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Question Number 212579 Answers: 0 Comments: 0

Have you ever wondered why the sum ofd igits in decimal system is a multiple of 3a nd the sum of digits in decimal system isa multiple of 9 Prove the abovei propertes.

$$\mathrm{Have}\:\mathrm{you}\:\mathrm{ever}\:\mathrm{wondered}\:\mathrm{why}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{ofd} \\ $$$$\mathrm{igits}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{system}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3a} \\ $$$$\mathrm{nd}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{system}\: \\ $$$$\mathrm{isa}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{9}\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{abovei} \\ $$$$\mathrm{propertes}. \\ $$

Question Number 212576 Answers: 0 Comments: 0

If ((x^2 − yz)/(a^2 − bc)) = ((y^2 − zx)/(b^2 − ca)) = ((z^2 − xy)/(c^2 − ab)) then prove that (x/a) = (y/b) = (z/c) .

$$\mathrm{If}\:\frac{{x}^{\mathrm{2}} \:−\:{yz}}{{a}^{\mathrm{2}} \:−\:{bc}}\:=\:\frac{{y}^{\mathrm{2}} \:−\:{zx}}{{b}^{\mathrm{2}} \:−\:{ca}}\:=\:\frac{{z}^{\mathrm{2}} \:−\:{xy}}{{c}^{\mathrm{2}} \:−\:{ab}}\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}}{{a}}\:=\:\frac{{y}}{{b}}\:=\:\frac{{z}}{{c}}\:. \\ $$

Question Number 212573 Answers: 0 Comments: 0

Prove that: ((5m^2 − n)/(n^2 + 3m)) = 1

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\frac{\mathrm{5m}^{\mathrm{2}} \:−\:\mathrm{n}}{\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{3m}}\:=\:\mathrm{1} \\ $$

Question Number 212569 Answers: 0 Comments: 1

Axis of C,P,N then concluat for Area[ OPN] ; ON:tangente au cercle

$$\mathrm{Axis}\:\mathrm{of}\:\mathrm{C},\mathrm{P},\mathrm{N}\:\mathrm{then}\:\mathrm{concluat}\:\mathrm{for} \\ $$$$\mathrm{Area}\left[\:\mathrm{OPN}\right]\:;\:\mathrm{ON}:\mathrm{tangente}\:\mathrm{au}\:\mathrm{cercle} \\ $$

Question Number 212560 Answers: 0 Comments: 0

Exact solution just to this please: 9x^2 (x+1)^3 =3(3x^2 −1)(3x^2 +3x+1)

$${Exact}\:{solution}\:{just}\:{to}\:{this}\:{please}: \\ $$$$\mathrm{9}{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} =\mathrm{3}\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}\right) \\ $$

Question Number 212557 Answers: 1 Comments: 0

Question Number 212556 Answers: 1 Comments: 1

Q:What is the most disgusting mathm proble you have ever done.?

$$\mathrm{Q}:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{most}\:\mathrm{disgusting}\:\mathrm{mathm} \\ $$$$\mathrm{proble}\:\mathrm{you}\:\mathrm{have}\:\mathrm{ever}\:\mathrm{done}.? \\ $$

Question Number 212554 Answers: 0 Comments: 0

lim_(x→∞) x^2 [e^((1+(1/x))^x ) −(1+(1/x))^(ex) ]=?

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

Question Number 212553 Answers: 0 Comments: 0

lim_(n→∞) (((2)^(1/n) −1)/( ((2n+1))^(1/n) ))∣∫_1 ^(1/(2n)) e^(−y^2 ) dy+…+∫^((2n+1)/(2n)) e^(−y^2 ) dy∣=?

$$ \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}}{\:\sqrt[{{n}}]{\mathrm{2}{n}+\mathrm{1}}}\mid\int_{\mathrm{1}} ^{\frac{\mathrm{1}}{\mathrm{2}{n}}} {e}^{−{y}^{\mathrm{2}} } {dy}+\ldots+\int^{\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}} {e}^{−{y}^{\mathrm{2}} } {dy}\mid=? \\ $$$$ \\ $$

Question Number 212552 Answers: 1 Comments: 0

^(Q:) In AB^Δ C : cos(A) +cos(B )+ 2cos(C )= 2 show that : a + b = 2c ■

$$ \\ $$$$\:\overset{\mathrm{Q}:} {\:}\:\mathrm{In}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\::\:\:\:{cos}\left(\mathrm{A}\right)\:+{cos}\left(\mathrm{B}\:\right)+\:\mathrm{2}{cos}\left(\mathrm{C}\:\right)=\:\mathrm{2} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\::\:\:\:{a}\:+\:{b}\:=\:\mathrm{2}{c}\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$ \\ $$

Question Number 212550 Answers: 1 Comments: 0

the following equation has no root . find the relationship between a , b , c : 1: c≤2 2: c >2 3: c >ab 4: c≤ ab eq^n : (√( x+1+b +2(√(x+b)) )) + (√(x+1+a +2(√(x+a)))) = c

$$ \\ $$$$\:\:\:\:{the}\:{following}\:{equation}\:{has} \\ $$$$\:\:\:\:\:{no}\:{root}\:.\:{find}\:{the}\:{relationship} \\ $$$$\:\:\:{between}\:{a}\:,\:{b}\:,\:{c}\:: \\ $$$$\:\:\:\:\mathrm{1}:\:\:{c}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\mathrm{2}:\:{c}\:>\mathrm{2} \\ $$$$\:\:\:\:\mathrm{3}:\:{c}\:>{ab} \\ $$$$\:\:\:\:\mathrm{4}:\:{c}\leqslant\:{ab} \\ $$$$\:\:\:\:{eq}^{{n}} \::\:\:\sqrt{\:{x}+\mathrm{1}+{b}\:+\mathrm{2}\sqrt{{x}+{b}}\:}\:+\:\sqrt{{x}+\mathrm{1}+{a}\:+\mathrm{2}\sqrt{{x}+{a}}}\:=\:{c} \\ $$$$ \\ $$

Question Number 212545 Answers: 1 Comments: 0

llim_(n→∞) Σ_(i=1) ^n ((√(1+(i/n^3 )))−1)=?

$$\underset{{n}\rightarrow\infty} {\mathrm{llim}}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\sqrt{\mathrm{1}+\frac{{i}}{{n}^{\mathrm{3}} }}−\mathrm{1}\right)=? \\ $$

Question Number 212544 Answers: 1 Comments: 0

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

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

Question Number 212541 Answers: 1 Comments: 0

Find: x = ? sin(((88π^2 )/x)) = (1/(cos(3x)))

$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{sin}\left(\frac{\mathrm{88}\pi^{\mathrm{2}} }{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{3x}\right)} \\ $$

Question Number 212533 Answers: 2 Comments: 0

given isoscele triangle with sides 10 and inradius 3. how find base?