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Question Number 33837 Answers: 2 Comments: 0

find y if ∣((y−3)/(y+1))∣<2 i mean modulus by ∣

$${find}\:{y}\:{if}\:\mid\frac{{y}−\mathrm{3}}{{y}+\mathrm{1}}\mid<\mathrm{2} \\ $$$$ \\ $$$${i}\:{mean}\:{modulus}\:{by}\:\mid \\ $$

Question Number 33836 Answers: 2 Comments: 0

for what values of x if ((x(x−1))/(2x+3))>0

$${for}\:{what}\:{values}\:{of}\:{x}\:{if} \\ $$$$\frac{{x}\left({x}−\mathrm{1}\right)}{\mathrm{2}{x}+\mathrm{3}}>\mathrm{0} \\ $$

Question Number 33835 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) ((cos(πx))/((x^2 +1+i)^2 )) dx

$${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left(\pi{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}+{i}\right)^{\mathrm{2}} }\:{dx} \\ $$

Question Number 33834 Answers: 0 Comments: 0

P(x)=x^n +a_(n−1) x^(n−1) +.... a_1 x+a_0 be a polynomial with all the real roots, prove that (n−1)a_(n−1) ^2 ≥ 2na_(n−2) .

$${P}\left({x}\right)={x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +....\:{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \:\:\:{be}\:{a}\:{polynomial}\:{with}\:{all}\:{the}\:{real}\:{roots}, \\ $$$${prove}\:{that}\:\:\:\:\:\:\:\:\:\left({n}−\mathrm{1}\right){a}_{{n}−\mathrm{1}} ^{\mathrm{2}} \:\geqslant\:\mathrm{2}{na}_{{n}−\mathrm{2}} \:\:. \\ $$

Question Number 33825 Answers: 0 Comments: 0

Question Number 33822 Answers: 0 Comments: 1

The following table shows the distributuons of 100 families according to their expenditure per week. The mode is given to be 24. ∣((expenditure)/(Number of families))∣((10−20)/x)∣((20−30)/(27))∣((30−40)/y)∣((40−50)/(15))∣ (a) calculate the missing frequency (b)calculate the mean (c)calculate the median

Question Number 33819 Answers: 0 Comments: 0

given a=3i−4j+2k b=−2i+j−3k find (i) v=a+b (ii)v into position vector (iii)unit vector of v

$$\boldsymbol{\mathrm{given}}\:\:\:\boldsymbol{\mathrm{a}}=\mathrm{3}\boldsymbol{\mathrm{i}}−\mathrm{4}\boldsymbol{\mathrm{j}}+\mathrm{2}\boldsymbol{\mathrm{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{b}}=−\mathrm{2}\boldsymbol{\mathrm{i}}+\boldsymbol{\mathrm{j}}−\mathrm{3}\boldsymbol{\mathrm{k}} \\ $$$$\boldsymbol{\mathrm{find}}\:\:\:\left(\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{v}}=\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{v}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{position}}\:\boldsymbol{\mathrm{vector}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{iii}}\right)\boldsymbol{\mathrm{unit}}\:\boldsymbol{\mathrm{vector}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{v}} \\ $$

Question Number 33818 Answers: 1 Comments: 0

Let f:R → [ 1, ∞) be defined as f(x) = log_(10) ((√(3x^2 −4x+k+1)) +10 ). If f(x) is surjective , then find the value of k ?

$$\boldsymbol{{L}}{et}\:{f}:\boldsymbol{{R}}\:\rightarrow\:\left[\:\mathrm{1},\:\infty\right)\:{be}\:{defined}\:{as}\: \\ $$$${f}\left({x}\right)\:=\:\mathrm{log}_{\mathrm{10}} \:\left(\sqrt{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\boldsymbol{{k}}+\mathrm{1}}\:+\mathrm{10}\:\right). \\ $$$$\boldsymbol{{I}}{f}\:{f}\left({x}\right)\:{is}\:\boldsymbol{{surjective}}\:,\:{then}\:{find} \\ $$$${the}\:{value}\:{of}\:\boldsymbol{{k}}\:? \\ $$

Question Number 33876 Answers: 0 Comments: 2

how can i write out 6 to thethird power divided by 2 to the fourth power pleasr help me write out this equation

$${how}\:{can}\:{i}\:{write}\:{out}\:\mathrm{6}\:{to}\:{thethird}\:{power}\:{divided}\:{by}\:\mathrm{2}\:{to}\:{the}\:{fourth}\:{power}\:{pleasr}\:{help}\:{me}\:{write}\:{out}\:{this}\:{equation}\: \\ $$

Question Number 33815 Answers: 1 Comments: 0

Let f:D → R be defined as f(x) = ((x^2 +2x+a)/(x^2 +4x+3a)) where D and R denote the domain of f and the set of all real numbers respectively. If f is ′′ surjective ′′ mapping then the range of a is ? a) 0≤a≤1 b) 0<a≤1 c) 0<a<1 d) 0≤a<1

$$\boldsymbol{{L}}{et}\:{f}:{D}\:\rightarrow\:\boldsymbol{{R}}\:{be}\:{defined}\:{as}\: \\ $$$${f}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}+{a}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}{a}}\:{where}\:{D}\:{and}\:{R} \\ $$$${denote}\:{the}\:{domain}\:{of}\:\boldsymbol{{f}}\:{and}\:{the}\:{set} \\ $$$${of}\:{all}\:{real}\:{numbers}\:{respectively}. \\ $$$${If}\:{f}\:{is}\:''\:{surjective}\:''\:\:{mapping}\:{then} \\ $$$${the}\:{range}\:{of}\:\boldsymbol{{a}}\:{is}\:? \\ $$$$\left.{a}\right)\:\mathrm{0}\leqslant{a}\leqslant\mathrm{1} \\ $$$$\left.{b}\right)\:\mathrm{0}<{a}\leqslant\mathrm{1} \\ $$$$\left.{c}\right)\:\mathrm{0}<{a}<\mathrm{1} \\ $$$$\left.{d}\right)\:\mathrm{0}\leqslant{a}<\mathrm{1}\: \\ $$

Question Number 33805 Answers: 1 Comments: 0

The perimeter of a square and a rectangle is the same. The width of the rectangle is 6 cm and its area is 16 cm^2 less than the area of the square. Find the area of the square.

$$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{and}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{same}.\:\mathrm{The}\:\mathrm{width}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{6}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{its}\:\mathrm{area} \\ $$$$\mathrm{is}\:\mathrm{16}\:\mathrm{cm}^{\mathrm{2}} \:\mathrm{less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$

Question Number 33800 Answers: 1 Comments: 0

Question Number 33787 Answers: 0 Comments: 0

lim_(n→∞) ((1/n) ∫_1 ^n n^(1/x) dx)

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{{n}}\:\underset{\mathrm{1}} {\overset{{n}} {\int}}\:{n}^{\frac{\mathrm{1}}{{x}}} \:{dx}\right) \\ $$

Question Number 33823 Answers: 1 Comments: 0

solve : I = ∫_0 ^π (((r−R cosθ) sin θ )/((R^(2 ) + r^2 − 2Rr cos θ)^(3/2) )) dθ for r < R and r > R respectively.

$$\:\:{solve}\::\: \\ $$$$\:{I}\:=\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\left({r}−{R}\:{cos}\theta\right)\:{sin}\:\theta\:}{\left({R}^{\mathrm{2}\:} +\:{r}^{\mathrm{2}} \:−\:\mathrm{2}{Rr}\:{cos}\:\theta\right)^{\mathrm{3}/\mathrm{2}} }\:{d}\theta \\ $$$${for}\:\:\:{r}\:<\:{R} \\ $$$${and}\:{r}\:>\:{R}\:\:{respectively}. \\ $$

Question Number 33783 Answers: 1 Comments: 0

Two commodities X and Y cost $70.00 and $80.00 per kg respectively. If 34.5 kg of X is mixed with 26kg of Y and the mixture is sold at $85.00 per kg, calculate the percentage profit.

$$\mathrm{Two}\:\mathrm{commodities}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{cost}\:\$\mathrm{70}.\mathrm{00}\:\mathrm{and}\:\$\mathrm{80}.\mathrm{00} \\ $$$$\mathrm{per}\:\mathrm{kg}\:\mathrm{respectively}.\:\mathrm{If}\:\mathrm{34}.\mathrm{5}\:\mathrm{kg}\:\mathrm{of}\:\mathrm{X}\:\mathrm{is}\:\mathrm{mixed}\:\mathrm{with}\: \\ $$$$\mathrm{26kg}\:\mathrm{of}\:\mathrm{Y}\:\mathrm{and}\:\mathrm{the}\:\mathrm{mixture}\:\mathrm{is}\:\mathrm{sold}\:\mathrm{at}\:\$\mathrm{85}.\mathrm{00}\:\mathrm{per}\:\mathrm{kg}, \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{profit}. \\ $$

Question Number 33824 Answers: 1 Comments: 0

two sphere with 10 cm radious and 1 kg mass and distence between this two is 1 m .after what time they will touch each other?

$$\mathrm{two}\:\mathrm{sphere}\:\mathrm{with}\:\mathrm{10}\:\mathrm{cm}\:\mathrm{radious}\:\mathrm{and} \\ $$$$\mathrm{1}\:\mathrm{kg}\:\mathrm{mass}\:\mathrm{and}\:\mathrm{distence}\:\mathrm{between} \\ $$$$\mathrm{this}\:\mathrm{two}\:\mathrm{is}\:\mathrm{1}\:\mathrm{m}\:.\mathrm{after}\:\mathrm{what}\:\mathrm{time}\:\mathrm{they} \\ $$$$\mathrm{will}\:\mathrm{touch}\:\mathrm{each}\:\mathrm{other}? \\ $$

Question Number 33767 Answers: 1 Comments: 0

Question Number 33766 Answers: 1 Comments: 0

a−(1/a)=4 (√(a^2 +(1/a^2 )))−(√((a+(1/a))^2 ))−(√((a−2)^2 ))=(√x)−(√y) what is [x+y]?

$${a}−\frac{\mathrm{1}}{{a}}=\mathrm{4} \\ $$$$\sqrt{{a}^{\mathrm{2}} +\frac{\mathrm{1}}{{a}^{\mathrm{2}} }}−\sqrt{\left({a}+\frac{\mathrm{1}}{{a}}\right)^{\mathrm{2}} }−\sqrt{\left({a}−\mathrm{2}\right)^{\mathrm{2}} }=\sqrt{{x}}−\sqrt{{y}} \\ $$$${what}\:{is}\:\left[{x}+{y}\right]? \\ $$

Question Number 33764 Answers: 1 Comments: 0

2x−y=(1/((√5)−2)) x+2y=(1/((√5)+2)) [3x^2 −8xy−3y^2 ]?

$$\mathrm{2}{x}−{y}=\frac{\mathrm{1}}{\sqrt{\mathrm{5}}−\mathrm{2}} \\ $$$${x}+\mathrm{2}{y}=\frac{\mathrm{1}}{\sqrt{\mathrm{5}}+\mathrm{2}} \\ $$$$\left[\mathrm{3}{x}^{\mathrm{2}} −\mathrm{8}{xy}−\mathrm{3}{y}^{\mathrm{2}} \right]? \\ $$

Question Number 33759 Answers: 0 Comments: 9

solve : ∫_(−π/2) ^(π/2) ((sin θ )/(√( R^2 + r^2 − 2rR cos θ))) dθ

$${solve}\::\: \\ $$$$\:\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\:\:\frac{{sin}\:\theta\:}{\sqrt{\:{R}^{\mathrm{2}} \:+\:{r}^{\mathrm{2}} \:−\:\mathrm{2}{rR}\:{cos}\:\theta}}\:{d}\theta \\ $$

Question Number 33756 Answers: 1 Comments: 0

Prove that if circum-circle and in-circle of a triangle are concentric, the triangle is an equalateral triangle.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\boldsymbol{\mathrm{circum}}-\boldsymbol{\mathrm{circle}}\:\mathrm{and} \\ $$$$\boldsymbol{\mathrm{in}}-\boldsymbol{\mathrm{circle}}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\boldsymbol{\mathrm{concentric}}, \\ $$$$\mathrm{the}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{an}\:\boldsymbol{\mathrm{equalateral}}\:\boldsymbol{\mathrm{triangle}}. \\ $$

Question Number 33789 Answers: 3 Comments: 0

If the equation 2x^2 +14x−15=0 is divided by (x−4), the remainder is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{14}{x}−\mathrm{15}=\mathrm{0}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\left({x}−\mathrm{4}\right),\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is} \\ $$

Question Number 34652 Answers: 2 Comments: 2

a point charge q is placed at (0,a/2,0) . find flux due to point charge through a square sheet of side a in xz plane whose centre coincides with orign. ( do not use gauss law)

$${a}\:{point}\:{charge}\:{q}\:{is}\:{placed} \\ $$$${at}\:\left(\mathrm{0},{a}/\mathrm{2},\mathrm{0}\right)\:.\:{find}\:{flux} \\ $$$${due}\:{to}\:{point}\:{charge}\:{through} \\ $$$${a}\:{square}\:{sheet}\:{of}\:{side}\:{a}\:\: \\ $$$${in}\:{xz}\:{plane}\:{whose}\:{centre} \\ $$$${coincides}\:{with}\:{orign}. \\ $$$$\left(\:{do}\:{not}\:{use}\:{gauss}\:{law}\right) \\ $$

Question Number 33753 Answers: 1 Comments: 0

Question Number 33747 Answers: 0 Comments: 0

Calculate ∫_(−∞) ^(+∞) e^(−x^2 ) dx using Residue theorem

$${Calculate}\:\int_{−\infty} ^{+\infty} {e}^{−{x}^{\mathrm{2}} } {dx}\:\:{using}\:\:{Residue}\:{theorem} \\ $$

Question Number 33743 Answers: 0 Comments: 1

let p(x)=(1+x^2 )(1+x^4 )....(1+x^2^n ) with n integr 1) find the roots of p(x) 2) factorize p(x) inside C[x]

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)....\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right)\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$

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