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Question Number 145003 Answers: 0 Comments: 0

Solve the equation: 2^a 3^b 7^c = c^2 cbb^6 ^(−) ; a;b;c∈P

$S o l v e t h e e q u a t i o n :$ $2^{a} 3^{b} 7^{c} = \overset{―}{c^{2} {c b b}^{6}}; a; b; c \in P$

Question Number 145002 Answers: 0 Comments: 2

Find the last digit of the number: 1^(1989) +2^(1989) +3^(1989) +...+1989^(1989)

$F i n d t h e l a s t d i g i t o f t h e n u m b e r :$ $1^{1989} + 2^{1989} + 3^{1989} + . . . + 1989^{1989}$

Question Number 145000 Answers: 0 Comments: 1

If F(x+1)=F(x−1)=x^2 then F^(−1) (x)=?

$If F (x + 1) = F (x - 1) = x^{2}$ $then F^{- 1} (x) = ?$

Question Number 144998 Answers: 1 Comments: 0

cos^2 1°+cos^2 2°+cos^2 3°+...+cos^2 360° = ?

$\cos^{2} 1 ° + \cos^{2} 2 ° + \cos^{2} 3 ° + . . . + \cos^{2} 360 ° = ?$

Question Number 144997 Answers: 0 Comments: 0

∫_0 ^1 ((ln(1+x)ln(1+x^2 ))/x)dx=(π/2)G−((33)/(32))ζ(3)

$\int_{0}^{1} \frac{\ln (1 + x) \ln (1 + x^{2})}{x} dx = \frac{π}{2} G - \frac{33}{32} ζ (3)$

Question Number 144996 Answers: 0 Comments: 0

Question Number 144995 Answers: 1 Comments: 0

Find the maximum distance between two points on the curve (x^4 /a^4 ) + (y^4 /b^4 ) = 1 .

$Find the maximum distance$ $between two points on the$ $curve \frac{x^{4}}{a^{4}} + \frac{y^{4}}{b^{4}} = 1 .$

Question Number 144989 Answers: 1 Comments: 0

lcm(2a;3a)=lcm(45;100)⇒a=?

$l c m (2 a; 3 a) = l c m (45; 100) \Rightarrow a = ?$

Question Number 144985 Answers: 1 Comments: 0

∫ (((2+(√x)))/((x+1+(√x))^2 )) dx =?

$\int \frac{(2 + \sqrt{x})}{{(x + 1 + \sqrt{x})}^{2}} dx = ?$

Question Number 144981 Answers: 1 Comments: 0

Σ_(k=1) ^(35) ((√k)/(k + (√(k^2 + k)))) = ?

$\underset{k = 1}{\sum^{35}} \frac{\sqrt{k}}{k + \sqrt{k^{2} + k}} = ?$

Question Number 144980 Answers: 1 Comments: 0

exercise Let a and b be natural integers such that 0<a<b. 1. Show that if a divides b, then for any naturel number n, n^a −1 divides n^b −1. 2. For any non−zero naturel number n, prove that the remainder of the euclidean division of n^b −1 by n^a −1 is n^r −1 where r is the remainder of the euclidean division of b by a. 3. For any non−zero naturel number n, show that gcd(n^b −1, n^a −1) = n^d −1 where d = gcd(b,c). by professor henderson^(−) .

$\underset{―}{exercise}$ $Let a and b be natural integers such that 0 < a < b .$ $1 . Show that if a divides b, then for any naturel$ $number n, n^{a} - 1 divides n^{b} - 1 .$ $2 . For any non - zero naturel number n, prove$ $that the remainder of the euclidean division of$ $n^{b} - 1 by n^{a} - 1 is n^{r} - 1 where r is the remainder$ $of the euclidean division of b by a .$ $3 . For any non - zero naturel number n, show$ $that g c d (n^{b} - 1, n^{a} - 1) = n^{d} - 1 where d = g c d (b, c) .$ $\overset{―}{b y p r o f e s s o r h e n d e r s o n} .$

Question Number 144975 Answers: 3 Comments: 0

Question Number 144959 Answers: 2 Comments: 0

Question Number 144961 Answers: 1 Comments: 0

x∈Z^+ 15^(48a+1) ≡ x (mod 17) find x=?

$x \in Z^{+}$ $15^{48 a + 1} \equiv x (m o d 17) f i n d x = ?$

Question Number 144951 Answers: 0 Comments: 1

Let a,b > 0 and a+b+1 = 3ab. Prove that (1) (a^2 /(a+1))+(b^2 /(b+1)) ≥ (a/(a^2 +1))+(b/(b^2 +1)) (2) (a^2 /(b+1))+(b^2 /(a+1)) ≥ (a/(b^2 +1))+(b/(a^2 +1))

$Let a, b > 0 and a + b + 1 = 3 a b . Prove that$ $(1) \frac{a^{2}}{a + 1} + \frac{b^{2}}{b + 1} ⩾ \frac{a}{a^{2} + 1} + \frac{b}{b^{2} + 1}$ $(2) \frac{a^{2}}{b + 1} + \frac{b^{2}}{a + 1} ⩾ \frac{a}{b^{2} + 1} + \frac{b}{a^{2} + 1}$

Question Number 144947 Answers: 1 Comments: 0

Π_(k=1) ^(12) 2∙sin(((πk)/(24))) = ?

$\underset{k = 1}{\prod^{12}} 2 \cdot s i n (\frac{π k}{24}) = ?$

Question Number 144946 Answers: 0 Comments: 0

𝛗 := ∫_( 0) ^( (π/2)) ((( x)/(cot ( x ))) )^( 3) dx=?

$ϕ := \int_{0}^{\frac{π}{2}} {(\frac{x}{\cot (x)})}^{3} dx = ?$

Question Number 144939 Answers: 0 Comments: 0

resoudre I=∫_0 ^(π/2) tan(nx)tan^n (x)dx

$resoudre$ $I = \int_{0}^{\frac{π}{2}} \tan (nx) \tan^{n} (x) dx$

Question Number 144936 Answers: 1 Comments: 0

Question Number 144930 Answers: 2 Comments: 0

solve (d^2 x/dt^2 )=cosx

$s o l v e$ $\frac{d^{2} x}{{d t}^{2}} = c o s x$

Question Number 144929 Answers: 1 Comments: 0

find the value lim_(n→∞) (1+((1+(1/2)+(1/3)+(1/4)+...+(1/n))/n^2 ))^n

$find the value$ $\lim_{n \to \infty} {(1 + \frac{1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + . . . + \frac{1}{n}}{n^{2}})}^{n}$

Question Number 144928 Answers: 1 Comments: 0

Σ_(n≥0) (((−1)^n )/((n+z)n!))

$\sum_{n ⩾ 0} \frac{{(- 1)}^{n}}{(n + z) n!}$

Question Number 144926 Answers: 1 Comments: 0

∫_0 ^∞ x^n (e^(ix) )^z dx=??? (z∈C)

$\int_{0}^{\infty} x^{n} {(e^{i x})}^{z} d x = ? ? ? (z \in C)$

Question Number 144925 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (((2n)!!)/(2^n ∙(n+1)∙(2n+1)!!))=?

$\underset{n = 1}{\sum^{\infty}} \frac{(2 n)!!}{2^{n} \cdot (n + 1) \cdot (2 n + 1)!!} = ?$

Question Number 144924 Answers: 1 Comments: 0

S(x)=Σ_(n=1) ^∞ (((2n)!!)/((2n+1)!!))x^(2n) =?........(∣x∣<1)

$S (x) = \underset{n = 1}{\sum^{\infty}} \frac{(2 n)!!}{(2 n + 1)!!} x^{2 n} = ? . . . . . . . . (∣ x ∣< 1)$

Question Number 144922 Answers: 1 Comments: 0

if z^2 - 16(√z) = 12 find z - 2(√z) = ?

$i f z^{2} - 16 \sqrt{z} = 12$ $f i n d z - 2 \sqrt{z} = ?$

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