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Question Number 76579 Answers: 1 Comments: 0

A uniform ladder of weight W and length 2a rest in limiting equilibrium with one end on a rough horizontal ground and the other end on a rough vertical wall. The coefficient of friction between the ladder and the ground and between the ladder and the wall are respectively μ and λ . If the ladder makes an angle θ with the ground where tan θ = (5/(12)), a) show that 5μ + 6λμ − 6 = 0. b) find the value of λ and μ given that λμ =(1/2).

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{ladder}\:\mathrm{of}\:\mathrm{weight}\:{W}\:\mathrm{and}\:\mathrm{length} \\ $$$$\mathrm{2}{a}\:\mathrm{rest}\:\mathrm{in}\:\mathrm{limiting}\:\mathrm{equilibrium}\:\mathrm{with}\:\mathrm{one}\: \\ $$$$\mathrm{end}\:\mathrm{on}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{horizontal}\:\mathrm{ground}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{other}\:\mathrm{end}\:\mathrm{on}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{vertical}\:\mathrm{wall}. \\ $$$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ladder} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{and}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{wall}\:\mathrm{are}\:\mathrm{respectively}\:\mu\:\mathrm{and}\:\lambda\:.\:\mathrm{If}\:\mathrm{the}\:\mathrm{ladder} \\ $$$$\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{where}\:\mathrm{tan}\:\theta\:=\:\frac{\mathrm{5}}{\mathrm{12}}, \\ $$$$\left.\mathrm{a}\right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{5}\mu\:+\:\mathrm{6}\lambda\mu\:−\:\mathrm{6}\:=\:\mathrm{0}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\lambda\:\mathrm{and}\:\mu\:\mathrm{given}\:\mathrm{that}\:\lambda\mu\:=\frac{\mathrm{1}}{\mathrm{2}}.\: \\ $$

Question Number 76577 Answers: 1 Comments: 0

given a sequence defined by {((3n)/(2n+ 5))}_(n=1) ^∞ , does this sequence converge or diverge, explain

$$\:{given}\:{a}\:{sequence}\:{defined}\:{by}\:\:\left\{\frac{\mathrm{3}{n}}{\mathrm{2}{n}+\:\mathrm{5}}\right\}_{{n}=\mathrm{1}} ^{\infty} ,\:{does}\:{this}\: \\ $$$${sequence}\:{converge}\:{or}\:{diverge},\:{explain} \\ $$

Question Number 76576 Answers: 1 Comments: 0

Compute the Gcd (greatest common divisor) of 45 and 1287

$${Compute}\:{the}\:{Gcd}\:\left({greatest}\:{common}\:{divisor}\right) \\ $$$${of}\:\:\mathrm{45}\:{and}\:\mathrm{1287}\: \\ $$

Question Number 76575 Answers: 1 Comments: 0

define the concept of a contingency Which of the following is a contingency and which is a tautology 1) (P ⇒∼P) ∨ Q 2) (P ⇒ ∼P) ⇒ Q

$${define}\:{the}\:{concept}\:{of}\:{a}\:\boldsymbol{{contingency}} \\ $$$${Which}\:{of}\:{the}\:{following}\:{is}\:{a}\:{contingency}\: \\ $$$${and}\:{which}\:{is}\:{a}\:{tautology} \\ $$$$\left.\mathrm{1}\right)\:\left({P}\:\Rightarrow\sim{P}\right)\:\vee\:{Q}\:\: \\ $$$$\left.\mathrm{2}\right)\:\left({P}\:\Rightarrow\:\sim{P}\right)\:\Rightarrow\:{Q} \\ $$

Question Number 76574 Answers: 0 Comments: 0

Question Number 76572 Answers: 1 Comments: 0

how do you find the least value of x^2 +2xy+3y^2 −6x−2y using the concepts of algebra or calculus?

$${how}\:{do}\:{you}\:{find}\:{the}\:{least}\:{value}\:{of}\:{x}^{\mathrm{2}} \\ $$$$+\mathrm{2}{xy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}{y}\:{using}\:{the}\: \\ $$$${concepts}\:{of}\:{algebra}\:{or}\:{calculus}?\: \\ $$

Question Number 76627 Answers: 1 Comments: 2

Question Number 76556 Answers: 1 Comments: 0

Question Number 76555 Answers: 1 Comments: 0

Question Number 76554 Answers: 1 Comments: 0

Question Number 76536 Answers: 1 Comments: 1

Question Number 76531 Answers: 1 Comments: 4

what is a and b such that a+b = a×b and a+b =a/b ?

$${what}\:{is}\:{a}\:{and}\:{b}\:{such}\:{that}\:{a}+{b}\:=\:{a}×{b}\: \\ $$$${and}\:{a}+{b}\:={a}/{b}\:? \\ $$

Question Number 76524 Answers: 3 Comments: 0

find vector unit perpendicular to vector a^− =(1,2,3) and b^− =(−1,0,2)

$${find}\:{vector}\:{unit}\:{perpendicular}\: \\ $$$${to}\:{vector}\:\overset{−} {{a}}=\left(\mathrm{1},\mathrm{2},\mathrm{3}\right)\:{and}\:\overset{−} {{b}}=\left(−\mathrm{1},\mathrm{0},\mathrm{2}\right) \\ $$

Question Number 76522 Answers: 0 Comments: 1

sir what′s difference (d/da) with (∂/∂a) ?

$${sir}\:{what}'{s}\:{difference}\:\frac{{d}}{{da}}\:{with}\:\frac{\partial}{\partial{a}}\:?\: \\ $$

Question Number 76514 Answers: 1 Comments: 1

calculate Π_(k=0) ^(n−1) (α^(k ) +α^−^k ) with α root of x^2 +2x+5 =0

$${calculate}\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(\alpha^{{k}\:} \:+\overset{−^{{k}} } {\alpha}\right)\:{with}\:\alpha\:{root}\:{of}\:{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\:=\mathrm{0} \\ $$

Question Number 76495 Answers: 1 Comments: 5

how that tan2x=((2tanx)/(1−tan^2 x))

$$\mathrm{how}\:\mathrm{that} \\ $$$$\mathrm{tan2}{x}=\frac{\mathrm{2}{tanx}}{\mathrm{1}−{tan}^{\mathrm{2}} {x}} \\ $$

Question Number 76497 Answers: 2 Comments: 0

calculate tan(3x) interms of tanx

$${calculate}\:{tan}\left(\mathrm{3}{x}\right)\:{interms}\:{of}\:{tanx} \\ $$

Question Number 76477 Answers: 2 Comments: 0

Hello Solve in ]−π;π[ ((2sinx)/(cosx−sinx))≥0 result should be in radian please help me ...

$$\mathrm{Hello}\:\mathrm{Solve}\:\mathrm{in}\: \\ $$$$\left.\right]−\pi;\pi\left[\right. \\ $$$$\frac{\mathrm{2sin}{x}}{{cosx}−{sinx}}\geqslant\mathrm{0} \\ $$$$\mathrm{result}\:\mathrm{should}\:\mathrm{be}\:\mathrm{in}\:\mathrm{radian} \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:... \\ $$

Question Number 76475 Answers: 1 Comments: 0

Question Number 76469 Answers: 2 Comments: 3

∫cothx dx

$$\int{cothx}\:{dx} \\ $$

Question Number 76468 Answers: 1 Comments: 2

∫((1−x^2 −8x+1)/(x^4 −x^3 −x+1))dx

$$\int\frac{\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$

Question Number 76467 Answers: 1 Comments: 0

∫(dx/((√(e^(2x) −4))(sec^(−1) ((e^x /4)))))

$$\int\frac{{dx}}{\sqrt{{e}^{\mathrm{2}{x}} −\mathrm{4}}\left({sec}^{−\mathrm{1}} \left(\frac{{e}^{{x}} }{\mathrm{4}}\right)\right)} \\ $$

Question Number 76465 Answers: 1 Comments: 0

∫e^(−x) (−e^(−3x) +5e^(−2x) −6)sin(2e^(−x) )dx

$$\int{e}^{−{x}} \left(−{e}^{−\mathrm{3}{x}} +\mathrm{5}{e}^{−\mathrm{2}{x}} −\mathrm{6}\right){sin}\left(\mathrm{2}{e}^{−{x}} \right){dx} \\ $$

Question Number 76462 Answers: 1 Comments: 4

∫cos3x e^(−2x) dx

$$\int{cos}\mathrm{3}{x}\:{e}^{−\mathrm{2}{x}} {dx} \\ $$

Question Number 76455 Answers: 1 Comments: 2

In a triangle whose sides measure 5 cm, 6 cm, and 7 cm a point P, inside the triangle is 2 cm from de long side 5 cm and 3 cm from the long side 6 cm. What is the distance from P beside 7 cm side?

$${In}\:{a}\:{triangle}\:{whose}\:{sides}\:{measure} \\ $$$$\mathrm{5}\:{cm},\:\mathrm{6}\:{cm},\:{and}\:\:\mathrm{7}\:{cm}\:{a}\:{point}\:{P},\:{inside} \\ $$$${the}\:{triangle}\:{is}\:\mathrm{2}\:{cm}\:{from}\:{de}\:{long}\:{side} \\ $$$$\mathrm{5}\:{cm}\:{and}\:\mathrm{3}\:{cm}\:{from}\:{the}\:{long}\:{side} \\ $$$$\mathrm{6}\:{cm}.\:{What}\:{is}\:{the}\:{distance}\:{from}\:{P} \\ $$$${beside}\:\mathrm{7}\:{cm}\:{side}? \\ $$

Question Number 76445 Answers: 0 Comments: 6

how evaluate lim_(x→0) (((1−(√(1+x^2 ))×cos x)/x^4 )).

$${how}\:{evaluate}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }×\mathrm{cos}\:{x}}{{x}^{\mathrm{4}} }\right). \\ $$

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