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AllQuestion and Answers: Page 1109

Question Number 105929 Answers: 1 Comments: 0

Question Number 105927 Answers: 3 Comments: 2

((x/(x−2)))^2 +((x/(x+2)))^2 = 2

$$\left(\frac{{x}}{{x}−\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{{x}}{{x}+\mathrm{2}}\right)^{\mathrm{2}} =\:\mathrm{2}\: \\ $$

Question Number 105925 Answers: 0 Comments: 1

Question Number 105945 Answers: 1 Comments: 0

Question Number 105916 Answers: 2 Comments: 0

prove that cot x. cot 2x +cot 2x. cot 3x+2 = cot x.(cot x−cot 3x)

$${prove}\:{that}\:\mathrm{cot}\:{x}.\:\mathrm{cot}\:\mathrm{2}{x}\:+\mathrm{cot}\:\mathrm{2}{x}.\:\mathrm{cot}\:\mathrm{3}{x}+\mathrm{2}\:= \\ $$$$\mathrm{cot}\:{x}.\left(\mathrm{cot}\:{x}−\mathrm{cot}\:\mathrm{3}{x}\right)\: \\ $$

Question Number 105904 Answers: 2 Comments: 0

∫ ((sin x)/(5−sin 2x)) dx ?

$$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{5}−\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:? \\ $$

Question Number 105897 Answers: 0 Comments: 12

App Updates: cyrillic alohabets are now available in app. Email us for any missing conjunctions.

$$\mathrm{App}\:\mathrm{Updates}: \\ $$$$\mathrm{cyrillic}\:\mathrm{alohabets}\:\mathrm{are}\:\mathrm{now}\:\mathrm{available} \\ $$$$\mathrm{in}\:\mathrm{app}.\:\mathrm{Email}\:\mathrm{us}\:\mathrm{for}\:\mathrm{any}\:\mathrm{missing} \\ $$$$\mathrm{conjunctions}. \\ $$

Question Number 105892 Answers: 1 Comments: 0

prove that sin(x)+cos(x)=(√2)cos(x−(π/4)) ?

$${prove}\:{that}\:{sin}\left({x}\right)+{cos}\left({x}\right)=\sqrt{\mathrm{2}}{cos}\left({x}−\frac{\pi}{\mathrm{4}}\right)\:\:? \\ $$

Question Number 105885 Answers: 3 Comments: 0

Question Number 105883 Answers: 3 Comments: 0

Question Number 105879 Answers: 3 Comments: 0

y′′+y′−6y = x

$${y}''+{y}'−\mathrm{6}{y}\:=\:{x}\: \\ $$

Question Number 105878 Answers: 2 Comments: 0

(d^3 y/dx^3 ) + 3 (d^2 y/dx^2 ) + 2 (dy/dx) = x^2

$$\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:+\:\mathrm{3}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}\:\frac{{dy}}{{dx}}\:=\:{x}^{\mathrm{2}} \\ $$

Question Number 105877 Answers: 1 Comments: 0

Question Number 105862 Answers: 3 Comments: 1

∫ (dx/(9+16cos^2 x)) ?

$$\int\:\frac{{dx}}{\mathrm{9}+\mathrm{16cos}\:^{\mathrm{2}} {x}}\:? \\ $$

Question Number 105861 Answers: 1 Comments: 1

Given { ((sin 2x−sin 2y=−(5/(12)))),((cos (x+y)= −(2/3)sin (x−y))) :} where 0 < x−y<π. find the value of cos (x+y)+2sin (x−y)

$$\mathcal{G}{iven}\:\begin{cases}{\mathrm{sin}\:\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{y}=−\frac{\mathrm{5}}{\mathrm{12}}}\\{\mathrm{cos}\:\left({x}+{y}\right)=\:−\frac{\mathrm{2}}{\mathrm{3}}\mathrm{sin}\:\left({x}−{y}\right)}\end{cases} \\ $$$${where}\:\mathrm{0}\:<\:{x}−{y}<\pi. \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{cos}\:\left({x}+{y}\right)+\mathrm{2sin}\:\left({x}−{y}\right) \\ $$

Question Number 105854 Answers: 2 Comments: 0

sin 2x (dy/dx) −y = tan x

$$\mathrm{sin}\:\mathrm{2}{x}\:\frac{{dy}}{{dx}}\:−{y}\:=\:\mathrm{tan}\:{x} \\ $$

Question Number 105853 Answers: 0 Comments: 5

A box contains 5 balls, 2 balls were drawn at random, both of which turned out tobe white. what is the probability that all the balls in the box are white ?

$${A}\:{box}\:{contains}\:\mathrm{5}\:{balls},\:\mathrm{2}\:{balls}\:{were} \\ $$$${drawn}\:{at}\:{random},\:{both}\:{of}\:{which} \\ $$$${turned}\:{out}\:{tobe}\:{white}.\:{what}\:{is}\:{the} \\ $$$${probability}\:{that}\:{all}\:{the}\:{balls}\:{in}\:{the}\:{box} \\ $$$${are}\:{white}\:? \\ $$

Question Number 105851 Answers: 1 Comments: 0

Each of the students in the class was in the theater exactly two times during the winter holidays,while performances A,B and C were seen by 25,12 and 23 students,respectively .How many students are there in the class?How many of them saw performances A and B,B and C,C and A?

$$\mathrm{Each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{class}\:\mathrm{was} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{theater}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{times}\:\mathrm{during}\: \\ $$$$\:\mathrm{the}\:\mathrm{winter}\:\mathrm{holidays},\mathrm{while} \\ $$$$\mathrm{performances}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{were}\:\mathrm{seen}\:\mathrm{by} \\ $$$$\mathrm{25},\mathrm{12}\:\mathrm{and}\:\mathrm{23}\:\mathrm{students},\mathrm{respectively} \\ $$$$.\mathrm{How}\:\mathrm{many}\:\mathrm{students}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{class}?\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{them}\:\mathrm{saw}\:\mathrm{performances} \\ $$$$\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\mathrm{B}\:\mathrm{and}\:\mathrm{C},\mathrm{C}\:\mathrm{and}\:\mathrm{A}? \\ $$

Question Number 105850 Answers: 0 Comments: 0

A bit modification of Mr. W′s question How many numbers are there with atleast one zero between 1 to 12345 ? For instance consider 10020 as 1 number ? Can the answer ofQ105791 be derived from the answer of this question ?

$$\mathrm{A}\:\mathrm{bit}\:\mathrm{modification}\:\mathrm{of}\:\mathrm{Mr}.\:\mathrm{W}'\mathrm{s}\:\mathrm{question} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{there}\:\mathrm{with}\:\mathrm{atleast}\:\mathrm{one} \\ $$$$\mathrm{zero}\:\mathrm{between}\:\mathrm{1}\:\mathrm{to}\:\mathrm{12345}\:?\:\mathrm{For}\:\mathrm{instance}\:\mathrm{consider} \\ $$$$\mathrm{10020}\:\mathrm{as}\:\mathrm{1}\:\mathrm{number}\:?\:\mathrm{Can}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{ofQ105791}\: \\ $$$$\mathrm{be}\:\mathrm{derived}\:\mathrm{from}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{of}\:\mathrm{this}\:\mathrm{question}\:? \\ $$

Question Number 105843 Answers: 3 Comments: 0

(3x)^(1+log _3 (3x)) > 81x^2 find the solution set

$$\left(\mathrm{3}{x}\right)^{\mathrm{1}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3}{x}\right)} \:>\:\mathrm{81}{x}^{\mathrm{2}} \\ $$$${find}\:{the}\:{solution}\:{set}\: \\ $$

Question Number 105842 Answers: 0 Comments: 0

A wheel revolving at 6rev/s has an angular acceleration of 4rad/s^2 . find the number of turns the wheel must take to reach 26rev/s and the time required.

$$\mathrm{A}\:\mathrm{wheel}\:\mathrm{revolving}\:\mathrm{at}\:\mathrm{6rev}/\mathrm{s}\:\mathrm{has}\:\mathrm{an}\:\mathrm{angular}\: \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{4rad}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{turns}\:\mathrm{the}\:\mathrm{wheel}\:\mathrm{must}\:\mathrm{take}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{26rev}/\mathrm{s} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{time}\:\mathrm{required}. \\ $$

Question Number 105840 Answers: 0 Comments: 0

A Car wheel 30cm in radius is turning at a rate of 8rev/s when the car begins to slow uniformly to rest in a time 14s. find the number of revolutions made by the wheel and the distance the car goes in the 14s.

$${A}\:{Car}\:{wheel}\:\mathrm{30}{cm}\:{in}\:{radius}\:{is}\:{turning}\:{at}\:{a} \\ $$$${rate}\:{of}\:\mathrm{8}{rev}/{s}\:{when}\:{the}\:{car}\:{begins}\:{to}\:{slow}\:\: \\ $$$${uniformly}\:{to}\:{rest}\:{in}\:{a}\:{time}\:\mathrm{14}{s}.\:{find}\:{the}\: \\ $$$${number}\:{of}\:{revolutions}\:{made}\:{by}\:{the}\:{wheel} \\ $$$${and}\:{the}\:{distance}\:{the}\:{car}\:{goes}\:{in}\:{the}\:\mathrm{14}{s}. \\ $$

Question Number 105868 Answers: 1 Comments: 1

lim_(x→0) cos((((√x)−1)/x))=????? please i need your help

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}cos}}\left(\frac{\sqrt{\boldsymbol{{x}}}−\mathrm{1}}{\boldsymbol{{x}}}\right)=????? \\ $$$${pl}\boldsymbol{{ease}}\:\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{your}}\:\boldsymbol{{help}} \\ $$

Question Number 105839 Answers: 0 Comments: 0

A wheel 25cm in a radius turning at 120rpm uniformly increases its frequency to 660rpm in 9s. Find (a) the constant angular acceleration in rad/s^2 and (b) tangential acceleration of a point on its rim.

$${A}\:{wheel}\:\mathrm{25}{cm}\:{in}\:{a}\:{radius}\:{turning}\:{at}\:\mathrm{120}{rpm} \\ $$$${un}\mathrm{i}{formly}\:{increases}\:{its}\:{frequency}\:{to}\:\mathrm{660}{rpm} \\ $$$${in}\:\mathrm{9}{s}.\:{Find}\:\left({a}\right)\:{the}\:{constant}\:{angular}\: \\ $$$${acceleration}\:{in}\:{rad}/{s}^{\mathrm{2}} \:{and}\:\left({b}\right)\:{tangential} \\ $$$${acceleration}\:{of}\:{a}\:{point}\:{on}\:{its}\:{rim}. \\ $$

Question Number 105838 Answers: 0 Comments: 0

A mass of 1.5kg out in space moves in a circle of radius 25cm at a constant 2rev/s. Calculate (a) the tangential speed (b) acceleration and (c) the required centripetal force for the motion.

$${A}\:{mass}\:{of}\:\mathrm{1}.\mathrm{5}{kg}\:{out}\:{in}\:{space}\:{moves}\:{in}\: \\ $$$${a}\:{circle}\:{of}\:{radius}\:\mathrm{25}{cm}\:{at}\:{a}\:{constant}\:\mathrm{2}{rev}/{s}. \\ $$$${Calculate}\:\left({a}\right)\:{the}\:{tangential}\:{speed}\: \\ $$$$\left({b}\right)\:{acceleration}\:{and}\:\left({c}\right)\:{the}\:{required}\: \\ $$$${centripetal}\:{force}\:{for}\:{the}\:{motion}. \\ $$

Question Number 105822 Answers: 2 Comments: 0

Given f(x+(1/(2x))) = x^2 +(1/(4x^2 ))+3x+(3/(2x)) find f(2)

$$\mathcal{G}{iven}\:{f}\left({x}+\frac{\mathrm{1}}{\mathrm{2}{x}}\right)\:=\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{2}} }+\mathrm{3}{x}+\frac{\mathrm{3}}{\mathrm{2}{x}} \\ $$$${find}\:{f}\left(\mathrm{2}\right)\: \\ $$

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