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Karanja and Ouma can do a certain job in 6 days. Karanja alone can do the work in 5 days more than Ouma. How many days can Karanja take to do the job alone?

$${Karanja}\:{and}\:{Ouma}\:{can}\:{do}\:{a}\: \\ $$$${certain}\:{job}\:{in}\:\mathrm{6}\:{days}.\:{Karanja}\: \\ $$$${alone}\:{can}\:{do}\:{the}\:{work}\:{in}\:\mathrm{5}\:{days} \\ $$$${more}\:{than}\:{Ouma}.\:{How}\:{many}\: \\ $$$${days}\:{can}\:{Karanja}\:{take}\:{to}\:{do}\:{the} \\ $$$${job}\:{alone}? \\ $$

Question Number 72453 Answers: 0 Comments: 0

Question Number 72430 Answers: 0 Comments: 0

Hello find finde ∫_0 ^(+∞) ((ln(x))/(x^2 +ax+b))dx conditions a^2 <4b in therm of x_1 ,x_2 root of X^2 +aX+b hint Residus theorem applied too ((log^2 (z))/(z^2 +az+b)) this is very usufull i find it in lecture yesterday because we can easly evaluat any kinde of ∫_0 ^(+∞) ((log^k (z))/(p(z)))dz withe p(z) eiwthout root in ]0,+∞[ deg(p(z))≥2

$$\mathrm{Hello}\:\mathrm{find} \\ $$$$\mathrm{finde}\:\:\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{ax}+\mathrm{b}}\mathrm{dx} \\ $$$$\mathrm{conditions}\:\mathrm{a}^{\mathrm{2}} <\mathrm{4b}\:\:\: \\ $$$$\mathrm{in}\:\mathrm{therm}\:\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} \:\:\mathrm{root}\:\mathrm{of}\:\mathrm{X}^{\mathrm{2}} +\mathrm{aX}+\mathrm{b}\: \\ $$$$\:\mathrm{hint}\:\mathrm{Residus}\:\mathrm{theorem}\:\mathrm{applied}\:\mathrm{too}\:\frac{\mathrm{log}^{\mathrm{2}} \left(\mathrm{z}\right)}{\mathrm{z}^{\mathrm{2}} +\mathrm{az}+\mathrm{b}} \\ $$$$\mathrm{this}\:\mathrm{is}\:\mathrm{very}\:\mathrm{usufull}\:\mathrm{i}\:\mathrm{find}\:\mathrm{it}\:\mathrm{in}\:\mathrm{lecture}\:\mathrm{yesterday} \\ $$$$\mathrm{because}\:\mathrm{we}\:\mathrm{can}\:\mathrm{easly}\:\mathrm{evaluat}\:\mathrm{any}\:\mathrm{kinde}\:\mathrm{of}\:\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{log}^{\mathrm{k}} \left(\mathrm{z}\right)}{\mathrm{p}\left(\mathrm{z}\right)}\mathrm{dz} \\ $$$$\left.\mathrm{withe}\:\mathrm{p}\left(\mathrm{z}\right)\:\mathrm{eiwthout}\:\:\mathrm{root}\:\mathrm{in}\:\right]\mathrm{0},+\infty\left[\:\mathrm{deg}\left(\mathrm{p}\left(\mathrm{z}\right)\right)\geqslant\mathrm{2}\right. \\ $$

Question Number 72416 Answers: 0 Comments: 1

Question Number 72394 Answers: 0 Comments: 3

let g(x)=((ln(1+x))/(3+x^2 )) 1) find g^((n)) (x)and g^((n)) (0) 2)developp g at integr serie

$${let}\:{g}\left({x}\right)=\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{3}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{g}^{\left({n}\right)} \left({x}\right){and}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{g}\:{at}\:{integr}\:{serie} \\ $$

Question Number 72343 Answers: 0 Comments: 3

given that y = ln ( 1 + cos^2 x) find (dy/(dx )) at the point x = ((3π)/4) and if y =ln(x^2 + 4) find (dy/dx) at x = 1

$${given}\:{that}\:{y}\:=\:{ln}\:\left(\:\mathrm{1}\:+\:{cos}^{\mathrm{2}} {x}\right)\:{find}\:\frac{{dy}}{{dx}\:\:}\:{at}\:{the}\:{point}\:\:{x}\:=\:\frac{\mathrm{3}\pi}{\mathrm{4}} \\ $$$${and}\:\:{if}\:\:{y}\:={ln}\left({x}^{\mathrm{2}} \:+\:\mathrm{4}\right)\:{find}\:\:\frac{{dy}}{{dx}}\:{at}\:{x}\:=\:\mathrm{1} \\ $$

Question Number 72232 Answers: 0 Comments: 6

to all those who deleted their posts after they had been answered: I will not answer you anymore this forum had been great but lately it has been filling with unpolite people I′m not a freebie solver for anybody′s homework

$$\mathrm{to}\:\mathrm{all}\:\mathrm{those}\:\mathrm{who}\:\mathrm{deleted}\:\mathrm{their}\:\mathrm{posts}\:\mathrm{after}\:\mathrm{they} \\ $$$$\mathrm{had}\:\mathrm{been}\:\mathrm{answered}:\:\mathrm{I}\:\mathrm{will}\:\mathrm{not}\:\mathrm{answer}\:\mathrm{you} \\ $$$$\mathrm{anymore} \\ $$$$\mathrm{this}\:\mathrm{forum}\:\mathrm{had}\:\mathrm{been}\:\mathrm{great}\:\mathrm{but}\:\mathrm{lately}\:\mathrm{it}\:\mathrm{has} \\ $$$$\mathrm{been}\:\mathrm{filling}\:\mathrm{with}\:\mathrm{unpolite}\:\mathrm{people} \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{a}\:\mathrm{freebie}\:\mathrm{solver}\:\mathrm{for}\:\mathrm{anybody}'\mathrm{s}\:\mathrm{homework} \\ $$

Question Number 72153 Answers: 1 Comments: 3

∫((sin^3 x)/(√(cos x)))dx ∫sin(lnx)dx

$$\int\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\sqrt{\mathrm{cos}\:\mathrm{x}}}\mathrm{dx} \\ $$$$\int\mathrm{sin}\left(\mathrm{lnx}\right)\mathrm{dx} \\ $$

Question Number 71852 Answers: 1 Comments: 0

show that 5^(22) + 17^(22) ≡ 6 (mod 11)

$${show}\:{that}\:\mathrm{5}^{\mathrm{22}} \:+\:\mathrm{17}^{\mathrm{22}} \:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{11}\right) \\ $$

Question Number 71838 Answers: 1 Comments: 3

solve the system of linear congruences x ≡ 2 (mod 3) x ≡ 4(mod 5) x ≡ 7 (mod 9) x≡ 11( mod 13) using the Brute force method

$${solve}\:{the}\:{system}\:{of}\:{linear}\:{congruences}\: \\ $$$$\:{x}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{3}\right) \\ $$$${x}\:\equiv\:\mathrm{4}\left({mod}\:\mathrm{5}\right) \\ $$$${x}\:\equiv\:\mathrm{7}\:\left({mod}\:\mathrm{9}\right) \\ $$$${x}\equiv\:\mathrm{11}\left(\:{mod}\:\mathrm{13}\right) \\ $$$${using}\:{the}\:{Brute}\:{force}\:{method} \\ $$

Question Number 71564 Answers: 1 Comments: 2

(z−i)^4 =−7+24i

$$\left(\mathrm{z}−\mathrm{i}\right)^{\mathrm{4}} =−\mathrm{7}+\mathrm{24i} \\ $$

Question Number 71432 Answers: 0 Comments: 2

is 1(5/(3 )) an example of a mixed fraction

$${is}\:\mathrm{1}\frac{\mathrm{5}}{\mathrm{3}\:}\:{an}\:{example}\:{of}\:{a}\:{mixed}\:{fraction} \\ $$

Question Number 71326 Answers: 2 Comments: 0

(−64)^(1/6) =?(Is there any short cut for mcq)

$$\left(−\mathrm{64}\right)^{\frac{\mathrm{1}}{\mathrm{6}}} =?\left(\boldsymbol{\mathrm{I}}\mathrm{s}\:\mathrm{there}\:\mathrm{any}\:\mathrm{short}\:\mathrm{cut}\:\mathrm{for}\:\mathrm{mcq}\right) \\ $$

Question Number 71235 Answers: 2 Comments: 1

sinh[ln (x + (√(1 + x^2 ))) ] ≡ A. 2x B. (1/x) C. x^2 D. x

$${sinh}\left[{ln}\:\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:\right]\:\equiv\: \\ $$$$ \\ $$$${A}.\:\:\mathrm{2}{x} \\ $$$${B}.\:\:\frac{\mathrm{1}}{{x}} \\ $$$${C}.\:\:{x}^{\mathrm{2}} \\ $$$${D}.\:\:{x} \\ $$

Question Number 70914 Answers: 2 Comments: 3

1+(z+2i)+(z+2i)^2 +(z+2i)^3 +(z+2i)^4 =0 find z , z∈C

$$\mathrm{1}+\left(\mathrm{z}+\mathrm{2i}\right)+\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{2}} +\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{3}} +\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{4}} =\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{z}\:,\:\mathrm{z}\in\mathrm{C} \\ $$

Question Number 70397 Answers: 0 Comments: 1

Question Number 70310 Answers: 3 Comments: 1

please help me find the term independent of x in the expansion of (x + (3/x))^(−12 )

$${please}\:{help}\:{me}\:{find}\:{the}\:{term}\:{independent}\:{of}\:{x} \\ $$$${in}\:{the}\:{expansion}\:{of}\: \\ $$$$\:\:\:\:\:\:\left({x}\:+\:\frac{\mathrm{3}}{{x}}\right)^{−\mathrm{12}\:} \\ $$

Question Number 70132 Answers: 1 Comments: 1

Σ_(n=1) ^(3050) i^n

$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{3050}} {\sum}}\:{i}^{{n}} \\ $$

Question Number 70069 Answers: 1 Comments: 2

Π_(n=1) ^5 (((12n−2)^4 +18^2 )/((12n−8)^4 +18^2 )) =(((10^4 +324)(22^4 +324)(34^4 +324)(46^4 +324)(58^4 +324))/((4^4 +324)(16^4 +324)(28^4 +324)(40^4 +324)(52^4 +324)))

Pg 79 Pg 80 Pg 81 Pg 82 Pg 83 Pg 84 Pg 85 Pg 86 Pg 87 Pg 88

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