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Question Number 160235 Answers: 2 Comments: 0

solve 3^x +3x=10

$${solve}\:\mathrm{3}^{{x}} +\mathrm{3}{x}=\mathrm{10} \\ $$

Question Number 160223 Answers: 0 Comments: 0

Ω:=∫_0 ^( ∞) (( x)/(( e^( x) +e^( −x) )^( 3) )) dx =?

$$ \\ $$$$\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{\left(\:{e}^{\:{x}} \:+{e}^{\:−{x}} \right)^{\:\mathrm{3}} }\:{dx}\:=? \\ $$

Question Number 160219 Answers: 0 Comments: 0

Σ_(k=1) ^n Π_(i=1) ^m (i^2 −k)k^4 how to solving is programming C++

$$\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{{m}} {\prod}}\left(\boldsymbol{{i}}^{\mathrm{2}} −\boldsymbol{{k}}\right)\boldsymbol{{k}}^{\mathrm{4}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{{solving}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{programming}}\:\:\boldsymbol{\mathrm{C}}++ \\ $$

Question Number 160215 Answers: 0 Comments: 0

Question Number 160221 Answers: 1 Comments: 4

Question Number 160204 Answers: 1 Comments: 1

∫_0 ^1 (x/(1−x^3 ))=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{3}} }=? \\ $$

Question Number 160205 Answers: 3 Comments: 0

Question Number 160194 Answers: 1 Comments: 1

∫_0 ^1 (x/(1−x^6 ))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{6}} }\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 160218 Answers: 1 Comments: 0

lim_(x→+∞) ((∫_0 ^x (arctan t)^2 dt)/( (√(1+x^2 ))))=?

$$\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{arctan}\:\mathrm{t}\right)^{\mathrm{2}} \mathrm{dt}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}=? \\ $$

Question Number 160191 Answers: 1 Comments: 0

∫_1 ^( 2) ∫_0 ^( π) y sin(xy) dy dx

$$\int_{\mathrm{1}} ^{\:\mathrm{2}} \:\int_{\mathrm{0}} ^{\:\pi} \:{y}\:{sin}\left({xy}\right)\:{dy}\:{dx} \\ $$

Question Number 160190 Answers: 3 Comments: 0

if a = (4)^(1/3) + (2)^(1/3) + 1 find (3/a) + (3/a^2 ) + (1/a^3 ) = ?

$$\mathrm{if}\:\:\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{4}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:+\:\mathrm{1} \\ $$$$\mathrm{find}\:\:\:\frac{\mathrm{3}}{\mathrm{a}}\:+\:\frac{\mathrm{3}}{\mathrm{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 160188 Answers: 0 Comments: 1

Question Number 160179 Answers: 1 Comments: 2

5^(2(x−2)) (5^(2(x−1)) )^((x+1)) > 125^(x−1)

$$\:\mathrm{5}^{\mathrm{2}\left({x}−\mathrm{2}\right)} \left(\mathrm{5}^{\mathrm{2}\left({x}−\mathrm{1}\right)} \right)^{\left({x}+\mathrm{1}\right)} \:>\:\mathrm{125}^{{x}−\mathrm{1}} \\ $$

Question Number 160171 Answers: 0 Comments: 0

Question Number 160170 Answers: 0 Comments: 0

Question Number 160169 Answers: 0 Comments: 0

Question Number 160168 Answers: 0 Comments: 0

Question Number 160165 Answers: 1 Comments: 1

7+4sin xcos x+(3/2)(cot x+tan x)=0

$$\:\:\mathrm{7}+\mathrm{4sin}\:{x}\mathrm{cos}\:{x}+\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{cot}\:{x}+\mathrm{tan}\:{x}\right)=\mathrm{0}\: \\ $$

Question Number 160163 Answers: 0 Comments: 0

what is the difference between a divergent sequence and a non-converging sequence

$$ \\ $$what is the difference between a divergent sequence and a non-converging sequence

Question Number 160160 Answers: 0 Comments: 0

Σ_(k=1) ^n (1/((2k)!(2n−k)!))=?

$$\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{2}{k}\right)!\left(\mathrm{2}{n}−{k}\right)!}=? \\ $$

Question Number 160159 Answers: 0 Comments: 0

prove that .. ∫_0 ^( ∞) (( x)/(cosh^( 3) (x ))) dx = G − (1/2) ■ G: catalan constant

$$ \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}\:.. \\ $$$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{{cosh}^{\:\mathrm{3}} \:\left({x}\:\right)}\:{dx}\:=\:\mathrm{G}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\blacksquare \\ $$$$\:\:\:\:\:\mathrm{G}:\:\:{catalan}\:{constant} \\ $$$$ \\ $$

Question Number 160142 Answers: 2 Comments: 0

Question Number 160141 Answers: 1 Comments: 0

Find the sum of all triples (x, y, z ; (x<y<z)) such that x, y, z, z−y, y−x, z−x are all prime positive integers. (First sum all the triples individually, then summ all the sums.)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{triples} \\ $$$$\left({x},\:{y},\:{z}\:;\:\left({x}<{y}<{z}\right)\right)\:\mathrm{such}\:\mathrm{that}\:{x},\:{y},\:{z}, \\ $$$${z}−{y},\:{y}−{x},\:{z}−{x}\:\mathrm{are}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{positive} \\ $$$$\mathrm{integers}.\:\left(\mathrm{First}\:\mathrm{sum}\:\mathrm{all}\:\mathrm{the}\:\mathrm{triples}\right. \\ $$$$\left.\mathrm{individually},\:\mathrm{then}\:\mathrm{summ}\:\mathrm{all}\:\mathrm{the}\:\mathrm{sums}.\right) \\ $$

Question Number 160138 Answers: 0 Comments: 2

The nucleus of a certain atom has mass of 3.8×10^(−25 ) and is at rest. The nucleus is radioactive and suddenly eject from its self, a particle of mass 6.6×10^(−27) kg and speed 1.5×10^3 m/s. Find the recoil speed of the nucleus as is left behind.

$$\mathrm{The}\:\mathrm{nucleus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{atom}\:\mathrm{has} \\ $$$$\mathrm{mass}\:\mathrm{of}\:\mathrm{3}.\mathrm{8}×\mathrm{10}^{−\mathrm{25}\:} \mathrm{and}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest}.\:\mathrm{The} \\ $$$$\mathrm{nucleus}\:\mathrm{is}\:\mathrm{radioactive}\:\mathrm{and}\:\mathrm{suddenly} \\ $$$$\mathrm{eject}\:\mathrm{from}\:\mathrm{its}\:\mathrm{self},\:\mathrm{a}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{6}.\mathrm{6}×\mathrm{10}^{−\mathrm{27}} \mathrm{kg}\:\mathrm{and}\:\mathrm{speed}\:\mathrm{1}.\mathrm{5}×\mathrm{10}^{\mathrm{3}} \mathrm{m}/\mathrm{s}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{recoil}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nucleus} \\ $$$$\mathrm{as}\:\mathrm{is}\:\mathrm{left}\:\mathrm{behind}. \\ $$$$ \\ $$

Question Number 160136 Answers: 1 Comments: 0

1+4+((16)/2)+((64)/6)+...+(4^n /(n!))=?

$$\mathrm{1}+\mathrm{4}+\frac{\mathrm{16}}{\mathrm{2}}+\frac{\mathrm{64}}{\mathrm{6}}+...+\frac{\mathrm{4}^{{n}} }{{n}!}=? \\ $$

Question Number 160178 Answers: 1 Comments: 1

lim_(x→π) ((sin (x/2)−1)/(cos (sin x)−1)) =?

$$\:\:\:\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)−\mathrm{1}}\:=? \\ $$

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