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Question Number 209217 Answers: 2 Comments: 0

calculate : I= ∫_(0 ) ^( ∞) (( tan^( −1) (x))/((1 + x^( 2) )^( 2) )) dx = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{calculate}}\:: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}\:+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\: \\ $$$$ \\ $$

Question Number 209167 Answers: 2 Comments: 0

please convert 2531_((5000) ) to base 5002. thanks.

$${please}\:{convert}\:\:\mathrm{2531}_{\left(\mathrm{5000}\right)\:} {to}\:\:{base}\:\mathrm{5002}.\:\:{thanks}.\:\: \\ $$

Question Number 209166 Answers: 1 Comments: 0

Question Number 209162 Answers: 2 Comments: 0

Cyclic quadrilateral ABCD is inscribed in circle. Point S is intersection of diagonals AC and BD (S is not center of the circle). If AB=BC=6 and BS=4, what is length of BD?

$$ \\ $$Cyclic quadrilateral ABCD is inscribed in circle. Point S is intersection of diagonals AC and BD (S is not center of the circle). If AB=BC=6 and BS=4, what is length of BD?

Question Number 209161 Answers: 3 Comments: 2

Question Number 209137 Answers: 2 Comments: 0

Question Number 209131 Answers: 1 Comments: 0

prove : curve { ((x(t)=((a+r.cos(t))/(a^2 +r^2 +2ar.cos(t))))),((y(t)=((r.sin(t))/(a^2 +r^2 +2ar.cos(t))))) :} 0≤t≤2π is circle , find center & radius

$${prove}\:: \\ $$$${curve}\:\begin{cases}{{x}\left({t}\right)=\frac{{a}+{r}.{cos}\left({t}\right)}{{a}^{\mathrm{2}} +{r}^{\mathrm{2}} +\mathrm{2}{ar}.{cos}\left({t}\right)}}\\{{y}\left({t}\right)=\frac{{r}.{sin}\left({t}\right)}{{a}^{\mathrm{2}} +{r}^{\mathrm{2}} +\mathrm{2}{ar}.{cos}\left({t}\right)}}\end{cases}\:\:\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2}\pi \\ $$$${is}\:{circle}\:,\:{find}\:{center}\:\&\:{radius} \\ $$

Question Number 209129 Answers: 1 Comments: 0

Question Number 209128 Answers: 2 Comments: 0

Question Number 209127 Answers: 1 Comments: 0

Question Number 209126 Answers: 2 Comments: 0

Question Number 209125 Answers: 3 Comments: 0

Question Number 209124 Answers: 3 Comments: 0

Question Number 209123 Answers: 2 Comments: 0

Question Number 209122 Answers: 1 Comments: 0

Question Number 209121 Answers: 1 Comments: 0

Question Number 209118 Answers: 0 Comments: 0

Question Number 209117 Answers: 0 Comments: 0

Question Number 209116 Answers: 1 Comments: 0

Question Number 209115 Answers: 0 Comments: 0

Question Number 209099 Answers: 3 Comments: 0

Question Number 209098 Answers: 2 Comments: 0

Question Number 209072 Answers: 0 Comments: 8

Question Number 209066 Answers: 1 Comments: 1

Question Number 209065 Answers: 1 Comments: 0

The cost of maintaining a school is partly constant and partly varies as the number of students. With 50 students the cost is $15705 and with 40 students the cost is $13305. If the fee per student is $360.00, what is the least number of students for which the school can be run without loss?

$${The}\:{cost}\:{of}\:{maintaining}\:{a}\:{school}\:{is} \\ $$$${partly}\:{constant}\:{and}\:{partly}\:{varies}\:{as} \\ $$$${the}\:{number}\:{of}\:{students}.\:{With}\:\mathrm{50}\:{students} \\ $$$${the}\:{cost}\:{is}\:\$\mathrm{15705}\:{and}\:{with}\:\mathrm{40}\:{students} \\ $$$${the}\:{cost}\:{is}\:\$\mathrm{13305}.\:{If}\:{the}\:{fee}\:{per}\:{student} \\ $$$${is}\:\$\mathrm{360}.\mathrm{00},\:{what}\:{is}\:{the}\:{least}\:{number}\:{of} \\ $$$${students}\:{for}\:{which}\:{the}\:{school}\:{can}\:{be} \\ $$$${run}\:{without}\:{loss}? \\ $$

Question Number 209424 Answers: 1 Comments: 2

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