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Use the substitution t = sin(θ) to solve the equation 2sin^4 (θ) − 9sin^3 (θ) + 14sin^2 (θ) − 9sin(θ) + 2 = 0, for possible values of θ in the range 0 ≤ θ ≤ 2π

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{substitution}\:\:\mathrm{t}\:=\:\mathrm{sin}\left(\theta\right)\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{2sin}^{\mathrm{4}} \left(\theta\right)\:−\:\mathrm{9sin}^{\mathrm{3}} \left(\theta\right)\:+\:\mathrm{14sin}^{\mathrm{2}} \left(\theta\right)\:−\:\mathrm{9sin}\left(\theta\right)\:+\:\mathrm{2}\:=\:\mathrm{0},\:\: \\ $$$$\mathrm{for}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{in}\:\mathrm{the}\:\mathrm{range}\:\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\mathrm{2}\pi \\ $$

Question Number 12517 Answers: 1 Comments: 0

A spring stretches by 15cm when a mass of 300g hangs down from it. if the spring is then strethed an additional 10cm and realeased, calculate (a) the spring constant (b) Angular velocity (c) The amplitude of the oscillation (d) The maximum velocity (e) The maximum acceleration of the mass (f) The period T and frequency f

$$\mathrm{A}\:\mathrm{spring}\:\mathrm{stretches}\:\mathrm{by}\:\mathrm{15cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{300g}\:\mathrm{hangs}\:\mathrm{down}\:\mathrm{from}\:\mathrm{it}. \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{spring}\:\mathrm{is}\:\mathrm{then}\:\mathrm{strethed}\:\mathrm{an}\:\mathrm{additional}\:\mathrm{10cm}\:\mathrm{and}\:\mathrm{realeased},\:\mathrm{calculate} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{spring}\:\mathrm{constant} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Angular}\:\mathrm{velocity} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{amplitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{oscillation} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{velocity} \\ $$$$\left(\mathrm{e}\right)\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mass} \\ $$$$\left(\mathrm{f}\right)\:\mathrm{The}\:\mathrm{period}\:\mathrm{T}\:\mathrm{and}\:\mathrm{frequency}\:\mathrm{f} \\ $$

Question Number 12513 Answers: 1 Comments: 0

lim_(x→∞) x^2 [sec ((2/x)) − 1]

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\left[\mathrm{sec}\:\left(\frac{\mathrm{2}}{{x}}\right)\:−\:\mathrm{1}\right] \\ $$

Question Number 12506 Answers: 2 Comments: 0

A wooden stick was broken randomly into three pieces. What is the probability that a triangle can be built from those three parts?

$$\mathrm{A}\:\mathrm{wooden}\:\mathrm{stick}\:\mathrm{was}\:\mathrm{broken}\:\mathrm{randomly}\:\mathrm{into} \\ $$$$\mathrm{three}\:\mathrm{pieces}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{built}\:\mathrm{from}\:\mathrm{those}\:\mathrm{three}\:\mathrm{parts}? \\ $$

Question Number 12500 Answers: 1 Comments: 0

Please help explain how to solve ∫e^(1/x) dx

$$\mathrm{Please}\:\mathrm{help}\:\mathrm{explain}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\int{e}^{\frac{\mathrm{1}}{{x}}} {dx} \\ $$

Question Number 12495 Answers: 1 Comments: 3

find the real values of x for which the function f(x)=(x^2 /(x^2 +3x+2))

$${find}\:{the}\:{real}\:{values}\:{of}\:{x}\:{for}\:{which} \\ $$$${the}\:{function}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}} \\ $$$$ \\ $$

Question Number 12492 Answers: 2 Comments: 1

this is calculus evaluate lim_(x→0) ((sin3xsin5x)/(7x^2 ))

$${this}\:{is}\:{calculus}\: \\ $$$${evaluate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\mathrm{3}{xsin}\mathrm{5}{x}}{\mathrm{7}{x}^{\mathrm{2}} } \\ $$

Question Number 12490 Answers: 0 Comments: 1

328976/256

$$\mathrm{328976}/\mathrm{256} \\ $$

Question Number 12489 Answers: 1 Comments: 0

log_2 x + log_(1/x) (1/2) ≥ 0 x = ?

$$\mathrm{log}_{\mathrm{2}} \:{x}\:+\:\mathrm{log}_{\mathrm{1}/{x}} \:\frac{\mathrm{1}}{\mathrm{2}}\:\geqslant\:\mathrm{0} \\ $$$${x}\:=\:? \\ $$

Question Number 12487 Answers: 0 Comments: 4

Someone has been solved Goldbach′s Conjecture??

$$\mathrm{Someone}\:\mathrm{has}\:\mathrm{been}\:\mathrm{solved}\:\mathrm{Goldbach}'\mathrm{s} \\ $$$$\mathrm{Conjecture}?? \\ $$

Question Number 12499 Answers: 1 Comments: 0

Water flows out of a tank through a hole of diameter 2cm above the hole (1) Determine the velocity of outflow (2) The rate of outflow when the level of the water in the tank is 2cm above the hole.

$$\mathrm{Water}\:\mathrm{flows}\:\mathrm{out}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tank}\:\mathrm{through}\:\mathrm{a}\:\mathrm{hole}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{2cm}\:\mathrm{above}\:\mathrm{the}\:\mathrm{hole} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{outflow} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{The}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{outflow}\:\mathrm{when}\:\mathrm{the}\:\mathrm{level}\:\mathrm{of}\:\mathrm{the}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{2cm}\:\mathrm{above} \\ $$$$\mathrm{the}\:\mathrm{hole}.\: \\ $$

Question Number 12470 Answers: 1 Comments: 0

((0.03125))^(1/5) =

$$\sqrt[{\mathrm{5}}]{\mathrm{0}.\mathrm{03125}}\:=\: \\ $$

Question Number 12464 Answers: 3 Comments: 0

∫ sin^3 (7x) dx

$$\int\:\mathrm{sin}^{\mathrm{3}} \left(\mathrm{7x}\right)\:\mathrm{dx} \\ $$

Question Number 12463 Answers: 1 Comments: 0

∫ ((x + 1)/((x^2 + 2x + 3)^(2/3) )) dx

$$\int\:\:\frac{\mathrm{x}\:+\:\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:+\:\mathrm{3}\right)^{\mathrm{2}/\mathrm{3}} }\:\:\mathrm{dx} \\ $$

Question Number 12446 Answers: 2 Comments: 1

find x (√x) = 8^x