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Question Number 179435    Answers: 1   Comments: 1

Question Number 179433    Answers: 0   Comments: 0

Question Number 179432    Answers: 2   Comments: 2

Question Number 179429    Answers: 0   Comments: 3

to tinku tara sir: for some reasons i don′t get any notifications about updates to my posts. can you please check sir? thank you!

$${to}\:{tinku}\:{tara}\:{sir}: \\ $$$${for}\:{some}\:{reasons}\:{i}\:{don}'{t}\:{get}\:{any} \\ $$$${notifications}\:{about}\:{updates}\:{to}\:{my} \\ $$$${posts}.\:{can}\:{you}\:{please}\:{check}\:{sir}?\: \\ $$$${thank}\:{you}! \\ $$

Question Number 179428    Answers: 1   Comments: 0

Find (dy/dx) if y = 3sin^2 (x−5x^2 )

$$\mathrm{Find}\:\:\frac{{dy}}{{dx}}\:\:\mathrm{if}\:\:{y}\:=\:\mathrm{3sin}^{\mathrm{2}} \left({x}−\mathrm{5}{x}^{\mathrm{2}} \right)\: \\ $$

Question Number 179420    Answers: 2   Comments: 4

a challening question: find the number of numbers which are divisible by 9 and consist of distinct digits.

$$\underline{{a}\:{challening}\:{question}:} \\ $$$${find}\:{the}\:{number}\:{of}\:{numbers}\:{which} \\ $$$${are}\:{divisible}\:{by}\:\mathrm{9}\:{and}\:{consist}\:{of} \\ $$$${distinct}\:{digits}. \\ $$

Question Number 179407    Answers: 0   Comments: 1

Study the relative position of the curve C_f with it asymptote; f(x)= x+ ((sin x)/x)

$${Study}\:{the}\:{relative}\:{position}\:{of}\:{the}\:{curve}\:{C}_{{f}} \:{with} \\ $$$$\:{it}\:{asymptote};\:{f}\left({x}\right)=\:{x}+\:\frac{\mathrm{sin}\:{x}}{{x}} \\ $$

Question Number 179405    Answers: 4   Comments: 0

Evaluate ∫ (dx/(x^4 (√(9−x^2 ))))

$$\:{Evaluate}\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} \:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }} \\ $$

Question Number 179390    Answers: 1   Comments: 0

lim_(x→∞) (1−(5/( (√(x^3 −1)))))^(√(((x^2 +x+1)(4x−1))/4)) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}−\frac{\mathrm{5}}{\:\sqrt{{x}^{\mathrm{3}} −\mathrm{1}}}\right)^{\sqrt{\frac{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left(\mathrm{4}{x}−\mathrm{1}\right)}{\mathrm{4}}}} =? \\ $$

Question Number 179386    Answers: 2   Comments: 0

Question Number 179383    Answers: 3   Comments: 0

1• Evaluate I=∫ ((√(25x^2 −4))/x) dx 2• Find value of ∫_(2/5) ^( (4/5)) f(x) dx 3• Find value of ∫_(− (4/5)) ^( − (2/5)) f(x) dx

$$\mathrm{1}\bullet\:{Evaluate}\:{I}=\int\:\:\frac{\sqrt{\mathrm{25}{x}^{\mathrm{2}} −\mathrm{4}}}{{x}}\:{dx} \\ $$$$\:\mathrm{2}\bullet\:{Find}\:{value}\:{of}\:\int_{\frac{\mathrm{2}}{\mathrm{5}}} ^{\:\frac{\mathrm{4}}{\mathrm{5}}} {f}\left({x}\right)\:{dx} \\ $$$$\:\mathrm{3}\bullet\:{Find}\:{value}\:{of}\:\int_{−\:\frac{\mathrm{4}}{\mathrm{5}}} ^{\:−\:\frac{\mathrm{2}}{\mathrm{5}}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$

Question Number 179371    Answers: 2   Comments: 2

Question Number 179369    Answers: 1   Comments: 0

Question Number 179366    Answers: 2   Comments: 5

lim_(x→π) ((sin(x/2)−1)/(x−π))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{{sin}\frac{{x}}{\mathrm{2}}−\mathrm{1}}{{x}−\pi}=? \\ $$

Question Number 179360    Answers: 1   Comments: 0

Donnes: AD=1; DB=6; ∡BCD=45° ; ∡BAC=90° Determiner 1) AC ? 2) AE? −−−−−−−−−−−− Solution △BAC ∡BAC=90° BC^2 =AB^2 +AC^2 CD (cote commun aux △BAC et BDC) DB^2 =CD^2 +BC^2 −2BC×CDcos 45° (1) △CAD CD^2 =AD^2 +AC^2 (1) DB^2 =(AD^2 +AC^2 )+(AB^2 +AC^2 )−2(√((AB^2 +AC^2 )(AD^2 +AC^2 ))) cos 45° DB^2 =(AD^2 +AB^2 +2AC^2 −(√(2(AB^2 +AC^2 )(AD^2 +AC^2 ))) 2(AB^2 +AC^2 )(AD^2 +AC^2 )=(AD^2 +AB^2 +2AC^2 −DB^2 )^2 posons: AC=x 2(49+x^2 )(1+x^2 )=(1+49+2x^2 −36)^2 (x^4 +50x^2 +49)=2(x^4 +14x^2 +49) x^4 −22x^2 +49=0 x^2 =11±6(√2) x=(√(11+6(√2) )) AC =4,4142135 2)AB et AC coupent le cercle en (D,B) et( E,C) Nous avons AD×AB=AE×AC AE=((AD×AB)/(AC))=(7/( (√(11+6(√2)))))=((7(√(11+6(√2))))/(11+6(√2))) AE=1,585786

$${Donnes}:\:\mathrm{AD}=\mathrm{1};\:\mathrm{DB}=\mathrm{6};\:\measuredangle{BCD}=\mathrm{45}°\:;\:\measuredangle{BAC}=\mathrm{90}° \\ $$$${Determiner} \\ $$$$\left.\mathrm{1}\right)\:\:\mathrm{A}{C}\:\:?\:\: \\ $$$$\left.\mathrm{2}\right)\:\:\mathrm{A}{E}? \\ $$$$−−−−−−−−−−−− \\ $$$${Solution} \\ $$$$\bigtriangleup{BAC}\:\:\:\:\:\:\measuredangle{BAC}=\mathrm{90}° \\ $$$${BC}^{\mathrm{2}} ={AB}^{\mathrm{2}} +{AC}^{\mathrm{2}} \\ $$$${CD}\:\left({cote}\:{commun}\:{aux}\:\bigtriangleup{BAC}\:{et}\:{BDC}\right) \\ $$$${DB}^{\mathrm{2}} ={CD}^{\mathrm{2}} +{BC}^{\mathrm{2}} −\mathrm{2}{BC}×{CD}\mathrm{cos}\:\mathrm{45}°\:\:\left(\mathrm{1}\right) \\ $$$$\bigtriangleup{CAD}\:\:\:{CD}^{\mathrm{2}} ={AD}^{\mathrm{2}} +{AC}^{\mathrm{2}} \\ $$$$\left(\mathrm{1}\right)\:{DB}^{\mathrm{2}} =\left({AD}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)+\left({AB}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)−\mathrm{2}\sqrt{\left({AB}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)\left({AD}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)}\:\mathrm{cos}\:\mathrm{45}° \\ $$$$\:\:{DB}^{\mathrm{2}} =\left({AD}^{\mathrm{2}} +{AB}^{\mathrm{2}} +\mathrm{2}{AC}^{\mathrm{2}} −\sqrt{\mathrm{2}\left({AB}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)\left({AD}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)}\:\:\right. \\ $$$$\mathrm{2}\left({AB}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)\left({AD}^{\mathrm{2}} +{AC}^{\mathrm{2}} \right)=\left({AD}^{\mathrm{2}} +{AB}^{\mathrm{2}} +\mathrm{2}{AC}^{\mathrm{2}} −{DB}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$$${posons}:\:\:\:{AC}={x} \\ $$$$\mathrm{2}\left(\mathrm{49}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)=\left(\mathrm{1}+\mathrm{49}+\mathrm{2}{x}^{\mathrm{2}} −\mathrm{36}\right)^{\mathrm{2}} \\ $$$$\left({x}^{\mathrm{4}} +\mathrm{50}{x}^{\mathrm{2}} +\mathrm{49}\right)=\mathrm{2}\left({x}^{\mathrm{4}} +\mathrm{14}{x}^{\mathrm{2}} +\mathrm{49}\right) \\ $$$$\:\:\:{x}^{\mathrm{4}} −\mathrm{22}{x}^{\mathrm{2}} +\mathrm{49}=\mathrm{0} \\ $$$$\:{x}^{\mathrm{2}} =\mathrm{11}\pm\mathrm{6}\sqrt{\mathrm{2}}\:\:\:\:{x}=\sqrt{\mathrm{11}+\mathrm{6}\sqrt{\mathrm{2}}\:}\: \\ $$$$\:{AC}\:=\mathrm{4},\mathrm{4142135} \\ $$$$\left.\:\mathrm{2}\right){AB}\:{et}\:\:{AC}\:{coupent}\:{le}\:{cercle}\:\:{en}\:\left({D},{B}\right)\:{et}\left(\:{E},{C}\right) \\ $$$$\:{Nous}\:{avons}\:\:{AD}×{AB}={AE}×{AC} \\ $$$$\:\:{AE}=\frac{{AD}×{AB}}{{AC}}=\frac{\mathrm{7}}{\:\sqrt{\mathrm{11}+\mathrm{6}\sqrt{\mathrm{2}}}}=\frac{\mathrm{7}\sqrt{\mathrm{11}+\mathrm{6}\sqrt{\mathrm{2}}}}{\mathrm{11}+\mathrm{6}\sqrt{\mathrm{2}}} \\ $$$$\:{AE}=\mathrm{1},\mathrm{585786} \\ $$$$ \\ $$

Question Number 179358    Answers: 0   Comments: 4

Number of 4 digited numbers with distinct digits...are divisible by 9..i got 516...i got confusion kidly help me

$${Number}\:{of}\:\mathrm{4}\:{digited}\:\:{numbers}\: \\ $$$${with}\:{distinct}\:{digits}...{are}\:{divisible} \\ $$$${by}\:\mathrm{9}..{i}\:{got}\:\mathrm{516}...{i}\:{got}\:{confusion} \\ $$$${kidly}\:{help}\:{me} \\ $$

Question Number 179344    Answers: 1   Comments: 2

Help-me! ∫_0 ^( 𝛑) ∫_0 ^( 3cos 𝛗) 𝛉sin 𝛗d𝛉d𝛗

$$\: \\ $$$$\:\mathrm{Help}-\mathrm{me}! \\ $$$$\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\boldsymbol{\pi}} \int_{\mathrm{0}} ^{\:\mathrm{3}\boldsymbol{\mathrm{cos}}\:\boldsymbol{\phi}} \boldsymbol{\theta\mathrm{sin}}\:\boldsymbol{\phi\mathrm{d}\theta\mathrm{d}\phi} \\ $$$$\: \\ $$

Question Number 179338    Answers: 3   Comments: 0

Question Number 179336    Answers: 0   Comments: 2

f(x)=((1−x)/(1+x)) (fofofo........of_(2004) )_x =?

$${f}\left({x}\right)=\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}} \\ $$$$\left(\underset{\mathrm{2004}} {\underbrace{{fofofo}........{of}}}\right)_{{x}} =? \\ $$

Question Number 179328    Answers: 1   Comments: 0

y(x)=cos2x, ((d/dx)y(x))^n = ?

$${y}\left({x}\right)={cos}\mathrm{2}{x},\:\:\left(\frac{{d}}{{dx}}{y}\left({x}\right)\right)^{{n}} =\:? \\ $$

Question Number 179327    Answers: 1   Comments: 0

Find polynomial u,v ∈Q[x] such that (x^4 −1)u(x)+(x^7 −1)v(x)=(x−1)

$$\:{Find}\:{polynomial}\:{u},{v}\:\in{Q}\left[{x}\right]\:{such} \\ $$$$\:\:{that}\:\left({x}^{\mathrm{4}} −\mathrm{1}\right){u}\left({x}\right)+\left({x}^{\mathrm{7}} −\mathrm{1}\right){v}\left({x}\right)=\left({x}−\mathrm{1}\right) \\ $$

Question Number 179302    Answers: 2   Comments: 2

Question Number 179301    Answers: 1   Comments: 0

Question Number 179289    Answers: 1   Comments: 0

A refrigerator use 1200joules of work to jump 300j of heat from a cold reservoir of 275k to a hot reservoir at 320k. 1. What is the coefficient of performance. 2 the maximum efficiency of performance.

A refrigerator use 1200joules of work to jump 300j of heat from a cold reservoir of 275k to a hot reservoir at 320k. 1. What is the coefficient of performance. 2 the maximum efficiency of performance.

Question Number 179284    Answers: 2   Comments: 0

Solve for x (a/(ax − 1)) + (b/(bx − 1)) = a + b [x ≠ (1/a), (1/b)]

$$\mathrm{Solve}\:\mathrm{for}\:\boldsymbol{{x}} \\ $$$$\frac{{a}}{{ax}\:−\:\mathrm{1}}\:+\:\frac{{b}}{{bx}\:−\:\mathrm{1}}\:=\:{a}\:+\:{b}\:\left[{x}\:\neq\:\frac{\mathrm{1}}{{a}},\:\frac{\mathrm{1}}{{b}}\right] \\ $$

Question Number 179282    Answers: 3   Comments: 0

m^2 = n + 2 n^2 = m + 2 4mn − m^3 − n^3 = ? (m≠n)

$$\mathrm{m}^{\mathrm{2}} \:=\:\mathrm{n}\:+\:\mathrm{2} \\ $$$$\mathrm{n}^{\mathrm{2}} \:=\:\mathrm{m}\:+\:\mathrm{2} \\ $$$$\mathrm{4mn}\:−\:\mathrm{m}^{\mathrm{3}} \:−\:\mathrm{n}^{\mathrm{3}} \:=\:?\:\:\:\left(\mathrm{m}\neq\mathrm{n}\right) \\ $$

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