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Question Number 173430 Answers: 0 Comments: 3

Question Number 173426 Answers: 0 Comments: 0

In △ABC the following relationship holds: (a^3 +b^3 +c^3 )(h_a ^3 +h_b ^3 +h_c ^3 ) ≥ 5832 (√3) r^6

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}: \\ $$$$\left(\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} \right)\left(\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{3}} +\mathrm{h}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{3}} +\mathrm{h}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{3}} \right)\:\geqslant\:\mathrm{5832}\:\sqrt{\mathrm{3}}\:\mathrm{r}^{\mathrm{6}} \\ $$

Question Number 173424 Answers: 1 Comments: 0

prove that ∫_0 ^( ∞) (( sin(x))/(sinh(x))) dx = (π/2)tanh((π/2))

$$ \\ $$$$\:\:\:\:\mathrm{prove}\:\:\mathrm{that} \\ $$$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{sinh}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\frac{\pi}{\mathrm{2}}\mathrm{tanh}\left(\frac{\pi}{\mathrm{2}}\right) \\ $$$$ \\ $$

Question Number 173421 Answers: 0 Comments: 0

In triangle ABC, AD is the bisector of ∠A meets BC at D, if 2∠C=∠B and AB=DC. Find ∠BAC

$$\mathrm{In}\:\mathrm{triangle}\:\:\mathrm{ABC},\:\mathrm{AD}\:\mathrm{is}\:\mathrm{the}\:\mathrm{bisector} \\ $$$$\mathrm{of}\:\:\angle\mathrm{A}\:\:\mathrm{meets}\:\:\mathrm{BC}\:\mathrm{at}\:\mathrm{D},\:\mathrm{if}\:\:\mathrm{2}\angle\mathrm{C}=\angle\mathrm{B} \\ $$$$\mathrm{and}\:\mathrm{AB}=\mathrm{DC}.\:\mathrm{Find}\:\angle\mathrm{BAC} \\ $$

Question Number 173420 Answers: 1 Comments: 0

Question Number 173418 Answers: 1 Comments: 0

Question Number 173417 Answers: 0 Comments: 1

Question Number 173447 Answers: 0 Comments: 4

Find tan (142.5°) without tables.

$${Find}\:\mathrm{tan}\:\left(\mathrm{142}.\mathrm{5}°\right)\:{without} \\ $$$${tables}. \\ $$

Question Number 173411 Answers: 1 Comments: 0

Q : ( 26 ! )^( 58) + k ≡^( 29) 0 and , k ∈ N , find: Min ( k )=?

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Q}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{26}\:!\:\right)^{\:\mathrm{58}} \:+\:\mathrm{k}\:\overset{\:\mathrm{29}} {\equiv}\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:,\:\:\mathrm{k}\:\in\:\mathbb{N}\:,\:\:\mathrm{find}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\mathrm{k}\:\right)=? \\ $$$$ \\ $$

Question Number 173408 Answers: 1 Comments: 1

Question Number 173406 Answers: 0 Comments: 0

Find: Ω =lim_(n→∞) ((√((1 + n!)^(n!) ))/(n ∙ (n!)!))

$$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\left(\mathrm{1}\:+\:\mathrm{n}!\right)^{\boldsymbol{\mathrm{n}}!} }}{\mathrm{n}\:\centerdot\:\left(\mathrm{n}!\right)!} \\ $$

Question Number 173403 Answers: 0 Comments: 4

Question Number 173401 Answers: 0 Comments: 1

1.show that lim_(n→+∝) ((2^(2022) n^2 )/3^n )=0 ?

$$\mathrm{1}.\mathrm{show}\:\mathrm{that}\:\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\frac{\mathrm{2}^{\mathrm{2022}} \mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{n}} }=\mathrm{0}\:? \\ $$

Question Number 173396 Answers: 1 Comments: 0

Consider the statements: x: Birds fly y: The sky is blue Which of the following statements can be represented aa x⇔y? (i) When the sky is blue, the birds fly. (ii) Either the bird is flying or the sky is blue. (iii) Birds fly if and only if the sky is blue. (iv) When birds fly, the sky is blue.

Question Number 173393 Answers: 0 Comments: 0

If a,b≥0 then prove that: ∫_a ^( b) ∫_a ^( b) ∣ay−ab + bx∣ dydx ≤ a^2 b^2

$$\mathrm{If}\:\:\mathrm{a},\mathrm{b}\geqslant\mathrm{0}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\int_{\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \int_{\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\mid\mathrm{ay}−\mathrm{ab}\:+\:\mathrm{bx}\mid\:\mathrm{dydx}\:\leqslant\:\mathrm{a}^{\mathrm{2}} \mathrm{b}^{\mathrm{2}} \\ $$

Question Number 173383 Answers: 1 Comments: 0