Question and Answers Forum

AlgebraQuestion and Answers: Page 348

Question Number 28288 Answers: 2 Comments: 0

Question Number 28275 Answers: 0 Comments: 2

Find area of the region [y]=[x] for x∈[2, 5] . [x] is greatest integer less than or equal to x .

$${Find}\:{area}\:{of}\:{the}\:{region} \\ $$$$\left[{y}\right]=\left[{x}\right]\:\:{for}\:\:{x}\in\left[\mathrm{2},\:\mathrm{5}\right]\:. \\ $$$$\left[{x}\right]\:{is}\:{greatest}\:{integer}\:{less}\:{than}\:{or} \\ $$$${equal}\:{to}\:{x}\:. \\ $$

Question Number 28267 Answers: 1 Comments: 1

let give the polynomial P(x)= (1/(2i))( (1+ix)^n −(1−ix)^n ) .find the roots of P(x) and factorize P(x).

$${let}\:{give}\:{the}\:{polynomial} \\ $$$${P}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}{i}}\left(\:\left(\mathrm{1}+{ix}\right)^{{n}} \:−\left(\mathrm{1}−{ix}\right)^{{n}} \right)\:.{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$${and}\:{factorize}\:{P}\left({x}\right). \\ $$

Question Number 28265 Answers: 0 Comments: 0

1) find P∈R[x] / P(sinx) =sin(2n+1)x 2) find the roots of P and degP 3) decompose (1/P) and prove that ((2n+1)/(sin(2n+1)x)) = Σ_(k=0) ^(2n) (((−1)^k cos(((kπ)/(2n+1))))/(sinx−sin (((kπ)/(2n+1)))))) .

$$\left.\mathrm{1}\right)\:\:{find}\:{P}\in{R}\left[{x}\right]\:/\:{P}\left({sinx}\right)\:={sin}\left(\mathrm{2}{n}+\mathrm{1}\right){x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\:{and}\:{degP} \\ $$$$\left.\mathrm{3}\right)\:{decompose}\:\:\frac{\mathrm{1}}{{P}}\:\:{and}\:{prove}\:{that} \\ $$$$\frac{\mathrm{2}{n}+\mathrm{1}}{{sin}\left(\mathrm{2}{n}+\mathrm{1}\right){x}}\:=\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{k}} \:{cos}\left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)}{{sinx}−{sin}\:\left(\frac{{k}\pi}{\left.\mathrm{2}{n}+\mathrm{1}\right)}\right)}\:\:. \\ $$

Question Number 28264 Answers: 0 Comments: 0

give the decomposition of F(x) = ((1 )/(Π_(k=1) ^n (x−k^2 ))) .

$${give}\:{the}\:{decomposition}\:{of}\: \\ $$$${F}\left({x}\right)\:\:\:=\:\:\:\:\:\:\frac{\mathrm{1}\:}{\prod_{{k}=\mathrm{1}} ^{{n}} \:\left({x}−{k}^{\mathrm{2}} \right)}\:. \\ $$

Question Number 28219 Answers: 0 Comments: 4

Question Number 28211 Answers: 0 Comments: 6

Question Number 28190 Answers: 1 Comments: 2

Question Number 28189 Answers: 0 Comments: 2

Question Number 28188 Answers: 0 Comments: 0

Question Number 28174 Answers: 0 Comments: 2

if the sum of root 7x+px−q=0 is 7 then p= ??

$$\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{root}\:\mathrm{7x}+\mathrm{px}−\mathrm{q}=\mathrm{0}\:\mathrm{is}\:\mathrm{7}\:\mathrm{then}\:\mathrm{p}= \\ $$$$?? \\ $$

Question Number 28166 Answers: 0 Comments: 0

let give w= e^(i((2π)/n)) and Z= Σ_(k=0) ^(n−1) w^k^2 find ∣Z∣^2 in form of double sum.

$${let}\:{give}\:{w}=\:{e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:\:{and}\:\:{Z}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{w}^{{k}^{\mathrm{2}} } \:\:\:{find}\:\mid{Z}\mid^{\mathrm{2}} \:{in} \\ $$$${form}\:{of}\:{double}\:{sum}. \\ $$

Question Number 28165 Answers: 0 Comments: 0

let give w= e^(i((2π)/n)) calculate Σ_(k=0) ^(n−1) (1+w^k )^n .

$${let}\:{give}\:{w}=\:{e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:{calculate}\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(\mathrm{1}+{w}^{{k}} \right)^{{n}} \:. \\ $$

Question Number 28139 Answers: 1 Comments: 0

Question Number 28143 Answers: 1 Comments: 0

x−(1/x)=3 x^2 −(1/x^2 )=?

$$\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{3} \\ $$$$\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=? \\ $$

Question Number 28124 Answers: 0 Comments: 3

f(R^+ →R) is a differentiable function obeying 2f(x)=f(xy)+f((x/y)) for all x,y ∈ R^+ and f(1)=0, f ′(1)=1 . Find f(x). More questions may follow..

$${f}\left({R}^{+} \rightarrow{R}\right)\:{is}\:{a}\:{differentiable} \\ $$$${function}\:{obeying} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({xy}\right)+{f}\left(\frac{{x}}{{y}}\right) \\ $$$${for}\:{all}\:{x},{y}\:\in\:{R}^{+} \:{and}\: \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{0},\:{f}\:'\left(\mathrm{1}\right)=\mathrm{1}\:. \\ $$$${Find}\:{f}\left({x}\right).\:{More}\:{questions}\:{may} \\ $$$${follow}.. \\ $$

Question Number 36365 Answers: 1 Comments: 2

Question Number 27996 Answers: 1 Comments: 0

p,q are two natural number and ((p^6 +2p^4 +4p^2 )/(p^9 −8p^3 ))−(1/(4q))=(5/(6q)), then find the minimum possible value of p+q

$$\mathrm{p},\mathrm{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{and}\: \\ $$$$\:\frac{\mathrm{p}^{\mathrm{6}} +\mathrm{2p}^{\mathrm{4}} +\mathrm{4p}^{\mathrm{2}} }{\mathrm{p}^{\mathrm{9}} −\mathrm{8p}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{4q}}=\frac{\mathrm{5}}{\mathrm{6q}}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}+\mathrm{q} \\ $$

Question Number 27983 Answers: 2 Comments: 0

1) find two factors of 1000001 other than 1 and 1000001 2)(x^2 −5x+5)^((x^2 +2x−24)) =1 what is the value of the product of the solutions?

$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{two}\:\:\mathrm{factors}\:\mathrm{of}\:\mathrm{1000001}\:\mathrm{other}\:\mathrm{than}\:\mathrm{1}\:\mathrm{and}\:\mathrm{1000001} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{5}\right)^{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{24}\right)} =\mathrm{1}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solutions}? \\ $$

Question Number 27977 Answers: 1 Comments: 0

∣2x+1∣≤2

$$\mid\mathrm{2}{x}+\mathrm{1}\mid\leqslant\mathrm{2} \\ $$

Question Number 27976 Answers: 1 Comments: 1

solve ((2x)/(x^2 +1))<((3x+1)/(2(x^2 +1)))

$${solve} \\ $$$$ \\ $$$$\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}<\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$ \\ $$

Question Number 27975 Answers: 1 Comments: 0

solve the inequality (1/(x^2 +x+1))>0

$${solve}\:{the}\:{inequality} \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}>\mathrm{0} \\ $$

Question Number 27761 Answers: 1 Comments: 0

4(2a+b)^2 −(a−b)^2

$$\mathrm{4}\left(\mathrm{2a}+\mathrm{b}\right)^{\mathrm{2}} −\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} \\ $$

Question Number 27681 Answers: 0 Comments: 2

Find square root of 7−30(√2)i .

$${Find}\:{square}\:{root}\:{of}\:\mathrm{7}−\mathrm{30}\sqrt{\mathrm{2}}{i}\:. \\ $$

Question Number 27662 Answers: 0 Comments: 0

factorize in C[x] x^2 +y^2 +z^2 .

$${factorize}\:{in}\:{C}\left[{x}\right]\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\:+{z}^{\mathrm{2}} \:\:.\: \\ $$

Question Number 27587 Answers: 1 Comments: 1

divide 12x(8x−20) by 4(2x−5)

$$\mathrm{divide}\:\mathrm{12x}\left(\mathrm{8x}−\mathrm{20}\right)\:\mathrm{by}\:\mathrm{4}\left(\mathrm{2x}−\mathrm{5}\right) \\ $$

Pg 343 Pg 344 Pg 345 Pg 346 Pg 347 Pg 348 Pg 349 Pg 350 Pg 351 Pg 352

Contact: info@tinkutara.com