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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

Question Number 49954 Answers: 1 Comments: 1

find f(α) =∫_0 ^1 ((arctan(αx))/(1+α^2 x^2 ))dx 2) calculate ∫_0 ^1 ((arctan(2x))/(1+4x^2 )) dx and ∫_0 ^1 ((arctan(3x))/(1+9x^2 )) dx .

$${find}\:\:\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+\alpha^{\mathrm{2}} {x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }\:\:{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)}{\mathrm{1}+\mathrm{9}{x}^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 49942 Answers: 0 Comments: 1

calculate ∫∫_D (√(x^4 −y^4 ))dxdy with D =[0,1]×[0,1]

$${calculate}\:\int\int_{{D}} \sqrt{{x}^{\mathrm{4}} −{y}^{\mathrm{4}} }{dxdy} \\ $$$${with}\:{D}\:=\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 49941 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−x) ln(1+x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

Question Number 49939 Answers: 0 Comments: 4

find ∫_0 ^(π/2) sinx ln(1+x) dx

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sinx}\:{ln}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$

Question Number 49938 Answers: 0 Comments: 1

find f(x)=∫_0 ^(π/4) ln(cost+xsint)dt

$${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cost}+{xsint}\right){dt} \\ $$

Question Number 49937 Answers: 1 Comments: 2

let u_n =(((−1)^n )/2^n ) + 3n+1 find Σ_(n=0) ^(49) u_n

$${let}\:{u}_{{n}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{{n}} }\:+\:\mathrm{3}{n}+\mathrm{1} \\ $$$${find}\:\sum_{{n}=\mathrm{0}} ^{\mathrm{49}} \:{u}_{{n}} \\ $$

Question Number 49935 Answers: 2 Comments: 1

Question Number 49930 Answers: 1 Comments: 0

Please help me solve this question How many 4 digits number with all digits different are tbere between 1000 and 9999 such tbat the difference between the first and the last digit is plus or ninus 3.

$${Please}\:{help}\:{me}\:{solve}\:{this}\:{question} \\ $$$${How}\:{many}\:\mathrm{4}\:{digits}\:{number}\:{with}\:{all}\:\:{digits}\: \\ $$$${different}\:{are}\:{tbere}\:{between}\:\mathrm{1000}\:{and}\:\mathrm{9999} \\ $$$${such}\:{tbat}\:{the}\:{difference}\:{between}\:{the}\:{first} \\ $$$${and}\:{the}\:{last}\:{digit}\:{is}\:{plus}\:{or}\:{ninus}\:\mathrm{3}. \\ $$$$ \\ $$

Question Number 49927 Answers: 0 Comments: 2

find lim_(x→a^+ ) (x−a)(a^x −x^a ) with a>0 .

$${find}\:{lim}_{{x}\rightarrow{a}^{+} } \:\:\:\:\left({x}−{a}\right)\left({a}^{{x}} −{x}^{{a}} \right)\:\:\:{with}\:{a}>\mathrm{0}\:. \\ $$

Question Number 49922 Answers: 1 Comments: 0

Question Number 49902 Answers: 1 Comments: 1

If F(t)= ∫_0 ^( t) e^(t−y) .ydy. Prove that F(t)= e^t −(1+t).

$${If}\:{F}\left({t}\right)=\:\int_{\mathrm{0}} ^{\:{t}} {e}^{{t}−{y}} .{ydy}. \\ $$$${Prove}\:{that}\:{F}\left({t}\right)=\:{e}^{{t}} −\left(\mathrm{1}+{t}\right). \\ $$

Question Number 49903 Answers: 1 Comments: 1

Question Number 49898 Answers: 0 Comments: 1

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