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AllQuestion and Answers: Page 159

Question Number 199226 Answers: 1 Comments: 0

find ((2 sin 2°+4 sin 4°+...+180 sin 180°)/(90))=? [an unsolved old question #198900]

$${find} \\ $$$$\frac{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}°+\mathrm{4}\:\mathrm{sin}\:\mathrm{4}°+...+\mathrm{180}\:\mathrm{sin}\:\mathrm{180}°}{\mathrm{90}}=? \\ $$$$ \\ $$$$\left[{an}\:{unsolved}\:{old}\:{question}\:#\mathrm{198900}\right] \\ $$

Question Number 199270 Answers: 2 Comments: 4

Question Number 199213 Answers: 1 Comments: 0

Question Number 199215 Answers: 0 Comments: 0

Question Number 199205 Answers: 0 Comments: 0

a_(n+1 ) = a_n + (√(a_n ^2 + 1)) , a_0 = α find a_(n ) = ??

$$\:\:\:\:{a}_{{n}+\mathrm{1}\:} =\:{a}_{{n}} \:+\:\sqrt{{a}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:\:,\:{a}_{\mathrm{0}} \:=\:\alpha \\ $$$$\:\:\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}\:} \:=\:\:?? \\ $$

Question Number 199218 Answers: 0 Comments: 0

in a triangle nmmm5gfkl

$$\mathrm{in}\:\mathrm{a}\:\mathrm{triangle}\: \\ $$$$\mathrm{nmmm5gfkl} \\ $$$$\: \\ $$$$ \\ $$$$ \\ $$

Question Number 199194 Answers: 1 Comments: 0

a_1 ,a_2 ,... a_1 =1 a_(2n) =n∙a_n a_2^(100) = ?

$$\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,... \\ $$$$\mathrm{a}_{\mathrm{1}} =\mathrm{1} \\ $$$$\mathrm{a}_{\mathrm{2n}} =\mathrm{n}\centerdot\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{a}_{\mathrm{2}^{\mathrm{100}} } \:=\:? \\ $$

Question Number 199184 Answers: 0 Comments: 3

Question Number 199183 Answers: 1 Comments: 0

B,O,M - Each is a distinct positive integer If B ∙ O ∙ M = 223 Find: max(B + O + M)=?

$$\mathrm{B},\mathrm{O},\mathrm{M}\:-\:\mathrm{Each}\:\mathrm{is}\:\mathrm{a}\:\mathrm{distinct}\:\mathrm{positive} \\ $$$$\mathrm{integer} \\ $$$$\mathrm{If}\:\:\:\mathrm{B}\:\centerdot\:\mathrm{O}\:\centerdot\:\mathrm{M}\:=\:\mathrm{223} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{max}\left(\mathrm{B}\:+\:\mathrm{O}\:+\:\mathrm{M}\right)=? \\ $$

Question Number 199181 Answers: 0 Comments: 1

Question Number 199177 Answers: 1 Comments: 1

Question Number 199176 Answers: 1 Comments: 0

If f(x) =(x^2 −4x) sin 4x find f^((6)) (x).

$$\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)\:=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4x}\right)\:\mathrm{sin}\:\mathrm{4x}\: \\ $$$$\:\:\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{6}\right)} \left(\mathrm{x}\right).\: \\ $$

Question Number 199175 Answers: 1 Comments: 0

Question Number 199174 Answers: 1 Comments: 0

Question Number 199170 Answers: 2 Comments: 9

n^4 +2n^3 +2n^2 +n+7 = a^2 (a∈N) →n=¿ (n∈N)

$${n}^{\mathrm{4}} +\mathrm{2}{n}^{\mathrm{3}} +\mathrm{2}{n}^{\mathrm{2}} +{n}+\mathrm{7}\:=\:{a}^{\mathrm{2}} \:\left({a}\in{N}\right) \\ $$$$\rightarrow{n}=¿\:\left({n}\in{N}\right) \\ $$

Question Number 199167 Answers: 0 Comments: 0

Give a function f: R→(0;+∞) continous on R and such that f(x+y) = f(x).f(y) a. Prove f(0) = 1 b. Let h(x) = ln[f(x)]. Prove that: h(x+y) = h(x) + h(y) c. Find all the function f such that problem request

$${Give}\:{a}\:{function}\: \\ $$$${f}:\:{R}\rightarrow\left(\mathrm{0};+\infty\right)\:{continous}\:{on}\:{R}\:{and}\:{such}\:{that} \\ $$$${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right).{f}\left({y}\right) \\ $$$${a}.\:{Prove}\:{f}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$$${b}.\:{Let}\:{h}\left({x}\right)\:=\:{ln}\left[{f}\left({x}\right)\right].\:{Prove}\:{that}: \\ $$$$\:{h}\left({x}+{y}\right)\:=\:{h}\left({x}\right)\:+\:{h}\left({y}\right) \\ $$$${c}.\:{Find}\:{all}\:{the}\:{function}\:{f}\:{such}\:{that}\:{problem}\:{request} \\ $$$$\:\:\: \\ $$$$\: \\ $$

Question Number 199187 Answers: 0 Comments: 1

x is a negative real number: If ∣x−2∣=p Find: x−p=?

$$\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{negative}\:\mathrm{real}\:\mathrm{number}: \\ $$$$\mathrm{If}\:\:\mid\mathrm{x}−\mathrm{2}\mid=\mathrm{p} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}−\mathrm{p}=? \\ $$

Question Number 199165 Answers: 1 Comments: 0

Question Number 199164 Answers: 0 Comments: 0

Question Number 199162 Answers: 0 Comments: 0

x=−2(√3)∫y^3 (√(1+(1/y))) dy Find ∫x(y)dy .

$${x}=−\mathrm{2}\sqrt{\mathrm{3}}\int{y}^{\mathrm{3}} \sqrt{\mathrm{1}+\frac{\mathrm{1}}{{y}}}\:{dy} \\ $$$${Find}\:\:\int{x}\left({y}\right){dy}\:\:\:. \\ $$

Question Number 199159 Answers: 1 Comments: 0

((8(x+1)))^(1/4) +(((x+1)/(x−1)))^(1/4) =((5(x^2 +1)^2 −3))^(1/4) x=?

$$\:\sqrt[{\mathrm{4}}]{\mathrm{8}\left(\mathrm{x}+\mathrm{1}\right)}\:+\sqrt[{\mathrm{4}}]{\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}}\:=\sqrt[{\mathrm{4}}]{\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\mathrm{3}}\: \\ $$$$\:\mathrm{x}=? \\ $$

Question Number 199355 Answers: 1 Comments: 0

Question Number 199358 Answers: 3 Comments: 1

Question Number 199362 Answers: 0 Comments: 0

Question Number 199155 Answers: 0 Comments: 1

$$\:\underbrace{ } \\ $$

Question Number 199135 Answers: 7 Comments: 0

a + (1/a) = 3 find: a^5 + (1/a^5 ) = ?

$$\mathrm{a}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:=\:\mathrm{3} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{5}} }\:\:=\:\:? \\ $$

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