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Question Number 150884 Answers: 1 Comments: 0

Question Number 150883 Answers: 1 Comments: 0

prove that any real root 𝛂 of the equation: x^(6n) = 4x^(2n) + 4 ; n∈N-{0} verify: ∣𝛂∣ > (2)^(1/(2n))

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{real}\:\mathrm{root}\:\boldsymbol{\alpha}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}:\:\:\mathrm{x}^{\mathrm{6}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:+\:\mathrm{4}\:;\:\mathrm{n}\in\mathbb{N}-\left\{\mathrm{0}\right\} \\ $$$$\mathrm{verify}:\:\:\mid\boldsymbol{\alpha}\mid\:>\:\sqrt[{\mathrm{2}\boldsymbol{\mathrm{n}}}]{\mathrm{2}} \\ $$

Question Number 150881 Answers: 1 Comments: 0

y = ((a/b))^x ∙ ((b/x))^a ∙ ((x/a))^b ⇒ y^′ = ?

$$\mathrm{y}\:=\:\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{\boldsymbol{\mathrm{x}}} \centerdot\:\left(\frac{\mathrm{b}}{\mathrm{x}}\right)^{\boldsymbol{\mathrm{a}}} \centerdot\:\left(\frac{\mathrm{x}}{\mathrm{a}}\right)^{\boldsymbol{\mathrm{b}}} \:\Rightarrow\:\mathrm{y}\:^{'} \:=\:? \\ $$

Question Number 150880 Answers: 2 Comments: 0

if a;b;c>0 and a+b+c=1 find min((1/a) + (9/b) + ((25)/c)) = ? a)73 b)75 c)105 d)81 e)83

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{min}}\left(\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{9}}{\mathrm{b}}\:+\:\frac{\mathrm{25}}{\mathrm{c}}\right)\:=\:? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{7}\left.\mathrm{3}\left.\:\:\:\mathrm{b}\right)\mathrm{75}\:\:\:\mathrm{c}\right)\mathrm{105}\:\:\:\mathrm{d}\right)\mathrm{81}\:\:\:\mathrm{e}\right)\mathrm{83} \\ $$

Question Number 150876 Answers: 0 Comments: 0

Question Number 150865 Answers: 0 Comments: 0

Im{f'(z)} = 6x(2y-1) and f(0) = 3 - 2i, f(1) = 6 - 5i. Find f(2 + i)

Question Number 150864 Answers: 1 Comments: 0

Question Number 150862 Answers: 0 Comments: 0

Question Number 150861 Answers: 1 Comments: 0

Find the solution of : {_(x^2 +3xy+2y^2 −4 = 0) ^(2x^2 −2xy−3y^2 +7 = 0) Please show your working...

$${Find}\:\:{the}\:\:{solution}\:\:{of}\:\:: \\ $$$$\left\{_{{x}^{\mathrm{2}} +\mathrm{3}{xy}+\mathrm{2}{y}^{\mathrm{2}} −\mathrm{4}\:=\:\mathrm{0}} ^{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} +\mathrm{7}\:=\:\mathrm{0}} \right. \\ $$$${Please}\:\:{show}\:\:{your}\:\:{working}... \\ $$

Question Number 150859 Answers: 0 Comments: 0

Question Number 150853 Answers: 0 Comments: 2

log_(2021) (√(x : (√(x : (√(x :..)))))) = 674 find x=?

$$\mathrm{log}_{\mathrm{2021}} \:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::..}}}\:=\:\mathrm{674} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 150852 Answers: 0 Comments: 0

x;y;z>0 and x^2 +y^2 +z^2 =3 prove that xyz ≤ (((x + y + z - 1)/2))^2 ≤ 1

$$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{xyz}\:\leqslant\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:-\:\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:\leqslant\:\mathrm{1} \\ $$

Question Number 150841 Answers: 2 Comments: 0

∫_( 0) ^( ∞) ((ln(1+a^2 x^2 ))/(1+b^2 x^2 )) dx = ?

$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{b}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$

Question Number 150840 Answers: 1 Comments: 0

∫_( 0) ^( ∞) ((arctan(x))/(x(x^2 +x+1))) dx = ?

$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$

Question Number 150839 Answers: 2 Comments: 0

e^x + y = x^2 y^2 find the expression for (dy/dx)

$$\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{for}\:\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$

Question Number 150838 Answers: 1 Comments: 0

Question Number 150828 Answers: 2 Comments: 0

∫_0 ^( ∞) (( sin^( 2) (x ))/(x(√x))) dx=^? (√π)

$$ \\ $$$$\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{2}} \left({x}\:\right)}{{x}\sqrt{{x}}}\:{dx}\overset{?} {=}\:\sqrt{\pi} \\ $$

Question Number 150827 Answers: 0 Comments: 0

Question Number 150807 Answers: 5 Comments: 0

For matris solution: { ((2x - 3y = 8)),((x + 5y = - 9)) :}

$$\mathrm{For}\:\mathrm{matris}\:\mathrm{solution}: \\ $$$$\begin{cases}{\mathrm{2x}\:-\:\mathrm{3y}\:=\:\mathrm{8}}\\{\mathrm{x}\:+\:\mathrm{5y}\:=\:-\:\mathrm{9}}\end{cases} \\ $$

Question Number 150946 Answers: 0 Comments: 0

Question Number 150944 Answers: 4 Comments: 3

Question Number 150804 Answers: 1 Comments: 0

Question Number 150794 Answers: 0 Comments: 0

Question Number 150793 Answers: 0 Comments: 2

(R−r)^2 + R^2 = (R + r)^2 ⇔ R^2 + r^2 −2rR + R^2 = R^2 + r^2 +2rR ⇒ R^2 = 4rR ⇒ r = (R/4) = 1cm A_S = πr^2 = π×1cm^2 = πcm^2

$$\left({R}−{r}\right)^{\mathrm{2}} \:+\:{R}^{\mathrm{2}} \:=\:\left({R}\:+\:{r}\right)^{\mathrm{2}} \:\Leftrightarrow \\ $$$${R}^{\mathrm{2}} \:+\:{r}^{\mathrm{2}} −\mathrm{2}{rR}\:+\:{R}^{\mathrm{2}} \:=\:{R}^{\mathrm{2}} \:+\:{r}^{\mathrm{2}} \:+\mathrm{2}{rR}\:\Rightarrow \\ $$$${R}^{\mathrm{2}} \:=\:\mathrm{4}{rR}\:\Rightarrow\:{r}\:=\:\frac{{R}}{\mathrm{4}}\:=\:\mathrm{1}{cm} \\ $$$$\mathscr{A}_{{S}} \:=\:\pi{r}^{\mathrm{2}} \:=\:\pi×\mathrm{1}{cm}^{\mathrm{2}} \:=\:\pi{cm}^{\mathrm{2}} \\ $$

Question Number 150789 Answers: 1 Comments: 0

Question Number 150786 Answers: 1 Comments: 0

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