Question and Answers Forum

AllQuestion and Answers: Page 1109

Question Number 106958 Answers: 2 Comments: 0

@bemath@ (1) Given { ((x=sin α+sin β)),((y=cos α+cos β)) :} maximum value of x^2 +y^2 when α=... (2) find solution set the equation sin^4 x + sin^4 (x+(π/4))=(1/4) where x ∈ [0,2π]

$$\:\:\:@{bemath}@ \\ $$$$\left(\mathrm{1}\right)\:{Given}\:\begin{cases}{{x}=\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta}\\{{y}=\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}\end{cases} \\ $$$${maximum}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{when}\:\alpha=... \\ $$$$\left(\mathrm{2}\right)\:{find}\:{solution}\:{set}\:{the}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} {x}\:+\:\mathrm{sin}\:^{\mathrm{4}} \left({x}+\frac{\pi}{\mathrm{4}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\:{where}\:{x}\:\in\:\left[\mathrm{0},\mathrm{2}\pi\right]\: \\ $$

Question Number 106956 Answers: 3 Comments: 0

Question Number 106996 Answers: 1 Comments: 1

@bemath@ log _(∣2x−(1/2)∣) (x+1+(1/x))≥log _(∣2x−(1/2)∣) (x^2 +1+(1/x^2 ))

$$\:\:\:\:\:\:\:@{bemath}@ \\ $$$$\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}+\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\geqslant\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right) \\ $$

Question Number 106948 Answers: 4 Comments: 0

let f(a) =∫_0 ^π (dx/(a+cos^2 x)) with a>0 1) explicite f(a) 2)explicite g(a) =∫_0 ^π (dx/((a+cos^2 x)^2 )) 3) find tbe valued of intevrsls ∫_0 ^π (dx/(1+cos^2 x)) and ∫_0 ^π (dx/((1+cos^2 x)^2 ))

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\mathrm{a}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\:\mathrm{with}\:\mathrm{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{explicite}\:\mathrm{f}\left(\mathrm{a}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{dx}}{\left(\mathrm{a}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{valued}\:\mathrm{of}\:\mathrm{intevrsls} \\ $$$$\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\:\mathrm{and}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} } \\ $$

Question Number 107051 Answers: 2 Comments: 0

∫_0 ^π ((cosx)/(2+sin^2 x))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cosx}}{\mathrm{2}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$

Question Number 106941 Answers: 1 Comments: 0

Find the maximum value of Σ_(i=1) ^n sin^5 θ_i with Σ_(i=1) ^n sin θ_i =0.

$${Find}\:{the}\:{maximum}\:{value}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}^{\mathrm{5}} \:\theta_{{i}} \\ $$$${with}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}\:\theta_{{i}} =\mathrm{0}. \\ $$

Question Number 106938 Answers: 0 Comments: 0

Question Number 106932 Answers: 3 Comments: 0

∫_0 ^π (x/(1+cos^2 x))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$

Question Number 106928 Answers: 1 Comments: 0

Imagine a planet having a mass twice that of the earth and a radius equal to 1.414 times that of the earth. Determine the acceleration due to gravity at its surface.

$${Imagine}\:{a}\:{planet}\:{having}\:{a}\:{mass}\:{twice}\:{that} \\ $$$${of}\:{the}\:{earth}\:{and}\:{a}\:{radius}\:{equal}\:{to}\:\mathrm{1}.\mathrm{414} \\ $$$${times}\:{that}\:{of}\:{the}\:{earth}.\:{Determine}\:{the} \\ $$$${acceleration}\:{due}\:{to}\:{gravity}\:{at}\:{its}\:{surface}. \\ $$

Question Number 106943 Answers: 3 Comments: 1

Question Number 106950 Answers: 1 Comments: 0

^(@bemath@) Given { ((2cos x+7cos y =5)),((2sin x+7sin y = 6)) :} cos (x−y) =?

$$\:\:\:\:\:\:\:\:\:\:^{@{bemath}@} \\ $$$${Given}\:\begin{cases}{\mathrm{2cos}\:{x}+\mathrm{7cos}\:{y}\:=\mathrm{5}}\\{\mathrm{2sin}\:{x}+\mathrm{7sin}\:{y}\:=\:\mathrm{6}}\end{cases} \\ $$$$\mathrm{cos}\:\left({x}−{y}\right)\:=?\: \\ $$

Question Number 106921 Answers: 1 Comments: 1

Question Number 106919 Answers: 0 Comments: 2

if the wheel of a car moved 56rev. what is the distance the car moved in 14s?

$$\mathrm{if}\:\mathrm{the}\:\mathrm{wheel}\:\mathrm{of}\:\mathrm{a}\:\mathrm{car}\:\mathrm{moved}\:\mathrm{56rev}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{the}\:\mathrm{car}\:\mathrm{moved}\:\mathrm{in}\:\mathrm{14s}? \\ $$

Question Number 106944 Answers: 1 Comments: 2

If Σ_(i= 1) ^n sin (θ_i ) = n then cos (θ_1 ) + cos (θ_2 ) + cos (θ_3 ) + ... + cos (θ_n ) = ? i got 0 as answer. please who can correct?

$$\mathrm{If}\:\underset{{i}=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{sin}\:\left(\theta_{{i}} \right)\:=\:{n}\:\mathrm{then}\:\:\mathrm{cos}\:\left(\theta_{\mathrm{1}} \right)\:+\:\mathrm{cos}\:\left(\theta_{\mathrm{2}} \right)\:+\:\mathrm{cos}\:\left(\theta_{\mathrm{3}} \right)\:+\:...\:+\:\mathrm{cos}\:\left(\theta_{{n}} \right)\:=\:? \\ $$$$\mathrm{i}\:\mathrm{got}\:\mathrm{0}\:\mathrm{as}\:\mathrm{answer}.\:\mathrm{please}\:\mathrm{who}\:\mathrm{can}\:\mathrm{correct}? \\ $$

Question Number 106908 Answers: 1 Comments: 0

Question Number 106907 Answers: 1 Comments: 0

Question Number 106906 Answers: 2 Comments: 0

Question Number 106899 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((tsin(2t))/(t^2 +4)) dt

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{tsin}\left(\mathrm{2t}\right)}{\mathrm{t}^{\mathrm{2}} +\mathrm{4}}\:\mathrm{dt} \\ $$

Question Number 106888 Answers: 2 Comments: 0

@bemath@ given { ((f(x)=log _2 (sin x)+log _2 (cos x))),((g(x)=log _2 (cos 2x)+log _2 (cos 4x))) :} find f((π/(48)))+g((π/(48))) .

$$@\mathrm{bemath}@ \\ $$$$\mathfrak{g}\mathrm{iven}\:\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{x}\right)}\\{\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{2x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{4x}\right)}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\frac{\pi}{\mathrm{48}}\right)+\mathrm{g}\left(\frac{\pi}{\mathrm{48}}\right)\:. \\ $$

Question Number 106883 Answers: 2 Comments: 0

◊JS⧫ lim_(x→−1) (((√(x^2 −1))+1−(√(−x)))/(√(x+1))) ?

$$\:\:\:\:\:\:\:\lozenge\mathrm{JS}\blacklozenge \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}+\mathrm{1}−\sqrt{−\mathrm{x}}}{\sqrt{\mathrm{x}+\mathrm{1}}}\:?\: \\ $$

Question Number 106880 Answers: 3 Comments: 2

^(@bemath@) What is m so the roots of x^4 −(m+2)x^2 +9=0 are in AP

$$\:\:\:\:\:\:\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{m}\:\mathrm{so}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{4}} \:−\left(\mathrm{m}+\mathrm{2}\right)\mathrm{x}^{\mathrm{2}} +\mathrm{9}=\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{AP} \\ $$

Question Number 106869 Answers: 1 Comments: 0

@bemath@ lim_(x→π) [((1/(2x−2π))) ∫_π ^x ((cos 2t dt)/(1−cos 3t)) ]=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\left[\left(\frac{\mathrm{1}}{\mathrm{2x}−\mathrm{2}\pi}\right)\:\underset{\pi} {\overset{\mathrm{x}} {\int}}\:\frac{\mathrm{cos}\:\mathrm{2t}\:\mathrm{dt}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3t}}\:\right]=? \\ $$

Question Number 106867 Answers: 2 Comments: 3

∀n∈(0, 1)∀x∈R : f(x) = (n/(n−1))x+n The given function gives a linear line that goes through points (0, n) and (1−n, 0). The function changes as n changes. What area is beneath the shape made as n goes from 0→1?

$$\forall{n}\in\left(\mathrm{0},\:\mathrm{1}\right)\forall{x}\in\mathbb{R}\::\:{f}\left({x}\right)\:=\:\frac{{n}}{{n}−\mathrm{1}}{x}+{n} \\ $$$$\mathrm{The}\:\mathrm{given}\:\mathrm{function}\:\mathrm{gives}\:\mathrm{a}\:\mathrm{linear}\:\mathrm{line}\:\mathrm{that} \\ $$$$\mathrm{goes}\:\mathrm{through}\:\mathrm{points}\:\left(\mathrm{0},\:{n}\right)\:\mathrm{and}\:\left(\mathrm{1}−{n},\:\mathrm{0}\right). \\ $$$$\mathrm{The}\:\mathrm{function}\:\mathrm{changes}\:\mathrm{as}\:{n}\:\mathrm{changes}. \\ $$$$\mathrm{What}\:\mathrm{area}\:\mathrm{is}\:\mathrm{beneath}\:\mathrm{the}\:\mathrm{shape}\:\mathrm{made}\:\mathrm{as} \\ $$$${n}\:\mathrm{goes}\:\mathrm{from}\:\mathrm{0}\rightarrow\mathrm{1}? \\ $$

Question Number 106860 Answers: 0 Comments: 3

1−1+(5/9)−(7/(27))+(9/(81))−((11)/(243))+.....

$$\mathrm{1}−\mathrm{1}+\frac{\mathrm{5}}{\mathrm{9}}−\frac{\mathrm{7}}{\mathrm{27}}+\frac{\mathrm{9}}{\mathrm{81}}−\frac{\mathrm{11}}{\mathrm{243}}+..... \\ $$

Question Number 106855 Answers: 0 Comments: 0

Question Number 106847 Answers: 3 Comments: 0

Given f(x)=((3(√3))/(sinx))+(1/(cosx)) show that f ′(x)=cosx(((tan^3 x−3(√3)))/(sin^2 x))

$${Given}\:{f}\left({x}\right)=\frac{\mathrm{3}\sqrt{\mathrm{3}}}{{sinx}}+\frac{\mathrm{1}}{{cosx}} \\ $$$${show}\:{that}\:{f}\:'\left({x}\right)={cosx}\frac{\left({tan}^{\mathrm{3}} {x}−\mathrm{3}\sqrt{\mathrm{3}}\right)}{{sin}^{\mathrm{2}} {x}} \\ $$

Pg 1104 Pg 1105 Pg 1106 Pg 1107 Pg 1108 Pg 1109 Pg 1110 Pg 1111 Pg 1112 Pg 1113

Contact: info@tinkutara.com