Question Number 168291 by MikeH last updated on 07/Apr/22 $$\int{t}^{\mathrm{7}} \mathrm{sin}\left({t}^{\mathrm{7}} \right){dt} \\ $$ Answered by Engr_Jidda last updated on 07/Apr/22 $${let}\:{t}^{\mathrm{7}} ={x}\:{then}\:{dt}=\mathrm{7}{t}^{\mathrm{6}} {dx} \\…
Question Number 167979 by nadovic last updated on 31/Mar/22 $$\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\:\mathrm{are}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{table}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{sitting}\:\mathrm{arrangements}\:\mathrm{if} \\ $$$$\:\left({a}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{men}\:\mathrm{must}\:\mathrm{not}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{other}. \\ $$$$\:\left({b}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{circular}\:\mathrm{pattern}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \\…
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Question Number 36784 by Joel579 last updated on 05/Jun/18 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}\:\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}^{\mathrm{2}} \:=\:{n}\:\begin{pmatrix}{\mathrm{2}{n}\:−\:\mathrm{1}}\\{\:\:{n}\:−\:\mathrm{1}}\end{pmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167765 by ArielVyny last updated on 24/Mar/22 $$ \\ $$show that two permutations are conjugate if their matrices are similar Terms of Service…
Question Number 36398 by NECx last updated on 01/Jun/18 $${Consider}\:{triangle}\:{ABC}.{If}\:\mathrm{206} \\ $$$${lines}\:{are}\:{drawn}\:{from}\:{A}\:{to}\:{BC}\:{how} \\ $$$${many}\:{triangles}\:{are}\:{formed}? \\ $$ Commented by Rasheed.Sindhi last updated on 02/Jun/18 $$\mathrm{207}+\mathrm{206}+…+\mathrm{1}=\frac{\mathrm{207}×\mathrm{208}}{\mathrm{2}}=\mathrm{21528} \\…
Question Number 101880 by mr W last updated on 05/Jul/20 $${Find}\:{the}\:{number}\:{of}\:{six}−{digit}\:{odd} \\ $$$${numbers}\:{without}\:{repeated}\:{digits}. \\ $$ Answered by bemath last updated on 05/Jul/20 $$\mathrm{5}×\mathrm{8}×{C}_{\mathrm{4}} ^{\mathrm{8}} ×\mathrm{4}!…
Question Number 101732 by mr W last updated on 04/Jul/20 $$\mathrm{There}\:\mathrm{are}\:\mathrm{10}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{7}\:\mathrm{identical}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{books}\:\mathrm{under}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that} \\ $$$$\mathrm{same}\:\mathrm{books}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually}\:\mathrm{adjacent}. \\ $$ Commented by…
Question Number 101393 by bemath last updated on 02/Jul/20 Answered by 1549442205 last updated on 02/Jul/20 $$\mathrm{Suppose}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{cars}\:\mathrm{manufactured} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{yeat}\:\mathrm{be}\:\mathrm{n}\:\mathrm{units}\:.\mathrm{Then}\:\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{year} \\ $$$$\mathrm{is}\:\frac{\mathrm{3n}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{in}\:\mathrm{the}\:\mathrm{third}\:\mathrm{year}\:\mathrm{is}\:\mathrm{2n}\:.\mathrm{Sum}\:\mathrm{of}\:\mathrm{cars} \\ $$$$\mathrm{manufactured}\:\mathrm{in}\:\mathrm{the}\:\mathrm{3\_years}\:\mathrm{period}\:\mathrm{is} \\ $$$$\frac{\mathrm{9}\boldsymbol{\mathrm{n}}}{\mathrm{2}\:}.\boldsymbol{\mathrm{Hence}}\:\boldsymbol{\mathrm{P}}=\frac{\frac{\mathrm{3}\boldsymbol{\mathrm{n}}}{\mathrm{2}}}{\frac{\mathrm{9}\boldsymbol{\mathrm{n}}}{\mathrm{2}}}=\frac{\mathrm{1}}{\mathrm{3}}\Rightarrow\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{A}}…
Question Number 166787 by nadovic last updated on 27/Feb/22 $$\mathrm{How}\:\mathrm{many}\:\mathrm{permutations}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{EINSTEIN}\:\mathrm{are} \\ $$$$\mathrm{possible}\:\mathrm{if}\:\mathrm{the}\:\mathrm{EIN}\:\mathrm{groups}\:\mathrm{must}\:\mathrm{not} \\ $$$$\mathrm{be}\:\mathrm{next}\:\mathrm{to}\:\mathrm{eachother}? \\ $$ Commented by mr W last updated on…