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Question Number 50052    Answers: 5   Comments: 1

Question Number 50047    Answers: 1   Comments: 0

Question Number 50048    Answers: 3   Comments: 4

Question Number 50017    Answers: 0   Comments: 4

CONGRATULATIONS ! Tinkutara- our forum on having above 50000 question posts.

$$\mathcal{CONGRATULATIONS}\:! \\ $$$${Tinkutara}-\:{our}\:{forum}\:{on} \\ $$$${having}\:{above}\:\mathrm{50000}\:{question}\:{posts}. \\ $$

Question Number 50016    Answers: 2   Comments: 0

Can you please help me how can i solve this equation x=0.055(1.44x^2 −6.336x+6.9696)

$${Can}\:{you}\:{please}\:{help}\:{me}\: \\ $$$${how}\:{can}\:{i}\:{solve}\:{this}\:{equation}\: \\ $$$${x}=\mathrm{0}.\mathrm{055}\left(\mathrm{1}.\mathrm{44}{x}^{\mathrm{2}} −\mathrm{6}.\mathrm{336}{x}+\mathrm{6}.\mathrm{9696}\right) \\ $$

Question Number 50012    Answers: 0   Comments: 0

help me sir plz

$$\mathrm{help}\:\mathrm{me}\:\mathrm{sir}\:\mathrm{plz} \\ $$$$ \\ $$$$ \\ $$

Question Number 50011    Answers: 3   Comments: 0

Question Number 50010    Answers: 0   Comments: 2

Question Number 50008    Answers: 1   Comments: 4

5−digit number divisible by 3 formed using 0,1,2,3,4,5 without repetition. Total number of such no.s is ?

$$\mathrm{5}−{digit}\:{number}\:{divisible}\:{by}\:\mathrm{3}\:{formed} \\ $$$${using}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:{without}\:{repetition}. \\ $$$${Total}\:{number}\:{of}\:{such}\:{no}.{s}\:{is}\:? \\ $$

Question Number 50007    Answers: 1   Comments: 1

For a < x < b, find ∫_a ^b (√(x−a)) . (√(b−x)) dx

$$\mathrm{For}\:{a}\:<\:{x}\:<\:{b},\:\mathrm{find}\: \\ $$$$\underset{{a}} {\overset{{b}} {\int}}\:\sqrt{{x}−{a}}\:.\:\sqrt{{b}−{x}}\:{dx} \\ $$

Question Number 49987    Answers: 1   Comments: 4

Question Number 49984    Answers: 1   Comments: 1

Question Number 49983    Answers: 1   Comments: 0

Find the domain of the function and sketch the graph f(x) = { ((2x − 1, if x < 0)),((x^2 , if 0 ≤ x ≤ 2)),((1 , if x ≤ 2)) :}

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{and}\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{graph} \\ $$$$\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:=\:\:\begin{cases}{\mathrm{2x}\:−\:\mathrm{1},\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\:\:\:\:\:\mathrm{x}\:<\:\mathrm{0}}\\{\mathrm{x}^{\mathrm{2}} \:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\:\:\:\mathrm{0}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{2}}\\{\mathrm{1}\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\:\:\:\:\mathrm{x}\:\leqslant\:\mathrm{2}}\end{cases} \\ $$

Question Number 49982    Answers: 1   Comments: 0

If (n_P_r /n_C_r ) −1=5, find the value of r

$$\mathrm{If}\:\frac{\mathrm{n}_{\mathrm{P}_{\mathrm{r}} } }{\mathrm{n}_{\mathrm{C}_{\mathrm{r}} } }\:−\mathrm{1}=\mathrm{5},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{r} \\ $$

Question Number 49976    Answers: 0   Comments: 3

Question Number 49970    Answers: 2   Comments: 1

Question Number 49968    Answers: 0   Comments: 1

find f(x) =∫_0 ^(+∞) ((t arctan(xt))/(1+t^4 )) dt

$${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{t}\:{arctan}\left({xt}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }\:{dt} \\ $$

Question Number 49967    Answers: 0   Comments: 1

calculate ∫_0 ^(+∞) (dx/((x^2 −i)^2 ))

$$\:\:{calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{i}\right)^{\mathrm{2}} } \\ $$

Question Number 49966    Answers: 1   Comments: 1

A conveyor belt is driven at velocity v by a motor.Sand drops vertically on to the belt at a rate of mkg/s. What is the additional power needed to keep the conveyor belt moving at a steady speed when the sand starts to fall on it? a)(1/2)mv b)mv c)(1/2)mv^2 d)mv^2

$${A}\:{conveyor}\:{belt}\:{is}\:{driven}\:{at}\:{velocity} \\ $$$${v}\:{by}\:{a}\:{motor}.{Sand}\:{drops}\:{vertically} \\ $$$${on}\:{to}\:{the}\:{belt}\:{at}\:{a}\:{rate}\:{of}\:\boldsymbol{{m}}{kg}/{s}. \\ $$$${What}\:{is}\:{the}\:{additional}\:{power} \\ $$$${needed}\:{to}\:{keep}\:{the}\:{conveyor}\:{belt} \\ $$$${moving}\:{at}\:{a}\:{steady}\:{speed}\:{when} \\ $$$${the}\:{sand}\:{starts}\:{to}\:{fall}\:{on}\:{it}? \\ $$$$\left.{a}\left.\right)\left.\frac{\mathrm{1}}{\mathrm{2}}\left.{mv}\:{b}\right){mv}\:{c}\right)\frac{\mathrm{1}}{\mathrm{2}}{mv}^{\mathrm{2}} \:{d}\right){mv}^{\mathrm{2}} \\ $$

Question Number 49964    Answers: 1   Comments: 2

Question Number 49963    Answers: 0   Comments: 0

find cos((π/7)) by solving the equation x^7 −1=0 inside C .

$${find}\:\:{cos}\left(\frac{\pi}{\mathrm{7}}\right)\:{by}\:{solving}\:{the}\:{equation}\:{x}^{\mathrm{7}} −\mathrm{1}=\mathrm{0}\:{inside}\:{C}\:. \\ $$

Question Number 49961    Answers: 0   Comments: 1

find the sequence (a_n ) wich verify (Σ_(n=1) ^∞ x^n )(Σ_(n=0) ^∞ (((−x)^n )/(n+1)))=Σ_(n=0) ^∞ a_n x^n also find the radius of this serie.

$${find}\:{the}\:{sequence}\:\left({a}_{{n}} \right)\:{wich}\:{verify}\: \\ $$$$\left(\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} \right)\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−{x}\right)^{{n}} }{{n}+\mathrm{1}}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:{a}_{{n}} {x}^{{n}} \:\:{also}\:{find}\:{the}\:{radius}\:{of}\:{this}\:{serie}. \\ $$

Question Number 49956    Answers: 1   Comments: 1

find ∫_0 ^1 cos(n arcosx)dx with n integr natural.

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left({n}\:{arcosx}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$

Question Number 49953    Answers: 0   Comments: 3

1) calculate ∫_0 ^1 ln(1+ix)dx and ∫_0 ^1 ln(1−ix)dx 2) find the value of ∫_0 ^1 ln(1+x^2 )dx .

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ix}\right){dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ix}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx}\:. \\ $$

Question Number 49952    Answers: 0   Comments: 2

1) simplify A_n = (1/((2+i(√3))^n )) +(1/((2−i(√3))^n )) 2) smplify B_n =(1/((2+(√3))^n )) +(1/((2−(√3))^n )) n integr natural.

$$\left.\mathrm{1}\right)\:{simplify}\:{A}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{2}+{i}\sqrt{\mathrm{3}}\right)^{{n}} }\:+\frac{\mathrm{1}}{\left(\mathrm{2}−{i}\sqrt{\mathrm{3}}\right)^{{n}} } \\ $$$$\left.\mathrm{2}\right)\:{smplify}\:\:{B}_{{n}} =\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{n}} }\:+\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural}. \\ $$

Question Number 49950    Answers: 1   Comments: 1

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