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Question Number 86902 Answers: 0 Comments: 2

Mr.mathmax by abdo i request you to check my process to your question 86375.

$${Mr}.{mathmax}\:{by}\:{abdo} \\ $$$${i}\:{request}\:{you}\:{to}\:{check} \\ $$$${my}\:{process}\:{to}\:{your} \\ $$$${question}\:\mathrm{86375}. \\ $$

Question Number 86897 Answers: 1 Comments: 1

If ∫ (1/((x^2 +1)(x^2 +4))) dx = A tan^(−1) x+B tan^(−1) (x/2)+C, then

$$\mathrm{If}\:\int\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:=\:\:{A}\:\mathrm{tan}^{−\mathrm{1}} {x}+{B}\:\mathrm{tan}^{−\mathrm{1}} \frac{{x}}{\mathrm{2}}+{C},\:\mathrm{then} \\ $$

Question Number 86895 Answers: 0 Comments: 0

A small mass rest on a horizontal plat form which vibrates vertically in simple harmonic motion with period 0.50s. Find the maximum amplitude of the motion which allow which allow the mass to remain in contact with the platform throughout the motion

$$\mathrm{A}\:\mathrm{small}\:\mathrm{mass}\:\mathrm{rest}\:\mathrm{on}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{plat}\:\mathrm{form}\:\mathrm{which}\:\mathrm{vibrates}\: \\ $$$$\mathrm{vertically}\:\mathrm{in}\:\mathrm{simple}\:\mathrm{harmonic}\:\mathrm{motion}\:\mathrm{with}\:\mathrm{period}\:\mathrm{0}.\mathrm{50s}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{amplitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{which}\:\mathrm{allow}\:\mathrm{which} \\ $$$$\mathrm{allow}\:\mathrm{the}\:\mathrm{mass}\:\mathrm{to}\:\mathrm{remain}\:\mathrm{in}\:\mathrm{contact}\:\mathrm{with}\:\mathrm{the}\:\mathrm{platform}\:\mathrm{throughout} \\ $$$$\mathrm{the}\:\mathrm{motion} \\ $$

Question Number 86894 Answers: 0 Comments: 2

let f(x)=((1−x^2 )/(⌈x−1⌉)) find the domain and f ′(−(1/2)) if exist. ⌈...⌉ ceiling function

$${let}\:{f}\left({x}\right)=\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\lceil{x}−\mathrm{1}\rceil} \\ $$$${find}\:{the}\:{domain}\:{and}\:{f}\:'\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)\:{if}\:{exist}. \\ $$$$ \\ $$$$\lceil...\rceil\:{ceiling}\:{function} \\ $$

Question Number 86886 Answers: 0 Comments: 1

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

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

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