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Question Number 40397    Answers: 1   Comments: 0

Solve : (dy/dx) = ((sin y + x)/(sin 2y − xcos y)) .

$$\mathrm{Solve}\:: \\ $$$$\frac{\mathrm{dy}}{{dx}}\:=\:\frac{\mathrm{sin}\:{y}\:+\:{x}}{\mathrm{sin}\:\mathrm{2}{y}\:−\:{x}\mathrm{cos}\:{y}}\:. \\ $$

Question Number 40396    Answers: 0   Comments: 1

A block lying on a horizontal conv− eyor belt moving at a constant velocity receives a velocity 5m/s at t=0 sec. relative to the ground in the direction opposite to the dir− ction of motion of the conveyor. Aftert=4sec,the velocity of the block becomes equal to the velocity of the belt . the coefficient of friction between the block and the belt is 0.2 . then the velocity of the conveyor belt is: (g=10m/s^2 ) (A) 13 m/s (B) −13m/s (C)3m/s (D) 6m/s

$${A}\:{block}\:{lying}\:{on}\:{a}\:{horizontal}\:{conv}− \\ $$$${eyor}\:{belt}\:{moving}\:{at}\:\:{a}\:{constant}\: \\ $$$${velocity}\:{receives}\:{a}\:{velocity}\:\mathrm{5}{m}/{s} \\ $$$${at}\:{t}=\mathrm{0}\:{sec}.\:{relative}\:{to}\:{the}\:{ground}\: \\ $$$${in}\:{the}\:{direction}\:{opposite}\:{to}\:{the}\:{dir}− \\ $$$${ction}\:{of}\:{motion}\:{of}\:{the}\:{conveyor}. \\ $$$${Aftert}=\mathrm{4}{sec},{the}\:{velocity}\:{of}\:{the}\: \\ $$$${block}\:{becomes}\:{equal}\:{to}\:{the}\:{velocity} \\ $$$${of}\:{the}\:{belt}\:.\:{the}\:{coefficient}\:{of}\: \\ $$$${friction}\:{between}\:{the}\:{block}\:{and}\:{the} \\ $$$${belt}\:{is}\:\mathrm{0}.\mathrm{2}\:.\:{then}\:{the}\:{velocity}\:{of}\:{the} \\ $$$${conveyor}\:{belt}\:{is}:\:\:\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$$$\left({A}\right)\:\mathrm{13}\:{m}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({B}\right)\:\:−\mathrm{13}{m}/{s} \\ $$$$\left({C}\right)\mathrm{3}{m}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\:\:\mathrm{6}{m}/{s} \\ $$

Question Number 40388    Answers: 1   Comments: 0

Question Number 40378    Answers: 1   Comments: 3

(1/(1!))+(1/(2!))+(1/(3!))+....+(1/(2018!))=?

$$\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+....+\frac{\mathrm{1}}{\mathrm{2018}!}=? \\ $$

Question Number 40376    Answers: 0   Comments: 3

Question Number 40375    Answers: 1   Comments: 0

Question Number 40380    Answers: 2   Comments: 1

Solve : (dy/dx) = ((x+y)/(x−y))

$${S}\mathrm{olve}\::\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{d}{x}}\:=\:\frac{{x}+{y}}{{x}−{y}} \\ $$

Question Number 40370    Answers: 0   Comments: 1

let u_n =Σ_(k=0) ^n (3k+1)(−1)^k 1) calculate interms of n S_n =u_0 +u_1 +u_2 +....+u_n 2) calculate u_0 +u_1 +u_2 +....+u_(57)

$${let}\:{u}_{{n}} \:=\sum_{{k}=\mathrm{0}} ^{{n}} \left(\mathrm{3}{k}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{k}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{interms}\:{of}\:{n} \\ $$$${S}_{{n}} ={u}_{\mathrm{0}} \:+{u}_{\mathrm{1}} +{u}_{\mathrm{2}} +....+{u}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{u}_{\mathrm{0}} \:+{u}_{\mathrm{1}} +{u}_{\mathrm{2}} +....+{u}_{\mathrm{57}} \\ $$

Question Number 40466    Answers: 1   Comments: 5

Q..cos^(−1) (1−2x^2 )=2sin^(−1) x,prove please

$$ \\ $$$$ \\ $$$$ \\ $$$${Q}..\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{1}−\mathrm{2}{x}^{\mathrm{2}} \right)=\mathrm{2sin}^{−\mathrm{1}} {x},{prove}\:\:\: \\ $$$${please} \\ $$$$ \\ $$$$ \\ $$

Question Number 40366    Answers: 0   Comments: 1

use newton raphson method to approximate the positive root x^2 −1=0 correct to 4 decimal places perform 3 iteration only setting with x=2

$$\boldsymbol{\mathrm{use}}\:\boldsymbol{\mathrm{newton}}\:\boldsymbol{\mathrm{raphson}}\:\boldsymbol{\mathrm{method}} \\ $$$$\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{approximate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{root}} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{to}}\:\mathrm{4}\:\boldsymbol{\mathrm{decimal}}\:\boldsymbol{\mathrm{places}} \\ $$$$\boldsymbol{\mathrm{perform}}\:\mathrm{3}\:\boldsymbol{\mathrm{iteration}}\:\boldsymbol{\mathrm{only}} \\ $$$$\boldsymbol{\mathrm{setting}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{{x}}=\mathrm{2} \\ $$

Question Number 40355    Answers: 1   Comments: 0

Question Number 40352    Answers: 0   Comments: 1

If A= [((4 −3)),((1 0)) ]use the fact that A^2 =4A−3I_2 and mathematical induction to prove A^n =(((3^n −1))/2)A +((3−3^n )/2)I if n≥1

$${If}\:{A}=\begin{bmatrix}{\mathrm{4}\:\:\:\:\:−\mathrm{3}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{bmatrix}{use}\:{the}\:{fact}\:{that}\: \\ $$$${A}^{\mathrm{2}} =\mathrm{4}{A}−\mathrm{3}{I}_{\mathrm{2}} \:\:{and}\:{mathematical}\:{induction}\:{to}\:{prove} \\ $$$$\:\:{A}^{{n}} =\frac{\left(\mathrm{3}^{{n}} −\mathrm{1}\right)}{\mathrm{2}}{A}\:\:+\frac{\mathrm{3}−\mathrm{3}^{{n}} }{\mathrm{2}}{I}\:\:{if}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 40467    Answers: 1   Comments: 2

∫ln ∣(√(x+1))+(√x)∣ dx=

$$\int\mathrm{ln}\:\mid\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}\mid\:{dx}= \\ $$

Question Number 40344    Answers: 1   Comments: 2

Question Number 40322    Answers: 1   Comments: 4

Solve : (d^2 y/dx^2 ) = ((dy/dx))^2

$$\mathrm{Solve}\:: \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{d}{x}^{\mathrm{2}} }\:=\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \\ $$

Question Number 40321    Answers: 0   Comments: 1

If abc=8 and (1/a) + (1/b) + (1/c) = (3/2) then find the value of ab+bc+ca.

$$\mathrm{If}\:{abc}=\mathrm{8}\:\mathrm{and}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{ab}+{bc}+{ca}. \\ $$

Question Number 40319    Answers: 1   Comments: 3

y=(a^2 +x^2 )tan^(−1) (x/a) Find (d^3 y/dx^3 ) .

$${y}=\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)\mathrm{tan}^{−\mathrm{1}} \frac{{x}}{{a}} \\ $$$${Find}\:\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:. \\ $$

Question Number 40306    Answers: 2   Comments: 2

Question Number 40300    Answers: 1   Comments: 0

10 men had the work of cultivating a farm for 18 days. when (1/3) of work was done 6 men were reduced. for how long was the work of cultivating the farm done?

$$\mathrm{10}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{had}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{cultivating}} \\ $$$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{farm}}\:\boldsymbol{\mathrm{for}}\:\mathrm{18}\:\boldsymbol{\mathrm{days}}.\:\boldsymbol{\mathrm{when}}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{done}}\:\mathrm{6}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{reduced}}. \\ $$$$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{long}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{cultivating}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{farm}}\:\boldsymbol{\mathrm{done}}? \\ $$

Question Number 40299    Answers: 1   Comments: 0

the present age of the son is ten years less than twice that of his father. if the sum of their age is 80 years. find the age of the father

$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{present}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{son}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{ten}}\:\boldsymbol{\mathrm{years}} \\ $$$$\boldsymbol{\mathrm{less}}\:\boldsymbol{\mathrm{than}}\:\boldsymbol{\mathrm{twice}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{his}}\:\boldsymbol{\mathrm{father}}. \\ $$$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{is}}\:\mathrm{80}\:\boldsymbol{\mathrm{years}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{father}} \\ $$

Question Number 40297    Answers: 0   Comments: 0

Question Number 40285    Answers: 3   Comments: 0

solve for 1 period sin (α/2) =sin 2α sin (β/3) =sin 3β cos (γ/2) =cos 2γ cos (δ/3) =cos 3δ tan (ε/2) =tan 2ε tan (ζ/3) =tan 3ζ

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{1}\:\mathrm{period} \\ $$$$\mathrm{sin}\:\frac{\alpha}{\mathrm{2}}\:=\mathrm{sin}\:\mathrm{2}\alpha \\ $$$$\mathrm{sin}\:\frac{\beta}{\mathrm{3}}\:=\mathrm{sin}\:\mathrm{3}\beta \\ $$$$\mathrm{cos}\:\frac{\gamma}{\mathrm{2}}\:=\mathrm{cos}\:\mathrm{2}\gamma \\ $$$$\mathrm{cos}\:\frac{\delta}{\mathrm{3}}\:=\mathrm{cos}\:\mathrm{3}\delta \\ $$$$\mathrm{tan}\:\frac{\epsilon}{\mathrm{2}}\:=\mathrm{tan}\:\mathrm{2}\epsilon \\ $$$$\mathrm{tan}\:\frac{\zeta}{\mathrm{3}}\:=\mathrm{tan}\:\mathrm{3}\zeta \\ $$

Question Number 40284    Answers: 1   Comments: 0

How many permutation can be made using the word CANADA each of the six letter being used mixed in each permutation? In how many of these permutation will the three A′s be together? In how many will two A′s be together but not the three?

$${How}\:{many}\:{permutation}\:{can}\:{be}\:{made}\:{using}\:{the}\:{word} \\ $$$${CANADA}\:{each}\:{of}\:{the}\:{six}\:{letter}\:{being}\:{used}\:{mixed} \\ $$$${in}\:{each}\:{permutation}?\:\:{In}\:{how}\:{many}\:{of}\:{these} \\ $$$${permutation}\:{will}\:{the}\:{three}\:{A}'{s}\:{be}\:{together}?\:{In}\: \\ $$$${how}\:{many}\:{will}\:{two}\:{A}'{s}\:{be}\:{together}\:{but}\:{not}\:{the}\:{three}? \\ $$

Question Number 40283    Answers: 0   Comments: 0

There are four ladies and four gentlemen ready to play tennis.if there is only one tennis court readily available. In how many ways is it possible to arrange for one mixed double to be played (a lady and gentleman)?

$${There}\:{are}\:{four}\:{ladies}\:{and}\:{four}\:{gentlemen}\:{ready}\:{to}\:{play}\: \\ $$$${tennis}.{if}\:{there}\:{is}\:{only}\:{one}\:{tennis}\:{court}\:{readily} \\ $$$${available}.\:{In}\:{how}\:{many}\:{ways}\:{is}\:{it}\:{possible}\:{to}\:{arrange}\:{for}\:{one}\:{mixed}\:{double}\:{to}\:{be}\:{played} \\ $$$$\left({a}\:{lady}\:{and}\:{gentleman}\right)? \\ $$

Question Number 40277    Answers: 2   Comments: 0

Question Number 40276    Answers: 2   Comments: 0

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