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Question Number 190811    Answers: 1   Comments: 0

If the angle between the vectors c =ai+2j and d=3i+j is 45Β° , find the two possible values of a

$$\:{If}\:{the}\:{angle}\:{between}\:{the}\:{vectors} \\ $$$$\:{c}\:={ai}+\mathrm{2}{j}\:{and}\:\:{d}=\mathrm{3}{i}+{j}\:{is}\:\mathrm{45}Β°\:,\:{find} \\ $$$$\:{the}\:{two}\:{possible}\:{values}\:{of}\:{a} \\ $$

Question Number 190809    Answers: 0   Comments: 2

Question Number 190802    Answers: 1   Comments: 0

log_x x=x^(5xβˆ’10) x=?

$${log}_{{x}} {x}={x}^{\mathrm{5}{x}βˆ’\mathrm{10}} \:\:\:\:\:{x}=? \\ $$

Question Number 190800    Answers: 0   Comments: 0

(d^n /da^n )πšͺ(a+1)=?

$$\frac{\boldsymbol{\mathrm{d}}^{\boldsymbol{\mathrm{n}}} }{\boldsymbol{\mathrm{da}}^{\boldsymbol{\mathrm{n}}} }\boldsymbol{\Gamma}\left(\boldsymbol{{a}}+\mathrm{1}\right)=? \\ $$

Question Number 190793    Answers: 1   Comments: 1

A projectile of mass M explodes at thee highst point of its trajectory when it hase vlocity . The horizontal distance travelede btween launch and explosion is x_0 . Two fragments are produced with initiale velocitis parallel to the ground. They thenfollow their trajectories until they hitt he ground. The fragment of mass m_1 retuns exactly to the launch point of thei orginal projectile (of mass M) while thee othr fragment of mass m_2 hits the grounda t a distance D from this point. Disregardn iteraction with air and assume that massa ws conserved in the explosion (m_1 +m_2 =M) Determine the magnitude of the velocity of fragment 2 just before it hits theground. (a) ((gx_0 )/v) (b)(√((25)/9))v (c) (√(((25)/9)v^2 +(((gx_0 )/5))2)) (d)(√((5/3)x_0 v^2 +(((gx_0 )/v))2))

$$ \\ $$$$\mathrm{A}\:\mathrm{projectile}\:\mathrm{of}\:\mathrm{mass}\:\boldsymbol{{M}}\:\mathrm{explodes}\:\mathrm{at}\:\mathrm{thee} \\ $$$$\mathrm{highst}\:\mathrm{point}\:\mathrm{of}\:\mathrm{its}\:\mathrm{trajectory}\:\mathrm{when}\:\mathrm{it}\:\mathrm{hase} \\ $$$$\mathrm{vlocity}\:.\:\mathrm{The}\:\mathrm{horizontal}\:\mathrm{distance}\:\mathrm{travelede} \\ $$$$\mathrm{btween}\:\mathrm{launch}\:\mathrm{and}\:\mathrm{explosion}\:\mathrm{is}\:\boldsymbol{{x}}_{\mathrm{0}} \:.\:\mathrm{Two} \\ $$$$\mathrm{fragments}\:\mathrm{are}\:\mathrm{produced}\:\mathrm{with}\:\mathrm{initiale} \\ $$$$\mathrm{velocitis}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{They}\: \\ $$$$\mathrm{thenfollow}\:\mathrm{their}\:\mathrm{trajectories}\:\mathrm{until}\:\mathrm{they}\:\mathrm{hitt} \\ $$$$\mathrm{he}\:\mathrm{ground}.\:\mathrm{The}\:\mathrm{fragment}\:\mathrm{of}\:\mathrm{mass}\:\boldsymbol{{m}}_{\mathrm{1}} \:\mathrm{retuns}\:\mathrm{exactly}\:\mathrm{to}\:\mathrm{the}\:\mathrm{launch}\:\mathrm{point}\:\mathrm{of}\:\mathrm{thei} \\ $$$$\mathrm{orginal}\:\mathrm{projectile}\:\left(\mathrm{of}\:\mathrm{mass}\:\mathrm{M}\right)\:\mathrm{while}\:\mathrm{thee} \\ $$$$\mathrm{othr}\:\mathrm{fragment}\:\mathrm{of}\:\mathrm{mass}\:\boldsymbol{{m}}_{\mathrm{2}} \:\mathrm{hits}\:\mathrm{the}\:\mathrm{grounda} \\ $$$$\mathrm{t}\:\mathrm{a}\:\mathrm{distance}\:\boldsymbol{{D}}\:\mathrm{from}\:\mathrm{this}\:\mathrm{point}.\:\mathrm{Disregardn} \\ $$$$\mathrm{iteraction}\:\mathrm{with}\:\mathrm{air}\:\mathrm{and}\:\mathrm{assume}\:\mathrm{that}\:\mathrm{massa} \\ $$$$\mathrm{ws}\:\mathrm{conserved}\:\mathrm{in}\:\mathrm{the}\:\mathrm{explosion}\:\left(\boldsymbol{{m}}_{\mathrm{1}} +\boldsymbol{{m}}_{\mathrm{2}} =\mathrm{M}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{fragment}\:\mathrm{2}\:\mathrm{just}\:\mathrm{before}\:\mathrm{it}\:\mathrm{hits}\:\mathrm{theground}. \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{g}{x}_{\mathrm{0}} }{{v}} \\ $$$$\left(\mathrm{b}\right)\sqrt{\frac{\mathrm{25}}{\mathrm{9}}}{v} \\ $$$$\left({c}\right)\:\sqrt{\frac{\mathrm{25}}{\mathrm{9}}{v}^{\mathrm{2}} +\left(\frac{{gx}_{\mathrm{0}} }{\mathrm{5}}\right)\mathrm{2}} \\ $$$$\left({d}\right)\sqrt{\frac{\mathrm{5}}{\mathrm{3}}{x}_{\mathrm{0}} {v}^{\mathrm{2}} +\left(\frac{{gx}_{\mathrm{0}} }{{v}}\right)\mathrm{2}} \\ $$

Question Number 190790    Answers: 0   Comments: 1

Question Number 190788    Answers: 1   Comments: 0

calculate Ξ©= Ξ£_(k=0) ^n (( 1)/((nβˆ’k)!.(n+k )!))

$$ \\ $$$$\:\:\:\:\mathrm{calculate}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\Omega=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\:\mathrm{1}}{\left({n}βˆ’{k}\right)!.\left({n}+{k}\:\right)!} \\ $$$$ \\ $$

Question Number 190784    Answers: 0   Comments: 0

If , 0 β‡’ Mβ€² β‡’^f Mβ‡’^g Mβ€²β€²β‡’0 is a short exact sequence and Mβ€² , Mβ€²β€² are two finitely generated R βˆ’modules then prove M is finitely generated. Hint: f , g are two R βˆ’ homomorphism.

$$ \\ $$$$\:\:\mathrm{If}\:,\:\mathrm{0}\:\dashrightarrow\:\mathrm{M}'\:\overset{{f}} {\dashrightarrow}\mathrm{M}\overset{{g}} {\dashrightarrow}\mathrm{M}''\dashrightarrow\mathrm{0}\:\mathrm{is} \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{short}\:\mathrm{exact}\:\mathrm{sequence}\:\:\mathrm{and}\:\:\mathrm{M}'\:,\:\mathrm{M}''\:\mathrm{are} \\ $$$$\:\:\:\mathrm{two}\:\:\mathrm{finitely}\:\mathrm{generated}\:\:\mathrm{R}\:βˆ’\mathrm{modules} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{prove}\:\:\:\mathrm{M}\:\:\mathrm{is}\:\:\mathrm{finitely}\:\mathrm{generated}.\: \\ $$$$\:\:\:\mathrm{Hint}:\:\:{f}\:\:,\:\:{g}\:\:\:{are}\:\:{two}\:\:\:{R}\:βˆ’\:{homomorphism}. \\ $$

Question Number 190781    Answers: 2   Comments: 1

Question Number 190779    Answers: 1   Comments: 0

Re((1/(1βˆ’a)))^(aβˆ’1)

$$\boldsymbol{\mathrm{R}{e}}\left(\frac{\mathrm{1}}{\mathrm{1}βˆ’\boldsymbol{{a}}}\right)^{\boldsymbol{{a}}βˆ’\mathrm{1}} \\ $$

Question Number 190774    Answers: 0   Comments: 0

Question Number 190769    Answers: 0   Comments: 0

Question Number 190765    Answers: 1   Comments: 0

Question Number 190760    Answers: 1   Comments: 0

Question Number 190754    Answers: 1   Comments: 0

I = ∫_0 ^( Ο€) e^(acos t) cos (asin t)dt

$$\:\:\:\:\:\:{I}\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\:\pi} {e}^{{a}\mathrm{cos}\:{t}} \:\mathrm{cos}\:\left({a}\mathrm{sin}\:\:{t}\right){dt} \\ $$

Question Number 190746    Answers: 2   Comments: 0

Question Number 190745    Answers: 0   Comments: 0

Give M is any point in ABC triangle. Prove that MA+MB+MC<AC+BC

$${Give}\:{M}\:{is}\:{any}\:{point}\:{in}\:{ABC}\:{triangle}.\:{Prove}\:{that}\:{MA}+{MB}+{MC}<{AC}+{BC} \\ $$

Question Number 190740    Answers: 1   Comments: 0

∫(dx/((x^2 +5)^2 ))=?

$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{5}\right)^{\mathrm{2}} }=? \\ $$

Question Number 190732    Answers: 3   Comments: 0

Question Number 190731    Answers: 2   Comments: 0

(4a^2 βˆ’19aβˆ’5)x^2 +a^2 x+a+3=0 x_1 ,x_2 are roots when , x_1 <0 ,x_2 >0 , ∣x_1 βˆ£βˆ’x_2 >0 interval of max(a)=? solution??

$$\left(\mathrm{4a}^{\mathrm{2}} βˆ’\mathrm{19a}βˆ’\mathrm{5}\right)\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \mathrm{x}+\mathrm{a}+\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} \mathrm{are}\:\mathrm{roots} \\ $$$$\mathrm{when}\:,\:\mathrm{x}_{\mathrm{1}} <\mathrm{0}\:\:\:,\mathrm{x}_{\mathrm{2}} >\mathrm{0}\:\:,\:\mid\mathrm{x}_{\mathrm{1}} \midβˆ’\mathrm{x}_{\mathrm{2}} >\mathrm{0} \\ $$$$\mathrm{interval}\:\mathrm{of}\:\:\:\mathrm{max}\left(\mathrm{a}\right)=? \\ $$$$\mathrm{solution}?? \\ $$

Question Number 190730    Answers: 3   Comments: 0

∣x^2 βˆ’8x+18∣+∣yβˆ’3∣=5 all value of y=?? how money value of y is possible??

$$\mid\mathrm{x}^{\mathrm{2}} βˆ’\mathrm{8x}+\mathrm{18}\mid+\mid\mathrm{y}βˆ’\mathrm{3}\mid=\mathrm{5} \\ $$$$\mathrm{all}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}=?? \\ $$$$\mathrm{how}\:\mathrm{money}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{is}\:\mathrm{possible}?? \\ $$

Question Number 190738    Answers: 0   Comments: 0

∫_0 ^( (Ο€/2)) (((sin((x/2^n )))/(sinx))) dx , n ∈ N

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\left(\frac{{sin}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)}{{sinx}}\right)\:{dx}\:,\:{n}\:\in\:\mathbb{N} \\ $$

Question Number 190719    Answers: 0   Comments: 0

Find the real part of Re(((πšͺ(a+1))/((1βˆ’a)^(a+1) )))=?

$$\boldsymbol{\mathrm{F}{ind}}\:\boldsymbol{{the}}\:\boldsymbol{{real}}\:\boldsymbol{{part}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{\mathrm{R}{e}}\left(\frac{\boldsymbol{\Gamma}\left({a}+\mathrm{1}\right)}{\left(\mathrm{1}βˆ’{a}\right)^{{a}+\mathrm{1}} }\right)=? \\ $$

Question Number 190717    Answers: 2   Comments: 0

if x^2 +(mβˆ’2)x+2m=0 and (x_1 βˆ’1)(x_2 βˆ’1)=1 then find the value of m=?

$${if}\:\:{x}^{\mathrm{2}} +\left({m}βˆ’\mathrm{2}\right){x}+\mathrm{2}{m}=\mathrm{0}\:\:{and} \\ $$$$\left({x}_{\mathrm{1}} βˆ’\mathrm{1}\right)\left({x}_{\mathrm{2}} βˆ’\mathrm{1}\right)=\mathrm{1}\:\:{then}\:{find}\:{the}\:{value} \\ $$$${of}\:\:\:{m}=? \\ $$

Question Number 190716    Answers: 0   Comments: 0

if x+2+((m+2)/(mβˆ’2))=1 and x_1 βˆ™x_2 =2 then find the value of m=?

$${if}\:{x}+\mathrm{2}+\frac{{m}+\mathrm{2}}{{m}βˆ’\mathrm{2}}=\mathrm{1}\:\:{and}\:\:\:{x}_{\mathrm{1}} \centerdot{x}_{\mathrm{2}} =\mathrm{2}\:\:{then} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{m}=? \\ $$

Question Number 190715    Answers: 1   Comments: 0

if (5mβˆ’1)x^2 βˆ’(5m+2)x+3mβˆ’2=0 and x_1 =x_2 then find m=?

$${if}\:\left(\mathrm{5}{m}βˆ’\mathrm{1}\right){x}^{\mathrm{2}} βˆ’\left(\mathrm{5}{m}+\mathrm{2}\right){x}+\mathrm{3}{m}βˆ’\mathrm{2}=\mathrm{0} \\ $$$${and}\:\:{x}_{\mathrm{1}} ={x}_{\mathrm{2}} \:\:{then}\:{find}\:\:{m}=? \\ $$

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