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Question Number 98618 Answers: 2 Comments: 0

Question Number 98616 Answers: 2 Comments: 0

Question Number 98607 Answers: 1 Comments: 0

Question Number 98602 Answers: 2 Comments: 6

find integral solution of y^2 = x^3 +1

$$\mathrm{find}\:\mathrm{integral}\:\mathrm{solution} \\ $$$$\mathrm{of}\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{1}\: \\ $$

Question Number 98598 Answers: 0 Comments: 2

let A=(3,4) and B is a variable point on the line ∣x∣=6. if AB^(−) <4, then the number of position of B with integral coordinates is? please help!

$$\boldsymbol{{let}}\:\boldsymbol{{A}}=\left(\mathrm{3},\mathrm{4}\right)\:\boldsymbol{{and}}\:\boldsymbol{{B}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{variable}}\:\boldsymbol{{point}} \\ $$$$\boldsymbol{{on}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\mid\boldsymbol{{x}}\mid=\mathrm{6}.\:\boldsymbol{{if}}\:\overline {\boldsymbol{{AB}}}<\mathrm{4},\:\boldsymbol{{then}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{of}}\:\boldsymbol{{position}}\:\boldsymbol{{of}}\:\boldsymbol{{B}}\:\boldsymbol{{with}}\:\boldsymbol{{integral}} \\ $$$$\boldsymbol{{coordinates}}\:\boldsymbol{{is}}? \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}}! \\ $$

Question Number 98596 Answers: 1 Comments: 2

Question Number 98594 Answers: 1 Comments: 0

Question Number 98589 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((sin(αx^2 ))/(x^2 +4))dx with α real

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left(\alpha\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx}\:\:\mathrm{with}\:\alpha\:\mathrm{real} \\ $$

Question Number 98588 Answers: 0 Comments: 0

calculate ∫_(−∞) ^∞ ((xsin(x))/((x^2 +x+1)^2 ))dx

$$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{xsin}\left(\mathrm{x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 98587 Answers: 1 Comments: 0

calculate ∫_(−∞) ^(+∞) ((cos(αx))/(x^4 +1))dx (α real)

$$\mathrm{calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\alpha\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}}\mathrm{dx}\:\:\left(\alpha\:\mathrm{real}\right) \\ $$

Question Number 98575 Answers: 0 Comments: 6

Calculate the force F needed to punch at 1.46cm diametre hole in a steel plate 1.27cm tjick. tbe ultimate shear stress of the steel is 3.45×10^(8N/m^2 )

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{force}\:\mathrm{F}\:\mathrm{needed}\:\mathrm{to}\:\mathrm{punch}\:\mathrm{at}\:\mathrm{1}.\mathrm{46cm}\:\mathrm{diametre}\:\mathrm{hole}\:\mathrm{in}\:\mathrm{a}\:\mathrm{steel}\:\mathrm{plate}\:\mathrm{1}.\mathrm{27cm}\:\mathrm{tjick}.\:\mathrm{tbe}\:\mathrm{ultimate}\:\mathrm{shear}\:\mathrm{stress}\:\mathrm{of}\:\mathrm{the}\:\mathrm{steel}\:\mathrm{is}\:\mathrm{3}.\mathrm{45}×\mathrm{10}^{\mathrm{8N}/\mathrm{m}^{\mathrm{2}} } \\ $$

Question Number 98570 Answers: 1 Comments: 1

a,b,c>0 prove: (a/(√(a^2 +8bc)))+(b/(√(b^2 +8ac)))+(c/(√(c^2 +8ab)))≥1 help please...

$$\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}>\mathrm{0}\:\:\:\:\:\:\:\boldsymbol{{prove}}: \\ $$$$\frac{\boldsymbol{{a}}}{\sqrt{\boldsymbol{{a}}^{\mathrm{2}} +\mathrm{8}\boldsymbol{{bc}}}}+\frac{\boldsymbol{{b}}}{\sqrt{\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{8}\boldsymbol{{ac}}}}+\frac{\boldsymbol{{c}}}{\sqrt{\boldsymbol{{c}}^{\mathrm{2}} +\mathrm{8}\boldsymbol{{ab}}}}\geqslant\mathrm{1} \\ $$$$\boldsymbol{{help}}\:\boldsymbol{{please}}... \\ $$

Question Number 98568 Answers: 1 Comments: 1

Question Number 98560 Answers: 2 Comments: 1

Question Number 98557 Answers: 0 Comments: 0

a_n =Σ_(k=1 ) ^(n−1) ((sin((((2k−1)π)/(2n))))/(cos^2 ((((k−1)π)/(2n)))cos^2 (((kπ)/(2n))))) find lim_(n→∞) (a_n /n^3 )

$${a}_{{n}} =\underset{{k}=\mathrm{1}\:} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{sin}\left(\frac{\left(\mathrm{2}{k}−\mathrm{1}\right)\pi}{\mathrm{2}{n}}\right)}{{cos}^{\mathrm{2}} \left(\frac{\left({k}−\mathrm{1}\right)\pi}{\mathrm{2}{n}}\right){cos}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}{n}}\right)} \\ $$$$ \\ $$$${find}\:\:\underset{{n}\rightarrow\infty} {{lim}}\frac{{a}_{{n}} }{{n}^{\mathrm{3}} } \\ $$

Question Number 98544 Answers: 1 Comments: 1

Question Number 98539 Answers: 2 Comments: 0

Given the function f(x) = ((ln x)/(x−1)) (a) State the domain D_f of f. (b) Find lim_(x→∞) ((ln x)/(x−1)). State its asymptotes. (c) Draw up a variation table for the curve y = f(x).

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{function} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{ln}\:{x}}{{x}−\mathrm{1}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{State}\:\mathrm{the}\:\mathrm{domain}\:{D}_{{f}} \:\mathrm{of}\:{f}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\:{x}}{{x}−\mathrm{1}}.\:\mathrm{State}\:\mathrm{its}\:\mathrm{asymptotes}. \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Draw}\:\mathrm{up}\:\mathrm{a}\:\mathrm{variation}\:\mathrm{table}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right).\: \\ $$

Question Number 98537 Answers: 1 Comments: 1