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Question-114288

Question Number 114288 by mathdave last updated on 18/Sep/20 Commented by bemath last updated on 18/Sep/20 $$\mathrm{56}{xyz}\:=\:\mathrm{3}! \\ $$$$\mathrm{6}{wxyz}\:=\:\mathrm{4}! \\ $$$$\mathrm{7}{qrstu}\:=\mathrm{4}! \\ $$$$\mathrm{8}{abcd}\:=\:\mathrm{4}! \\ $$$$\Sigma\:{number}\:=\:\mathrm{6}+\mathrm{3}×\mathrm{24}\:=\mathrm{78}…

Question-114290

Question Number 114290 by mathdave last updated on 18/Sep/20 Answered by 1549442205PVT last updated on 18/Sep/20 $$\mathrm{From}\:\mathrm{the}\:\mathrm{hypothesis}\:\overline {\mathrm{abc}},\overline {\mathrm{bca}},\overline {\mathrm{cab}} \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}\:\mathrm{we}\:\mathrm{infer}\:\overline {\mathrm{abc}}×\overline {\mathrm{cab}}=\left(\overline {\mathrm{bca}}\right)^{\mathrm{2}}…

Question-179799

Question Number 179799 by yaslm last updated on 02/Nov/22 Answered by MJS_new last updated on 02/Nov/22 $$\int\frac{{dx}}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} \:{x}}\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\:+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\:\Leftrightarrow\:{x}=\mathrm{arctan}\:\frac{{t}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{t}}\:\rightarrow\:{dx}=\frac{\mathrm{2}{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{t}^{\mathrm{2}} +\mathrm{1}}{{t}^{\mathrm{5}/\mathrm{2}}…

For-a-cubic-function-in-the-form-f-x-ax-3-bx-2-cx-d-What-must-be-true-of-a-b-c-and-d-in-order-for-the-function-to-be-able-to-be-converted-to-the-form-f-x-a-x-h-3-k-

Question Number 114253 by Dat_Das last updated on 18/Sep/20 $$\mathrm{For}\:\mathrm{a}\:\mathrm{cubic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}: \\ $$$${f}\left({x}\right)\:=\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d} \\ $$$$\mathrm{What}\:\mathrm{must}\:\mathrm{be}\:\mathrm{true}\:\mathrm{of}\:{a},\:{b},\:{c},\:\mathrm{and}\:{d}\:\mathrm{in} \\ $$$$\mathrm{order}\:\mathrm{for}\:\mathrm{the}\:\mathrm{function}\:\mathrm{to}\:\mathrm{be}\:\mathrm{able}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{converted}\:\mathrm{to}\:\mathrm{the}\:\mathrm{form}: \\ $$$${f}\left({x}\right)\:=\:{a}\left({x}−{h}\right)^{\mathrm{3}} +{k} \\ $$…

y-3y-2y-xsin-x-

Question Number 114225 by mohammad17 last updated on 17/Sep/20 $${y}^{''} −\mathrm{3}{y}^{'} +\mathrm{2}{y}={xsin}\left({x}\right) \\ $$ Answered by mathmax by abdo last updated on 18/Sep/20 $$\mathrm{h}\rightarrow\mathrm{r}^{\mathrm{2}} −\mathrm{3r}+\mathrm{2}=\mathrm{0}\rightarrow\Delta\:=\mathrm{9}−\mathrm{8}=\mathrm{1}\:\Rightarrow\mathrm{r}_{\mathrm{1}}…

Question-114223

Question Number 114223 by mathdave last updated on 17/Sep/20 Answered by mr W last updated on 18/Sep/20 $${a}={g}\left(\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta\right) \\ $$$${v}_{\mathrm{2}} ^{\mathrm{2}} −{v}_{\mathrm{1}} ^{\mathrm{2}} =\mathrm{2}{as} \\…