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Question Number 181437 Answers: 2 Comments: 0

Question Number 181435 Answers: 0 Comments: 0

((𝛅^2 u)/(𝛅t^2 )) = 4 ((𝛅^2 u)/(𝛅x^2 )) ; u∣_(t=0) =sin(x) ; ((𝛅u)/(𝛅t))∣_(t=0) =x

$$\:\:\:\frac{\boldsymbol{\delta}^{\mathrm{2}} \boldsymbol{\mathrm{u}}}{\boldsymbol{\delta\mathrm{t}}^{\mathrm{2}} }\:=\:\mathrm{4}\:\frac{\boldsymbol{\delta}^{\mathrm{2}} \boldsymbol{\mathrm{u}}}{\boldsymbol{\delta\mathrm{x}}^{\mathrm{2}} }\:\:\:;\:\:\boldsymbol{\mathrm{u}}\mid_{\boldsymbol{\mathrm{t}}=\mathrm{0}} =\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)\:\:\:;\:\:\:\frac{\boldsymbol{\delta\mathrm{u}}}{\boldsymbol{\delta\mathrm{t}}}\mid_{\boldsymbol{\mathrm{t}}=\mathrm{0}} =\boldsymbol{\mathrm{x}} \\ $$

Question Number 181432 Answers: 1 Comments: 5

Question Number 174096 Answers: 2 Comments: 0

f(x)= ax^( 2) + bx +c is given a ≠ b ≠ c , a , b , c ∈ R a≠0 and : f(ax + b )=f (bx + c) find : (1/2) (f(b) − f(a ))=?

$$ \\ $$$$\:\:\:{f}\left({x}\right)=\:{ax}^{\:\mathrm{2}} +\:{bx}\:+{c}\:\:{is}\:{given} \\ $$$$\:\:\:\:\:\:{a}\:\neq\:{b}\:\neq\:{c}\:\:,\:{a}\:,\:{b}\:,\:{c}\:\in\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:{a}\neq\mathrm{0}\:\:\:{and}\:\:\:: \\ $$$$\:\:\:\:\:\:\:\:{f}\left({ax}\:+\:{b}\:\right)={f}\:\left({bx}\:+\:{c}\right) \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({f}\left({b}\right)\:\:−\:{f}\left({a}\:\right)\right)=? \\ $$

Question Number 174094 Answers: 1 Comments: 0

The circles x^2 +y^2 −2ax+8y+13=0 and x^2 +y^2 +2x+2by+1=0 are congruent. If they are 2(√(10)) units apart, find the possible values of a and b.

$$\mathrm{The}\:\mathrm{circles}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{ax}+\mathrm{8}{y}+\mathrm{13}=\mathrm{0} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}{by}+\mathrm{1}=\mathrm{0}\:\mathrm{are}\: \\ $$$$\mathrm{congruent}.\:\mathrm{If}\:\mathrm{they}\:\mathrm{are}\:\mathrm{2}\sqrt{\mathrm{10}}\:\mathrm{units}\: \\ $$$$\mathrm{apart},\:\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of} \\ $$$${a}\:\mathrm{and}\:{b}. \\ $$

Question Number 174095 Answers: 0 Comments: 0

prove the distance between object and image of glass slab.

$${prove}\:{the}\:{distance}\:{between}\:{object}\:{and} \\ $$$${image}\:{of}\:{glass}\:{slab}. \\ $$

Question Number 174084 Answers: 2 Comments: 1

Question Number 174074 Answers: 1 Comments: 1

Question Number 174071 Answers: 2 Comments: 0

Question Number 174069 Answers: 1 Comments: 1

Question Number 174092 Answers: 2 Comments: 0

x^4 +ax^2 +14x−210=0 x_1 .x_2 =22, a=?

$$\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{ax}}^{\mathrm{2}} +\mathrm{14}\boldsymbol{{x}}−\mathrm{210}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{x}}_{\mathrm{1}} .\boldsymbol{{x}}_{\mathrm{2}} =\mathrm{22},\:\:\:\:\:\:\:\boldsymbol{{a}}=? \\ $$

Question Number 174062 Answers: 2 Comments: 3

find all prime p and q such that p^2 − p = 37q^2 − q

$$\mathrm{find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\:\mathrm{such}\:\mathrm{that}\:\:\:\:\mathrm{p}^{\mathrm{2}} \:\:−\:\:\mathrm{p}\:\:\:\:=\:\:\:\mathrm{37q}^{\mathrm{2}} \:\:−\:\:\mathrm{q} \\ $$

Question Number 174059 Answers: 2 Comments: 3

if x^3 +y^3 +3xy=1, then x+y=?

$${if}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\mathrm{3}{xy}=\mathrm{1},\:{then}\:{x}+{y}=? \\ $$

Question Number 174057 Answers: 0 Comments: 1

Question Number 174056 Answers: 0 Comments: 0

Question Number 174036 Answers: 1 Comments: 0

Factorize x^2 + (√(2x ))+ x + 2

$$\:\:\mathrm{Factorize}\:{x}^{\mathrm{2}} \:+\:\sqrt{\mathrm{2}{x}\:}+\:{x}\:+\:\mathrm{2} \\ $$

Question Number 174029 Answers: 1 Comments: 1

x+y=1 x^5 +xy+y^5 =x^2 y^(2 ) faind the volue of x^(2022) +xy+y^(2022) =?

$${x}+{y}=\mathrm{1} \\ $$$${x}^{\mathrm{5}} +{xy}+{y}^{\mathrm{5}} ={x}^{\mathrm{2}} {y}^{\mathrm{2}\:\:\:\:\:\:} \\ $$$${faind}\:{the}\:{volue}\:{of}\:\:\:{x}^{\mathrm{2022}} +{xy}+{y}^{\mathrm{2022}} =? \\ $$

Question Number 174023 Answers: 2 Comments: 1

Question Number 173997 Answers: 2 Comments: 0

If (x)^(1/3) − 3 = ((x−36))^(1/3) then ((x^( 2) −1)/x) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{If}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{3}}]{{x}}\:−\:\mathrm{3}\:=\:\sqrt[{\mathrm{3}}]{{x}−\mathrm{36}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{x}^{\:\mathrm{2}} −\mathrm{1}}{{x}}\:=\:?\: \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 173993 Answers: 1 Comments: 0

Question Number 173992 Answers: 1 Comments: 1

Question Number 173984 Answers: 0 Comments: 0

Question Number 173983 Answers: 1 Comments: 0

in AB^Δ C prove : (( cos(A ))/a^( 3) ) +((cos(B))/b^( 3) ) +((cos(C))/c^( 3) ) ≥((81)/(16p^( 3) )) where : p= (a+b +c )/2

$$ \\ $$$$\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:\:{prove}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\:{cos}\left({A}\:\right)}{{a}^{\:\mathrm{3}} }\:+\frac{{cos}\left({B}\right)}{{b}^{\:\mathrm{3}} }\:+\frac{{cos}\left({C}\right)}{{c}^{\:\mathrm{3}} }\:\geqslant\frac{\mathrm{81}}{\mathrm{16}{p}^{\:\mathrm{3}} } \\ $$$$\:\:\:{where}\::\:\:{p}=\:\left({a}+{b}\:+{c}\:\right)/\mathrm{2} \\ $$$$ \\ $$

Question Number 173981 Answers: 2 Comments: 0

Question Number 173978 Answers: 1 Comments: 0

Solve system of equations: x+((3x−y)/(x^2 +y^2 ))=3 y−((x+3y)/(x^2 +y^2 ))=0

$$\mathrm{Solve}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\mathrm{x}+\frac{\mathrm{3x}−\mathrm{y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\mathrm{3} \\ $$$$\mathrm{y}−\frac{\mathrm{x}+\mathrm{3y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\mathrm{0} \\ $$$$ \\ $$

Question Number 173976 Answers: 1 Comments: 0

B(a,b)=∫_0 ^1 x^(a−1) (1−x)^(b−1) dx Γ(s)= ∫_0 ^∞ t^(s−1) e^(−t) dt Why B(a,b)= ((Γ(a)Γ(b))/(Γ(a+b))) ?

$$ \\ $$$$\:\:\:\:{B}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{a}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{b}−\mathrm{1}} {dx}\: \\ $$$$\:\:\:\:\:\:\:\Gamma\left({s}\right)=\:\int_{\mathrm{0}} ^{\infty} {t}^{{s}−\mathrm{1}} {e}^{−{t}} {dt} \\ $$$$ \\ $$$$\:\:{Why}\:\:\:\:{B}\left({a},{b}\right)=\:\frac{\Gamma\left({a}\right)\Gamma\left({b}\right)}{\Gamma\left({a}+{b}\right)}\:? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

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