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Question Number 171613 Answers: 0 Comments: 0

Question Number 171612 Answers: 0 Comments: 4

f(f(x))=(1/(1+x^2 )) f(x)=?

$${f}\left({f}\left({x}\right)\right)=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:{f}\left({x}\right)=? \\ $$

Question Number 171611 Answers: 1 Comments: 0

∫_0 ^∞ xe^(−x) cos(x)log^n (x)dx how can we do these

$$\int_{\mathrm{0}} ^{\infty} \boldsymbol{\mathrm{xe}}^{−\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{log}}^{\boldsymbol{\mathrm{n}}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{these}} \\ $$

Question Number 171608 Answers: 1 Comments: 0

montrer que ∫_o ^(+oo) ((sin^2 t)/t^2 )e^(−xt) dt est continu sur R^+

$${montrer}\:{que} \\ $$$$\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt} \\ $$$${est}\:{continu}\:{sur}\:{R}^{+} \\ $$

Question Number 171601 Answers: 0 Comments: 0

Question Number 171599 Answers: 0 Comments: 0

Ω=∫_0 ^1 Log(((Log^2 (x))/x^(x^5 −x^4 +x^3 −x^2 +x−1) ))dx Mastermind

$$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} {Log}\left(\frac{{Log}^{\mathrm{2}} \left({x}\right)}{{x}^{{x}^{\mathrm{5}} −{x}^{\mathrm{4}} +{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}} }\right){dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171596 Answers: 1 Comments: 3

Show that ((cos 70°−cos 20°)/(sin 70°−sin 20°)) = −1

$${Show}\:{that}\:\frac{\mathrm{cos}\:\mathrm{70}°−\mathrm{cos}\:\mathrm{20}°}{\mathrm{sin}\:\mathrm{70}°−\mathrm{sin}\:\mathrm{20}°}\:=\:−\mathrm{1} \\ $$

Question Number 171594 Answers: 1 Comments: 0

charis wants to resize a 4 inch by 6 inch photo by a factor of 4/3. what are the dimensions of the new photo?

$$ \\ $$charis wants to resize a 4 inch by 6 inch photo by a factor of 4/3. what are the dimensions of the new photo?

Question Number 171583 Answers: 2 Comments: 3

if f(f(x))=x^2 −x+1, find f(0)=?

$${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −{x}+\mathrm{1},\:{find}\:{f}\left(\mathrm{0}\right)=? \\ $$

Question Number 171575 Answers: 0 Comments: 3

Question Number 171574 Answers: 1 Comments: 0

Question Number 171572 Answers: 1 Comments: 1

Show that 4^(3n−2) +5 is divisible by 9 then simplify ((4^(3n−2) +5)/9)

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{4}^{\mathrm{3}{n}−\mathrm{2}} +\mathrm{5}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{9} \\ $$$$\mathrm{then}\:\mathrm{simplify}\:\frac{\mathrm{4}^{\mathrm{3}{n}−\mathrm{2}} +\mathrm{5}}{\mathrm{9}} \\ $$

Question Number 171566 Answers: 0 Comments: 0

prove that ∫_o ^(+oo) ((sin^2 t)/t^2 )e^(−xt) dt is continious R^+

$${prove}\:{that}\:\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt}\: \\ $$$${is}\:{continious}\:{R}^{+} \\ $$

Question Number 171565 Answers: 0 Comments: 4

Question Number 171563 Answers: 1 Comments: 0

evaluate ((√(((a−b)^7 + (b−c)^7 + (c−a)^7 )/((a−b)^3 + (b−c)^3 + (c−a)^3 )))/(a^2 +b^2 +c^2 −ab−bc−ca)) = ??

$$\:\:\:\:\:\:\:\:{evaluate}\:\:\: \\ $$$$\:\:\:\:\:\frac{\sqrt{\frac{\left({a}−{b}\right)^{\mathrm{7}} \:+\:\left({b}−{c}\right)^{\mathrm{7}} \:+\:\left({c}−{a}\right)^{\mathrm{7}} }{\left({a}−{b}\right)^{\mathrm{3}} \:+\:\left({b}−{c}\right)^{\mathrm{3}} \:+\:\left({c}−{a}\right)^{\mathrm{3}} }}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}}\:=\:\:?? \\ $$

Question Number 171558 Answers: 0 Comments: 0

In △ABC , I-incenter ID⊥BC , IE⊥CA , IF⊥AB D∈(BC) , E∈(CA) , F∈(AB) I_a , I_b , I_c -excenters. Prove that: Σ_(cyc) ((EF)/(sin (A/2))) + Π_(cyc) ((EF)/(sin (A/2))) = ((1 + 4r^2 )/R) ∙ [I_a I_b I_c ]

Question Number 171552 Answers: 2 Comments: 0

Question Number 171593 Answers: 0 Comments: 2

The maximum value of the expression ∣(√(sin^2 x+2a^2 )) −(√(2a^2 −1−cos^2 x)) ∣ where a and x real numbers is−−−

$$\:{The}\:{maximum}\:{value}\:{of}\:{the} \\ $$$${expression}\:\mid\sqrt{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{2}{a}^{\mathrm{2}} }\:−\sqrt{\mathrm{2}{a}^{\mathrm{2}} −\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}\:\mid\: \\ $$$${where}\:{a}\:{and}\:{x}\:{real}\:{numbers}\:{is}−−− \\ $$

Question Number 171549 Answers: 1 Comments: 0

Solve for real numbers: { ((2x^2 + 3y^2 + z^2 = 7)),((x^2 + y^2 + z^2 = (√2) z (x + y))) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{3y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{7}}\\{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\sqrt{\mathrm{2}}\:\mathrm{z}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}\end{cases} \\ $$

Question Number 171546 Answers: 0 Comments: 1

f(x)=((−ln∣x∣)/x)+x−2 , g(x)=−x^2 +1−ln∣x∣ Calculate the derivative of f(x) as a function of g(x)

$${f}\left({x}\right)=\frac{−{ln}\mid{x}\mid}{{x}}+{x}−\mathrm{2}\:\:,\:\:\:{g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$$$ \\ $$Calculate the derivative of f(x) as a function of g(x)

Question Number 171530 Answers: 0 Comments: 0

Question Number 171529 Answers: 4 Comments: 1

Question Number 171528 Answers: 1 Comments: 0

Question Number 171527 Answers: 0 Comments: 0

Question Number 171519 Answers: 0 Comments: 0

Question Number 171518 Answers: 0 Comments: 2

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