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Question Number 53924 Answers: 2 Comments: 0

If the non−zero numbers x, y, z are in AP, and tan^(−1) x, tan^(−1) y, tan^(−1) z are also in AP, then

$$\mathrm{If}\:\mathrm{the}\:\mathrm{non}−\mathrm{zero}\:\mathrm{numbers}\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}, \\ $$$$\mathrm{and}\:\mathrm{tan}^{−\mathrm{1}} {x},\:\mathrm{tan}^{−\mathrm{1}} {y},\:\mathrm{tan}^{−\mathrm{1}} {z}\:\mathrm{are}\:\mathrm{also}\:\mathrm{in}\:\mathrm{AP}, \\ $$$$\mathrm{then} \\ $$

Question Number 53919 Answers: 1 Comments: 0

Question Number 53912 Answers: 3 Comments: 0

{ ((2^x −2^y =1)),((4^x −4^y =(5/3))) :}

$$\begin{cases}{\mathrm{2}^{{x}} −\mathrm{2}^{{y}} =\mathrm{1}}\\{\mathrm{4}^{{x}} −\mathrm{4}^{{y}} =\frac{\mathrm{5}}{\mathrm{3}}}\end{cases} \\ $$

Question Number 53910 Answers: 1 Comments: 12

Question Number 53909 Answers: 1 Comments: 0

a angle is 14° more than its complement then its measure

$${a}\:{angle}\:{is}\:\mathrm{14}°\:{more}\:{than}\:{its}\:{complement}\:\:{then}\:{its}\:{measure} \\ $$

Question Number 53907 Answers: 1 Comments: 0

Question Number 53902 Answers: 1 Comments: 3

How many zeros and how many ones are there in the numbers from 1 to 9999? Example: in the number 1010 there are 2 zeros and 2 ones.

$${How}\:{many}\:{zeros}\:{and}\:{how}\:{many}\:{ones} \\ $$$${are}\:{there}\:{in}\:{the}\:{numbers}\:{from}\:\mathrm{1}\:{to} \\ $$$$\mathrm{9999}? \\ $$$${Example}:\:{in}\:{the}\:{number}\:\mathrm{1010}\:{there} \\ $$$${are}\:\mathrm{2}\:{zeros}\:{and}\:\mathrm{2}\:{ones}. \\ $$

Question Number 53901 Answers: 1 Comments: 0

Question Number 53890 Answers: 1 Comments: 0

pls. help me solve this if y=((x−2)/(2x−1)) show that (2x−1)(d^2 y/dx^2 )+4(dy/dx)=0

$$\mathrm{pls}.\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this} \\ $$$$\mathrm{if}\:\mathrm{y}=\frac{\mathrm{x}−\mathrm{2}}{\mathrm{2x}−\mathrm{1}}\:\mathrm{show}\:\mathrm{that}\:\left(\mathrm{2x}−\mathrm{1}\right)\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{4}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{0} \\ $$

Question Number 53881 Answers: 0 Comments: 2

Question Number 53894 Answers: 2 Comments: 0

∫_(π/6) ^(5π/6) (√(4−4 sin^2 t)) dt =

$$\underset{\pi/\mathrm{6}} {\overset{\mathrm{5}\pi/\mathrm{6}} {\int}}\sqrt{\mathrm{4}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} {t}}\:{dt}\:= \\ $$

Question Number 53867 Answers: 1 Comments: 0

Question Number 53852 Answers: 0 Comments: 0

G_(μν) = R_(μν) − (1/2) Rg_(μν) + 𝚲g_(μν) Wich theory of modern physic belongs this equation? and what does it mean?

$${G}_{\mu\nu} =\:{R}_{\mu\nu} −\:\frac{\mathrm{1}}{\mathrm{2}}\:{Rg}_{\mu\nu} \:+\:\boldsymbol{\Lambda}{g}_{\mu\nu} \\ $$$$\mathrm{Wich}\:\mathrm{theory}\:\mathrm{of}\:\mathrm{modern}\:\mathrm{physic}\:\mathrm{belongs}\:\mathrm{this}\:\mathrm{equation}? \\ $$$$\mathrm{and}\:\mathrm{what}\:\mathrm{does}\:\mathrm{it}\:\mathrm{mean}? \\ $$

Question Number 53843 Answers: 1 Comments: 0

Question Number 53842 Answers: 0 Comments: 0

Find all the real valued f satisfying f[2x + f(2y)] + f[f(y)] = 4x + 8y for all real numbers x and y.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{valued}\:\:\mathrm{f}\:\:\mathrm{satisfying}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}\left[\mathrm{2x}\:+\:\mathrm{f}\left(\mathrm{2y}\right)\right]\:+\:\mathrm{f}\left[\mathrm{f}\left(\mathrm{y}\right)\right]\:\:=\:\:\mathrm{4x}\:+\:\mathrm{8y} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{numbers}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}.\: \\ $$

Question Number 53841 Answers: 0 Comments: 8

Question Number 53839 Answers: 0 Comments: 4

Question Number 53828 Answers: 1 Comments: 1

Question Number 53827 Answers: 1 Comments: 0

5×6^x −3×4^x = 2×9^x I need an explanation.

$$\mathrm{5}×\mathrm{6}^{{x}} −\mathrm{3}×\mathrm{4}^{{x}} =\:\mathrm{2}×\mathrm{9}^{{x}} \\ $$$$ \\ $$$${I}\:{need}\:{an}\:{explanation}. \\ $$

Question Number 53824 Answers: 2 Comments: 1

Question Number 53877 Answers: 2 Comments: 1

2×4^(x+2) −5×4^(x+1) −3×2^(2x+1) −4^x = 20

$$\mathrm{2}×\mathrm{4}^{{x}+\mathrm{2}} −\mathrm{5}×\mathrm{4}^{{x}+\mathrm{1}} −\mathrm{3}×\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} −\mathrm{4}^{{x}} =\:\mathrm{20} \\ $$

Question Number 53814 Answers: 0 Comments: 0

Question Number 53813 Answers: 0 Comments: 0

Question Number 53811 Answers: 1 Comments: 1

Question Number 53805 Answers: 1 Comments: 4

Question Number 53795 Answers: 1 Comments: 1

calculate Σ_(n=0) ^∞ (((−1)^n )/(4n+1)) =1−(1/5) +(1/9) −(1/(13)) +....

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+\mathrm{1}}\:=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\:+\frac{\mathrm{1}}{\mathrm{9}}\:−\frac{\mathrm{1}}{\mathrm{13}}\:+.... \\ $$

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