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AllQuestion and Answers: Page 273

Question Number 193435    Answers: 1   Comments: 1

Question Number 193426    Answers: 1   Comments: 0

∫((x^3 +1))^(1/3) dx=? solution?

$$\int\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}\mathrm{dx}=? \\ $$$$\mathrm{solution}? \\ $$

Question Number 193423    Answers: 3   Comments: 0

when tan(θ/2)=(1/a) then find cosθ=? from the a

$$\mathrm{when}\:\:\:\mathrm{tan}\frac{\theta}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{a}} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{cos}\theta=?\:\mathrm{from}\:\mathrm{the}\:\mathrm{a} \\ $$

Question Number 193414    Answers: 2   Comments: 0

Question Number 193411    Answers: 2   Comments: 1

∫_0 ^1 (√((1−x)/(1+x))) dx =?

$$\:\: \\ $$$$ \underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx}\:=? \\ $$

Question Number 193410    Answers: 2   Comments: 0

{ ((x=(√(3−(√(5+2(√3))))))),((y=(√(3+(√(5+2(√3))))))) :}

$$\:\:\begin{cases}{\mathrm{x}=\sqrt{\mathrm{3}−\sqrt{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{3}}}}}\\{\mathrm{y}=\sqrt{\mathrm{3}+\sqrt{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{3}}}}}\end{cases}\: \\ $$$$\:\:\: \\ $$

Question Number 193409    Answers: 0   Comments: 0

lim_(n→∞) ((∫_0 ^2 (1+6x−7x^2 +4x^3 −x^4 )^n dx))^(1/n)

$$\:\: \underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{n}}]{\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\left(\mathrm{1}+\mathrm{6x}−\mathrm{7x}^{\mathrm{2}} +\mathrm{4x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{4}} \right)^{\mathrm{n}} \:\mathrm{dx}} \\ $$

Question Number 193408    Answers: 1   Comments: 0

lim_(n→∞) ((1/n). ((1−(e^(a/n) )^(n−1) )/(1−e^(a/n) )) )

$$ \\ $$$$ \underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}}.\:\frac{\mathrm{1}−\left(\mathrm{e}^{\frac{\mathrm{a}}{\mathrm{n}}} \right)^{\mathrm{n}−\mathrm{1}} }{\mathrm{1}−\mathrm{e}^{\frac{\mathrm{a}}{\mathrm{n}}} }\:\right)\: \\ $$

Question Number 193405    Answers: 0   Comments: 0

Question Number 193399    Answers: 1   Comments: 0

Question Number 193398    Answers: 1   Comments: 0

Question Number 193391    Answers: 2   Comments: 0

Question Number 193390    Answers: 0   Comments: 0

A ship X sailing with a velocity (21 kmh 052⁰) observes a light from a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship. ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship. iii) the distance in km of the ship from then lighthoue when the lighthouse is due West of the ship

$$ \\ $$A ship X sailing with a velocity (21 kmh 052⁰) observes a light from a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship. ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship. iii) the distance in km of the ship from then lighthoue when the lighthouse is due West of the ship

Question Number 193389    Answers: 0   Comments: 0

Question Number 193387    Answers: 0   Comments: 1

Question Number 193385    Answers: 1   Comments: 0

Question Number 193381    Answers: 1   Comments: 0

Question Number 193377    Answers: 1   Comments: 1

Evaluate I=∫_0 ^( ∞) (1/(x^5 +x^4 +x^3 +x^2 +x+1))dx

$${Evaluate} \\ $$$${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$

Question Number 193375    Answers: 0   Comments: 0

Quantitative Reasoning Example: P_4 +M_3 =16 M_4 −P_3 =18, P_5 +M_3 =2 Find: P_6 +M_4 =? P_5 −M_8 =? M_3 +M_2 =? M_5 −P_(10) =?

$${Quantitative}\:{Reasoning} \\ $$$${Example}:\:\:{P}_{\mathrm{4}} +{M}_{\mathrm{3}} =\mathrm{16} \\ $$$${M}_{\mathrm{4}} −{P}_{\mathrm{3}} =\mathrm{18},\:{P}_{\mathrm{5}} +{M}_{\mathrm{3}} =\mathrm{2} \\ $$$${Find}: \\ $$$${P}_{\mathrm{6}} +{M}_{\mathrm{4}} =? \\ $$$${P}_{\mathrm{5}} −{M}_{\mathrm{8}} =? \\ $$$${M}_{\mathrm{3}} +{M}_{\mathrm{2}} =? \\ $$$${M}_{\mathrm{5}} −{P}_{\mathrm{10}} =? \\ $$$$ \\ $$

Question Number 193371    Answers: 3   Comments: 0

Reduce to first order and solve , showing each step in detail. 1. y′′ +(y′)^3 siny=0 2. y′′=1+(y′)^2

$$\mathrm{Reduce}\:\mathrm{to}\:\mathrm{first}\:\mathrm{order}\:\mathrm{and}\:\mathrm{solve}\:, \\ $$$$\mathrm{showing}\:\mathrm{each}\:\mathrm{step}\:\mathrm{in}\:\mathrm{detail}. \\ $$$$\mathrm{1}.\:\mathrm{y}''\:+\left(\mathrm{y}'\right)^{\mathrm{3}} \mathrm{siny}=\mathrm{0} \\ $$$$\mathrm{2}.\:\mathrm{y}''=\mathrm{1}+\left(\mathrm{y}'\right)^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 193368    Answers: 2   Comments: 0

If log_a y = (1/3) and log_8 a = x + 1 then show that y = 2^(x + 1)

$$\mathrm{If}\:\mathrm{log}_{{a}} {y}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{log}_{\mathrm{8}} {a}\:=\:{x}\:+\:\mathrm{1}\:\mathrm{then}\:\mathrm{show} \\ $$$$\mathrm{that}\:{y}\:=\:\mathrm{2}^{{x}\:+\:\mathrm{1}} \\ $$

Question Number 193366    Answers: 1   Comments: 0

2sin^2 2x>3cos x+3

$$\mathrm{2sin}\:^{\mathrm{2}} \mathrm{2}{x}>\mathrm{3cos}\:{x}+\mathrm{3} \\ $$

Question Number 193363    Answers: 1   Comments: 0

y = 4 × 10^(2x) Express x in terms of y, giving an exact simplified answer in terms of log base 10.

$${y}\:=\:\mathrm{4}\:×\:\mathrm{10}^{\mathrm{2}{x}} \\ $$$$\mathrm{Express}\:{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{y},\:\mathrm{giving}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{simplified}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{log}\:\mathrm{base}\:\mathrm{10}. \\ $$

Question Number 193360    Answers: 2   Comments: 0

If x = 2^p and y = 4^q then prove that log_2 (x^3 y) = 3p + 2q

$$\mathrm{If}\:{x}\:=\:\mathrm{2}^{{p}} \:\mathrm{and}\:{y}\:=\:\mathrm{4}^{{q}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{log}_{\mathrm{2}} \left({x}^{\mathrm{3}} {y}\right)\:=\:\mathrm{3}{p}\:+\:\mathrm{2}{q} \\ $$

Question Number 193356    Answers: 2   Comments: 0

Question Number 193351    Answers: 0   Comments: 0

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