Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 665

Question Number 145047    Answers: 3   Comments: 1

Question Number 145046    Answers: 0   Comments: 0

find ∫_0 ^∞ ∣cosx +sinx∣e^(−x) dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mid\mathrm{cosx}\:+\mathrm{sinx}\mid\mathrm{e}^{−\mathrm{x}} \:\mathrm{dx} \\ $$

Question Number 145044    Answers: 3   Comments: 0

calculate ∫_0 ^∞ e^(−2x) (√(1+sinx))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{2x}} \sqrt{\mathrm{1}+\mathrm{sinx}}\mathrm{dx} \\ $$

Question Number 145025    Answers: 2   Comments: 0

Σ_(n=1) ^∞ (1/((n+1)(√n)+n(√(n+1)))) = ?

$$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\sqrt{{n}}+{n}\sqrt{{n}+\mathrm{1}}}\:=\:? \\ $$

Question Number 145023    Answers: 0   Comments: 4

Question Number 145021    Answers: 2   Comments: 0

Question Number 145019    Answers: 1   Comments: 0

Solve the equation: y+1=x^6 −9x^4 +6x^2 ; x;y∈P

$${Solve}\:{the}\:{equation}: \\ $$$${y}+\mathrm{1}={x}^{\mathrm{6}} −\mathrm{9}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} \:\:;\:\:{x};{y}\in{P} \\ $$

Question Number 145012    Answers: 1   Comments: 0

Question Number 145011    Answers: 2   Comments: 0

Question Number 145010    Answers: 2   Comments: 0

Question Number 145009    Answers: 3   Comments: 0

Question Number 145004    Answers: 0   Comments: 1

Question Number 145003    Answers: 0   Comments: 0

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

$${Solve}\:{the}\:{equation}: \\ $$$$\mathrm{2}^{\boldsymbol{{a}}} \mathrm{3}^{\boldsymbol{{b}}} \mathrm{7}^{\boldsymbol{{c}}} \:=\:\overline {\boldsymbol{{c}}^{\mathrm{2}} \boldsymbol{{cbb}}^{\mathrm{6}} \:}\:\:;\:\:\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\in\boldsymbol{{P}} \\ $$

Question Number 145002    Answers: 0   Comments: 2

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

$${Find}\:{the}\:{last}\:{digit}\:{of}\:{the}\:{number}: \\ $$$$\mathrm{1}^{\mathrm{1989}} +\mathrm{2}^{\mathrm{1989}} +\mathrm{3}^{\mathrm{1989}} +...+\mathrm{1989}^{\mathrm{1989}} \\ $$

Question Number 145000    Answers: 0   Comments: 1

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

$$\mathrm{If}\:\mathrm{F}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{F}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{F}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$

Question Number 144998    Answers: 1   Comments: 0

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

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

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)

$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}\mathrm{dx}=\frac{\pi}{\mathrm{2}}\mathrm{G}−\frac{\mathrm{33}}{\mathrm{32}}\zeta\left(\mathrm{3}\right) \\ $$

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 .

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

Question Number 144989    Answers: 1   Comments: 0

lcm(2a;3a)=lcm(45;100)⇒a=?

$${lcm}\left(\mathrm{2}{a};\mathrm{3}{a}\right)={lcm}\left(\mathrm{45};\mathrm{100}\right)\Rightarrow{a}=? \\ $$

Question Number 144985    Answers: 1   Comments: 0

∫ (((2+(√x)))/((x+1+(√x))^2 )) dx =?

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

Question Number 144981    Answers: 1   Comments: 0

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

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

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^(−) .

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

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=?

$${x}\in\mathbb{Z}^{+} \\ $$$$\mathrm{15}^{\mathrm{48}\boldsymbol{{a}}+\mathrm{1}} \:\equiv\:{x}\:\left({mod}\:\mathrm{17}\right)\:\:{find}\:\:{x}=?\: \\ $$

  Pg 660      Pg 661      Pg 662      Pg 663      Pg 664      Pg 665      Pg 666      Pg 667      Pg 668      Pg 669   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com