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Question-203573

Question Number 203573 by sonukgindia last updated on 22/Jan/24 Answered by esmaeil last updated on 22/Jan/24 $$\int−{e}^{{cosx}} \left(\mathrm{1}−{cos}^{\mathrm{2}} {x}−{cosx}\right){dx} \\ $$$$\int−{e}^{{cosx}} \left({sin}^{\mathrm{2}} {x}−{cosx}\right){dx}= \\ $$$$\int−{e}^{{cosx}}…

Reduce-a-differential-equation-x-ax-bx-cx-0-where-a-b-c-are-constants-to-an-equivalent-system-of-first-order-equation-x-1-x-x-2-x-x-3-x-Thank-you-

Question Number 203568 by Mastermind last updated on 22/Jan/24 $$\mathrm{Reduce}\:\mathrm{a}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{x}^{'''} \:+\:\mathrm{ax}^{''} \:+\:\mathrm{bx}^{'} \:+\:\mathrm{cx}\:=\:\mathrm{0}\:\left(\mathrm{where}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\right. \\ $$$$\left.\mathrm{constants}\right)\:\mathrm{to}\:\mathrm{an}\:\mathrm{equivalent}\:\mathrm{system}\:\mathrm{of}\:\mathrm{first} \\ $$$$\mathrm{order}\:\mathrm{equation}. \\ $$$$\mathrm{x}_{\mathrm{1}} =\:\mathrm{x},\:\mathrm{x}_{\mathrm{2}} \:=\:\mathrm{x}^{'} ,\:\mathrm{x}_{\mathrm{3}} \:=\:\mathrm{x}^{''}…

Question-203569

Question Number 203569 by cherokeesay last updated on 22/Jan/24 Commented by a.lgnaoui last updated on 22/Jan/24 $$\mathrm{2}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\right)=\mathrm{360} \\ $$$$\:\:\left(\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\right)=\mathrm{180} \\ $$$$\:\:\left(\mathrm{a}+\mathrm{b}\right)=\mathrm{180}−\left(\mathrm{c}+\mathrm{d}\right) \\ $$$$ \\ $$$$\:\:\:\:\mathrm{tan}\:\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}\right)=−\mathrm{tan}\:\left(\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{d}}\right)…

Suggested-solution-method-to-question-203502-ze-z-1-Obviously-the-only-real-solution-is-z-W-1-567143290-z-a-bi-b-0-a-bi-e-a-bi-1-a-bi-cos-b-isin-b-e-a-1-e-a-acos-b-bsin-b-e-a-asin-b-

Question Number 203570 by Frix last updated on 22/Jan/24 $$\mathrm{Suggested}\:\mathrm{solution}\:\mathrm{method}\:\mathrm{to} \\ $$$$\mathrm{question}\:\mathrm{203502} \\ $$$$ \\ $$$${z}\mathrm{e}^{{z}} =\mathrm{1} \\ $$$$\mathrm{Obviously}\:\mathrm{the}\:\mathrm{only}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{is} \\ $$$${z}={W}\left(\mathrm{1}\right)\approx.\mathrm{567143290} \\ $$$$ \\ $$$${z}={a}+{b}\mathrm{i}\wedge{b}\neq\mathrm{0}…

Solve-the-following-equation-simultaneously-and-find-the-stationary-points-2xy-2-c-2-4x-3-y-2-2xy-4-0-1-2x-2-yc-2-2x-4-y-4x-2-y-3-0-2-Please-I-need-a-well-detail-cal

Question Number 203565 by Mastermind last updated on 22/Jan/24 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation}\:\mathrm{simultaneously} \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{stationary}\:\mathrm{points}: \\ $$$$\mathrm{2xy}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} \:−\:\mathrm{4x}^{\mathrm{3}} \mathrm{y}^{\mathrm{2}} \:−\:\mathrm{2xy}^{\mathrm{4}} \:=\:\mathrm{0}\:—–\left(\mathrm{1}\right) \\ $$$$\mathrm{2x}^{\mathrm{2}} \mathrm{yc}^{\mathrm{2}} \:−\:\mathrm{2x}^{\mathrm{4}} \mathrm{y}\:−\:\mathrm{4x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}}…

P-is-a-prime-number-P-gt-1000-If-P-r-mod-1000-how-many-value-of-r-

Question Number 203566 by BaliramKumar last updated on 22/Jan/24 $$'\mathrm{P}'\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\left(\mathrm{P}>\mathrm{1000}\right).\: \\ $$$$\mathrm{If}\:\:\:\mathrm{P}\:\equiv\:\mathrm{r}\:\left(\mathrm{mod}\:\mathrm{1000}\right).\:\mathrm{how}\:\mathrm{many}\:\mathrm{value}\:\mathrm{of}\:'\mathrm{r}'. \\ $$ Answered by MM42 last updated on 22/Jan/24 $${p}=\mathrm{1000}{k}+{r}\:\:\&\:\:\mathrm{0}<{r}<\mathrm{1000}\: \\ $$$$\Rightarrow“{p}''\:{is}\:{prime}\:{number}\: \\…