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Question Number 104428 Answers: 4 Comments: 0

given a_(n+1) =a_(n−1) +2a_n if a_3 = 0 & a_5 = −1 find a_n

$${given}\:{a}_{{n}+\mathrm{1}} ={a}_{{n}−\mathrm{1}} +\mathrm{2}{a}_{{n}} \\ $$$${if}\:{a}_{\mathrm{3}} =\:\mathrm{0}\:\&\:{a}_{\mathrm{5}} \:=\:−\mathrm{1} \\ $$$${find}\:{a}_{{n}} \\ $$

Question Number 104426 Answers: 0 Comments: 0

Question Number 104421 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) ((ch(arctan(2x)))/(x^2 +x+1))dx

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

Question Number 104419 Answers: 2 Comments: 0

Now the sum of your father and your is 90 years. 5 years ago your father′s age was 3 times than your age. Write the your age and your father′s age 3 years after.

Question Number 104413 Answers: 2 Comments: 0

The sum of two integers is 304 and their GCD is 19. What are the numbers?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{integers}}\:\boldsymbol{\mathrm{is}}\:\mathrm{304} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{is}}\:\mathrm{19}.\:\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{numbers}}? \\ $$

Question Number 104411 Answers: 0 Comments: 5

Question Number 104410 Answers: 1 Comments: 0

If 11×11=121, 111×111=12321,1111×1111=1234321 then what is the answer of 111111×111111 ? (It is a short question)

Question Number 104406 Answers: 1 Comments: 1

Evaluate (1/2) + (3/8) + (3/(16)) + (5/(64)) + .....

$$\:\:\:\:\mathrm{Evaluate} \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{8}}\:+\:\frac{\mathrm{3}}{\mathrm{16}}\:+\:\frac{\mathrm{5}}{\mathrm{64}}\:+\:..... \\ $$

Question Number 104404 Answers: 1 Comments: 0

(4/5)=(?/(45))=((20)/?)=((144)/?)=((200)/?)

$$\frac{\mathrm{4}}{\mathrm{5}}=\frac{?}{\mathrm{45}}=\frac{\mathrm{20}}{?}=\frac{\mathrm{144}}{?}=\frac{\mathrm{200}}{?} \\ $$

Question Number 104391 Answers: 0 Comments: 1

(x−a)(x−b)(x−c)....(x−z) = ?

$$\left(\boldsymbol{{x}}−\boldsymbol{{a}}\right)\left(\boldsymbol{{x}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{x}}−\boldsymbol{{c}}\right)....\left(\boldsymbol{{x}}−\boldsymbol{{z}}\right)\:=\:? \\ $$

Question Number 104390 Answers: 1 Comments: 0

Question Number 104394 Answers: 1 Comments: 0

Question Number 104388 Answers: 1 Comments: 0

∫(dx/(x^2 ((x^3 −1))^(1/3) ))

$$\int\frac{\mathrm{d}{x}}{{x}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} −\mathrm{1}}} \\ $$

Question Number 104383 Answers: 1 Comments: 1

When f(x) is a differentiable function satisfying x∙f(x)=x^2 +∫_0 ^( x) (x−t)∙f ′(t)dt Find ⇒ f(1)

$$\mathrm{When}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\mathrm{satisfying}\:\:{x}\centerdot{f}\left({x}\right)={x}^{\mathrm{2}} +\int_{\mathrm{0}} ^{\:{x}} \left({x}−{t}\right)\centerdot{f}\:'\left({t}\right){dt} \\ $$$$\mathrm{Find}\:\Rightarrow\:{f}\left(\mathrm{1}\right) \\ $$

Question Number 104377 Answers: 1 Comments: 6

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 .... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{196}\:\:\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:....\:\left(\mathrm{iii}\right) \\ $$

Question Number 104371 Answers: 1 Comments: 0

Question Number 104370 Answers: 1 Comments: 0

Question Number 104369 Answers: 1 Comments: 0

Question Number 104368 Answers: 1 Comments: 0

CH_3 CH_2 −CH=CH_2 +HCl→ help me

$${CH}_{\mathrm{3}} {CH}_{\mathrm{2}} −{CH}={CH}_{\mathrm{2}} +{HCl}\rightarrow \\ $$$${help}\:{me} \\ $$

Question Number 104367 Answers: 1 Comments: 0

CH_3 −CH_2 −CH_2 −CH_2 Cl+KOH→ help me

$${CH}_{\mathrm{3}} −{CH}_{\mathrm{2}} −{CH}_{\mathrm{2}} −{CH}_{\mathrm{2}} {Cl}+{KOH}\rightarrow \\ $$$${help}\:{me} \\ $$

Question Number 104366 Answers: 0 Comments: 2

CH_3 −CH_2 −CHMgCl−CH_3 +H_2 O→ help me

$${CH}_{\mathrm{3}} −{CH}_{\mathrm{2}} −{CHMgCl}−{CH}_{\mathrm{3}} +{H}_{\mathrm{2}} {O}\rightarrow \\ $$$${help}\:{me} \\ $$

Question Number 104364 Answers: 2 Comments: 1

Question Number 104853 Answers: 0 Comments: 0

lim_(x→1) Li(x^2 )−Li(x)=ln2

$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{Li}\left({x}^{\mathrm{2}} \right)−{Li}\left({x}\right)={ln}\mathrm{2} \\ $$

Question Number 104359 Answers: 1 Comments: 0

solve this using Riemann sum f(x)=2x ; [0,4] for n=4

$${solve}\:{this}\:{using}\:{Riemann} \\ $$$${sum}\:{f}\left({x}\right)=\mathrm{2}{x}\:;\:\left[\mathrm{0},\mathrm{4}\right]\:{for}\:{n}=\mathrm{4} \\ $$

Question Number 104357 Answers: 2 Comments: 0

(x+y+1) (dy/dx) = 1

$$\left({x}+{y}+\mathrm{1}\right)\:\frac{{dy}}{{dx}}\:=\:\mathrm{1}\: \\ $$

Question Number 104852 Answers: 0 Comments: 0

if g∈C(R,R) and. ∫_0 ^1 g(x)dx=(1/3)+∫_0 ^1 g^2 (x^2 )dx then ∫_0 ^1 g(x)dx=(2/3) and ∫_0 ^1 g^2 (x)dx=(1/2)

$$\:\:{if}\:\:{g}\in{C}\left(\mathbb{R},\mathbb{R}\right)\:{and}.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{3}}+\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right){dx}\: \\ $$$${then}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}\left({x}\right){dx}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$

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