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AllQuestion and Answers: Page 1935

Question Number 8350 Answers: 1 Comments: 0

solve: (5/(3x+2))+(8/(4x+2))=((33)/(9x+8))

$${solve}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{3}{x}+\mathrm{2}}+\frac{\mathrm{8}}{\mathrm{4}{x}+\mathrm{2}}=\frac{\mathrm{33}}{\mathrm{9}{x}+\mathrm{8}} \\ $$

Question Number 8347 Answers: 0 Comments: 5

a_1 =2 , a_(n+1) >a_n (a_(n+1) −a_n )^2 = 2(a_(n+1) +a_n ) a_n =?? help me please.

$${a}_{\mathrm{1}} =\mathrm{2}\:,\:\:{a}_{{n}+\mathrm{1}} >{a}_{{n}} \\ $$$$\left({a}_{{n}+\mathrm{1}} −{a}_{{n}} \right)^{\mathrm{2}} =\:\mathrm{2}\left({a}_{{n}+\mathrm{1}} +{a}_{{n}} \right) \\ $$$$\:{a}_{{n}} =?? \\ $$$${help}\:{me}\:{please}. \\ $$

Question Number 8345 Answers: 1 Comments: 0

y=(x+2)^2 −3 Translation T_1 = ((a),(b) ) y′=x^2 a=? b=?

$${y}=\left({x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{3} \\ $$$${Translation}\:{T}_{\mathrm{1}} =\begin{pmatrix}{{a}}\\{{b}}\end{pmatrix} \\ $$$${y}'={x}^{\mathrm{2}} \\ $$$${a}=?\:{b}=? \\ $$

Question Number 8341 Answers: 1 Comments: 0

What are necessary and sufficient conditions that (a+ib)^n is cyclic for an n not equal to 0?

$$\mathrm{What}\:\mathrm{are}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient}\:\mathrm{conditions} \\ $$$$\mathrm{that}\:\left(\mathrm{a}+\mathrm{ib}\right)^{\mathrm{n}} \:\mathrm{is}\:\mathrm{cyclic}\:\mathrm{for}\:\mathrm{an}\:\:\mathrm{n}\:\mathrm{not}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{0}? \\ $$

Question Number 8338 Answers: 1 Comments: 1

Question Number 8334 Answers: 0 Comments: 0

Question Number 8336 Answers: 0 Comments: 2

Determine smallest n(≠0), for which (ω+i)^n =1.

$$\mathrm{Determine}\:\mathrm{smallest}\:\mathrm{n}\left(\neq\mathrm{0}\right),\:\mathrm{for}\:\mathrm{which} \\ $$$$\left(\omega+\mathrm{i}\right)^{\mathrm{n}} =\mathrm{1}. \\ $$

Question Number 8311 Answers: 1 Comments: 1

Solve the equation 6cos2a−5sin2a=1.8 for0°≤a≤180°.

$${Solve}\:{the}\:{equation}\:\mathrm{6}{cos}\mathrm{2}{a}−\mathrm{5}{sin}\mathrm{2}{a}=\mathrm{1}.\mathrm{8} \\ $$$${for}\mathrm{0}°\leqslant{a}\leqslant\mathrm{180}°. \\ $$

Question Number 8310 Answers: 1 Comments: 0

Given that cosecA+cotA=3 evaluate cosecA−cotA and cosA.

$${Given}\:{that}\:{cosecA}+{cotA}=\mathrm{3}\:{evaluate} \\ $$$${cosecA}−{cotA}\:{and}\:{cosA}. \\ $$$$ \\ $$

Question Number 8314 Answers: 2 Comments: 9

Question Number 8325 Answers: 0 Comments: 0

In Δ ABC,∠A=90° , AD⊥BC, DE⊥AC, AF⊥FG,GH⊥FC. (a)How many triangles are there? (b)If AB=((16)/9) , ∠B=60°,find the length of GH.

$${In}\:\Delta\:{ABC},\angle{A}=\mathrm{90}°\:,\:{AD}\bot{BC},\:{DE}\bot{AC}, \\ $$$${AF}\bot{FG},{GH}\bot{FC}. \\ $$$$\left({a}\right){How}\:{many}\:{triangles}\:{are}\:{there}? \\ $$$$\left({b}\right){If}\:{AB}=\frac{\mathrm{16}}{\mathrm{9}}\:,\:\angle{B}=\mathrm{60}°,{find}\:{the}\:{length} \\ $$$$\:\:\:\:\:\:{of}\:{GH}. \\ $$

Question Number 8305 Answers: 0 Comments: 3

Question Number 8296 Answers: 0 Comments: 2

Give the integral representation of 2333!

$$\mathrm{Give}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{representation}\:\mathrm{of}\:\:\mathrm{2333}! \\ $$

Question Number 8289 Answers: 1 Comments: 2

what is value sin 36° plese give me answer

$${what}\:{is}\:{value} \\ $$$${sin}\:\mathrm{36}° \\ $$$${plese}\:{give}\:{me}\:{answer} \\ $$

Question Number 8287 Answers: 1 Comments: 0

Show that tan(α+β)=((tanα+tanβ)/(1−tanαtanβ)).

$${Show}\:{that}\:{tan}\left(\alpha+\beta\right)=\frac{{tan}\alpha+{tan}\beta}{\mathrm{1}−{tan}\alpha{tan}\beta}. \\ $$

Question Number 8297 Answers: 1 Comments: 0

B_ y expessing each side of the equation in terms of tanA ,or otherwise show that ((sin2A+cos2A+1)/(sin2A+cos2A−1))=((tan(45°+A))/(tanA))

$$\underset{} {{B}y}\:{expessing}\:{each}\:{side}\:{of}\:{the} \\ $$$${equation}\:{in}\:{terms}\:{of}\:{tanA}\:,{or}\: \\ $$$${otherwise}\:{show}\:{that} \\ $$$$\frac{{sin}\mathrm{2}{A}+{cos}\mathrm{2}{A}+\mathrm{1}}{{sin}\mathrm{2}{A}+{cos}\mathrm{2}{A}−\mathrm{1}}=\frac{{tan}\left(\mathrm{45}°+{A}\right)}{{tanA}} \\ $$

Question Number 8306 Answers: 0 Comments: 1

If 270°<x<360°, simplify (√(2+(√(2+2cosx)))).

$${If}\:\mathrm{270}°<{x}<\mathrm{360}°,\:{simplify} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2}{cosx}}}. \\ $$

Question Number 8302 Answers: 0 Comments: 0

find all possible values of x and y satisfying 1! + 2! + 3! + ... + x! = y^2

$$\mathrm{find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{satisfying}\: \\ $$$$\mathrm{1}!\:+\:\mathrm{2}!\:+\:\mathrm{3}!\:+\:...\:+\:\mathrm{x}!\:=\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 8300 Answers: 0 Comments: 2

Question Number 8301 Answers: 1 Comments: 1

Is { (ω+i)^0 , (ω+i)^1 , (ω+i)^2 , ...., (ω+i)^n } cyclic for any value of n? Determine the smallest such n if it exists. ω is a complex cuberoot of unity and i=(√(−1))

$$\mathrm{Is}\:\:\left\{\:\left(\omega+\mathrm{i}\right)^{\mathrm{0}} ,\:\left(\omega+\mathrm{i}\right)^{\mathrm{1}} ,\:\left(\omega+\mathrm{i}\right)^{\mathrm{2}} ,\:....,\:\left(\omega+\mathrm{i}\right)^{\mathrm{n}} \:\right\} \\ $$$$\mathrm{cyclic}\:\mathrm{for}\:\mathrm{any}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}? \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{such}\:\mathrm{n}\:\mathrm{if}\:\mathrm{it}\:\mathrm{exists}. \\ $$$$\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{cuberoot}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{and} \\ $$$$\mathrm{i}=\sqrt{−\mathrm{1}} \\ $$

Question Number 8282 Answers: 1 Comments: 3

Find x, y in R { ((x^2 + y^2 = 1)),((x^8 + y^8 = x^(10) + y^(10) )) :}

$$\mathrm{Find}\:\mathrm{x},\:\mathrm{y}\:\mathrm{in}\:\mathbb{R} \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{1}}\\{\mathrm{x}^{\mathrm{8}} \:+\:\mathrm{y}^{\mathrm{8}} \:=\:\mathrm{x}^{\mathrm{10}} \:+\:\mathrm{y}^{\mathrm{10}} }\end{cases} \\ $$

Question Number 8281 Answers: 1 Comments: 0

∫((6 sinx cosx)/(sinx + cosx)) dx

$$\int\frac{\mathrm{6}\:\mathrm{sinx}\:\mathrm{cosx}}{\mathrm{sinx}\:+\:\mathrm{cosx}}\:\mathrm{dx} \\ $$

Question Number 8277 Answers: 0 Comments: 0

Show that one representation for π≈3.14... is π=12cos^(−1) [((3/4))^(1/4) (1+Σ_(r=1) ^∞ ((Π_(k=1) ^(2r) ((3/2)−k))/((2r)!))(((−1)/3))^r )].

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{one}\:\mathrm{representation}\:\mathrm{for}\:\pi\approx\mathrm{3}.\mathrm{14}... \\ $$$$\mathrm{is}\:\pi=\mathrm{12cos}^{−\mathrm{1}} \left[\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{1}/\mathrm{4}} \left(\mathrm{1}+\underset{\mathrm{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{2r}} {\prod}}\left(\frac{\mathrm{3}}{\mathrm{2}}−\mathrm{k}\right)}{\left(\mathrm{2r}\right)!}\left(\frac{−\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{r}} \right)\right]. \\ $$$$ \\ $$

Question Number 8275 Answers: 0 Comments: 2

Show that the followings (i)sin(a+b)=sina cosb +cosa sinb (ii)cos(a−b)=cosa cosb +sina sinb

$${Show}\:{that}\:{the}\:{followings} \\ $$$$\left({i}\right){sin}\left({a}+{b}\right)={sina}\:{cosb}\:+{cosa}\:{sinb} \\ $$$$\left({ii}\right){cos}\left({a}−{b}\right)={cosa}\:{cosb}\:+{sina}\:{sinb} \\ $$$$ \\ $$

Question Number 8273 Answers: 1 Comments: 0

Express sinα+(√3)cosα in the form Rsin(α+β) where R>0 and 0°<β<90°. Hence solve the equation sinα+(√3)cosα=2 for 0°<α<270°.

$${Express}\:{sin}\alpha+\sqrt{\mathrm{3}}{cos}\alpha\:{in}\:{the}\:{form}\: \\ $$$${Rsin}\left(\alpha+\beta\right)\:{where}\:{R}>\mathrm{0}\:{and}\:\mathrm{0}°<\beta<\mathrm{90}°. \\ $$$${Hence}\:{solve}\:{the}\:{equation}\:{sin}\alpha+\sqrt{\mathrm{3}}{cos}\alpha=\mathrm{2} \\ $$$${for}\:\mathrm{0}°<\alpha<\mathrm{270}°. \\ $$

Question Number 8269 Answers: 1 Comments: 1

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