Question and Answers Forum

AllQuestion and Answers: Page 536

Question Number 164941 Answers: 1 Comments: 1

Question Number 164940 Answers: 0 Comments: 1

−−−−−−−−− 1!−2!+3!−4!+5!−…−14!+15!=? −−−−−−−−−−by M.A

$$−−−−−−−−− \\ $$$$\mathrm{1}!−\mathrm{2}!+\mathrm{3}!−\mathrm{4}!+\mathrm{5}!−\ldots−\mathrm{14}!+\mathrm{15}!=? \\ $$$$ \\ $$$$−−−−−−−−−−\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$

Question Number 164924 Answers: 0 Comments: 1

Question Number 164923 Answers: 2 Comments: 1

Question Number 164927 Answers: 0 Comments: 0

Question Number 164929 Answers: 3 Comments: 0

∫_(−2) ^2 [x]dx=?

$$\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\left[{x}\right]{dx}=? \\ $$

Question Number 164928 Answers: 0 Comments: 0

Question Number 164918 Answers: 0 Comments: 0

Question Number 164912 Answers: 3 Comments: 1

If x^2 +y^2 = 9 , then max value of ((x^3 +y^3 )/(x+y))

$$\:\:\mathrm{If}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{9}\:,\:\mathrm{then}\:\mathrm{max}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\mathrm{x}+\mathrm{y}} \\ $$

Question Number 164926 Answers: 0 Comments: 0

⌊Given positive numbers a,b,c,d⌉ Prove that; ⌊((a^3 +b^3 +c^3 )/(a+b+c)) + ((b^3 +c^3 +d^3 )/(b+c+d)) + ((c^3 +d^3 +a^3 )/(c+d+a)) + ((d^3 +a^3 +b^3 )/(d+a+b)) > a^2 +b^2 +c^2 +d^2 ⌋

$$\:\:\:\:\:\:\:\:\:\:\:\lfloor\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}},\boldsymbol{{d}}\rceil \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}; \\ $$$$\:\:\:\:\:\:\:\:\lfloor\frac{\boldsymbol{{a}}^{\mathrm{3}} +\boldsymbol{{b}}^{\mathrm{3}} +\boldsymbol{{c}}^{\mathrm{3}} }{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}}\:+\:\frac{\boldsymbol{{b}}^{\mathrm{3}} +\boldsymbol{{c}}^{\mathrm{3}} +\boldsymbol{{d}}^{\mathrm{3}} }{\boldsymbol{{b}}+\boldsymbol{{c}}+\boldsymbol{{d}}}\:+\:\frac{\boldsymbol{{c}}^{\mathrm{3}} +\boldsymbol{{d}}^{\mathrm{3}} +\boldsymbol{{a}}^{\mathrm{3}} }{\boldsymbol{{c}}+\boldsymbol{{d}}+\boldsymbol{{a}}}\:+\:\frac{\boldsymbol{{d}}^{\mathrm{3}} +\boldsymbol{{a}}^{\mathrm{3}} +\boldsymbol{{b}}^{\mathrm{3}} }{\boldsymbol{{d}}+\boldsymbol{{a}}+\boldsymbol{{b}}}\:>\:\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} +\boldsymbol{{d}}^{\mathrm{2}} \rfloor \\ $$

Question Number 164904 Answers: 0 Comments: 0

∫_0 ^∞ ((cos^(−1) .(x))/(In ((x) − 3^((x^2 −1)) ))) dx {z.a}

$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}^{−\mathrm{1}} \:.\left(\boldsymbol{{x}}\right)}{\boldsymbol{\mathrm{I}}\mathrm{n}\:\left(\left(\boldsymbol{{x}}\right)\:−\:\mathrm{3}^{\left(\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1}\right)} \right)}\:\boldsymbol{{dx}} \\ $$$$\left\{\boldsymbol{{z}}.\boldsymbol{{a}}\right\} \\ $$

Question Number 164901 Answers: 1 Comments: 0

Question Number 164890 Answers: 0 Comments: 0

Question Number 164879 Answers: 1 Comments: 1

Question Number 164875 Answers: 0 Comments: 0

Solve for natural numbers: 𝛟(n) ∙ 𝛟(n + 1) = 288n 𝛟-Euler′s totient function

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\boldsymbol{\varphi}\left(\boldsymbol{\mathrm{n}}\right)\:\centerdot\:\boldsymbol{\varphi}\left(\boldsymbol{\mathrm{n}}\:+\:\mathrm{1}\right)\:=\:\mathrm{288}\boldsymbol{\mathrm{n}} \\ $$$$\boldsymbol{\varphi}-\mathrm{Euler}'\mathrm{s}\:\mathrm{totient}\:\mathrm{function} \\ $$

Question Number 164874 Answers: 1 Comments: 0

Question Number 164871 Answers: 0 Comments: 0

Question Number 164856 Answers: 0 Comments: 1

Let a,b,c >0; 42abc + 4bca +1cab ≤ 24 Then (1/(ab)) + (2/(bc)) + (3/(ca)) = ?? ^({Z.A})

$$\:\:\:\:\boldsymbol{\mathrm{Let}}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}\:>\mathrm{0}; \\ $$$$\:\:\:\:\mathrm{42}\boldsymbol{{abc}}\:+\:\mathrm{4}\boldsymbol{{bca}}\:+\mathrm{1}\boldsymbol{{cab}}\:\leqslant\:\mathrm{24} \\ $$$$\:\:\:\:\mathrm{T}\boldsymbol{\mathrm{hen}}\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{ab}}}\:+\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{bc}}}\:+\:\frac{\mathrm{3}}{\boldsymbol{\mathrm{ca}}}\:=\:?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:^{\left\{{Z}.\mathrm{A}\right\}} \\ $$

Question Number 164854 Answers: 1 Comments: 0

Evaluate the Integral; [∫_0 ^∞ ((x^2 − 1)/(1−x)) dx =??] ^({Z.A})

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{Integral}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{1}−\boldsymbol{{x}}}\:\boldsymbol{{dx}}\:=??\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:^{\left\{\boldsymbol{{Z}}.\mathrm{A}\right\}} \\ $$

Question Number 164853 Answers: 0 Comments: 0

Ω = ∫_0 ^( 1) (( ln(1+x ).ln(x))/(1−x)) dx

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

Question Number 164842 Answers: 3 Comments: 13

Question Number 164826 Answers: 2 Comments: 0

if h(x) = x − ⌊(1/x)⌋ , x>0 then h^( −1) ( x ) = ?

$$ \\ $$$$\:\:\:\:\:\:{if}\:\:\:\:{h}\left({x}\right)\:=\:{x}\:−\:\lfloor\frac{\mathrm{1}}{{x}}\rfloor\:\:,\:\:{x}>\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:{then}\:\:\:{h}^{\:−\mathrm{1}} \left(\:{x}\:\right)\:=\:? \\ $$$$ \\ $$

Question Number 164821 Answers: 0 Comments: 9

prove that n=((360^° )/∝)−1 n=number of multiple images

$${prove}\:{that}\:\:{n}=\frac{\mathrm{360}^{°} }{\propto}−\mathrm{1} \\ $$$${n}={number}\:{of}\:\:{multiple}\:{images}\: \\ $$

Question Number 164820 Answers: 1 Comments: 0

Question Number 164814 Answers: 0 Comments: 2

does the forum support animated images in gif format?

$${does}\:{the}\:{forum}\:{support}\:{animated} \\ $$$${images}\:{in}\:{gif}\:{format}? \\ $$

Question Number 164810 Answers: 1 Comments: 2

find n^(th) terms of <1,0,1,0,1,0,....>

$${find}\:{n}^{{th}} \:{terms}\:{of}\:<\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{0},....> \\ $$

Pg 531 Pg 532 Pg 533 Pg 534 Pg 535 Pg 536 Pg 537 Pg 538 Pg 539 Pg 540

Contact: info@tinkutara.com