Question and Answers Forum

AllQuestion and Answers: Page 1611

Question Number 46923 Answers: 1 Comments: 0

a, b, c are in AP or GP or HP according as ((a−b)/(b−c)) is equal to

$${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{or}\:\mathrm{GP}\:\mathrm{or}\:\mathrm{HP}\:\mathrm{according} \\ $$$$\mathrm{as}\:\frac{{a}−{b}}{{b}−{c}}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 46922 Answers: 1 Comments: 0

Thr 6th term of an AP is equal to 2, the value of the common difference of the AP. Which makes the product a_1 a_4 a_5 least is given by

$$\mathrm{Thr}\:\mathrm{6th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{2},\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}. \\ $$$$\mathrm{Which}\:\mathrm{makes}\:\mathrm{the}\:\mathrm{product}\:{a}_{\mathrm{1}} \:{a}_{\mathrm{4}} \:{a}_{\mathrm{5}} \:\mathrm{least} \\ $$$$\mathrm{is}\:\mathrm{given}\:\:\mathrm{by} \\ $$

Question Number 46921 Answers: 1 Comments: 0

The sum of first two terms of an infinite GP is 1 and every term is twice the sum of the successive terms. Its first term is

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{two}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{GP}\:\mathrm{is}\:\mathrm{1}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{successive}\:\mathrm{terms}.\:\mathrm{Its}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is} \\ $$

Question Number 46920 Answers: 0 Comments: 0

If the sides of a triangle are in AP, and the greatest angle of the triangle is double the smallest angle, the ratio of the sides of the triangle is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{double}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{angle},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$

Question Number 46919 Answers: 0 Comments: 9

Question Number 46918 Answers: 1 Comments: 0

Let S_n denote the sum of first n terms of an AP. If S_(2n) = 3 S_n , then the ratio (S_(3n) /S_n ) is equal to

$$\mathrm{Let}\:{S}_{{n}} \:\mathrm{denote}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:{n}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{an}\:\mathrm{AP}.\:\mathrm{If}\:\:\:{S}_{\mathrm{2}{n}} =\:\mathrm{3}\:{S}_{{n}} \:,\:\mathrm{then}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{S}_{\mathrm{3}{n}} }{{S}_{{n}} }\:\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 46907 Answers: 1 Comments: 0

Question Number 46906 Answers: 0 Comments: 1

Question Number 46898 Answers: 2 Comments: 2

∫((tanx)/((tanx+1)^2 −2tan^2 x ))dx=??

$$\int\frac{{tanx}}{\left({tanx}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2}{tan}^{\mathrm{2}} {x}\:\:}{dx}=?? \\ $$

Question Number 46891 Answers: 1 Comments: 0

X can finish a work in 15 days at 8hrs. a day. Y can finish it in 6(2/3) days at 9 hrs. a day. Find in how many days X and Y can finish it working together 10 hrs. a day?

$$\mathrm{X}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{15}\:\mathrm{days}\:\mathrm{at}\:\mathrm{8hrs}. \\ $$$$\mathrm{a}\:\mathrm{day}.\:\mathrm{Y}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{in}\:\mathrm{6}\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{days}\:\mathrm{at} \\ $$$$\mathrm{9}\:\mathrm{hrs}.\:\mathrm{a}\:\mathrm{day}.\:\mathrm{Find}\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{days} \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{working}\:\mathrm{together}\: \\ $$$$\mathrm{10}\:\mathrm{hrs}.\:\mathrm{a}\:\mathrm{day}? \\ $$

Question Number 46889 Answers: 1 Comments: 1

Question Number 46882 Answers: 0 Comments: 2

factorize inside C[x] x^2 +y^2 +z^2

$${factorize}\:{inside}\:{C}\left[{x}\right]\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} \\ $$

Question Number 46881 Answers: 0 Comments: 1

factorize inside C[x] the polynom x^n +y^n

$${factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:\:{x}^{{n}} \:+{y}^{{n}} \\ $$

Question Number 46880 Answers: 0 Comments: 0

factorize inside C[x] x^n −y^n with n natural integr

$${factorize}\:{inside}\:{C}\left[{x}\right]\:{x}^{{n}} −{y}^{{n}} \:\:{with}\:{n}\:{natural}\:{integr} \\ $$

Question Number 46864 Answers: 1 Comments: 2

Question Number 46860 Answers: 1 Comments: 2

Find the sum to infinity whose n^(th) term is (n/2^(n−1) ) .

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{whose}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\frac{\mathrm{n}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\:. \\ $$

Question Number 46858 Answers: 0 Comments: 0

solve (1+x^2 )y^(′′) −((2x)/(x^3 +1))y^′ +xy =x e^(−2x) .

$${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} \:−\frac{\mathrm{2}{x}}{{x}^{\mathrm{3}} \:+\mathrm{1}}{y}^{'} \:\:+{xy}\:={x}\:{e}^{−\mathrm{2}{x}} . \\ $$

Question Number 46857 Answers: 1 Comments: 2

solve 2x y^′ +(1+x^2 )y =xe^(−x) withy(o)=1

$${solve}\:\mathrm{2}{x}\:{y}^{'} \:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}\:={xe}^{−{x}} \:\:\:{withy}\left({o}\right)=\mathrm{1}\: \\ $$

Question Number 46856 Answers: 0 Comments: 1

find f(t) =∫_0 ^1 x^2 arctan(1+tx)dx

$${find}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\mathrm{2}} \:{arctan}\left(\mathrm{1}+{tx}\right){dx}\: \\ $$

Question Number 46855 Answers: 0 Comments: 1

calculate ∫_0 ^1 x arctan(1+x)dx

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

Question Number 46854 Answers: 1 Comments: 1

find =∫_0 ^π ((sinx)/(2+cos(2x)))dx

$${find}\:\:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sinx}}{\mathrm{2}+{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 46853 Answers: 1 Comments: 1

fnd ∫ (dx/(1+cos(tx)))

$${fnd}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({tx}\right)} \\ $$

Question Number 46852 Answers: 1 Comments: 1

find the value of Σ_(n=1) ^∞ (n^3 /3^n )

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}^{\mathrm{3}} }{\mathrm{3}^{{n}} } \\ $$

Question Number 46851 Answers: 0 Comments: 3

let f(x)=∫_0 ^(2π) ((sint)/(x +sint))dt withx>1 1) calculate f(x) 2) calculate ∫_0 ^(2π) ((sint)/((x+sint)^2 ))dt 3)find the value of ∫_0 ^(2π) ((sint)/(2+sint))dt and ∫_0 ^(2π) ((sint)/((2+sint)^2 ))dt

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{{x}\:+{sint}}{dt}\:\:{withx}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{sint}}{\left({x}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\mathrm{2}+{sint}}{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left(\mathrm{2}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$

Question Number 46850 Answers: 1 Comments: 1

let a^2 >b^(2 ) +c^2 calculate ∫_0 ^(2π) (dθ/(a+bsinθ +c cosθ))

$${let}\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}\:} +{c}^{\mathrm{2}} \:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{d}\theta}{{a}+{bsin}\theta\:+{c}\:{cos}\theta} \\ $$

Question Number 46849 Answers: 0 Comments: 0

let A_p =Σ_(n=1) ^∞ n^p x^n with p integr . and x ∈]−1,1[ . 1) calculate A_1 ,A_2 and A_3 2) find a relation of recurrence betwen the A_n 3) calculate Σ_(n=1) ^∞ n^4 x^n and Σ_(n=1) ^∞ n^5 x^n .

$$\left.{let}\:{A}_{{p}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{{p}} {x}^{{n}} \:\:\:\:{with}\:{p}\:{integr}\:.\:{and}\:{x}\:\in\right]−\mathrm{1},\mathrm{1}\left[\:.\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{relation}\:{of}\:{recurrence}\:\:{betwen}\:{the}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{\mathrm{4}} {x}^{{n}} \:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{\mathrm{5}} {x}^{{n}} \:. \\ $$

Pg 1606 Pg 1607 Pg 1608 Pg 1609 Pg 1610 Pg 1611 Pg 1612 Pg 1613 Pg 1614 Pg 1615

Contact: info@tinkutara.com