Question and Answers Forum

AllQuestion and Answers: Page 1775

Question Number 31038 Answers: 0 Comments: 0

let give α ∈]−π ,π[ 1)prove that sin^2 α −2(1+cosα) =−4cos^4 ((α/2)) 2)solve inside C z^2 −2z sinα +2(1+cosα)=0 find the module and arg of the roots.

$$\left.{let}\:{give}\:\alpha\:\in\right]−\pi\:,\pi\left[\right. \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:\:{sin}^{\mathrm{2}} \alpha\:−\mathrm{2}\left(\mathrm{1}+{cos}\alpha\right)\:=−\mathrm{4}{cos}^{\mathrm{4}} \left(\frac{\alpha}{\mathrm{2}}\right) \\ $$$$\left.\mathrm{2}\right){solve}\:{inside}\:{C}\:\:{z}^{\mathrm{2}} \:−\mathrm{2}{z}\:{sin}\alpha\:+\mathrm{2}\left(\mathrm{1}+{cos}\alpha\right)=\mathrm{0}\:{find} \\ $$$${the}\:{module}\:{and}\:{arg}\:{of}\:{the}\:{roots}. \\ $$

Question Number 31037 Answers: 0 Comments: 0

let θ∈[0,π] and Z=1+cosθ +isinθ Z^′ =cosθ +(1+sinθ)i find ∣ZZ^′ ∣ arg(ZZ^′ ) ∣(Z/Z^′ )∣ , arg((Z/Z^, )) , ∣Z−Z^, ∣ and arg(Z−Z^, ).

$${let}\:\:\theta\in\left[\mathrm{0},\pi\right]\:\:{and}\:{Z}=\mathrm{1}+{cos}\theta\:+{isin}\theta \\ $$$${Z}^{'} ={cos}\theta\:+\left(\mathrm{1}+{sin}\theta\right){i}\:\:{find}\:\mid{ZZ}^{'} \mid\:\:{arg}\left({ZZ}^{'} \right) \\ $$$$\mid\frac{{Z}}{{Z}^{'} }\mid\:,\:{arg}\left(\frac{{Z}}{{Z}^{,} }\right)\:\:,\:\:\mid{Z}−{Z}^{,} \mid\:{and}\:{arg}\left({Z}−{Z}^{,} \right). \\ $$

Question Number 31036 Answers: 0 Comments: 0

solve inside C z^6 = (z^− )^2 .

$${solve}\:{inside}\:{C}\:\:{z}^{\mathrm{6}} =\:\left({z}^{−} \right)^{\mathrm{2}} \:\:. \\ $$

Question Number 31035 Answers: 0 Comments: 0

1) solve x^5 =1 2) if x_i are roots of this equation prove that Σ_i x_i =0 3)prove that cos(((2π)/5)) +cos(((4π)/5)) =−(1/2) 4)calculate cos(((4π)/5)) interms cos(((2π)/5)) then find its values.

$$\left.\mathrm{1}\right)\:{solve}\:{x}^{\mathrm{5}} =\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{if}\:{x}_{{i}} \:{are}\:{roots}\:{of}\:{this}\:{equation}\:{prove}\:{that}\:\sum_{{i}} \:{x}_{{i}} =\mathrm{0} \\ $$$$\left.\mathrm{3}\right){prove}\:{that}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)\:+{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{4}\right){calculate}\:{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:{interms}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)\:{then}\:{find}\:{its} \\ $$$${values}. \\ $$

Question Number 31034 Answers: 0 Comments: 0

1) solve inside C z^4 =6 2)sove inside C (((z+i)/(z−i)))^3 +(((z+i)/(z−i)))^2 +(((z+i)/(z−i))) +1=0

$$\left.\mathrm{1}\right)\:{solve}\:{inside}\:{C}\:\:{z}^{\mathrm{4}} =\mathrm{6} \\ $$$$\left.\mathrm{2}\right){sove}\:{inside}\:{C}\:\left(\frac{{z}+{i}}{{z}−{i}}\right)^{\mathrm{3}} \:+\left(\frac{{z}+{i}}{{z}−{i}}\right)^{\mathrm{2}} \:+\left(\frac{{z}+{i}}{{z}−{i}}\right)\:+\mathrm{1}=\mathrm{0} \\ $$

Question Number 31033 Answers: 0 Comments: 0

factorize p(x)=(1+ix)^n −e^(inθ) wth θ∈R.

$${factorize}\:{p}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} \:−{e}^{{in}\theta} \:\:\:{wth}\:\theta\in{R}. \\ $$

Question Number 31032 Answers: 0 Comments: 0

let give x_0 =0 ,y_0 =1 and {_(y_n =x_(n−1) +y_(n−1) ) ^(x_n =x_(n−1) −y_(n−1) ) for n≥1 let z_n =x_n +i y_n ∀n∈N 1)calculate z_0 ,z_1 and z_2 2)prove that ∀n∈N^ ,n≥1 z_n =(1+i)z_(n−1) find z_n then find the expression of x_n and y_n 3)let put S_n =z_0 +z_1 +....z_n s_n =x_0 +x_1 +...+x_n s_n ^′ =y_0 +y_1 +...+y_n find those sum interms of n.

$${let}\:{give}\:{x}_{\mathrm{0}} =\mathrm{0}\:,{y}_{\mathrm{0}} =\mathrm{1}\:{and}\:\left\{_{{y}_{{n}} ={x}_{{n}−\mathrm{1}} \:+{y}_{{n}−\mathrm{1}} } ^{{x}_{{n}} ={x}_{{n}−\mathrm{1}} \:−{y}_{{n}−\mathrm{1}} } \:\:\:\:\:\:{for}\:{n}\geqslant\mathrm{1}\:{let}\right. \\ $$$${z}_{{n}} ={x}_{{n}} \:+{i}\:{y}_{{n}} \:\:\:\:\:\forall{n}\in{N} \\ $$$$\left.\mathrm{1}\right){calculate}\:{z}_{\mathrm{0}} \:,{z}_{\mathrm{1}} \:{and}\:{z}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\forall{n}\in{N}^{} ,{n}\geqslant\mathrm{1}\:\:{z}_{{n}} =\left(\mathrm{1}+{i}\right){z}_{{n}−\mathrm{1}} \:{find}\:{z}_{{n}} {then} \\ $$$${find}\:{the}\:{expression}\:{of}\:{x}_{{n}} \:{and}\:{y}_{{n}} \\ $$$$\left.\mathrm{3}\right){let}\:{put}\:{S}_{{n}} ={z}_{\mathrm{0}} \:+{z}_{\mathrm{1}} \:+....{z}_{{n}} \\ $$$${s}_{{n}} ={x}_{\mathrm{0}} \:+{x}_{\mathrm{1}} \:+...+{x}_{{n}} \\ $$$${s}_{{n}} ^{'} ={y}_{\mathrm{0}} \:+{y}_{\mathrm{1}} \:+...+{y}_{{n}} \:\:{find}\:{those}\:{sum}\:{interms}\:{of}\:{n}. \\ $$$$ \\ $$

Question Number 31031 Answers: 0 Comments: 0

1) solve inside C z^(12) =1 and give the solution at form r e^(iθ) 2)calculate 1+u +u^2 +... +u^n then find the solution of z∈C z^8 +z^4 +1=0

$$\left.\mathrm{1}\right)\:{solve}\:{inside}\:{C}\:\:{z}^{\mathrm{12}} =\mathrm{1}\:{and}\:{give}\:{the}\:{solution}\:{at}\:{form} \\ $$$${r}\:{e}^{{i}\theta} \\ $$$$\left.\mathrm{2}\right){calculate}\:\mathrm{1}+{u}\:+{u}^{\mathrm{2}} \:+...\:+{u}^{{n}} \:{then}\:{find}\:{the}\:{solution} \\ $$$${of}\:{z}\in{C}\:\:\:\:\:\:\:{z}^{\mathrm{8}} \:+{z}^{\mathrm{4}} \:+\mathrm{1}=\mathrm{0} \\ $$

Question Number 31030 Answers: 0 Comments: 0

1) solvein R the equation 16u^5 −20u^3 +5u =0 2) solve in R sin(5x)=0 3) prove that sin(5x)=16 sin^5 x −20 sin^3 x +5sinx by using moivre formula. 4) find the values of sin((π/5)) and sin(((2π)/5)) 5) find cos((π/5)) and tan((π/5)).

$$\left.\mathrm{1}\right)\:{solvein}\:{R}\:{the}\:{equation}\:\mathrm{16}{u}^{\mathrm{5}} \:−\mathrm{20}{u}^{\mathrm{3}} \:+\mathrm{5}{u}\:=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{solve}\:{in}\:{R}\:\:{sin}\left(\mathrm{5}{x}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:{sin}\left(\mathrm{5}{x}\right)=\mathrm{16}\:{sin}^{\mathrm{5}} {x}\:−\mathrm{20}\:{sin}^{\mathrm{3}} {x}\:+\mathrm{5}{sinx}\:{by} \\ $$$${using}\:{moivre}\:{formula}. \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{values}\:{of}\:{sin}\left(\frac{\pi}{\mathrm{5}}\right)\:{and}\:{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right) \\ $$$$\left.\mathrm{5}\right)\:{find}\:{cos}\left(\frac{\pi}{\mathrm{5}}\right)\:{and}\:{tan}\left(\frac{\pi}{\mathrm{5}}\right). \\ $$

Question Number 31029 Answers: 0 Comments: 1

Question Number 31026 Answers: 0 Comments: 2

Question Number 31023 Answers: 0 Comments: 0

Question Number 31018 Answers: 0 Comments: 1

Question Number 31016 Answers: 1 Comments: 0

show that 1/cosecx−cotx+1/cosecx+cotx=2cosecx

$${show}\:{that}\:\mathrm{1}/\mathrm{cosec}{x}−{cotx}+\mathrm{1}/\mathrm{cosec}{x}+\mathrm{cot}{x}=\mathrm{2cosec}{x} \\ $$

Question Number 31017 Answers: 1 Comments: 0

solve (√(1+tan^2 x/1+cot^2 x= tanx))

$${solve}\:\sqrt{\mathrm{1}+{tan}^{\mathrm{2}} {x}/\mathrm{1}+{cot}^{\mathrm{2}} {x}=\:\:\:{tanx}} \\ $$

Question Number 31148 Answers: 1 Comments: 1

A body is projected at an angle 35° with an initial speed of 45m/s. What is the velocity of the body after 2s and the angle made with the horizontal axis? [g=9.81ms^(−2) ]

$${A}\:{body}\:{is}\:{projected}\:{at}\:{an}\:{angle} \\ $$$$\mathrm{35}°\:{with}\:{an}\:{initial}\:{speed}\:{of}\:\mathrm{45}{m}/{s}. \\ $$$${What}\:{is}\:{the}\:{velocity}\:{of}\:{the}\:{body} \\ $$$${after}\:\mathrm{2}{s}\:{and}\:{the}\:{angle}\:{made}\:{with} \\ $$$${the}\:{horizontal}\:{axis}?\:\left[{g}=\mathrm{9}.\mathrm{81}{ms}^{−\mathrm{2}} \right] \\ $$

Question Number 31147 Answers: 1 Comments: 0

if point of intersection of curves C_1 =λx^2 +4y^2 −2xy−9x+3 and C_2 =2x^2 +3y^2 −4xy+3x−1 subtends a right angle at origin the value of λ is?

$${if}\:{point}\:{of}\:{intersection}\:{of}\:{curves} \\ $$$${C}_{\mathrm{1}} =\lambda{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{9}{x}+\mathrm{3}\:{and} \\ $$$${C}_{\mathrm{2}} =\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} −\mathrm{4}{xy}+\mathrm{3}{x}−\mathrm{1}\: \\ $$$${subtends}\:{a}\:{right}\:{angle}\:{at}\:{origin}\:{the} \\ $$$${value}\:{of}\:\lambda\:{is}? \\ $$

Question Number 31145 Answers: 1 Comments: 0

Given ∫_0 ^1 f(x) dx = (((2018)),(( 0)) ) + (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) + ... + (1/(2019)) (((2018)),((2018)) ) ∫_0 ^1 g(x) dx = (((2018)),(( 0)) ) − (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) − ... + (1/(2019)) (((2018)),((2018)) ) h(x) is an odd function Then what is the value of ∫_(−3) ^( 3) f(x).g(x).h(x) dx ?

$$\mathrm{Given} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right)\:{dx}\:=\:\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{2019}}\begin{pmatrix}{\mathrm{2018}}\\{\mathrm{2018}}\end{pmatrix} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right)\:{dx}\:=\:\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:−\:...\:+\:\frac{\mathrm{1}}{\mathrm{2019}}\begin{pmatrix}{\mathrm{2018}}\\{\mathrm{2018}}\end{pmatrix} \\ $$$${h}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function} \\ $$$$\mathrm{Then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{−\mathrm{3}} ^{\:\mathrm{3}} \:{f}\left({x}\right).{g}\left({x}\right).{h}\left({x}\right)\:{dx}\:? \\ $$

Question Number 31144 Answers: 0 Comments: 2

A mass oscillating on a spring has amplitude of 1.2m and a period of 2.0s. (a)Deduce the equation for the displacement x if the timing starts at the instant where the mass has its maximum displacement. b)calculate the time interval c)the velocity at this position.

$${A}\:{mass}\:{oscillating}\:{on}\:{a}\:{spring} \\ $$$${has}\:{amplitude}\:{of}\:\mathrm{1}.\mathrm{2}{m}\:{and}\:{a} \\ $$$${period}\:{of}\:\mathrm{2}.\mathrm{0}{s}. \\ $$$$\left({a}\right){Deduce}\:{the}\:{equation}\:{for}\:{the} \\ $$$${displacement}\:{x}\:{if}\:{the}\:{timing}\:{starts} \\ $$$${at}\:{the}\:{instant}\:{where}\:{the}\:{mass} \\ $$$${has}\:{its}\:{maximum}\:{displacement}. \\ $$$$\left.{b}\right){calculate}\:{the}\:{time}\:{interval} \\ $$$$\left.{c}\right){the}\:{velocity}\:{at}\:{this}\:{position}. \\ $$

Question Number 31143 Answers: 1 Comments: 0

A cyclist is travelling down a hill at a speed of 9.2m/s . The hillside makes an angle of 6.3° with the horizontal .Calculate, for the cyclist: (i)the vertical speed (ii)horizontal speed

$${A}\:{cyclist}\:{is}\:{travelling}\:{down}\:{a} \\ $$$${hill}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{9}.\mathrm{2}{m}/{s}\:.\:{The} \\ $$$${hillside}\:{makes}\:{an}\:{angle}\:{of}\:\mathrm{6}.\mathrm{3}° \\ $$$${with}\:{the}\:{horizontal}\:.{Calculate}, \\ $$$${for}\:{the}\:{cyclist}: \\ $$$$\left({i}\right){the}\:{vertical}\:{speed} \\ $$$$\left({ii}\right){horizontal}\:{speed} \\ $$

Question Number 31141 Answers: 1 Comments: 0

using the limit defination find the area of f(x)= cos(x) [0,π/2]

$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\:\boldsymbol{{defination}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{area}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\:\:\left[\mathrm{0},\pi/\mathrm{2}\right] \\ $$

Question Number 31004 Answers: 1 Comments: 0

Question Number 31003 Answers: 1 Comments: 0

Number of positive integers x for which f(x)=x^3 −8x^2 +20x−13 is a prime number are ?

$${Number}\:{of}\:{positive}\:{integers}\:{x}\:{for} \\ $$$${which}\:{f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{8}{x}^{\mathrm{2}} +\mathrm{20}{x}−\mathrm{13}\:{is}\:\:{a}\: \\ $$$${prime}\:{number}\:{are}\:? \\ $$

Question Number 30994 Answers: 0 Comments: 3

Question Number 30990 Answers: 1 Comments: 0

Question Number 30984 Answers: 0 Comments: 3

Pg 1770 Pg 1771 Pg 1772 Pg 1773 Pg 1774 Pg 1775 Pg 1776 Pg 1777 Pg 1778 Pg 1779

Contact: info@tinkutara.com