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Question Number 45963    Answers: 1   Comments: 1

find the value of Σ_(n=1) ^∞ (n/((4n^2 −1)^2 )) .

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}}{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$

Question Number 45941    Answers: 1   Comments: 0

Find 0<θ<2π with x,y ∈R x∙sinθ=y∙cosθ

$$\mathrm{Find}\:\mathrm{0}<\theta<\mathrm{2}\pi\:\mathrm{with}\:{x},{y}\:\in\mathbb{R} \\ $$$$ \\ $$$${x}\centerdot{sin}\theta={y}\centerdot{cos}\theta \\ $$

Question Number 45936    Answers: 0   Comments: 1

Question Number 45932    Answers: 1   Comments: 4

Show that: ((1.2^2 + 2.3^2 + ... + n(n + 1)^2 )/(1^2 .2 + 2^2 .3 + ... + n^2 (n + 1))) = ((3n + 5)/(3n + 1))

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\frac{\mathrm{1}.\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{2}.\mathrm{3}^{\mathrm{2}} \:+\:...\:+\:\mathrm{n}\left(\mathrm{n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}^{\mathrm{2}} .\mathrm{2}\:+\:\mathrm{2}^{\mathrm{2}} .\mathrm{3}\:+\:...\:+\:\mathrm{n}^{\mathrm{2}} \left(\mathrm{n}\:+\:\mathrm{1}\right)}\:\:=\:\:\frac{\mathrm{3n}\:+\:\mathrm{5}}{\mathrm{3n}\:+\:\mathrm{1}} \\ $$

Question Number 45931    Answers: 0   Comments: 0

Question Number 45930    Answers: 1   Comments: 0

Question Number 45920    Answers: 1   Comments: 0

Question Number 45916    Answers: 1   Comments: 0

∫f(x)dx=f(×)+c

$$\int{f}\left({x}\right){dx}={f}\left(×\right)+{c} \\ $$

Question Number 45901    Answers: 0   Comments: 1

Question Number 45898    Answers: 1   Comments: 1

Question Number 45907    Answers: 1   Comments: 3

7×(6+x)−10=60 plz help me

$$\mathrm{7}×\left(\mathrm{6}+\mathrm{x}\right)−\mathrm{10}=\mathrm{60}\:\:\:\:\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 45905    Answers: 2   Comments: 0

Question Number 45896    Answers: 2   Comments: 2

solve for x x^4 −4x+1=0

$$\boldsymbol{{solve}}\:\boldsymbol{{for}}\:\boldsymbol{{x}} \\ $$$$\boldsymbol{{x}}^{\mathrm{4}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 45885    Answers: 1   Comments: 3

Question Number 45879    Answers: 0   Comments: 0

2^x =log_(0.5) x find x−?

$$\mathrm{2}^{\boldsymbol{{x}}} =\boldsymbol{{log}}_{\mathrm{0}.\mathrm{5}} \boldsymbol{{x}} \\ $$$$\boldsymbol{{find}}\:\:\boldsymbol{{x}}−? \\ $$

Question Number 45876    Answers: 1   Comments: 0

Question Number 45856    Answers: 0   Comments: 1

Prove that the length of the perpendicular from the origin to the plane passing through point a^→ and containing the line r^→ =b^→ +λc^→ is (([a^→ b^→ c^→ ])/(∣b^→ ×c^→ +c^→ ×a^→ ∣)) . Here [a^→ b^→ c^→ ] = scalar triple product.

$${Prove}\:{that}\:{the}\:{length}\:{of}\:{the}\:{perpendicular} \\ $$$${from}\:{the}\:{origin}\:{to}\:{the}\:{plane}\:{passing} \\ $$$${through}\:{point}\:\overset{\rightarrow} {{a}}\:{and}\:{containing}\:{the} \\ $$$${line}\:\overset{\rightarrow} {{r}}=\overset{\rightarrow} {{b}}+\lambda\overset{\rightarrow} {{c}}\:{is}\:\frac{\left[\overset{\rightarrow} {{a}}\:\:\overset{\rightarrow} {{b}}\:\:\overset{\rightarrow} {{c}}\:\right]}{\mid\overset{\rightarrow} {{b}}×\overset{\rightarrow} {{c}}\:+\overset{\rightarrow} {{c}}×\overset{\rightarrow} {{a}}\mid}\:. \\ $$$${Here}\:\left[\overset{\rightarrow} {{a}}\:\overset{\rightarrow} {{b}}\:\overset{\rightarrow} {{c}}\right]\:=\:{scalar}\:{triple}\:{product}. \\ $$

Question Number 45846    Answers: 1   Comments: 1

ph=−log[H]

$${ph}=−{log}\left[{H}\right] \\ $$

Question Number 45844    Answers: 1   Comments: 1

If y=((sec^2 θ−tan θ)/(sec^2 θ+tan θ)) , then

$$\mathrm{If}\:\:{y}=\frac{\mathrm{sec}^{\mathrm{2}} \theta−\mathrm{tan}\:\theta}{\mathrm{sec}^{\mathrm{2}} \theta+\mathrm{tan}\:\theta}\:,\:\mathrm{then} \\ $$

Question Number 45842    Answers: 1   Comments: 8

Question Number 45841    Answers: 1   Comments: 2

∫_0 ^( ∞) e^(−ix^2 ) dx=?? plz..

$$\int_{\mathrm{0}} ^{\:\infty} \:{e}^{−{ix}^{\mathrm{2}} } {dx}=?? \\ $$$$\mathrm{plz}.. \\ $$

Question Number 45840    Answers: 0   Comments: 0

a≦7⇒P(!∃x_a )=0, b≦9⇒Q(!∃y_b )=0 for a, b∈N And A⊋A′: A={(x, y)∣P(x)∙Q(y)=0}=A′, B_(∈A) ={(x, y)∈A∣x=y} Then ∀t∈N: ∣B∣=n(t)=f(P(x), Q(y)), also only t can be in [N, M]. find M. :(

$${a}\leqq\mathrm{7}\Rightarrow\mathrm{P}\left(!\exists{x}_{{a}} \right)=\mathrm{0}, \\ $$$${b}\leqq\mathrm{9}\Rightarrow\mathrm{Q}\left(!\exists{y}_{{b}} \right)=\mathrm{0}\:\mathrm{for}\:{a},\:{b}\in\mathbb{N} \\ $$$$\mathrm{And}\:{A}\supsetneq{A}':\:{A}=\left\{\left({x},\:{y}\right)\mid\mathrm{P}\left({x}\right)\centerdot\mathrm{Q}\left({y}\right)=\mathrm{0}\right\}={A}', \\ $$$${B}_{\in{A}} =\left\{\left({x},\:{y}\right)\in{A}\mid{x}={y}\right\} \\ $$$$\mathrm{Then}\:\forall{t}\in\mathbb{N}:\:\mid{B}\mid={n}\left({t}\right)={f}\left(\mathrm{P}\left({x}\right),\:\mathrm{Q}\left({y}\right)\right), \\ $$$$\mathrm{also}\:\mathrm{only}\:{t}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\left[{N},\:{M}\right]. \\ $$$$\mathrm{find}\:{M}. \\ $$$$:\left(\right. \\ $$

Question Number 45830    Answers: 0   Comments: 1

Given A= sin^2 θ + cos^4 θ, then for all real θ

$$\mathrm{Given}\:{A}=\:\mathrm{sin}^{\mathrm{2}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta,\:\mathrm{then}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\theta \\ $$

Question Number 45829    Answers: 0   Comments: 2

Given A= sin^2 θ + cos^4 θ, then for all real θ

$$\mathrm{Given}\:{A}=\:\mathrm{sin}^{\mathrm{2}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta,\:\mathrm{then}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\theta \\ $$

Question Number 45814    Answers: 0   Comments: 0

thank you sis

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sis} \\ $$

Question Number 45812    Answers: 0   Comments: 0

plz help me

$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

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