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Question Number 175081 Answers: 0 Comments: 0

If in △ABC , m(∢B)=3m(∢C) then: a = (b − c) (√((b/c) + 1)) , b > a + (c/2) R = (√(c^3 /(3c − b)))

$$\mathrm{If}\:\mathrm{in}\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{m}\left(\sphericalangle\mathrm{B}\right)=\mathrm{3m}\left(\sphericalangle\mathrm{C}\right)\:\mathrm{then}: \\ $$$$\mathrm{a}\:=\:\left(\mathrm{b}\:−\:\mathrm{c}\right)\:\sqrt{\frac{\mathrm{b}}{\mathrm{c}}\:+\:\mathrm{1}}\:\:,\:\:\mathrm{b}\:>\:\mathrm{a}\:+\:\frac{\mathrm{c}}{\mathrm{2}} \\ $$$$\mathrm{R}\:=\:\sqrt{\frac{\mathrm{c}^{\mathrm{3}} }{\mathrm{3c}\:−\:\mathrm{b}}} \\ $$

Question Number 175080 Answers: 0 Comments: 0

calculate .. lim_( x→ 0^( +) ) ∫_0 ^( (𝛑/2)) J_0 ( x.cos(∅ )).cos(∅)d∅ = ? where : J_𝛎 ( x )= x^( v) .Σ_(n=0) ^∞ (((−1 )^( n) .x^( 2n) )/(2^( 2n+v) .𝚪 (n + 𝛎 +1 )))

$$ \\ $$$$\:\:\:\boldsymbol{{calculate}}\:.. \\ $$$$\:\boldsymbol{{lim}}_{\:\boldsymbol{{x}}\rightarrow\:\mathrm{0}^{\:+} } \int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{{J}}_{\mathrm{0}} \:\left(\:\boldsymbol{{x}}.\boldsymbol{{cos}}\left(\boldsymbol{\emptyset}\:\right)\right).\boldsymbol{{cos}}\left(\boldsymbol{\emptyset}\right)\boldsymbol{{d}\emptyset}\:=\:? \\ $$$$\:\:\:\boldsymbol{{where}}\:: \\ $$$$\:\:\:\:\:\boldsymbol{{J}}_{\boldsymbol{\nu}} \:\left(\:\boldsymbol{{x}}\:\right)=\:\boldsymbol{{x}}^{\:\boldsymbol{{v}}} .\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\:\right)^{\:\boldsymbol{{n}}} .\boldsymbol{{x}}^{\:\mathrm{2}\boldsymbol{{n}}} }{\mathrm{2}^{\:\mathrm{2}\boldsymbol{{n}}+\boldsymbol{{v}}} .\boldsymbol{\Gamma}\:\left(\boldsymbol{{n}}\:+\:\boldsymbol{\nu}\:+\mathrm{1}\:\right)} \\ $$

Question Number 175077 Answers: 1 Comments: 0

Show that ∫_0 ^1 ((x^b −x^a )/(lnx))=ln(((b+1)/(a+1)))

$${Show}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{b}} −{x}^{{a}} }{{lnx}}={ln}\left(\frac{{b}+\mathrm{1}}{{a}+\mathrm{1}}\right) \\ $$

Question Number 175066 Answers: 1 Comments: 0

Question Number 175068 Answers: 0 Comments: 0

Question Number 175061 Answers: 1 Comments: 1

Question Number 175059 Answers: 1 Comments: 2

Question Number 175053 Answers: 0 Comments: 2

Question Number 175051 Answers: 0 Comments: 2

find the value of ∫_0 ^∞ ((arctanx)/((x^2 +1)^3 ))dx

$${find}\:{the}\:{value}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{arctanx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 175050 Answers: 0 Comments: 0

Question Number 175049 Answers: 1 Comments: 2

Z_( p) , is a field ...( p is prime )

$$ \\ $$$$\:\:\:\:\:\:\mathbb{Z}_{\:{p}} \:,\:{is}\:\:{a}\:\:{field}\:...\left(\:\:{p}\:{is}\:{prime}\:\right) \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 175045 Answers: 0 Comments: 5

In the figure ABCD is an square and BM=MC. If the area of PCD=14u. What is the value of: (1) Area of ABC; (2) Area of ABMP; (3) The area of ABCD

$${In}\:{the}\:{figure}\:{ABCD}\:{is}\:{an}\:{square}\:{and} \\ $$$${BM}={MC}.\:{If}\:{the}\:{area}\:{of}\:{PCD}=\mathrm{14}{u}.\: \\ $$$${What}\:{is}\:{the}\:{value}\:{of}: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{Area}\:{of}\:{ABC}; \\ $$$$\left(\mathrm{2}\right)\:{Area}\:{of}\:\:{ABMP}; \\ $$$$\left(\mathrm{3}\right)\:{The}\:{area}\:{of}\:{ABCD} \\ $$$$ \\ $$

Question Number 175042 Answers: 1 Comments: 0

Question Number 175041 Answers: 0 Comments: 0

Solve the differential (dy/dx)=((x^2 −3xy)/(x+y))

$${Solve}\:{the}\:{differential} \\ $$$$\frac{{dy}}{{dx}}=\frac{{x}^{\mathrm{2}} −\mathrm{3}{xy}}{{x}+{y}} \\ $$

Question Number 175040 Answers: 1 Comments: 0

hello, please, someone help me to correct the equation? It's typed wrong and I can't find where Solve: 5,76[((log_a ((√(log _b ((√a))))))/(log((√(log(a)))))) + log_(log (a)) (2)]((log _2 (x)))^(1/5) + ((log_2 (x))/(25)) = [log _2 (x)]^(3/5) Answers x_1 =1 , x_2 =2^(243) , x_3 =2^(−243) , x_4 =2^(1024) , x_5 =2^(−1024)

$$ \\ $$hello, please, someone help me to correct the equation? It's typed wrong and I can't find where $${Solve}: \\ $$$$\mathrm{5},\mathrm{76}\left[\frac{\mathrm{log}_{{a}} \left(\sqrt{\mathrm{log}\:_{{b}} \left(\sqrt{{a}}\right)}\right)}{\mathrm{log}\left(\sqrt{\mathrm{log}\left({a}\right)}\right)}\:+\:\mathrm{log}_{\mathrm{log}\:\left({a}\right)} \left(\mathrm{2}\right)\right]\sqrt[{\mathrm{5}}]{\mathrm{log}\:_{\mathrm{2}} \left({x}\right)}\:+\:\frac{\mathrm{log}_{\mathrm{2}} \left({x}\right)}{\mathrm{25}}\:=\:\left[\mathrm{log}\:_{\mathrm{2}} \left({x}\right)\right]^{\frac{\mathrm{3}}{\mathrm{5}}} \\ $$$${Answers} \\ $$$${x}_{\mathrm{1}} =\mathrm{1}\:,\:{x}_{\mathrm{2}} =\mathrm{2}^{\mathrm{243}} \:,\:{x}_{\mathrm{3}} =\mathrm{2}^{−\mathrm{243}} \:,\:{x}_{\mathrm{4}} =\mathrm{2}^{\mathrm{1024}} \:,\:{x}_{\mathrm{5}} =\mathrm{2}^{−\mathrm{1024}} \\ $$

Question Number 175028 Answers: 0 Comments: 1

Question Number 175032 Answers: 0 Comments: 0

Question Number 175017 Answers: 0 Comments: 2

Question Number 175012 Answers: 1 Comments: 0

prove: Use the residus form ∫_0 ^(+∞) ((xsinx)/((x^2 +1)^2 ))dx=(π/(4e))

$${prove}:\:{Use}\:{the}\:{residus}\:{form} \\ $$$$\int_{\mathrm{0}} ^{+\infty} \frac{{xsinx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{4}{e}} \\ $$

Question Number 175011 Answers: 0 Comments: 2

A large lot of tires contain 5% defectives. 4 tires are to be chosen for a car. Find the probability that you find (a) 2 defective tires before 4 good ones (b) at most 2 defective tires before 4 good ones.

$$\mathrm{A}\:\mathrm{large}\:\mathrm{lot}\:\mathrm{of}\:\mathrm{tires}\:\mathrm{contain}\:\mathrm{5\%}\:\mathrm{defectives}. \\ $$$$\mathrm{4}\:\mathrm{tires}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{for}\:\mathrm{a}\:\mathrm{car}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{you}\:\mathrm{find} \\ $$$$\:\left(\mathrm{a}\right)\:\mathrm{2}\:\mathrm{defective}\:\mathrm{tires}\:\mathrm{before}\:\mathrm{4}\:\mathrm{good}\:\mathrm{ones} \\ $$$$\:\left(\mathrm{b}\right)\:\mathrm{at}\:\mathrm{most}\:\mathrm{2}\:\mathrm{defective}\:\mathrm{tires}\:\mathrm{before}\:\mathrm{4}\:\mathrm{good}\:\mathrm{ones}. \\ $$

Question Number 175010 Answers: 1 Comments: 1

A ball of p of mass 0.25kg losses (1/3) of its velocity when it makes an head on collision with an identical ball q at rest. After collision, q moves off with a velocity of 2ms^(−1) in the original direction of p. Calculate the initial velocity of p.

$$\:\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{25kg}\:\mathrm{losses}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{of}\: \\ $$$$\mathrm{its}\:\mathrm{velocity}\:\mathrm{when}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{head}\:\mathrm{on} \\ $$$$\mathrm{collision}\:\mathrm{with}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{ball}\:\boldsymbol{\mathrm{q}}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{After}\:\mathrm{collision},\:\boldsymbol{\mathrm{q}}\:\mathrm{moves}\:\mathrm{off}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{2ms}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{original}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$

Question Number 175008 Answers: 0 Comments: 2

Find The Centroid Coordinate If Trapezoid With B_1 =4, B_2 =3 And Height=5 With Positions Like This

$${Find}\:{The}\:{Centroid}\:{Coordinate}\: \\ $$$${If}\:{Trapezoid}\:{With}\:{B}_{\mathrm{1}} =\mathrm{4},\:{B}_{\mathrm{2}} =\mathrm{3} \\ $$$${And}\:{Height}=\mathrm{5}\:{With}\:{Positions}\: \\ $$$${Like}\:{This} \\ $$

Question Number 175023 Answers: 0 Comments: 0

𝚺_(n=0) ^∞ (((−1)^n )/(7+6n))[𝛙^((0)) (((9+6n)/2))−𝛙^((0)) (((7+6n)/2))]

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{7}+\mathrm{6}\boldsymbol{\mathrm{n}}}\left[\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\frac{\mathrm{9}+\mathrm{6}\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right)−\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\frac{\mathrm{7}+\mathrm{6}\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right)\right] \\ $$

Question Number 175004 Answers: 0 Comments: 1

Question Number 175000 Answers: 1 Comments: 1

Question Number 174983 Answers: 0 Comments: 3

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