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AlgebraQuestion and Answers: Page 2

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 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 225613 Answers: 7 Comments: 0

Question Number 225503 Answers: 2 Comments: 0

find x∈C for r∈R\{0} (−r)^x =r

$${find}\:{x}\in\mathbb{C}\:{for}\:{r}\in\mathbb{R}\backslash\left\{\mathrm{0}\right\} \\ $$$$\left(−{r}\right)^{{x}} ={r} \\ $$

Question Number 225392 Answers: 2 Comments: 1

Question Number 225330 Answers: 1 Comments: 0

if (fogoh)(x)=cos^2 (x+9) then f(x)=? , g(x)=? , h(x)=?

$${if}\:\:\left({fogoh}\right)\left({x}\right)={cos}^{\mathrm{2}} \left({x}+\mathrm{9}\right) \\ $$$${then}\:\:\:{f}\left({x}\right)=?\:,\:\:{g}\left({x}\right)=?\:\:,\:{h}\left({x}\right)=? \\ $$

Question Number 225323 Answers: 1 Comments: 0

Find: (((3 + 2 (5)^(1/4) )/(3 - 2 (5)^(1/4) )))^(1/4) . (((5)^(1/4) - 1)/( (5)^(1/4) + 1)) = ?

$$\mathrm{Find}:\:\:\:\left(\frac{\mathrm{3}\:+\:\mathrm{2}\:\sqrt[{\mathrm{4}}]{\mathrm{5}}}{\mathrm{3}\:-\:\mathrm{2}\:\sqrt[{\mathrm{4}}]{\mathrm{5}}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} .\:\:\:\frac{\sqrt[{\mathrm{4}}]{\mathrm{5}}\:-\:\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{5}}\:+\:\mathrm{1}}\:\:=\:? \\ $$

Question Number 225282 Answers: 2 Comments: 4

Q225146 here if the wedge and the ground had no friction it would start going → what is acc. at time t? μ=kx

$${Q}\mathrm{225146} \\ $$$${here}\:{if}\:{the}\:{wedge}\:{and}\:{the} \\ $$$${ground}\:\:{had}\:{no}\:{friction} \\ $$$${it}\:{would}\:{start}\:{going}\:\rightarrow \\ $$$${what}\:{is}\:{acc}.\:{at}\:{time}\:{t}? \\ $$$$\mu={kx} \\ $$

Question Number 225230 Answers: 1 Comments: 3

tg^4 10°+tg^4 50°+tg^4 70°=?

$$\:\:\:{tg}^{\mathrm{4}} \mathrm{10}°+{tg}^{\mathrm{4}} \mathrm{50}°+{tg}^{\mathrm{4}} \mathrm{70}°=? \\ $$

Question Number 225240 Answers: 1 Comments: 0

Question Number 225239 Answers: 0 Comments: 0

Question Number 225241 Answers: 1 Comments: 0

Question Number 225153 Answers: 0 Comments: 0

Question Number 225152 Answers: 0 Comments: 0

Question Number 225150 Answers: 0 Comments: 0

Question Number 225075 Answers: 2 Comments: 0

Question Number 225098 Answers: 2 Comments: 0

Question Number 225020 Answers: 0 Comments: 1

tgx+tgy+tgz=A tg^3 x+tg^3 y+tg^3 z=?

$$\:\:\:{tgx}+{tgy}+{tgz}={A} \\ $$$$\:\:\:{tg}^{\mathrm{3}} {x}+{tg}^{\mathrm{3}} {y}+{tg}^{\mathrm{3}} {z}=? \\ $$

Question Number 224989 Answers: 1 Comments: 0

Calculate D_n = determinant (((x_1 +a_1 ^2 ),(a_1 a_2 ),…,(a_1 a_n )),((a_2 a_1 ),(x_2 +a_2 ^2 ),…,(a_2 a_n )),(⋮,⋮,⋱,⋮),((a_n a_1 ),(a_n a_2 ),…,(x_n +a_n ^2 )))

$$\mathrm{Calculate} \\ $$$${D}_{{n}} =\begin{vmatrix}{{x}_{\mathrm{1}} +{a}_{\mathrm{1}} ^{\mathrm{2}} }&{{a}_{\mathrm{1}} {a}_{\mathrm{2}} }&{\ldots}&{{a}_{\mathrm{1}} {a}_{{n}} }\\{{a}_{\mathrm{2}} {a}_{\mathrm{1}} }&{{x}_{\mathrm{2}} +{a}_{\mathrm{2}} ^{\mathrm{2}} }&{\ldots}&{{a}_{\mathrm{2}} {a}_{{n}} }\\{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{{a}_{{n}} {a}_{\mathrm{1}} }&{{a}_{{n}} {a}_{\mathrm{2}} }&{\ldots}&{{x}_{{n}} +{a}_{{n}} ^{\mathrm{2}} }\end{vmatrix} \\ $$

Question Number 224888 Answers: 0 Comments: 2

Question Number 224886 Answers: 1 Comments: 0

Find for acute θ, sin θ and cos θ in terms of 0<k<1, if ((sin θ(1−cos θ))/(cos θ(1−sin θ)))=k.

$${Find}\:{for}\:{acute}\:\theta,\:\mathrm{sin}\:\theta\:{and}\:\mathrm{cos}\:\theta \\ $$$${in}\:{terms}\:{of}\:\mathrm{0}<{k}<\mathrm{1}, \\ $$$${if}\:\:\:\:\frac{\mathrm{sin}\:\theta\left(\mathrm{1}−\mathrm{cos}\:\theta\right)}{\mathrm{cos}\:\theta\left(\mathrm{1}−\mathrm{sin}\:\theta\right)}={k}. \\ $$

Question Number 224873 Answers: 0 Comments: 5

Question Number 224872 Answers: 0 Comments: 0

Question Number 224847 Answers: 0 Comments: 0

Question Number 224819 Answers: 2 Comments: 0

Question Number 224770 Answers: 0 Comments: 1

(2x^3 +x−3)^3 =3−x^2

$$\:\:\:\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−\mathrm{3}\right)^{\mathrm{3}} =\mathrm{3}−{x}^{\mathrm{2}} \\ $$

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