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Question Number 134097    Answers: 2   Comments: 0

In a square ABCD , a triangle APQ inscribed in it. AP=4 cm, PQ=3 cm and AQ=5 cm. Point P is on the side BC and point Q is on side CD. Find the area of the square ABCD.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD}\:,\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{APQ}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{it}.\:\mathrm{AP}=\mathrm{4}\:\mathrm{cm}, \\ $$$$\mathrm{PQ}=\mathrm{3}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{AQ}=\mathrm{5}\:\mathrm{cm}.\:\mathrm{Point} \\ $$$$\mathrm{P}\:\mathrm{is}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:\mathrm{BC}\:\mathrm{and}\:\mathrm{point}\:\mathrm{Q} \\ $$$$\mathrm{is}\:\mathrm{on}\:\mathrm{side}\:\mathrm{CD}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{square}\:\mathrm{ABCD}. \\ $$

Question Number 132230    Answers: 1   Comments: 0

S=Σ_(k=1) ^(+∞) ((1/( (√(k^2 −1))))−(1/( (√(k^2 +1))))) S =l or S=∞ ???

$$ \\ $$$$ \\ $$$$\boldsymbol{{S}}=\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{+\infty} {\sum}}\left(\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} −\mathrm{1}}}−\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} +\mathrm{1}}}\right) \\ $$$$\boldsymbol{{S}}\:={l}\:{or}\:\boldsymbol{{S}}=\infty\:\:??? \\ $$

Question Number 131847    Answers: 1   Comments: 0

Let (𝛀,ϝ,P) be a probalistics space show that, A,B∈ϝ if (P(A∣B)≤P(A) and P(B∣A)≪P(B)) then P(A∣B^_ )≥P(A)

$$\:\boldsymbol{{Let}}\:\left(\boldsymbol{\Omega},\digamma,\boldsymbol{{P}}\right)\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{probalistics}}\:\boldsymbol{{space}}\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}},\: \\ $$$$\boldsymbol{{A}},\boldsymbol{{B}}\in\digamma \\ $$$$\boldsymbol{{if}}\:\left(\boldsymbol{{P}}\left(\boldsymbol{{A}}\mid\boldsymbol{{B}}\right)\leqslant{P}\left(\boldsymbol{{A}}\right)\:\boldsymbol{{and}}\:\boldsymbol{{P}}\left(\boldsymbol{{B}}\mid\boldsymbol{{A}}\right)\ll\boldsymbol{{P}}\left({B}\right)\right) \\ $$$${t}\boldsymbol{{h}}{en}\:\boldsymbol{{P}}\left({A}\mid\overset{\_} {\boldsymbol{{B}}}\right)\geqslant\boldsymbol{{P}}\left(\boldsymbol{{A}}\right) \\ $$$$ \\ $$

Question Number 131590    Answers: 2   Comments: 0

show that U_n =∫_0 ^1 (dx/(1+x+x^2 +....+x^n )) converges!!

$$\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\boldsymbol{{U}}_{\boldsymbol{{n}}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\boldsymbol{{x}}+\boldsymbol{{x}}^{\mathrm{2}} +....+\boldsymbol{{x}}^{\boldsymbol{{n}}} }\: \\ $$$$\boldsymbol{{converges}}!! \\ $$

Question Number 131465    Answers: 1   Comments: 0

Let a,b and c be three positive real numbers . Prove that a+b+c ≤ ((a^2 +bc)/(b+c))+((b^2 +ca)/(c+a))+((c^2 +ab)/(a+b))

$${Let}\:{a},{b}\:{and}\:{c}\:{be}\:{three}\:{positive}\:{real}\:{numbers} \\ $$$$.\:{Prove}\:{that}\:{a}+{b}+{c}\:\leqslant\:\frac{{a}^{\mathrm{2}} +{bc}}{{b}+{c}}+\frac{{b}^{\mathrm{2}} +{ca}}{{c}+{a}}+\frac{{c}^{\mathrm{2}} +{ab}}{{a}+{b}} \\ $$

Question Number 127382    Answers: 1   Comments: 0

Question Number 125593    Answers: 2   Comments: 0

Question Number 125491    Answers: 1   Comments: 1

Question Number 125444    Answers: 1   Comments: 1

Question Number 125337    Answers: 1   Comments: 1

Question Number 125215    Answers: 2   Comments: 2

Question Number 125108    Answers: 0   Comments: 3

Question Number 125084    Answers: 1   Comments: 3

Question Number 125021    Answers: 1   Comments: 0

Question Number 124821    Answers: 1   Comments: 2

Question Number 124743    Answers: 1   Comments: 1

Question Number 124367    Answers: 0   Comments: 4

Question Number 124189    Answers: 0   Comments: 5

Question Number 124117    Answers: 0   Comments: 0

Question Number 123738    Answers: 1   Comments: 1

Question Number 123587    Answers: 1   Comments: 1

Question Number 123528    Answers: 1   Comments: 1

Question Number 123507    Answers: 0   Comments: 6

Question Number 123489    Answers: 1   Comments: 0

Question Number 123302    Answers: 2   Comments: 0

Question Number 123212    Answers: 1   Comments: 1

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