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AllQuestion and Answers: Page 1916

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