Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 650

Question Number 153757 Answers: 1 Comments: 1

Question Number 153755 Answers: 0 Comments: 0

Question Number 153742 Answers: 1 Comments: 0

Question Number 153737 Answers: 2 Comments: 0

Show that ∫_0 ^( (π/2)) (1/((cos θ+ (√3) sin θ)^2 )) dθ= (1/( (√3) ))

$$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\left(\mathrm{cos}\:\theta+\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta\right)^{\mathrm{2}} }\:{d}\theta=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}\:} \\ $$

Question Number 153734 Answers: 0 Comments: 0

Question Number 153733 Answers: 0 Comments: 0

Question Number 153728 Answers: 0 Comments: 0

Question Number 153722 Answers: 0 Comments: 0

lim_(x→0) ((tan x+x sec x−sin x−x)/(x^3 cos x)) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}+{x}\:\mathrm{sec}\:{x}−\mathrm{sin}\:{x}−{x}}{{x}^{\mathrm{3}} \:\mathrm{cos}\:{x}}\:=? \\ $$

Question Number 153721 Answers: 2 Comments: 0

prove that : I:= ∫_0 ^( ∞) (( x^( 3) )/(sinh ( x ))) dx = ((π^4 )/8) ■ m.n

$$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}^{\:\mathrm{3}} }{{sinh}\:\left(\:{x}\:\right)}\:{dx}\:=\:\frac{\pi\:^{\mathrm{4}} }{\mathrm{8}}\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 153716 Answers: 1 Comments: 1

Question Number 153714 Answers: 2 Comments: 0

How many three−digit numbers can be formed using the digits 2,3,5,7,8 if the number is odd and no digit is repeted?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{three}−\mathrm{digit}\:\mathrm{numbers}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{8}\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{repeted}? \\ $$

Question Number 153708 Answers: 2 Comments: 0

Question Number 153704 Answers: 1 Comments: 1

Question Number 153696 Answers: 1 Comments: 0

Question Number 153867 Answers: 0 Comments: 2

Question Number 153698 Answers: 2 Comments: 0

solve in R { ((x^3 −y^3 =19)),((xy=6)) :}

$${solve}\:{in}\:\mathbb{R} \\ $$$$\begin{cases}{{x}^{\mathrm{3}} −{y}^{\mathrm{3}} =\mathrm{19}}\\{{xy}=\mathrm{6}}\end{cases} \\ $$

Question Number 153685 Answers: 3 Comments: 2

Question Number 153682 Answers: 1 Comments: 0

((i)^(1/i) )^(xi) = i^x x=?

$$\:\left(\sqrt[{{i}}]{{i}}\:\right)^{{xi}} \:=\:{i}^{{x}} \: \\ $$$$\:\:{x}=?\: \\ $$

Question Number 153681 Answers: 1 Comments: 0

24^(log _(10) (x)) −26^(log _(10) (x)) =1 x=?

$$\:\:\mathrm{24}^{\mathrm{log}\:_{\mathrm{10}} \left({x}\right)} −\mathrm{26}^{\mathrm{log}\:_{\mathrm{10}} \left({x}\right)} =\mathrm{1} \\ $$$$\:{x}=? \\ $$

Question Number 153679 Answers: 1 Comments: 0

Find the constant of polynom P(11x−2) if given the equation 3P(x+2)−P(2x+3)=−4x^2 −x+3

$${Find}\:{the}\:{constant}\:{of}\:{polynom} \\ $$$$\:{P}\left(\mathrm{11}{x}−\mathrm{2}\right)\:{if}\:{given}\:{the}\:{equation} \\ $$$$\mathrm{3}{P}\left({x}+\mathrm{2}\right)−{P}\left(\mathrm{2}{x}+\mathrm{3}\right)=−\mathrm{4}{x}^{\mathrm{2}} −{x}+\mathrm{3} \\ $$

Question Number 153676 Answers: 2 Comments: 0

Question Number 153671 Answers: 0 Comments: 1

Question Number 153668 Answers: 0 Comments: 0

probability question let T_(V ) be the volume of tetrahedron T that is in a cone C with volume C_V find P(T_V ≥ (1/8) C_V )

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\mathrm{probability}\:\mathrm{question}} \\ $$$$\: \\ $$$$\:\mathrm{let}\:{T}_{{V}\:} \:\mathrm{be}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{tetrahedron}\:{T}\:\:\: \\ $$$$\:\mathrm{that}\:\mathrm{is}\:\mathrm{in}\:\mathrm{a}\:\mathrm{cone}\:{C}\:\mathrm{with}\:\mathrm{volume}\:{C}_{{V}} \\ $$$$\:\mathrm{find}\:\mathrm{P}\left({T}_{{V}} \:\:\geqslant\:\frac{\mathrm{1}}{\mathrm{8}}\:{C}_{{V}} \right) \\ $$$$\: \\ $$

Question Number 153657 Answers: 0 Comments: 2

let d(n) denote the sum of the digits of n. i.e d(1000) = 1 , d(999) = 27 find minimum k such that d(d(....._(k times) d(5^(10^(100) ) ).....) ≪ 10

$$\: \\ $$$$\:\mathrm{let}\:{d}\left({n}\right)\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\: \\ $$$$\:\mathrm{of}\:{n}. \\ $$$$\:\mathrm{i}.\mathrm{e}\:\:\:\:{d}\left(\mathrm{1000}\right)\:=\:\mathrm{1}\:,\:\:\:\:\:{d}\left(\mathrm{999}\right)\:=\:\mathrm{27} \\ $$$$\: \\ $$$$\:\mathrm{find}\:\mathrm{minimum}\:{k}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\underset{{k}\:\mathrm{times}} {\underbrace{{d}\left({d}\left(.....}{d}}\left(\mathrm{5}^{\mathrm{10}^{\mathrm{100}} } \right).....\right)\:\ll\:\mathrm{10}\right. \\ $$$$\: \\ $$

Question Number 153651 Answers: 2 Comments: 0

Question Number 153638 Answers: 1 Comments: 2

Pg 645 Pg 646 Pg 647 Pg 648 Pg 649 Pg 650 Pg 651 Pg 652 Pg 653 Pg 654

Contact: info@tinkutara.com