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Question Number 95014    Answers: 0   Comments: 10

If y_(n + 1) − y_n = 6, and y_0 = 7 Find y_n

$$\boldsymbol{\mathrm{If}}\:\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \:\:\:=\:\:\:\mathrm{6},\:\:\:\:\:\:\:\boldsymbol{\mathrm{and}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\mathrm{0}} \:\:=\:\:\:\mathrm{7} \\ $$$$\boldsymbol{\mathrm{Find}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \\ $$

Question Number 95012    Answers: 0   Comments: 1

∫(1/(√((x−1)(x−2)(x−3)(x−4))))dx

$$\int\frac{\mathrm{1}}{\sqrt{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)}}{dx} \\ $$

Question Number 95011    Answers: 0   Comments: 0

Given tbat a disk has 18 sectors, 80 tracks and a sector capacity of 512bytes. Prove that the storage capacity is 1.44MB

$${Given}\:{tbat}\:{a}\:{disk}\:{has}\:\mathrm{18}\:{sectors},\:\mathrm{80}\:{tracks} \\ $$$${and}\:{a}\:{sector}\:{capacity}\:{of}\:\mathrm{512}{bytes}.\:{Prove}\: \\ $$$${that}\:{the}\:{storage}\:{capacity}\:{is}\:\mathrm{1}.\mathrm{44}{MB} \\ $$

Question Number 95009    Answers: 0   Comments: 3

∫ ((e^x +2xe^x sin x−2xe^x cos x)/((√x) sin^2 x)) dx

$$\int\:\:\frac{{e}^{{x}} +\mathrm{2}{xe}^{{x}} \mathrm{sin}\:{x}−\mathrm{2}{xe}^{{x}} \mathrm{cos}\:{x}}{\sqrt{{x}}\:\mathrm{sin}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 95001    Answers: 2   Comments: 0

Exercise Given a, b ∈ R^∗ and t is a variable real. 1) Solve in R^2 for x,y this system: { ((xsin t−ycos t=−a)),((xcos t+ysin t=b.)) :} 2)/Demonstrate that these solutions can be written like this ( r and θ ∈ R). { ((x=rcos(t+θ))),((y=rsin(t+θ))) :} 3) we suppose now that a=b=1 and θ=(π/(12)) solve this in [0;2π[ { ((rcos(t+θ)≥−1)),((rsin(t+θ)<−1)) :}

$$\mathrm{Exercise} \\ $$$$\mathrm{Given}\:\mathrm{a},\:\mathrm{b}\:\in\:\mathbb{R}^{\ast} \:\mathrm{and}\:{t}\:\mathrm{is}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{real}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Solve}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2}} \:\mathrm{for}\:{x},{y}\:\mathrm{this}\:\mathrm{system}:\: \\ $$$$\begin{cases}{{x}\mathrm{sin}\:{t}−{y}\mathrm{cos}\:{t}=−\mathrm{a}}\\{{x}\mathrm{cos}\:{t}+{y}\mathrm{sin}\:{t}={b}.}\end{cases} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)/\mathrm{Demonstrate}\:\mathrm{that}\:\mathrm{these}\:\mathrm{solutions}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{written}\:\mathrm{like}\:\mathrm{this}\:\left(\:{r}\:\mathrm{and}\:\theta\:\in\:\mathbb{R}\right). \\ $$$$\begin{cases}{{x}={rcos}\left({t}+\theta\right)}\\{{y}={rsin}\left({t}+\theta\right)}\end{cases} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\:\mathrm{we}\:\mathrm{suppose}\:\mathrm{now}\:\mathrm{that}\:\mathrm{a}=\mathrm{b}=\mathrm{1}\:\mathrm{and}\:\theta=\frac{\pi}{\mathrm{12}} \\ $$$$\mathrm{solve}\:\mathrm{this}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\left[\right.\right. \\ $$$$\begin{cases}{{rcos}\left({t}+\theta\right)\geqslant−\mathrm{1}}\\{{rsin}\left({t}+\theta\right)<−\mathrm{1}}\end{cases} \\ $$

Question Number 94997    Answers: 2   Comments: 0

Question Number 94992    Answers: 4   Comments: 0

1. Show that: ∫_0 ^( π) ((xdx)/((a^2 sin^2 x+b^2 cos^2 x)^2 )) = ((π^2 (a^2 +b^2 ))/(4a^3 b^3 )) 2.The density at the point (x,y) of a lamina bounded by the circle x^2 +y^2 −2ax=0 is ϱ =x find its mass. 3.∗ 4. If z= ((cos y)/x) and x=u^2 −v , y=e^x find (dz/dv).

$$\:\mathrm{1}.\:\mathrm{Show}\:\:\mathrm{that}: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\:\pi} \:\:\:\frac{\mathrm{xdx}}{\left(\mathrm{a}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \mathrm{x}+\mathrm{b}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} }\:=\:\frac{\pi^{\mathrm{2}} \left(\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \right)}{\mathrm{4a}^{\mathrm{3}} \mathrm{b}^{\mathrm{3}} } \\ $$$$\:\: \\ $$$$\:\mathrm{2}.\mathrm{The}\:\mathrm{density}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{of}\:\mathrm{a}\:\mathrm{lamina}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{2ax}=\mathrm{0}\:\mathrm{is}\:\varrho\:=\mathrm{x}\:\:\:\mathrm{find}\:\mathrm{its}\:\mathrm{mass}. \\ $$$$\:\mathrm{3}.\ast \\ $$$$\:\mathrm{4}.\:\mathrm{If}\:\:\mathrm{z}=\:\frac{\mathrm{cos}\:\mathrm{y}}{\mathrm{x}}\:\mathrm{and}\:\mathrm{x}=\mathrm{u}^{\mathrm{2}} −\mathrm{v}\:,\:\mathrm{y}=\mathrm{e}^{\mathrm{x}} \:\mathrm{find}\:\frac{\mathrm{dz}}{\mathrm{dv}}. \\ $$$$\:\: \\ $$

Question Number 94984    Answers: 1   Comments: 2

(d/dx) [(1/x) +(√x) ] ?

$$\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\frac{\mathrm{1}}{\mathrm{x}}\:+\sqrt{\mathrm{x}}\:\right]\:? \\ $$

Question Number 94969    Answers: 1   Comments: 0

y′′−3y′+2y=0 ; y=0,y′=3 for x=0

$$\mathrm{y}''−\mathrm{3y}'+\mathrm{2y}=\mathrm{0}\:;\:\mathrm{y}=\mathrm{0},\mathrm{y}'=\mathrm{3}\:\mathrm{for}\:\mathrm{x}=\mathrm{0} \\ $$

Question Number 94960    Answers: 2   Comments: 0

Question Number 94956    Answers: 1   Comments: 7

Question Number 94955    Answers: 0   Comments: 0

Prove by set theory or otherwise lcm( gcd(x,y),gcd(y,z),gcd(z,x) ) is equal to gcd( lcm(x,y),lcm(y,z),lcm(z,x) ) Or give a counter example.

$${Prove}\:{by}\:{set}\:{theory}\:{or}\:{otherwise} \\ $$$$\:\:\mathrm{lcm}\left(\:\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right),\mathrm{gcd}\left(\mathrm{y},\mathrm{z}\right),\mathrm{gcd}\left(\mathrm{z},\mathrm{x}\right)\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\:\mathrm{gcd}\left(\:\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right),\mathrm{lcm}\left(\mathrm{y},\mathrm{z}\right),\mathrm{lcm}\left(\mathrm{z},\mathrm{x}\right)\:\right) \\ $$$$\:\:{Or}\:{give}\:{a}\:{counter}\:{example}. \\ $$

Question Number 94954    Answers: 1   Comments: 0

For any curve, prove that: ((d^2 x/ds^2 ))^2 +((d^2 y/dx^2 ))^2 = (1/ρ^2 )

$$\:\:\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{any}}\:\boldsymbol{\mathrm{curve}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\:\:\:\left(\frac{\mathrm{d}^{\mathrm{2}} \mathrm{x}}{\mathrm{ds}^{\mathrm{2}} }\right)^{\mathrm{2}} +\left(\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\right)^{\mathrm{2}} =\:\frac{\mathrm{1}}{\rho^{\mathrm{2}} } \\ $$$$\:\: \\ $$

Question Number 94945    Answers: 0   Comments: 2

How do you make p the subject of equation q = (m/((√p) )) + (p^2 /m)

$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{make}\:\mathrm{p}\:\mathrm{the}\:\mathrm{subject} \\ $$$$\mathrm{of}\:\mathrm{equation}\:{q}\:=\:\frac{{m}}{\sqrt{{p}}\:}\:+\:\frac{{p}^{\mathrm{2}} }{{m}}\: \\ $$

Question Number 94934    Answers: 3   Comments: 1

Question Number 94931    Answers: 1   Comments: 0

f is a 2(×) derivable function and L laplace transfom determine L(f^′ ) a L(f^(′′) )

$$\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{2}\left(×\right)\:\mathrm{derivable}\:\mathrm{function}\:\:\mathrm{and}\:\mathrm{L}\:\mathrm{laplace}\:\mathrm{transfom} \\ $$$$\mathrm{determine}\:\mathrm{L}\left(\mathrm{f}^{'} \right)\:\mathrm{a}\:\mathrm{L}\left(\mathrm{f}^{''} \right) \\ $$

Question Number 94925    Answers: 1   Comments: 2

Question Number 94923    Answers: 1   Comments: 0

Question Number 94922    Answers: 1   Comments: 0

Question Number 94921    Answers: 2   Comments: 0

Question Number 94915    Answers: 2   Comments: 0

We suppose in R^2 the base (i^→ ;j^→ ). we have these vectors: u^→ =(m^2 −m)i^→ +2mj^→ ; v^→ =(m−1)i^→ +(m+1)j^→ m ∈ R^∗ 1)Determinate m for which the system (u^→ ;v^→ ) is linear dependant( det(u^→ ;v^→ )=0)

$$\mathrm{We}\:\mathrm{suppose}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2}} \:\mathrm{the}\:\mathrm{base}\:\left(\overset{\rightarrow} {{i}};\overset{\rightarrow} {{j}}\right). \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{these}\:\mathrm{vectors}: \\ $$$$\overset{\rightarrow} {\mathrm{u}}=\left(\mathrm{m}^{\mathrm{2}} −\mathrm{m}\right)\overset{\rightarrow} {{i}}+\mathrm{2m}\overset{\rightarrow} {{j}}\:;\: \\ $$$$\overset{\rightarrow} {\mathrm{v}}=\left(\mathrm{m}−\mathrm{1}\right)\overset{\rightarrow} {{i}}+\left(\mathrm{m}+\mathrm{1}\right)\overset{\rightarrow} {{j}}\:\mathrm{m}\:\in\:\mathbb{R}^{\ast} \\ $$$$\left.\mathrm{1}\right)\mathrm{Determinate}\:\mathrm{m}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{system} \\ $$$$\left(\overset{\rightarrow} {\mathrm{u}};\overset{\rightarrow} {\mathrm{v}}\right)\:\mathrm{is}\:\mathrm{linear}\:\mathrm{dependant}\left(\:\mathrm{det}\left(\overset{\rightarrow} {\mathrm{u}};\overset{\rightarrow} {\mathrm{v}}\right)=\mathrm{0}\right) \\ $$$$ \\ $$

Question Number 94914    Answers: 1   Comments: 0

Question Number 94910    Answers: 1   Comments: 0

Solve in [0;2π] 2sin(4x−(π/6))≥1 Please sirs...

$$\mathrm{Solve}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\right] \\ $$$$\mathrm{2sin}\left(\mathrm{4}{x}−\frac{\pi}{\mathrm{6}}\right)\geqslant\mathrm{1} \\ $$$$\mathrm{Please}\:\mathrm{sirs}... \\ $$

Question Number 94907    Answers: 2   Comments: 0

1)calculate ∫ (dx/((2+(√(x−1)))^2 )) 2) find the value of ∫_2 ^(+∞) (dx/((2+(√(x−1)))^2 ))

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{2}+\sqrt{\mathrm{x}−\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2}+\sqrt{\mathrm{x}−\mathrm{1}}\right)^{\mathrm{2}} } \\ $$

Question Number 94906    Answers: 2   Comments: 0

calculate ∫_1 ^(+∞) (dx/(x^2 (x+1)^3 (x+2)^4 ))

$$\mathrm{calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$

Question Number 94905    Answers: 2   Comments: 0

calculate ∫_3 ^(+∞) ((xdx)/((x+1)^3 (x−2)^2 ))

$$\mathrm{calculate}\:\:\int_{\mathrm{3}} ^{+\infty} \:\:\:\:\:\frac{\mathrm{xdx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$

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