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Question Number 76229 Answers: 1 Comments: 0

Let P(x) be polynomial in x with integral coefficients. If n is a solution of P(x)≡0(mod n) , and a≡b(mod n), prove that b is also a solution.

$${Let}\:{P}\left({x}\right)\:{be}\:{polynomial}\:{in}\:{x}\:{with}\:{integral} \\ $$$${coefficients}.\:{If}\:{n}\:{is}\:{a}\:{solution}\:{of}\: \\ $$$${P}\left({x}\right)\equiv\mathrm{0}\left({mod}\:{n}\right)\:,\:{and}\:{a}\equiv{b}\left({mod}\:{n}\right), \\ $$$${prove}\:{that}\:{b}\:{is}\:{also}\:{a}\:{solution}. \\ $$

Question Number 76228 Answers: 1 Comments: 2

prove that 6^n ≡ 6 (mod 10), for any n ∈ Z^( +)

$${prove}\:{that}\:\mathrm{6}^{{n}} \:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{10}\right),\:{for}\:{any}\:{n}\:\in\:{Z}^{\:+} \\ $$

Question Number 76220 Answers: 1 Comments: 1

Question Number 76214 Answers: 3 Comments: 0

x^2 +2x−9+(9/((x+1)^2 ))=0 please

$$\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{9}+\frac{\mathrm{9}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{0} \\ $$$$\mathrm{please} \\ $$

Question Number 76213 Answers: 1 Comments: 0

((1/(64))×5^(−3) )^(−(1/3))

$$\left(\frac{\mathrm{1}}{\mathrm{64}}×\mathrm{5}^{−\mathrm{3}} \right)^{−\frac{\mathrm{1}}{\mathrm{3}}} \\ $$

Question Number 76207 Answers: 4 Comments: 0

if a_1 =1 and a_(n+1) =3a_n +n^2 find a_n =?

$${if}\:{a}_{\mathrm{1}} =\mathrm{1}\:{and}\:{a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +{n}^{\mathrm{2}} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 76200 Answers: 0 Comments: 2

Question Number 76194 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((cos(x^2 ))/(x^4 −x^2 +1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 76193 Answers: 1 Comments: 4

calculate ∫ (x^2 −1)sh(3x)dx

$${calculate}\:\int\:\:\left({x}^{\mathrm{2}} −\mathrm{1}\right){sh}\left(\mathrm{3}{x}\right){dx} \\ $$

Question Number 76192 Answers: 1 Comments: 0

calculate lim_(x→0) ((arctan(sin(2x))−sin(arctan(2x)))/x^2 )

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{arctan}\left({sin}\left(\mathrm{2}{x}\right)\right)−{sin}\left({arctan}\left(\mathrm{2}{x}\right)\right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 76191 Answers: 1 Comments: 0

find lim_(x→0) ((e^x −e^([x]) )/x)

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{e}^{{x}} −{e}^{\left[{x}\right]} }{{x}} \\ $$

Question Number 76190 Answers: 0 Comments: 2

let f(x)=((arctan(1+x))/(2+x)) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie.

$${let}\:{f}\left({x}\right)=\frac{{arctan}\left(\mathrm{1}+{x}\right)}{\mathrm{2}+{x}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 76232 Answers: 2 Comments: 2

how do we find ∫_0 ^(π/2) sinh^(−1) x dx and ∫_0 ^(π/2) cosh^(−1) xdx

$${how}\:{do}\:{we}\:{find} \\ $$$$\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:{sinh}^{−\mathrm{1}} {x}\:{dx}\:{and}\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{cosh}\:^{−\mathrm{1}} {xdx} \\ $$

Question Number 76176 Answers: 0 Comments: 4

Question Number 76171 Answers: 0 Comments: 0

Question Number 76169 Answers: 2 Comments: 0

Question Number 76167 Answers: 3 Comments: 0

Question Number 76245 Answers: 1 Comments: 0

The lines ax+2y+1=0, bx+3y+1=0 and cx+4y+1=0 are concurrent if a, b, c are in G.P. ??

$$\mathrm{The}\:\mathrm{lines}\:{ax}+\mathrm{2}{y}+\mathrm{1}=\mathrm{0},\:{bx}+\mathrm{3}{y}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{and}\:{cx}+\mathrm{4}{y}+\mathrm{1}=\mathrm{0}\:\mathrm{are}\:\mathrm{concurrent} \\ $$$$\mathrm{if}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{G}.\mathrm{P}.\:?? \\ $$

Question Number 76153 Answers: 0 Comments: 0

Question Number 76151 Answers: 0 Comments: 6

lim_(x→∞) x^k e^(−4x) , k>0

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{{k}} {e}^{−\mathrm{4}{x}} ,\:{k}>\mathrm{0} \\ $$

Question Number 76146 Answers: 1 Comments: 5

Question Number 76143 Answers: 2 Comments: 1

Question Number 76127 Answers: 0 Comments: 0

Question Number 76126 Answers: 1 Comments: 9

Question Number 76112 Answers: 1 Comments: 0

If the sides of a triangle are consecutive integers and the maximum angle is twice the minimum, determine the sides of the triangle.

$${If}\:{the}\:{sides}\:{of}\:{a}\:{triangle}\:{are}\:{consecutive} \\ $$$${integers}\:{and}\:{the}\:{maximum}\:{angle} \\ $$$${is}\:{twice}\:{the}\:{minimum},\:{determine} \\ $$$${the}\:{sides}\:{of}\:{the}\:{triangle}. \\ $$

Question Number 76110 Answers: 1 Comments: 0

hello solve in R tanx>(√3) please explain me if possible.

$${hello}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\mathrm{tan}{x}>\sqrt{\mathrm{3}} \\ $$$${please}\:{explain}\:{me}\:{if}\:{possible}. \\ $$

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