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Question Number 227373 Answers: 0 Comments: 1

Question Number 227371 Answers: 0 Comments: 0

3^(444) + 4^(333) Find the remainder when dividing the number by 7

$$\mathrm{3}^{\mathrm{444}} \:\:+\:\:\mathrm{4}^{\mathrm{333}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{dividing}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{7} \\ $$

Question Number 227370 Answers: 1 Comments: 0

((16∙3^(x−1) + 16∙3^x )/(4∙3^(x+1) − 2∙3^(x−1) )) = ((2^(x−1) )^(1/3) /(17)) find: x=?

$$\frac{\mathrm{16}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}−\mathrm{1}} \:+\:\mathrm{16}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}} }{\mathrm{4}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:−\:\mathrm{2}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}−\mathrm{1}} }\:=\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}^{\boldsymbol{\mathrm{x}}−\mathrm{1}} }}{\mathrm{17}}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{x}=? \\ $$

Question Number 227369 Answers: 0 Comments: 0

{ ((3^m + 2∙4^(n+1) = 17)),((4^n − 5∙3^m = −44)) :} find: m+n=?

$$\begin{cases}{\mathrm{3}^{\boldsymbol{\mathrm{m}}} \:+\:\mathrm{2}\centerdot\mathrm{4}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:=\:\mathrm{17}}\\{\mathrm{4}^{\boldsymbol{\mathrm{n}}} \:−\:\mathrm{5}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{m}}} \:=\:−\mathrm{44}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{m}+\mathrm{n}=? \\ $$

Question Number 227368 Answers: 1 Comments: 0

If sin9° = a Find ((cos3°)/(sin15°)) − ((sin3°)/(cos15°)) = ?

$$\mathrm{If}\:\:\:\mathrm{sin9}°\:=\:\mathrm{a} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{cos3}°}{\mathrm{sin15}°}\:−\:\frac{\mathrm{sin3}°}{\mathrm{cos15}°}\:=\:? \\ $$

Question Number 227361 Answers: 0 Comments: 1

Question Number 227357 Answers: 1 Comments: 0

Question Number 227353 Answers: 1 Comments: 0

Question Number 227346 Answers: 1 Comments: 0

Question Number 227328 Answers: 5 Comments: 0

Question Number 227325 Answers: 0 Comments: 0

Prove that in any acute △ABC if I is the in-center and H is the ortho-center then: (1/(IA)) + (1/(IB)) + (1/(IC)) ≤ (1/(HA)) + (1/(HB)) + (1/(HC))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\mathrm{acute}\:\bigtriangleup\mathrm{ABC}\: \\ $$$$\mathrm{if}\:\mathrm{I}\:\mathrm{is}\:\mathrm{the}\:\mathrm{in}-\mathrm{center}\:\mathrm{and}\:\mathrm{H}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ortho}-\mathrm{center} \\ $$$$\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{IA}}\:+\:\frac{\mathrm{1}}{\mathrm{IB}}\:+\:\frac{\mathrm{1}}{\mathrm{IC}}\:\:\leqslant\:\:\frac{\mathrm{1}}{\mathrm{HA}}\:+\:\frac{\mathrm{1}}{\mathrm{HB}}\:+\:\frac{\mathrm{1}}{\mathrm{HC}} \\ $$

Question Number 227326 Answers: 1 Comments: 0

∣ x+1 ∣ + ∣ x ∣ + ∣ x−3∣ > 8

$$\:\:\:\mid\:{x}+\mathrm{1}\:\mid\:+\:\mid\:{x}\:\mid\:+\:\mid\:{x}−\mathrm{3}\mid\:>\:\mathrm{8}\:\: \\ $$

Question Number 227323 Answers: 0 Comments: 0

Is there an n>11 such that every digit of 2^n in decimal representation is even?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{an}\:{n}>\mathrm{11}\:\mathrm{such}\:\mathrm{that}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{2}^{{n}} \\ $$$$\mathrm{in}\:\mathrm{decimal}\:\mathrm{representation}\:\mathrm{is}\:\mathrm{even}? \\ $$

Question Number 227341 Answers: 0 Comments: 8

find the surface area of a spherical cap

$${find}\:{the}\:{surface}\:{area}\:{of}\:{a}\:{spherical} \\ $$$${cap} \\ $$

Question Number 227340 Answers: 0 Comments: 0

Question Number 227319 Answers: 2 Comments: 0

f(z^3 +(1/z^3 ))=z f(z)=?

$${f}\left({z}^{\mathrm{3}} +\frac{\mathrm{1}}{{z}^{\mathrm{3}} }\right)={z} \\ $$$${f}\left({z}\right)=? \\ $$

Question Number 227312 Answers: 2 Comments: 0

tg(15) + ctg(5) = ?

$$\mathrm{tg}\left(\mathrm{15}\right)\:+\:\mathrm{ctg}\left(\mathrm{5}\right)\:=\:? \\ $$

Question Number 227306 Answers: 1 Comments: 1

Question Number 227295 Answers: 1 Comments: 0

Question Number 227294 Answers: 6 Comments: 1

Question Number 227286 Answers: 2 Comments: 0

tg(4) + ctg(4) = ?

$$\mathrm{tg}\left(\mathrm{4}\right)\:+\:\mathrm{ctg}\left(\mathrm{4}\right)\:=\:? \\ $$

Question Number 227283 Answers: 1 Comments: 0

Proof that (√2) is irrational

$${Proof}\:{that}\:\sqrt{\mathrm{2}}\:{is}\:{irrational} \\ $$

Question Number 227276 Answers: 4 Comments: 1

Question Number 227274 Answers: 1 Comments: 0

Does condition sup_(x∈R) ∣∣f^((1)) (x)∣∣<∞ , Gaurantee f(x) is Bounded in R?

$$\mathrm{Does}\:\mathrm{condition} \\ $$$$\underset{{x}\in\mathbb{R}} {\mathrm{sup}}\:\mid\mid{f}^{\left(\mathrm{1}\right)} \left({x}\right)\mid\mid<\infty\:,\:\:\mathrm{Gaurantee}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{Bounded}\:\mathrm{in}\:\mathbb{R}? \\ $$

Question Number 227273 Answers: 1 Comments: 0

Question Number 227272 Answers: 1 Comments: 0

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