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Question Number 227667 Answers: 1 Comments: 0

sin7xcos5x−cos7xsin5x = (1/2) x = ?

$$\mathrm{sin7xcos5x}−\mathrm{cos7xsin5x}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 227651 Answers: 1 Comments: 0

log_5 x = 25 x = ?

$$\mathrm{log}_{\mathrm{5}} \:\mathrm{x}\:=\:\mathrm{25} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 227649 Answers: 1 Comments: 0

25^(log_5 (√2) + 1) = ?

$$\mathrm{25}^{\boldsymbol{\mathrm{log}}_{\mathrm{5}} \:\sqrt{\mathrm{2}}\:+\:\mathrm{1}} \:\:\:=\:\:\:? \\ $$

Question Number 227634 Answers: 0 Comments: 0

prove: p>1,n≥2 (1/n^p )<(1/(p−1))∙[(1/((n−1)^(p− 1) ))−(1/n^(p−1) )]

$$\mathrm{prove}:\:\:\:\:\:\:\:\:\:{p}>\mathrm{1},{n}\geqslant\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{n}^{{p}} }<\frac{\mathrm{1}}{{p}−\mathrm{1}}\centerdot\left[\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)^{{p}−\:\mathrm{1}} }−\frac{\mathrm{1}}{{n}^{{p}−\mathrm{1}} }\right] \\ $$

Question Number 227633 Answers: 1 Comments: 0

(3/(log_2 23!)) + (3/(log_3 23!)) + (3/(log_4 23!)) +...+ (3/(log_(22) 23!)) + (3/(log_(23) 23!)) = ?

$$\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{2}} \mathrm{23}!}\:+\:\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{3}} \mathrm{23}!}\:+\:\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{4}} \mathrm{23}!}\:+...+\:\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{22}} \mathrm{23}!}\:+\:\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{23}} \mathrm{23}!}\:=\:? \\ $$

Question Number 227632 Answers: 1 Comments: 0

If 4a^2 + 9b^2 = 13ab Find ((2lg(2a + 3b)−lg25)/(5lg(ab))) = ?

$$\mathrm{If}\:\:\:\mathrm{4a}^{\mathrm{2}} \:+\:\mathrm{9b}^{\mathrm{2}} \:=\:\mathrm{13ab} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{2}\boldsymbol{\mathrm{lg}}\left(\mathrm{2a}\:+\:\mathrm{3b}\right)−\boldsymbol{\mathrm{lg}}\mathrm{25}}{\mathrm{5}\boldsymbol{\mathrm{lg}}\left(\mathrm{ab}\right)}\:=\:? \\ $$

Question Number 227582 Answers: 1 Comments: 0

cos^2 (((3x)/2) + ((11π)/2)) - sin^2 (((3x)/2) + ((11π)/2)) = - (1/2) x = ?

$$\mathrm{cos}^{\mathrm{2}} \left(\frac{\mathrm{3x}}{\mathrm{2}}\:+\:\frac{\mathrm{11}\pi}{\mathrm{2}}\right)\:-\:\mathrm{sin}^{\mathrm{2}} \left(\frac{\mathrm{3x}}{\mathrm{2}}\:+\:\frac{\mathrm{11}\pi}{\mathrm{2}}\right)\:=\:-\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 227580 Answers: 1 Comments: 0

(π/4)arctan(tan((7π)/8))+tan2x=(1/2)cos(arccos(−(1/2))+(π/3)) x = ?

$$\frac{\pi}{\mathrm{4}}\mathrm{arctan}\left(\mathrm{tan}\frac{\mathrm{7}\pi}{\mathrm{8}}\right)+\mathrm{tan2x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\left(\mathrm{arccos}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\frac{\pi}{\mathrm{3}}\right) \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 227579 Answers: 1 Comments: 0

cos6x = ((2tan(π/8))/(1−tan^2 (π/8))) ⇒ x = ?

$$\mathrm{cos6x}\:=\:\frac{\mathrm{2tan}\frac{\pi}{\mathrm{8}}}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \frac{\pi}{\mathrm{8}}}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{x}\:=\:? \\ $$

Question Number 227578 Answers: 1 Comments: 0

sin3x + sin^2 (π/4) = cos^2 (π/4) + ((√3)/2) x = ?

$$\mathrm{sin3x}\:+\:\mathrm{sin}^{\mathrm{2}} \frac{\pi}{\mathrm{4}}\:=\:\mathrm{cos}^{\mathrm{2}} \frac{\pi}{\mathrm{4}}\:+\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 227489 Answers: 1 Comments: 1

1+2−3−4+5+6−7−8+9+10−11−12+ ... +100 =?

$$\mathrm{1}+\mathrm{2}−\mathrm{3}−\mathrm{4}+\mathrm{5}+\mathrm{6}−\mathrm{7}−\mathrm{8}+\mathrm{9}+\mathrm{10}−\mathrm{11}−\mathrm{12}+ \\ $$$$...\:+\mathrm{100}\:=? \\ $$

Question Number 227476 Answers: 3 Comments: 0

Question Number 227474 Answers: 1 Comments: 0

Question Number 227471 Answers: 1 Comments: 0

{ ((log_3 x=a)),((log_3 y=b)) :} ⇒ log_3 (x^3 ∙y^2 )=?

$$\begin{cases}{\mathrm{log}_{\mathrm{3}} \mathrm{x}=\mathrm{a}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{y}=\mathrm{b}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{x}^{\mathrm{3}} \centerdot\mathrm{y}^{\mathrm{2}} \right)=? \\ $$

Question Number 227465 Answers: 2 Comments: 0

How many hydrogen atoms are there in 2.57×10^(−6) g of hydrogen

$${How}\:{many}\:{hydrogen}\:{atoms}\:{are} \\ $$$${there}\:{in}\:\mathrm{2}.\mathrm{57}×\mathrm{10}^{−\mathrm{6}} {g}\:\:{of}\:{hydrogen} \\ $$

Question Number 227433 Answers: 1 Comments: 0

Question Number 227422 Answers: 2 Comments: 0

Question Number 227373 Answers: 1 Comments: 1

Question Number 227371 Answers: 2 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: 1 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: 2 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 227346 Answers: 2 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 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

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