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AlgebraQuestion and Answers: Page 307

Question Number 43971    Answers: 1   Comments: 0

Question Number 43902    Answers: 2   Comments: 4

(√(a−b)) + (√(a+b)) = c (√(a−c)) + (√(a+c)) = b Solve for real b, and c ; in terms of real a.

$$\sqrt{{a}−{b}}\:+\:\sqrt{{a}+{b}}\:=\:{c} \\ $$$$\sqrt{{a}−{c}}\:+\:\sqrt{{a}+{c}}\:=\:{b} \\ $$$${Solve}\:{for}\:{real}\:{b},\:{and}\:{c}\:;\:{in}\:{terms}\: \\ $$$${of}\:{real}\:{a}. \\ $$

Question Number 43894    Answers: 0   Comments: 0

∣z∣=∣Arg ((a/b)π)∣=1∧k, n∈Z∧b≠0≤k<n: x^n =z⇒x=e^(((2k+a)/(bm))πi) To prove that, please.

$$\mid{z}\mid=\mid{Arg}\:\left(\frac{{a}}{{b}}\pi\right)\mid=\mathrm{1}\wedge{k},\:{n}\in\mathbb{Z}\wedge{b}\neq\mathrm{0}\leqslant{k}<{n}: \\ $$$${x}^{{n}} ={z}\Rightarrow{x}={e}^{\frac{\mathrm{2}{k}+{a}}{{bm}}\pi{i}} \\ $$$$\mathrm{To}\:\mathrm{prove}\:\mathrm{that},\:\mathrm{please}. \\ $$

Question Number 43804    Answers: 1   Comments: 0

solve for ε s(1−α)=(1−ε)σT^4

$${solve}\:{for}\:\epsilon \\ $$$$ \\ $$$${s}\left(\mathrm{1}−\alpha\right)=\left(\mathrm{1}−\epsilon\right)\sigma{T}^{\mathrm{4}} \\ $$

Question Number 43759    Answers: 2   Comments: 0

Question Number 43757    Answers: 0   Comments: 0

Probably if x^n =Am ((a/b)π), x=e^(((2k+a)/(bn))iπ) about 0<(k∈N∪{0})<(n∈N) and b≠0. p.s. Am (0°)=1, Am (90°)=i etc., and s°=(π/(180))s rad(ians)=(π/(180))s.

$$\mathrm{Probably}\:\mathrm{if}\:{x}^{{n}} ={Am}\:\left(\frac{{a}}{{b}}\pi\right),\:{x}={e}^{\frac{\mathrm{2}{k}+{a}}{{bn}}{i}\pi} \\ $$$$\mathrm{about}\:\mathrm{0}<\left({k}\in\mathbb{N}\cup\left\{\mathrm{0}\right\}\right)<\left({n}\in\mathbb{N}\right)\:\mathrm{and}\:{b}\neq\mathrm{0}. \\ $$$$\mathrm{p}.\mathrm{s}.\:{Am}\:\left(\mathrm{0}°\right)=\mathrm{1},\:{Am}\:\left(\mathrm{90}°\right)={i}\:\mathrm{etc}., \\ $$$$\mathrm{and}\:{s}°=\frac{\pi}{\mathrm{180}}{s}\:\mathrm{rad}\left(\mathrm{ians}\right)=\frac{\pi}{\mathrm{180}}{s}. \\ $$

Question Number 43756    Answers: 1   Comments: 0

x^3 +px+q = 0 If equation has all its roots real, find them.

$$\:\:\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{px}}+\boldsymbol{{q}}\:=\:\mathrm{0} \\ $$$$\boldsymbol{{If}}\:\boldsymbol{{equation}}\:\boldsymbol{{has}}\:\boldsymbol{{all}}\:\boldsymbol{{its}}\:\boldsymbol{{roots}} \\ $$$$\boldsymbol{{real}},\:\boldsymbol{{find}}\:\boldsymbol{{them}}. \\ $$

Question Number 43753    Answers: 0   Comments: 0

Question Number 43716    Answers: 1   Comments: 3

Question Number 43707    Answers: 1   Comments: 3

Simplify: (x + y + z)(x^(−1) + y^(−1) + z^(−1) ) = (x^(−1) y^(−1) z^(−1) )(x + y)(y + z)(z + x)

$$\mathrm{Simplify}:\:\:\: \\ $$$$\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{x}^{−\mathrm{1}} \:+\:\mathrm{y}^{−\mathrm{1}} \:+\:\mathrm{z}^{−\mathrm{1}} \right)\:=\:\left(\mathrm{x}^{−\mathrm{1}} \:\mathrm{y}^{−\mathrm{1}} \:\mathrm{z}^{−\mathrm{1}} \right)\left(\mathrm{x}\:+\:\mathrm{y}\right)\left(\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{z}\:+\:\mathrm{x}\right) \\ $$

Question Number 43706    Answers: 1   Comments: 2

If pqr = 1 Hence evaluate: (1/(1 + e + f^(−1) )) + (1/(1 + f + g^(−1) )) + (1/(1 + g + e^(−1) ))

$$\mathrm{If}\:\:\mathrm{pqr}\:=\:\mathrm{1} \\ $$$$\mathrm{Hence}\:\mathrm{evaluate}:\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{e}\:+\:\mathrm{f}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{f}\:+\:\mathrm{g}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{g}\:+\:\mathrm{e}^{−\mathrm{1}} } \\ $$

Question Number 43705    Answers: 0   Comments: 0

Prove that to each quadratic factor in the denominator of the form ax^2 + bx + c which does not have linear factors, there corresponds to a partial fraction of the form ((Ax + B)/(ax^2 + bx + c)) where A and B are constant.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{to}\:\mathrm{each}\:\mathrm{quadratic}\:\mathrm{factor}\:\mathrm{in}\:\mathrm{the}\:\mathrm{denominator}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\: \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{bx}\:+\:\mathrm{c}\:\:\:\mathrm{which}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{linear}\:\mathrm{factors},\:\mathrm{there}\:\mathrm{corresponds}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{partial}\:\mathrm{fraction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\:\:\:\frac{\mathrm{Ax}\:+\:\mathrm{B}}{\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{bx}\:+\:\mathrm{c}}\:\:\:\mathrm{where}\:\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{constant}. \\ $$

Question Number 43702    Answers: 1   Comments: 0

simplify [((12^(1/5) )/(27^(1/5) ))]^(5/2)

$${simplify}\:\:\:\left[\frac{\mathrm{12}^{\mathrm{1}/\mathrm{5}} }{\mathrm{27}^{\mathrm{1}/\mathrm{5}} }\right]^{\mathrm{5}/\mathrm{2}} \\ $$

Question Number 43665    Answers: 1   Comments: 1

1) if s_(n ) =α^n +β^n +λ^(n ) where α,β,λ are the root of ax^3 +bx^2 +cx+d=0 then show that s_(4 ) =((4abd+4b^2 c−2c)/a^3 )

$$\left.\mathrm{1}\right)\:{if}\:\:{s}_{{n}\:\:} \:=\alpha^{{n}} +\beta^{{n}} +\lambda^{{n}\:} \:{where}\:\alpha,\beta,\lambda \\ $$$${are}\:{the}\:{root}\:{of}\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\:{then}\:\:{show}\:{that}\:{s}_{\mathrm{4}\:} =\frac{\mathrm{4}{abd}+\mathrm{4}{b}^{\mathrm{2}} {c}−\mathrm{2}{c}}{{a}^{\mathrm{3}} } \\ $$

Question Number 43608    Answers: 0   Comments: 3

MJS [ 12/9/18 ] Code − 43569 I solved one of these , where and how do i get the prize ? the google+ page doesn′t really tell. i cannot see where to send my solution and I can′t see any guarantee to keep my copyright LYCON TRIX − Gentlemen , Download Slack app then provide your email , further regime will be operated there we won′t trouble you either , we care for your comfort level I′m the general manager of NS7UC initiave , LYCON TRIX

$$\mathrm{MJS}\:\left[\:\:\mathrm{12}/\mathrm{9}/\mathrm{18}\:\right]\:\mathrm{Code}\:−\:\mathrm{43569}\: \\ $$$$\mathrm{I}\:\mathrm{solved}\:\mathrm{one}\:\mathrm{of}\:\mathrm{these}\:,\:\mathrm{where}\:\mathrm{and}\:\mathrm{how}\:\mathrm{do} \\ $$$$\mathrm{i}\:\mathrm{get}\:\mathrm{the}\:\mathrm{prize}\:?\: \\ $$$$\mathrm{the}\:\mathrm{google}+\:\mathrm{page}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{really}\:\mathrm{tell}. \\ $$$$\mathrm{i}\:\mathrm{cannot}\:\mathrm{see}\:\mathrm{where}\:\mathrm{to}\:\mathrm{send}\:\mathrm{my}\:\mathrm{solution}\: \\ $$$$\mathrm{and}\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{see}\:\mathrm{any}\:\mathrm{guarantee}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{my} \\ $$$$\mathrm{copyright}\: \\ $$$$\mathrm{LYCON}\:\mathrm{TRIX}\:−\: \\ $$$$\mathrm{Gentlemen}\:,\:\mathrm{Download}\:\mathrm{Slack}\:\mathrm{app}\: \\ $$$$\mathrm{then}\:\mathrm{provide}\:\mathrm{your}\:\mathrm{email}\:,\:\mathrm{further}\:\mathrm{regime} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{operated}\:\mathrm{there}\: \\ $$$$\mathrm{we}\:\mathrm{won}'\mathrm{t}\:\mathrm{trouble}\:\mathrm{you}\:\mathrm{either}\:,\:\mathrm{we}\:\mathrm{care}\: \\ $$$$\mathrm{for}\:\mathrm{your}\:\mathrm{comfort}\:\mathrm{level}\: \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{the}\:\mathrm{general}\:\mathrm{manager}\:\mathrm{of}\:\mathrm{NS7UC}\: \\ $$$$\mathrm{initiave}\:,\:\mathrm{LYCON}\:\mathrm{TRIX} \\ $$

Question Number 43574    Answers: 1   Comments: 0

Two cyclists Musa and Amadu left point p at the same time in opposite directions. If their speeds are 8 km/h and12 km/h respectively; i. how will it take them to be 40 km apart? ii. calculate the distance covered by Musa within the time in (i)

$$\mathrm{Two}\:\mathrm{cyclists}\:\mathrm{Musa}\:\mathrm{and}\:\mathrm{Amadu}\:\mathrm{left}\:\mathrm{point}\:\mathrm{p}\:\mathrm{at}\:\mathrm{the}\: \\ $$$$\mathrm{same}\:\mathrm{time}\:\mathrm{in}\:\mathrm{opposite}\:\mathrm{directions}.\:\mathrm{If}\:\mathrm{their}\:\mathrm{speeds}\:\mathrm{are} \\ $$$$\mathrm{8}\:\mathrm{km}/\mathrm{h}\:\mathrm{and12}\:\mathrm{km}/\mathrm{h}\:\mathrm{respectively};\: \\ $$$$\mathrm{i}.\:\mathrm{how}\:\mathrm{will}\:\mathrm{it}\:\mathrm{take}\:\mathrm{them}\:\mathrm{to}\:\mathrm{be}\:\mathrm{40}\:\mathrm{km}\:\mathrm{apart}? \\ $$$$\mathrm{ii}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{covered}\:\mathrm{by}\:\mathrm{Musa}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{time}\:\mathrm{in}\:\left(\mathrm{i}\right) \\ $$

Question Number 43569    Answers: 0   Comments: 1

Please solve these questions − 43496 , 42473 , 42474 , 42472 , 42471 , 42470 , 42469 , 42468 , 42408

$$\mathrm{Please}\:\mathrm{solve}\:\mathrm{these}\:\mathrm{questions}\:−\: \\ $$$$\mathrm{43496}\:,\:\mathrm{42473}\:,\:\mathrm{42474}\:,\:\mathrm{42472}\:,\:\mathrm{42471}\:, \\ $$$$\mathrm{42470}\:,\:\mathrm{42469}\:,\:\mathrm{42468}\:,\:\mathrm{42408}\: \\ $$

Question Number 43549    Answers: 1   Comments: 1

solve x : (5+2(√6))^(x^2 −3) +(5−2(√6))^(x^2 −3) =10

$${solve}\:{x}\::\:\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} +\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} =\mathrm{10} \\ $$

Question Number 43544    Answers: 1   Comments: 0

Question Number 43540    Answers: 2   Comments: 0

prove that 111 divide 10^(6n+2) +10^(3n+1) +1

$${prove}\:{that}\:\mathrm{111}\:{divide}\:\mathrm{10}^{\mathrm{6}{n}+\mathrm{2}} \:+\mathrm{10}^{\mathrm{3}{n}+\mathrm{1}} \:+\mathrm{1} \\ $$

Question Number 43514    Answers: 0   Comments: 0

Question Number 43587    Answers: 1   Comments: 0

a and b are the digit in a four digit number 12ab.if 12ab is divisble by 5 and 9 .find the sum of all possible value of a.

$${a}\:{and}\:{b}\:\:{are}\:{the}\:{digit}\:{in}\:{a}\:{four}\:{digit} \\ $$$${number}\:\mathrm{12}{ab}.{if}\:\mathrm{12}{ab}\:{is}\:{divisble}\:{by}\: \\ $$$$\mathrm{5}\:{and}\:\mathrm{9}\:.{find}\:{the}\:{sum}\:{of}\:{all}\:{possible} \\ $$$${value}\:{of}\:\:{a}. \\ $$

Question Number 43496    Answers: 1   Comments: 4

(√(a−(√(a+x)))) + (√(a+(√(a−x)))) =2x Solve for “ x ” in terms of “ a ”

$$\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}\:\:+\:\:\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}\:\:=\mathrm{2x}\: \\ $$$$\mathrm{Solve}\:\mathrm{for}\:``\:\mathrm{x}\:''\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\:``\:\:\mathrm{a}\:\:'' \\ $$$$ \\ $$

Question Number 43488    Answers: 1   Comments: 0

if the root of x^3 +px_ ^2 +qx+30=0 are in the ratio 2:3:5find the value of p and q

$${if}\:{the}\:{root}\:{of}\:\:{x}^{\mathrm{3}} +{px}_{} ^{\mathrm{2}} +{qx}+\mathrm{30}=\mathrm{0}\:{are} \\ $$$${in}\:{the}\:{ratio}\:\mathrm{2}:\mathrm{3}:\mathrm{5}{find}\:{the}\:{value}\:{of}\:{p}\:{and}\:{q} \\ $$

Question Number 43486    Answers: 3   Comments: 1

Question Number 43471    Answers: 1   Comments: 0

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