Question and Answers Forum

AllQuestion and Answers: Page 605

Question Number 149036 Answers: 1 Comments: 0

if x;y;z>0 and xyz=8 prove that: (1/(x^2 + 8)) + (1/(y^2 + 8)) + (1/(z^2 + 8)) ≤ (1/4)

$${if}\:\:\:{x};{y};{z}>\mathrm{0}\:\:\:{and}\:\:\:{xyz}=\mathrm{8}\:\:\:{prove}\:{that}: \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} \:+\:\mathrm{8}}\:+\:\frac{\mathrm{1}}{{y}^{\mathrm{2}} \:+\:\mathrm{8}}\:+\:\frac{\mathrm{1}}{{z}^{\mathrm{2}} \:+\:\mathrm{8}}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 149031 Answers: 2 Comments: 0

Question Number 149030 Answers: 0 Comments: 0

f(x)=4_−_(5^x +1) x=0,1,2..... find the moment generating function

$$\mathrm{f}\left(\mathrm{x}\right)=\underset{\underset{\mathrm{5}^{\mathrm{x}} +\mathrm{1}} {−}} {\mathrm{4}}\:\:\:\:\mathrm{x}=\mathrm{0},\mathrm{1},\mathrm{2}.....\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{moment}\: \\ $$$$\mathrm{generating}\:\mathrm{function} \\ $$

Question Number 149077 Answers: 1 Comments: 0

Ω := ∫_0 ^( 1) ((ln ( 1+ (√x) ))/(1+x)) dx =? .....m.n.....

$$ \\ $$$$\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\:\left(\:\mathrm{1}+\:\sqrt{{x}}\:\right)}{\mathrm{1}+{x}}\:{dx}\:=? \\ $$$$\:.....{m}.{n}..... \\ $$

Question Number 149025 Answers: 1 Comments: 3

Solve for equation: cos^3 (x) - sin^3 (x) + 1

$${Solve}\:{for}\:{equation}: \\ $$$${cos}^{\mathrm{3}} \left({x}\right)\:-\:{sin}^{\mathrm{3}} \left({x}\right)\:+\:\mathrm{1} \\ $$

Question Number 149024 Answers: 2 Comments: 0

Question Number 149023 Answers: 1 Comments: 0

∫_0 ^(π/4) ((tsint)/(1+cos^2 t))dt=∫_0 ^(π/4) ((tcost)/(1+sin^2 t))dt true or false ??

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{tsint}}{\mathrm{1}+{cos}^{\mathrm{2}} {t}}{dt}=\overset{\frac{\pi}{\mathrm{4}}} {\int}_{\mathrm{0}} \frac{{tcost}}{\mathrm{1}+{sin}^{\mathrm{2}} {t}}{dt} \\ $$$${true}\:{or}\:{false}\:?? \\ $$

Question Number 149008 Answers: 2 Comments: 3

Question Number 148997 Answers: 0 Comments: 0

find number of rational terms in the expansion of ((3)^(1/5) +(2)^(1/3) )^(15) . prove sum of all irrarional terms is greater than sum of all rational terms.

$${find}\:{number}\:{of}\:{rational}\:{terms}\: \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left(\sqrt[{\mathrm{5}}]{\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{2}}\right)^{\mathrm{15}} . \\ $$$${prove}\:{sum}\:{of}\:{all}\:{irrarional}\:{terms}\: \\ $$$${is}\:{greater}\:{than}\:{sum}\:{of}\:{all}\:{rational} \\ $$$${terms}. \\ $$

Question Number 148994 Answers: 1 Comments: 0

(102)^4 easy way to caculate

$$\left(\mathrm{102}\right)^{\mathrm{4}} \\ $$$${easy}\:{way}\:{to}\:{caculate} \\ $$

Question Number 148993 Answers: 2 Comments: 5

if M is a point on the line y=x and points P(0,1),Q(2,0) are such that PM+PQ is minimum then find P

$${if}\:{M}\:{is}\:{a}\:{point}\:{on}\:{the}\:{line}\:{y}={x}\:{and} \\ $$$${points}\:{P}\left(\mathrm{0},\mathrm{1}\right),{Q}\left(\mathrm{2},\mathrm{0}\right)\:{are}\:{such}\:{that} \\ $$$${PM}+{PQ}\:{is}\:{minimum}\:{then}\:{find}\:{P} \\ $$

Question Number 148992 Answers: 2 Comments: 0

Question Number 148991 Answers: 1 Comments: 0

The largest value of k for which the circle x^2 +y^2 =k^2 lies completely in the interior of the parabola y^2 =4x+16 ?

$${The}\:{largest}\:{value}\:{of}\:{k}\:{for}\:{which}\: \\ $$$${the}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={k}^{\mathrm{2}} \:{lies}\:{completely} \\ $$$${in}\:{the}\:{interior}\:{of}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}+\mathrm{16}\:? \\ $$

Question Number 148990 Answers: 0 Comments: 0

let f:R→R be a continuius function such that for any two real numbers x and y ∣f(x)−f(y)∣≤10∣x−y∣^(201) then prove that f(2019)+f(2022)=2 f(2021)

$${let}\:{f}:{R}\rightarrow{R}\:{be}\:{a}\:{continuius}\:{function} \\ $$$${such}\:{that}\:{for}\:{any}\:{two}\:{real}\:{numbers} \\ $$$${x}\:{and}\:{y}\:\mid{f}\left({x}\right)−{f}\left({y}\right)\mid\leqslant\mathrm{10}\mid{x}−{y}\mid^{\mathrm{201}} \\ $$$${then}\:{prove}\:{that} \\ $$$${f}\left(\mathrm{2019}\right)+{f}\left(\mathrm{2022}\right)=\mathrm{2}\:{f}\left(\mathrm{2021}\right) \\ $$

Question Number 148987 Answers: 1 Comments: 0

if tg(0,5x) = −2 find ((sin(x) + 2)/(cos(x) - 3)) = ?

$${if}\:\:\:{tg}\left(\mathrm{0},\mathrm{5}{x}\right)\:=\:−\mathrm{2} \\ $$$${find}\:\:\:\frac{{sin}\left({x}\right)\:+\:\mathrm{2}}{{cos}\left({x}\right)\:-\:\mathrm{3}}\:=\:? \\ $$

Question Number 148986 Answers: 1 Comments: 0

lim_(x→0) ((tg^2 x^3 + 3x^6 )/(5sin^2 x^3 )) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{tg}^{\mathrm{2}} {x}^{\mathrm{3}} \:+\:\mathrm{3}{x}^{\mathrm{6}} }{\mathrm{5}{sin}^{\mathrm{2}} {x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 148981 Answers: 0 Comments: 0

∫_((√2)/2) ^1 ((arc cosu)/(u^2 +1))du

$$\int_{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} ^{\mathrm{1}} \frac{{arc}\:{cosu}}{{u}^{\mathrm{2}} +\mathrm{1}}{du} \\ $$

Question Number 148975 Answers: 1 Comments: 1

Question Number 149447 Answers: 0 Comments: 0

Solve the following system { ((sin 2x+cos 3y=−1)),(((√(sin^2 x+sin^2 y)) +(√(cos^2 x+cos^2 y)) =1+sin (x+y))) :}

$$\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\: \\ $$$$\:\begin{cases}{\mathrm{sin}\:\mathrm{2x}+\mathrm{cos}\:\mathrm{3y}=−\mathrm{1}}\\{\sqrt{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{y}}\:+\sqrt{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{y}}\:=\mathrm{1}+\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)}\end{cases} \\ $$$$ \\ $$

Question Number 149440 Answers: 1 Comments: 0

Question Number 149439 Answers: 1 Comments: 1

Question Number 149437 Answers: 1 Comments: 1

Question Number 148973 Answers: 0 Comments: 0

Question Number 148971 Answers: 0 Comments: 0

2^(2+x) −3^(2x+y) =−11 and 2^(x+1) +3^(3y) =11 find x and y

$$\:\mathrm{2}^{\mathrm{2}+{x}} −\mathrm{3}^{\mathrm{2}{x}+{y}} =−\mathrm{11} \\ $$$${and}\:\:\:\mathrm{2}^{{x}+\mathrm{1}} +\mathrm{3}^{\mathrm{3}{y}} =\mathrm{11} \\ $$$$\:{find}\:\:{x}\:{and}\:\:{y} \\ $$

Question Number 148932 Answers: 1 Comments: 0

(((b+c)^2 )/(bc))l_a ^2 +(((a+b)^2 )/(ab))l_c ^2 +(((a+c)^2 )/(ac))l_b ^2 =(a+b+c)^2 l_b ,l_a ,l_c −bissekterissa prove

$$\frac{\left(\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} }{\boldsymbol{{bc}}}\boldsymbol{{l}}_{\boldsymbol{{a}}} ^{\mathrm{2}} +\frac{\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)^{\mathrm{2}} }{\boldsymbol{{ab}}}\boldsymbol{{l}}_{\boldsymbol{{c}}} ^{\mathrm{2}} +\frac{\left(\boldsymbol{{a}}+\boldsymbol{{c}}\right)^{\mathrm{2}} }{\boldsymbol{{ac}}}\boldsymbol{{l}}_{\boldsymbol{{b}}} ^{\mathrm{2}} =\left(\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} \\ $$$$\boldsymbol{{l}}_{\boldsymbol{{b}}} ,\boldsymbol{{l}}_{\boldsymbol{{a}}} ,\boldsymbol{{l}}_{\boldsymbol{{c}}} −\boldsymbol{{bissekterissa}} \\ $$$$\boldsymbol{{prove}} \\ $$

Question Number 148939 Answers: 0 Comments: 0

(B^3 −2B^2 −4B+8)y=0 solve the differencial equation

$$\:\left({B}^{\mathrm{3}} −\mathrm{2}{B}^{\mathrm{2}} −\mathrm{4}{B}+\mathrm{8}\right){y}=\mathrm{0} \\ $$$${solve}\:{the}\:{differencial}\:{equation} \\ $$

Pg 600 Pg 601 Pg 602 Pg 603 Pg 604 Pg 605 Pg 606 Pg 607 Pg 608 Pg 609

Contact: info@tinkutara.com