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Question Number 56641 Answers: 1 Comments: 2

x^5 +ax^4 +cx^2 +dx+e=0 let x=((rt+s)/(t+p)) . Find r,s,p such that equation gets transformed to λt^5 +Dt+E=0.

$$\mathrm{x}^{\mathrm{5}} +\mathrm{ax}^{\mathrm{4}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{e}=\mathrm{0} \\ $$$$\mathrm{let}\:\mathrm{x}=\frac{\mathrm{rt}+\mathrm{s}}{\mathrm{t}+\mathrm{p}}\:\:.\:\mathrm{Find}\:\mathrm{r},\mathrm{s},\mathrm{p}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{equation}\:\mathrm{gets}\:\mathrm{transformed} \\ $$$$\mathrm{to}\:\:\:\:\:\lambda\mathrm{t}^{\mathrm{5}} +\mathrm{Dt}+\mathrm{E}=\mathrm{0}. \\ $$

Question Number 56639 Answers: 0 Comments: 1

Question Number 56635 Answers: 0 Comments: 1

∫((√(tanx))/(sinx))dx

$$\int\frac{\sqrt{\mathrm{tan}{x}}}{\mathrm{sin}{x}}\mathrm{d}{x} \\ $$

Question Number 56624 Answers: 0 Comments: 2

How many numbers greater than 2000 can be formed using the digits 1,3,4,5,6? how many of these will be even? repetition not allowed.

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2000} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}? \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{will}\:\mathrm{be}\:\mathrm{even}? \\ $$$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}. \\ $$

Question Number 56615 Answers: 0 Comments: 4

In how many different ways can the letters of the word OKINKWO be arranged? In how many of these arrangements does an O occupy both end points of the word?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{OKINKWO}\:\mathrm{be}\:\mathrm{arranged}?\: \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{arrangements} \\ $$$$\mathrm{does}\:\mathrm{an}\:\mathrm{O}\:\mathrm{occupy}\:\mathrm{both}\:\mathrm{end}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{word}? \\ $$

Question Number 56612 Answers: 1 Comments: 0

Question Number 56607 Answers: 0 Comments: 2

Question Number 56602 Answers: 1 Comments: 1

Sum the series: sin^2 (α) + sin^2 (2α) + sin^2 (3α) + ... + sin^2 (nα)

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{sin}^{\mathrm{2}} \left(\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2}\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}\alpha\right)\:+\:...\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{n}\alpha\right) \\ $$

Question Number 56597 Answers: 0 Comments: 3

Question Number 56594 Answers: 1 Comments: 0

Find the nth term of the sequence (a) (1/2), (1/4), (1/8), (7/(62)), ... (b) (1/2), (1/4), (1/8), 0, ...

$$\mathrm{Find}\:\mathrm{the}\:{n}\mathrm{th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence} \\ $$$$\left({a}\right)\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{4}},\:\frac{\mathrm{1}}{\mathrm{8}},\:\frac{\mathrm{7}}{\mathrm{62}},\:... \\ $$$$\left({b}\right)\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{4}},\:\frac{\mathrm{1}}{\mathrm{8}},\:\mathrm{0},\:... \\ $$

Question Number 56585 Answers: 0 Comments: 3

Question Number 56584 Answers: 1 Comments: 0

Question Number 56583 Answers: 0 Comments: 1

let f(x) =((cosx)/(x^2 +1)) 1) calculate f^((n)) (x) then f^((n)) (0) 2)calculste f^((n)) (0) 3) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\frac{{cosx}}{{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{then}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){calculste}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 56580 Answers: 1 Comments: 0

(D^3 −2D^2 +9D−18)y=6cos3x

$$\left(\mathrm{D}^{\mathrm{3}} −\mathrm{2D}^{\mathrm{2}} +\mathrm{9D}−\mathrm{18}\right)\mathrm{y}=\mathrm{6cos3x} \\ $$

Question Number 56578 Answers: 0 Comments: 3

Question Number 56629 Answers: 0 Comments: 2

1) calculate I =∫_(−∞) ^(+∞) (dx/(x^2 −i)) and J =∫_(−∞) ^(+∞) (dx/(x^2 −i)) 2) find the value of ∫_(−∞) ^(+∞) (dx/(x^4 +1))

$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 56575 Answers: 1 Comments: 2

Question Number 56569 Answers: 0 Comments: 0

Question Number 56565 Answers: 0 Comments: 2

It is my kind request to those who post questions ...pls go through the details of answer...and give feed back...pls activate yourselves to pay your attention in the details of answer...do not become self satisfied by getting your desired results.. unfurl your mind and act in such away that we get a tip of iceberg of your satisfation.Tanmay

$${It}\:{is}\:{my}\:{kind}\:{request}\:{to}\:{those}\:{who}\:{post}\:{questions} \\ $$$$...{pls}\:{go}\:{through}\:{the}\:{details}\:{of}\:{answer}...{and}\:{give} \\ $$$${feed}\:{back}...{pls}\:{activate}\:{yourselves}\:{to}\:{pay}\:{your} \\ $$$${attention}\:{in}\:{the}\:{details}\:{of}\:{answer}...{do}\:{not}\:{become} \\ $$$${self}\:{satisfied}\:{by}\:{getting}\:{your}\:{desired}\:{results}.. \\ $$$${unfurl}\:{your}\:{mind}\:{and}\:{act}\:{in}\:{such}\:{away}\:{that} \\ $$$${we}\:{get}\:{a}\:{tip}\:{of}\:{iceberg}\:{of}\:{your}\:{satisfation}.{Tanmay} \\ $$

Question Number 56555 Answers: 0 Comments: 7

Question Number 56553 Answers: 1 Comments: 0

solve for m m^8 =3125

$$\mathrm{solve}\:\mathrm{for}\:{m} \\ $$$${m}^{\mathrm{8}} =\mathrm{3125} \\ $$

Question Number 56525 Answers: 4 Comments: 2

Question Number 56524 Answers: 0 Comments: 2

Question Number 56523 Answers: 0 Comments: 2

∫x(√(3x^3 +2)) dx=?

$$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}}\:{dx}=? \\ $$

Question Number 56534 Answers: 1 Comments: 1

Question Number 56510 Answers: 1 Comments: 2

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