Question and Answers Forum

All Questions   Topic List

OthersQuestion and Answers: Page 63

Question Number 99853    Answers: 2   Comments: 0

(1/1^2 )+(1/2^2 )+(1/3^2 )+(1/4^2 )+(1/6^2 )+.....∞=?

$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{2}} }+.....\infty=? \\ $$

Question Number 99670    Answers: 0   Comments: 2

Question Number 99669    Answers: 0   Comments: 0

Question Number 99623    Answers: 1   Comments: 1

obtain the modulus and arguement of (((1−i)^4 )/((2+2(√(3i)^3 ))))

$${obtain}\:{the}\:{modulus}\:{and}\:{arguement}\:{of} \\ $$$$\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{4}} }{\left(\mathrm{2}+\mathrm{2}\sqrt{\left.\mathrm{3}{i}\right)^{\mathrm{3}} }\right.} \\ $$

Question Number 99568    Answers: 1   Comments: 4

Find the value of (√(2+(√(2+(√(2+(√(2+(√(2+(√(2+))))))))))))...∞ by cos function

$${Find}\:{the}\:{value}\:{of}\:\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+}}}}}}...\infty\:\:\:\:\:{by}\:{cos}\:{function} \\ $$

Question Number 99485    Answers: 2   Comments: 0

∫tan^(1/5) xdx

$$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {xdx} \\ $$

Question Number 99411    Answers: 0   Comments: 2

Solve the equation xa^(1/x) +(1/x)a^x =2a where,a{−1,0,1}

$${Solve}\:{the}\:{equation} \\ $$$${xa}^{\frac{\mathrm{1}}{{x}}} +\frac{\mathrm{1}}{{x}}{a}^{{x}} =\mathrm{2}{a} \\ $$$${where},{a}\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\} \\ $$

Question Number 99368    Answers: 0   Comments: 1

please sir my problem in my solution is where?

$${please}\:{sir}\:{my}\:{problem}\:{in}\:{my}\:{solution} \\ $$$${is}\:{where}? \\ $$

Question Number 99314    Answers: 0   Comments: 2

Find[]the[]value[]of (√(1+2(√(1+3(√(1+4(√(1+5(√(1+6(√(1+7))))))))))))....∞

$${Find}\left[\right]{the}\left[\right]{value}\left[\right]{of} \\ $$$$\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\mathrm{5}\sqrt{\mathrm{1}+\mathrm{6}\sqrt{\mathrm{1}+\mathrm{7}}}}}}}....\infty \\ $$

Question Number 99097    Answers: 0   Comments: 1

Hello verry nice day for all of you god bless You pleas Can you use black Color shen You post Quation or Give answer is verry hard to read withe other colors

$${Hello}\: \\ $$$${verry}\:{nice}\:{day}\:{for}\:{all}\:{of}\:{you}\:{god}\:{bless}\:{You} \\ $$$${pleas}\:{Can}\:{you}\:{use}\:{black}\:{Color}\:{shen}\:{You}\:{post}\:{Quation}\: \\ $$$${or}\:{Give}\:{answer}\:{is}\:{verry}\:{hard}\:{to}\:{read}\:{withe}\:{other}\:{colors} \\ $$

Question Number 98953    Answers: 2   Comments: 0

Given f(x)=sin^2 x find the expansion of f(x) up to the n^(th) term.

$$\mathcal{G}\mathrm{iven}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\mathrm{find}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}. \\ $$

Question Number 98924    Answers: 0   Comments: 0

Prove that if a+ bi is a root to pz^2 + qz + r = 0 , where a,b,p,q,r ∈R then a−bi is also a root to that equation.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{a}+\:{bi}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to} \\ $$$$\:{pz}^{\mathrm{2}} \:+\:{qz}\:+\:{r}\:=\:\mathrm{0}\:,\:\mathrm{where}\:{a},{b},{p},{q},{r}\:\in\mathbb{R} \\ $$$$\mathrm{then}\:{a}−{bi}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to}\:\mathrm{that}\:\mathrm{equation}. \\ $$

Question Number 98887    Answers: 0   Comments: 0

Question Number 98673    Answers: 2   Comments: 0

find a_n in terms of n (I can′t find it...) a_1 =1; a_2 =4 a_3 =a_2 ×4×((2^2 −1)/2^2 ) a_4 =a_3 ×4×((2^2 −1)/2^2 )×((3^2 −1)/3^2 ) a_5 =a_4 ×4×((2^2 −1)/2^2 )×((3^2 −1)/3^2 )×((4^2 −1)/4^2 ) ... n≥2: a_(n+1) =4a_n Π_(k=2) ^n ((k^2 −1)/k^2 )

$$\mathrm{find}\:{a}_{{n}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n} \\ $$$$\left(\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{find}\:\mathrm{it}...\right) \\ $$$${a}_{\mathrm{1}} =\mathrm{1};\:{a}_{\mathrm{2}} =\mathrm{4} \\ $$$${a}_{\mathrm{3}} ={a}_{\mathrm{2}} ×\mathrm{4}×\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}^{\mathrm{2}} } \\ $$$${a}_{\mathrm{4}} ={a}_{\mathrm{3}} ×\mathrm{4}×\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }×\frac{\mathrm{3}^{\mathrm{2}} −\mathrm{1}}{\mathrm{3}^{\mathrm{2}} } \\ $$$${a}_{\mathrm{5}} ={a}_{\mathrm{4}} ×\mathrm{4}×\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }×\frac{\mathrm{3}^{\mathrm{2}} −\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }×\frac{\mathrm{4}^{\mathrm{2}} −\mathrm{1}}{\mathrm{4}^{\mathrm{2}} } \\ $$$$... \\ $$$${n}\geqslant\mathrm{2}:\:{a}_{{n}+\mathrm{1}} =\mathrm{4}{a}_{{n}} \underset{{k}=\mathrm{2}} {\overset{{n}} {\prod}}\frac{{k}^{\mathrm{2}} −\mathrm{1}}{{k}^{\mathrm{2}} } \\ $$

Question Number 98640    Answers: 0   Comments: 1

Question Number 98638    Answers: 0   Comments: 2

Le plan complexe est rapporte^ a^ un repe^ re orthornorme directe (0,e_1 ^→ ,e_2 ^→ ). On note A et B les points d′affixes respectives i, et 2i. Soit f, l′application du plan prive^ de A dans lui-me^ me qui a^ tout point M d′affixe z distincte i associe le point M d′affixe z′ definie par: z′=((2z−i)/(iz+1)) 1\ Soit z≠i a\ On pose z−i=re^(iθ) . Interpreter ge^ ometriquement r et θ a^ l′aide des points A et M.

$$\mathrm{Le}\:\mathrm{plan}\:\mathrm{complexe}\:\mathrm{est}\:\mathrm{rapport}\acute {\mathrm{e}}\:\grave {\mathrm{a}}\:\mathrm{un}\:\mathrm{rep}\grave {\mathrm{e}re} \\ $$$$\mathrm{orthornorme}\:\mathrm{directe}\:\left(\mathrm{0},\overset{\rightarrow} {\mathrm{e}}_{\mathrm{1}} ,\overset{\rightarrow} {\mathrm{e}}_{\mathrm{2}} \right).\:\mathcal{O}\mathrm{n}\:\mathrm{note}\:\mathrm{A}\:\mathrm{et}\:\mathrm{B}\:\mathrm{les} \\ $$$$\mathrm{points}\:\mathrm{d}'\mathrm{affixes}\:\mathrm{respectives}\:\boldsymbol{\mathrm{i}},\:\mathrm{et}\:\mathrm{2}\boldsymbol{\mathrm{i}}.\:\mathrm{Soit}\:\mathrm{f},\:\mathrm{l}'\mathrm{application} \\ $$$$\mathrm{du}\:\mathrm{plan}\:\mathrm{priv}\acute {\mathrm{e}}\:\mathrm{de}\:\mathrm{A}\:\mathrm{dans}\:\mathrm{lui}-\mathrm{m}\hat {\mathrm{e}me}\:\mathrm{qui}\:\grave {\mathrm{a}}\:\mathrm{tout}\:\mathrm{point} \\ $$$$\mathrm{M}\:\mathrm{d}'\mathrm{affixe}\:\mathrm{z}\:\mathrm{distincte}\:\boldsymbol{\mathrm{i}}\:\mathrm{associe}\:\mathrm{le}\:\mathrm{point}\:\mathrm{M}\:\mathrm{d}'\mathrm{affixe} \\ $$$$\boldsymbol{\mathrm{z}}'\:\mathrm{definie}\:\mathrm{par}:\:\mathrm{z}'=\frac{\mathrm{2z}−\mathrm{i}}{\mathrm{iz}+\mathrm{1}} \\ $$$$\mathrm{1}\backslash\:\mathrm{Soit}\:\mathrm{z}\neq\mathrm{i} \\ $$$$\mathrm{a}\backslash\:\mathrm{On}\:\mathrm{pose}\:\mathrm{z}−\mathrm{i}=\mathrm{re}^{\mathrm{i}\theta} .\:\mathcal{I}\mathrm{nterpreter}\:\mathrm{g}\acute {\mathrm{e}ometriquement}\:\mathrm{r}\:\mathrm{et}\:\theta \\ $$$$\grave {\mathrm{a}}\:\mathrm{l}'\mathrm{aide}\:\mathrm{des}\:\mathrm{points}\:\mathrm{A}\:\mathrm{et}\:\mathrm{M}. \\ $$

Question Number 98620    Answers: 1   Comments: 0

how do i make use of the function gamma(n). example, gamma(n)=∫_0 ^∞ x^(n−1) e^(−x) dx? instead of typing gamma(n). i can′t find it in the app.

$$\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{make}}\:\boldsymbol{{use}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$$$\boldsymbol{{gamma}}\left(\boldsymbol{{n}}\right). \\ $$$$\boldsymbol{{example}},\:\boldsymbol{{gamma}}\left(\boldsymbol{{n}}\right)=\underset{\mathrm{0}} {\overset{\infty} {\int}}\boldsymbol{{x}}^{\boldsymbol{{n}}−\mathrm{1}} \boldsymbol{{e}}^{−\boldsymbol{{x}}} \boldsymbol{{dx}}? \\ $$$$\boldsymbol{{instead}}\:\boldsymbol{{of}}\:\boldsymbol{{typing}}\:\boldsymbol{{gamma}}\left(\boldsymbol{{n}}\right). \\ $$$$\boldsymbol{{i}}\:\boldsymbol{{can}}'\boldsymbol{{t}}\:\boldsymbol{{find}}\:\boldsymbol{{it}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\:\boldsymbol{{app}}. \\ $$

Question Number 98468    Answers: 2   Comments: 10

Question Number 98443    Answers: 1   Comments: 0

Given the sequence (U_n )_(n∈N) defined by U_0 =1 and U_(n+1) =f(U_n ) where f(x)=(x/((x+1)^2 )) Show by mathematical induction that ∀n∈N^∗ 0<U_n ≤(1/n)

$$\mathcal{G}\mathrm{iven}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{U}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{defined}\:\mathrm{by}\:\mathrm{U}_{\mathrm{0}} =\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{U}_{\mathrm{n}+\mathrm{1}} =\mathrm{f}\left(\mathrm{U}_{\mathrm{n}} \right)\:\mathrm{where}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$$$\mathcal{S}\mathrm{how}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\mathrm{0}<\mathrm{U}_{\mathrm{n}} \leqslant\frac{\mathrm{1}}{\mathrm{n}} \\ $$

Question Number 98320    Answers: 1   Comments: 0

Question Number 98208    Answers: 0   Comments: 2

suppose a force given as F_1 = 24 N and F_2 = 50 N act through points AB and AC where OA = 2i +3j , OB = 5i + 6j and OC = 7i + 8j (a) find in vector notation F_1 and F_2 then find thier resultant.

$$\mathrm{suppose}\:\mathrm{a}\:\mathrm{force}\:\mathrm{given}\:\mathrm{as}\:{F}_{\mathrm{1}} \:=\:\mathrm{24}\:{N}\:\mathrm{and}\:{F}_{\mathrm{2}} \:=\:\mathrm{50}\:{N}\:\mathrm{act}\:\mathrm{through}\: \\ $$$$\mathrm{points}\:{AB}\:\mathrm{and}\:{AC}\:\mathrm{where}\:\:{OA}\:=\:\mathrm{2}{i}\:+\mathrm{3}{j}\:,\:{OB}\:=\:\mathrm{5}{i}\:+\:\mathrm{6}{j}\:\:\mathrm{and}\: \\ $$$${OC}\:=\:\mathrm{7}{i}\:+\:\mathrm{8}{j} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{in}\:\mathrm{vector}\:\mathrm{notation}\:{F}_{\mathrm{1}} \:\mathrm{and}\:{F}_{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{thier}\:\mathrm{resultant}. \\ $$

Question Number 98290    Answers: 0   Comments: 1

Question Number 98022    Answers: 1   Comments: 0

Derive the relation between an Arithmetic Mean and a Geometric Mean ((x_1 x_2 ...x_n ))^(1/n) ≤((x_1 +x_2 +∙∙∙+x_n )/n) ∀n∈N^∗ , ∀(x_1 ,x_2 ,...x_n )∈(R_+ ^∗ )^n

$$\mathcal{D}\mathrm{erive}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{an}\:\mathcal{A}\mathrm{rithmetic}\:\mathcal{M}\mathrm{ean} \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathcal{G}\mathrm{eometric}\:\mathcal{M}\mathrm{ean} \\ $$$$\sqrt[{\mathrm{n}}]{\mathrm{x}_{\mathrm{1}} \mathrm{x}_{\mathrm{2}} ...\mathrm{x}_{\mathrm{n}} }\leqslant\frac{\mathrm{x}_{\mathrm{1}} +\mathrm{x}_{\mathrm{2}} +\centerdot\centerdot\centerdot+\mathrm{x}_{\mathrm{n}} }{\mathrm{n}}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} ,\:\forall\left(\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,...\mathrm{x}_{\mathrm{n}} \right)\in\left(\mathbb{R}_{+} ^{\ast} \right)^{\mathrm{n}} \\ $$

Question Number 97953    Answers: 1   Comments: 3

Question Number 97833    Answers: 0   Comments: 10

Hello members of maths editor i want to say something concerning this forum. Well it is my own point of view: This forum is a place where people from all over the world come to interact together. A place where people from different back grounds, class and qualification speak a common language − mathematics. I in particular thank Tinkutara′s team for such a great platform. But i notice some people literally don′t show respect to others, like persuading others to answer thier questions, others show no appreciation for the given answers while others give rude comments with no reason behind them. please i just want to urge the Maths editor users to show more respect for others since we don′t know the identity or qualification of people who post and solve questions here. we remain one family as God guides us through our endervous.

$$\:\mathrm{Hello}\:\mathrm{members}\:\mathrm{of}\:\mathrm{maths}\:\mathrm{editor}\:\mathrm{i}\:\mathrm{want}\:\mathrm{to}\:\mathrm{say} \\ $$$$\mathrm{something}\:\mathrm{concerning}\:\mathrm{this}\:\mathrm{forum}.\:\mathrm{Well}\:\mathrm{it} \\ $$$$\mathrm{is}\:\mathrm{my}\:\mathrm{own}\:\mathrm{point}\:\mathrm{of}\:\mathrm{view}:\:\mathrm{This}\:\mathrm{forum}\:\mathrm{is}\:\mathrm{a}\:\mathrm{place}\:\mathrm{where} \\ $$$$\mathrm{people}\:\mathrm{from}\:\mathrm{all}\:\mathrm{over}\:\mathrm{the}\:\mathrm{world}\:\mathrm{come}\:\mathrm{to}\:\mathrm{interact}\:\mathrm{together}. \\ $$$$\mathrm{A}\:\mathrm{place}\:\mathrm{where}\:\mathrm{people}\:\mathrm{from}\:\mathrm{different}\:\mathrm{back}\:\mathrm{grounds}, \\ $$$$\mathrm{class}\:\mathrm{and}\:\mathrm{qualification}\:\mathrm{speak}\:\mathrm{a}\:\mathrm{common}\:\mathrm{language}\:−\: \\ $$$$\mathrm{mathematics}.\:\mathrm{I}\:\mathrm{in}\:\mathrm{particular}\:\mathrm{thank}\:\mathrm{Tinkutara}'\mathrm{s}\:\mathrm{team}\:\mathrm{for} \\ $$$$\mathrm{such}\:\mathrm{a}\:\mathrm{great}\:\mathrm{platform}.\:\mathrm{But}\:\mathrm{i}\:\mathrm{notice}\:\mathrm{some}\:\mathrm{people}\:\mathrm{literally} \\ $$$$\mathrm{don}'\mathrm{t}\:\mathrm{show}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{others},\:\mathrm{like}\:\mathrm{persuading}\:\mathrm{others} \\ $$$$\mathrm{to}\:\mathrm{answer}\:\mathrm{thier}\:\mathrm{questions},\:\mathrm{others}\:\mathrm{show}\:\mathrm{no}\: \\ $$$$\mathrm{appreciation}\:\mathrm{for}\:\mathrm{the}\:\mathrm{given}\:\mathrm{answers}\:\mathrm{while}\:\mathrm{others}\:\mathrm{give}\:\mathrm{rude} \\ $$$$\mathrm{comments}\:\mathrm{with}\:\mathrm{no}\:\mathrm{reason}\:\mathrm{behind}\:\mathrm{them}. \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{just}\:\mathrm{want}\:\mathrm{to}\:\mathrm{urge}\:\mathrm{the}\:\mathrm{Maths}\:\mathrm{editor}\:\mathrm{users}\:\mathrm{to}\:\mathrm{show} \\ $$$$\mathrm{more}\:\mathrm{respect}\:\mathrm{for}\:\mathrm{others}\:\mathrm{since}\:\mathrm{we}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{the}\:\mathrm{identity}\:\mathrm{or} \\ $$$$\mathrm{qualification}\:\mathrm{of}\:\mathrm{people}\:\mathrm{who}\:\mathrm{post}\:\mathrm{and}\:\mathrm{solve}\:\mathrm{questions}\:\mathrm{here}. \\ $$$$\mathrm{we}\:\mathrm{remain}\:\mathrm{one}\:\mathrm{family}\:\mathrm{as}\:\mathrm{God}\:\mathrm{guides}\:\mathrm{us}\:\mathrm{through}\:\mathrm{our}\:\mathrm{endervous}. \\ $$

Question Number 97803    Answers: 1   Comments: 0

The annual salaries of employees in a large company are approximately normally disributed with a mean of $50,000 and a standard deviation of $20,000. a. what percent of people earn less than $40,000? b. what percent of people earn between $45,000 and $65,000? c. what percent of people earn more than $70,000?

$$\mathrm{The}\:\mathrm{annual}\:\mathrm{salaries}\:\mathrm{of}\:\mathrm{employees}\:\mathrm{in}\:\mathrm{a}\:\mathrm{large} \\ $$$$\mathrm{company}\:\mathrm{are}\:\mathrm{approximately}\:\mathrm{normally}\: \\ $$$$\mathrm{disributed}\:\mathrm{with}\:\mathrm{a}\:\mathrm{mean}\:\mathrm{of}\:\$\mathrm{50},\mathrm{000}\:\mathrm{and}\:\mathrm{a}\:\mathrm{standard} \\ $$$$\mathrm{deviation}\:\mathrm{of}\:\$\mathrm{20},\mathrm{000}. \\ $$$$\mathrm{a}.\:\mathrm{what}\:\mathrm{percent}\:\mathrm{of}\:\mathrm{people}\:\mathrm{earn}\:\mathrm{less}\:\mathrm{than} \\ $$$$\$\mathrm{40},\mathrm{000}? \\ $$$$\mathrm{b}.\:\mathrm{what}\:\mathrm{percent}\:\mathrm{of}\:\mathrm{people}\:\mathrm{earn}\:\mathrm{between} \\ $$$$\$\mathrm{45},\mathrm{000}\:\mathrm{and}\:\$\mathrm{65},\mathrm{000}? \\ $$$$\mathrm{c}.\:\mathrm{what}\:\mathrm{percent}\:\mathrm{of}\:\mathrm{people}\:\mathrm{earn}\:\mathrm{more}\:\mathrm{than} \\ $$$$\$\mathrm{70},\mathrm{000}? \\ $$

  Pg 58      Pg 59      Pg 60      Pg 61      Pg 62      Pg 63      Pg 64      Pg 65      Pg 66      Pg 67   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com