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AllQuestion and Answers: Page 1223

Question Number 91770 Answers: 1 Comments: 2

y′′+3y=x^3 +3x

$${y}''+\mathrm{3}{y}={x}^{\mathrm{3}} +\mathrm{3}{x} \\ $$

Question Number 91763 Answers: 0 Comments: 0

Question Number 91760 Answers: 1 Comments: 3

Question Number 91753 Answers: 1 Comments: 3

∫3 (ln x)^2 dx = ??

$$\int\mathrm{3}\:\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:=\:?? \\ $$

Question Number 91750 Answers: 0 Comments: 2

(2x−y+1)dx = (x−4y+3)dy

$$\left(\mathrm{2}{x}−{y}+\mathrm{1}\right){dx}\:=\:\left({x}−\mathrm{4}{y}+\mathrm{3}\right){dy} \\ $$

Question Number 91735 Answers: 0 Comments: 1

∫_0 ^(π/2) ((tan^m α))^(1/k) dα for m>1

$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt[{{k}}]{\mathrm{tan}^{{m}} \:\alpha}\:{d}\alpha\:{for}\:{m}>\mathrm{1} \\ $$

Question Number 91732 Answers: 0 Comments: 2

Find the least possible value of x 8x ≡ 24 (mod 16) .... (i) 3x ≡ 6 (mod 25) .... (ii)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x} \\ $$$$\:\:\:\:\mathrm{8x}\:\equiv\:\mathrm{24}\:\left(\mathrm{mod}\:\mathrm{16}\right)\:\:\:\:\:....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{3x}\:\equiv\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{25}\right)\:\:\:\:\:\:....\:\left(\mathrm{ii}\right) \\ $$

Question Number 91744 Answers: 1 Comments: 1

Question Number 91715 Answers: 0 Comments: 4

Question Number 91714 Answers: 0 Comments: 1

Question Number 91703 Answers: 0 Comments: 0

∫_(−∞) ^(+∞) f^2 (x)dx ∀f

$$\int_{−\infty} ^{+\infty} {f}^{\mathrm{2}} \left({x}\right){dx}\:\forall{f} \\ $$

Question Number 91690 Answers: 1 Comments: 1

Question Number 91689 Answers: 0 Comments: 5

sec^2 1^o +sec^2 2^o +sec^2 3^o +...+sec^2 89^o

$$\mathrm{sec}\:^{\mathrm{2}} \mathrm{1}^{{o}} +\mathrm{sec}\:^{\mathrm{2}} \mathrm{2}^{{o}} +\mathrm{sec}\:^{\mathrm{2}} \mathrm{3}^{{o}} +...+\mathrm{sec}\:^{\mathrm{2}} \mathrm{89}^{{o}} \\ $$

Question Number 91688 Answers: 0 Comments: 2

solve equations x^(x ) + y^y = 31 and x + y = 5

$${solve}\:{equations}\:{x}^{{x}\:} +\:{y}^{{y}} \:=\:\mathrm{31}\:{and}\:{x}\:+\:{y}\:=\:\mathrm{5} \\ $$

Question Number 91681 Answers: 1 Comments: 3

Se f((√3^(x)^(1/3) ) + 3^(x)^(1/3) ) = (x)^(1/3) , calcule ((f(2))/(f(1)))∙

$$\: \\ $$$$\:\boldsymbol{\mathrm{Se}}\:\:\boldsymbol{\mathrm{f}}\left(\sqrt{\mathrm{3}^{\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}}} }\:+\:\mathrm{3}^{\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}}} \right)\:=\:\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}},\:\:\boldsymbol{\mathrm{calcule}}\:\:\frac{\boldsymbol{\mathrm{f}}\left(\mathrm{2}\right)}{\boldsymbol{\mathrm{f}}\left(\mathrm{1}\right)}\centerdot \\ $$$$\: \\ $$

Question Number 91678 Answers: 0 Comments: 0

(y+2px)^2 = 2px^2 solve by Clairaut′s method

$$\left({y}+\mathrm{2}{px}\right)^{\mathrm{2}} \:=\:\mathrm{2}{px}^{\mathrm{2}} \\ $$$${solve}\:{by}\:{Clairaut}'{s}\:{method}\: \\ $$

Question Number 91668 Answers: 0 Comments: 0

∫e^x^2 erf(x) dx

$$\int{e}^{{x}^{\mathrm{2}} } \:{erf}\left({x}\right)\:{dx} \\ $$

Question Number 91667 Answers: 0 Comments: 6

find the limits of 1. u_n =Σ_(k=1) ^n (n/(n^2 +k^2 )) 2. v_n =Σ_(k=1) ^n (1/(√(n^2 +2kn)))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{of}\: \\ $$$$\mathrm{1}.\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} }\:\:\: \\ $$$$\mathrm{2}.\:\mathrm{v}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\ $$

Question Number 91660 Answers: 0 Comments: 4

Question Number 91656 Answers: 1 Comments: 2

Question Number 91655 Answers: 2 Comments: 12

A particle is projected with an intial velocity of u ms^(−1) at an angle α to the ground from a point O on the ground. Given that it clears two walls of hieght h and distances 2h and 4h respectively from O. (a) find the tangent of α (b) the maximum hieght (c) the range and period of the particle (d) show that u^2 = (4/(26)) gh please sir can you help me using the actual equations of projectile motion?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{an}\:\mathrm{intial}\:\mathrm{velocity}\:\mathrm{of}\:{u}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\alpha\:\mathrm{to}\: \\ $$$$\mathrm{the}\:\mathrm{ground}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{O}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{it}\:\mathrm{clears} \\ $$$$\mathrm{two}\:\mathrm{walls}\:\mathrm{of}\:\mathrm{hieght}\:{h}\:\mathrm{and}\:\mathrm{distances}\:\mathrm{2h}\:\mathrm{and}\:\mathrm{4h}\:\mathrm{respectively}\:\mathrm{from}\:\mathrm{O}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{of}\:\alpha \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{hieght} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{range}\:\mathrm{and}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{show}\:\mathrm{that}\:{u}^{\mathrm{2}} \:=\:\frac{\mathrm{4}}{\mathrm{26}}\:\mathrm{g}{h}\: \\ $$$$\mathrm{please}\:\mathrm{sir}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{using}\:\mathrm{the}\:\mathrm{actual}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{projectile}\:\mathrm{motion}? \\ $$$$ \\ $$

Question Number 91654 Answers: 1 Comments: 0

th position vector of a particle p of mass 3 kg is given by r = [(cos 2t) i + (sin 2t)j] m given that p was intitialy at rest. find the cartesian equation of its path and describe it.

$$\mathrm{th}\:\mathrm{position}\:\mathrm{vector}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:{p}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\: \\ $$$$\:{r}\:=\:\left[\left(\mathrm{cos}\:\mathrm{2}{t}\right)\:{i}\:+\:\left(\mathrm{sin}\:\mathrm{2}{t}\right){j}\right]\:\mathrm{m} \\ $$$$\mathrm{given}\:\mathrm{that}\:{p}\:\:\mathrm{was}\:\mathrm{intitialy}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{cartesian}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{its}\:\mathrm{path}\:\mathrm{and}\:\mathrm{describe}\:\mathrm{it}. \\ $$

Question Number 91683 Answers: 0 Comments: 1

Question Number 91647 Answers: 1 Comments: 0

solve x⌊x⌊x⌊x⌋⌋⌋=2020

$${solve} \\ $$$${x}\lfloor{x}\lfloor{x}\lfloor{x}\rfloor\rfloor\rfloor=\mathrm{2020} \\ $$

Question Number 91643 Answers: 0 Comments: 4

(dy/dx) = ((y−x)/x)

$$\frac{{dy}}{{dx}}\:=\:\frac{{y}−{x}}{{x}}\: \\ $$$$ \\ $$

Question Number 91641 Answers: 0 Comments: 0

find ∫ ((cos^4 x+sin^4 x)/(cos^3 x+sin^3 x))dx

$${find}\:\int\:\frac{{cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}}{{cos}^{\mathrm{3}} {x}+{sin}^{\mathrm{3}} {x}}{dx} \\ $$

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