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Question Number 95417 Answers: 1 Comments: 0

find the solution of eq 3cot 2x + 2sin x = 0 for x∈[0,360^o ]

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{eq}\: \\ $$$$\mathrm{3cot}\:\mathrm{2x}\:+\:\mathrm{2sin}\:\mathrm{x}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{360}^{\mathrm{o}} \right] \\ $$

Question Number 95416 Answers: 1 Comments: 4

It takes 12 hours to fill a swimming pool using 2 pipes. If the larger pipe used , for 4 hours and the small pipe for 9 hours, only half the pool is filled. How long would it take for each pipe alone to fill the pool?

$$\mathrm{It}\:\mathrm{takes}\:\mathrm{12}\:\mathrm{hours}\:\mathrm{to}\:\mathrm{fill}\:\mathrm{a}\:\mathrm{swimming}\: \\ $$$$\mathrm{pool}\:\mathrm{using}\:\mathrm{2}\:\mathrm{pipes}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{larger}\: \\ $$$$\mathrm{pipe}\:\mathrm{used}\:,\:\mathrm{for}\:\mathrm{4}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{small}\:\mathrm{pipe}\:\mathrm{for}\:\mathrm{9}\:\mathrm{hours},\:\mathrm{only}\:\mathrm{half} \\ $$$$\mathrm{the}\:\mathrm{pool}\:\mathrm{is}\:\mathrm{filled}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{would}\: \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{each}\:\mathrm{pipe}\:\mathrm{alone}\:\mathrm{to}\: \\ $$$$\mathrm{fill}\:\mathrm{the}\:\mathrm{pool}? \\ $$

Question Number 95405 Answers: 1 Comments: 3

∫ e^x (tan x−ln(cos x)) dx ?

$$\int\:\mathrm{e}^{\mathrm{x}} \:\left(\mathrm{tan}\:\mathrm{x}−\mathrm{ln}\left(\mathrm{cos}\:\mathrm{x}\right)\right)\:\mathrm{dx}\:? \\ $$

Question Number 95401 Answers: 2 Comments: 0

lim_(n→∞) n^(3/2) {(√(n+1))+(√(n−1))−2(√n) }

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}^{\frac{\mathrm{3}}{\mathrm{2}}} \left\{\sqrt{\mathrm{n}+\mathrm{1}}+\sqrt{\mathrm{n}−\mathrm{1}}−\mathrm{2}\sqrt{\mathrm{n}}\:\right\}\: \\ $$

Question Number 95397 Answers: 0 Comments: 2

f(x)=(1/(lnx)) −(1/(x−1)) 1) lim_(x→1) f(x)=(1/2) 2) ∫_0 ^1 f(x)dx= γ

$${f}\left({x}\right)=\frac{\mathrm{1}}{{lnx}}\:−\frac{\mathrm{1}}{{x}−\mathrm{1}}\: \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx}=\:\gamma\: \\ $$

Question Number 95396 Answers: 0 Comments: 2

∫_0 ^∞ e^(−x^2 −(1/x^2 )) dx = ((√π)/(2e^2 ))

$$\:\:\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} {dx}\:=\:\frac{\sqrt{\pi}}{\mathrm{2}{e}^{\mathrm{2}} }\:\: \\ $$$$\: \\ $$

Question Number 95394 Answers: 0 Comments: 31

Solve: x + y = 3 .... (i) x^y + y^x = 6 ..... (ii)

$$\mathrm{Solve}:\:\:\:\mathrm{x}\:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{3}\:\:\:\:\:\:....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:+\:\:\mathrm{y}^{\mathrm{x}} \:\:=\:\:\mathrm{6}\:\:\:\:.....\:\:\left(\mathrm{ii}\right) \\ $$

Question Number 95378 Answers: 1 Comments: 1

If I (m, n)=∫_( 0) ^1 x^(m−1) (1−x)^(n−1) dx, then

$$\mathrm{If}\:\:{I}\:\left({m},\:{n}\right)=\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{{m}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{n}−\mathrm{1}} {dx},\:\mathrm{then} \\ $$

Question Number 95373 Answers: 1 Comments: 2

Find the value of m for which the roots of the equation x^3 + 6x^2 + 11x +m = 0 form a linear sequence.

$$\: \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{m}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{roots} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:+\:\mathrm{6}{x}^{\mathrm{2}} \:+\:\mathrm{11}{x}\:+{m}\:=\:\mathrm{0} \\ $$$$\:\mathrm{form}\:\mathrm{a}\:\mathrm{linear}\:\mathrm{sequence}. \\ $$$$ \\ $$

Question Number 95371 Answers: 2 Comments: 1

∫(x^(2/3) /(√(1+x^(2/3) )))dx=?

$$\int\frac{{x}^{\mathrm{2}/\mathrm{3}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{2}/\mathrm{3}} }}{dx}=? \\ $$

Question Number 95363 Answers: 2 Comments: 1

lim_(x→∞) (((x!)^2 )/((2x)!)) = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{x}!\right)^{\mathrm{2}} }{\left(\mathrm{2x}\right)!}\:=\:? \\ $$

Question Number 95328 Answers: 0 Comments: 3

Question Number 95326 Answers: 0 Comments: 4

sin 72^o = p(√3) cos 48^o find tan 12^o ?

$$\mathrm{sin}\:\mathrm{72}^{\mathrm{o}} \:=\:\mathrm{p}\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{48}^{\mathrm{o}} \\ $$$$\mathrm{find}\:\mathrm{tan}\:\mathrm{12}^{\mathrm{o}} \:? \\ $$

Question Number 95325 Answers: 0 Comments: 1

lim_(n→∞) (1/n)HCF(20,n) = 0 ?

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\:\:\frac{\mathrm{1}}{{n}}{HCF}\left(\mathrm{20},{n}\right)\:=\:\mathrm{0}\:\:\:\:\:\:\:? \\ $$

Question Number 95324 Answers: 0 Comments: 2

If sin A + (sin A)^2 = 1 Then the value of (cos A)^(12) + 3(cos A)^(10) + 3(cos A)^8 + (cos A)^6 − 1 is ? (a) 0 (b) 1 (c) − 1 (d) 2

$$\mathrm{If}\:\:\:\mathrm{sin}\:\mathrm{A}\:\:+\:\:\left(\mathrm{sin}\:\mathrm{A}\right)^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1} \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\:\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{12}} \:\:+\:\:\mathrm{3}\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{10}} \:\:+\:\:\mathrm{3}\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{8}} \:\:+\:\:\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{6}} \:\:−\:\:\mathrm{1}\:\:\:\:\:\mathrm{is}\:? \\ $$$$ \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\:\:\:\mathrm{0} \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\:\:\:\:\mathrm{1} \\ $$$$\left(\mathrm{c}\right)\:\:\:\:−\:\mathrm{1} \\ $$$$\left(\mathrm{d}\right)\:\:\:\:\:\:\mathrm{2} \\ $$

Question Number 95323 Answers: 1 Comments: 0

lim_(x→0) ∫_x ^(2x) ((ln(2+t))/t)dt = (ln2)^2

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{ln}\left(\mathrm{2}+{t}\right)}{{t}}{dt}\:=\:\left({ln}\mathrm{2}\right)^{\mathrm{2}} \\ $$

Question Number 95316 Answers: 1 Comments: 0

(dy/dx)−y = xy^5

$$\frac{{dy}}{{dx}}−{y}\:=\:{xy}^{\mathrm{5}} \: \\ $$

Question Number 95309 Answers: 1 Comments: 0

if y = [ 2x+5 ] = 3[x−4] then [ 3x+y ] = ?

$$\mathrm{if}\:\mathrm{y}\:=\:\left[\:\mathrm{2x}+\mathrm{5}\:\right]\:=\:\mathrm{3}\left[\mathrm{x}−\mathrm{4}\right]\: \\ $$$$\mathrm{then}\:\left[\:\mathrm{3x}+\mathrm{y}\:\right]\:=\:?\: \\ $$

Question Number 95294 Answers: 1 Comments: 2

3 men, 4 women & 6 boy together working a job within 25 day. if 2 men , 3 women and 4 boy working the same job, complete in ?

$$\mathrm{3}\:\mathrm{men},\:\mathrm{4}\:\mathrm{women}\:\&\:\mathrm{6}\:\mathrm{boy}\:\mathrm{together} \\ $$$$\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{within}\:\mathrm{25}\:\mathrm{day}.\:\mathrm{if}\:\mathrm{2}\:\mathrm{men}\: \\ $$$$,\:\mathrm{3}\:\mathrm{women}\:\mathrm{and}\:\mathrm{4}\:\mathrm{boy}\:\mathrm{working}\:\mathrm{the}\: \\ $$$$\mathrm{same}\:\mathrm{job},\:\mathrm{complete}\:\mathrm{in}\:? \\ $$

Question Number 95277 Answers: 2 Comments: 4

Question Number 95269 Answers: 0 Comments: 3

Question Number 100664 Answers: 1 Comments: 0

A matrix 2x2 & B = (((−2 3)),(( 2 4)) ) such that A^T B+3A^T = ((( 5 4)),((−1 1)) ) so find det(4A^(−1) )

$$\mathrm{A}\:\mathrm{matrix}\:\mathrm{2x2}\:\&\:\mathrm{B}\:=\:\begin{pmatrix}{−\mathrm{2}\:\:\:\:\mathrm{3}}\\{\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{4}}\end{pmatrix}\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{A}^{\mathrm{T}} \mathrm{B}+\mathrm{3A}^{\mathrm{T}} \:=\:\begin{pmatrix}{\:\:\:\mathrm{5}\:\:\:\:\mathrm{4}}\\{−\mathrm{1}\:\:\:\mathrm{1}}\end{pmatrix}\:\:\mathrm{so}\:\mathrm{find}\:\mathrm{det}\left(\mathrm{4A}^{−\mathrm{1}} \right) \\ $$

Question Number 95262 Answers: 3 Comments: 0

3x^2 +5x^4 −7 plz help to solve this equation

$$\mathrm{3x}^{\mathrm{2}} +\mathrm{5x}^{\mathrm{4}} −\mathrm{7} \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{equation} \\ $$

Question Number 95260 Answers: 1 Comments: 3

if the line 3x+2y−1=0 transformed by matrix A= (((1 a)),((b 2)) ) such that the image is the line 2x+8y+c=0 find the value of a×b×c

$$\mathrm{if}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}+\mathrm{2y}−\mathrm{1}=\mathrm{0}\:\mathrm{transformed} \\ $$$$\mathrm{by}\:\mathrm{matrix}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{a}}\\{\mathrm{b}\:\:\:\mathrm{2}}\end{pmatrix}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{2x}+\mathrm{8y}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}×\mathrm{b}×\mathrm{c}\: \\ $$

Question Number 95259 Answers: 1 Comments: 1

find all roots ((√6) −(√2)i)^(1/3) by using demover theorem ?

$${find}\:{all}\:{roots}\:\left(\sqrt{\mathrm{6}}\:−\sqrt{\mathrm{2}}{i}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {by}\:{using}\:{demover}\:{theorem}\:? \\ $$

Question Number 95246 Answers: 4 Comments: 0

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