Question and Answers Forum

AllQuestion and Answers: Page 1029

Question Number 116503 Answers: 2 Comments: 0

If tan α and tan β are the roots of equation 2x^2 −5x+1=0 find { ((tan ((α/2)+2β))),((tan (2α−(β/2)))) :}

$$\mathrm{If}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{equation}\:\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{tan}\:\left(\frac{\alpha}{\mathrm{2}}+\mathrm{2}\beta\right)}\\{\mathrm{tan}\:\left(\mathrm{2}\alpha−\frac{\beta}{\mathrm{2}}\right)}\end{cases} \\ $$

Question Number 116501 Answers: 1 Comments: 0

∫ ((sin x−cos x)/( (√(sin 2x)))) dx ?

$$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx}\:? \\ $$

Question Number 116500 Answers: 2 Comments: 0

∫_0 ^∞ ((sin^3 (x))/x) dx =?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 116493 Answers: 3 Comments: 0

Given sin^2 x+sin x = 1 , find the value of cos^8 x+cos^6 x+cos^4 x =?

$$\mathrm{Given}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{1}\:,\:\mathrm{find}\: \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{8}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}\:=? \\ $$

Question Number 116491 Answers: 1 Comments: 0

(0.16)^(log _(2.5) ((1/3)+(1/3^2 )+(1/3^3 )+...)) =?

$$\left(\mathrm{0}.\mathrm{16}\right)^{\mathrm{log}\:_{\mathrm{2}.\mathrm{5}} \left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }+...\right)} \:=? \\ $$

Question Number 116486 Answers: 2 Comments: 0

Question Number 116483 Answers: 2 Comments: 0

If 8 cos x−8 sin x = 3 , what is the value of 55 tan x + ((55)/(tan x)) ?

$$\mathrm{If}\:\mathrm{8}\:\mathrm{cos}\:\mathrm{x}−\mathrm{8}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{3}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{55}\:\mathrm{tan}\:\mathrm{x}\:+\:\frac{\mathrm{55}}{\mathrm{tan}\:\mathrm{x}}\:? \\ $$

Question Number 116480 Answers: 1 Comments: 0

(1/8)+(1/(18))+(1/(30))+(1/(44))+(1/(60))+(1/(78))+(1/(98))+(1/(120))+........

$$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+........ \\ $$

Question Number 116466 Answers: 0 Comments: 5

Question Number 116459 Answers: 2 Comments: 0

Question Number 116457 Answers: 1 Comments: 0

Use Laplace transform to solve the initial value problem ty′′+(4t−2)y′+(13t−4)y=0 where y(0)=0 and y′(0)=0

$$\mathrm{Use}\:\mathrm{Laplace}\:\mathrm{transform}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\: \\ $$$$\mathrm{initial}\:\mathrm{value}\:\mathrm{problem}\:\mathrm{ty}''+\left(\mathrm{4t}−\mathrm{2}\right)\mathrm{y}'+\left(\mathrm{13t}−\mathrm{4}\right)\mathrm{y}=\mathrm{0} \\ $$$$\mathrm{where}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 116455 Answers: 0 Comments: 0

Question Number 116452 Answers: 2 Comments: 0

Question Number 116451 Answers: 3 Comments: 1

lim_(n→∞) ((((n+1)(n+2)(n+3)...(n+n)))^(1/n) /n) =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{n}}]{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)\left(\mathrm{n}+\mathrm{3}\right)...\left(\mathrm{n}+\mathrm{n}\right)}}{\mathrm{n}}\:=? \\ $$

Question Number 116448 Answers: 2 Comments: 0

If sin (P) = −(8/(17)) ,where ((3π)/2)<P<2π and cos (Q)=−((24)/(25)), where π<Q<((3π)/2) what is the value of cos (2P+Q) =?

$$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{P}\right)\:=\:−\frac{\mathrm{8}}{\mathrm{17}}\:,\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\mathrm{P}<\mathrm{2}\pi \\ $$$$\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{24}}{\mathrm{25}},\:\mathrm{where}\:\pi<\mathrm{Q}<\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\left(\mathrm{2P}+\mathrm{Q}\right)\:=? \\ $$

Question Number 116443 Answers: 0 Comments: 0

Question Number 116441 Answers: 2 Comments: 0

If sin (45°−x) = −(1/3) , where 45°<x<90° .What is the value of (6sin x−(√2))^2

$$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{45}°−\mathrm{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\:,\:\mathrm{where}\:\mathrm{45}°<\mathrm{x}<\mathrm{90}° \\ $$$$.\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{6sin}\:\mathrm{x}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \\ $$

Question Number 116437 Answers: 2 Comments: 0

Prove that π<((22)/7)

$$\mathrm{Prove}\:\mathrm{that}\:\pi<\frac{\mathrm{22}}{\mathrm{7}} \\ $$

Question Number 116433 Answers: 2 Comments: 0

Given f(θ) = 2^(cos^2 (θ)) + 2^(sin^2 (θ)) find { ((maximum value)),((minimum value)) :}

$$\mathrm{Given}\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{2}^{\mathrm{cos}\:^{\mathrm{2}} \left(\theta\right)} \:+\:\mathrm{2}^{\mathrm{sin}\:^{\mathrm{2}} \left(\theta\right)} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{maximum}\:\mathrm{value}}\\{\mathrm{minimum}\:\mathrm{value}}\end{cases} \\ $$

Question Number 116427 Answers: 1 Comments: 0

∫ (sec x−tan x)^2 dx =?

$$\:\int\:\left(\mathrm{sec}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$

Question Number 116425 Answers: 2 Comments: 1

y′−y = −2xy^3

$$\:\mathrm{y}'−\mathrm{y}\:=\:−\mathrm{2xy}^{\mathrm{3}} \\ $$

Question Number 116418 Answers: 2 Comments: 0

∫ (dx/(x^5 (√(4+x^2 )))) =?

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{5}} \:\sqrt{\mathrm{4}+\mathrm{x}^{\mathrm{2}} }}\:=? \\ $$

Question Number 116417 Answers: 2 Comments: 0

lim_(x→0) (((√(1+x sin x)) −(√(cos 2x)) )/(tan^2 ((x/2)))) =?

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

Question Number 116413 Answers: 0 Comments: 0

Question Number 116397 Answers: 2 Comments: 0

The number 1,2,3,4,...,7 are randomly divided into two non −empty subsets. The probability that the sum of the numbers in the two subsets being equal is (r/s) expressed in the lowest term. Find r+s ?

$${The}\:{number}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},...,\mathrm{7}\:{are}\:{randomly} \\ $$$${divided}\:{into}\:{two}\:{non}\:−{empty}\:{subsets}. \\ $$$${The}\:{probability}\:{that}\:{the}\:{sum}\:{of}\:{the} \\ $$$${numbers}\:{in}\:{the}\:{two}\:{subsets}\:{being} \\ $$$${equal}\:{is}\:\frac{{r}}{{s}}\:{expressed}\:{in}\:{the}\:{lowest} \\ $$$${term}.\:{Find}\:{r}+{s}\:? \\ $$

Question Number 116436 Answers: 3 Comments: 2

... advanced calculus... evaluate :: I= ∫_( 0) ^( ∞) (((sin(x).sin(2x))/x)) dx =??? ... m.n.1970...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\:\mathrm{0}} ^{\:\:\infty} \:\:\left(\frac{{sin}\left({x}\right).{sin}\left(\mathrm{2}{x}\right)}{{x}}\right)\:{dx}\:=???\: \\ $$$$\:\:\:\:\:\:\:\:\:...\:{m}.{n}.\mathrm{1970}... \\ $$$$\: \\ $$$$ \\ $$

Pg 1024 Pg 1025 Pg 1026 Pg 1027 Pg 1028 Pg 1029 Pg 1030 Pg 1031 Pg 1032 Pg 1033

Contact: info@tinkutara.com