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AlgebraQuestion and Answers: Page 263

Question Number 87737 Answers: 1 Comments: 0

solve sin((π/([(([x])/4)])))=(1/2)

$${solve} \\ $$$${sin}\left(\frac{\pi}{\left[\frac{\left[{x}\right]}{\mathrm{4}}\right]}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 87733 Answers: 1 Comments: 2

Question Number 87726 Answers: 0 Comments: 0

Question Number 87724 Answers: 1 Comments: 0

solve the equation sin^(−1) (cos ⌊x⌋)=1

$${solve}\:{the}\:{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{cos}}\:\lfloor\boldsymbol{{x}}\rfloor\right)=\mathrm{1} \\ $$

Question Number 87656 Answers: 1 Comments: 3

((1+sin((1/8))π+i cos((1/8))π)/(1+sin((1/8))π−i cos((1/8))π))=?

$$\frac{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi+{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi−{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}=? \\ $$

Question Number 87625 Answers: 2 Comments: 0

if f(x)=sin^(−1) (cos[x]) find Df and Rf the function notice/ [...] is floor

$${if}\:{f}\left({x}\right)={sin}^{−\mathrm{1}} \left({cos}\left[{x}\right]\right) \\ $$$${find}\:{Df}\:{and}\:\:{Rf}\:{the}\:{function} \\ $$$$ \\ $$$${notice}/\:\left[...\right]\:{is}\:{floor} \\ $$

Question Number 87598 Answers: 0 Comments: 1

Question Number 87586 Answers: 1 Comments: 0

l.c.m of two numbers is p^2 q^4 r^4 p q r are primes.find the possible no. of pairs

$${l}.{c}.{m}\:{of}\:{two}\:{numbers}\:{is}\:{p}^{\mathrm{2}} {q}^{\mathrm{4}} {r}^{\mathrm{4}} \:{p}\:{q}\:{r}\:{are} \\ $$$${primes}.{find}\:{the}\:{possible}\:{no}.\:{of}\:{pairs} \\ $$

Question Number 87581 Answers: 2 Comments: 1

Question Number 87553 Answers: 1 Comments: 0

Question Number 87533 Answers: 3 Comments: 2

Question Number 87492 Answers: 1 Comments: 0

((2+3^2 )/(1!+2!+3!+4!))+((3+4^2 )/(2!+3!+4!+5!))+...+((2013+2014^2 )/(2012!+2013!+2014!+2015!))

$$\frac{\mathrm{2}+\mathrm{3}^{\mathrm{2}} }{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+\frac{\mathrm{3}+\mathrm{4}^{\mathrm{2}} }{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}+...+\frac{\mathrm{2013}+\mathrm{2014}^{\mathrm{2}} }{\mathrm{2012}!+\mathrm{2013}!+\mathrm{2014}!+\mathrm{2015}!} \\ $$

Question Number 87398 Answers: 0 Comments: 5

dear mr w a_(n+2) = a_(n+1) − a_n find a_n

$$\mathrm{dear}\:\mathrm{mr}\:\mathrm{w} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:−\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \\ $$

Question Number 87382 Answers: 1 Comments: 0

Show that tan((5π)/(12)) is a solution of this equation: x^3 −3x^2 −3x+1=0

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{tan}\frac{\mathrm{5}\pi}{\mathrm{12}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{this}\: \\ $$$$\mathrm{equation}:\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 87379 Answers: 1 Comments: 2

Π_(k = 2) ^(2010) ((k^2 −1)/k^2 ) = ?

$$\underset{\mathrm{k}\:=\:\mathrm{2}} {\overset{\mathrm{2010}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 87321 Answers: 0 Comments: 0

Question Number 87313 Answers: 1 Comments: 4

a,b,c=1,2,3,...,n find Σ_(a≠b≠c) abc

$${a},{b},{c}=\mathrm{1},\mathrm{2},\mathrm{3},...,{n} \\ $$$${find}\:\underset{{a}\neq{b}\neq{c}} {\sum}{abc} \\ $$

Question Number 87302 Answers: 1 Comments: 3

for ∣z−1∣=1 show that tan(((arg(z−1))/2))−((2i)/z)=−1

$${for}\:\mid{z}−\mathrm{1}\mid=\mathrm{1}\:{show}\:{that} \\ $$$${tan}\left(\frac{{arg}\left({z}−\mathrm{1}\right)}{\mathrm{2}}\right)−\frac{\mathrm{2}{i}}{{z}}=−\mathrm{1} \\ $$

Question Number 87253 Answers: 1 Comments: 0

Three pair of socks are placed in a box.If two socks are drawn at random from the box What is the probability (a)of drawing a match pair (b)of drawing a socks for the left and right feet (c)of drawing two socks of the right feet d)drawing two socks of left feet (e)drawing socks of the same feet

$${Three}\:{pair}\:{of}\:{socks}\:{are} \\ $$$${placed}\:{in}\:{a}\:{box}.{If}\:{two} \\ $$$${socks}\:{are}\:{drawn}\:{at} \\ $$$${random}\:{from}\:{the}\:{box} \\ $$$${What}\:{is}\:{the}\:{probability} \\ $$$$\left({a}\right){of}\:{drawing}\:\:{a}\:{match} \\ $$$${pair} \\ $$$$\left({b}\right){of}\:{drawing}\:{a}\:{socks} \\ $$$${for}\:{the}\:{left}\:{and}\:{right} \\ $$$${feet} \\ $$$$\left({c}\right){of}\:{drawing}\:{two}\:{socks}\:{of} \\ $$$${the}\:{right}\:{feet} \\ $$$$\left.{d}\right){drawing}\:{two}\:{socks}\:{of} \\ $$$${left}\:{feet} \\ $$$$\left({e}\right){drawing}\:{socks}\:{of}\:{the} \\ $$$${same}\:{feet} \\ $$$$ \\ $$

Question Number 87224 Answers: 1 Comments: 7

how to simply the boolean algebra (X+Y+Z)(X′ +Y+Z) (X+Y′+Z)

$$\mathrm{how}\:\mathrm{to}\:\mathrm{simply}\:\mathrm{the}\: \\ $$$$\mathrm{boolean}\:\mathrm{algebra}\:\left(\mathrm{X}+\mathrm{Y}+\mathrm{Z}\right)\left(\mathrm{X}'\:+\mathrm{Y}+\mathrm{Z}\right) \\ $$$$\left(\mathrm{X}+\mathrm{Y}'+\mathrm{Z}\right)\: \\ $$

Question Number 87130 Answers: 0 Comments: 5

find the slope for the curve r = 3 sin 2θ at θ =(π/4) ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{at}\:\theta\:=\frac{\pi}{\mathrm{4}}\:? \\ $$

Question Number 87093 Answers: 0 Comments: 6

⌊((x−1)/4)⌋+⌊((x−2)/3)⌋=⌊((x−3)/2)⌋

$$\lfloor\frac{{x}−\mathrm{1}}{\mathrm{4}}\rfloor+\lfloor\frac{{x}−\mathrm{2}}{\mathrm{3}}\rfloor=\lfloor\frac{{x}−\mathrm{3}}{\mathrm{2}}\rfloor \\ $$

Question Number 87050 Answers: 0 Comments: 3

what are the roots of the system of equation (x/y)+(y/(x+1)) = (4/3) and x+y + xy = 5 ?