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Question Number 212516 Answers: 0 Comments: 0

Question Number 212515 Answers: 1 Comments: 1

The numbers of pairs of natural numbers (x,y) with x,y ≤ 33 that satisfy 5 ∣ 3^x^(y−1) + 2^y^(2x) is ... (A) 295 (B) 296 (C) 297 (D) 298 (E) 299

$$\:\:\mathrm{The}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural}\: \\ $$$$\:\:\:\mathrm{numbers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{with}\:\mathrm{x},\mathrm{y}\:\leqslant\:\mathrm{33}\:\mathrm{that}\: \\ $$$$\:\:\:\mathrm{satisfy}\:\mathrm{5}\:\mid\:\mathrm{3}^{\mathrm{x}^{\mathrm{y}−\mathrm{1}} } \:+\:\mathrm{2}^{\mathrm{y}^{\mathrm{2x}} } \:\mathrm{is}\:...\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\mathrm{295}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{296}\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{297}\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{298}\:\:\:\left(\mathrm{E}\right)\:\mathrm{299} \\ $$

Question Number 212514 Answers: 1 Comments: 0

Question Number 212513 Answers: 1 Comments: 0

certificate: x^(2n) −1 Can always be x+1 be divisible

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}{n}} −\mathrm{1} \\ $$$$\mathrm{Can}\:\mathrm{always}\:\mathrm{be}\:{x}+\mathrm{1}\:\mathrm{be}\:\mathrm{divisible}\:\:\:\:\:\:\:\:\: \\ $$

Question Number 212508 Answers: 1 Comments: 1

Question Number 212506 Answers: 1 Comments: 0

Find: ((− ((18)/(1 + i (√3)))))^(1/4)

$$\mathrm{Find}:\:\:\:\:\:\:\sqrt[{\mathrm{4}}]{−\:\frac{\mathrm{18}}{\mathrm{1}\:+\:\boldsymbol{\mathrm{i}}\:\sqrt{\mathrm{3}}}} \\ $$

Question Number 212503 Answers: 0 Comments: 0

Question Number 212500 Answers: 1 Comments: 0

Can we exactly find r_(max) (a). r^2 +((2rt)/a)(t+2(√(ar)))=t^2 ∀ t is parameter

$${Can}\:{we}\:{exactly}\:{find}\:{r}_{{max}} \left({a}\right). \\ $$$${r}^{\mathrm{2}} +\frac{\mathrm{2}{rt}}{{a}}\left({t}+\mathrm{2}\sqrt{{ar}}\right)={t}^{\mathrm{2}} \:\:\:\:\forall\:{t}\:{is}\:{parameter} \\ $$

Question Number 212499 Answers: 2 Comments: 0

Given a,b,c and d are reals numbers such that { ((a^2 +b^2 =10)),((c^2 +d^2 =10 )),((ab+cd=0)) :} Find ac + bd.

$$\:\:\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{are}\:\mathrm{reals}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\begin{cases}{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{10}}\\{\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} =\mathrm{10}\:}\\{\mathrm{ab}+\mathrm{cd}=\mathrm{0}}\end{cases} \\ $$$$\:\:\mathrm{Find}\:\mathrm{ac}\:+\:\mathrm{bd}. \\ $$

Question Number 212498 Answers: 0 Comments: 0

Question Number 212496 Answers: 0 Comments: 0

If 1.1!+3.2!+...+(2n−1).n! = a.(n+1)!+b(1!+2!+...+(n+1)!)+c for a,b,c integers number find 2a−b+3c

$$\:\mathrm{If}\:\mathrm{1}.\mathrm{1}!+\mathrm{3}.\mathrm{2}!+...+\left(\mathrm{2n}−\mathrm{1}\right).\mathrm{n}!\: \\ $$$$\:=\:\mathrm{a}.\left(\mathrm{n}+\mathrm{1}\right)!+\mathrm{b}\left(\mathrm{1}!+\mathrm{2}!+...+\left(\mathrm{n}+\mathrm{1}\right)!\right)+\mathrm{c}\: \\ $$$$\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{integers}\:\mathrm{number} \\ $$$$\:\mathrm{find}\:\mathrm{2a}−\mathrm{b}+\mathrm{3c}\: \\ $$

Question Number 212495 Answers: 0 Comments: 0

Question Number 212479 Answers: 1 Comments: 0

{ ((2x + 3y − z = 7)),((4x − y + 2z = 1)),((−x + 5y + 3z = 14)) :} find: x,y,z = ?

$$\begin{cases}{\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{z}\:=\:\mathrm{7}}\\{\mathrm{4x}\:−\:\mathrm{y}\:+\:\mathrm{2z}\:=\:\mathrm{1}}\\{−\mathrm{x}\:+\:\mathrm{5y}\:+\:\mathrm{3z}\:=\:\mathrm{14}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{x},\mathrm{y},\mathrm{z}\:=\:? \\ $$

Question Number 212477 Answers: 3 Comments: 0

Question Number 212470 Answers: 1 Comments: 0

Question Number 212467 Answers: 1 Comments: 0

Use the integration by parts. ∫ (2/( (√(r^2 −4)))) dr

$$\mathrm{Use}\:\:\mathrm{the}\:\:\mathrm{integration}\:\:\mathrm{by}\:\:\mathrm{parts}. \\ $$$$ \\ $$$$\int\:\frac{\mathrm{2}}{\:\sqrt{{r}^{\mathrm{2}} −\mathrm{4}}}\:{dr}\: \\ $$

Question Number 212464 Answers: 1 Comments: 1

Question Number 212460 Answers: 0 Comments: 0

Question Number 212448 Answers: 3 Comments: 0

If x^2 − x + 3 = 0 Find x + (9/x^2 ) = ?

$$\mathrm{If}\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\:\mathrm{x}\:+\:\frac{\mathrm{9}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 212445 Answers: 1 Comments: 1

Question Number 212444 Answers: 0 Comments: 0

Question Number 212435 Answers: 1 Comments: 0

Question Number 212432 Answers: 2 Comments: 0

(9/(2∙4)) + (9/(4∙6)) +...+ (9/(4n∙(n + 1))) = ((15)/8) Find: n = ?

$$\frac{\mathrm{9}}{\mathrm{2}\centerdot\mathrm{4}}\:+\:\frac{\mathrm{9}}{\mathrm{4}\centerdot\mathrm{6}}\:+...+\:\frac{\mathrm{9}}{\mathrm{4n}\centerdot\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:=\:\frac{\mathrm{15}}{\mathrm{8}} \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{n}}\:=\:? \\ $$

Question Number 212430 Answers: 0 Comments: 0

Question Number 212428 Answers: 3 Comments: 0

Question Number 212427 Answers: 0 Comments: 1

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