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Question Number 147397 Answers: 1 Comments: 0

hmmmm ! 11×11=4 22×22=16 33×33=?

$$\boldsymbol{\mathrm{hmmmm}}\:! \\ $$$$\mathrm{11}×\mathrm{11}=\mathrm{4} \\ $$$$\mathrm{22}×\mathrm{22}=\mathrm{16} \\ $$$$\mathrm{33}×\mathrm{33}=? \\ $$

Question Number 147396 Answers: 0 Comments: 0

Question Number 147381 Answers: 1 Comments: 0

On pose H_n (α)=Π_(k=1) ^(n−1) sin((α/(2n))+((kπ)/n)) a) montrer que ∀α≠0, 2^(n−1) H_n (α)=((sin((α/2)))/(sin((α/(2n))))) b) Calculer lim_(α→0) H_n (α) c) De^ duire que ∀α≥2, sin((π/n))×sin(((2π)/n))×....×sin((((n−1)π)/n))=(π/2^(n−1) )..

$${On}\:{pose}\:{H}_{{n}} \left(\alpha\right)=\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}{sin}\left(\frac{\alpha}{\mathrm{2}{n}}+\frac{{k}\pi}{{n}}\right) \\ $$$$\left.{a}\right)\:{montrer}\:{que}\:\forall\alpha\neq\mathrm{0},\: \\ $$$$\mathrm{2}^{{n}−\mathrm{1}} {H}_{{n}} \left(\alpha\right)=\frac{{sin}\left(\frac{\alpha}{\mathrm{2}}\right)}{{sin}\left(\frac{\alpha}{\mathrm{2}{n}}\right)} \\ $$$$\left.{b}\right)\:{Calculer}\:{lim}_{\alpha\rightarrow\mathrm{0}} \:{H}_{{n}} \left(\alpha\right) \\ $$$$\left.{c}\right)\:{D}\acute {{e}duire}\:{que}\:\forall\alpha\geqslant\mathrm{2},\: \\ $$$${sin}\left(\frac{\pi}{{n}}\right)×{sin}\left(\frac{\mathrm{2}\pi}{{n}}\right)×....×{sin}\left(\frac{\left({n}−\mathrm{1}\right)\pi}{{n}}\right)=\frac{\pi}{\mathrm{2}^{{n}−\mathrm{1}} }.. \\ $$

Question Number 147413 Answers: 0 Comments: 0

An experiment consist of flipping a coin and then flipping it a second time if a head occurs.If a tail appears on thei first flip then a die is tossed once. a. Listthe element of the sample space S.b b. List the element of S corresponding to the event A that a number less than 4 occurred on the die. c. List thet element of S corresponding to the event B that 2 tails occurred.

$$ \\ $$$$\mathrm{An}\:\mathrm{experiment}\:\mathrm{consist}\:\mathrm{of}\:\mathrm{flipping}\:\mathrm{a} \\ $$$$\mathrm{coin}\:\mathrm{and}\:\mathrm{then}\:\mathrm{flipping}\:\mathrm{it}\:\mathrm{a}\:\mathrm{second}\:\mathrm{time}\: \\ $$$$\mathrm{if}\:\mathrm{a}\:\mathrm{head}\:\mathrm{occurs}.\mathrm{If}\:\mathrm{a}\:\mathrm{tail}\:\mathrm{appears}\:\mathrm{on}\:\mathrm{thei} \\ $$$$\mathrm{first}\:\mathrm{flip}\:\mathrm{then}\:\mathrm{a}\:\mathrm{die}\:\mathrm{is}\:\mathrm{tossed}\:\mathrm{once}.\: \\ $$$$\mathrm{a}.\:\mathrm{Listthe}\:\mathrm{element}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{space}\:\mathrm{S}.\mathrm{b} \\ $$$$\mathrm{b}.\:\mathrm{List}\:\mathrm{the}\:\mathrm{element}\:\mathrm{of}\:\mathrm{S}\:\mathrm{corresponding} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{event}\:\mathrm{A}\:\mathrm{that}\:\mathrm{a}\:\mathrm{number}\:\mathrm{less}\:\mathrm{than}\: \\ $$$$\mathrm{4}\:\mathrm{occurred}\:\mathrm{on}\:\mathrm{the}\:\mathrm{die}.\: \\ $$$$\mathrm{c}.\:\mathrm{List}\:\mathrm{thet}\:\mathrm{element}\:\mathrm{of}\:\mathrm{S}\:\mathrm{corresponding}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{event}\:\mathrm{B}\:\mathrm{that}\:\mathrm{2}\:\mathrm{tails}\:\mathrm{occurred}. \\ $$

Question Number 147412 Answers: 1 Comments: 0