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Question Number 72824    Answers: 1   Comments: 0

fnd all integers n for which 13∣ 4(n^2 + 1)

$${fnd}\:{all}\:{integers}\:{n}\:{for}\:{which}\: \\ $$$$\:\mathrm{13}\mid\:\mathrm{4}\left({n}^{\mathrm{2}} \:+\:\mathrm{1}\right) \\ $$

Question Number 72823    Answers: 1   Comments: 0

What is derivative for this function a×b^(x−1) ×c^((1/2)(x−1)(x−2)) ×d^((1/6)(x−1)(x−2)(x−3))

$$\mathrm{What}\:\mathrm{is}\:\mathrm{derivative}\:\mathrm{for}\:\mathrm{this}\:\mathrm{function} \\ $$$$\: \\ $$$${a}×{b}^{{x}−\mathrm{1}} ×{c}^{\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)} ×{d}^{\frac{\mathrm{1}}{\mathrm{6}}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)} \\ $$

Question Number 72934    Answers: 1   Comments: 0

Question Number 72813    Answers: 0   Comments: 3

Find the area of the region enclosed by the line 5y=x+6 and the curve y=(√(∣x∣)) .

$${Find}\:{the}\:{area}\:{of}\:{the}\:{region}\:{enclosed} \\ $$$${by}\:{the}\:{line}\:\mathrm{5}{y}={x}+\mathrm{6}\:{and}\:{the}\:{curve} \\ $$$${y}=\sqrt{\mid{x}\mid}\:. \\ $$

Question Number 72806    Answers: 1   Comments: 2

show that lim_( x→0) [ x] does not exist. Hence define [x] and sketch a graph for y = 3x^2 + [x]

$$\underset{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\rightarrow\mathrm{0}} {\:{show}\:{that}\:\:\mathrm{lim}}\:\left[\:{x}\right]\:\:{does}\:{not}\:{exist}. \\ $$$${Hence}\:{define}\:\:\left[{x}\right]\:\:{and}\:{sketch}\:{a}\:{graph}\:{for}\: \\ $$$$\:{y}\:=\:\mathrm{3}{x}^{\mathrm{2}} \:+\:\left[{x}\right] \\ $$

Question Number 72805    Answers: 0   Comments: 0

PARTIAL VARIATION The success rate of government variws inversly as the number of corrupt mi nded individual and varies directly as the number of clean minded individal .if the goverment attain 95% success rate when there are two corrupt minded and 75% success rate when there are 5 corrupt minded and 20 clean minded individual. How many corrupr minded individual must be in administration with one clean minded individual to attain 99% success rate?

$${PARTIAL}\:{VARIATION} \\ $$$${The}\:{success}\:{rate}\:{of}\:{government}\:{variws}\: \\ $$$${inversly}\:{as}\:{the}\:{number}\:{of}\:{corrupt}\:{mi} \\ $$$${nded}\:{individual}\:{and}\:{varies}\:{directly} \\ $$$${as}\:{the}\:{number}\:{of}\:{clean}\:{minded}\:{individal} \\ $$$$.{if}\:\:{the}\:{goverment}\:{attain}\:\mathrm{95\%}\:{success} \\ $$$${rate}\:{when}\:{there}\:{are}\:{two}\:{corrupt}\:{minded} \\ $$$${and}\:\mathrm{75\%}\:{success}\:{rate}\:{when}\:{there}\:{are} \\ $$$$\mathrm{5}\:{corrupt}\:{minded}\:{and}\:\mathrm{20}\:{clean}\:{minded} \\ $$$${individual}.\:{How}\:{many}\:{corrupr}\:{minded} \\ $$$${individual}\:{must}\:{be}\:{in}\:{administration}\: \\ $$$${with}\:{one}\:{clean}\:{minded}\:{individual}\:{to}\: \\ $$$${attain}\:\mathrm{99\%}\:{success}\:{rate}? \\ $$

Question Number 72803    Answers: 2   Comments: 1

Question Number 72796    Answers: 1   Comments: 0

Integrate f(x,y)=(1/((1+x^2 +y^2 )^2 )) over the triangle with vertices (0,0) ,(1,0), (1,(√3)) after changing it to polar form.

$${Integrate}\:{f}\left({x},{y}\right)=\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{over} \\ $$$${the}\:{triangle}\:{with}\:{vertices}\:\left(\mathrm{0},\mathrm{0}\right)\:,\left(\mathrm{1},\mathrm{0}\right), \\ $$$$\left(\mathrm{1},\sqrt{\mathrm{3}}\right)\:{after}\:{changing}\:{it}\:{to}\:{polar}\:{form}. \\ $$

Question Number 72789    Answers: 1   Comments: 4

Find the area of the surface generated by revolving the curve x=(y^4 /4)+(1/(8y^2 )) about the x−axis . (given:1≤y≤2)

$${Find}\:{the}\:{area}\:{of}\:{the}\:{surface}\:{generated} \\ $$$${by}\:{revolving}\:{the}\:{curve}\:{x}=\frac{{y}^{\mathrm{4}} }{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}{y}^{\mathrm{2}} }\: \\ $$$${about}\:{the}\:{x}−{axis}\:.\:\left({given}:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\right) \\ $$

Question Number 72787    Answers: 1   Comments: 1

If z_1 =6(cos (π/4)+sin (π/4)) and z_2 =2(cos (π/5)+i×sin (π/5)) calculate (z_1 /z_2 ).

$${If}\:{z}_{\mathrm{1}} =\mathrm{6}\left(\mathrm{cos}\:\frac{\pi}{\mathrm{4}}+\mathrm{sin}\:\frac{\pi}{\mathrm{4}}\right)\:{and} \\ $$$${z}_{\mathrm{2}} =\mathrm{2}\left(\mathrm{cos}\:\frac{\pi}{\mathrm{5}}+\mathrm{i}×\mathrm{sin}\:\frac{\pi}{\mathrm{5}}\right)\:{calculate}\:\frac{{z}_{\mathrm{1}} }{{z}_{\mathrm{2}} }. \\ $$

Question Number 72784    Answers: 1   Comments: 1

Determine the independent term of x: (3x−(2/x))^4

$${Determine}\:{the}\:{independent}\:{term}\:{of} \\ $$$${x}: \\ $$$$\left(\mathrm{3}{x}−\frac{\mathrm{2}}{{x}}\right)^{\mathrm{4}} \\ $$

Question Number 72782    Answers: 1   Comments: 1

Question Number 72775    Answers: 0   Comments: 0

Question Number 72773    Answers: 1   Comments: 2

Question Number 72746    Answers: 1   Comments: 0

Σ_(n=0) ^∞ (1/((5n)!))

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{5}{n}\right)!} \\ $$

Question Number 72744    Answers: 0   Comments: 0

Question Number 72741    Answers: 0   Comments: 1

Question Number 72734    Answers: 3   Comments: 0

A triangle ABC is inscribed in a circle.AC=10cm,BC=7cm and AB=10cm.Find the radius of the circle.

$${A}\:{triangle}\:{ABC}\:{is}\:{inscribed}\:{in}\:{a} \\ $$$${circle}.{AC}=\mathrm{10}{cm},{BC}=\mathrm{7}{cm}\:{and}\: \\ $$$${AB}=\mathrm{10}{cm}.{Find}\:{the}\:{radius}\:{of}\:{the} \\ $$$${circle}. \\ $$

Question Number 72724    Answers: 0   Comments: 2

Question Number 72721    Answers: 1   Comments: 12

Question Number 72718    Answers: 0   Comments: 3

given that a ≡ b(mod n) show that a^k ≡ b^k (mod n)

$${given}\:{that}\: \\ $$$$\:{a}\:\equiv\:{b}\left({mod}\:{n}\right)\: \\ $$$${show}\:{that}\:{a}^{{k}} \:\equiv\:{b}^{{k}} \:\left({mod}\:{n}\right) \\ $$

Question Number 72689    Answers: 1   Comments: 0

Question Number 72688    Answers: 3   Comments: 0

Evaluate lim_(t→9) ((9−t)/(3−(√t) ))

$${Evaluate}\: \\ $$$$\:\underset{{t}\rightarrow\mathrm{9}} {\:{lim}}\frac{\mathrm{9}−{t}}{\mathrm{3}−\sqrt{{t}}\:} \\ $$

Question Number 72672    Answers: 2   Comments: 2

Question Number 72671    Answers: 0   Comments: 1

Question Number 72694    Answers: 0   Comments: 3

convergent or divergent? S=(2/1)−(1/1)+(2/3)−(1/3)+(2/5)−(1/5)+(2/7)−(1/7)...

$$\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}? \\ $$$${S}=\frac{\mathrm{2}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{2}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{2}}{\mathrm{7}}−\frac{\mathrm{1}}{\mathrm{7}}... \\ $$

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