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Question Number 96829    Answers: 0   Comments: 1

If 2f(x) + f(1−x) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} .\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 96826    Answers: 1   Comments: 0

If 2f(x) + f(x−1) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:.\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$

Question Number 96823    Answers: 2   Comments: 2

Question Number 96821    Answers: 3   Comments: 0

{ (((u^2 /v) + (v^2 /u) = 12)),(((1/u) + (1/v) = (1/3))) :} . find u and v ?

$$\begin{cases}{\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{v}}\:+\:\frac{\mathrm{v}^{\mathrm{2}} }{\mathrm{u}}\:=\:\mathrm{12}}\\{\frac{\mathrm{1}}{\mathrm{u}}\:+\:\frac{\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases}\:.\:\mathrm{find}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:? \\ $$

Question Number 96817    Answers: 1   Comments: 2

Question Number 96815    Answers: 1   Comments: 0

In how many ways can 3 boys and 3 girls be sitted in a line?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{be} \\ $$$$\mathrm{sitted}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}? \\ $$

Question Number 96811    Answers: 1   Comments: 0

Prove that; a\ A+A∙B=A c\ (A+B^ )∙(A+B^− )=A b\ A∙(A+B)=A d\ A+A^− B=A+B

$$\mathrm{Prove}\:\mathrm{that}; \\ $$$$\mathrm{a}\backslash\:\mathrm{A}+\mathrm{A}\centerdot\mathrm{B}=\mathrm{A}\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\backslash\:\left(\mathrm{A}+\mathrm{B}^{} \right)\centerdot\left(\mathrm{A}+\overset{−} {\mathrm{B}}\right)=\mathrm{A} \\ $$$$\mathrm{b}\backslash\:\mathrm{A}\centerdot\left(\mathrm{A}+\mathrm{B}\right)=\mathrm{A}\:\:\:\:\:\:\:\mathrm{d}\backslash\:\mathrm{A}+\overset{−} {\mathrm{A}B}=\mathrm{A}+\mathrm{B} \\ $$

Question Number 96792    Answers: 1   Comments: 12

Question Number 96785    Answers: 1   Comments: 0

Question Number 96784    Answers: 1   Comments: 0

Question Number 96782    Answers: 3   Comments: 1

1)((cos^4 (θ))/x)−((sin^4 (θ))/y)=(1/(x+y)) find (dy/dx) 2)solve:2⌊x−4+⌊x⌋⌋=6−3⌊x⌋ 3)lim_(x→4) (((cos(x))^x −(sin(x))^x −cos(2x))/((x−4)))

$$\left.\mathrm{1}\right)\frac{{cos}^{\mathrm{4}} \left(\theta\right)}{{x}}−\frac{{sin}^{\mathrm{4}} \left(\theta\right)}{{y}}=\frac{\mathrm{1}}{{x}+{y}} \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){solve}:\mathrm{2}\lfloor{x}−\mathrm{4}+\lfloor{x}\rfloor\rfloor=\mathrm{6}−\mathrm{3}\lfloor{x}\rfloor \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\underset{{x}\rightarrow\mathrm{4}} {{lim}}\frac{\left({cos}\left({x}\right)\right)^{{x}} −\left({sin}\left({x}\right)\right)^{{x}} −{cos}\left(\mathrm{2}{x}\right)}{\left({x}−\mathrm{4}\right)} \\ $$$$ \\ $$$$ \\ $$

Question Number 96780    Answers: 0   Comments: 5

Question Number 96773    Answers: 1   Comments: 0

solve y^(′′) −y =((sinx)/x)

$$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{y}\:=\frac{\mathrm{sinx}}{\mathrm{x}} \\ $$

Question Number 96772    Answers: 2   Comments: 0

solve y^(′′) −2y =x^2 sinx and y(0)=0 ,y^′ (0) =1

$$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{2y}\:=\mathrm{x}^{\mathrm{2}} \mathrm{sinx}\:\:\mathrm{and}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}\:,\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{1} \\ $$

Question Number 96771    Answers: 1   Comments: 0

solve y^(′′) −y^′ +y = cos(2t) with y(0)=y^′ (0)=−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2t}\right)\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 96766    Answers: 1   Comments: 0

solve : tan x−tan (2x) = 2(√3)

$$\mathrm{solve}\::\:\mathrm{tan}\:{x}−\mathrm{tan}\:\left(\mathrm{2}{x}\right)\:=\:\mathrm{2}\sqrt{\mathrm{3}}\: \\ $$

Question Number 96764    Answers: 1   Comments: 5

A particle P of mass m, is projected vertically upward with a speed u from a point A, on horizontal ground. When P is at x above its initial position, its speed is v. The only forces acting on P is its weight and resistance mgkv^2 . where k is a positive constant. (a) Show that the greatest height reached is (1/(2gk)) ln(1 +ku^2 ). (b) show that the speed with which P returns to A is (u/(√(1+ ku^2 ))) .

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{P}\:\mathrm{of}\:\mathrm{mass}\:{m},\:\mathrm{is}\:\mathrm{projected}\:\mathrm{vertically}\:\mathrm{upward}\:\mathrm{with} \\ $$$$\mathrm{a}\:\mathrm{speed}\:{u}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:{A},\:\mathrm{on}\:\mathrm{horizontal}\:\mathrm{ground}.\:\mathrm{When}\:\mathrm{P}\:\mathrm{is}\:\mathrm{at}\:{x}\:\mathrm{above} \\ $$$$\mathrm{its}\:\mathrm{initial}\:\mathrm{position},\:\mathrm{its}\:\mathrm{speed}\:\mathrm{is}\:{v}.\:\mathrm{The}\:\mathrm{only}\:\mathrm{forces}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{P}\:\mathrm{is} \\ $$$$\mathrm{its}\:\mathrm{weight}\:\mathrm{and}\:\mathrm{resistance}\:{m}\mathrm{g}{kv}^{\mathrm{2}} .\:\mathrm{where}\:{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{constant}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{height}\:\mathrm{reached}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{2g}{k}}\:\mathrm{ln}\left(\mathrm{1}\:+{ku}^{\mathrm{2}} \right). \\ $$$$\left(\mathrm{b}\right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{with}\:\mathrm{which}\:\mathrm{P}\:\mathrm{returns}\:\mathrm{to}\:\mathrm{A}\:\mathrm{is}\:\frac{{u}}{\sqrt{\mathrm{1}+\:{ku}^{\mathrm{2}} }}\:. \\ $$

Question Number 96763    Answers: 2   Comments: 0

∫ ((sin ((x/2)) tan ((x/2)) dx)/(cos x)) = ?

$$\int\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:\mathrm{dx}}{\mathrm{cos}\:\mathrm{x}}\:=\:? \\ $$

Question Number 96761    Answers: 0   Comments: 0

A particle P moving at constant angular velocity describes a part y = f(θ). At time t = 0, the particle is at the point with coordinate (a,(π/2)) and moving with a transverse acceleration of −2aω^2 sinθ. find the polar equation of the curve described by this particle.Show that the radial component of the acceleration of P is −aω^2 (1 + cos θ).

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{P}\:\:\:\mathrm{moving}\:\mathrm{at}\:\mathrm{constant}\:\mathrm{angular}\:\mathrm{velocity} \\ $$$$\mathrm{describes}\:\mathrm{a}\:\mathrm{part}\:{y}\:=\:{f}\left(\theta\right).\:\mathrm{At}\:\mathrm{time}\:{t}\:=\:\mathrm{0},\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{with}\:\mathrm{coordinate}\:\left({a},\frac{\pi}{\mathrm{2}}\right)\:\mathrm{and}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\: \\ $$$$\mathrm{transverse}\:\mathrm{acceleration}\:\mathrm{of}\:−\mathrm{2}{a}\omega^{\mathrm{2}} \:\mathrm{sin}\theta.\:\mathrm{find}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{described}\:\mathrm{by}\:\mathrm{this}\:\mathrm{particle}.\mathrm{Show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{radial}\:\mathrm{component}\:\mathrm{of}\:\mathrm{the}\:\:\mathrm{acceleration}\:\:\mathrm{of}\:\mathrm{P}\:\mathrm{is}\:−{a}\omega^{\mathrm{2}} \left(\mathrm{1}\:+\:\mathrm{cos}\:\theta\right). \\ $$

Question Number 96758    Answers: 0   Comments: 1

Let x∈ [ −((5π)/(12)) , −(π/3) ] . The maximum value of y = tan (x+((2π)/3))−tan (x+(π/6)) +cos (x+(π/6)) is ___

$$\mathrm{Let}\:{x}\in\:\left[\:−\frac{\mathrm{5}\pi}{\mathrm{12}}\:,\:−\frac{\pi}{\mathrm{3}}\:\right]\:.\:\mathrm{The}\:\mathrm{maximum}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{tan}\:\left({x}+\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{6}}\right)\:+\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{6}}\right) \\ $$$$\mathrm{is}\:\_\_\_ \\ $$

Question Number 96749    Answers: 1   Comments: 0

how we can calclate triple factorial?

$$\mathrm{how}\:\mathrm{we}\:\mathrm{can}\:\mathrm{calclate}\:\mathrm{triple}\:\mathrm{factorial}? \\ $$

Question Number 96748    Answers: 0   Comments: 1

nobody tried question 94184...

$$\mathrm{nobody}\:\mathrm{tried}\:\mathrm{question}\:\mathrm{94184}... \\ $$

Question Number 96730    Answers: 1   Comments: 0

A third of a population has been vaccined against an illness. During the pandemie it is noticed that; out of 15 patients, 2 have been vaccined. Assuming that out of a hundred vaccined, 8 are ill. An individual is choosen at random from this population. Let M imply the individual is ill and V imply the individual has been vaccined. 1\ Determine the probabilities: P(V); P(V/M) and P(M/V) 2\ Calculate P(M∩V) then P(M). Deduce the percentage of patients.

$$\:\:\:\:\:\:\mathcal{A}\:\mathrm{third}\:\mathrm{of}\:\mathrm{a}\:\mathrm{population}\:\mathrm{has}\:\mathrm{been}\:\mathrm{vaccined}\:\mathrm{against} \\ $$$$\mathrm{an}\:\mathrm{illness}.\:\mathcal{D}\mathrm{uring}\:\mathrm{the}\:\mathrm{pandemie}\:\mathrm{it}\:\mathrm{is}\:\mathrm{noticed}\:\mathrm{that}; \\ $$$$\mathrm{out}\:\mathrm{of}\:\mathrm{15}\:\mathrm{patients},\:\mathrm{2}\:\mathrm{have}\:\mathrm{been}\:\mathrm{vaccined}. \\ $$$$\:\:\:\:\:\:\:\mathcal{A}\mathrm{ssuming}\:\mathrm{that}\:\mathrm{out}\:\mathrm{of}\:\mathrm{a}\:\mathrm{hundred}\:\mathrm{vaccined},\:\mathrm{8}\:\mathrm{are}\:\mathrm{ill}. \\ $$$$\mathcal{A}\mathrm{n}\:\mathrm{individual}\:\mathrm{is}\:\mathrm{choosen}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{this}\:\mathrm{population}. \\ $$$$\mathcal{L}\mathrm{et}\:\boldsymbol{\mathrm{M}}\:\mathrm{imply}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{individual}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{ill}}\:\mathrm{and}\:\boldsymbol{\mathrm{V}}\:\mathrm{imply}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{individual}} \\ $$$$\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{been}}\:\boldsymbol{\mathrm{vaccined}}. \\ $$$$\mathrm{1}\backslash\:\mathcal{D}\mathrm{etermine}\:\mathrm{the}\:\mathrm{probabilities}:\:\mathrm{P}\left(\mathrm{V}\right);\:\mathrm{P}\left(\mathrm{V}/\mathrm{M}\right)\:\mathrm{and}\:\mathrm{P}\left(\mathrm{M}/\mathrm{V}\right) \\ $$$$\mathrm{2}\backslash\:\mathcal{C}\mathrm{alculate}\:\mathrm{P}\left(\mathrm{M}\cap\mathrm{V}\right)\:\mathrm{then}\:\mathrm{P}\left(\mathrm{M}\right).\:\mathcal{D}\mathrm{educe}\:\mathrm{the} \\ $$$$\mathrm{percentage}\:\mathrm{of}\:\mathrm{patients}. \\ $$

Question Number 96729    Answers: 2   Comments: 1

Prove that ln∣sec(x)+tan(x)∣=tanh^(−1) (sin(x))

$${Prove}\:{that}\:\mathrm{ln}\mid\mathrm{sec}\left({x}\right)+\mathrm{tan}\left({x}\right)\mid=\mathrm{tanh}^{−\mathrm{1}} \left(\mathrm{sin}\left({x}\right)\right) \\ $$

Question Number 96746    Answers: 3   Comments: 2

∫((√x)/((1+x^3 )(√(1−x^3 ))))dx=? ∫((√x)/((1−x^3 )(√(1+x^3 ))))dx=?

$$\int\frac{\sqrt{{x}}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}=? \\ $$$$\int\frac{\sqrt{{x}}}{\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }}{dx}=? \\ $$

Question Number 96715    Answers: 1   Comments: 0

find real solution of equation x^5 +x^4 +1 = 0

$$\mathrm{find}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{5}} +{x}^{\mathrm{4}} +\mathrm{1}\:=\:\mathrm{0} \\ $$

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