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Question Number 6475 Answers: 0 Comments: 3

Find a solution of the form ∅(x)=x^r Σ_(k=0) ^α c_k x^k (x > 0) for xy^(′′) + y′ − y = 0.

$${Find}\:{a}\:{solution}\:{of}\:{the}\:{form}\:\emptyset\left({x}\right)={x}^{{r}} \underset{{k}=\mathrm{0}} {\overset{\alpha} {\sum}}{c}_{{k}} {x}^{{k}} \:\left({x}\:>\:\mathrm{0}\right)\:{for}\: \\ $$$${xy}^{''} +\:{y}'\:−\:{y}\:=\:\mathrm{0}. \\ $$

Question Number 6419 Answers: 1 Comments: 0

Convert 34.8989898989 and 0.789789789789 to fraction.

$${Convert}\:\:\:\:\mathrm{34}.\mathrm{8989898989}\:\:\:\:{and}\:\:\:\:\mathrm{0}.\mathrm{789789789789}\: \\ $$$${to}\:{fraction}. \\ $$

Question Number 6432 Answers: 0 Comments: 3

Question Number 6384 Answers: 1 Comments: 3

Question Number 6240 Answers: 0 Comments: 6

∫e^x^2 dx

$$\int{e}^{{x}^{\mathrm{2}} } \:\:{dx}\: \\ $$

Question Number 6217 Answers: 1 Comments: 2

Question Number 6169 Answers: 1 Comments: 0

A telephone wire hangs from two points P, Q 60m apart P, Q are on the same level . the mid point of the telephone wire is 3m below the level of P, Q. Assuming that it hangs in form of a curve , find it equation. please help. thanks for your time.

$${A}\:{telephone}\:{wire}\:{hangs}\:{from}\:{two}\:{points}\:{P},\:{Q}\:\:\mathrm{60}{m}\:{apart} \\ $$$${P},\:{Q}\:\:{are}\:{on}\:{the}\:{same}\:{level}\:.\:{the}\:{mid}\:{point}\:{of}\:{the}\:{telephone} \\ $$$${wire}\:{is}\:\:\mathrm{3}{m}\:\:{below}\:{the}\:{level}\:{of}\:{P},\:{Q}.\:{Assuming}\:{that}\:{it}\:{hangs}\:{in}\: \\ $$$${form}\:{of}\:{a}\:{curve}\:,\:\:{find}\:{it}\:{equation}. \\ $$$$ \\ $$$${please}\:{help}.\:{thanks}\:{for}\:{your}\:{time}. \\ $$

Question Number 6157 Answers: 1 Comments: 0

Question Number 6132 Answers: 0 Comments: 1

Evaluate the integral of ... [(x−(x^3 /2)+(x^5 /(2.4))−(x^7 /(2.4.6))+....)(1−(x^2 /2^2 )+(x^4 /(2^2 .4^2 ))−(x^6 /(2^2 .4^2 .6^2 ))+....)]dx for 0 < x < ∞ The answer is saying ............ (√e) How is the answer (√e)

$${Evaluate}\:{the}\:{integral}\:{of}\:... \\ $$$$ \\ $$$$\left[\left({x}−\frac{{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{{x}^{\mathrm{5}} }{\mathrm{2}.\mathrm{4}}−\frac{{x}^{\mathrm{7}} }{\mathrm{2}.\mathrm{4}.\mathrm{6}}+....\right)\left(\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{{x}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{2}} .\mathrm{4}^{\mathrm{2}} }−\frac{{x}^{\mathrm{6}} }{\mathrm{2}^{\mathrm{2}} .\mathrm{4}^{\mathrm{2}} .\mathrm{6}^{\mathrm{2}} }+....\right)\right]{dx} \\ $$$$ \\ $$$${for}\:\:\mathrm{0}\:<\:\:{x}\:\:<\:\:\infty \\ $$$$ \\ $$$${The}\:{answer}\:{is}\:{saying}\:\:............\:\:\sqrt{{e}} \\ $$$$ \\ $$$${How}\:{is}\:{the}\:{answer}\:\:\sqrt{{e}} \\ $$

Question Number 6056 Answers: 1 Comments: 3

Question Number 6054 Answers: 1 Comments: 2

Determine distance between opposite corners of a cubic room of dimention x units.

$$\mathcal{D}{etermine}\:{distance}\:{between} \\ $$$${opposite}\:{corners}\:\:{of}\:{a}\:{cubic} \\ $$$${room}\:{of}\:{dimention}\:{x}\:{units}. \\ $$$$ \\ $$

Question Number 5998 Answers: 1 Comments: 5

determine equation of circle that offensive the both of coordinate and through (2,−1)

$${determine}\:{equation}\:{of}\:{circle}\:{that}\:{offensive}\:{the} \\ $$$${both}\:{of}\:{coordinate}\:{and}\:{through}\:\left(\mathrm{2},−\mathrm{1}\right) \\ $$

Question Number 6077 Answers: 0 Comments: 0

Question Number 5982 Answers: 0 Comments: 1

the center of circle in 2x+y−11=0 determine the equation of circle that passing through (−1,3),(7,−1)

$${the}\:{center}\:{of}\:{circle}\:{in}\:\mathrm{2}{x}+{y}−\mathrm{11}=\mathrm{0} \\ $$$${determine}\:{the}\:{equation}\:{of}\:{circle}\:{that} \\ $$$${passing}\:{through}\:\left(−\mathrm{1},\mathrm{3}\right),\left(\mathrm{7},−\mathrm{1}\right) \\ $$

Question Number 5825 Answers: 1 Comments: 1

Question Number 6081 Answers: 0 Comments: 1

∫e^(−st) (t^n /(n!))dt=?

$$\int{e}^{−{st}} \frac{{t}^{{n}} }{{n}!}{dt}=? \\ $$

Question Number 5822 Answers: 0 Comments: 0

Prove that among all triangles, which have same circum-radius, the equilateral triangle has maximum area.

$$\mathcal{P}{rove}\:{that}\:{among}\:{all}\:\boldsymbol{{triangles}}, \\ $$$${which}\:{have}\:{same}\:\boldsymbol{{circum}}-\boldsymbol{{radius}}, \\ $$$${the}\:\boldsymbol{{equilateral}}\:\boldsymbol{{triangle}}\:{has} \\ $$$$\boldsymbol{{maximum}}\:\boldsymbol{{area}}. \\ $$

Question Number 5816 Answers: 0 Comments: 2

Prove that among all cyclic n-gons, which have same radius, regular n-gon has maximum area.

$$\mathcal{P}{rove}\:{that}\:{among}\:{all}\:{cyclic}\:\:{n}-{gons},\: \\ $$$${which}\:{have}\:{same}\:{radius},\:{regular}\:{n}-{gon} \\ $$$${has}\:{maximum}\:{area}. \\ $$

Question Number 5763 Answers: 0 Comments: 1

Thanks. please can you show me the rest solution. i want to see the last steps. 2^x = 4x . Thanks for the time and the previous solution.

$${Thanks}.\:{please}\:{can}\:{you}\:{show}\:{me}\:{the}\:{rest}\:{solution}.\:{i}\:{want}\:{to}\: \\ $$$${see}\:{the}\:{last}\:{steps}.\:\:\mathrm{2}^{{x}} \:=\:\mathrm{4}{x}\:.\:\:{Thanks}\:{for}\:{the}\:{time}\:{and}\:{the}\: \\ $$$${previous}\:{solution}. \\ $$

Question Number 5672 Answers: 1 Comments: 0

Differentiate ((lnx)/e^x ) fom the first principle. Please help me.

$${Differentiate}\:\:\:\:\frac{{lnx}}{{e}^{{x}} }\:\:\:\:{fom}\:{the}\:{first}\:{principle}. \\ $$$$ \\ $$$${Please}\:{help}\:{me}. \\ $$

Question Number 5695 Answers: 1 Comments: 5

Question Number 5704 Answers: 1 Comments: 0

Show that ... Limit [((3^x − 3^(−x) )/(3^(x ) + 3^(−x) ))] = − 1 x → −∞

$${Show}\:{that}\:... \\ $$$$ \\ $$$${Limit}\:\:\:\:\:\:\left[\frac{\mathrm{3}^{{x}} \:−\:\mathrm{3}^{−{x}} }{\mathrm{3}^{{x}\:} \:+\:\mathrm{3}^{−{x}} }\right]\:=\:−\:\mathrm{1} \\ $$$${x}\:\rightarrow\:−\infty \\ $$

Question Number 5630 Answers: 0 Comments: 8

Question Number 5626 Answers: 1 Comments: 0

What is the length of chord in a circle of radius r which divides the circumference of circle in m : n ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{chord}}\:\mathrm{in}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{which}\:\:\mathrm{divides}\:\mathrm{the}\:\boldsymbol{\mathrm{circumference}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circle}}\:\mathrm{in}\:\boldsymbol{\mathrm{m}}\::\:\boldsymbol{\mathrm{n}}\:? \\ $$

Question Number 5620 Answers: 0 Comments: 2

Find the resolved part of the vector a = 6i − 3j + 9k in the diection of b = 2i + 2j − k please help. i got the answer to be (−1)

$${Find}\:{the}\:{resolved}\:{part}\:{of}\:{the}\:{vector}\:{a}\:=\:\mathrm{6}{i}\:−\:\mathrm{3}{j}\:+\:\mathrm{9}{k}\: \\ $$$${in}\:{the}\:{diection}\:{of}\:{b}\:=\:\mathrm{2}{i}\:+\:\mathrm{2}{j}\:−\:{k} \\ $$$$ \\ $$$${please}\:{help}. \\ $$$$ \\ $$$${i}\:{got}\:{the}\:{answer}\:{to}\:{be}\:\left(−\mathrm{1}\right) \\ $$

Question Number 5624 Answers: 0 Comments: 0

What is the length of chord in a circle of radius r which divides the region of circle in m : n ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{chord}}\:\mathrm{in}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{which}\:\mathrm{divides}\:\mathrm{the}\:\boldsymbol{\mathrm{region}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circle}}\:\mathrm{in}\:\boldsymbol{\mathrm{m}}\::\:\boldsymbol{\mathrm{n}}\:? \\ $$

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