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Question Number 113375 Answers: 0 Comments: 1

(i) How does one find the equation of the perpendicular to a line? (ii) How does one calculate standard deviation. Explain in details.

$$\left(\mathrm{i}\right)\:\mathrm{How}\:\mathrm{does}\:\mathrm{one}\:\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{a}\:\mathrm{line}? \\ $$$$ \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{How}\:\mathrm{does}\:\mathrm{one}\:\mathrm{calculate}\:\mathrm{standard} \\ $$$$\mathrm{deviation}.\:\mathrm{Explain}\:\mathrm{in}\:\mathrm{details}. \\ $$

Question Number 113374 Answers: 1 Comments: 5

Find the next term in this sequence: 26,63,124, __

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{next}\:\mathrm{term}\:\mathrm{in}\:\mathrm{this} \\ $$$$\mathrm{sequence}:\:\mathrm{26},\mathrm{63},\mathrm{124},\:\_\_ \\ $$

Question Number 113372 Answers: 1 Comments: 2

2^a +2^b +2^c +2^d =57, find a+b+c+d. a≠b≠c≠d and a,b,c,d are positive integers.

$$\mathrm{2}^{\mathrm{a}} +\mathrm{2}^{\mathrm{b}} +\mathrm{2}^{\mathrm{c}} +\mathrm{2}^{\mathrm{d}} =\mathrm{57},\:\mathrm{find}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}. \\ $$$$\mathrm{a}\neq\mathrm{b}\neq\mathrm{c}\neq\mathrm{d}\:\mathrm{and}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{integers}. \\ $$

Question Number 113278 Answers: 2 Comments: 0

solve ∫((√(x^2 +x+2−(√(4x^2 +4x+4))))/(x(√(x^4 +x^3 +x^2 ))))dx

$${solve} \\ $$$$\int\frac{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{2}−\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{4}}}}{{x}\sqrt{{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 113275 Answers: 2 Comments: 0

∫ (dx/(3sin x+sin^3 x)) ?

$$\:\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}\:? \\ $$

Question Number 113274 Answers: 4 Comments: 2

(1) lim_(x→0) ((tan x+4tan 2x−3tan 3x)/(x^2 tan x)) (2) lim_(x→0) (((√x)−(√(sin x)))/x^(3/2) ) (3) lim_(x→0) (((√x)+(√(sin x)))/x^(5/2) )

$$\:\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{x}+\mathrm{4tan}\:\mathrm{2x}−\mathrm{3tan}\:\mathrm{3x}}{\mathrm{x}^{\mathrm{2}} \:\mathrm{tan}\:\mathrm{x}} \\ $$$$\:\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\frac{\mathrm{3}}{\mathrm{2}}} }\: \\ $$$$\:\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}}+\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\frac{\mathrm{5}}{\mathrm{2}}} } \\ $$

Question Number 113272 Answers: 2 Comments: 0

Solve the following equations: a)(x^2 −a)^2 −6x^2 +4x+2a=0 b)x^4 −4x^3 −10x^3 +37x−14=0,if it known that the left−hand side of the equation can be decomposed into factors with integral coefficients.

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equations}: \\ $$$$\left.\mathrm{a}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{a}\right)^{\mathrm{2}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{2a}=\mathrm{0} \\ $$$$\left.\mathrm{b}\right)\mathrm{x}^{\mathrm{4}} −\mathrm{4x}^{\mathrm{3}} −\mathrm{10x}^{\mathrm{3}} +\mathrm{37x}−\mathrm{14}=\mathrm{0},\mathrm{if}\:\mathrm{it} \\ $$$$\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{left}−\mathrm{hand}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{can}\:\mathrm{be}\:\mathrm{decomposed}\:\mathrm{into} \\ $$$$\mathrm{factors}\:\mathrm{with}\:\mathrm{integral}\:\mathrm{coefficients}. \\ $$

Question Number 113271 Answers: 0 Comments: 0

solve the initial boundary value problem of wave equation ((∂^2 u(x,t))/∂t^2 )=9((∂^2 u(x,t))/∂x^2 ),0<x<2,t>0 u(0,t)=1,u(2,t)=3,t>0 u(x,0)=2,0<x<2 (∂u/∂t)(x,0)=sin2x,0<x<2

$${solve}\:{the}\:{initial}\:{boundary}\:{value} \\ $$$${problem}\:{of}\:{wave}\:{equation} \\ $$$$\frac{\partial^{\mathrm{2}} {u}\left({x},{t}\right)}{\partial{t}^{\mathrm{2}} }=\mathrm{9}\frac{\partial^{\mathrm{2}} {u}\left({x},{t}\right)}{\partial{x}^{\mathrm{2}} },\mathrm{0}<{x}<\mathrm{2},{t}>\mathrm{0} \\ $$$${u}\left(\mathrm{0},{t}\right)=\mathrm{1},{u}\left(\mathrm{2},{t}\right)=\mathrm{3},{t}>\mathrm{0} \\ $$$${u}\left({x},\mathrm{0}\right)=\mathrm{2},\mathrm{0}<{x}<\mathrm{2} \\ $$$$\frac{\partial{u}}{\partial{t}}\left({x},\mathrm{0}\right)=\mathrm{sin2}{x},\mathrm{0}<{x}<\mathrm{2} \\ $$

Question Number 113262 Answers: 2 Comments: 0

find the complex form of equation 4x^2 −2y^2 =5

$$\mathrm{find}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{form}\:\mathrm{of}\: \\ $$$$\mathrm{equation}\:\mathrm{4x}^{\mathrm{2}} −\mathrm{2y}^{\mathrm{2}} =\mathrm{5} \\ $$

Question Number 113261 Answers: 1 Comments: 0

(((√((√5)+2))+(√((√5)−2)))/( (√((√5)+1))))−(√(3−2(√2)))

$$\frac{\sqrt{\sqrt{\mathrm{5}}+\mathrm{2}}+\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}}{\:\sqrt{\sqrt{\mathrm{5}}+\mathrm{1}}}−\sqrt{\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}} \\ $$

Question Number 113246 Answers: 1 Comments: 1

Question Number 113243 Answers: 1 Comments: 3

Question Number 113241 Answers: 1 Comments: 0

Question Number 113237 Answers: 1 Comments: 0

Question Number 121155 Answers: 0 Comments: 0

Question Number 113221 Answers: 0 Comments: 3

Does anyone know a good website for nested radicals? ((7((20))^(1/3) −19))^(1/6) =((5/3))^(1/3) −((2/3))^(1/3)

$${Does}\:{anyone}\:{know}\:{a}\:{good} \\ $$$${website}\:{for}\:{nested}\:{radicals}? \\ $$$$\sqrt[{\mathrm{6}}]{\mathrm{7}\sqrt[{\mathrm{3}}]{\mathrm{20}}−\mathrm{19}}=\sqrt[{\mathrm{3}}]{\mathrm{5}/\mathrm{3}}−\sqrt[{\mathrm{3}}]{\mathrm{2}/\mathrm{3}} \\ $$

Question Number 113219 Answers: 1 Comments: 0

Question Number 113218 Answers: 1 Comments: 0

Question Number 113211 Answers: 3 Comments: 0

If α is a root of the equation 4x^2 +2x−1=0 . How do you prove the other root is 4α^3 −3α ?

$$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{4x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{1}=\mathrm{0}\:.\:\mathrm{How}\:\mathrm{do}\:\mathrm{you} \\ $$$$\mathrm{prove}\:\mathrm{the}\:\mathrm{other}\:\mathrm{root}\:\mathrm{is} \\ $$$$\mathrm{4}\alpha^{\mathrm{3}} −\mathrm{3}\alpha\:?\: \\ $$

Question Number 113203 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^4 +2x^2 +3))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}} \\ $$

Question Number 113200 Answers: 2 Comments: 0

prove that 2tan^(−1) ((1/3))+tan^(−1) ((1/7))=(π/4)

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{2tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{7}}\right)=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 113199 Answers: 1 Comments: 8

Change the following decimal number into binary number: 73.108

$${Change}\:{the}\:{following}\:{decimal} \\ $$$${number}\:{into}\:{binary}\:{number}: \\ $$$$\mathrm{73}.\mathrm{108} \\ $$

Question Number 113198 Answers: 1 Comments: 0

.... calculus.... Evaluate ::: I :=∫_0 ^( 1) (1/( (√(x(x+1)(x+2)(x+3)+1))−3x))dx=??? M.N.july 1970#

$$\:\:\:\:\:\:\:\:\:....\:{calculus}.... \\ $$$$\:\:\:\:\:\:\mathscr{E}{valuate}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{I}\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)+\mathrm{1}}−\mathrm{3}{x}}{dx}=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.{july}\:\mathrm{1970}# \\ $$$$\:\: \\ $$

Question Number 113196 Answers: 1 Comments: 0

y = sinh^(−1) (sin x) , (dy/dx) =?

$$\:\mathrm{y}\:=\:\mathrm{sinh}\:^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\:,\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=? \\ $$

Question Number 113191 Answers: 1 Comments: 0

Solve 2cos^2 (x/2)+3cos(x/2)+1=0

$$\mathrm{Solve}\:\mathrm{2cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+\mathrm{3cos}\frac{{x}}{\mathrm{2}}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 113190 Answers: 1 Comments: 3

∫_0 ^1 ((logx)/(x−1))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{logx}}{{x}−\mathrm{1}}{dx} \\ $$

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