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AllQuestion and Answers: Page 1048

Question Number 105769 Answers: 2 Comments: 1

Question Number 105766 Answers: 1 Comments: 0

If p = sin ((π/(18)))sin (((5π)/(18)))sin (((7π)/(18))) find the value of p.

$${If}\:{p}\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{18}}\right)\mathrm{sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{18}}\right)\mathrm{sin}\:\left(\frac{\mathrm{7}\pi}{\mathrm{18}}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{p}. \\ $$

Question Number 105764 Answers: 4 Comments: 1

(1)If cos (α+β) = (4/5) and sin (α−β) = (5/(13)) where 0 < α< (π/4). Find tan 2α . (2) cos^4 ((π/8))+cos^4 (((3π)/8))+cos^4 (((5π)/8))+cos^4 (((7π)/8))?

$$\left(\mathrm{1}\right){If}\:\mathrm{cos}\:\left(\alpha+\beta\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{and}\:\mathrm{sin}\:\left(\alpha−\beta\right)\:=\:\frac{\mathrm{5}}{\mathrm{13}} \\ $$$${where}\:\mathrm{0}\:<\:\alpha<\:\frac{\pi}{\mathrm{4}}.\:{Find}\:\mathrm{tan}\:\mathrm{2}\alpha\:. \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right)? \\ $$

Question Number 105759 Answers: 2 Comments: 1

If α and β are the solution of equation a tan θ + b sec θ = c . find the value of tan (α+β).

$${If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{solution}\:{of} \\ $$$${equation}\:{a}\:\mathrm{tan}\:\theta\:+\:{b}\:\mathrm{sec}\:\theta\:=\:{c}\:.\: \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{tan}\:\left(\alpha+\beta\right). \\ $$

Question Number 105755 Answers: 2 Comments: 0

∫ (dx/(√(x(√x) −x^2 ))) ?

$$\int\:\frac{{dx}}{\sqrt{{x}\sqrt{{x}}\:−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 105753 Answers: 1 Comments: 1

∫ ((x^2 +sin^2 x)/(x^2 +cos^2 x)) dx

$$\int\:\frac{{x}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} +\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 105748 Answers: 2 Comments: 0

lim_(x→∞) (((x−1)^(100) (6x+1)^(100) )/((3x+5)^(200) ))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{100}} \left(\mathrm{6x}+\mathrm{1}\right)^{\mathrm{100}} }{\left(\mathrm{3x}+\mathrm{5}\right)^{\mathrm{200}} }=? \\ $$

Question Number 105743 Answers: 1 Comments: 1

Question Number 105742 Answers: 0 Comments: 0

Let a differentiable function f:R→R satisfies ∣f′(x)∣≤1 for all x∈[0,2] and f(0)=f(2)=1 Prove that 1≤∫_0 ^2 f(x)dx≤3

$$\mathrm{Let}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function}\:\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\mathrm{satisfies}\:\mid\mathrm{f}'\left(\mathrm{x}\right)\mid\leqslant\mathrm{1}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{2}\right]\:\mathrm{and} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{f}\left(\mathrm{2}\right)=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{1}\leqslant\int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{3}\: \\ $$

Question Number 105738 Answers: 1 Comments: 0

(x tan ((y/x))−y sec^2 ((y/x))) dx−x sec^2 ((y/x))dy=0

$$\left({x}\:\mathrm{tan}\:\left(\frac{{y}}{{x}}\right)−{y}\:\mathrm{sec}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right)\right)\:{dx}−{x}\:\mathrm{sec}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right){dy}=\mathrm{0} \\ $$

Question Number 105734 Answers: 0 Comments: 0

(2x+(x^2 +y^2 )cot x) dx +2y dy = 0

$$\left(\mathrm{2}{x}+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\mathrm{cot}\:{x}\right)\:{dx}\:+\mathrm{2}{y}\:{dy}\:=\:\mathrm{0} \\ $$

Question Number 105722 Answers: 4 Comments: 1

∫ (√(x−(√x))) dx

$$\int\:\sqrt{{x}−\sqrt{{x}}}\:{dx}\: \\ $$

Question Number 105725 Answers: 0 Comments: 5

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

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

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