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Question Number 59114 Answers: 4 Comments: 1

Question Number 59113 Answers: 1 Comments: 0

Let a is a real number . How many solutions can the equation in θ (sin θ + cos θ)(sin θ cos θ − 1) = a have for 0 < θ < (π/2) ?

$${Let}\:\:{a}\:\:{is}\:\:{a}\:\:{real}\:\:{number}\:.\:\:{How}\:\:{many}\:\:{solutions} \\ $$$${can}\:\:{the}\:\:{equation}\:\:{in}\:\:\theta\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta\right)\left(\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:−\:\mathrm{1}\right)\:\:=\:\:{a} \\ $$$${have}\:\:{for}\:\:\mathrm{0}\:<\:\theta\:<\:\frac{\pi}{\mathrm{2}}\:\:? \\ $$

Question Number 59104 Answers: 0 Comments: 0

i want of ask in mechanics is this possible?? power=((work done)/(time taken)) if power = p_w , Work= W_d , and time=t ⇒ p_w = (W_d /t) but W_d = force(f)×distance(s) W_d = fs ⇒ p_w = ((f×s)/t) p_w = f × (s/t)(distance/time) p_w = f × velocity but f=ma p_w = m×a×v rearranging ⇒ p_(w ) = m×v×a p_w = momentum(P)×Acceleration(a) Power = momentum × Acceleration. the momentum of a system is directly propotional to the power of that system but will have a minimum momentum when accelerating. what do you think?

$${i}\:{want}\:{of}\:{ask}\:{in}\:{mechanics}\:{is}\:{this} \\ $$$${possible}?? \\ $$$$ \\ $$$${power}=\frac{{work}\:{done}}{{time}\:{taken}} \\ $$$${if}\:{power}\:=\:{p}_{{w}} \:,\:{Work}=\:{W}_{{d}} ,\:{and}\:{time}={t} \\ $$$$\Rightarrow\:{p}_{{w}} =\:\frac{{W}_{{d}} }{{t}} \\ $$$${but}\:{W}_{{d}} =\:{force}\left({f}\right)×{distance}\left({s}\right) \\ $$$$\:\:\:\:\:\:\:\:{W}_{{d}} =\:{fs} \\ $$$$\Rightarrow\:{p}_{{w}} =\:\frac{{f}×{s}}{{t}} \\ $$$$\:\:\:\:\:{p}_{{w}} =\:{f}\:×\:\frac{{s}}{{t}}\left({distance}/{time}\right) \\ $$$$\:\:\:{p}_{{w}} =\:{f}\:×\:{velocity} \\ $$$$\:\:\:{but}\:{f}={ma} \\ $$$${p}_{{w}} =\:{m}×{a}×{v} \\ $$$${rearranging} \\ $$$$\Rightarrow\:{p}_{{w}\:} =\:{m}×{v}×{a} \\ $$$$\:\:\:\:\:\:{p}_{{w}} =\:{momentum}\left({P}\right)×{Acceleration}\left({a}\right) \\ $$$${Power}\:=\:{momentum}\:×\:{Acceleration}. \\ $$$${the}\:{momentum}\:{of}\:{a}\:{system}\:{is}\:{directly} \\ $$$${propotional}\:{to}\:{the}\:{power}\:{of}\:{that}\:{system} \\ $$$${but}\:{will}\:{have}\:{a}\:{minimum}\:{momentum} \\ $$$${when}\:{accelerating}. \\ $$$$ \\ $$$${what}\:{do}\:{you}\:{think}? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 59103 Answers: 0 Comments: 0

Question Number 59102 Answers: 1 Comments: 0

use remainder theorem to factorize completetly the expression x^3 (y − z) + y^3 (z − x) + z^3 (x − y)

$$\mathrm{use}\:\mathrm{remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{factorize}\:\mathrm{completetly}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\:\:\:\:\:\mathrm{x}^{\mathrm{3}} \left(\mathrm{y}\:−\:\mathrm{z}\right)\:+\:\mathrm{y}^{\mathrm{3}} \left(\mathrm{z}\:−\:\mathrm{x}\right)\:+\:\mathrm{z}^{\mathrm{3}} \left(\mathrm{x}\:−\:\mathrm{y}\right) \\ $$

Question Number 59100 Answers: 1 Comments: 4

Question Number 59099 Answers: 0 Comments: 0

A sample of 20 cigarettes is tested to determine nicotine vomtent and the average value observed was 1.2mg.Compute a 99 percentage two−sided confidence interval or the mean nicotine content if it is known that the standard deviation of a cigarette′s nicotine content is 0.2mg.

$${A}\:{sample}\:{of}\:\mathrm{20}\:{cigarettes}\:{is}\:{tested}\:{to}\:{determine}\:{nicotine}\:{vomtent} \\ $$$${and}\:{the}\:{average}\:{value}\:{observed}\:{was}\:\mathrm{1}.\mathrm{2}{mg}.{Compute} \\ $$$${a}\:\mathrm{99}\:{percentage}\:{two}−{sided}\:{confidence}\:{interval} \\ $$$${or}\:{the}\:{mean}\:{nicotine}\:{content}\:{if}\:{it}\:{is}\:{known}\:{that}\:{the}\:{standard}\:{deviation}\:{of}\:{a}\:{cigarette}'{s}\: \\ $$$${nicotine}\:{content}\:{is}\:\mathrm{0}.\mathrm{2}{mg}. \\ $$

Question Number 59098 Answers: 0 Comments: 0

Question Number 59097 Answers: 0 Comments: 0

Question Number 59095 Answers: 1 Comments: 0

An building student makes a floor plan of a building on a scale of 1:75.At what % change will he need to convert it to a scale of 1:250?

$${An}\:{building}\:{student}\:{makes}\:{a}\:{floor} \\ $$$${plan}\:{of}\:{a}\:{building}\:{on}\:{a}\:{scale}\:{of}\:\mathrm{1}:\mathrm{75}.{At} \\ $$$${what}\:\%\:{change}\:{will}\:{he}\:{need}\:{to}\:{convert} \\ $$$${it}\:{to}\:{a}\:{scale}\:{of}\:\mathrm{1}:\mathrm{250}? \\ $$

Question Number 59094 Answers: 1 Comments: 1

Question Number 59092 Answers: 1 Comments: 0

what % increase will it be to transform an image on a scale of 1:75 to 1:300?

$${what}\:\%\:{increase}\:{will}\:{it}\:{be}\:{to}\:{transform} \\ $$$${an}\:{image}\:{on}\:{a}\:{scale}\:{of}\:\mathrm{1}:\mathrm{75}\:{to}\:\mathrm{1}:\mathrm{300}? \\ $$

Question Number 59089 Answers: 1 Comments: 0

Question Number 59080 Answers: 0 Comments: 0

Question Number 59079 Answers: 0 Comments: 0

Question Number 59077 Answers: 0 Comments: 0

Question Number 59076 Answers: 0 Comments: 0

Question Number 59075 Answers: 0 Comments: 1

Question Number 59074 Answers: 0 Comments: 0

Question Number 59070 Answers: 3 Comments: 0

Question Number 59060 Answers: 2 Comments: 0

Question Number 59059 Answers: 0 Comments: 0

Question Number 59058 Answers: 2 Comments: 1

Question Number 59053 Answers: 0 Comments: 0

f=v v=47×48 f=?

$${f}={v} \\ $$$${v}=\mathrm{47}×\mathrm{48} \\ $$$${f}=? \\ $$

Question Number 59052 Answers: 0 Comments: 0

let f(x) =∫_0 ^(π/2) ln(cosθ +xsinθ)dθ with x fromR 1) determine a explicit form for f(x) 2) calculate ∫_0 ^(π/2) ln(cosθ +sinθ) dθ and ∫_0 ^(π/2) ln(cosθ +2sinθ)dθ .

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cos}\theta\:+{xsin}\theta\right){d}\theta\:\:\:{with}\:{x}\:{fromR} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cos}\theta\:+{sin}\theta\right)\:{d}\theta\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cos}\theta\:+\mathrm{2}{sin}\theta\right){d}\theta\:. \\ $$

Question Number 59050 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(1+x^2 )) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\: \\ $$

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