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AlgebraQuestion and Answers: Page 253

Question Number 97136 Answers: 0 Comments: 3

Evaluate (3/(1! + 2! + 3!)) + (4/(2! + 3! + 4!)) + ... + ((2001)/(1999! + 2000! + 2001!))

$$\mathrm{Evaluate} \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{1}!\:+\:\mathrm{2}!\:+\:\mathrm{3}!}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{2}!\:+\:\mathrm{3}!\:+\:\mathrm{4}!}\:\:+\:\:...\:+\:\:\frac{\mathrm{2001}}{\mathrm{1999}!\:\:+\:\:\mathrm{2000}!\:\:+\:\:\mathrm{2001}!} \\ $$

Question Number 97135 Answers: 0 Comments: 1

prove that: sin(16x) cot(x)=1+2cos(2x)+2cos(4x)+2cos(6x)+...+2cos(16x)

$${prove}\:{that}: \\ $$$${sin}\left(\mathrm{16}{x}\right)\:{cot}\left({x}\right)=\mathrm{1}+\mathrm{2}{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}\left(\mathrm{4}{x}\right)+\mathrm{2}{cos}\left(\mathrm{6}{x}\right)+...+\mathrm{2}{cos}\left(\mathrm{16}{x}\right) \\ $$

Question Number 97134 Answers: 0 Comments: 0

find the laplace transform of t^(3/2) erf(t)

$${find}\:{the}\:{laplace}\:{transform}\:{of}\:{t}^{\frac{\mathrm{3}}{\mathrm{2}}} {erf}\left({t}\right) \\ $$

Question Number 97114 Answers: 0 Comments: 0

pls find x x^x^x +ln(2x)−1=0

$${pls}\:{find}\:{x} \\ $$$$ \\ $$$${x}^{{x}^{{x}} } +{ln}\left(\mathrm{2}{x}\right)−\mathrm{1}=\mathrm{0} \\ $$

Question Number 97067 Answers: 2 Comments: 1

if p is the natural number then what is the degree of x^(6p+1) +3x^(4p−3) +4x^(8p−10) +8 polynomial?

$$\mathrm{if}\:\mathrm{p}\:\mathrm{is}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{degree}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{6p}+\mathrm{1}} +\mathrm{3x}^{\mathrm{4p}−\mathrm{3}} +\mathrm{4x}^{\mathrm{8p}−\mathrm{10}} +\mathrm{8}\:\:\mathrm{polynomial}? \\ $$

Question Number 97064 Answers: 0 Comments: 1

find the value of (an) in this utility (3xy^2 )^3

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{an}\right)\:\mathrm{in}\:\mathrm{this}\:\mathrm{utility}\:\:\left(\mathrm{3xy}^{\mathrm{2}} \right)^{\mathrm{3}} \\ $$

Question Number 97051 Answers: 2 Comments: 2

what is the perimeter of a regular dodecagon (12 sides) whose area is 24+12(√3) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\: \\ $$$$\mathrm{dodecagon}\:\left(\mathrm{12}\:\mathrm{sides}\right)\:\mathrm{whose}\: \\ $$$$\mathrm{area}\:\mathrm{is}\:\mathrm{24}+\mathrm{12}\sqrt{\mathrm{3}}\:?\: \\ $$

Question Number 97019 Answers: 0 Comments: 1

Question Number 96951 Answers: 1 Comments: 5

prove that 1−(1/2)+(1/3)−(1/4)+(1/5)+...+((−1^(n−1) )/n) is always positive

$${prove}\:{that}\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+...+\frac{−\mathrm{1}^{{n}−\mathrm{1}} }{{n}}\:\:{is}\:{always}\:{positive} \\ $$$$ \\ $$

Question Number 96868 Answers: 0 Comments: 1

Question Number 96839 Answers: 0 Comments: 0

Question Number 96829 Answers: 0 Comments: 1

If 2f(x) + f(1−x) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} .\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 96821 Answers: 3 Comments: 0

{ (((u^2 /v) + (v^2 /u) = 12)),(((1/u) + (1/v) = (1/3))) :} . find u and v ?

$$\begin{cases}{\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{v}}\:+\:\frac{\mathrm{v}^{\mathrm{2}} }{\mathrm{u}}\:=\:\mathrm{12}}\\{\frac{\mathrm{1}}{\mathrm{u}}\:+\:\frac{\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases}\:.\:\mathrm{find}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:? \\ $$

Question Number 96749 Answers: 1 Comments: 0

how we can calclate triple factorial?

$$\mathrm{how}\:\mathrm{we}\:\mathrm{can}\:\mathrm{calclate}\:\mathrm{triple}\:\mathrm{factorial}? \\ $$

Question Number 96715 Answers: 1 Comments: 0

find real solution of equation x^5 +x^4 +1 = 0

$$\mathrm{find}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{5}} +{x}^{\mathrm{4}} +\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 96712 Answers: 1 Comments: 0

Question Number 96650 Answers: 1 Comments: 0

solve 2 ((2y−1))^(1/(3 )) = y^3 +1

$$\mathrm{solve}\:\mathrm{2}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{2y}−\mathrm{1}}\:=\:\mathrm{y}^{\mathrm{3}} +\mathrm{1} \\ $$

Question Number 96584 Answers: 1 Comments: 4

Question Number 96527 Answers: 2 Comments: 1

proof that 1^2 +2^2 +3^2 +....+n^2 =((n(2n+1)(n+1))/6)

$$\mathrm{proof}\:\mathrm{that}\:\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +....+\mathrm{n}^{\mathrm{2}} =\frac{\mathrm{n}\left(\mathrm{2n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$

Question Number 96505 Answers: 2 Comments: 2

((√((8)^(1/(4 )) −(√((√2)+1))))/((√((8)^(1/(4 )) +(√((√2)−1))))−(√((8)^(1/(4 )) −(√((√2)−1)))))) ?

$$\frac{\sqrt{\sqrt[{\mathrm{4}\:\:}]{\mathrm{8}}−\sqrt{\sqrt{\mathrm{2}}+\mathrm{1}}}}{\sqrt{\sqrt[{\mathrm{4}\:\:}]{\mathrm{8}}+\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}}−\sqrt{\sqrt[{\mathrm{4}\:\:}]{\mathrm{8}}−\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}}}\:? \\ $$

Question Number 96460 Answers: 1 Comments: 8

Question Number 96407 Answers: 1 Comments: 4

Question Number 96390 Answers: 1 Comments: 0

Question Number 96340 Answers: 0 Comments: 4

The equations of two circles S_1 and S_2 are given by S_1 : x^2 + y^2 +2x +2y + 1 = 0 S_2 : x^2 + y^2 −4x + 2y +1 = 0. Show that S_1 and S_2 touch each other externally and obtain the equation of the common tangent T at the point of contact.

$$\mathrm{The}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{two}\:\mathrm{circles}\:{S}_{\mathrm{1}} \:\mathrm{and}\:{S}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:{S}_{\mathrm{1}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\mathrm{2}{x}\:+\mathrm{2}{y}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\:\:\:{S}_{\mathrm{2}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{4}{x}\:+\:\mathrm{2}{y}\:+\mathrm{1}\:=\:\mathrm{0}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:{S}_{\mathrm{1}} \:\mathrm{and}\:{S}_{\mathrm{2}} \:\mathrm{touch}\:\mathrm{each}\:\mathrm{other}\:\mathrm{externally}\:\mathrm{and}\:\mathrm{obtain} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{tangent}\:{T}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{contact}. \\ $$

Question Number 96329 Answers: 0 Comments: 2

x⌊x⌊x⌊x⌋⌋⌋=88 x>0

$${x}\lfloor{x}\lfloor{x}\lfloor{x}\rfloor\rfloor\rfloor=\mathrm{88} \\ $$$${x}>\mathrm{0} \\ $$

Question Number 96321 Answers: 1 Comments: 1

It is given that x^2 =2^x . Find x.

$${It}\:{is}\:{given}\:{that}\:{x}^{\mathrm{2}} =\mathrm{2}^{{x}} .\:{Find}\:{x}. \\ $$

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