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AlgebraQuestion and Answers: Page 255

Question Number 100330 Answers: 0 Comments: 1

Question Number 100370 Answers: 1 Comments: 2

Find the maximum value of f(x) = (3/(2cosh (ln x) + 3))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\:{f}\left({x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{2cosh}\:\left(\mathrm{ln}\:{x}\right)\:+\:\mathrm{3}} \\ $$

Question Number 100302 Answers: 0 Comments: 2

(√(3^(−(1/2)) +1)) = ((√(a+1))/3^(−(1/4)) ) . find a ?

$$\sqrt{\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{1}}\:=\:\frac{\sqrt{\mathrm{a}+\mathrm{1}}}{\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{4}}} }\:.\:\mathrm{find}\:\mathrm{a}\:? \\ $$

Question Number 100198 Answers: 0 Comments: 1

Question Number 100193 Answers: 1 Comments: 3

(√(7+2(√(7−2(√(7+2(√(7−2(√(7+...)))))))))) ?

$$\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+...}}}}}\:? \\ $$

Question Number 100341 Answers: 1 Comments: 1

An open box with a square base is to be made out of a given quantity of a cardboard of area c^2 square units.show the maximum volume of the box (c^2 /(6(√3))) cubic units

$$\mathrm{An}\:\mathrm{open}\:\mathrm{box}\:\mathrm{with}\:\mathrm{a}\:\mathrm{square} \\ $$$$\mathrm{base}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{made}\:\mathrm{out} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{given}\:\mathrm{quantity}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{cardboard}\:\mathrm{of}\:\mathrm{area}\:\mathrm{c}^{\mathrm{2}} \\ $$$$\mathrm{square}\:\mathrm{units}.\mathrm{show}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{box}\:\frac{\mathrm{c}^{\mathrm{2}} }{\mathrm{6}\sqrt{\mathrm{3}}}\:\:\mathrm{cubic}\:\mathrm{units} \\ $$$$ \\ $$

Question Number 100040 Answers: 0 Comments: 2

Question Number 100002 Answers: 0 Comments: 0

Question Number 99916 Answers: 1 Comments: 0

can anyone recommend a good textbook from which i can learn calculus..^

$$\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{anyone}}\:\boldsymbol{\mathrm{recommend}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{good}}\:\boldsymbol{\mathrm{textbook}} \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{learn}}\:\boldsymbol{\mathrm{calculus}}.\hat {.} \\ $$

Question Number 99900 Answers: 0 Comments: 0

An insulated wire of diameter 1.22 mm carries a steady current of 5.4 A. The insulation material is 1.22 mm thick and has a? coeffiecient of thermal conductivity of 0.23 W/Km. the electrical resistivity of the material of the wire is 5.2 ×10^(−7) Ωm. find the temperature difference between the inner and outer surface of the insulated material when steady state is reached.

$$\mathrm{An}\:\mathrm{insulated}\:\mathrm{wire}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{1}.\mathrm{22}\:\mathrm{mm}\:\mathrm{carries}\:\mathrm{a}\:\mathrm{steady}\:\mathrm{current} \\ $$$$\mathrm{of}\:\mathrm{5}.\mathrm{4}\:\mathrm{A}.\:\mathrm{The}\:\mathrm{insulation}\:\mathrm{material}\:\mathrm{is}\:\mathrm{1}.\mathrm{22}\:\mathrm{mm}\:\mathrm{thick}\:\mathrm{and}\:\mathrm{has}\:\mathrm{a}? \\ $$$$\mathrm{coeffiecient}\:\mathrm{of}\:\mathrm{thermal}\:\mathrm{conductivity}\:\mathrm{of}\:\mathrm{0}.\mathrm{23}\:\mathrm{W}/\mathrm{Km}.\:\mathrm{the}\:\mathrm{electrical} \\ $$$$\mathrm{resistivity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{material}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is}\:\mathrm{5}.\mathrm{2}\:×\mathrm{10}^{−\mathrm{7}} \Omega\mathrm{m}.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{temperature}\:\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{inner}\:\mathrm{and}\:\mathrm{outer}\:\mathrm{surface}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{insulated}\:\mathrm{material}\:\mathrm{when}\:\mathrm{steady}\:\mathrm{state}\:\mathrm{is}\:\mathrm{reached}. \\ $$

Question Number 99877 Answers: 0 Comments: 5

Question Number 99869 Answers: 2 Comments: 0

tng(𝛑/9) + 4sin(𝛑/9) =(√3)

$$\:\boldsymbol{{tng}}\frac{\boldsymbol{\pi}}{\mathrm{9}}\:\:+\:\mathrm{4}\boldsymbol{{sin}}\frac{\boldsymbol{\pi}}{\mathrm{9}}\:=\sqrt{\mathrm{3}} \\ $$

Question Number 99846 Answers: 0 Comments: 1

lim_(n→∞) (1−(1/(2!)))^(((1/(2!))−(1/(3!)))^(.........((1/(n!))−(1/((n+1)!)))) ) =?

$$\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{m}}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\left(\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}\right)^{.........\left(\frac{\mathrm{1}}{\boldsymbol{{n}}!}−\frac{\mathrm{1}}{\left(\boldsymbol{{n}}+\mathrm{1}\right)!}\right)} } =? \\ $$

Question Number 99827 Answers: 0 Comments: 0

How many days after 12/7/1941 (pearl harbour bombed) was 9/11/2001 (the september 11 terrorist attack? please help, i′m having 27175days, which apparently isn′t correct.

$$\mathrm{How}\:\mathrm{many}\:\mathrm{days}\:\mathrm{after}\:\mathrm{12}/\mathrm{7}/\mathrm{1941} \\ $$$$\left(\mathrm{pearl}\:\mathrm{harbour}\:\mathrm{bombed}\right)\:\mathrm{was}\:\mathrm{9}/\mathrm{11}/\mathrm{2001} \\ $$$$\left(\mathrm{the}\:\mathrm{september}\:\mathrm{11}\:\mathrm{terrorist}\:\mathrm{attack}?\right. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help},\:\mathrm{i}'\mathrm{m}\:\mathrm{having}\:\mathrm{27175days},\: \\ $$$$\mathrm{which}\:\mathrm{apparently}\:\mathrm{isn}'\mathrm{t}\:\mathrm{correct}. \\ $$

Question Number 99807 Answers: 3 Comments: 0

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