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Question Number 157175 Answers: 2 Comments: 1

Question Number 157171 Answers: 1 Comments: 0

calculate lim_(n→+∞) (((n+ln(n)+1)/((5+(√n))^2 )))

$${calculate}\:\underset{{n}\rightarrow+\infty} {{lim}}\left(\frac{{n}+{ln}\left({n}\right)+\mathrm{1}}{\left(\mathrm{5}+\sqrt{{n}}\right)^{\mathrm{2}} }\right) \\ $$

Question Number 157169 Answers: 1 Comments: 0

Question Number 157168 Answers: 1 Comments: 0

x , y and z are numbers. Show that max(x, y)=((x+y+∣x−y∣)/2) and min(x,y)=((x+y−∣x−y∣)/2) then find a formula for max(x,y,z).

$${x}\:,\:{y}\:{and}\:{z}\:{are}\:{numbers}. \\ $$$${Show}\:{that}\:{max}\left({x},\:{y}\right)=\frac{{x}+{y}+\mid{x}−{y}\mid}{\mathrm{2}}\:{and}\:{min}\left({x},{y}\right)=\frac{{x}+{y}−\mid{x}−{y}\mid}{\mathrm{2}} \\ $$$${then}\:{find}\:{a}\:{formula}\:{for}\: \\ $$$${max}\left({x},{y},{z}\right). \\ $$

Question Number 157156 Answers: 1 Comments: 0

{ ((a_1 =((√3)/2))),((a_(n+1) =4a_n ^3 −3a_n ; ∀n≥1)) :} a_n =?

$$ \\ $$$$\:\begin{cases}{{a}_{\mathrm{1}} =\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\\{{a}_{{n}+\mathrm{1}} =\mathrm{4}{a}_{{n}} ^{\mathrm{3}} −\mathrm{3}{a}_{{n}} \:;\:\forall{n}\geqslant\mathrm{1}}\end{cases} \\ $$$$\:{a}_{{n}} =? \\ $$

Question Number 157163 Answers: 1 Comments: 1

Find the positive integer solution of the equation: x^3 + y^3 = 7∙(14xy + 3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{solution} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{7}\centerdot\left(\mathrm{14xy}\:+\:\mathrm{3}\right) \\ $$

Question Number 157150 Answers: 0 Comments: 0

Question Number 157209 Answers: 2 Comments: 2

Question Number 157207 Answers: 0 Comments: 1

sin lnxdx

$$\mathrm{sin}\:\mathrm{ln}{xdx} \\ $$

Question Number 157141 Answers: 1 Comments: 1

{ (((d^2 y/dx^2 )−2 (dy/dx)+y =3e^(4x) )),((y(0)=−(2/3) ; (dy/dx)∣_(x=0) = ((13)/3))) :}

$$\:\begin{cases}{\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{2}\:\frac{{dy}}{{dx}}+{y}\:=\mathrm{3}{e}^{\mathrm{4}{x}} }\\{{y}\left(\mathrm{0}\right)=−\frac{\mathrm{2}}{\mathrm{3}}\:;\:\frac{{dy}}{{dx}}\mid_{{x}=\mathrm{0}} =\:\frac{\mathrm{13}}{\mathrm{3}}}\end{cases}\: \\ $$

Question Number 157139 Answers: 1 Comments: 1

The figure given below is the section of the reinforced concrete short column. Calculate the stress in the concrete and the stress in the steel,if the axial load of 780KN is applied to the column. Young′s modulus of steel=210KN/mm^2 Young′s modulus of concrete=14KN/mm^2 diameter of the steel bars=20mm

$${The}\:{figure}\:{given}\:{below}\:{is}\:{the}\:{section} \\ $$$${of}\:{the}\:{reinforced}\:{concrete}\:{short}\:{column}. \\ $$$${Calculate}\:{the}\:{stress}\:{in}\:{the}\:{concrete} \\ $$$${and}\:{the}\:{stress}\:{in}\:{the}\:{steel},{if}\:{the} \\ $$$${axial}\:{load}\:{of}\:\mathrm{780}{KN}\:{is}\:{applied}\:{to} \\ $$$${the}\:{column}. \\ $$$$ \\ $$$${Young}'{s}\:{modulus}\:{of}\:{steel}=\mathrm{210}{KN}/{mm}^{\mathrm{2}} \\ $$$${Young}'{s}\:{modulus}\:{of}\:{concrete}=\mathrm{14}{KN}/{mm}^{\mathrm{2}} \\ $$$${diameter}\:{of}\:{the}\:{steel}\:{bars}=\mathrm{20}{mm} \\ $$

Question Number 157138 Answers: 0 Comments: 4

∫_0 ^1 x^x (1−x)^(1−x) sin(πx)dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)^{\mathrm{1}−\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{sin}}\left(\pi\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 157126 Answers: 0 Comments: 9

how many ways can you exchange 1 dollar using (1,5,10,25,50) cents example 1 dollar(100 cents)=2×50cents =1×50+2×25=4×25 =1×50+1×25+1×10+1×5+10×1 and so on how many all the ways ?

$${how}\:{many}\:{ways}\:{can}\:{you} \\ $$$${exchange}\:\mathrm{1}\:{dollar}\:{using} \\ $$$$\left(\mathrm{1},\mathrm{5},\mathrm{10},\mathrm{25},\mathrm{50}\right)\:{cents} \\ $$$${example} \\ $$$$\mathrm{1}\:{dollar}\left(\mathrm{100}\:{cents}\right)=\mathrm{2}×\mathrm{50}{cents} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{2}×\mathrm{25}=\mathrm{4}×\mathrm{25} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{1}×\mathrm{25}+\mathrm{1}×\mathrm{10}+\mathrm{1}×\mathrm{5}+\mathrm{10}×\mathrm{1} \\ $$$${and}\:{so}\:{on} \\ $$$${how}\:{many}\:{all}\:{the}\:{ways}\:? \\ $$

Question Number 157123 Answers: 0 Comments: 1

lim_(x→0) ((log _(sin x) (cos x))/(log _(sin ((x/2))) (cos (x/2))))=?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{log}\:_{\mathrm{sin}\:{x}} \left(\mathrm{cos}\:{x}\right)}{\mathrm{log}\:_{\mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\right)} \left(\mathrm{cos}\:\frac{{x}}{\mathrm{2}}\right)}=? \\ $$

Question Number 157120 Answers: 2 Comments: 0

Σ_(n=0) ^∞ ((1/((3n+1)(3n+2))))=?

$$\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}\right)=? \\ $$

Question Number 157116 Answers: 1 Comments: 2

max ∧ min of f(x) =(√x) +4(√((1−x)/2))

$$\:{max}\:\wedge\:{min}\:{of}\:{f}\left({x}\right)\:=\sqrt{{x}}\:+\mathrm{4}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{2}}} \\ $$

Question Number 157114 Answers: 0 Comments: 2

Question Number 157198 Answers: 1 Comments: 0

Montrer que l′ensemble Q n′est ni ferme ni ouvert

$$\mathrm{M}{ontrer}\:{que}\:{l}'{ensemble}\:{Q}\:{n}'{est}\:{ni}\:{ferme}\:{ni}\:{ouvert} \\ $$

Question Number 157197 Answers: 1 Comments: 0

Question Number 157196 Answers: 1 Comments: 0

Question Number 157104 Answers: 2 Comments: 0

prove lim_(△x→0) ((e^(△x) −1)/(△x))=1

$${prove}\:\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\bigtriangleup{x}} −\mathrm{1}}{\bigtriangleup{x}}=\mathrm{1} \\ $$

Question Number 157099 Answers: 0 Comments: 2

Question Number 157098 Answers: 1 Comments: 0

n ∈ N^∗ ; n is not a square of any integer. Show that (√n) ∉ Q .

$${n}\:\in\:\mathbb{N}^{\ast} \:;\:{n}\:{is}\:{not}\:{a}\:{square}\:{of}\:{any} \\ $$$${integer}.\:{Show}\:{that}\:\sqrt{{n}}\:\notin\:{Q}\:. \\ $$

Question Number 157096 Answers: 1 Comments: 0

∫_0 ^(π/2) xsin(x)ln(sin(x))dx=?

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{xsin}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)\right)\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 157087 Answers: 0 Comments: 0

Let ABCD be a tetrahedron, G, G' and G" the centers of gravity of faces ABC, ACD and ADB, I and J the midpoints of edges [BC] and [CD]. 1) Show that lines (IJ) and (GG' ) are parallel. 2) Prove that the points G, G' and G" are not aligned. 3) Show that the planes (GG 'G ") and (BCD) are parallel.

$$ \\ $$Let ABCD be a tetrahedron, G, G' and G" the centers of gravity of faces ABC, ACD and ADB, I and J the midpoints of edges [BC] and [CD]. 1) Show that lines (IJ) and (GG' ) are parallel. 2) Prove that the points G, G' and G" are not aligned. 3) Show that the planes (GG 'G ") and (BCD) are parallel.

Question Number 157083 Answers: 0 Comments: 0

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