda last updated on 31/Oct/20 $$\mathrm{It}\:\mathrm{takes}\:\mathrm{Musa}\:\mathrm{3}\:\mathrm{days}\:\mathrm{to}\:\mathrm{buid}\:\mathrm{a}\:\mathrm{room} \\ $$$$\mathrm{while}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{John}\:\mathrm{4}\:\mathrm{days}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}? \\ $$ Answered by Olaf last updated on 31/Oct/20 $$\mathrm{3}×\mathrm{4}\:=\:\mathrm{12}. \\…

Determine-the-sum-of-the-1st-nth-term-of-the-Sequence-1-4-10-22-46-Almighty-Formula-

Question Number 120363 by Lordose last updated on 30/Oct/20 $$ \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{1st}\:\mathrm{nth}\:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{Sequence} \\ $$$$ \\ $$$$\:\mathrm{1},\mathrm{4},\mathrm{10},\mathrm{22},\mathrm{46},…. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bigstar\mathrm{Almighty}\:\mathrm{Formula} \\ $$ Answered…