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Question Number 203605    Answers: 0   Comments: 3

Value of x?

$$\mathrm{Value}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}? \\ $$

Question Number 200249    Answers: 1   Comments: 1

Solve: find the distance of the point P(3,4) from the line y=−2x+3

$$\boldsymbol{{Solve}}:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\left(\mathrm{3},\mathrm{4}\right)\:\boldsymbol{{from}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\boldsymbol{{y}}=−\mathrm{2}\boldsymbol{{x}}+\mathrm{3} \\ $$

Question Number 198749    Answers: 0   Comments: 0

Find area bounded by curve below cx^3 +c^2 +y(y+1)^2 =x^2 y+cx(3y+1)

$${Find}\:{area}\:{bounded}\:{by}\:{curve}\:{below} \\ $$$${cx}^{\mathrm{3}} +{c}^{\mathrm{2}} +{y}\left({y}+\mathrm{1}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} {y}+{cx}\left(\mathrm{3}{y}+\mathrm{1}\right) \\ $$

Question Number 197950    Answers: 0   Comments: 0

Let x,y,z>0 , x+y+z=3 Prove That : (1/( (√(x^2 +2x))))+(1/( (√(z^2 +2z))))+(√3)((1/(y+2))−(y/9))+((((√x)+(√y)+(√z)+24))^(1/3) /( (√3)))≥((17)/(3(√3)))

$${Let}\:{x},{y},{z}>\mathrm{0}\:,\:{x}+{y}+{z}=\mathrm{3}\:{Prove}\:{That}\:: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}}}+\frac{\mathrm{1}}{\:\sqrt{{z}^{\mathrm{2}} +\mathrm{2}{z}}}+\sqrt{\mathrm{3}}\left(\frac{\mathrm{1}}{{y}+\mathrm{2}}−\frac{{y}}{\mathrm{9}}\right)+\frac{\sqrt[{\mathrm{3}}]{\sqrt{{x}}+\sqrt{{y}}+\sqrt{{z}}+\mathrm{24}}}{\:\sqrt{\mathrm{3}}}\geqslant\frac{\mathrm{17}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$

Question Number 197834    Answers: 2   Comments: 0

Question Number 197569    Answers: 0   Comments: 2

Question Number 197128    Answers: 1   Comments: 1

Question Number 196571    Answers: 2   Comments: 0

Question Number 196320    Answers: 1   Comments: 0

If a regular n−polygon can be divided into n identical equilateral triangles then n=6

$$\:\:{If}\:\:{a}\:\:{regular}\:{n}−{polygon}\:{can} \\ $$$$\:{be}\:{divided}\:{into}\:\:{n}\:\:{identical}\:\: \\ $$$${equilateral}\:{triangles}\:{then}\:\:{n}=\mathrm{6} \\ $$

Question Number 196084    Answers: 1   Comments: 0

Question Number 195790    Answers: 1   Comments: 2

a,b,c are positive real numbers and abc =1 prove that (a−1+(1/b))(b−1+(1/c))(c−1+(1/a))≤1

$${a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers}\:{and}\:{abc}\:=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left({a}−\mathrm{1}+\frac{\mathrm{1}}{{b}}\right)\left({b}−\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)\left({c}−\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)\leqslant\mathrm{1} \\ $$

Question Number 195611    Answers: 1   Comments: 0

Question Number 195570    Answers: 1   Comments: 2

Given three Real numbers (x,y,z),such that x^2 +y^2 +z^2 =1 maximize x^4 +y^4 −2z^4 −3(√2)xyz

$$\mathrm{Given}\:\mathrm{three}\:\mathrm{Real}\:\mathrm{numbers}\:\left({x},{y},{z}\right),{such}\:{that} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{1} \\ $$$${maximize} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} −\mathrm{2}{z}^{\mathrm{4}} −\mathrm{3}\sqrt{\mathrm{2}}{xyz} \\ $$

Question Number 195590    Answers: 1   Comments: 0

Question Number 195484    Answers: 1   Comments: 0

Question Number 195470    Answers: 2   Comments: 0

Question Number 195322    Answers: 1   Comments: 0

Question Number 195178    Answers: 2   Comments: 0

Question Number 194985    Answers: 0   Comments: 0

lim_(n→+∞) [((1/n))^n +((2/n))^n +...(((n−1)/n))^n ]=?

$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\left[\left(\frac{\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} +\left(\frac{\mathrm{2}}{\mathrm{n}}\right)^{\mathrm{n}} +...\left(\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} \right]=? \\ $$

Question Number 194967    Answers: 1   Comments: 0

Question Number 194796    Answers: 1   Comments: 0

A 1m^2 rectangle which length is less than 1 is a square. Why?

$${A}\:\mathrm{1}{m}^{\mathrm{2}} \:{rectangle}\:{which}\:{length}\:{is}\: \\ $$$${less}\:{than}\:\mathrm{1}\:{is}\:\:{a}\:{square}.\:{Why}? \\ $$

Question Number 194713    Answers: 0   Comments: 2

Question Number 194464    Answers: 1   Comments: 0

Question Number 194463    Answers: 1   Comments: 0

Question Number 194384    Answers: 0   Comments: 1

Question Number 194201    Answers: 1   Comments: 3

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