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Question Number 27467 Answers: 0 Comments: 0

Question Number 27464 Answers: 0 Comments: 5

Show that: ∫_( 0) ^( 2π) ((cos(3x))/(5 − 4cos(x))) dx = (π/(12))

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{5}\:−\:\mathrm{4cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:\:=\:\:\frac{\pi}{\mathrm{12}} \\ $$

Question Number 27449 Answers: 2 Comments: 0

factorise a^4 −(b+c)^4

$${factorise}\:{a}^{\mathrm{4}} −\left({b}+{c}\right)^{\mathrm{4}} \\ $$

Question Number 27447 Answers: 1 Comments: 0

∫^∞ _0 v^(4 ) e ((−mv^2 )/(2KT))dv solve it

$$\underset{\mathrm{0}} {\int}^{\infty} \:\mathrm{v}^{\mathrm{4}\:} \:\mathrm{e}\:\frac{−\mathrm{mv}^{\mathrm{2}} }{\mathrm{2KT}}\mathrm{dv}\: \\ $$$$\mathrm{solve}\:\mathrm{it} \\ $$

Question Number 27446 Answers: 0 Comments: 3

Question Number 27445 Answers: 1 Comments: 0

If a planet is suddenly stopped in its orbit, supposed to be circular, then it would fall into the sun in a time (T/(4(√2))), where T is the time period of revolution. Prove this.

$${If}\:{a}\:{planet}\:{is}\:{suddenly}\:{stopped}\:{in}\:{its} \\ $$$${orbit},\:{supposed}\:{to}\:{be}\:{circular},\:{then}\:{it} \\ $$$${would}\:{fall}\:{into}\:{the}\:{sun}\:{in}\:{a}\:{time}\:\frac{{T}}{\mathrm{4}\sqrt{\mathrm{2}}}, \\ $$$${where}\:{T}\:{is}\:{the}\:{time}\:{period}\:{of} \\ $$$${revolution}.\:{Prove}\:{this}. \\ $$

Question Number 27436 Answers: 1 Comments: 1

Car A is moving at a speed of 45km/h towards car B which is moving towards car A at a speed of 55km/h.If the two cars where initially seperated at a distance of 150m.Determine how long it will take the two cars to meet.

$${Car}\:{A}\:{is}\:{moving}\:{at}\:{a}\:{speed}\:{of}\: \\ $$$$\mathrm{45}{km}/{h}\:{towards}\:{car}\:{B}\:{which}\:{is} \\ $$$${moving}\:{towards}\:{car}\:{A}\:{at}\:{a}\:{speed}\: \\ $$$${of}\:\mathrm{55}{km}/{h}.{If}\:{the}\:{two}\:{cars}\:{where} \\ $$$${initially}\:{seperated}\:{at}\:{a}\:{distance} \\ $$$${of}\:\mathrm{150}{m}.{Determine}\:{how}\:{long}\:{it}\: \\ $$$${will}\:{take}\:{the}\:{two}\:{cars}\:{to}\:{meet}. \\ $$

Question Number 27435 Answers: 1 Comments: 0

An object has a constant acceleration a=4ms^(−2) .Its velocity is 1m/s at t=0,when it is at x=7m. How fast is it at x=8m?At what time is this?

$${An}\:{object}\:{has}\:{a}\:{constant} \\ $$$${acceleration}\:{a}=\mathrm{4}{ms}^{−\mathrm{2}} .{Its}\:{velocity} \\ $$$${is}\:\mathrm{1}{m}/{s}\:{at}\:{t}=\mathrm{0},{when}\:{it}\:{is}\:{at}\:{x}=\mathrm{7}{m}. \\ $$$${How}\:{fast}\:{is}\:{it}\:{at}\:{x}=\mathrm{8}{m}?{At}\:{what} \\ $$$${time}\:{is}\:{this}? \\ $$

Question Number 27430 Answers: 0 Comments: 0

A 2000kg space capsule is traveling away from the earth, determine the gravitational field strenght and gravitational force on the capsule due to the earth when it is (a) At a distance from the earth′s surface equal to the radius of the earth (b) At a very large distance away from the earth (Take g = 9.8Nkg^(−1) on earth surface)

$$\mathrm{A}\:\mathrm{2000kg}\:\mathrm{space}\:\mathrm{capsule}\:\mathrm{is}\:\mathrm{traveling}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth},\:\mathrm{determine}\:\mathrm{the} \\ $$$$\mathrm{gravitational}\:\mathrm{field}\:\mathrm{strenght}\:\mathrm{and}\:\mathrm{gravitational}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the}\:\mathrm{capsule}\:\mathrm{due}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{earth}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{At}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth}'\mathrm{s}\:\mathrm{surface}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{At}\:\mathrm{a}\:\mathrm{very}\:\mathrm{large}\:\mathrm{distance}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth}\:\left(\mathrm{Take}\:\:\mathrm{g}\:=\:\mathrm{9}.\mathrm{8Nkg}^{−\mathrm{1}} \:\mathrm{on}\right. \\ $$$$\left.\mathrm{earth}\:\mathrm{surface}\right) \\ $$

Question Number 27429 Answers: 1 Comments: 0

Question Number 27427 Answers: 0 Comments: 0

A particle of mass 2kg moves in a force field depending on a time t given by F = 24t^2 i + (36t − 16)j − 12tk assuming that at t = 0 the particle is located at r_0 = 3i − j + 4k and has v_0 = 6i + 5j − 8k. Find (a) Velocity at any time t (b) Position at any time t (c) τ (torgue) at any time t (d) Angular momentum at any time t above the Origin

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2kg}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{force}\:\mathrm{field}\:\mathrm{depending}\:\mathrm{on}\:\mathrm{a}\:\mathrm{time}\:\mathrm{t}\:\mathrm{given}\:\mathrm{by} \\ $$$$\mathrm{F}\:=\:\mathrm{24t}^{\mathrm{2}} \mathrm{i}\:+\:\left(\mathrm{36t}\:−\:\mathrm{16}\right)\mathrm{j}\:−\:\mathrm{12tk}\:\:\:\mathrm{assuming}\:\mathrm{that}\:\mathrm{at}\:\mathrm{t}\:=\:\mathrm{0}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{located} \\ $$$$\mathrm{at}\:\:\mathrm{r}_{\mathrm{0}} \:=\:\mathrm{3i}\:−\:\mathrm{j}\:+\:\mathrm{4k}\:\:\mathrm{and}\:\:\mathrm{has}\:\:\:\mathrm{v}_{\mathrm{0}} \:=\:\mathrm{6i}\:+\:\mathrm{5j}\:−\:\mathrm{8k}.\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Velocity}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Position}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{c}\right)\:\tau\:\left(\mathrm{torgue}\right)\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{Angular}\:\mathrm{momentum}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t}\:\mathrm{above}\:\mathrm{the}\:\mathrm{Origin} \\ $$

Question Number 27428 Answers: 0 Comments: 0

Find the workdone in moving an object along a vector r = 3i + 2j − 5k if the applied force is F = 2i − j − k

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{workdone}\:\mathrm{in}\:\mathrm{moving}\:\mathrm{an}\:\mathrm{object}\:\mathrm{along}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{r}\:=\:\mathrm{3i}\:+\:\mathrm{2j}\:−\:\mathrm{5k}\:\:\:\mathrm{if}\:\mathrm{the}\:\mathrm{applied}\:\mathrm{force}\:\mathrm{is}\:\:\mathrm{F}\:=\:\mathrm{2i}\:−\:\mathrm{j}\:−\:\mathrm{k} \\ $$

Question Number 27469 Answers: 1 Comments: 3

Question Number 27475 Answers: 0 Comments: 6

Question Number 27422 Answers: 0 Comments: 2

A,B,C & D are four distinct points of a circle in such a way that chords AB & CD cut each other inside the circle at the point E. Consequently the circle is divided in four parts (AEC,CEB,BED & DEA). [AEC means the region outlined by AC^(⌢) ,AE^(−) & CE^(−) ] If AE : BE=a:b and CE : DE=c:d, what is ratio between the four parts of the circle?

$$\mathrm{A},\mathrm{B},\mathrm{C}\:\&\:\mathrm{D}\:\mathrm{are}\:\mathrm{four}\:\mathrm{distinct}\:\mathrm{points}\: \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{chords} \\ $$$$\mathrm{AB}\:\&\:\mathrm{CD}\:\mathrm{cut}\:\mathrm{each}\:\mathrm{other}\:\mathrm{inside} \\ $$$$\mathrm{the}\:\mathrm{circle}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{E}.\:\mathrm{Consequently} \\ $$$$\mathrm{the}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{in}\:\mathrm{four}\:\mathrm{parts} \\ $$$$\left(\mathrm{AEC},\mathrm{CEB},\mathrm{BED}\:\&\:\mathrm{DEA}\right). \\ $$$$\left[\mathrm{AEC}\:\mathrm{means}\:\:\mathrm{the}\:\mathrm{region}\:\mathrm{outlined}\:\:\right. \\ $$$$\left.\mathrm{by}\:\overset{\frown} {\mathrm{AC}},\overline {\mathrm{AE}}\:\&\:\overline {\mathrm{CE}}\right] \\ $$$$\mathrm{If}\:\mathrm{AE}\::\:\mathrm{BE}=\mathrm{a}:\mathrm{b}\:\mathrm{and}\:\mathrm{CE}\::\:\mathrm{DE}=\mathrm{c}:\mathrm{d}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{ratio}\:\mathrm{between}\:\mathrm{the}\:\mathrm{four} \\ $$$$\mathrm{parts}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}? \\ $$

Question Number 27421 Answers: 1 Comments: 0

pls help find x 0.5^x = 0.25 find x

$$\mathrm{pls}\:\mathrm{help}\:\mathrm{find}\:\mathrm{x} \\ $$$$\mathrm{0}.\mathrm{5}^{\mathrm{x}} \:=\:\mathrm{0}.\mathrm{25} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 27410 Answers: 0 Comments: 2

∫_0 ^∞ ((sinxdx)/x)

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{sinxdx}}{{x}} \\ $$

Question Number 27404 Answers: 1 Comments: 0

(1).the mean of 14.9.22.14.22.18

$$\left(\mathrm{1}\right).{the}\:{mean}\:{of}\:\mathrm{14}.\mathrm{9}.\mathrm{22}.\mathrm{14}.\mathrm{22}.\mathrm{18} \\ $$

Question Number 27419 Answers: 1 Comments: 0

(x^3 +5x^3 −2)/(x−1)

$$\left({x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{2}\right)/\left({x}−\mathrm{1}\right) \\ $$

Question Number 27403 Answers: 1 Comments: 0

perimeter of a squre 112m.what is its area..

$${perimeter}\:{of}\:{a}\:{squre}\:\mathrm{112}{m}.{what}\:{is}\:{its}\:{area}.. \\ $$

Question Number 27402 Answers: 1 Comments: 0

5(√(243^2 ))

$$\mathrm{5}\sqrt{\mathrm{243}^{\mathrm{2}} \:} \\ $$

Question Number 27400 Answers: 1 Comments: 4

Evaluate ∫_r ^0 (√(x/(r−x))) dx

$${Evaluate}\:\underset{{r}} {\overset{\mathrm{0}} {\int}}\sqrt{\frac{{x}}{{r}−{x}}}\:{dx} \\ $$

Question Number 27399 Answers: 1 Comments: 0

A and B are walking along a circular track.They start from same point at 8:00 am. A can walk 2 rounds per hour and B can walk 3 rounds per hour. How many times they cross each other before 9:30 am if they walk (i) Opposite to each other. (ii) In same direction. ?

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{walking}\:\mathrm{along}\:\mathrm{a} \\ $$$$\mathrm{circular}\:\mathrm{track}.\mathrm{They}\:\mathrm{start}\:\mathrm{from} \\ $$$$\mathrm{same}\:\mathrm{point}\:\mathrm{at}\:\mathrm{8}:\mathrm{00}\:\mathrm{am}. \\ $$$$\mathrm{A}\:\mathrm{can}\:\mathrm{walk}\:\mathrm{2}\:\mathrm{rounds}\:\mathrm{per}\:\mathrm{hour} \\ $$$$\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{walk}\:\mathrm{3}\:\mathrm{rounds}\:\mathrm{per}\:\mathrm{hour}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{they}\:\mathrm{cross}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{before}\:\mathrm{9}:\mathrm{30}\:\mathrm{am}\:\mathrm{if}\:\mathrm{they}\:\mathrm{walk} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Opposite}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{In}\:\mathrm{same}\:\mathrm{direction}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:? \\ $$

Question Number 27397 Answers: 2 Comments: 0

The roots of x^2 −(a+1)x+b^2 =0 are equal. Then which of the following can be the values of a and b .

$$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:{x}^{\mathrm{2}} −\left({a}+\mathrm{1}\right){x}+{b}^{\mathrm{2}} =\mathrm{0}\:\mathrm{are} \\ $$$$\mathrm{equal}.\:\mathrm{Then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\:{a}\:\:\mathrm{and}\:\:{b}\:\:. \\ $$

Question Number 27393 Answers: 1 Comments: 0

solve tan^(−1) (2x/1−x^2 )+cot^(−1) (1−x^2 /2x)=π/3

$${solve} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2}{x}/\mathrm{1}−{x}^{\mathrm{2}} \right)+\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} /\mathrm{2}{x}\right)=\pi/\mathrm{3} \\ $$

Question Number 27392 Answers: 0 Comments: 0

Show that the integral: ∫ e^(−x^2 ) dx Can′t be calculated trivially.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integral}: \\ $$$$ \\ $$$$\int\:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Can}'\mathrm{t}\:\mathrm{be}\:\mathrm{calculated}\:\mathrm{trivially}. \\ $$

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