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Question Number 54578 Answers: 1 Comments: 1

A particle of mass 1.5kg rests on a rough plane inclined at 45° to the horizontal. It is maintained in equilibrium by a horizontal force of p newtons. Given that the coefficient of friction between the particle and the plane is (1/4), calculate the value of p when the particle is on the point of moving i. down the plane ii. up the plane [take g=10ms^(−2) ].

Question Number 54573 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((cos(e^(−x^2 ) ))/(1+x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({e}^{−{x}^{\mathrm{2}} } \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\: \\ $$

Question Number 54566 Answers: 0 Comments: 3

lim_(n→∞) (((1+c)/(1+μ^(1/n) )))^n =? with 0≤c≤1, μ>0

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}+{c}}{\mathrm{1}+\mu^{\frac{\mathrm{1}}{{n}}} }\right)^{{n}} =? \\ $$$${with}\:\mathrm{0}\leqslant{c}\leqslant\mathrm{1},\:\mu>\mathrm{0} \\ $$

Question Number 54563 Answers: 1 Comments: 1

If ((sin^3 α)/(sin β)) + ((cos^3 α)/(cos β)) = 1 show that sin 2α+2sin (α+β)=0

$$\mathrm{If}\:\frac{\mathrm{sin}\:^{\mathrm{3}} \alpha}{\mathrm{sin}\:\beta}\:+\:\frac{\mathrm{cos}\:^{\mathrm{3}} \alpha}{\mathrm{cos}\:\beta}\:=\:\mathrm{1}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{sin}\:\mathrm{2}\alpha+\mathrm{2sin}\:\left(\alpha+\beta\right)=\mathrm{0} \\ $$

Question Number 54562 Answers: 1 Comments: 0

Question Number 54556 Answers: 0 Comments: 4

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

$$\int_{−\mathrm{2}\pi^{\mathrm{2}} } ^{\mathrm{2}\pi^{\mathrm{2}} } \frac{\mathrm{sin}\:\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 54543 Answers: 1 Comments: 1

Prove that: ((z^2 − 1)/(z^2 + 1)) = i tan(θ) where z = cos(θ) + i sin(θ)

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\frac{\mathrm{z}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{1}}\:\:=\:\:\mathrm{i}\:\mathrm{tan}\left(\theta\right) \\ $$$$\mathrm{where}\:\:\:\:\:\mathrm{z}\:\:=\:\:\mathrm{cos}\left(\theta\right)\:+\:\mathrm{i}\:\mathrm{sin}\left(\theta\right) \\ $$

Question Number 54541 Answers: 1 Comments: 0

The value of x between 0 and 2π which satisfy the equation sin x (√(8 cos^2 x)) = 1 are in AP Find the common difference.

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{between}\:\:\:\mathrm{0}\:\:\mathrm{and}\:\:\:\mathrm{2}\pi\: \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{sin}\:{x}\:\sqrt{\mathrm{8}\:\mathrm{cos}\:^{\mathrm{2}} {x}}\:=\:\mathrm{1}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}. \\ $$

Question Number 54537 Answers: 1 Comments: 2

tan^2 20+tan^2 40+tan^2 80=33 (please solve this and i want to know that which standard that question belongs?) help needed

$${tan}^{\mathrm{2}} \mathrm{20}+{tan}^{\mathrm{2}} \mathrm{40}+{tan}^{\mathrm{2}} \mathrm{80}=\mathrm{33}\:\:\: \\ $$$$\left({please}\:{solve}\:{this}\:{and}\:{i}\:{want}\:{to}\:{know}\:\right. \\ $$$$\left.{that}\:{which}\:{standard}\:{that}\:{question}\:{belongs}?\right) \\ $$$${help}\:{needed} \\ $$

Question Number 54536 Answers: 1 Comments: 0

If A,B,C are angles of a triangle show that tan^(−1) (cot Acot B)+tan^(−1) (cot Bcot C)+tan^(−1) (cot Ccot A) = tan^(−1) {1+((8cos Acos Bcos C)/(sin^2 2A+sin^2 2B+sin^2 2C))}

$$\mathrm{If}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{are}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{cot}\:\mathrm{Acot}\:\mathrm{B}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{cot}\:\mathrm{Bcot}\:\mathrm{C}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{cot}\:\mathrm{Ccot}\:\mathrm{A}\right) \\ $$$$=\:\mathrm{tan}^{−\mathrm{1}} \left\{\mathrm{1}+\frac{\mathrm{8cos}\:\mathrm{Acos}\:\mathrm{Bcos}\:\mathrm{C}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2A}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{2B}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{2C}}\right\} \\ $$

Question Number 54526 Answers: 1 Comments: 1

Question Number 54517 Answers: 2 Comments: 0

Prove that (((√(h+1))−1)/h) = (1/((√(h+1))+1)) please...

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$ \\ $$$$\frac{\sqrt{{h}+\mathrm{1}}−\mathrm{1}}{{h}}\:=\:\frac{\mathrm{1}}{\sqrt{{h}+\mathrm{1}}+\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{please}... \\ $$

Question Number 54529 Answers: 1 Comments: 2

∫5cos x−4sin x/2cos x+sin x dx

$$\int\mathrm{5cos}\:{x}−\mathrm{4sin}\:{x}/\mathrm{2cos}\:{x}+\mathrm{sin}\:{x}\:{dx} \\ $$

Question Number 54513 Answers: 1 Comments: 0

Calculate the interquartile range: 20,26,27,30,34,41,41,64,65,65,72,85

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{interquartile}\:\mathrm{range}: \\ $$$$\mathrm{20},\mathrm{26},\mathrm{27},\mathrm{30},\mathrm{34},\mathrm{41},\mathrm{41},\mathrm{64},\mathrm{65},\mathrm{65},\mathrm{72},\mathrm{85} \\ $$

Question Number 54506 Answers: 3 Comments: 0

L′Hopital rule lim_(x→α) ((f(x))/(g(x)))=lim_(x→α) ((f ′(x))/(g′(x)))= ((f ′(α))/(g′(α))) f ′(x)=(d/dx)f(x) , g′(x)=(d/dx)g(x) differential What is it? Proof of the rule.. plz :)

$${L}'{Hopital}\:{rule} \\ $$$$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}=\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\:\frac{{f}\:'\left({x}\right)}{{g}'\left({x}\right)}=\:\frac{{f}\:'\left(\alpha\right)}{{g}'\left(\alpha\right)} \\ $$$${f}\:'\left({x}\right)=\frac{{d}}{{dx}}{f}\left({x}\right)\:,\:{g}'\left({x}\right)=\frac{{d}}{{dx}}{g}\left({x}\right)\:{differential} \\ $$$$\left.{What}\:{is}\:{it}?\:{Proof}\:{of}\:{the}\:{rule}..\:\mathrm{plz}\::\right) \\ $$

Question Number 54504 Answers: 1 Comments: 0

please,Sir. Would u explain to me how ? if f((x/(x − 1))) + 2f(((x − 1)/x)) = (x/(x − 1)) , then f(x) is ....

$$\boldsymbol{\mathrm{please}},\boldsymbol{\mathrm{Sir}}.\:\:\:\boldsymbol{\mathrm{Would}}\:\boldsymbol{\mathrm{u}}\:\boldsymbol{\mathrm{explain}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{how}}\:? \\ $$$$\boldsymbol{\mathrm{if}}\:\:\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}\:−\:\mathrm{1}}\right)\:\:+\:\:\mathrm{2}\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}\:−\:\mathrm{1}}{\boldsymbol{{x}}}\right)\:\:=\:\:\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}\:−\:\mathrm{1}}\:\:\:, \\ $$$$\boldsymbol{\mathrm{then}}\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:\:\boldsymbol{\mathrm{is}}\:.... \\ $$

Question Number 54502 Answers: 0 Comments: 5

In △ABC cos A+cos B+cos C=(3/2) prove that trianle is equilateral

$${In}\:\bigtriangleup{ABC}\:\mathrm{cos}\:{A}+\mathrm{cos}\:{B}+\mathrm{cos}\:{C}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${prove}\:{that}\:{trianle}\:{is}\:{equilateral} \\ $$

Question Number 54480 Answers: 2 Comments: 0

show that tan α +tan (α+((2Λ^− )/5)) +tan (α+((4Λ^− )/5)) +tan (α+((6Λ^− )/5)) + tan (α+((8Λ^− )/5)) = 5tan 5α

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}\:\alpha\:+\mathrm{tan}\:\left(\alpha+\frac{\mathrm{2}\overset{−} {\Lambda}}{\mathrm{5}}\right)\:+\mathrm{tan}\:\left(\alpha+\frac{\mathrm{4}\overset{−} {\Lambda}}{\mathrm{5}}\right)\:+\mathrm{tan}\:\left(\alpha+\frac{\mathrm{6}\overset{−} {\Lambda}}{\mathrm{5}}\right)\:+\:\mathrm{tan}\:\left(\alpha+\frac{\mathrm{8}\overset{−} {\Lambda}}{\mathrm{5}}\right)\:=\:\mathrm{5tan}\:\mathrm{5}\alpha \\ $$

Question Number 54481 Answers: 1 Comments: 1