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App updates: • Image are saved as a background task so that you dont get app not responding when saving images. • Bug Fix: Background color was ignored while sharing • Support added for Bangla • Fixes for crashes reported. Please update from playstore.

$$\mathrm{App}\:\mathrm{updates}: \\ $$$$\bullet\:\mathrm{Image}\:\mathrm{are}\:\mathrm{saved}\:\mathrm{as}\:\mathrm{a}\:\mathrm{background} \\ $$$$\:\:\:\mathrm{task}\:\mathrm{so}\:\mathrm{that}\:\mathrm{you}\:\mathrm{dont}\:\mathrm{get}\:\mathrm{app}\:\mathrm{not} \\ $$$$\:\:\:\mathrm{responding}\:\mathrm{when}\:\mathrm{saving}\:\mathrm{images}. \\ $$$$\bullet\:\mathrm{Bug}\:\mathrm{Fix}:\:\mathrm{Background}\:\mathrm{color}\:\mathrm{was}\: \\ $$$$\:\:\:\:\mathrm{ignored}\:\mathrm{while}\:\mathrm{sharing} \\ $$$$\bullet\:\mathrm{Support}\:\mathrm{added}\:\mathrm{for}\:\mathrm{Bangla} \\ $$$$\bullet\:\mathrm{Fixes}\:\mathrm{for}\:\mathrm{crashes}\:\mathrm{reported}. \\ $$$$\mathrm{Please}\:\mathrm{update}\:\mathrm{from}\:\mathrm{playstore}. \\ $$

Question Number 105710 Answers: 3 Comments: 0

(2xy+cos y) dx +(x^2 −xsiny−2y)dy=0

$$\left(\mathrm{2}{xy}+\mathrm{cos}\:{y}\right)\:{dx}\:+\left({x}^{\mathrm{2}} −{x}\mathrm{sin}{y}−\mathrm{2}{y}\right){dy}=\mathrm{0} \\ $$

Question Number 105707 Answers: 4 Comments: 1

Find a polynomial f(x) which satisfy the following conditions: i) f(x) of degree 4 ii) (x−1) is a factor of f(x) and f′(x) iii) f(0)=3 and f′(0)=−5 iv) when f(x) is divided by (x−2), the remainder is 13.

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{conditions}: \\ $$$$\left.\mathrm{i}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{of}\:\mathrm{degree}\:\mathrm{4} \\ $$$$\left.\mathrm{ii}\right)\:\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}'\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{iii}\right)\:\mathrm{f}\left(\mathrm{0}\right)=\mathrm{3}\:\mathrm{and}\:\mathrm{f}'\left(\mathrm{0}\right)=−\mathrm{5} \\ $$$$\left.\mathrm{iv}\right)\:\mathrm{when}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{2}\right),\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{13}. \\ $$

Question Number 105706 Answers: 1 Comments: 0

∫_0 ^π (dx/(((√5)−cos x)^3 )) ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{dx}}{\left(\sqrt{\mathrm{5}}−\mathrm{cos}\:{x}\right)^{\mathrm{3}} }\:? \\ $$

Question Number 105704 Answers: 1 Comments: 2

Solve the following system of equations: { ((x^3 y+x^3 y^2 +2x^2 y^2 +x^2 y^3 +xy^3 =30)),((x^2 y+xy+x+y+xy^2 =11)) :}

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{3}} \mathrm{y}+\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{2}} +\mathrm{2x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}} +\mathrm{xy}^{\mathrm{3}} =\mathrm{30}}\\{\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{xy}+\mathrm{x}+\mathrm{y}+\mathrm{xy}^{\mathrm{2}} =\mathrm{11}}\end{cases} \\ $$

Question Number 105700 Answers: 1 Comments: 0

∫_(−π) ^π ((x^2 dx)/(1+sin (sin x)+(√(1+sin^2 (sin x)))))

$$\underset{−\pi} {\overset{\pi} {\int}}\:\frac{{x}^{\mathrm{2}} \:{dx}}{\mathrm{1}+\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)+\sqrt{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{sin}\:{x}\right)}} \\ $$$$ \\ $$

Question Number 105692 Answers: 1 Comments: 0

cos^2 (5x)+sin^2 (7x)=1

$$\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{5}{x}\right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{7}{x}\right)=\mathrm{1} \\ $$

Question Number 105687 Answers: 3 Comments: 0

{ ((x^2 +y^2 = 13)),((x^3 +y^3 = 35 )) :}

$$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:=\:\mathrm{13}}\\{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{35}\:}\end{cases} \\ $$

Question Number 105686 Answers: 1 Comments: 0

solve 7^x + 24^x = 25^x

$${solve}\:\mathrm{7}^{{x}} \:+\:\mathrm{24}^{{x}} \:=\:\mathrm{25}^{{x}} \: \\ $$

Question Number 105673 Answers: 2 Comments: 0

Question Number 105670 Answers: 1 Comments: 0

A machine manufactures washers, and 20% of the production is substandard. A random sample o f 10 washers is selected. Find the mean and standard deviation of the number of substandard washers in the sample.

$$\mathrm{A}\:\mathrm{machine}\:\mathrm{manufactures}\:\mathrm{washers},\:\mathrm{and}\:\mathrm{20\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{production}\:\mathrm{is} \\ $$$$\mathrm{substandard}.\:\mathrm{A}\:\mathrm{random}\:\mathrm{sample}\:\mathrm{o}\:\mathrm{f}\:\mathrm{10}\:\mathrm{washers}\:\mathrm{is}\:\mathrm{selected}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\:\mathrm{deviation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{substandard}\:\mathrm{washers}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sample}. \\ $$

Question Number 105661 Answers: 2 Comments: 1

lim_(x→π/2) tan^2 x (√((x−(π/2))−cos ^2 x)) ?

$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\mathrm{tan}\:^{\mathrm{2}} {x}\:\sqrt{\left({x}−\frac{\pi}{\mathrm{2}}\right)−\mathrm{cos}\:\:^{\mathrm{2}} {x}}\:? \\ $$

Question Number 105659 Answers: 2 Comments: 0

(d^2 y/dx^2 ) + (dy/dx)−2y=2x

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}−\mathrm{2}{y}=\mathrm{2}{x}\: \\ $$

Question Number 105650 Answers: 2 Comments: 0

cos^(−1) (2x)+ cos^(−1) (x)=(π/6) find x

$$\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)+\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)=\frac{\pi}{\mathrm{6}} \\ $$$${find}\:{x} \\ $$

Question Number 105646 Answers: 1 Comments: 0

Solve the differential equation; y′′−2ay′+(1+a^2 )y=te^(at) +sint

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}} +\mathrm{sint} \\ $$

Question Number 105638 Answers: 2 Comments: 0

(d^2 y/dx^2 ) + 9y = cos 4x

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{9}{y}\:=\:\mathrm{cos}\:\mathrm{4}{x} \\ $$

Question Number 105634 Answers: 0 Comments: 0

Question Number 105632 Answers: 1 Comments: 0

Given I_n =∫_0 ^1 (((1−x)^n )/(n!))e^x dx , n∈N a\Show that ∀x∈[0,1], (1−x)^n e^x ≤e and deduce that the Sequence (I_n )_n converges to zero. b\Establish a recurrence relation between I_n and I_(n+1) c\ Deduce that e=lim_(n→∞) Σ_(k=0) ^n ((1/(k!)))

$$\mathrm{Given}\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} }{\mathrm{n}!}\mathrm{e}^{\mathrm{x}} \mathrm{dx}\:,\:\mathrm{n}\in\mathbb{N} \\ $$$$\mathrm{a}\backslash\mathrm{Show}\:\mathrm{that}\:\forall\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right],\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} \mathrm{e}^{\mathrm{x}} \leqslant\mathrm{e}\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\mathrm{Sequence}\:\left(\mathrm{I}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{converges}\:\mathrm{to}\:\mathrm{zero}. \\ $$$$\mathrm{b}\backslash\mathrm{Establish}\:\mathrm{a}\:\mathrm{recurrence}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{I}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{I}_{\mathrm{n}+\mathrm{1}} \\ $$$$\mathrm{c}\backslash\:\mathrm{Deduce}\:\mathrm{that}\:\mathrm{e}=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{k}!}\right) \\ $$

Question Number 105630 Answers: 0 Comments: 2

Question Number 105625 Answers: 1 Comments: 0

prove that ((m),(m) ) ((( n)),((n−k)) )+ ((( m)),((m−1)) ) ((( n)),((n−k+1)) ) + ((( m)),((m−2)) ) ((( n)),((n−k+2)) )+......+ ((( m)),((m−k)) ) ((n),(n) ) = (((m+n)),(( k)) )

$${prove}\:{that} \\ $$$$\begin{pmatrix}{{m}}\\{{m}}\end{pmatrix}\begin{pmatrix}{\:\:\:{n}}\\{{n}−{k}}\end{pmatrix}+\begin{pmatrix}{\:\:\:\:{m}}\\{{m}−\mathrm{1}}\end{pmatrix}\begin{pmatrix}{\:\:\:\:\:\:\:{n}}\\{{n}−{k}+\mathrm{1}}\end{pmatrix} \\ $$$$+\begin{pmatrix}{\:\:\:{m}}\\{{m}−\mathrm{2}}\end{pmatrix}\begin{pmatrix}{\:\:\:\:\:\:\:\:{n}}\\{{n}−{k}+\mathrm{2}}\end{pmatrix}+......+\begin{pmatrix}{\:\:\:\:{m}}\\{{m}−{k}}\end{pmatrix}\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix} \\ $$$$=\begin{pmatrix}{{m}+{n}}\\{\:\:\:\:\:{k}}\end{pmatrix} \\ $$

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