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Question Number 61147 Answers: 1 Comments: 0

prove ∫((1+cos x)/(1−cos x))dx=−2cot (x/2)−x+c

$$\boldsymbol{{prove}} \\ $$$$\int\frac{\mathrm{1}+{cos}\:{x}}{\mathrm{1}−{cos}\:{x}}{dx}=−\mathrm{2}{cot}\:\frac{{x}}{\mathrm{2}}−{x}+{c} \\ $$$$ \\ $$

Question Number 61003 Answers: 3 Comments: 0

Question Number 60984 Answers: 2 Comments: 9

(a/(a−b)) + (b/(b−c)) + (c/(c−a)) = 4 ab^2 + bc^2 + abc + ca^2 = a^2 b + b^2 c + c^2 a ((a/(a−b)))^3 + ((b/(b−c)))^3 + ((c/(c−a)))^3 = ?

$$\frac{{a}}{{a}−{b}}\:\:+\:\:\frac{{b}}{{b}−{c}}\:\:+\:\:\frac{{c}}{{c}−{a}}\:\:=\:\:\mathrm{4} \\ $$$${ab}^{\mathrm{2}} \:+\:{bc}^{\mathrm{2}} \:+\:{abc}\:+\:{ca}^{\mathrm{2}} \:\:=\:\:{a}^{\mathrm{2}} {b}\:+\:{b}^{\mathrm{2}} {c}\:+\:{c}^{\mathrm{2}} {a} \\ $$$$\left(\frac{{a}}{{a}−{b}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{b}}{{b}−{c}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{c}}{{c}−{a}}\right)^{\mathrm{3}} \:\:=\:\:? \\ $$$$ \\ $$

Question Number 60955 Answers: 1 Comments: 4

Question Number 60765 Answers: 0 Comments: 2

express in partial fraction 14/(x^2 +3)(x+2)

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{14}/\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}+\mathrm{2}\right) \\ $$

Question Number 60756 Answers: 1 Comments: 1

express in partial fraction 5/(x−2)(x+3)^2

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{5}/\left({x}−\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$

Question Number 60735 Answers: 3 Comments: 0

express in partial fraction 3/(x+1)(x^2 −4)

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{3}/\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right) \\ $$

Question Number 60702 Answers: 0 Comments: 0

Question Number 60587 Answers: 2 Comments: 1

x∈[0,(π/2)] sinx+cosx=tg3x

$$\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right] \\ $$$$\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}=\boldsymbol{\mathrm{tg}}\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$

Question Number 60545 Answers: 1 Comments: 0

Question Number 60514 Answers: 1 Comments: 5

i found some interesting basic question hence sharing... 1)if A∈[1,4] A^2 ∈ ? ←find interval 2)if A ∈ [−1,4] A^2 ∈ ? 3) y=(1/(A )) and A∈ [1,4] y∈ ? 4)y=(1/(∣A∣)) A∈[−1,4] y∈ ?

$${i}\:{found}\:{some}\:{interesting}\:{basic}\:{question} \\ $$$${hence}\:{sharing}... \\ $$$$\left.\mathrm{1}\right){if}\:{A}\in\left[\mathrm{1},\mathrm{4}\right]\:\:{A}^{\mathrm{2}} \:\in\:\:?\:\leftarrow{find}\:{interval}\: \\ $$$$\left.\mathrm{2}\right){if}\:{A}\:\in\:\left[−\mathrm{1},\mathrm{4}\right]\:\:{A}^{\mathrm{2}} \:\in\:? \\ $$$$\left.\mathrm{3}\right)\:{y}=\frac{\mathrm{1}}{{A}\:\:}\:\:{and}\:{A}\in\:\:\:\:\left[\mathrm{1},\mathrm{4}\right]\:\:{y}\in\:? \\ $$$$\left.\mathrm{4}\right){y}=\frac{\mathrm{1}}{\mid{A}\mid}\:\:{A}\in\left[−\mathrm{1},\mathrm{4}\right]\:\:\:{y}\in\:? \\ $$

Question Number 60508 Answers: 0 Comments: 0

prof Abdo pls restrict the numbers of input of question...

$${prof}\:{Abdo}\:\:{pls}\:{restrict}\:{the}\:\:{numbers}\:{of}\:{input}\:{of}\:{question}... \\ $$$$ \\ $$

Question Number 60423 Answers: 1 Comments: 0

Question Number 60422 Answers: 1 Comments: 5

Question Number 60421 Answers: 1 Comments: 0

Question Number 60410 Answers: 0 Comments: 2

lim_(x→0) [(x^2 /(tanxsinx))] [.]=grestest integer function

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{{x}^{\mathrm{2}} }{{tanxsinx}}\right]\:\left[.\right]={grestest}\:{integer}\:{function} \\ $$

Question Number 60337 Answers: 0 Comments: 2

15,25,42,...?

$$\mathrm{15},\mathrm{25},\mathrm{42},...? \\ $$

Question Number 60308 Answers: 0 Comments: 0

Question Number 60307 Answers: 0 Comments: 0

Question Number 60257 Answers: 0 Comments: 4

The maximum value of Z=4x+2y subject to constraints 2x+3y≤18 , x+y≥10 and x,y≥0 is ?

$${The}\:{maximum}\:{value}\:{of}\:{Z}=\mathrm{4}{x}+\mathrm{2}{y} \\ $$$${subject}\:{to}\:{constraints}\:\mathrm{2}{x}+\mathrm{3}{y}\leqslant\mathrm{18}\:, \\ $$$${x}+{y}\geqslant\mathrm{10}\:{and}\:{x},{y}\geqslant\mathrm{0}\:{is}\:? \\ $$

Question Number 60256 Answers: 1 Comments: 0

Question Number 60247 Answers: 0 Comments: 0

A uniform pole PQ, 30 m long and of mass 4 kg is carried by a boy at P and a man 8 m away from Q. Find the distance from P where a mass of 20 kg should be attached so that the man′s support is twice that of the boy, if the system is in equilibrium [Take g=10ms^(−2) ]

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{pole}\:\mathrm{PQ},\:\mathrm{30}\:\mathrm{m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{4}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{carried}\:\mathrm{by}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{at}\:\mathrm{P}\:\mathrm{and}\:\mathrm{a}\:\mathrm{man}\: \\ $$$$\mathrm{8}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{Q}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from} \\ $$$$\mathrm{P}\:\mathrm{where}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{20}\:\mathrm{kg}\:\mathrm{should}\:\mathrm{be}\:\mathrm{attached} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{man}'\mathrm{s}\:\mathrm{support}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{that} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{boy},\:\mathrm{if}\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{in}\:\mathrm{equilibrium} \\ $$$$\left[\mathrm{Take}\:\mathrm{g}=\mathrm{10ms}^{−\mathrm{2}} \right] \\ $$

Question Number 60227 Answers: 0 Comments: 0

Question Number 60219 Answers: 1 Comments: 1

C=((2𝛑𝛜𝛜_0 L)/(ln((R_2 /R_1 )))). prove.

$$\boldsymbol{\mathrm{C}}=\frac{\mathrm{2}\boldsymbol{\pi\varepsilon\varepsilon}_{\mathrm{0}} \boldsymbol{\mathrm{L}}}{\boldsymbol{\mathrm{ln}}\left(\frac{\boldsymbol{\mathrm{R}}_{\mathrm{2}} }{\boldsymbol{\mathrm{R}}_{\mathrm{1}} }\right)}. \\ $$$$\boldsymbol{\mathrm{prove}}. \\ $$

Question Number 60202 Answers: 0 Comments: 0

construct the point M^′ =(1/2)((((z+∣z∣))/2))

$${construct}\:{the}\:{point}\:{M}^{'} =\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\left({z}+\mid{z}\mid\right)}{\mathrm{2}}\right) \\ $$

Question Number 60143 Answers: 1 Comments: 0

Two passenger trains, A and B, 450km apart, start to move towards each other at the same time and meet after 2 hours. If train B, travels (8/7) as fast as train A, find the speed of each train.

$$\mathrm{Two}\:\mathrm{passenger}\:\mathrm{trains},\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\:\mathrm{450km}\:\mathrm{apart}, \\ $$$$\mathrm{start}\:\mathrm{to}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{time}\:\mathrm{and}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{train}\:\mathrm{B}, \\ $$$$\mathrm{travels}\:\frac{\mathrm{8}}{\mathrm{7}}\:\mathrm{as}\:\mathrm{fast}\:\mathrm{as}\:\mathrm{train}\:\mathrm{A},\:\mathrm{find}\:\mathrm{the}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{train}. \\ $$

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