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AllQuestion and Answers: Page 69

Question Number 214495 Answers: 0 Comments: 1

Question Number 214485 Answers: 1 Comments: 0

lim_(n→∞) ((1/(2∙4))+(1/(5∙7))+...+(1/((3n−1)(3n+1))))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{7}}+...+\frac{\mathrm{1}}{\left(\mathrm{3}{n}−\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{1}\right)}\right) \\ $$

Question Number 214569 Answers: 2 Comments: 0

Question Number 214568 Answers: 1 Comments: 0

∫((b+ax)/(1+sin x)) dx

$$\int\frac{{b}+{ax}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx} \\ $$

Question Number 214566 Answers: 2 Comments: 0

somebody has posted following question and then deleted it again. { ((u_(n+1) =((4u_n −9)/(u_n −2)))),((u_0 =5)) :} find u_n =? (or something like this)

$${somebody}\:{has}\:{posted}\:{following} \\ $$$${question}\:{and}\:{then}\:{deleted}\:{it}\:{again}. \\ $$$$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{\mathrm{4}{u}_{{n}} −\mathrm{9}}{{u}_{{n}} −\mathrm{2}}}\\{{u}_{\mathrm{0}} =\mathrm{5}}\end{cases} \\ $$$${find}\:{u}_{{n}} =?\:\left({or}\:{something}\:{like}\:{this}\right) \\ $$

Question Number 214483 Answers: 1 Comments: 0

Question Number 214479 Answers: 2 Comments: 0

Question Number 214471 Answers: 1 Comments: 0

d^2 −d+2=0 Σ_(k; d^2 −d+2=0) (1/k)=??

$${d}^{\mathrm{2}} −{d}+\mathrm{2}=\mathrm{0} \\ $$$$\underset{{k};\:{d}^{\mathrm{2}} −{d}+\mathrm{2}=\mathrm{0}} {\sum}\:\frac{\mathrm{1}}{{k}}=?? \\ $$

Question Number 214491 Answers: 0 Comments: 0

Question Number 214457 Answers: 2 Comments: 2

If (((x + 2y + 3z)^2 )/(x^2 + y^2 + z^2 )) = 14 find: ((x + y)/z) = ?

$$\mathrm{If}\:\:\:\frac{\left(\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{3z}\right)^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} }\:=\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\frac{\mathrm{x}\:+\:\mathrm{y}}{\mathrm{z}}\:=\:? \\ $$

Question Number 214456 Answers: 2 Comments: 1

If (x/(a^2 − bc)) = (y/(b^2 − ac)) = (z/(c^2 − ab)) Find: ((ax + by + cz)/(x + y + z)) = ?

$$\mathrm{If}\:\:\:\frac{\mathrm{x}}{\mathrm{a}^{\mathrm{2}} −\:\mathrm{bc}}\:=\:\frac{\mathrm{y}}{\mathrm{b}^{\mathrm{2}} −\:\mathrm{ac}}\:=\:\frac{\mathrm{z}}{\mathrm{c}^{\mathrm{2}} −\:\mathrm{ab}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{ax}\:+\:\mathrm{by}\:+\:\mathrm{cz}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}}\:=\:? \\ $$

Question Number 214455 Answers: 0 Comments: 4

If x+y+z=xyz Find: ((x(1−y^2 )(1−z^2 )+y(1−x^2 )(1−z^2 )+z(1−x^2 )(1−y^2 ))/(2xyz))

$$\mathrm{If}\:\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{xyz} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{z}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{2xyz}} \\ $$

Question Number 214454 Answers: 0 Comments: 1

a,b,c ∈ R^+ S = ((9a)/(b + c)) + ((16b)/(a + c)) + ((49c)/(a + b)) min(S) = ?

$$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{R}^{+} \\ $$$$\mathrm{S}\:\:=\:\:\frac{\mathrm{9a}}{\mathrm{b}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{16b}}{\mathrm{a}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{49c}}{\mathrm{a}\:+\:\mathrm{b}} \\ $$$$\boldsymbol{\mathrm{min}}\left(\mathrm{S}\right)\:=\:? \\ $$

Question Number 214443 Answers: 1 Comments: 0

a,b,c,d,e,f ∈ Q (1/( (√2) − (2)^(1/3) )) = 2^a + 2^b + 2^c + 2^d + 2^e + 2^f find: a,b,c,d,e,f = ?

$$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:\in\:\mathrm{Q} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{2}}}\:=\:\mathrm{2}^{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{c}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{d}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{e}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{f}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:=\:? \\ $$

Question Number 214449 Answers: 2 Comments: 1

Question Number 214448 Answers: 0 Comments: 0

x^− = ((Σf_i x_i )/(Σf_i )) , u^− = ((Σf_i u_i )/(Σf_i )) , u = ((x−a)/h) , proved that x^− = a + hu^−

$$ \\ $$$$\overset{−} {{x}}\:=\:\frac{\Sigma{f}_{{i}} {x}_{{i}} }{\Sigma{f}_{{i}} \:}\:,\:\:\:\overset{−} {{u}}\:=\:\frac{\Sigma{f}_{{i}} {u}_{{i}} }{\Sigma{f}_{{i}} }\:,\:{u}\:=\:\frac{{x}−{a}}{{h}}\:, \\ $$$${proved}\:{that}\:\overset{−} {{x}}\:=\:{a}\:+\:{h}\overset{−} {{u}} \\ $$

Question Number 214447 Answers: 1 Comments: 1

Question Number 214427 Answers: 3 Comments: 1

Question Number 214421 Answers: 1 Comments: 0

Question Number 214419 Answers: 1 Comments: 0

Question Number 214414 Answers: 1 Comments: 0

Given that the roots of the equation ax^2 +bx+c=0 are α and β, show that; λμb^2 =ac(λ+μ)^2 where (α/β)=(λ/μ) Mr Hans

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0}\:\mathrm{are}\:\alpha\:\mathrm{and}\:\beta, \\ $$$$\:\mathrm{show}\:\mathrm{that}; \\ $$$$\lambda\mu\mathrm{b}^{\mathrm{2}} =\mathrm{ac}\left(\lambda+\mu\right)^{\mathrm{2}} \:\mathrm{where}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Mr}\:{Hans} \\ $$

Question Number 214408 Answers: 2 Comments: 0

Question Number 214409 Answers: 3 Comments: 0

Question Number 214402 Answers: 3 Comments: 0

If ((a+b)/c) = ((b+c)/a) = ((a+c)/b) then find ((a+b)/c) .

$$\:\:\:\mathrm{If}\:\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}\:=\:\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}\:=\:\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\:\:\:\:\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}\:. \\ $$

Question Number 214398 Answers: 1 Comments: 1

Question Number 214395 Answers: 1 Comments: 1

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