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Question Number 18092    Answers: 1   Comments: 0

A value of θ satisfying 4cos^2 θsinθ − 2sin^2 θ = 3sinθ is (1) ((9π)/(10)) (2) (π/(10)) (3) −((13π)/(10)) (4) −((17π)/(10))

$$\mathrm{A}\:\mathrm{value}\:\mathrm{of}\:\theta\:\mathrm{satisfying} \\ $$$$\mathrm{4cos}^{\mathrm{2}} \theta\mathrm{sin}\theta\:−\:\mathrm{2sin}^{\mathrm{2}} \theta\:=\:\mathrm{3sin}\theta\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{9}\pi}{\mathrm{10}} \\ $$$$\left(\mathrm{2}\right)\:\frac{\pi}{\mathrm{10}} \\ $$$$\left(\mathrm{3}\right)\:−\frac{\mathrm{13}\pi}{\mathrm{10}} \\ $$$$\left(\mathrm{4}\right)\:−\frac{\mathrm{17}\pi}{\mathrm{10}} \\ $$

Question Number 18091    Answers: 1   Comments: 0

Which of the following statement(s) is/are correct? (1) cos(sin1) > sin(cos1) (2) cos(sin1.5) > sin(cos1.5) (3) cos(sin((7π)/(18))) > sin(cos((7π)/(18))) (4) cos(sin((5π)/(18))) > sin(cos((5π)/(18)))

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statement}\left(\mathrm{s}\right) \\ $$$$\mathrm{is}/\mathrm{are}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{cos}\left(\mathrm{sin1}\right)\:>\:\mathrm{sin}\left(\mathrm{cos1}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{cos}\left(\mathrm{sin1}.\mathrm{5}\right)\:>\:\mathrm{sin}\left(\mathrm{cos1}.\mathrm{5}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{cos}\left(\mathrm{sin}\frac{\mathrm{7}\pi}{\mathrm{18}}\right)\:>\:\mathrm{sin}\left(\mathrm{cos}\frac{\mathrm{7}\pi}{\mathrm{18}}\right) \\ $$$$\left(\mathrm{4}\right)\:\mathrm{cos}\left(\mathrm{sin}\frac{\mathrm{5}\pi}{\mathrm{18}}\right)\:>\:\mathrm{sin}\left(\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{18}}\right) \\ $$

Question Number 18077    Answers: 1   Comments: 0

A mango in a tree is located (30,40) from the point of projection of stone.Find the minimum speed and the angle of projevtion of the stone so as to hit the mango

$${A}\:{mango}\:{in}\:{a}\:{tree}\:{is}\:{located}\:\left(\mathrm{30},\mathrm{40}\right)\:{from}\:{the} \\ $$$${point}\:{of}\:{projection}\:{of}\:{stone}.{Find}\:{the}\: \\ $$$${minimum}\:{speed}\:{and}\:{the}\:{angle}\:{of}\:{projevtion} \\ $$$${of}\:{the}\:{stone}\:{so}\:{as}\:{to}\:{hit}\:{the}\:{mango} \\ $$

Question Number 18069    Answers: 0   Comments: 1

ai) If θ is the angle in the fourth quadrant satisfying the equation : cot^2 θ = 4 find the value of the function: f(θ) = (1/(√5)) (secθ − cosecθ) aii) Prove that: (√((1 + cosθ)/(1 − cosθ))) = cosecθ + cotθ, if cosθ ≠ 1 (b) Let R be a positive real number and let α satisfy the inequality 0 < α < 360. express the function 2sinθ + cosθ in the form Rsin(θ + α). Hence, find the value of θ between 0 and 360 which satisfy the equation. 3cosθ + 6sinθ = 1

$$\left.\mathrm{ai}\right)\:\:\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{in}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{quadrant}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation}\::\:\mathrm{cot}^{\mathrm{2}} \theta\:=\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}:\:\:\mathrm{f}\left(\theta\right)\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}\:\left(\mathrm{sec}\theta\:−\:\mathrm{cosec}\theta\right) \\ $$$$\left.\mathrm{aii}\right)\:\:\mathrm{Prove}\:\mathrm{that}:\:\:\:\sqrt{\frac{\mathrm{1}\:+\:\mathrm{cos}\theta}{\mathrm{1}\:−\:\mathrm{cos}\theta}}\:\:=\:\:\mathrm{cosec}\theta\:+\:\mathrm{cot}\theta,\:\:\:\:\:\:\:\:\mathrm{if}\:\:\mathrm{cos}\theta\:\neq\:\mathrm{1} \\ $$$$\left(\mathrm{b}\right)\:\:\:\mathrm{Let}\:\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number}\:\mathrm{and}\:\mathrm{let}\:\alpha\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{inequality}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:<\:\alpha\:<\:\mathrm{360}.\:\mathrm{express}\:\mathrm{the}\:\mathrm{function}\:\:\mathrm{2sin}\theta\:+\:\mathrm{cos}\theta\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\:\mathrm{Rsin}\left(\theta\:+\:\alpha\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Hence},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\theta\:\mathrm{between}\:\mathrm{0}\:\mathrm{and}\:\mathrm{360}\:\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3cos}\theta\:+\:\mathrm{6sin}\theta\:=\:\mathrm{1} \\ $$

Question Number 18066    Answers: 0   Comments: 1

(a) Evaluate the integral of the function: y(x) = ((3x + 1)/(2x^2 − 2x + 3)) (b) Find the constant A, B, C in the identity: ((3x^2 − ax)/((x − 2a)(x^2 + a^2 ))) ≡ (A/((x − 2a))) + ((Bx + Ca)/((x^2 + a^2 ))) where a is a constant, hence prove that. ∫_0 ^( 2) ((3x^2 − ax)/((x − 2a)(x^2 + a^2 ))) dx = (π/4) − (3/2) ln(2)

$$\left(\mathrm{a}\right)\:\:\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}:\:\:\mathrm{y}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\mathrm{1}}{\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{3}} \\ $$$$\left(\mathrm{b}\right)\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\mathrm{in}\:\mathrm{the}\:\mathrm{identity}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} \:−\:\mathrm{ax}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)}\:\equiv\:\frac{\mathrm{A}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)}\:+\:\frac{\mathrm{Bx}\:+\:\mathrm{Ca}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)} \\ $$$$\mathrm{where}\:\:\mathrm{a}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant},\:\:\mathrm{hence}\:\mathrm{prove}\:\mathrm{that}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\:\frac{\mathrm{3x}^{\mathrm{2}} \:−\:\mathrm{ax}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)}\:\mathrm{dx}\:=\:\frac{\pi}{\mathrm{4}}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{ln}\left(\mathrm{2}\right) \\ $$

Question Number 18063    Answers: 1   Comments: 3

The angles A, B, C of a triangle ABC satisfy 4cosAcosB + sin2A + sin2B + sin2C = 4. Then which of the following statements is/are correct? (1) The triangle ABC is right angled (2) The triangle ABC is isosceles (3) The triangle ABC is neither isosceles nor right angled (4) The triangle ABC is equilateral

$$\mathrm{The}\:\mathrm{angles}\:{A},\:{B},\:{C}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:{ABC} \\ $$$$\mathrm{satisfy}\:\mathrm{4cos}{A}\mathrm{cos}{B}\:+\:\mathrm{sin2}{A}\:+\:\mathrm{sin2}{B}\:+ \\ $$$$\mathrm{sin2}{C}\:=\:\mathrm{4}.\:\mathrm{Then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{statements}\:\mathrm{is}/\mathrm{are}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{The}\:\mathrm{triangle}\:{ABC}\:\mathrm{is}\:\mathrm{right}\:\mathrm{angled} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{The}\:\mathrm{triangle}\:{ABC}\:\mathrm{is}\:\mathrm{isosceles} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{The}\:\mathrm{triangle}\:{ABC}\:\mathrm{is}\:\mathrm{neither} \\ $$$$\mathrm{isosceles}\:\mathrm{nor}\:\mathrm{right}\:\mathrm{angled} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{The}\:\mathrm{triangle}\:{ABC}\:\mathrm{is}\:\mathrm{equilateral} \\ $$

Question Number 18062    Answers: 1   Comments: 0

If 0 < α, β < π and they satisfy cos α + cos β − cos (α + β) = (3/2) (1) α = β (2) α + β = ((2π)/3) (3) α = 2β (4) β = 2α

$$\mathrm{If}\:\mathrm{0}\:<\:\alpha,\:\beta\:<\:\pi\:\mathrm{and}\:\mathrm{they}\:\mathrm{satisfy} \\ $$$$\mathrm{cos}\:\alpha\:+\:\mathrm{cos}\:\beta\:−\:\mathrm{cos}\:\left(\alpha\:+\:\beta\right)\:=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left(\mathrm{1}\right)\:\alpha\:=\:\beta \\ $$$$\left(\mathrm{2}\right)\:\alpha\:+\:\beta\:=\:\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\left(\mathrm{3}\right)\:\alpha\:=\:\mathrm{2}\beta \\ $$$$\left(\mathrm{4}\right)\:\beta\:=\:\mathrm{2}\alpha \\ $$

Question Number 18501    Answers: 0   Comments: 2

In a triangle ABC (1) sinA.sinB.sinC = (Δ/(2R^2 )) (2) sinA.sinB.sinC = (r/(2R))(sinA + sinB + sinC) (3) acosA + bcosB + ccosC = ((abc)/(2R^2 )) (4) sinA.sinB.sinC = (R/(2r))(sinA + sinB + sinC)

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{ABC} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}{A}.\mathrm{sin}{B}.\mathrm{sin}{C}\:=\:\frac{\Delta}{\mathrm{2}{R}^{\mathrm{2}} } \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}{A}.\mathrm{sin}{B}.\mathrm{sin}{C}\:=\:\frac{{r}}{\mathrm{2}{R}}\left(\mathrm{sin}{A}\:+\:\mathrm{sin}{B}\:+\:\mathrm{sin}{C}\right) \\ $$$$\left(\mathrm{3}\right)\:{a}\mathrm{cos}{A}\:+\:{b}\mathrm{cos}{B}\:+\:{c}\mathrm{cos}{C}\:=\:\frac{{abc}}{\mathrm{2}{R}^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\mathrm{sin}{A}.\mathrm{sin}{B}.\mathrm{sin}{C}\:=\:\frac{{R}}{\mathrm{2}{r}}\left(\mathrm{sin}{A}\:+\:\mathrm{sin}{B}\:+\:\mathrm{sin}{C}\right) \\ $$

Question Number 18053    Answers: 0   Comments: 5

Question Number 18046    Answers: 1   Comments: 0

Question Number 18036    Answers: 0   Comments: 4

solve: 4cos(x) + 2sin(x) = 2 + (√3)

$$\mathrm{solve}: \\ $$$$ \\ $$$$\mathrm{4cos}\left(\mathrm{x}\right)\:+\:\mathrm{2sin}\left(\mathrm{x}\right)\:=\:\mathrm{2}\:+\:\sqrt{\mathrm{3}} \\ $$

Question Number 18034    Answers: 2   Comments: 0

solve for a 5log _4 a+48log _a 4=(a/8)

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{a} \\ $$$$ \\ $$$$\mathrm{5log}\:_{\mathrm{4}} \mathrm{a}+\mathrm{48log}\:_{\mathrm{a}} \mathrm{4}=\frac{\mathrm{a}}{\mathrm{8}} \\ $$

Question Number 18031    Answers: 1   Comments: 0

What is the solution set of ((x + 2)/(x + 1)) = 1

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\:\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\mathrm{x}\:+\:\mathrm{1}}\:=\:\mathrm{1} \\ $$

Question Number 18022    Answers: 1   Comments: 0

The first term of an A.P is log^a and second term is log^b .show that the sum of first n terms in (1/2)log[(b^(n(n−1)) /a^(n(−3)) )]

$${The}\:{first}\:{term}\:{of}\:{an}\:{A}.{P}\:\:{is}\:{log}^{{a}} \:{and}\:{second}\:{term}\:{is}\: \\ $$$${log}^{{b}} .{show}\:{that}\:{the}\:{sum}\:{of}\:{first}\:{n}\:{terms}\:{in}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{log}\left[\frac{{b}^{{n}\left({n}−\mathrm{1}\right)} }{{a}^{{n}\left(−\mathrm{3}\right)} }\right] \\ $$

Question Number 18024    Answers: 2   Comments: 0

Question Number 18015    Answers: 2   Comments: 1

Just for fun Prove that there are no real numbers A and B that satisfy sinA=(2/(sinB))

$${Just}\:{for}\:{fun} \\ $$$${Prove}\:{that}\:{there}\:{are}\:{no}\:{real}\:{numbers}\:{A}\:{and}\:{B}\:{that} \\ $$$${satisfy}\: \\ $$$${sinA}=\frac{\mathrm{2}}{{sinB}} \\ $$

Question Number 23721    Answers: 1   Comments: 0

If symbols have their usual meaning then (1/r^2 ) + (1/r_1 ^2 ) + (1/r_2 ^2 ) + (1/r_3 ^2 ) = (1) ((a^2 + b^2 + c^2 )/s^2 ) (2) (Δ/(a^2 + b^2 + c^2 )) (3) ((a^2 + b^2 + c^2 )/Δ^2 ) (4) ((a + b + c)/Δ^2 )

$$\mathrm{If}\:\mathrm{symbols}\:\mathrm{have}\:\mathrm{their}\:\mathrm{usual}\:\mathrm{meaning} \\ $$$$\mathrm{then}\:\frac{\mathrm{1}}{{r}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{1}} ^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{2}} ^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{3}} ^{\mathrm{2}} }\:= \\ $$$$\left(\mathrm{1}\right)\:\frac{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} }{{s}^{\mathrm{2}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{\Delta}{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} }{\Delta^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{{a}\:+\:{b}\:+\:{c}}{\Delta^{\mathrm{2}} } \\ $$

Question Number 23722    Answers: 0   Comments: 4

A block of mass m is pulled on the smooth horizontal floor using two methods I and II. The ratio of acceleration (a_I /a_(II) ) is

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{pulled}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{floor}\:\mathrm{using}\:\mathrm{two} \\ $$$$\mathrm{methods}\:\mathrm{I}\:\mathrm{and}\:\mathrm{II}.\:\mathrm{The}\:\mathrm{ratio}\:\mathrm{of} \\ $$$$\mathrm{acceleration}\:\frac{{a}_{{I}} }{{a}_{{II}} }\:\mathrm{is} \\ $$

Question Number 18004    Answers: 1   Comments: 1

Question Number 18003    Answers: 1   Comments: 0

The value of cosA∙cos2A∙cos2^2 A ..... cos(2^(n − 1) A), where A ∈ R may be (1) 1 (2) 2 (3) −1 (4) ((sin 2^n A)/(2^n sin A))

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}{A}\centerdot\mathrm{cos2}{A}\centerdot\mathrm{cos2}^{\mathrm{2}} {A}\:.....\:\mathrm{cos}\left(\mathrm{2}^{{n}\:−\:\mathrm{1}} {A}\right), \\ $$$$\mathrm{where}\:{A}\:\in\:{R}\:\mathrm{may}\:\mathrm{be} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:−\mathrm{1} \\ $$$$\left(\mathrm{4}\right)\:\frac{\mathrm{sin}\:\mathrm{2}^{{n}} \:{A}}{\mathrm{2}^{{n}} \:\mathrm{sin}\:{A}} \\ $$

Question Number 17999    Answers: 1   Comments: 0

A large number of bullets are fired in all direction with same speed u. The maximum area on the ground covered by these bullets will be (1) π.(u^2 /g) (2) π.(u^4 /g^2 ) (3) (π/4).(u^4 /g^2 ) (4) (π/2).(u^4 /g^2 )

$$\mathrm{A}\:\mathrm{large}\:\mathrm{number}\:\mathrm{of}\:\mathrm{bullets}\:\mathrm{are}\:\mathrm{fired}\:\mathrm{in} \\ $$$$\mathrm{all}\:\mathrm{direction}\:\mathrm{with}\:\mathrm{same}\:\mathrm{speed}\:{u}.\:\mathrm{The} \\ $$$$\mathrm{maximum}\:\mathrm{area}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{covered} \\ $$$$\mathrm{by}\:\mathrm{these}\:\mathrm{bullets}\:\mathrm{will}\:\mathrm{be} \\ $$$$\left(\mathrm{1}\right)\:\pi.\frac{{u}^{\mathrm{2}} }{{g}} \\ $$$$\left(\mathrm{2}\right)\:\pi.\frac{{u}^{\mathrm{4}} }{{g}^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{\pi}{\mathrm{4}}.\frac{{u}^{\mathrm{4}} }{{g}^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{\pi}{\mathrm{2}}.\frac{{u}^{\mathrm{4}} }{{g}^{\mathrm{2}} } \\ $$

Question Number 17997    Answers: 0   Comments: 0

Solve on Z_(18) { (([6]_(18) x+[7]_(18) y=[1]_(18) )),(([2]_(18) x+[3]_(18) y=[11]_(18) )) :}

$${Solve}\:{on}\:\mathbb{Z}_{\mathrm{18}} \\ $$$$\begin{cases}{\left[\mathrm{6}\right]_{\mathrm{18}} {x}+\left[\mathrm{7}\right]_{\mathrm{18}} {y}=\left[\mathrm{1}\right]_{\mathrm{18}} }\\{\left[\mathrm{2}\right]_{\mathrm{18}} {x}+\left[\mathrm{3}\right]_{\mathrm{18}} {y}=\left[\mathrm{11}\right]_{\mathrm{18}} }\end{cases} \\ $$

Question Number 17995    Answers: 0   Comments: 0

A pendulum bob of mass 2kg is attached to a string 2m long and made to revolve in horizontal circle of radius 0.8 , find the tension in the string.

$$\mathrm{A}\:\mathrm{pendulum}\:\mathrm{bob}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{a}\:\mathrm{string}\:\:\mathrm{2m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{made}\:\mathrm{to} \\ $$$$\mathrm{revolve}\:\mathrm{in}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{0}.\mathrm{8}\:,\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{string}. \\ $$

Question Number 17991    Answers: 2   Comments: 3

Evaluate (√(1+2(√(1+3(√(1+4(√(1+...))))))))

$${Evaluate}\:\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+...}}}} \\ $$

Question Number 17989    Answers: 0   Comments: 8

Solve for x x^x^x^x^(....) = 4

$${Solve}\:{for}\:{x} \\ $$$${x}^{{x}^{{x}^{{x}^{....} } } } =\:\mathrm{4} \\ $$

Question Number 17985    Answers: 1   Comments: 0

solve simultaneously. x^3 + y^3 = 35 x^4 + y^4 = 97

$$\mathrm{solve}\:\mathrm{simultaneously}. \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:=\:\mathrm{97} \\ $$

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