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Question Number 167189 Answers: 0 Comments: 1

Question Number 167179 Answers: 1 Comments: 0

Demonstrate that ∀ x, y ∈ R_+ ^∗ , ∀ q ∈ Q_+ ^∗ such that q>xy, ∃ a,b ∈ Q such that a>x, b>y and ab=q.

$${Demonstrate}\:{that}\:\forall\:{x},\:{y}\:\in\:\mathbb{R}_{+} ^{\ast} ,\:\forall\:{q}\:\in\:\mathbb{Q}_{+} ^{\ast} \\ $$$${such}\:{that}\:{q}>{xy},\:\exists\:{a},{b}\:\in\:\mathbb{Q}\:{such}\: \\ $$$${that}\:{a}>{x},\:{b}>{y}\:{and}\:{ab}={q}. \\ $$

Question Number 167176 Answers: 0 Comments: 1

Question Number 167173 Answers: 1 Comments: 0

∫_(−2) ^(−1) e^(−(t/2)) (√(t+2)) dt = ???

$$\int_{−\mathrm{2}} ^{−\mathrm{1}} {e}^{−\frac{{t}}{\mathrm{2}}} \sqrt{{t}+\mathrm{2}}\:{dt}\:=\:??? \\ $$

Question Number 167167 Answers: 1 Comments: 0

Find minimum value of function f(x)=2x−(√(x+1))−(√(x^2 −1))

$$\:\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}−\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 167164 Answers: 1 Comments: 0

Ω=∫_0 ^( (π/2)) (( sin^( 2) (x))/((sin(x)+cos(x))^( 6) )) dx=?

$$ \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\:\:\:{sin}^{\:\mathrm{2}} \left({x}\right)}{\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)^{\:\mathrm{6}} }\:{dx}=? \\ $$

Question Number 167165 Answers: 1 Comments: 0

Question Number 167160 Answers: 0 Comments: 0

calculate :: lim_(n→∞) ncos(∫_0 ^1 ((sin (2πnx))/x)dx)=(1/(2π))

$$\mathrm{calculate}\:::\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}ncos}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{nx}\right)}{\mathrm{x}}\mathrm{dx}\right)=\frac{\mathrm{1}}{\mathrm{2}\pi} \\ $$

Question Number 167159 Answers: 0 Comments: 0

Question Number 167158 Answers: 1 Comments: 0

Question Number 167152 Answers: 1 Comments: 2

Question Number 167150 Answers: 1 Comments: 0

Question Number 167145 Answers: 0 Comments: 1

∫ (dx/(x^2 −3(√x)+10))

$$\int\:\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{3}\sqrt{{x}}+\mathrm{10}} \\ $$

Question Number 167144 Answers: 1 Comments: 0

Calculate Σ_(k=1) ^n ((sin(1))/(cos(k)cos(k−1)))

$${Calculate}\: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{sin}\left(\mathrm{1}\right)}{{cos}\left({k}\right){cos}\left({k}−\mathrm{1}\right)} \\ $$

Question Number 167137 Answers: 1 Comments: 0

Question Number 167126 Answers: 0 Comments: 9

Assuming one of the WiFi towers of a building is 20km high, and has a perpendicular distance of 15km to a straight road. Calculate the distance of the road which receives a good WiFi signal if it has a limited range of 45km (Calculate to four significant figures)

$$ \\ $$Assuming one of the WiFi towers of a building is 20km high, and has a perpendicular distance of 15km to a straight road. Calculate the distance of the road which receives a good WiFi signal if it has a limited range of 45km (Calculate to four significant figures)

Question Number 167122 Answers: 0 Comments: 0