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GeometryQuestion and Answers: Page 109

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 ?

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

Question Number 5561 Answers: 1 Comments: 2

A chord is drawn in a circle that divides the circle in 1:2 (ratio). In what ratio the chord divides the diameter perpendicular to the chord?

$$\mathrm{A}\:\mathrm{chord}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{that} \\ $$$$\mathrm{divides}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{1}:\mathrm{2}\:\left(\mathrm{ratio}\right). \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{ratio}\:\mathrm{the}\:\mathrm{chord}\:\mathrm{divides} \\ $$$$\mathrm{the}\:\mathrm{diameter}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{chord}? \\ $$

Question Number 5556 Answers: 0 Comments: 2

The area of a circle is diretly proportional to the square of its diameter. What is the constant of proportionality?

$$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{diretly}\: \\ $$$$\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{diameter}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{proportionality}? \\ $$

Question Number 5543 Answers: 0 Comments: 0

•What plane geometrical figures could be produced by joining vertices of a cube? (for example : square) •What largest area(2 dimensional) can be obtained by joining vertices of a cube when its side is x?

$$\bullet\mathrm{What}\:\boldsymbol{\mathrm{plane}}\:\boldsymbol{\mathrm{geometrical}}\:\boldsymbol{\mathrm{figures}} \\ $$$$\mathrm{could}\:\mathrm{be}\:\mathrm{produced}\:\mathrm{by}\:\mathrm{joining} \\ $$$$\boldsymbol{\mathrm{vertices}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{cube}}? \\ $$$$\left(\mathrm{for}\:\mathrm{example}\::\:\mathrm{square}\right) \\ $$$$\bullet\mathrm{What}\:\mathrm{largest}\:\mathrm{area}\left(\mathrm{2}\:\mathrm{dimensional}\right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{obtained} \\ $$$$\mathrm{by}\:\mathrm{joining}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{when}\:\mathrm{its}\:\mathrm{side}\:\mathrm{is}\:\mathrm{x}? \\ $$

Question Number 5542 Answers: 0 Comments: 1

The surface area of a cylinder is: A=2πr^2 +2πrh As h→0, the shape becomes a 2D circle, so should lim_(h→0) A = πr^2 ??? Or is it that as h→0, it creates a circle of 3 dimensions with infintesimally small height, so it has two circles making it: lim_(h→0) A = 2πr^2 ???

$$\mathrm{The}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cylinder}\:\mathrm{is}: \\ $$$${A}=\mathrm{2}\pi{r}^{\mathrm{2}} +\mathrm{2}\pi{rh} \\ $$$$ \\ $$$$\mathrm{As}\:{h}\rightarrow\mathrm{0},\:\mathrm{the}\:\mathrm{shape}\:\mathrm{becomes}\:\mathrm{a}\:\mathrm{2D}\:\mathrm{circle}, \\ $$$$\mathrm{so}\:\mathrm{should}\:\:\:\:\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{A}\:=\:\pi{r}^{\mathrm{2}} \:\:\:??? \\ $$$$\mathrm{Or}\:\mathrm{is}\:\mathrm{it}\:\mathrm{that}\:\mathrm{as}\:{h}\rightarrow\mathrm{0},\:\mathrm{it}\:\mathrm{creates}\:\mathrm{a}\:\mathrm{circle} \\ $$$$\mathrm{of}\:\mathrm{3}\:\mathrm{dimensions}\:\mathrm{with}\:\mathrm{infintesimally}\:\mathrm{small} \\ $$$$\mathrm{height},\:\mathrm{so}\:\mathrm{it}\:\mathrm{has}\:\mathrm{two}\:\mathrm{circles}\:\mathrm{making}\:\mathrm{it}: \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{A}\:=\:\mathrm{2}\pi{r}^{\mathrm{2}} \:\:\:\:??? \\ $$

Question Number 5539 Answers: 0 Comments: 0

How many planes can pass through vertices of a cube, a) when each plane contains at least three vertices. b) when each plane contains exactly four vertices. c) Could we say that a plane can pass at most four vertices?

Question Number 5533 Answers: 0 Comments: 1

Measure of the side of a cube is double of the the side of the cube inside it. What is empty space in larger cube?

$$\mathrm{Measure}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{double} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{inside}\:\mathrm{it}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{empty}\:\mathrm{space}\:\mathrm{in}\:\mathrm{larger}\:\mathrm{cube}? \\ $$

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