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AllQuestion and Answers: Page 1877

Question Number 14244    Answers: 1   Comments: 0

Question Number 14219    Answers: 1   Comments: 0

Question Number 14211    Answers: 0   Comments: 11

x^2 +y^2 +xy=4 y^2 +z^2 +yz=9 z^2 +x^2 +zx=16

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{4} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{9} \\ $$$${z}^{\mathrm{2}} +{x}^{\mathrm{2}} +{zx}=\mathrm{16} \\ $$

Question Number 14330    Answers: 0   Comments: 1

tanθ+tan2θ=tan3θ ((tanθ+tan2θ)/(1−tanθtan2θ))(1−tanθtan2θ)=tan3θ tan3θ(1−tanθtan2θ)=tan3θ tanθtan2θtan3θ 0 3θ=kπ, where k=0,1,2,3,... θ=((kπ)/3) tanθ=0 or tan2θ=0 or tan 3θ = 0 θ=mπ, where m=0,1,2,3,... 2θ=nπ, where n=0,1,2,3,... θ=((nπ)/2) but θ∉(((p+1)π)/2), p=0,1,2,3,... The exhaustive set ={θ/θ=((kπ)/3) or θ=mπ}

$${tan}\theta+{tan}\mathrm{2}\theta={tan}\mathrm{3}\theta \\ $$$$\frac{{tan}\theta+{tan}\mathrm{2}\theta}{\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta}\left(\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta\right)={tan}\mathrm{3}\theta \\ $$$${tan}\mathrm{3}\theta\left(\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta\right)={tan}\mathrm{3}\theta \\ $$$${tan}\theta{tan}\mathrm{2}\theta{tan}\mathrm{3}\theta\:\mathrm{0} \\ $$$$\mathrm{3}\theta={k}\pi,\:{where}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\theta=\frac{{k}\pi}{\mathrm{3}} \\ $$$${tan}\theta=\mathrm{0}\:\:{or}\:\:{tan}\mathrm{2}\theta=\mathrm{0}\:{or}\:{tan}\:\mathrm{3}\theta\:=\:\mathrm{0} \\ $$$$\theta={m}\pi,\:{where}\:{m}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\mathrm{2}\theta={n}\pi,\:{where}\:{n}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\theta=\frac{{n}\pi}{\mathrm{2}}\:{but}\:\theta\notin\frac{\left({p}+\mathrm{1}\right)\pi}{\mathrm{2}},\:{p}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$${The}\:{exhaustive}\:{set}\:=\left\{\theta/\theta=\frac{{k}\pi}{\mathrm{3}}\:{or}\:\theta={m}\pi\right\} \\ $$

Question Number 14215    Answers: 1   Comments: 0

Question Number 14243    Answers: 2   Comments: 0

∫ [x (lnx)^2 ] dx

$$\int\:\left[\mathrm{x}\:\left(\mathrm{lnx}\right)^{\mathrm{2}} \right]\:\mathrm{dx} \\ $$

Question Number 14189    Answers: 2   Comments: 0

Solve: (√(sinx)) + (√(cosx)) = 1 x ∈ R

$$\mathrm{Solve}:\:\:\:\sqrt{\mathrm{sinx}}\:+\:\sqrt{\mathrm{cosx}}\:=\:\mathrm{1} \\ $$$$\mathrm{x}\:\in\:\mathrm{R} \\ $$

Question Number 14181    Answers: 1   Comments: 0

∫ sec^6 (x) dx

$$\int\:\mathrm{sec}^{\mathrm{6}} \left(\mathrm{x}\right)\:\:\mathrm{dx}\:\: \\ $$

Question Number 14174    Answers: 1   Comments: 0

xtan(cos^(−1) x)=cos(sin^(−1) x) prove it.....

$$\:\:{xtan}\left({cos}^{−\mathrm{1}} {x}\right)={cos}\left({sin}^{−\mathrm{1}} {x}\right) \\ $$$${prove}\:{it}..... \\ $$

Question Number 14172    Answers: 0   Comments: 0

Question Number 14171    Answers: 0   Comments: 0

Question Number 14170    Answers: 0   Comments: 0

Question Number 14169    Answers: 0   Comments: 0

Question Number 14157    Answers: 2   Comments: 11

Question Number 14156    Answers: 1   Comments: 0

please what does ω mean?

$$\mathrm{please}\:\mathrm{what}\:\mathrm{does}\:\omega\:\mathrm{mean}? \\ $$

Question Number 14152    Answers: 1   Comments: 0

Question Number 14148    Answers: 2   Comments: 0

Determine (a) i^i (b) ω^ω (c) i^ω (d) ω^i

$$\mathrm{Determine} \\ $$$$\left({a}\right)\:{i}^{{i}} \\ $$$$\left({b}\right)\:\omega^{\omega} \\ $$$$\left({c}\right)\:{i}^{\omega} \\ $$$$\left({d}\right)\:\omega^{{i}} \\ $$

Question Number 14147    Answers: 0   Comments: 1

Determine: (a) e^ω (b) ω^e

$$\mathrm{Determine}: \\ $$$$\left({a}\right)\:\mathrm{e}^{\omega} \\ $$$$\left({b}\right)\:\omega^{\mathrm{e}} \\ $$

Question Number 14145    Answers: 1   Comments: 1

Question Number 14144    Answers: 1   Comments: 0

Question Number 14139    Answers: 1   Comments: 1

Question Number 14130    Answers: 1   Comments: 4

How to find maximum value of k if ((5 − cos 2θ)/(sin θ)) ≥ 2k 0 ≤ θ ≤ π

$$\mathrm{How}\:\mathrm{to}\:\mathrm{find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{if} \\ $$$$\frac{\mathrm{5}\:−\:\mathrm{cos}\:\mathrm{2}\theta}{\mathrm{sin}\:\theta}\:\:\geqslant\:\mathrm{2}{k}\:\:\:\:\:\:\:\:\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\pi \\ $$

Question Number 14128    Answers: 1   Comments: 0

If ((Px)/((b−c))) = ((Qy)/((c−a))) = ((Rz)/((a−b))) , then find Pax + Qby + Rcz.

$$\mathrm{If}\:\:\frac{\mathrm{P}{x}}{\left({b}−{c}\right)}\:=\:\frac{\mathrm{Q}{y}}{\left({c}−{a}\right)}\:=\:\frac{\mathrm{R}{z}}{\left({a}−{b}\right)}\:,\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{P}{ax}\:+\:\mathrm{Q}{by}\:+\:\mathrm{R}{cz}. \\ $$

Question Number 14119    Answers: 0   Comments: 10

For what values of n∈N, ω^(1/n) can be expressed as ω^m where m∈Z?

$$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\in\mathbb{N}, \\ $$$$\omega^{\mathrm{1}/\mathrm{n}} \:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\omega^{\mathrm{m}} \\ $$$$\mathrm{where}\:\mathrm{m}\in\mathbb{Z}? \\ $$

Question Number 14113    Answers: 0   Comments: 4

Is this incorrect: S=2×2×... S=2(2×2×...) S=2S S=0 Please explain why

$$\mathrm{Is}\:\mathrm{this}\:\mathrm{incorrect}: \\ $$$${S}=\mathrm{2}×\mathrm{2}×... \\ $$$${S}=\mathrm{2}\left(\mathrm{2}×\mathrm{2}×...\right) \\ $$$${S}=\mathrm{2}{S} \\ $$$${S}=\mathrm{0} \\ $$$$\: \\ $$$$\mathrm{Please}\:\mathrm{explain}\:\mathrm{why} \\ $$

Question Number 14109    Answers: 0   Comments: 3

(a^p −a) mod p = 0 when is this true? a,p∈Z

$$\left({a}^{{p}} −{a}\right)\:\mathrm{mod}\:{p}\:=\:\mathrm{0} \\ $$$$\mathrm{when}\:\mathrm{is}\:\mathrm{this}\:\mathrm{true}? \\ $$$${a},{p}\in\mathbb{Z} \\ $$

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