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Question Number 47481 Answers: 1 Comments: 0

Three six−faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is k (3≤ k ≤ 8) is

$$\mathrm{Three}\:\mathrm{six}−\mathrm{faced}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{thrown} \\ $$$$\mathrm{together}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{appearing}\:\mathrm{on}\:\mathrm{the}\:\mathrm{dice} \\ $$$$\mathrm{is}\:\:{k}\:\left(\mathrm{3}\leqslant\:{k}\:\leqslant\:\mathrm{8}\right)\:\mathrm{is} \\ $$

Question Number 47480 Answers: 1 Comments: 0

Question Number 47477 Answers: 1 Comments: 0

Let n ∈ Z^+ f(1) = 1 f(2n) = f(n) f(2n+1) = (f(n))^2 − 2 f(1) + f(2) + f(3) + …+ f(100) = ...

$${Let}\:\:{n}\:\:\in\:\:\mathbb{Z}^{+} \\ $$$${f}\left(\mathrm{1}\right)\:\:=\:\:\mathrm{1} \\ $$$${f}\left(\mathrm{2}{n}\right)\:\:=\:\:{f}\left({n}\right) \\ $$$${f}\left(\mathrm{2}{n}+\mathrm{1}\right)\:\:=\:\:\left({f}\left({n}\right)\right)^{\mathrm{2}} \:−\:\mathrm{2} \\ $$$${f}\left(\mathrm{1}\right)\:+\:{f}\left(\mathrm{2}\right)\:+\:{f}\left(\mathrm{3}\right)\:+\:\ldots+\:{f}\left(\mathrm{100}\right)\:\:=\:\:... \\ $$

Question Number 47476 Answers: 2 Comments: 1

How may I prove the following theorem ? ((a + b)/2) ≥ (√( ab )) Thank you

$$\mathrm{How}\:\mathrm{may}\:\mathrm{I}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{theorem}\:? \\ $$$$ \\ $$$$\:\:\:\frac{\boldsymbol{{a}}\:+\:\boldsymbol{{b}}}{\mathrm{2}}\:\:\:\geqslant\:\:\sqrt{\:\boldsymbol{{ab}}\:\:} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 47471 Answers: 1 Comments: 2

Question Number 47467 Answers: 0 Comments: 1

Question Number 47457 Answers: 1 Comments: 0

A straight line through (2,2) intersects lines (√3)x+y=0 and (√3)x−y=0 at pts. A & B respectively. Find equation of line AB so that ΔOAB is equilateral?

$${A}\:{straight}\:{line}\:{through}\:\left(\mathrm{2},\mathrm{2}\right)\:{intersects} \\ $$$${lines}\:\sqrt{\mathrm{3}}{x}+{y}=\mathrm{0}\:{and}\:\sqrt{\mathrm{3}}{x}−{y}=\mathrm{0}\:{at}\:{pts}. \\ $$$${A}\:\&\:{B}\:{respectively}.\:{Find}\:{equation} \\ $$$${of}\:{line}\:{AB}\:{so}\:{that}\:\Delta{OAB}\:{is}\:{equilateral}? \\ $$

Question Number 47455 Answers: 0 Comments: 1

Question Number 47454 Answers: 1 Comments: 0

prove that the locus of middle point of the normal chord of the parabola y^2 =4ax is (y^2 /(2a))+((4a^3 )/y^2 )=x−2a

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{locus} \\ $$$$\mathrm{of}\:\mathrm{middle}\:\mathrm{point}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{normal}\:\mathrm{chord}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{parabola}\:\mathrm{y}^{\mathrm{2}} =\mathrm{4ax}\:\mathrm{is} \\ $$$$\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{2a}}+\frac{\mathrm{4a}^{\mathrm{3}} }{\mathrm{y}^{\mathrm{2}} }=\mathrm{x}−\mathrm{2a} \\ $$

Question Number 47449 Answers: 1 Comments: 1

Question Number 47447 Answers: 1 Comments: 0

Question Number 47438 Answers: 2 Comments: 0

Find locus of a point P which moves such that its distance from the line y=(√3)x−7 is same as its distance from (2(√3),−1) ?

$${Find}\:{locus}\:{of}\:{a}\:{point}\:{P}\:{which}\:{moves} \\ $$$${such}\:{that}\:{its}\:{distance}\:{from}\:{the}\:{line} \\ $$$${y}=\sqrt{\mathrm{3}}{x}−\mathrm{7}\:{is}\:{same}\:{as}\:{its}\:{distance}\:{from} \\ $$$$\left(\mathrm{2}\sqrt{\mathrm{3}},−\mathrm{1}\right)\:? \\ $$

Question Number 47433 Answers: 1 Comments: 6

Find the square root of − 5 − 12i, hence solve: z^2 − (4 + i)z + (5 + 6i) = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{of}\:\:−\:\mathrm{5}\:−\:\mathrm{12i},\:\:\mathrm{hence}\:\mathrm{solve}:\:\:\mathrm{z}^{\mathrm{2}} \:−\:\left(\mathrm{4}\:+\:\mathrm{i}\right)\mathrm{z}\:+\:\left(\mathrm{5}\:+\:\mathrm{6i}\right)\:=\:\mathrm{0} \\ $$

Question Number 47432 Answers: 0 Comments: 1

what is the nth derivative of e^(ax) sin (bx+c)?

$$ \\ $$$${what}\:{is}\:{the}\:{nth}\:{derivative}\:{of} \\ $$$${e}^{{ax}} \mathrm{sin}\:\left({bx}+{c}\right)? \\ $$

Question Number 47425 Answers: 1 Comments: 1

Question Number 47422 Answers: 1 Comments: 1

Question Number 47413 Answers: 1 Comments: 0

Calculate: 1999^2 − 1998^2 + 1997^2 − 1996^2 ... − 2^2 + 1^2

$$\mathrm{Calculate}:\:\:\mathrm{1999}^{\mathrm{2}} \:−\:\mathrm{1998}^{\mathrm{2}} \:+\:\mathrm{1997}^{\mathrm{2}} \:−\:\mathrm{1996}^{\mathrm{2}} \:...\:−\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{1}^{\mathrm{2}} \\ $$

Question Number 47407 Answers: 1 Comments: 0

Question Number 47402 Answers: 2 Comments: 2

Question Number 47401 Answers: 2 Comments: 1

Question Number 47421 Answers: 1 Comments: 0

(√(400^2 +100^2 =))

$$\sqrt{\mathrm{400}^{\mathrm{2}} +\mathrm{100}^{\mathrm{2}} =} \\ $$

Question Number 47420 Answers: 0 Comments: 0

$$ \\ $$

Question Number 47394 Answers: 1 Comments: 1

f(z)=((3z+1)/(2−4z)) f(f(z))=...

$${f}\left({z}\right)=\frac{\mathrm{3}{z}+\mathrm{1}}{\mathrm{2}−\mathrm{4}{z}} \\ $$$${f}\left({f}\left({z}\right)\right)=... \\ $$

Question Number 47391 Answers: 2 Comments: 1

z_1 =3+i z_2 =1−2i determinant ((((2z_2 +z_1 −5−i)/(2z_1 −z_2 +3−i))))^2 =..

$${z}_{\mathrm{1}} =\mathrm{3}+{i} \\ $$$${z}_{\mathrm{2}} =\mathrm{1}−\mathrm{2}{i} \\ $$$$\begin{vmatrix}{\frac{\mathrm{2}{z}_{\mathrm{2}} +{z}_{\mathrm{1}} −\mathrm{5}−{i}}{\mathrm{2}{z}_{\mathrm{1}} −{z}_{\mathrm{2}} +\mathrm{3}−{i}}}\end{vmatrix}^{\mathrm{2}} =.. \\ $$

Question Number 47389 Answers: 0 Comments: 1

((√3)−i)^(1+2i) =...

$$\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{1}+\mathrm{2}{i}} =... \\ $$

Question Number 47387 Answers: 0 Comments: 3

Find∫(√(sin2x)) dx=??

$$\mathscr{F}{ind}\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$

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