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AllQuestion and Answers: Page 170

Question Number 204739 Answers: 2 Comments: 0

Question Number 204742 Answers: 1 Comments: 4

Solve for real x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:{x} \\ $$

Question Number 204733 Answers: 2 Comments: 0

Find: ((59^2 + 48^2 + 41^2 − 30^2 )/(68^2 + 52^2 + 32^2 − 48^2 )) = ?

$$\mathrm{Find}:\:\:\:\frac{\mathrm{59}^{\mathrm{2}} \:+\:\mathrm{48}^{\mathrm{2}} \:+\:\mathrm{41}^{\mathrm{2}} \:−\:\mathrm{30}^{\mathrm{2}} }{\mathrm{68}^{\mathrm{2}} \:+\:\mathrm{52}^{\mathrm{2}} \:+\:\mathrm{32}^{\mathrm{2}} \:−\:\mathrm{48}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 204729 Answers: 1 Comments: 0

Question Number 204753 Answers: 0 Comments: 7

A wave has an amplitude of 20cm from rest. If the angle of oscillation is 30⁰. Find the displacement of the wave.

A wave has an amplitude of 20cm from rest. If the angle of oscillation is 30⁰. Find the displacement of the wave.

Question Number 204715 Answers: 2 Comments: 0

prove that ∫_0 ^1 ((ln^2 (1−x))/x)dx=2ζ(3)

$${prove}\:{that} \\ $$$$\overset{\mathrm{1}} {\int}_{\mathrm{0}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}}{dx}=\mathrm{2}\zeta\left(\mathrm{3}\right) \\ $$$$ \\ $$

Question Number 204712 Answers: 5 Comments: 1

Find all real solution (√(3x^2 +x−1)) +(√(x^2 −2x−3)) = (√(3x^2 +3x+5)) + (√(x^2 +3))

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{real}\:\mathrm{solution}\: \\ $$$$\:\:\:\:\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}}\:=\: \\ $$$$\:\:\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{5}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}\: \\ $$

Question Number 204707 Answers: 1 Comments: 0

integrate ∫_0 ^∞ (e^(−x^2 ) /(1+e^x ))dx

$$\boldsymbol{{integrate}}\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } }{\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{x}}} }\boldsymbol{{dx}} \\ $$

Question Number 204706 Answers: 0 Comments: 0

evaluate ∫_0 ^∞ 2^(−𝚪(x)) dx

$$\boldsymbol{{evaluate}}\:\int_{\mathrm{0}} ^{\infty} \mathrm{2}^{−\boldsymbol{\Gamma}\left(\boldsymbol{{x}}\right)} \boldsymbol{{dx}} \\ $$

Question Number 204705 Answers: 0 Comments: 1

evalute ∫_0 ^∞ 2^(−(√(tanx))) dx

$$\boldsymbol{{evalute}}\:\int_{\mathrm{0}} ^{\infty} \mathrm{2}^{−\sqrt{\boldsymbol{{tanx}}}} \boldsymbol{{dx}} \\ $$

Question Number 204702 Answers: 1 Comments: 0

prove that : cl(Q×Q )=^? R^2 note: (X ,d ) is a metric space , A ⊆ X : x∈ A^( −) =cl(A) ⇔ ∀ r >0 , B_r (x) ∩ A ≠ φ

$$ \\ $$$$\:\:\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\:\mathrm{cl}\left(\mathbb{Q}×\mathbb{Q}\:\right)\overset{?} {=}\:\mathbb{R}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{note}:\:\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space} \\ $$$$\:\:\:\:\:\:\:\:\:\:,\:\:\:{A}\:\subseteq\:{X}\::\:\:\:\:\:{x}\in\:\overset{\:\:−} {{A}}=\mathrm{cl}\left({A}\right)\:\Leftrightarrow\:\forall\:{r}\:>\mathrm{0}\:,\:{B}_{{r}} \:\left({x}\right)\:\cap\:{A}\:\neq\:\phi \\ $$

Question Number 204701 Answers: 3 Comments: 0

Question Number 204717 Answers: 1 Comments: 0

((3^0 +3^1 +3^2 +.........+ 3^(200) )/(13)) =^(Remainder) ?

$$\frac{\mathrm{3}^{\mathrm{0}} +\mathrm{3}^{\mathrm{1}} +\mathrm{3}^{\mathrm{2}} \:+.........+\:\mathrm{3}^{\mathrm{200}} }{\mathrm{13}}\:\overset{\mathrm{Remainder}} {=}\:? \\ $$

Question Number 204691 Answers: 1 Comments: 0

(√(a÷(√(a÷(√(a÷∙∙∙÷(√a)))))))=?

$$\sqrt{{a}\boldsymbol{\div}\sqrt{{a}\boldsymbol{\div}\sqrt{{a}\boldsymbol{\div}\centerdot\centerdot\centerdot\boldsymbol{\div}\sqrt{{a}}}}}=? \\ $$

Question Number 204690 Answers: 1 Comments: 0

((a^x ÷((b^y ÷(c^z )^(1/r) ))^(1/q) ))^(1/p) =?

$$\sqrt[{{p}}]{{a}^{{x}} \boldsymbol{\div}\sqrt[{{q}}]{{b}^{{y}} \boldsymbol{\div}\sqrt[{{r}}]{{c}^{{z}} }}}=? \\ $$

Question Number 204689 Answers: 1 Comments: 0

y=∣f(x)∣ ; (dy/dx)=?

$${y}=\mid{f}\left({x}\right)\mid\:\:;\:\:\:\:\frac{{dy}}{{dx}}=? \\ $$

Question Number 204688 Answers: 1 Comments: 0

f(x)=sgn(x); f^′ (x)=(d/dx)[f(x)]=?

$${f}\left({x}\right)={sgn}\left({x}\right);\:\:\:\:\:{f}^{'} \left({x}\right)=\frac{{d}}{{dx}}\left[{f}\left({x}\right)\right]=? \\ $$

Question Number 204687 Answers: 0 Comments: 0

(√(a−(√(b−(√c)))))=?

$$\sqrt{{a}−\sqrt{{b}−\sqrt{{c}}}}=? \\ $$

Question Number 204684 Answers: 0 Comments: 2

Question Number 204674 Answers: 1 Comments: 1

Question Number 204671 Answers: 3 Comments: 0

if f(f(x))=x^2 −3x+4, find f(1)=?

$${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4},\:{find}\:{f}\left(\mathrm{1}\right)=? \\ $$

Question Number 204666 Answers: 0 Comments: 0

this is a closed curve: f(θ)=(e^(iθ) )^((e^(iθ) )) =e^(−θsin θ) e^(iθcos θ) ; −π<θ≤π f: { ((x(θ)=e^(−θsin θ) cos (θcos θ))),((y(θ)=e^(−θsin θ) sin (θcos θ))) :} find the area

$$\mathrm{this}\:\mathrm{is}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{curve}: \\ $$$${f}\left(\theta\right)=\left(\mathrm{e}^{\mathrm{i}\theta} \right)^{\left(\mathrm{e}^{\mathrm{i}\theta} \right)} =\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{e}^{\mathrm{i}\theta\mathrm{cos}\:\theta} ;\:−\pi<\theta\leqslant\pi \\ $$$${f}:\:\begin{cases}{{x}\left(\theta\right)=\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{cos}\:\left(\theta\mathrm{cos}\:\theta\right)}\\{{y}\left(\theta\right)=\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{sin}\:\left(\theta\mathrm{cos}\:\theta\right)}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{area} \\ $$

Question Number 204664 Answers: 2 Comments: 0

8+(√(8^2 +(√(8^4 +(√(8^8 +(√(8^(16) +(√(...)))))))))) = ?

$$\:\:\mathrm{8}+\sqrt{\mathrm{8}^{\mathrm{2}} +\sqrt{\mathrm{8}^{\mathrm{4}} +\sqrt{\mathrm{8}^{\mathrm{8}} +\sqrt{\mathrm{8}^{\mathrm{16}} +\sqrt{...}}}}}\:=\:?\: \\ $$

Question Number 204663 Answers: 1 Comments: 0

Question Number 204658 Answers: 2 Comments: 0

If a = (9)^(1/3) − (3)^(1/3) + 1 Find (((4 − a)/a))^6 = ?

$$\mathrm{If}\:\:\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\:\left(\frac{\mathrm{4}\:−\:\mathrm{a}}{\mathrm{a}}\right)^{\mathrm{6}} =\:? \\ $$

Question Number 204657 Answers: 1 Comments: 0

Consider point A inside a triangle with sides 3,4 and 5. if d is the sum of the distances of this point from the sides.what is the smallest value of d?

$${Consider}\:{point}\:{A}\:{inside}\:{a}\:{triangle} \\ $$$${with}\:{sides}\:\mathrm{3},\mathrm{4}\:{and}\:\mathrm{5}.\:{if}\:{d}\:\:{is}\:{the}\:{sum} \\ $$$$\:{of}\:{the}\:{distances}\:\:{of}\:{this}\:{point}\:{from} \\ $$$${the}\:{sides}.{what}\:{is}\:{the}\:{smallest} \\ $$$${value}\:{of}\:{d}? \\ $$$$ \\ $$

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