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Question Number 83654 Answers: 2 Comments: 1

solve this equation sin^2 x−sin^4 x=cos^2 x−cos^4 x

$$\mathrm{solve}\:\mathrm{this}\:\mathrm{equation}\: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{4}} {x}=\mathrm{cos}\:^{\mathrm{2}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x} \\ $$

Question Number 83653 Answers: 2 Comments: 0

find range of function y= (4/((x^2 −4)))

$$\mathrm{find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{y}=\:\frac{\mathrm{4}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)} \\ $$

Question Number 83649 Answers: 1 Comments: 0

Question Number 83644 Answers: 0 Comments: 0

Question Number 83642 Answers: 0 Comments: 0

Find the surface area of the solid generated by the revolution of the cardioids r=a(1+cos θ) about the initial line.

$$ \\ $$$$\: \\ $$$$\mathfrak{Find}\:\mathfrak{the}\:\mathfrak{surface}\:\mathfrak{area}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{solid}\:\mathfrak{generated} \\ $$$$\:\:\mathfrak{by}\:\mathfrak{the}\:\mathfrak{revolution}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{cardioids}\:\mathfrak{r}=\mathfrak{a}\left(\mathrm{1}+\mathfrak{cos}\:\theta\right)\:\mathfrak{about}\:\mathfrak{the}\:\mathfrak{initial}\:\mathfrak{line}. \\ $$

Question Number 83637 Answers: 0 Comments: 0

Question Number 83639 Answers: 4 Comments: 0

Find the differential equations: (i) log((dy/dx))=ax+by (ii) x cos y dy=(x e^x log x +e^x )dx

$$ \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\mathrm{log}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{ax}+\mathrm{by} \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\mathrm{x}\:\mathrm{cos}\:\mathrm{y}\:\mathrm{dy}=\left(\mathrm{x}\:\mathrm{e}^{\mathrm{x}} \mathrm{log}\:\mathrm{x}\:+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$ \\ $$

Question Number 83638 Answers: 1 Comments: 0

Question Number 83629 Answers: 1 Comments: 0

show that Σ_(n,k=0) ^∞ ((n! k!)/((n+k+2)!))=(π^2 /6)

$${show}\:{that} \\ $$$$\underset{{n},{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}!\:{k}!}{\left({n}+{k}+\mathrm{2}\right)!}=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 83619 Answers: 0 Comments: 0

Show that the differetial equation is a Sturm−Louville equation (x^(−1) y^1 )^1 +(4+λ)x^(−3) y=0, y(1)=0,y(ϱ^t )=0 Solve the equation to determine the eigenvalue and the corresponding eigen functions of the problem. Show also that the set of eigen function forms and orthogonal and orthonormal set. Thanks as usual.

$${Show}\:{that}\:{the}\:{differetial}\:{equation}\:{is}\:{a}\:{Sturm}−{Louville}\:{equation} \\ $$$$\left({x}^{−\mathrm{1}} {y}^{\mathrm{1}} \right)^{\mathrm{1}} +\left(\mathrm{4}+\lambda\right){x}^{−\mathrm{3}} {y}=\mathrm{0},\:\:{y}\left(\mathrm{1}\right)=\mathrm{0},{y}\left(\varrho^{{t}} \right)=\mathrm{0} \\ $$$${Solve}\:{the}\:{equation}\:{to}\:{determine}\:{the}\:{eigenvalue}\:{and}\:{the}\:{corresponding}\:{eigen}\:{functions}\:{of}\:{the}\:{problem}. \\ $$$${Show}\:{also}\:{that}\:{the}\:{set}\:{of}\:{eigen}\:{function}\:{forms}\:{and}\:{orthogonal}\:{and}\:{orthonormal}\:{set}. \\ $$$$ \\ $$$${Thanks}\:{as}\:{usual}. \\ $$

Question Number 83614 Answers: 1 Comments: 1

(3x−5)(3x+4)

$$\left(\mathrm{3}{x}−\mathrm{5}\right)\left(\mathrm{3}{x}+\mathrm{4}\right) \\ $$$$ \\ $$

Question Number 83610 Answers: 0 Comments: 2

(1/(x−1)) + (5/(6−3(√(6+x−x^2 )))) > (1/(1+∣x−1∣))

$$\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\:+\:\frac{\mathrm{5}}{\mathrm{6}−\mathrm{3}\sqrt{\mathrm{6}+\mathrm{x}−\mathrm{x}^{\mathrm{2}} }}\:>\:\frac{\mathrm{1}}{\mathrm{1}+\mid\mathrm{x}−\mathrm{1}\mid} \\ $$

Question Number 83608 Answers: 1 Comments: 4

((17+x))^(1/(4 )) + ((17−x))^(1/(4 )) = 2 find x

$$\sqrt[{\mathrm{4}\:\:}]{\mathrm{17}+\mathrm{x}}\:+\:\sqrt[{\mathrm{4}\:\:}]{\mathrm{17}−\mathrm{x}}\:=\:\mathrm{2}\: \\ $$$$\mathrm{find}\:\mathrm{x}\: \\ $$

Question Number 83606 Answers: 1 Comments: 0

a car drives at a speed of 120 km/hr it starts to brake at a road mark A and passes a road mark B at a speed of 60 km/hr. acceleration is constant. the distance AB is 4 km. (1) calculate the acceleration (2) calculate the time between A and B (3) there are n reflector posts between A and B. calculate the speed of the car at each of them (find a function for the speed depending on the distance traveled)

$$\mathrm{a}\:\mathrm{car}\:\mathrm{drives}\:\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{120}\:\mathrm{km}/\mathrm{hr} \\ $$$$\mathrm{it}\:\mathrm{starts}\:\mathrm{to}\:\mathrm{brake}\:\mathrm{at}\:\mathrm{a}\:\mathrm{road}\:\mathrm{mark}\:{A}\:\mathrm{and} \\ $$$$\mathrm{passes}\:\mathrm{a}\:\mathrm{road}\:\mathrm{mark}\:{B}\:\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{60}\:\mathrm{km}/\mathrm{hr}.\:\mathrm{acceleration}\:\mathrm{is}\:\mathrm{constant}.\:\mathrm{the} \\ $$$$\mathrm{distance}\:{AB}\:\mathrm{is}\:\mathrm{4}\:\mathrm{km}. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{time}\:\mathrm{between}\:{A}\:\mathrm{and}\:{B} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{there}\:\mathrm{are}\:{n}\:\mathrm{reflector}\:\mathrm{posts}\:\mathrm{between}\:{A} \\ $$$$\:\:\:\:\:\:\:\mathrm{and}\:{B}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{at} \\ $$$$\:\:\:\:\:\:\:\mathrm{each}\:\mathrm{of}\:\mathrm{them}\:\left(\mathrm{find}\:\mathrm{a}\:\mathrm{function}\:\mathrm{for}\:\mathrm{the}\right. \\ $$$$\left.\:\:\:\:\:\:\:\mathrm{speed}\:\mathrm{depending}\:\mathrm{on}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{traveled}\right) \\ $$

Question Number 83604 Answers: 0 Comments: 7

need help. When typing with microsoft word i face some difficulties like when typing lim_(x→0) f(x) it turns to lim_(x→0) f(x) and Σ_(r=0) ^n a_n turns to Σ_(r=0) ^n a_n please how do i rectify this problem? and any suggestion on a better application to type my maths papers? thanks in advance.

$$\mathrm{need}\:\mathrm{help}.\:\mathrm{When}\:\mathrm{typing}\:\mathrm{with}\:\mathrm{microsoft}\:\mathrm{word} \\ $$$$\mathrm{i}\:\mathrm{face}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{like}\:\mathrm{when}\:\mathrm{typing}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:\mathrm{it}\:\mathrm{turns}\:\mathrm{to}\:\mathrm{lim}_{{x}\rightarrow\mathrm{0}} \:{f}\left({x}\right)\:\mathrm{and}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{n}} \: \\ $$$$\mathrm{turns}\:\mathrm{to}\:\sum_{{r}=\mathrm{0}} ^{{n}} {a}_{{n}} \:\:\mathrm{please}\:\mathrm{how}\:\mathrm{do}\:\mathrm{i}\:\mathrm{rectify}\:\mathrm{this} \\ $$$$\mathrm{problem}?\:\mathrm{and}\:\mathrm{any}\:\mathrm{suggestion}\:\mathrm{on}\:\mathrm{a}\:\mathrm{better}\:\mathrm{application} \\ $$$$\mathrm{to}\:\mathrm{type}\:\mathrm{my}\:\mathrm{maths}\:\mathrm{papers}?\:\mathrm{thanks}\:\mathrm{in}\:\mathrm{advance}. \\ $$

Question Number 83603 Answers: 0 Comments: 4

∫ (dx/(1−2cos x))

$$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{x}} \\ $$

Question Number 83599 Answers: 0 Comments: 0