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Question Number 81458 Answers: 0 Comments: 2

if a_1 = 3 ,a_2 =2 a_(n+2) = a_(n+1) +(a_1 /2) find a_6 =? mister W method a_n =A(((1+(√3))/2))^n +B(((1−(√3))/2))^n a_1 = A(((1+(√3))/2))+B(((1−(√3))/2))=3 a_2 = A(((1+(√3))/2))^2 +B(((1−(√3))/2))^2 =2 ⇒A+B+(A−B)(√3) =6 ⇒2(A+B)+(A−B)(√3) =4 A= ((4−(√3))/(√3)) , B = ((−4−(√3))/3) a_n = (((4−(√3))/(√3)))(((1+(√3))/2))^n −(((4+(√3))/(√3)))(((1−(√3))/2))^n

Question Number 81124 Answers: 1 Comments: 0

Question Number 81115 Answers: 0 Comments: 0

e^x ∫((2csec^2 θ dθ)/([4+(2tanθ)^2 ]^(3/2) )) = e^x ∫((2csec^2 θ dθ)/([4+(2tanθ)^2 ]^(3/2) )) =

$$\mathrm{e}^{\mathrm{x}} \int\frac{\mathrm{2}{csec}^{\mathrm{2}} \theta\:{d}\theta}{\left[\mathrm{4}+\left(\mathrm{2}{tan}\theta\right)^{\mathrm{2}} \right]^{\mathrm{3}/\mathrm{2}} }\:\:= \\ $$$$\mathrm{e}^{\mathrm{x}} \int\frac{\mathrm{2}{csec}^{\mathrm{2}} \theta\:{d}\theta}{\left[\mathrm{4}+\left(\mathrm{2}{tan}\theta\right)^{\mathrm{2}} \right]^{\mathrm{3}/\mathrm{2}} }\:\:= \\ $$

Question Number 80997 Answers: 0 Comments: 4

give a rational fraction example : cancelling in -1 and 2 having as a set defnition R

$${give}\:{a}\:{rational}\:{fraction}\:{example}\:: \\ $$$${cancelling}\:{in}\:-\mathrm{1}\:{and}\:\mathrm{2}\:{having}\:{as}\:{a}\:{set}\:{defnition}\:\mathbb{R} \\ $$

Question Number 80994 Answers: 0 Comments: 1

donnre un exenple de fraction rationnelle: 1)s′annulant en -1 et 2 ayant pour ensemble definition R

$$\mathrm{donnre}\:\mathrm{un}\:\mathrm{exenple}\:\mathrm{de}\:\mathrm{fraction}\:\mathrm{rationnelle}: \\ $$$$\left.\mathrm{1}\right)\mathrm{s}'\mathrm{annulant}\:\mathrm{en}\:-\mathrm{1}\:\mathrm{et}\:\mathrm{2}\:\mathrm{ayant}\:\mathrm{pour}\:\mathrm{ensemble}\:\mathrm{definition}\:\mathbb{R} \\ $$

Question Number 80974 Answers: 0 Comments: 2

Show that gcd (a , a + x) ∣ x hence show that any two consecutive integers are coprime

$$\:\mathrm{Show}\:\mathrm{that}\:\mathrm{gcd}\:\left({a}\:,\:{a}\:+\:{x}\right)\:\mid\:{x} \\ $$$${hence}\:{show}\:{that}\:{any}\:{two}\:{consecutive} \\ $$$${integers}\:{are}\:{coprime} \\ $$

Question Number 80973 Answers: 0 Comments: 0

Given that f(x) = { ((2x−7, 0 < x < 6)),((2^x , 7 < x < 8)) :} and f is periodic of period 4. find f(200)

$$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2}{x}−\mathrm{7},\:\:\mathrm{0}\:<\:{x}\:<\:\mathrm{6}}\\{\mathrm{2}^{{x}} ,\:\:\:\mathrm{7}\:<\:{x}\:<\:\mathrm{8}}\end{cases} \\ $$$$\mathrm{and}\:\mathrm{f}\:\mathrm{is}\:\mathrm{periodic}\:\mathrm{of}\:\mathrm{period}\:\mathrm{4}. \\ $$$$\mathrm{find}\:{f}\left(\mathrm{200}\right) \\ $$

Question Number 80890 Answers: 1 Comments: 0

(((1+i)/(2−i))+((2+i)/(1−i)))^3 =500x+500yi find x,y

$$\left(\frac{\mathrm{1}+\mathrm{i}}{\mathrm{2}−\mathrm{i}}+\frac{\mathrm{2}+\mathrm{i}}{\mathrm{1}−\mathrm{i}}\right)^{\mathrm{3}} =\mathrm{500}{x}+\mathrm{500}{y}\mathrm{i} \\ $$$${find}\:{x},{y} \\ $$

Question Number 80613 Answers: 1 Comments: 2

Q.find (d/dx)(x!)

$${Q}.{find}\:\:\:\frac{{d}}{{dx}}\left({x}!\right) \\ $$

Question Number 80550 Answers: 1 Comments: 1

Question Number 80540 Answers: 0 Comments: 1

Question Number 80515 Answers: 0 Comments: 1

∫(dx/((1+x^φ )^φ ))

$$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\phi} \right)^{\phi} } \\ $$

Question Number 80505 Answers: 0 Comments: 8

Given that 7^k ≡1 (mod 15) a) Write down three values of k. b) Find the general solution of the equation 7^k ≡ 1 (mod 15)

$$\mathrm{Given}\:\mathrm{that}\:\:\mathrm{7}^{{k}} \:\equiv\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{15}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Write}\:\mathrm{down}\:\mathrm{three}\:\mathrm{values}\:\mathrm{of}\:{k}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\:\mathrm{7}^{{k}} \:\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{15}\right) \\ $$

Question Number 80504 Answers: 0 Comments: 2

Solve the system of congruences x ≡ 2 (mod 3) x ≡ 5( mod 7)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{congruences} \\ $$$${x}\:\equiv\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$$${x}\:\equiv\:\mathrm{5}\left(\:\mathrm{mod}\:\mathrm{7}\right) \\ $$$$\: \\ $$

Question Number 80341 Answers: 1 Comments: 0

A particle moves round the polar curve r = a(1 + cos θ) with constant angular velocity ω . Find the transverse component of the velocity.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{round}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{curve} \\ $$$${r}\:=\:{a}\left(\mathrm{1}\:+\:\mathrm{cos}\:\theta\right)\:\mathrm{with}\:\mathrm{constant}\:\mathrm{angular}\: \\ $$$$\mathrm{velocity}\:\omega\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{transverse}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{velocity}. \\ $$

Question Number 80340 Answers: 1 Comments: 0

If P = ((a,b,c,d),(c,d,a,b) ) , Q = ((a,b,c,d),(b,a,d,c) ) are permutations of the elements (a,b,c,d), then QP ≡

$$\mathrm{If}\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{c}}&{{d}}&{{a}}&{{b}}\end{pmatrix}\:\:,\:{Q}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{a}}&{{d}}&{{c}}\end{pmatrix}\:\mathrm{are} \\ $$$$\mathrm{permutations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements}\:\left({a},{b},{c},{d}\right),\:\mathrm{then}\: \\ $$$${QP}\:\equiv \\ $$$$\: \\ $$

Question Number 80293 Answers: 0 Comments: 12

Find all functions that satisfy to (E): ∀ x∈R xf(x)+∫_0 ^x f(x−t)cos(2t)dt=sin(2x)

$${Find}\:{all}\:{functions}\:{that}\:\:{satisfy}\:{to}\:\: \\ $$$$\left({E}\right):\:\forall\:{x}\in\mathbb{R}\:\:\:\:\:\:{xf}\left({x}\right)+\int_{\mathrm{0}} ^{{x}} {f}\left({x}−{t}\right){cos}\left(\mathrm{2}{t}\right){dt}={sin}\left(\mathrm{2}{x}\right) \\ $$$$\: \\ $$

Question Number 80175 Answers: 1 Comments: 1

∫_0 ^1 (dx/(√(x^2 +x+1))) = ?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:=\:? \\ $$

Question Number 80172 Answers: 0 Comments: 2

Given that lim_(x→0) ((√(f(x)+ x))/h) = L then lim_(x→0) ((√(f(x) + 2x))/h) = ?

$${Given}\:{that}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{f}\left({x}\right)+\:{x}}}{{h}}\:=\:{L}\:{then} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{{f}\left({x}\right)\:+\:\mathrm{2}{x}}}{{h}}\:=\:? \\ $$

Question Number 80159 Answers: 1 Comments: 4

IF THE SUM OF p TERMS OF AN A.P. IS EQUAL TO SUM OF ITS q TERMS. PROVE THAT THE SUM OF (p+q) TERMS OF IT IS EQUAL TO 0(ZERO).

$$\boldsymbol{{IF}}\:\:\boldsymbol{{THE}}\:\:\:\boldsymbol{{SUM}}\:\:\:\boldsymbol{{OF}}\:\:\:\boldsymbol{{p}}\:\:\boldsymbol{{TERMS}} \\ $$$$\boldsymbol{{OF}}\:\:\boldsymbol{{AN}}\:\:\:\:\boldsymbol{{A}}.\boldsymbol{{P}}.\:\:\:\boldsymbol{{IS}}\:\:\:\boldsymbol{{EQUAL}}\:\:\boldsymbol{{TO}} \\ $$$$\boldsymbol{{SUM}}\:\:\boldsymbol{{OF}}\:\:\:\boldsymbol{{ITS}}\:\:\:\boldsymbol{{q}}\:\:\:\boldsymbol{{TERMS}}.\:\: \\ $$$$\boldsymbol{{PROVE}}\:\:\boldsymbol{{THAT}}\:\:\boldsymbol{{THE}}\:\:\boldsymbol{{SUM}}\:\:\boldsymbol{{OF}} \\ $$$$\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)\:\:\boldsymbol{{TERMS}}\:\:\boldsymbol{{OF}}\:\:\:\boldsymbol{{IT}}\:\:\:\boldsymbol{{IS}}\:\:\: \\ $$$$\boldsymbol{{EQUAL}}\:\:\boldsymbol{{TO}}\:\:\mathrm{0}\left(\boldsymbol{{ZERO}}\right). \\ $$

Question Number 80102 Answers: 0 Comments: 0

Question Number 80088 Answers: 0 Comments: 0

When the father was son′s age, the son was ten years old; when the son will be father′s age, the father will be seventy. What are their ages ?

$$\:{When}\:\:{the}\:\:{father}\:\:{was}\:{son}'{s}\:\:{age},\:\:{the}\:\:{son} \\ $$$$\:\:{was}\:\:{ten}\:\:{years}\:\:{old};\:\:{when}\:\:{the}\:\:{son}\:\:{will}\:\:{be}\:\:{father}'{s}\:\:{age}, \\ $$$$\:\:{the}\:\:{father}\:\:{will}\:\:{be}\:\:{seventy}. \\ $$$$\:\:{What}\:\:{are}\:\:{their}\:\:{ages}\:\:? \\ $$

Question Number 79969 Answers: 1 Comments: 0

find the general solution for 2sin 3x = sin 2x

$${find}\:{the}\:{general}\:{solution}\:{for}\: \\ $$$$\:\:\mathrm{2sin}\:\mathrm{3}{x}\:=\:\mathrm{sin}\:\mathrm{2}{x} \\ $$

Question Number 79968 Answers: 0 Comments: 3

Find the 50^(th) entry of 3.127356432...

$${Find}\:{the}\:\mathrm{50}^{{th}} \:{entry}\:{of}\:\:\mathrm{3}.\mathrm{127356432}... \\ $$

Question Number 79943 Answers: 1 Comments: 5

Question Number 79751 Answers: 2 Comments: 0

prove that cos^6 θ + sin^6 θ = 1 − (3/4) sin^2 2θ

$${prove}\:{that}\:\mathrm{cos}\:^{\mathrm{6}} \theta\:+\:\mathrm{sin}\:^{\mathrm{6}} \theta\:=\:\mathrm{1}\:−\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}\theta \\ $$

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