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Question Number 102233 Answers: 1 Comments: 0

Find the area under the curve y=(√(a^2 −x^2 )) included between the lines x=0 and x=4 plz help.....

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{under}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{included}\:\mathrm{between}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{4} \\ $$$$ \\ $$$$\mathrm{plz}\:\mathrm{help}..... \\ $$

Question Number 102231 Answers: 0 Comments: 3

Tutorial video for using shape and drawing tools

$$\mathrm{Tutorial}\:\mathrm{video}\:\mathrm{for}\:\mathrm{using}\:\mathrm{shape} \\ $$$$\mathrm{and}\:\mathrm{drawing}\:\mathrm{tools} \\ $$

Question Number 102204 Answers: 1 Comments: 4

New updates: ∙ You can save/load equation in a file and edit it again. This enables sharing of editable equation. ∙ New symbols added ∙ A few bug fixes. v2.093.

$$\mathrm{New}\:\mathrm{updates}: \\ $$$$\centerdot\:\mathrm{You}\:\mathrm{can}\:\mathrm{save}/\mathrm{load}\:\mathrm{equation}\:\mathrm{in}\:\mathrm{a}\:\mathrm{file} \\ $$$$\:\:\:\mathrm{and}\:\mathrm{edit}\:\mathrm{it}\:\mathrm{again}. \\ $$$$\:\:\:\mathrm{This}\:\mathrm{enables}\:\mathrm{sharing}\:\mathrm{of}\:\mathrm{editable} \\ $$$$\:\:\:\:\mathrm{equation}. \\ $$$$\centerdot\:\:\mathrm{New}\:\mathrm{symbols}\:\mathrm{added} \\ $$$$\centerdot\:\:\:\mathrm{A}\:\mathrm{few}\:\mathrm{bug}\:\mathrm{fixes}. \\ $$$$\mathrm{v2}.\mathrm{093}. \\ $$

Question Number 102201 Answers: 0 Comments: 0

Question Number 102198 Answers: 2 Comments: 0

∫(x/(sin^2 x−3))dx=?

$$\int\frac{{x}}{{sin}^{\mathrm{2}} {x}−\mathrm{3}}{dx}=? \\ $$

Question Number 102195 Answers: 2 Comments: 0

∫sinx d(sinx)=?

$$\int{sinx}\:{d}\left({sinx}\right)=? \\ $$

Question Number 102194 Answers: 0 Comments: 3

Question Number 102190 Answers: 2 Comments: 0

Find the value of x ∙∙[Trigonometric Subs.] x−(x/(√(1−x^2 )))=((91)/(60))

$${Find}\:{the}\:{value}\:{of}\:\:{x}\:\centerdot\centerdot\left[{Trigonometric}\:{Subs}.\right] \\ $$$${x}−\frac{{x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}=\frac{\mathrm{91}}{\mathrm{60}} \\ $$

Question Number 102186 Answers: 0 Comments: 0

Question Number 102179 Answers: 1 Comments: 0

Question Number 102178 Answers: 1 Comments: 0

Question Number 102177 Answers: 1 Comments: 2

Question Number 102169 Answers: 5 Comments: 0

∫_0 ^1 x^(3/2) (√(1−x)) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{3}/\mathrm{2}} \:\sqrt{\mathrm{1}−{x}}\:{dx}\:? \\ $$

Question Number 102165 Answers: 2 Comments: 0

calculate ∫_(−∞) ^∞ ((x^2 dx)/((x^2 −x+1)^3 ))

$$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 102164 Answers: 1 Comments: 0

solve y^(′′) −y^′ +3y = e^(−x) sin(2x)

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:\:+\mathrm{3y}\:=\:\mathrm{e}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{2x}\right) \\ $$

Question Number 102163 Answers: 1 Comments: 0

solve y^(′′) −2xy^′ =xe^(−x^2 )

$$\mathrm{solve}\:\:\mathrm{y}^{''} \:−\mathrm{2xy}^{'} \:\:=\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 102162 Answers: 0 Comments: 0

let f(x) =arctan((2/(x+1))) 1)find f^((n)) (x) and f^((n)) (0) 2)developp f at integer serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}+\mathrm{1}}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integer}\:\mathrm{serie} \\ $$

Question Number 102161 Answers: 0 Comments: 0

find ∫ ((x(√(x−1))−(x−1)(√x))/((x+1)(√x)−x(√(x+1)))) dx

$$\mathrm{find}\:\int\:\frac{\mathrm{x}\sqrt{\mathrm{x}−\mathrm{1}}−\left(\mathrm{x}−\mathrm{1}\right)\sqrt{\mathrm{x}}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}}−\mathrm{x}\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$

Question Number 102160 Answers: 0 Comments: 0

1) let a<1 calculate ∫_0 ^π ((cosθdθ)/((a^2 −2acosθ +1)^2 )) 2) find the value of ∫_0 ^π ((cosθ)/((4−2(√3)cosθ)^2 ))dθ

$$\left.\mathrm{1}\right)\:\mathrm{let}\:\mathrm{a}<\mathrm{1}\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{cos}\theta\mathrm{d}\theta}{\left(\mathrm{a}^{\mathrm{2}} −\mathrm{2acos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}}\mathrm{cos}\theta\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$$$ \\ $$

Question Number 102158 Answers: 1 Comments: 0

calculate ∫_(−∞) ^(+∞) (dx/((x^2 +1)^2 (x^2 +9)^2 ))

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}\right)^{\mathrm{2}} } \\ $$

Question Number 102159 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+3)^2 ( 2x^2 +5)))

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} \left(\:\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5}\right)} \\ $$

Question Number 105285 Answers: 1 Comments: 2

simplify ((sin θ)/(1+cot θ)) + ((cos θ)/(1+ tan θ)) ?

$${simplify}\:\frac{\mathrm{sin}\:\theta}{\mathrm{1}+\mathrm{cot}\:\theta}\:+\:\frac{\mathrm{cos}\:\theta}{\mathrm{1}+\:\mathrm{tan}\:\theta}\:? \\ $$

Question Number 102146 Answers: 0 Comments: 14

I decided it′s time to leave for a while. I need some peace and calm, I′m losing my zenter... I′ll put more time and energy into my music. I guess I′ll be back; until then, kindest regards & thanks for the teachings!

$$\mathrm{I}\:\mathrm{decided}\:\mathrm{it}'\mathrm{s}\:\mathrm{time}\:\mathrm{to}\:\mathrm{leave}\:\mathrm{for}\:\mathrm{a}\:\mathrm{while}.\:\mathrm{I}\:\mathrm{need} \\ $$$$\mathrm{some}\:\mathrm{peace}\:\mathrm{and}\:\mathrm{calm},\:\mathrm{I}'\mathrm{m}\:\mathrm{losing}\:\mathrm{my}\:{zen}\mathrm{ter}... \\ $$$$\mathrm{I}'\mathrm{ll}\:\mathrm{put}\:\mathrm{more}\:\mathrm{time}\:\mathrm{and}\:\mathrm{energy}\:\mathrm{into}\:\mathrm{my}\:\mathrm{music}. \\ $$$$\mathrm{I}\:\mathrm{guess}\:\mathrm{I}'\mathrm{ll}\:\mathrm{be}\:\mathrm{back};\:\mathrm{until}\:\mathrm{then}, \\ $$$$\mathrm{kindest}\:\mathrm{regards}\:\&\:\mathrm{thanks}\:\mathrm{for}\:\mathrm{the}\:\mathrm{teachings}! \\ $$

Question Number 105283 Answers: 3 Comments: 0

(1) (dy/dx) = ((2xy)/(4x^2 −y^3 )) (2) (dy/dx) = ((sin x+cos x)/(y(2ln y + 1)))

$$\left(\mathrm{1}\right)\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{2}{xy}}{\mathrm{4}{x}^{\mathrm{2}} −{y}^{\mathrm{3}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{{y}\left(\mathrm{2ln}\:{y}\:+\:\mathrm{1}\right)} \\ $$

Question Number 102142 Answers: 0 Comments: 0

A four-sidex dice with numbered 1, 2, 3, and 4 is thrown and the number at the base is read. The dice is biased such that the probabilies P_1 , P_2 , P_3 , and P_4 to obtain 1, 2, 3, and 4 respectively are in an arithmetic progression. 1\ Given P_4 =0.4, calculate P_1 , P_2 , and P_3 . 2\ The dice is thrown n-times (n≥1). The throws are assumed to be independent, 2 by 2, and identical. Given U_n -the probability of obtaining for the first time the fourth-n^(th) throw; a\Express U_n in terms of n= b\Given S_n =Σ_(i=1) ^n U_i i. Express Sn in terms of n, and find its limit. ii. Determine the smallest natural number such that S_n >0.999

$$\mathrm{A}\:\mathrm{four}-\mathrm{sidex}\:\mathrm{dice}\:\mathrm{with}\:\mathrm{numbered}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{and}\:\mathrm{4}\:\mathrm{is}\:\mathrm{thrown} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{number}\:\mathrm{at}\:\mathrm{the}\:\mathrm{base}\:\mathrm{is}\:\mathrm{read}. \\ $$$$\mathrm{The}\:\mathrm{dice}\:\mathrm{is}\:\mathrm{biased}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{probabilies}\:\mathrm{P}_{\mathrm{1}} ,\:\mathrm{P}_{\mathrm{2}} ,\:\mathrm{P}_{\mathrm{3}} , \\ $$$$\mathrm{and}\:\mathrm{P}_{\mathrm{4}} \:\mathrm{to}\:\mathrm{obtain}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{and}\:\mathrm{4}\:\mathrm{respectively}\:\mathrm{are}\:\mathrm{in}\:\mathrm{an} \\ $$$$\mathrm{arithmetic}\:\mathrm{progression}. \\ $$$$\mathrm{1}\backslash\:\mathrm{Given}\:\mathrm{P}_{\mathrm{4}} =\mathrm{0}.\mathrm{4},\:\mathrm{calculate}\:\mathrm{P}_{\mathrm{1}} ,\:\mathrm{P}_{\mathrm{2}} ,\:\mathrm{and}\:\mathrm{P}_{\mathrm{3}} . \\ $$$$\mathrm{2}\backslash\:\mathrm{The}\:\mathrm{dice}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{n}-\mathrm{times}\:\left(\mathrm{n}\geqslant\mathrm{1}\right).\:\mathrm{The}\:\mathrm{throws}\:\mathrm{are}\:\mathrm{assumed} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{independent},\:\mathrm{2}\:\mathrm{by}\:\mathrm{2},\:\mathrm{and}\:\mathrm{identical}.\:\mathrm{Given}\:\mathrm{U}_{\mathrm{n}} -\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{of}\:\mathrm{obtaining}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{time}\:\mathrm{the}\:\mathrm{fourth}-\mathrm{n}^{\mathrm{th}} \mathrm{throw}; \\ $$$$\mathrm{a}\backslash\mathrm{Express}\:\mathrm{U}_{\mathrm{n}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{n}= \\ $$$$\mathrm{b}\backslash\mathrm{Given}\:\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{U}_{\mathrm{i}} \\ $$$$\:\:\mathrm{i}.\:\mathrm{Express}\:\mathrm{Sn}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{n},\:\mathrm{and}\:\mathrm{find}\:\mathrm{its}\:\mathrm{limit}. \\ $$$$\:\mathrm{ii}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\mathrm{S}_{\mathrm{n}} >\mathrm{0}.\mathrm{999} \\ $$

Question Number 102139 Answers: 1 Comments: 1

We have 4 boys and 2 girls. we choose at random and simultaneous 2 boys and 1 girl to for a group. 1) How many possibilities do we have?

$${We}\:{have}\:\mathrm{4}\:{boys}\:{and}\:\mathrm{2}\:{girls}.\:{we} \\ $$$${choose}\:{at}\:{random}\:{and}\:{simultaneous} \\ $$$$\mathrm{2}\:{boys}\:{and}\:\mathrm{1}\:{girl}\:{to}\:{for}\:{a}\:{group}. \\ $$$$\left.\mathrm{1}\right)\:{How}\:{many}\:{possibilities}\:{do}\:{we}\:{have}? \\ $$

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