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AllQuestion and Answers: Page 1209

Question Number 94857 Answers: 2 Comments: 7

Question Number 94855 Answers: 1 Comments: 0

Solve for x in R x(√(x+3))−4(√(x+3))+2x−8=0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{in}\:\mathbb{R} \\ $$$${x}\sqrt{{x}+\mathrm{3}}−\mathrm{4}\sqrt{{x}+\mathrm{3}}+\mathrm{2}{x}−\mathrm{8}=\mathrm{0} \\ $$

Question Number 94849 Answers: 1 Comments: 0

Calculate limits of f at +∞; −1 and 1 f(x)=2x+3−(x/(1−x^2 ))

$$\mathrm{Calculate}\:\mathrm{limits}\:\mathrm{of}\:{f}\:\mathrm{at}\:+\infty;\:−\mathrm{1}\:\mathrm{and}\:\mathrm{1} \\ $$$${f}\left({x}\right)=\mathrm{2}{x}+\mathrm{3}−\frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$

Question Number 94847 Answers: 2 Comments: 0

Question Number 94835 Answers: 0 Comments: 0

proof or disproof that if a quotient group (G/H) is abelian then G must be abelian.

$$\mathrm{proof}\:\mathrm{or}\:\mathrm{disproof}\:\mathrm{that}\:\mathrm{if}\:\mathrm{a}\:\mathrm{quotient} \\ $$$$\mathrm{group}\:\frac{\mathrm{G}}{\mathrm{H}}\:\mathrm{is}\:\mathrm{abelian}\:\mathrm{then}\:\mathrm{G}\:\mathrm{must}\:\mathrm{be}\:\mathrm{abelian}. \\ $$

Question Number 94820 Answers: 1 Comments: 0

A train which travels at a uniform speed due to mechanical fault after traveling for an hour goes at 3/5 th of the original speed and reaches the destination 2 hours late. If the fault occured after traveling another 50 miles the train would have reached 40 minutes earlier. What is the distance between the two stations ?

$${A}\:{train}\:{which}\:{travels}\:{at}\:{a}\:{uniform}\:{speed}\:{due}\:{to}\:{mechanical}\:{fault}\:{after}\: \\ $$$${traveling}\:{for}\:{an}\:{hour}\:{goes}\:{at}\:\mathrm{3}/\mathrm{5}\:{th}\:{of}\:{the}\:{original}\:{speed}\:{and}\:{reaches}\:{the}\: \\ $$$${destination}\:\mathrm{2}\:{hours}\:{late}.\:{If}\:{the}\:{fault}\:{occured}\:{after}\:{traveling}\:{another}\:\mathrm{50} \\ $$$${miles}\:{the}\:{train}\:{would}\:{have}\:{reached}\:\mathrm{40}\:{minutes}\:{earlier}.\:{What}\:{is}\:{the}\: \\ $$$${distance}\:{between}\:{the}\:{two}\:{stations}\:? \\ $$

Question Number 94818 Answers: 1 Comments: 7

find such a polynomial if is divided by (x−2) then the remainder is 5, if it isdivided by (x−3) the remainder is 9, if it is divided by (x−4) the remainder is 13, if divide by (x−10) and the remaider becomes 37 and if (x−(3/4)) divided by the remainder becomes zero?

$$\:\mathrm{find}\:\mathrm{such}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{if}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{2}\right)\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{remainder}\:\mathrm{is}\:\mathrm{5},\:\mathrm{if}\:\mathrm{it}\:\mathrm{isdivided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{3}\right)\:\mathrm{the}\:\mathrm{remainder} \\ $$$$\mathrm{is}\:\mathrm{9},\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{4}\right)\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{13},\:\mathrm{if}\: \\ $$$$\mathrm{divide}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{10}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaider}\:\mathrm{becomes}\:\mathrm{37}\:\mathrm{and} \\ $$$$\mathrm{if}\:\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)\:\mathrm{divided}\:\mathrm{by}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{becomes}\:\mathrm{zero}? \\ $$

Question Number 94816 Answers: 1 Comments: 2

Question Number 94811 Answers: 3 Comments: 0

∫(dx/(x+(√x))) (2,3)=?

$$\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}}}\:\:\:\left(\mathrm{2},\mathrm{3}\right)=? \\ $$

Question Number 94806 Answers: 0 Comments: 2

Question Number 94803 Answers: 1 Comments: 0

Question Number 94801 Answers: 0 Comments: 0

Question Number 94797 Answers: 1 Comments: 0

Question Number 94786 Answers: 0 Comments: 1

x, y ∈N\{0, 1} ∧ x≤y find z∈N with z!=x!y!

$${x},\:{y}\:\in\mathbb{N}\backslash\left\{\mathrm{0},\:\mathrm{1}\right\}\:\wedge\:{x}\leqslant{y} \\ $$$$\mathrm{find}\:{z}\in\mathbb{N}\:\mathrm{with}\:{z}!={x}!{y}! \\ $$

Question Number 94782 Answers: 1 Comments: 0

The velocity of physical quantities is given by v = (√((P + (1/n))/x)) , where P is the pressure. Find the dimention of n and x.

$$\mathrm{The}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{physical}\:\mathrm{quantities}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:\:\mathrm{v}\:\:=\:\:\sqrt{\frac{\mathrm{P}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{n}}}{\mathrm{x}}}\:,\:\:\mathrm{where}\:\:\mathrm{P}\:\mathrm{is}\:\mathrm{the}\:\mathrm{pressure}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{dimention}\:\mathrm{of}\:\:\:\mathrm{n}\:\:\mathrm{and}\:\:\mathrm{x}. \\ $$

Question Number 94780 Answers: 0 Comments: 1

x!(x−4)!=12(2x−7)! x=?

$$\mathrm{x}!\left(\mathrm{x}−\mathrm{4}\right)!=\mathrm{12}\left(\mathrm{2x}−\mathrm{7}\right)! \\ $$$$\mathrm{x}=? \\ $$

Question Number 94776 Answers: 0 Comments: 0

Question Number 94774 Answers: 2 Comments: 1

Question Number 94773 Answers: 1 Comments: 0

Question Number 94772 Answers: 0 Comments: 0

Question Number 94769 Answers: 2 Comments: 0

Question Number 94768 Answers: 1 Comments: 0

Question Number 94767 Answers: 1 Comments: 0

Question Number 94764 Answers: 2 Comments: 0

Question Number 94765 Answers: 0 Comments: 0

Question Number 94756 Answers: 0 Comments: 2

solution: Q1)a) n=((ln(m/m_0 ))/(ln0.5)) = ((ln(12/75))/(ln0.5)) =2.64 N=N_0 (0.5)^n = 6.02×10^(23) (0.5)^(2.64) = 9.66×10^(22) A=λN=1.5×10^(−4) × 9.66×10^(22) =1.45×10^(19) Bq

$$\left.{s}\left.{olution}:\:\mathrm{Q1}\right){a}\right)\:{n}=\frac{{ln}\left({m}/{m}_{\mathrm{0}} \right)}{{ln}\mathrm{0}.\mathrm{5}}\:=\:\frac{{ln}\left(\mathrm{12}/\mathrm{75}\right)}{{ln}\mathrm{0}.\mathrm{5}}\:=\mathrm{2}.\mathrm{64} \\ $$$${N}=\mathrm{N}_{\mathrm{0}} \left(\mathrm{0}.\mathrm{5}\right)^{{n}} \:=\:\mathrm{6}.\mathrm{02}×\mathrm{10}^{\mathrm{23}} \left(\mathrm{0}.\mathrm{5}\right)^{\mathrm{2}.\mathrm{64}} =\:\mathrm{9}.\mathrm{66}×\mathrm{10}^{\mathrm{22}} \\ $$$${A}=\lambda{N}=\mathrm{1}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} \:×\:\mathrm{9}.\mathrm{66}×\mathrm{10}^{\mathrm{22}} =\mathrm{1}.\mathrm{45}×\mathrm{10}^{\mathrm{19}} \:{Bq} \\ $$

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