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AllQuestion and Answers: Page 1407

Question Number 70598 Answers: 1 Comments: 0

If a,b,c ∈ ℜ and (a^2 /(b+c))+(b^2 /(c+a))+(c^2 /(a+b))=((12)/(a+b+c)) , (a/(b+c))+(b/(a+c))+(c/(a+b))=(4/3) then find a+b+c=?

$$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\Re\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}+\mathrm{c}}+\frac{\mathrm{b}^{\mathrm{2}} }{\mathrm{c}+\mathrm{a}}+\frac{\mathrm{c}^{\mathrm{2}} }{\mathrm{a}+\mathrm{b}}=\frac{\mathrm{12}}{\mathrm{a}+\mathrm{b}+\mathrm{c}} \\ $$$$,\:\frac{\mathrm{a}}{\mathrm{b}+\mathrm{c}}+\frac{\mathrm{b}}{\mathrm{a}+\mathrm{c}}+\frac{\mathrm{c}}{\mathrm{a}+\mathrm{b}}=\frac{\mathrm{4}}{\mathrm{3}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{a}+\mathrm{b}+\mathrm{c}=? \\ $$

Question Number 70597 Answers: 4 Comments: 0

solve cos^2 β+cos^2 3β=1

$${solve} \\ $$$$\mathrm{cos}\:^{\mathrm{2}} \beta+\mathrm{cos}\:^{\mathrm{2}} \mathrm{3}\beta=\mathrm{1} \\ $$

Question Number 70596 Answers: 1 Comments: 1

caoculate lim_(x→0) ((cos(sin(x^2 ))−1)/x^2 )

$${caoculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{cos}\left({sin}\left({x}^{\mathrm{2}} \right)\right)−\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$

Question Number 70595 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+1)^3 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 70594 Answers: 1 Comments: 1

calculate by residus method the integral ∫_0 ^∞ (dx/((1+x^2 )^n )) with n integr and n≥1

$${calculate}\:{by}\:{residus}\:{method}\:{the}\:{integral}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} } \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 70592 Answers: 1 Comments: 1

Question Number 70590 Answers: 1 Comments: 1

Question Number 70583 Answers: 1 Comments: 0

Given that y=(4/(√((x^3 +1)))) show that 2(x^3 +1)(dy/dx)=−3x^2 y.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{y}=\frac{\mathrm{4}}{\sqrt{\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)}}\:\mathrm{show}\:\mathrm{that}\:\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{3x}^{\mathrm{2}} \mathrm{y}. \\ $$

Question Number 70587 Answers: 0 Comments: 1

Question Number 70568 Answers: 0 Comments: 1

Question Number 70562 Answers: 0 Comments: 0

Question Number 70571 Answers: 0 Comments: 1

Question Number 70582 Answers: 0 Comments: 1

Given that y=(4/(√((x^3 +1)))) show that 2(x^3 +1)(dy/dx)=−3x^2 y.

Question Number 70543 Answers: 0 Comments: 6

Question Number 70525 Answers: 1 Comments: 0

If x,y,z is a primitive Pythagorean triple,prove that x+y and x−y are congruent modulo 8 to either 1 or 7.

$${If}\:{x},{y},{z}\:{is}\:{a}\:{primitive}\:{Pythagorean} \\ $$$${triple},{prove}\:{that}\:{x}+{y}\:{and}\:{x}−{y}\:{are} \\ $$$${congruent}\:{modulo}\:\mathrm{8}\:{to}\:{either}\:\mathrm{1}\:{or}\:\mathrm{7}. \\ $$

Question Number 70519 Answers: 0 Comments: 3

Question Number 70518 Answers: 2 Comments: 2

If a^3 −b^3 = 513 and ab= 54 then find a−b= ?

$$\mathrm{If}\:\mathrm{a}^{\mathrm{3}} −\mathrm{b}^{\mathrm{3}} =\:\mathrm{513}\:\mathrm{and}\:\mathrm{ab}=\:\mathrm{54}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\mathrm{a}−\mathrm{b}=\:? \\ $$

Question Number 70516 Answers: 1 Comments: 1

Question Number 70513 Answers: 0 Comments: 1

Question Number 70512 Answers: 1 Comments: 1

The faculty of science news paper reports that the combined membership of the mathematics club and science club is 122 students. What is the total membership of the chemistry club?

$$\mathrm{The}\:\mathrm{faculty}\:\mathrm{of}\:\mathrm{science}\:\mathrm{news}\:\mathrm{paper}\:\mathrm{reports}\:\mathrm{that}\:\mathrm{the}\:\mathrm{combined}\:\mathrm{membership}\:\mathrm{of}\:\mathrm{the}\:\:\mathrm{mathematics}\:\mathrm{club}\:\mathrm{and}\:\mathrm{science}\:\:\mathrm{club}\:\mathrm{is}\:\mathrm{122}\:\mathrm{students}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{total}\:\mathrm{membership}\:\mathrm{of}\:\mathrm{the}\:\mathrm{chemistry}\:\mathrm{club}? \\ $$

Question Number 70499 Answers: 0 Comments: 2

Question Number 70497 Answers: 1 Comments: 1

Question Number 70520 Answers: 0 Comments: 0

Question Number 70483 Answers: 1 Comments: 3

∫((ln2x)/(ln4x)).(dx/x)

$$\int\frac{{ln}\mathrm{2}{x}}{{ln}\mathrm{4}{x}}.\frac{{dx}}{{x}} \\ $$

Question Number 70482 Answers: 1 Comments: 2

∫((sin^3 x)/(√(cosx)))dx

$$\int\frac{{sin}^{\mathrm{3}} {x}}{\sqrt{{cosx}}}{dx} \\ $$

Question Number 70473 Answers: 0 Comments: 1

While posting photos of printed material please use app (like camscanner) so that picture will look clean. Also please crop pictures and upload in correct orientation. In built editor support near all maths symbols and constructs. Please go thru tutorial video and you will be able to write basic math like fraction, integral etc in less than 15 mins and you wont need to use pictures except for shapes.

$$ \\ $$$$\mathrm{While}\:\mathrm{posting}\:\mathrm{photos}\:\mathrm{of}\:\mathrm{printed}\:\mathrm{material} \\ $$$$\mathrm{please}\:\mathrm{use}\:\mathrm{app}\:\left(\mathrm{like}\:\mathrm{camscanner}\right)\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{picture}\:\mathrm{will}\:\mathrm{look}\:\mathrm{clean}. \\ $$$$\mathrm{Also}\:\mathrm{please}\:\mathrm{crop}\:\mathrm{pictures}\:\mathrm{and}\:\mathrm{upload} \\ $$$$\mathrm{in}\:\mathrm{correct}\:\mathrm{orientation}. \\ $$$$ \\ $$$$\mathrm{In}\:\mathrm{built}\:\mathrm{editor}\:\mathrm{support}\:\mathrm{near}\:\mathrm{all}\:\mathrm{maths} \\ $$$$\mathrm{symbols}\:\mathrm{and}\:\mathrm{constructs}.\:\mathrm{Please}\:\mathrm{go} \\ $$$$\mathrm{thru}\:\mathrm{tutorial}\:\mathrm{video}\:\mathrm{and}\:\mathrm{you}\:\mathrm{will}\:\mathrm{be}\:\mathrm{able} \\ $$$$\mathrm{to}\:\mathrm{write}\:\mathrm{basic}\:\mathrm{math}\:\mathrm{like}\:\mathrm{fraction},\: \\ $$$$\mathrm{integral}\:\mathrm{etc}\:\mathrm{in}\:\mathrm{less}\:\mathrm{than}\:\mathrm{15}\:\mathrm{mins}\:\mathrm{and} \\ $$$$\mathrm{you}\:\mathrm{wont}\:\mathrm{need}\:\mathrm{to}\:\mathrm{use}\:\mathrm{pictures}\:\mathrm{except} \\ $$$$\mathrm{for}\:\mathrm{shapes}. \\ $$$$ \\ $$

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