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AllQuestion and Answers: Page 1213

Question Number 86878 Answers: 2 Comments: 1

If sin^(10) (x) + cos^(10) (x) = ((11)/(36)) find sin^(12) (x) + cos ^(12) (x) = ?

$$\mathrm{If}\:\mathrm{sin}\:^{\mathrm{10}} \:\left(\mathrm{x}\right)\:+\:\mathrm{cos}\:^{\mathrm{10}} \:\left(\mathrm{x}\right)\:=\:\frac{\mathrm{11}}{\mathrm{36}} \\ $$$$\mathrm{find}\:\mathrm{sin}\:^{\mathrm{12}} \:\left(\mathrm{x}\right)\:+\:\mathrm{cos}\:\:^{\mathrm{12}} \left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 86874 Answers: 0 Comments: 0

A businessman bought 300 company shares at K60.00. The nominal price was K30.00. How much does he pay for the shares?

$${A}\:{businessman}\:{bought}\:\mathrm{300}\:{company}\:{shares}\:{at}\:\boldsymbol{\mathrm{K}}\mathrm{60}.\mathrm{00}.\:{The}\:{nominal}\:{price}\:{was}\:\boldsymbol{\mathrm{K}}\mathrm{30}.\mathrm{00}.\:{How}\:{much}\:{does}\:{he}\:{pay}\:{for}\:{the}\:{shares}? \\ $$

Question Number 86873 Answers: 0 Comments: 0

A company paid a total dividend of K12 600.00 at the end of 2018 on 6000 shares. If Freddy owned 200 shares in the company, how much was paid out in dividents to him?

$${A}\:{company}\:{paid}\:{a}\:{total}\:{dividend}\:{of}\:\boldsymbol{\mathrm{K}}\mathrm{12}\:\mathrm{600}.\mathrm{00}\:{at}\:{the}\:{end}\:{of}\:\mathrm{2018}\:{on}\:\mathrm{6000}\:{shares}.\:{If}\:{Freddy}\:{owned}\:\mathrm{200}\:{shares}\:{in}\:{the}\:{company},\:{how}\:{much}\:{was}\:{paid}\:{out}\:{in}\:{dividents}\:{to}\:{him}? \\ $$

Question Number 86871 Answers: 2 Comments: 1

∫ (dx/((x^4 +1)^3 ))

$$\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 87017 Answers: 1 Comments: 0

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Question Number 86855 Answers: 1 Comments: 0

If a,b ,c are the roots of the equation x^3 +6x^2 −4x+3 = 0 . find the equation with roots a+b , b+c , a+c ?

$$\mathrm{If}\:\mathrm{a},\mathrm{b}\:,\mathrm{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{6x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{3}\:=\:\mathrm{0}\:.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{equation}\:\mathrm{with}\:\mathrm{roots}\:\mathrm{a}+\mathrm{b}\:,\:\mathrm{b}+\mathrm{c}\:,\:\mathrm{a}+\mathrm{c}\:? \\ $$

Question Number 86853 Answers: 1 Comments: 0

∫((x^6 −x^3 +2)/(x^4 −x^2 −2))dx

$$\int\frac{{x}^{\mathrm{6}} −{x}^{\mathrm{3}} +\mathrm{2}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}{dx} \\ $$

Question Number 86850 Answers: 1 Comments: 1

∫ (dx/(x^2 ((((x^4 +1)))^(1/(4 )) )^3 ))

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \:\left(\sqrt[{\mathrm{4}\:\:}]{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)}\right)^{\mathrm{3}} } \\ $$

Question Number 86849 Answers: 0 Comments: 0

If z,w ε C and ∣z∣>1, ∣w∣<1 so ∣((z−w)/(1−z^− w))∣>1, demostrate thr veracity of the statment. (V or F)

$${If}\:\:{z},{w}\:\epsilon\:\mathbb{C}\:{and}\:\mid{z}\mid>\mathrm{1},\:\mid{w}\mid<\mathrm{1} \\ $$$${so}\:\mid\frac{{z}−{w}}{\mathrm{1}−\overset{−} {{z}w}}\mid>\mathrm{1},\:{demostrate} \\ $$$${thr}\:{veracity}\:{of}\:{the} \\ $$$$\:{statment}.\:\left({V}\:{or}\:{F}\right) \\ $$

Question Number 86845 Answers: 0 Comments: 0

Question Number 86837 Answers: 1 Comments: 0

solve 1)(√(xy)) (dy/dx)=1 2)e^y sec(x)dx+cos(x)dy=0

$${solve} \\ $$$$\left.\mathrm{1}\right)\sqrt{{xy}}\:\frac{{dy}}{{dx}}=\mathrm{1} \\ $$$$\left.\mathrm{2}\right){e}^{{y}} \:{sec}\left({x}\right){dx}+{cos}\left({x}\right){dy}=\mathrm{0} \\ $$

Question Number 86830 Answers: 2 Comments: 0

Prove that ∫_0 ^∞ ((sin x)/x)dx = (π/2)

$${Prove}\:\:{that}\:\int_{\mathrm{0}} ^{\infty} \frac{{sin}\:{x}}{{x}}{dx}\:=\:\frac{\pi}{\mathrm{2}} \\ $$

Question Number 86825 Answers: 1 Comments: 1

a^3 +(1/a^3 )=18 a^4 +(1/a^4 )=?

$${a}^{\mathrm{3}} +\frac{\mathrm{1}}{{a}^{\mathrm{3}} }=\mathrm{18} \\ $$$${a}^{\mathrm{4}} +\frac{\mathrm{1}}{{a}^{\mathrm{4}} }=? \\ $$

Question Number 86824 Answers: 2 Comments: 0

∫((x^6 +x^2 )/(x^8 −x^4 +1))dx

$$\int\frac{{x}^{\mathrm{6}} +{x}^{\mathrm{2}} }{{x}^{\mathrm{8}} −{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 86821 Answers: 0 Comments: 1

Question Number 86802 Answers: 1 Comments: 1

Question Number 86791 Answers: 4 Comments: 0

Solve the equation: x ≡ 3 (mod 5) x ≡ 4 (mod 7) x ≡ 2 (mod 3)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\mathrm{x}\:\:\equiv\:\:\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$\:\:\:\:\mathrm{x}\:\:\equiv\:\:\mathrm{4}\:\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$$$\:\:\:\:\mathrm{x}\:\:\equiv\:\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$

Question Number 86789 Answers: 2 Comments: 1

Question Number 86786 Answers: 0 Comments: 6

show that Σ_(n=2) ^∞ (1/(n^2 (1−n^2 )^2 ))=0.2999

$${show}\:{that} \\ $$$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left(\mathrm{1}−{n}^{\mathrm{2}} \right)^{\mathrm{2}} }=\mathrm{0}.\mathrm{2999} \\ $$

Question Number 86779 Answers: 1 Comments: 0

ssolve 1)x−[x]≥0 2)x−[x]≤0 3)x+[x]≥0 4)x+[x]≤0

$${ssolve} \\ $$$$\left.\mathrm{1}\right){x}−\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){x}−\left[{x}\right]\leqslant\mathrm{0} \\ $$$$\left.\mathrm{3}\right){x}+\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{4}\right){x}+\left[{x}\right]\leqslant\mathrm{0}\: \\ $$

Question Number 86762 Answers: 0 Comments: 4

Find the sum of the series 1+(1/2)+(1/3)+(1/4)+(1/6)+(1/8)+(1/9)+(1/(12))+∙∙∙ where the terms are the reciprocals of the positive integers whose only prime factors are 2s and 3s

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{series} \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{12}}+\centerdot\centerdot\centerdot \\ $$$${where}\:{the}\:{terms}\:{are}\:{the}\:{reciprocals} \\ $$$${of}\:{the}\:{positive}\:{integers}\:{whose}\:{only}\: \\ $$$${prime}\:{factors}\:{are}\:\mathrm{2}{s}\:{and}\:\mathrm{3}{s} \\ $$

Question Number 86761 Answers: 0 Comments: 0

∫ ((x+ sin x)/(x+ cos x)) dx =

$$\int\:\:\frac{\mathrm{x}+\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}+\:\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$

Question Number 86741 Answers: 1 Comments: 4

{ ((x+10y+50z=500)),((x+y+z=100)) :} find x,y,z

$$\begin{cases}{{x}+\mathrm{10}{y}+\mathrm{50}{z}=\mathrm{500}}\\{{x}+{y}+{z}=\mathrm{100}}\end{cases} \\ $$$$ \\ $$$${find}\:{x},{y},{z} \\ $$

Question Number 86737 Answers: 2 Comments: 4

prove that 1/cos2x+cosx+1=((sin((5x)/2))/(2sin(x/2)))+(1/2) 2/((cos(x)+isin(x)−1)/(cos(x)+isin(x)+1))=−i tan(x) 3/((cos(5x)+isin(5x)+1)/(cos(5x)−isin(x)+1))=cos(5x)+isin(5x)

$${prove}\:{that} \\ $$$$\mathrm{1}/{cos}\mathrm{2}{x}+{cosx}+\mathrm{1}=\frac{{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}}{\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{2}/\frac{{cos}\left({x}\right)+{isin}\left({x}\right)−\mathrm{1}}{{cos}\left({x}\right)+{isin}\left({x}\right)+\mathrm{1}}=−{i}\:{tan}\left({x}\right) \\ $$$$ \\ $$$$\mathrm{3}/\frac{{cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right)+\mathrm{1}}{{cos}\left(\mathrm{5}{x}\right)−{isin}\left({x}\right)+\mathrm{1}}={cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right) \\ $$

Question Number 86734 Answers: 1 Comments: 0

Find all functions that satisfy the equation [∫f(x)dx][∫(1/(f(x)))dx]=−1

$${Find}\:{all}\:{functions}\:{that}\:{satisfy}\:{the} \\ $$$${equation} \\ $$$$\left[\int{f}\left({x}\right){dx}\right]\left[\int\frac{\mathrm{1}}{{f}\left({x}\right)}{dx}\right]=−\mathrm{1} \\ $$

Question Number 86728 Answers: 0 Comments: 1

∫_0 ^∞ ln(1+(b^2 /x^2 )) dx

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

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