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Question Number 93540    Answers: 0   Comments: 7

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what is the super hexagon?

$${what}\:{is}\:{the}\:{super}\:{hexagon}? \\ $$

Question Number 91836    Answers: 1   Comments: 1

Question Number 91760    Answers: 1   Comments: 3

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each vertex of a cube is to be labeled with an integer 1 through 8 , with each integer being used once,in such a way that the sum of the four numbers on the vertices of a face is the same for each face.Arrangements that can be obtained from each other through rotations of the cube are considered to be the same. Find all the arrangements

$${each}\:{vertex}\:{of}\:{a}\:{cube}\:{is}\:{to}\:{be}\:{labeled} \\ $$$${with}\:{an}\:{integer}\:\mathrm{1}\:{through}\:\mathrm{8}\:,\:{with} \\ $$$${each}\:{integer}\:{being}\:{used}\:{once},{in}\:{such} \\ $$$${a}\:{way}\:{that}\:{the}\:{sum}\:{of}\:{the}\:{four}\:{numbers} \\ $$$${on}\:{the}\:{vertices}\:{of}\:{a}\:{face}\:{is}\:{the}\:{same}\: \\ $$$${for}\:{each}\:{face}.{Arrangements}\:{that}\:{can} \\ $$$${be}\:{obtained}\:{from}\:{each}\:{other}\:{through} \\ $$$${rotations}\:{of}\:{the}\:{cube}\:{are}\:{considered} \\ $$$${to}\:{be}\:{the}\:{same}.\: \\ $$$${Find}\:{all}\:{the}\:{arrangements} \\ $$$$ \\ $$$$ \\ $$

Question Number 90087    Answers: 0   Comments: 1

Σ_(k = 1) ^∞ (1/k^k ) = ?

$$\underset{{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{k}^{{k}} }\:=\:? \\ $$

Question Number 89493    Answers: 0   Comments: 1

Question Number 89560    Answers: 0   Comments: 1

without use intergration by party ∫_0 ^(π/4) e^θ cos 2θ dθ

$${without}\:{use}\:{intergration} \\ $$$${by}\:{party} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {e}^{\theta} \mathrm{cos}\:\mathrm{2}\theta\:{d}\theta \\ $$

Question Number 88997    Answers: 0   Comments: 5

Question Number 88301    Answers: 0   Comments: 2

A circle touches the four sides of quadrilateral ABCD. Show/prove that AB+CD=BC+DA. Please help.

$${A}\:{circle}\:{touches}\:{the}\:{four}\:{sides} \\ $$$${of}\:{quadrilateral}\:{ABCD}.\:\mathrm{Show}/\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{A}{B}+{CD}={BC}+{DA}. \\ $$$$\mathrm{Please}\:\mathrm{help}. \\ $$

Question Number 88300    Answers: 0   Comments: 0

A circle touches the four sides of quadrilateral ABCD. Show/prove that AB+CD=BC+DA. Please help.

$${A}\:{circle}\:{touches}\:{the}\:{four}\:{sides} \\ $$$${of}\:{quadrilateral}\:{ABCD}.\:\mathrm{Show}/\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{A}{B}+{CD}={BC}+{DA}. \\ $$$$\mathrm{Please}\:\mathrm{help}. \\ $$

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Question Number 87648    Answers: 0   Comments: 4

the sequence a_1 ,a_2 ,a_3 , ... satisfies the relation a_(n+1) = a_n +a_(n−1) , for n>1. given that a_(20) = 6765 and a_(18) = 2584 what is a_(16)

$$\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} ,\:...\:\mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} +\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:,\:\mathrm{for} \\ $$$$\mathrm{n}>\mathrm{1}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{a}_{\mathrm{20}} \:=\:\mathrm{6765}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{18}} \:=\:\mathrm{2584}\:\mathrm{what}\:\mathrm{is}\:\mathrm{a}_{\mathrm{16}} \\ $$

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