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AlgebraQuestion and Answers: Page 263

Question Number 99803 Answers: 2 Comments: 0

Π_(k=1) ^∞ (1+(1/k^2 ))=? helpe me

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\right)=? \\ $$$$\mathrm{helpe}\:\mathrm{me} \\ $$

Question Number 99796 Answers: 1 Comments: 0

Question Number 99789 Answers: 0 Comments: 2

{ ((2^x .3^y = 6)),((3^x .4^y = 12)) :}

$$\begin{cases}{\mathrm{2}^{{x}} .\mathrm{3}^{{y}} \:=\:\mathrm{6}}\\{\mathrm{3}^{{x}} .\mathrm{4}^{{y}} \:=\:\mathrm{12}}\end{cases} \\ $$

Question Number 99744 Answers: 1 Comments: 0

A wire that is highly insulated has a radius of 2.1 mm and a current of 6 Agoes through it. The material used in insulation has thickness of 2.1 mm with a thermal conductivity of 0.2 W/Km. the material used in constructing the wire has a resistivity of 4.2 × 10^(−7) Ωm. assume the the materials reach steady state. Find the difference in temperature between the outer suface and inner surface.

$$\mathrm{A}\:\mathrm{wire}\:\mathrm{that}\:\mathrm{is}\:\mathrm{highly}\:\mathrm{insulated}\:\mathrm{has}\:\mathrm{a}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current} \\ $$$$\mathrm{of}\:\mathrm{6}\:\mathrm{Agoes}\:\mathrm{through}\:\mathrm{it}.\:\mathrm{The}\:\mathrm{material}\:\mathrm{used}\:\mathrm{in}\:\mathrm{insulation}\:\mathrm{has}\:\mathrm{thickness} \\ $$$$\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{with}\:\mathrm{a}\:\mathrm{thermal}\:\mathrm{conductivity}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{W}/\mathrm{Km}.\:\mathrm{the}\:\mathrm{material}\:\mathrm{used} \\ $$$$\mathrm{in}\:\mathrm{constructing}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{a}\:\mathrm{resistivity}\:\mathrm{of}\:\mathrm{4}.\mathrm{2}\:×\:\mathrm{10}^{−\mathrm{7}} \Omega\mathrm{m}.\:\mathrm{assume}\:\mathrm{the}\: \\ $$$$\mathrm{the}\:\mathrm{materials}\:\mathrm{reach}\:\mathrm{steady}\:\mathrm{state}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{in}\:\mathrm{temperature} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{outer}\:\mathrm{suface}\:\mathrm{and}\:\mathrm{inner}\:\mathrm{surface}. \\ $$

Question Number 99737 Answers: 0 Comments: 0

((3−9x^2 )/(5−25x^2 )) = ((5−125x^3 )/(1−x^2 ))

$$\frac{\mathrm{3}−\mathrm{9x}^{\mathrm{2}} }{\mathrm{5}−\mathrm{25x}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}−\mathrm{125x}^{\mathrm{3}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 99698 Answers: 0 Comments: 2

Question Number 99655 Answers: 1 Comments: 1

Question Number 99645 Answers: 1 Comments: 1

If x,y > 0 then ∣(√(xy))−((x+y)/2)∣ + ∣((x+y)/2) + (√(xy)) ∣ =

$${If}\:{x},{y}\:>\:\mathrm{0}\:{then}\:\mid\sqrt{{xy}}−\frac{{x}+{y}}{\mathrm{2}}\mid\:+\:\mid\frac{{x}+{y}}{\mathrm{2}}\:+\:\sqrt{{xy}}\:\mid\:= \\ $$

Question Number 99621 Answers: 2 Comments: 1

6^x =x^(5 ) x=? help me

$$\mathrm{6}^{\mathrm{x}} =\mathrm{x}^{\mathrm{5}\:\:\:\:\:\:\:} \mathrm{x}=?\:\:\:\:\:\:\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 99575 Answers: 2 Comments: 0

if a,b,c,d,e are in AP. find the value of a−4b+6c−4d+e. please help, i do not know where to begin.

$$\mathrm{if}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{a}−\mathrm{4b}+\mathrm{6c}−\mathrm{4d}+\mathrm{e}. \\ $$$$\mathrm{please}\:\mathrm{help},\:\mathrm{i}\:\mathrm{do}\:\mathrm{not}\:\mathrm{know}\:\mathrm{where}\:\mathrm{to} \\ $$$$\mathrm{begin}. \\ $$

Question Number 99486 Answers: 0 Comments: 0

∫(√(sinx))

$$\int\sqrt{{sinx}} \\ $$

Question Number 99430 Answers: 1 Comments: 0

Question Number 99319 Answers: 1 Comments: 0

solve (x^2 −(1/x^2 ))−11(x−(1/x))=14

$${solve} \\ $$$$\left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)−\mathrm{11}\left({x}−\frac{\mathrm{1}}{{x}}\right)=\mathrm{14} \\ $$

Question Number 99257 Answers: 2 Comments: 0

Question Number 99256 Answers: 1 Comments: 0

(√2)^((√2)^((√2)^((√2) .....) ) ) =? help me

$$\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:.....} } } =?\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 99218 Answers: 0 Comments: 3

Question Number 99175 Answers: 2 Comments: 0

A man and a woman have 3 boys and 3 girls. (i) in how many ways will they sit in a row such that the 3 boys and 3 girls are inbetween the man and woman. (ii) Say the man decides of the 3 boys and 3 girls he has 2 of the kids should help him out in a project, in how many ways can this be done, if heyoungest boy and oldest girl can′t join.

$$\:\:\mathrm{A}\:\mathrm{man}\:\mathrm{and}\:\mathrm{a}\:\mathrm{woman}\:\mathrm{have}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}.\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{will}\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{the}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{are}\:\mathrm{inbetween}\:\mathrm{the}\:\mathrm{man}\:\mathrm{and}\:\mathrm{woman}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Say}\:\mathrm{the}\:\mathrm{man}\:\mathrm{decides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{he}\:\mathrm{has}\:\mathrm{2}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{kids}\:\mathrm{should}\:\mathrm{help}\:\mathrm{him}\:\mathrm{out}\:\mathrm{in}\:\mathrm{a}\:\mathrm{project}, \\ $$$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done},\:\mathrm{if}\:\mathrm{heyoungest}\:\mathrm{boy}\:\mathrm{and}\:\mathrm{oldest} \\ $$$$\mathrm{girl}\:\mathrm{can}'\mathrm{t}\:\mathrm{join}. \\ $$

Question Number 99171 Answers: 0 Comments: 3

Question Number 99117 Answers: 1 Comments: 0

let a,b,c ∈R determine the minimum value ((3a)/(b+c))+((4b)/(a+c))+((5c)/(a+b))

$${let}\:{a},{b},{c}\:\in\mathbb{R}\:{determine}\:{the}\:{minimum} \\ $$$${value} \\ $$$$ \\ $$$$\frac{\mathrm{3}{a}}{{b}+{c}}+\frac{\mathrm{4}{b}}{{a}+{c}}+\frac{\mathrm{5}{c}}{{a}+{b}} \\ $$

Question Number 99094 Answers: 1 Comments: 0

find ((9+9((9+9((9+9((9+...))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) − (√(8−(√(8−(√(8+(√(8−(√(8−(√(8−(√(8−(√)))))))...))))))))

$$\mathrm{find}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+...}}}}− \\ $$$$\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}+\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{}}}}...}}}}\: \\ $$

Question Number 99089 Answers: 1 Comments: 0

((9+((9+((9+((9+...))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) −(√(8−(√(8−(√(8−(√(8−...))))))))

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+...}}}}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−...}}}} \\ $$

Question Number 99045 Answers: 1 Comments: 0

{ ((x^2 +y^2 = 10)),((x^2 −5xy+6y^2 = 0)) :} find x &y

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{10}}\\{\mathrm{x}^{\mathrm{2}} −\mathrm{5xy}+\mathrm{6y}^{\mathrm{2}} \:=\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\mathrm{y}\: \\ $$

Question Number 99005 Answers: 2 Comments: 0

Σ_(m = 1) ^∞ Σ_(n = 1) ^∞ (1/(mn(m+n))) ?

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

Question Number 98983 Answers: 0 Comments: 2

let a,b,c be positive real numbers such that ab+bc+ac=3 prove the inquality ((a(b^2 +c^2 ))/(a^2 +bc))+((b(c^2 +a^2 ))/(b^2 +ac))+((c(b^2 +a^2 ))/(c^2 +ab))≥3

$${let}\:{a},{b},{c}\:{be}\:{positive}\:{real}\:{numbers}\:{such} \\ $$$${that}\:{ab}+{bc}+{ac}=\mathrm{3}\: \\ $$$${prove}\:{the}\:{inquality} \\ $$$$ \\ $$$$\frac{{a}\left({b}^{\mathrm{2}} +{c}^{\mathrm{2}} \right)}{{a}^{\mathrm{2}} +{bc}}+\frac{{b}\left({c}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{{b}^{\mathrm{2}} +{ac}}+\frac{{c}\left({b}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{{c}^{\mathrm{2}} +{ab}}\geqslant\mathrm{3} \\ $$

Question Number 98925 Answers: 1 Comments: 1

If the curve shown below has the equation, y=(x−p)(x^3 −bx−c) then find q/p in terms of b and c.

$${If}\:{the}\:{curve}\:{shown}\:{below}\:{has}\:{the}\: \\ $$$${equation},\:\:{y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}} −{bx}−{c}\right) \\ $$$${then}\:{find}\:\:{q}/{p}\:\:{in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$

Question Number 98914 Answers: 3 Comments: 2

2x+3y=5 (x^2 +y^2 )_(min) =?

$$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{5} \\ $$$$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \underset{{min}} {\right)}=? \\ $$

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