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Question Number 188267    Answers: 2   Comments: 0

Question Number 188268    Answers: 1   Comments: 2

Question Number 188263    Answers: 0   Comments: 0

Question Number 188262    Answers: 1   Comments: 0

solve the equation; {: ((x + y +z = 30(√2))),((x − y − z = 7,5)),((x + y − z = (√(22)))) } x ; y ; z = ?? they form funny positions

$$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{equation}};\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\left.\begin{matrix}{\boldsymbol{{x}}\:+\:\boldsymbol{{y}}\:+\boldsymbol{{z}}\:=\:\:\mathrm{30}\sqrt{\mathrm{2}}}\\{\boldsymbol{{x}}\:−\:\boldsymbol{{y}}\:−\:\boldsymbol{{z}}\:=\:\mathrm{7},\mathrm{5}}\\{\boldsymbol{{x}}\:+\:\boldsymbol{{y}}\:−\:\boldsymbol{{z}}\:=\:\sqrt{\mathrm{22}}}\end{matrix}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}\:;\:\boldsymbol{{y}}\:;\:\boldsymbol{{z}}\:=\:?? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{they}\:{form}\:{funny}\:{positions}\: \\ $$$$ \\ $$

Question Number 188327    Answers: 3   Comments: 0

if the roots of 2x^2 −xn = 2x + m is 5, then find : 4n + m − 5

$${if}\:{the}\:{roots}\:{of}\:\:\mathrm{2}{x}^{\mathrm{2}} \:−{xn}\:=\:\mathrm{2}{x}\:+\:{m}\:\:{is}\:\mathrm{5}, \\ $$$$\:{then}\:{find}\::\:\mathrm{4}{n}\:+\:{m}\:−\:\mathrm{5}\: \\ $$$$\: \\ $$

Question Number 188260    Answers: 0   Comments: 0

ABCD is a rectangle such that ∣AB∣>∣BC∣ and O is the mid−point of DC, if ∣OB∣=0.1m and ∠BOC =𝛉, find an expression for the perimeter of the rectangle in terms of 𝛉. Find also, the values of R and 𝛃 for which the perimeter is Rcos(𝛉−𝛃). Deduce, the greatest possible value oc the perimeter.

$$\boldsymbol{{ABCD}}\:{is}\:{a}\:{rectangle}\:{such}\:{that} \\ $$$$\:\mid\boldsymbol{{AB}}\mid>\mid\boldsymbol{{BC}}\mid\:{and}\:{O}\:{is}\:{the}\:{mid}−{point} \\ $$$$\:{of}\:\boldsymbol{{DC}},\:{if}\:\mid\boldsymbol{{OB}}\mid=\mathrm{0}.\mathrm{1}{m}\:{and}\:\angle\boldsymbol{{BOC}}\:=\boldsymbol{\theta}, \\ $$$$\:{find}\:{an}\:{expression}\:{for}\:{the}\:{perimeter}\:{of} \\ $$$$\:{the}\:{rectangle}\:{in}\:{terms}\:{of}\:\boldsymbol{\theta}.\:{Find}\:{also},\: \\ $$$${the}\:{values}\:{of}\:\boldsymbol{{R}}\:{and}\:\boldsymbol{\beta}\:{for}\:{which}\:{the}\: \\ $$$${perimeter}\:{is}\:\boldsymbol{{Rcos}}\left(\boldsymbol{\theta}−\boldsymbol{\beta}\right).\:{Deduce},\:{the}\: \\ $$$${greatest}\:{possible}\:{value}\:{oc}\:{the}\:{perimeter}. \\ $$

Question Number 188259    Answers: 1   Comments: 0

Question Number 188258    Answers: 0   Comments: 0

Solve y=x(y′)^2 −(1/(y′))

$${Solve}\: \\ $$$${y}={x}\left({y}'\right)^{\mathrm{2}} −\frac{\mathrm{1}}{{y}'} \\ $$$$ \\ $$

Question Number 188251    Answers: 0   Comments: 0

Question Number 188250    Answers: 1   Comments: 0

Question Number 188248    Answers: 0   Comments: 0

(x^3 −y−3x)[(x^3 −3x)^2 −y^2 ]=200 (x^3 +y−3x)[(x^3 −3x)^2 +y^2 ]=600 solved in R

$$\left({x}^{\mathrm{3}} −{y}−\mathrm{3}{x}\right)\left[\left({x}^{\mathrm{3}} −\mathrm{3}{x}\right)^{\mathrm{2}} −{y}^{\mathrm{2}} \right]=\mathrm{200} \\ $$$$\left({x}^{\mathrm{3}} +{y}−\mathrm{3}{x}\right)\left[\left({x}^{\mathrm{3}} −\mathrm{3}{x}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} \right]=\mathrm{600} \\ $$$${solved}\:{in}\:{R} \\ $$

Question Number 188247    Answers: 1   Comments: 0

Prove that (1) 5555^(2222) +2222^(5555) divisible by 7 (2) 3^(105) +4^(105) divisible by 7

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{5555}^{\mathrm{2222}} +\mathrm{2222}^{\mathrm{5555}} \:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{3}^{\mathrm{105}} +\mathrm{4}^{\mathrm{105}} \:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7}\: \\ $$

Question Number 188239    Answers: 3   Comments: 0

The perimeter of a triangle is 16 units. How many triangles with integer sides can be made?

$$ \\ $$The perimeter of a triangle is 16 units. How many triangles with integer sides can be made?

Question Number 188226    Answers: 1   Comments: 0

If Ω = Σ_(cyc) ((sin(A − (π/6)))/(cos(B − (π/6))cos(C − (π/6)))) in △ABC Solve for real numbers: x^4 − 4Ωx^3 + 6Ωx^2 − 4Ωx + 1 = 0

$$\mathrm{If}\:\:\:\Omega\:=\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{sin}\left(\mathrm{A}\:−\:\frac{\pi}{\mathrm{6}}\right)}{\mathrm{cos}\left(\mathrm{B}\:−\:\frac{\pi}{\mathrm{6}}\right)\mathrm{cos}\left(\mathrm{C}\:−\:\frac{\pi}{\mathrm{6}}\right)}\:\:\:\mathrm{in}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{4}} \:−\:\mathrm{4}\Omega\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{6}\Omega\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\Omega\mathrm{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 188224    Answers: 1   Comments: 0

If Ω = Σ_(n=1) ^∞ (Π_(k=2) ^∞ ((k^3 − 1)/(k^3 + 1)))^n Solve for complex numbees: z^4 + 3z^3 + Ωz^2 + 3z + 1 = 0

$$\mathrm{If}\:\:\:\Omega\:=\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\underset{\boldsymbol{\mathrm{k}}=\mathrm{2}} {\overset{\infty} {\prod}}\:\frac{\mathrm{k}^{\mathrm{3}} \:−\:\mathrm{1}}{\mathrm{k}^{\mathrm{3}} \:+\:\mathrm{1}}\right)^{\boldsymbol{\mathrm{n}}} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{complex}\:\mathrm{numbees}: \\ $$$$\mathrm{z}^{\mathrm{4}} \:+\:\mathrm{3z}^{\mathrm{3}} \:+\:\Omega\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{3z}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 188219    Answers: 1   Comments: 0

Question Number 188218    Answers: 1   Comments: 0

Question Number 188209    Answers: 1   Comments: 0

Question Number 188208    Answers: 2   Comments: 0

Question Number 188207    Answers: 0   Comments: 0

Question Number 188203    Answers: 1   Comments: 0

Question Number 188196    Answers: 3   Comments: 2

(1)solve Diopthantine equation 754x+221y=13 (2) find the number abcd such that 4×(abcd)=dcba

$$\left(\mathrm{1}\right)\mathrm{solve}\:\mathrm{Diopthantine}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\mathrm{754x}+\mathrm{221y}=\mathrm{13} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{abcd}\: \\ $$$$\:\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{4}×\left(\mathrm{abcd}\right)=\mathrm{dcba} \\ $$

Question Number 188195    Answers: 0   Comments: 0

Question Number 188192    Answers: 2   Comments: 0

prove that ∫_0 ^∞ e^(−a^2 x^2 ) cos(2bx) dx = ((√π)/(2a))e^(−b^2 /a^2 )

$$\:\:\: \\ $$$$\:\:\:\:{prove}\:{that} \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {e}^{−{a}^{\mathrm{2}} {x}^{\mathrm{2}} } \mathrm{cos}\left(\mathrm{2}{bx}\right)\:{dx}\:\:\:=\:\:\:\frac{\sqrt{\pi}}{\mathrm{2}{a}}{e}^{−{b}^{\mathrm{2}} /{a}^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$

Question Number 188181    Answers: 0   Comments: 0

Question Number 188177    Answers: 2   Comments: 2

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