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AlgebraQuestion and Answers: Page 1

Question Number 226743 Answers: 0 Comments: 0

Prove:(1/(2ne))<(1/e)−(1−(1/n))^n <(1/(ne))

$$ \\ $$$${Prove}:\frac{\mathrm{1}}{\mathrm{2}{ne}}<\frac{\mathrm{1}}{{e}}−\left(\mathrm{1}−\frac{\mathrm{1}}{{n}}\right)^{{n}} <\frac{\mathrm{1}}{{ne}} \\ $$

Question Number 226728 Answers: 1 Comments: 0

Find: ∫_0 ^( (𝛑/4)) (dx/(1 + sin^2 x)) = ?

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$

Question Number 226713 Answers: 0 Comments: 0

If p=(1/x)−(1/x^2 ) what should p=(((N)_4 )/((D)_4 )) (N)_4 means numerator of p in quaternary for x to be 777?

$$\:\:{If}\: \\ $$$${p}=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$${what}\:{should}\:{p}=\frac{\left({N}\right)_{\mathrm{4}} }{\left({D}\right)_{\mathrm{4}} } \\ $$$$\left({N}\right)_{\mathrm{4}} \:{means}\:{numerator}\:{of}\:{p}\:\:{in} \\ $$$${quaternary}\:{for}\:{x}\:{to}\:{be}\:\mathrm{777}? \\ $$

Question Number 226675 Answers: 0 Comments: 5

Question Number 226603 Answers: 3 Comments: 0

Formulate the differential equation of the solution (a)y=Ae^(bx+1) (b)y=Asin x+Bcos x

$${Formulate}\:{the}\:{differential} \\ $$$${equation}\:{of}\:{the}\:{solution} \\ $$$$\left({a}\right){y}={Ae}^{{bx}+\mathrm{1}} \\ $$$$\left({b}\right){y}={A}\mathrm{sin}\:{x}+{B}\mathrm{cos}\:{x} \\ $$$$ \\ $$

Question Number 226577 Answers: 2 Comments: 0

Question Number 226558 Answers: 1 Comments: 0

Question Number 226569 Answers: 1 Comments: 2

a^4 + b^4 + c^4 = 2d^2 Prove that the equation has an infinite number of natural solutions

$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:=\:\mathrm{2d}^{\mathrm{2}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{solutions} \\ $$

Question Number 226536 Answers: 2 Comments: 0

If (x+(2a^2 +5))(x−(2a^2 +7)) ≤ 0 x∈[−(a^2 +8a−10) ; (a^2 +9a−11)] Find: a = ?

$$\mathrm{If}\:\:\:\left(\mathrm{x}+\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{5}\right)\right)\left(\mathrm{x}−\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{7}\right)\right)\:\leqslant\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\mathrm{x}\in\left[−\left(\mathrm{a}^{\mathrm{2}} +\mathrm{8a}−\mathrm{10}\right)\:;\:\left(\mathrm{a}^{\mathrm{2}} +\mathrm{9a}−\mathrm{11}\right)\right] \\ $$$$\mathrm{Find}:\:\boldsymbol{\mathrm{a}}\:=\:? \\ $$

Question Number 226533 Answers: 1 Comments: 0

Question Number 226515 Answers: 2 Comments: 2

Question Number 226509 Answers: 1 Comments: 0

Find: Σ_(n=1) ^∞ (1/(n∙(2n + 1)^2 )) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}\centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 226471 Answers: 2 Comments: 2

If, x^2 +2y^2 ∞xy then prove that, 2x^2 +y^2 ∞xy

$$\:{If},\:{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \infty{xy}\: \\ $$$$\:\:{then}\:{prove}\:{that},\:\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \infty{xy} \\ $$

Question Number 226409 Answers: 2 Comments: 0

Question Number 226362 Answers: 1 Comments: 0

Question Number 226176 Answers: 1 Comments: 1

Question Number 226149 Answers: 2 Comments: 0

Question Number 226144 Answers: 2 Comments: 0

6^x + 6^y = 42 x + y =3 Find x and y ?

$$\mathrm{6}^{{x}} \:+\:\mathrm{6}^{{y}} \:=\:\mathrm{42} \\ $$$${x}\:+\:{y}\:=\mathrm{3} \\ $$$${Find}\:{x}\:{and}\:{y}\:? \\ $$

Question Number 226118 Answers: 2 Comments: 0

Question Number 226117 Answers: 3 Comments: 0

Question Number 226115 Answers: 0 Comments: 3

can we find the black area (the shadow of earth)on the moon during moon eclipse after time t of its starting? Given: Moon radius=R_m Earth rafius=R_e Sun radius=R_s ω_e and ω_m given(both anticlockwise) ω_m ⇒Earth is center ω_e ⇒Sun is center Sun Earth distance(center)=L_(S−E) Earth Moon distance(center)=L_(E−M)

$${can}\:{we}\:{find}\:{the}\:{black}\:{area} \\ $$$$\left({the}\:{shadow}\:{of}\:{earth}\right){on}\:{the}\:{moon}\:{during} \\ $$$${moon}\:{eclipse}\:{after}\:{time}\:{t}\:{of} \\ $$$${its}\:{starting}? \\ $$$${Given}: \\ $$$${Moon}\:{radius}={R}_{{m}} \\ $$$${Earth}\:{rafius}={R}_{{e}} \\ $$$${Sun}\:{radius}={R}_{{s}} \\ $$$$\omega_{{e}} \:{and}\:\omega_{{m}} \:{given}\left({both}\:{anticlockwise}\right) \\ $$$$\omega_{{m}} \Rightarrow{Earth}\:{is}\:{center} \\ $$$$\omega_{{e}} \Rightarrow{Sun}\:{is}\:{center} \\ $$$${Sun}\:{Earth}\:{distance}\left({center}\right)={L}_{{S}−{E}} \\ $$$${Earth}\:{Moon}\:{distance}\left({center}\right)={L}_{{E}−{M}} \\ $$

Question Number 226112 Answers: 2 Comments: 0

Question Number 226111 Answers: 1 Comments: 0

Show that the equation (1/(sinθ+cosθ)) + (1/(sinθ−cosθ)) = 1 may be express in the form a(sinθ)^2 +bsinθ+c=0 where a b and c are constants to be found.

$${Show}\:{that}\:{the}\:{equation} \\ $$$$\frac{\mathrm{1}}{{sin}\theta+{cos}\theta}\:+\:\frac{\mathrm{1}}{{sin}\theta−{cos}\theta}\:=\:\mathrm{1} \\ $$$${may}\:{be}\:{express}\:{in}\:{the}\:{form} \\ $$$${a}\left({sin}\theta\right)^{\mathrm{2}} +{bsin}\theta+{c}=\mathrm{0}\:{where}\:{a}\:{b}\: \\ $$$${and}\:{c}\:{are}\:{constants}\:{to}\:{be}\:{found}. \\ $$

Question Number 226053 Answers: 1 Comments: 0

The coefficient of x^2 in the expansion of (1+ (2/p)x)^5 + (1+px)^6 is 70. Find the possible values of the constant p.

$${The}\:{coefficient}\:{of}\:{x}^{\mathrm{2}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\:\left(\mathrm{2}/{p}\right){x}\right)^{\mathrm{5}} \:+\:\left(\mathrm{1}+{px}\right)^{\mathrm{6}} \:{is}\:\mathrm{70}. \\ $$$${Find}\:{the}\:{possible}\:{values}\:{of}\:{the} \\ $$$${constant}\:{p}. \\ $$

Question Number 226045 Answers: 0 Comments: 0

Question Number 226015 Answers: 1 Comments: 0

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