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Question Number 226003 Answers: 0 Comments: 1

If r^2 +r((√3)−(1/( (√3))))sin θ=(2/3) find A=∫_(π/6) ^( π/2) ((r^2 /2))dθ

$${If}\:\:{r}^{\mathrm{2}} +{r}\left(\sqrt{\mathrm{3}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right)\mathrm{sin}\:\theta=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${find}\:{A}=\int_{\pi/\mathrm{6}} ^{\:\pi/\mathrm{2}} \left(\frac{{r}^{\mathrm{2}} }{\mathrm{2}}\right){d}\theta \\ $$$$\: \\ $$

Question Number 225994 Answers: 0 Comments: 0

Question Number 225993 Answers: 0 Comments: 0

Question Number 225980 Answers: 0 Comments: 0

Question Number 225970 Answers: 0 Comments: 1

2^(100!) ? 2^(100) ![=,<or >]

$$\mathrm{2}^{\mathrm{100}!} \:?\:\mathrm{2}^{\mathrm{100}} !\left[=,<{or}\:>\right] \\ $$

Question Number 225954 Answers: 2 Comments: 0

(√(x−(1/x)))+(√(1−(1/x)))=x

$$\sqrt{{x}−\frac{\mathrm{1}}{{x}}}+\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}={x} \\ $$$$ \\ $$

Question Number 225955 Answers: 0 Comments: 7

can we find the perimeter of an ellipse?

$${can}\:{we}\:{find}\:{the}\:{perimeter} \\ $$$${of}\:{an}\:{ellipse}? \\ $$

Question Number 225941 Answers: 2 Comments: 1

Question Number 225934 Answers: 1 Comments: 0

{ ((⌈ ((8−2x)/3) ⌉ ; x≥ 0)),((⌊ ((3x−1)/4) ⌋ ; x<0)) :}. − −1)+

$$\:\: \begin{cases}{\lceil\:\frac{\mathrm{8}−\mathrm{2}{x}}{\mathrm{3}}\:\rceil\:;\:{x}\geqslant\:\mathrm{0}}\\{\lfloor\:\frac{\mathrm{3}{x}−\mathrm{1}}{\mathrm{4}}\:\rfloor\:;\:{x}<\mathrm{0}}\end{cases}. \\ $$$$\left.\:\: − −\mathrm{1}\right)+\: \\ $$$$ \\ $$

Question Number 225932 Answers: 1 Comments: 0

If, ((by+cz)/(b^2 +c^2 ))=((cz+ax)/(c^2 +a^2 ))=((ax+by)/(a^2 +b^2 )) then prove that, (x/a)=(y/b)=(z/c)

$$\:{If},\:\frac{{by}+{cz}}{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }=\frac{{cz}+{ax}}{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} }=\frac{{ax}+{by}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$$$\:{then}\:{prove}\:{that},\:\frac{{x}}{{a}}=\frac{{y}}{{b}}=\frac{{z}}{{c}} \\ $$

Question Number 225939 Answers: 2 Comments: 0

Question Number 225938 Answers: 6 Comments: 0

Question Number 225904 Answers: 1 Comments: 1

Question Number 225892 Answers: 2 Comments: 0

Question Number 225885 Answers: 3 Comments: 2

Question Number 225856 Answers: 2 Comments: 12

Question Number 225866 Answers: 1 Comments: 0

Question 222520

$${Question}\:\mathrm{222520} \\ $$

Question Number 225861 Answers: 0 Comments: 0

∫_0 ^1 (√((ln^(12) (1−x))/( (√((ln^(12) (1−x))/( (√((ln^(12) (1−x))/( (√((ln^(12) (1−x))/(...))))))))))))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{\:\sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{\:\sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{\:\sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{...}}}}}}}}{dx}=? \\ $$

Question Number 225840 Answers: 1 Comments: 1

Question Number 225837 Answers: 3 Comments: 0

Show that, log(√(7(√(7(√(7(√(7....α)))))))) =1

$${Show}\:{that},\:{log}\sqrt{\mathrm{7}\sqrt{\mathrm{7}\sqrt{\mathrm{7}\sqrt{\mathrm{7}....\alpha}}}}\:=\mathrm{1} \\ $$

Question Number 225832 Answers: 2 Comments: 3

Question Number 225820 Answers: 1 Comments: 1

Question Number 225814 Answers: 1 Comments: 0

∫∣x∣dx

$$\int\mid{x}\mid{dx} \\ $$

Question Number 225810 Answers: 0 Comments: 0

Prove that in any triangle: ((4R)/r) ≥ ((w_a w_b w_c )/(h_a h_b h_c )) ∙ ((1/a) + (1/b))∙((√a) + (√b))^2

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\mathrm{triangle}: \\ $$$$\frac{\mathrm{4R}}{\mathrm{r}}\:\geqslant\:\frac{\mathrm{w}_{\boldsymbol{\mathrm{a}}} \:\mathrm{w}_{\boldsymbol{\mathrm{b}}} \:\mathrm{w}_{\boldsymbol{\mathrm{c}}} }{\mathrm{h}_{\boldsymbol{\mathrm{a}}} \:\mathrm{h}_{\boldsymbol{\mathrm{b}}} \:\mathrm{h}_{\boldsymbol{\mathrm{c}}} }\:\centerdot\:\left(\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\right)\centerdot\left(\sqrt{\mathrm{a}}\:+\:\sqrt{\mathrm{b}}\right)^{\mathrm{2}} \\ $$

Question Number 225776 Answers: 1 Comments: 3

Question Number 225788 Answers: 1 Comments: 25

∫_( (√2)−1) ^( y) (√((2(√2))y−1))dy

$$\int_{\:\sqrt{\mathrm{2}}−\mathrm{1}} ^{\:{y}} \sqrt{\left(\mathrm{2}\sqrt{\mathrm{2}}\right){y}−\mathrm{1}}{dy} \\ $$

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