Question and Answers Forum

OthersQuestion and Answers: Page 32

Question Number 168613 Answers: 3 Comments: 1

Resolve 1) x(dy/dx)−y=y^3 2) (x−y)ydx−x^2 dy=0 3) (2x−y)dx+(4x−2y+3)dy=0

$${Resolve}\: \\ $$$$\left.\mathrm{1}\right)\:{x}\frac{{dy}}{{dx}}−{y}={y}^{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:\left({x}−{y}\right){ydx}−{x}^{\mathrm{2}} {dy}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\left(\mathrm{2}{x}−{y}\right){dx}+\left(\mathrm{4}{x}−\mathrm{2}{y}+\mathrm{3}\right){dy}=\mathrm{0} \\ $$

Question Number 168608 Answers: 2 Comments: 0

Question Number 168549 Answers: 1 Comments: 0

Resolve (x−2)^2 y^(′′) −3(x−2)y′+y=x

$${Resolve} \\ $$$$\left({x}−\mathrm{2}\right)^{\mathrm{2}} {y}^{''} −\mathrm{3}\left({x}−\mathrm{2}\right){y}'+{y}={x} \\ $$

Question Number 168548 Answers: 1 Comments: 0

Question Number 168546 Answers: 0 Comments: 0

Question Number 168538 Answers: 2 Comments: 0

Question Number 168537 Answers: 2 Comments: 0

4^(61) +4^(62) +4^(63) +4^(64 ) is divisible by (1) 17 (2) 3 (3) 11 (4) 13 Mastermind

$$\mathrm{4}^{\mathrm{61}} +\mathrm{4}^{\mathrm{62}} +\mathrm{4}^{\mathrm{63}} +\mathrm{4}^{\mathrm{64}\:} \:{is}\:{divisible}\:{by} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{17}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right)\:\mathrm{3} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{11}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{4}\right)\:\mathrm{13} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168527 Answers: 1 Comments: 0

Find the value of x x^3 +64=0 Mastermind

$${Find}\:{the}\:{value}\:{of}\:{x} \\ $$$${x}^{\mathrm{3}} +\mathrm{64}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168525 Answers: 1 Comments: 0

Resolve x^2 y^(′′) +xy^′ +y=1

$${Resolve} \\ $$$${x}^{\mathrm{2}} {y}^{''} +{xy}^{'} +{y}=\mathrm{1} \\ $$

Question Number 168518 Answers: 1 Comments: 1

Re^ soudre l′e^ quation aux differentielles totales 2xydx+(x^2 −y^2 )dy=0

$${R}\acute {{e}soudre}\:{l}'\acute {{e}quation}\:{au}\mathrm{x}\:\mathrm{differentiel}{les} \\ $$$$\mathrm{totales} \\ $$$$\mathrm{2}{xydx}+\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$

Question Number 168492 Answers: 0 Comments: 3

Question Number 168421 Answers: 0 Comments: 0

Calculate the compound interest on the sum of #400 000 for 2years at the rate of 10% . Mastermind

$${Calculate}\:{the}\:{compound}\:{interest}\: \\ $$$${on}\:{the}\:{sum}\:{of}\:#\mathrm{400}\:\mathrm{000}\: \\ $$$${for}\:\mathrm{2}{years}\:{at}\:{the}\:{rate}\:{of} \\ $$$$\mathrm{10\%}\:. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168399 Answers: 1 Comments: 0

solve z^(1/4) −i=0 Mastermind

$${solve} \\ $$$${z}^{\frac{\mathrm{1}}{\mathrm{4}}} −{i}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168280 Answers: 1 Comments: 0

Wath is your favourite formula ???

$${Wath}\:{is}\:{your}\:{favourite}\:{formula}\:??? \\ $$

Question Number 168278 Answers: 1 Comments: 2

((log_3 (12))/(log_(36) (3)))−((log_3 (4))/(log_(108) (3))) = x x =

$$\:\:\:\:\:\frac{{log}_{\mathrm{3}} \left(\mathrm{12}\right)}{{log}_{\mathrm{36}} \left(\mathrm{3}\right)}−\frac{{log}_{\mathrm{3}} \left(\mathrm{4}\right)}{{log}_{\mathrm{108}} \left(\mathrm{3}\right)}\:=\:{x} \\ $$$$\:\:\:\:\:{x}\:=\: \\ $$

Question Number 168274 Answers: 1 Comments: 0

Question Number 168264 Answers: 1 Comments: 0

Question Number 168247 Answers: 2 Comments: 0

Solve for x ((8^x +27^x )/(12^x +18^x ))=(7/6) Mastermind

$${Solve}\:{for}\:{x} \\ $$$$\frac{\mathrm{8}^{{x}} +\mathrm{27}^{{x}} }{\mathrm{12}^{{x}} +\mathrm{18}^{{x}} }=\frac{\mathrm{7}}{\mathrm{6}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168187 Answers: 2 Comments: 0

Prove that : sinh^(−1) tanθ = log tan((θ/2)+(π/4)) Mastermind

$${Prove}\:{that}\::\: \\ $$$${sinh}^{−\mathrm{1}} {tan}\theta\:=\:{log}\:{tan}\left(\frac{\theta}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168185 Answers: 0 Comments: 0

Separate cos^(−1) e^(iθ) into real and imaginary parts. Mastermind

$${Separate}\:{cos}^{−\mathrm{1}} {e}^{{i}\theta} \:{into}\: \\ $$$${real}\:{and}\:{imaginary}\:{parts}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168118 Answers: 1 Comments: 0

If tan(θ+iφ)=cosα+isinα, prove that : θ=((nΠ)/2)+(Π/4) and φ=(1/2)log tan((Π/4)+(α/2))

$${If}\:{tan}\left(\theta+{i}\phi\right)={cos}\alpha+{isin}\alpha,\: \\ $$$${prove}\:{that}\::\:\theta=\frac{{n}\Pi}{\mathrm{2}}+\frac{\Pi}{\mathrm{4}}\:{and}\:\phi=\frac{\mathrm{1}}{\mathrm{2}}{log}\:{tan}\left(\frac{\Pi}{\mathrm{4}}+\frac{\alpha}{\mathrm{2}}\right) \\ $$

Question Number 167978 Answers: 0 Comments: 0

(((3 2 )),((4 5)) ) [A] = determinant (((3 2)),((4 5)))

$$\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{2}\:}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{pmatrix}\:\:\left[{A}\right]\:=\begin{vmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{vmatrix} \\ $$

Question Number 167977 Answers: 1 Comments: 0

Prove that I_n =(1/2^(n+1) )∫_π ^(4nπ) xcos (x/2)dx=((2−π)/2^(np) )

$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\int_{\pi} ^{\mathrm{4}{n}\pi} {x}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx}=\frac{\mathrm{2}−\pi}{\mathrm{2}^{{np}} } \\ $$

Question Number 167963 Answers: 0 Comments: 0

show that_β_(1 =( nΣxy−ΣxΣy)/(nΣx^2 −(Σx)^2 )=Σxy/Σ(xy)^(2 ) where x=(x−x^− ) and y=(y−y^− ) )

$$\:{show}\:{that}_{\beta_{\mathrm{1}\:=\left(\:{n}\Sigma{xy}−\Sigma{x}\Sigma{y}\right)/\left({n}\Sigma{x}^{\mathrm{2}} −\left(\Sigma{x}\right)^{\mathrm{2}} \right)=\Sigma{xy}/\Sigma\left({xy}\right)^{\mathrm{2}\:} \:\:\:\:\:\:\:{where}\:{x}=\left({x}−\overset{−} {{x}}\right)\:{and}\:{y}=\left({y}−\overset{−} {{y}}\right)\:\:} } \: \\ $$$$ \\ $$

Question Number 167928 Answers: 1 Comments: 0

Show that ∣1−i∣^x =2^x has no nonzero integral solution

$${Show}\:{that}\:\mid\mathrm{1}−{i}\mid^{{x}} =\mathrm{2}^{{x}} \:{has}\:{no}\:{nonzero}\:{integral}\:{solution}\: \\ $$

Question Number 167882 Answers: 2 Comments: 0

Calculate I=∫(1/x)((√((1−x)/(1+x))))dx Indication poser t=(√((1−x)/(1+x)))

$${Calculate} \\ $$$${I}=\int\frac{\mathrm{1}}{{x}}\left(\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\right){dx} \\ $$$${Indication}\:{poser}\:{t}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}} \\ $$

Pg 27 Pg 28 Pg 29 Pg 30 Pg 31 Pg 32 Pg 33 Pg 34 Pg 35 Pg 36

Contact: info@tinkutara.com