Question Number 139874 by bramlexs22 last updated on 02/May/21 $$\begin{cases}{\mathrm{xy}+\mathrm{24}\:=\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{y}}}\\{\mathrm{xy}−\mathrm{6}\:=\:\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{x}}}\end{cases} \\ $$ Answered by EDWIN88 last updated on 03/May/21 $$\left(\mathrm{1}\right)\mathrm{xy}\:+\mathrm{24}\:=\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{y}}\:\:\:\:\:\:\left(\mathrm{2}\right)\:\mathrm{xy}−\mathrm{6}\:=\:\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{x}} \\…
Question Number 74337 by Maclaurin Stickker last updated on 22/Nov/19 $${find}\:{the}\:{contracted}\:{form}\:{of}: \\ $$$$\begin{pmatrix}{{n}}\\{{p}}\end{pmatrix}+\mathrm{2}\begin{pmatrix}{\:\:\:{n}}\\{{p}+\mathrm{1}}\end{pmatrix}+\begin{pmatrix}{\:\:\:{n}}\\{{p}+\mathrm{2}}\end{pmatrix} \\ $$ Answered by MJS last updated on 23/Nov/19 $$\begin{pmatrix}{{n}}\\{{p}}\end{pmatrix}\:=\frac{{n}!}{{p}!\left({n}−{p}\right)!}=\frac{{n}!\left({p}+\mathrm{1}\right)\left({p}+\mathrm{2}\right)}{{p}!\left({n}−{p}\right)!\left({p}+\mathrm{1}\right)\left({p}+\mathrm{2}\right)} \\ $$$$\mathrm{2}\begin{pmatrix}{{n}}\\{{p}+\mathrm{1}}\end{pmatrix}\:=\frac{\mathrm{2}{n}!}{\left({p}+\mathrm{1}\right)!\left({n}−{p}−\mathrm{1}\right)!}=\frac{\mathrm{2}{n}!\left({n}−{p}\right)}{{p}!\left({n}−{p}\right)!\left({p}+\mathrm{1}\right)}=…
Question Number 74334 by malikmasood3535@gmail.com last updated on 22/Nov/19 $$\int{te}^{{t}} \mathrm{cos}\:{e}^{{t}} .{e}^{{t}} {dt} \\ $$ Commented by prakash jain last updated on 23/Nov/19 $$\mathrm{write}\:\mathrm{cos}\:{t}=\frac{{e}^{{it}} +{e}^{−{it}}…
Question Number 139868 by I want to learn more last updated on 01/May/21 Answered by TheSupreme last updated on 02/May/21 $$\mathrm{10}\:{question} \\ $$$${P}\left({Answer}\:{correct}\:{per}\:{question}\right)=\mathrm{0}.\mathrm{5} \\ $$$${P}\left({N}\:{Answer}\:{correct}\right)=\begin{pmatrix}{\mathrm{10}}\\{{n}}\end{pmatrix}\mathrm{0}.\mathrm{5}^{\mathrm{10}}…
Question Number 74335 by arthur.kangdani@gmail.com last updated on 22/Nov/19 $$\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{6}}{\mathrm{7}}=?\: \\ $$$${The}\:{end}\:{result}\:{must}\:{in}\:{the} \\ $$$$\boldsymbol{{mixed}}\:\boldsymbol{{fraction}}. \\ $$ Answered by arthur.kangdani@gmail.com last updated on 26/Nov/19 $$\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{6}}{\mathrm{7}}=\frac{\mathrm{11}}{\mathrm{2}}×\frac{\mathrm{6}}{\mathrm{7}}=\frac{\mathrm{66}}{\mathrm{14}}=\frac{\mathrm{33}}{\mathrm{7}}=\mathrm{4}\frac{\mathrm{5}}{\mathrm{7}} \\…
Question Number 8798 by javawithfish last updated on 28/Oct/16 $${please}\:{solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} {f}\left({x}\right){dx}={g}\left({x}\right) \\ $$ Commented by Yozzias last updated on 28/Oct/16 $$\mathrm{Impossible}\:\mathrm{unless}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)=\mathrm{0}\:\forall\mathrm{x}\in\mathbb{R}.\:\mathrm{The}\:\mathrm{definite}\: \\…
Question Number 8794 by faster1998 last updated on 28/Oct/16 $${f}\left({x}\right)=×^{\frac{\mathrm{4}}{\mathrm{3}}} −\mathrm{2}×^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Commented by ridwan balatif last updated on 28/Oct/16 $$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} .\mathrm{x}−\mathrm{2x}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}}…
Question Number 139867 by Maclaurin Stickker last updated on 01/May/21 $${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{0} \\ $$$${a}^{\mathrm{12}} +{b}^{\mathrm{12}} +{c}^{\mathrm{12}} =\mathrm{8} \\ $$$${a}^{\mathrm{6}} +{b}^{\mathrm{6}} +{c}^{\mathrm{6}} =? \\…
Question Number 74328 by arthur.kangdani@gmail.com last updated on 22/Nov/19 Answered by ajfour last updated on 22/Nov/19 $${x}=\frac{\begin{vmatrix}{\mathrm{10}}&{\mathrm{2}}&{\mathrm{4}}\\{\mathrm{4}}&{\mathrm{10}}&{\mathrm{7}}\\{\mathrm{9}}&{\mathrm{5}}&{\mathrm{16}}\end{vmatrix}_{} }{\begin{vmatrix}{\mathrm{6}}&{\mathrm{2}}&{\mathrm{4}}\\{\mathrm{9}}&{\mathrm{10}}&{\mathrm{7}}\\{\mathrm{12}}&{\mathrm{5}}&{\mathrm{16}}\end{vmatrix}^{} } \\ $$$$\Rightarrow\:\:{x}=\frac{\mathrm{10}\left(\mathrm{160}−\mathrm{35}\right)−\mathrm{2}\left(\mathrm{64}−\mathrm{63}\right)+\mathrm{4}\left(\mathrm{20}−\mathrm{90}\right)}{\mathrm{6}\left(\mathrm{160}−\mathrm{35}\right)−\mathrm{2}\left(\mathrm{144}−\mathrm{84}\right)+\mathrm{4}\left(\mathrm{45}−\mathrm{120}\right)} \\ $$$$\:\:\:\:\:{x}=\frac{\mathrm{1250}−\mathrm{2}−\mathrm{280}}{\mathrm{750}−\mathrm{120}−\mathrm{300}}\:=\:\frac{\mathrm{968}}{\mathrm{330}}\:=\:\frac{\mathrm{88}}{\mathrm{30}} \\ $$$$…..…
Question Number 74329 by Learner-123 last updated on 22/Nov/19 $${Solve}\:: \\ $$$${ax}+{by}={r} \\ $$$${bx}−{ay}={s} \\ $$ Commented by Learner-123 last updated on 22/Nov/19 $${any}\:{short}\:{method}\:{when}\:{a},{b},{r},{s}\:{are}\: \\…