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Question Number 43606 Answers: 0 Comments: 0

Question Number 43603 Answers: 1 Comments: 0

If the sum of first two terms of an infinite GP is 1 and every term is twice the sum of all the successive terms, then its first term is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{two}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{GP}\:\mathrm{is}\:\mathrm{1}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{successive}\:\mathrm{terms},\:\mathrm{then}\:\mathrm{its} \\ $$$$\mathrm{first}\:\mathrm{term}\:\mathrm{is} \\ $$

Question Number 43602 Answers: 1 Comments: 0

If a, b, c are in GP and log_c a, log_b c, log_a b are in AP, then the common difference of the AP is

$$\mathrm{If}\:\:{a},\:{b},\:{c}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{log}_{{c}} {a},\:\mathrm{log}_{{b}} {c},\:\mathrm{log}_{{a}} {b} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{then}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{AP}\:\mathrm{is} \\ $$

Question Number 43596 Answers: 0 Comments: 0

Question Number 43574 Answers: 1 Comments: 0

Two cyclists Musa and Amadu left point p at the same time in opposite directions. If their speeds are 8 km/h and12 km/h respectively; i. how will it take them to be 40 km apart? ii. calculate the distance covered by Musa within the time in (i)

$$\mathrm{Two}\:\mathrm{cyclists}\:\mathrm{Musa}\:\mathrm{and}\:\mathrm{Amadu}\:\mathrm{left}\:\mathrm{point}\:\mathrm{p}\:\mathrm{at}\:\mathrm{the}\: \\ $$$$\mathrm{same}\:\mathrm{time}\:\mathrm{in}\:\mathrm{opposite}\:\mathrm{directions}.\:\mathrm{If}\:\mathrm{their}\:\mathrm{speeds}\:\mathrm{are} \\ $$$$\mathrm{8}\:\mathrm{km}/\mathrm{h}\:\mathrm{and12}\:\mathrm{km}/\mathrm{h}\:\mathrm{respectively};\: \\ $$$$\mathrm{i}.\:\mathrm{how}\:\mathrm{will}\:\mathrm{it}\:\mathrm{take}\:\mathrm{them}\:\mathrm{to}\:\mathrm{be}\:\mathrm{40}\:\mathrm{km}\:\mathrm{apart}? \\ $$$$\mathrm{ii}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{covered}\:\mathrm{by}\:\mathrm{Musa}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{time}\:\mathrm{in}\:\left(\mathrm{i}\right) \\ $$

Question Number 43571 Answers: 1 Comments: 0

Question Number 43569 Answers: 0 Comments: 1

Please solve these questions − 43496 , 42473 , 42474 , 42472 , 42471 , 42470 , 42469 , 42468 , 42408

$$\mathrm{Please}\:\mathrm{solve}\:\mathrm{these}\:\mathrm{questions}\:−\: \\ $$$$\mathrm{43496}\:,\:\mathrm{42473}\:,\:\mathrm{42474}\:,\:\mathrm{42472}\:,\:\mathrm{42471}\:, \\ $$$$\mathrm{42470}\:,\:\mathrm{42469}\:,\:\mathrm{42468}\:,\:\mathrm{42408}\: \\ $$

Question Number 43551 Answers: 1 Comments: 0

evaluate ∫(1/(cos (x−a)cos (x−b)))dx

$${evaluate}\:\int\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)}{dx} \\ $$

Question Number 43550 Answers: 0 Comments: 1

prove that ∫_ 4_( ) ^4^4^x .4^4^x .4^x dx=(4^4^x /((log 4_e )))

$${prove}\:{that} \\ $$$$\int_{\:} \:\mathrm{4}_{\:\:\:\:\:} ^{\mathrm{4}^{\mathrm{4}^{{x}} } } .\mathrm{4}^{\mathrm{4}^{{x}} } .\mathrm{4}^{{x}} {dx}=\frac{\mathrm{4}^{\mathrm{4}^{{x}} } }{\left(\mathrm{log}\:\underset{{e}} {\mathrm{4}}\right)} \\ $$

Question Number 43549 Answers: 1 Comments: 1

solve x : (5+2(√6))^(x^2 −3) +(5−2(√6))^(x^2 −3) =10

$${solve}\:{x}\::\:\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} +\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} =\mathrm{10} \\ $$

Question Number 43546 Answers: 1 Comments: 0

let S_n =Σ_(k=1) ^n (1/(√(k^2 +n^2 ))) calculate lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{\sqrt{{k}^{\mathrm{2}} \:+{n}^{\mathrm{2}} }}\:\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$

Question Number 43545 Answers: 1 Comments: 0

prove that ∫ _0 ^1 ((x^2 +6)/((x^2 +4)(x^2 +9)))=(Π/(20))

$${prove}\:{that}\:\int\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\:}}\:\frac{{x}^{\mathrm{2}} +\mathrm{6}}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)\left({x}^{\mathrm{2}} +\mathrm{9}\right)}=\frac{\Pi}{\mathrm{20}} \\ $$

Question Number 43544 Answers: 1 Comments: 0

Question Number 43543 Answers: 1 Comments: 0

prove that (√(2+(√(2+(√(2+2cos 8θ)))))) 2cos θ

$${prove}\:{that}\:\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2cos}\:\mathrm{8}\theta}}} \\ $$$$\mathrm{2cos}\:\theta \\ $$

Question Number 43540 Answers: 2 Comments: 0

prove that 111 divide 10^(6n+2) +10^(3n+1) +1

$${prove}\:{that}\:\mathrm{111}\:{divide}\:\mathrm{10}^{\mathrm{6}{n}+\mathrm{2}} \:+\mathrm{10}^{\mathrm{3}{n}+\mathrm{1}} \:+\mathrm{1} \\ $$

Question Number 43539 Answers: 0 Comments: 1

calculate ∫∫_(0≤x≤1 ,0≤y≤1) (x+2y)e^(2x−y) dxdy

$${calculate}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1}} \:\:\left({x}+\mathrm{2}{y}\right){e}^{\mathrm{2}{x}−{y}} {dxdy} \\ $$

Question Number 43538 Answers: 0 Comments: 1

calculate ∫∫_((x^2 /a^2 ) +(y^2 /b^2 ) ≤1) (x^2 −y^2 )dxdy whit a>0 and b>0 .

$${calculate}\:\int\int_{\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\leqslant\mathrm{1}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right){dxdy}\:{whit} \\ $$$${a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:. \\ $$

Question Number 43541 Answers: 1 Comments: 0

let u_0 =u_1 =1 and u_(n+1) =u_n +u_(n−1) 2) find u_n 3)let x_0 the positif roots of x^2 =x+1 4) prove that ∀n≥2 x_0 ^(n−2) ≤u_n ≤x_0 ^(n−1) .

$${let}\:{u}_{\mathrm{0}} ={u}_{\mathrm{1}} =\mathrm{1}\:{and}\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} \:+{u}_{{n}−\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{u}_{{n}} \\ $$$$\left.\mathrm{3}\right){let}\:{x}_{\mathrm{0}} \:\:{the}\:{positif}\:{roots}\:{of}\:{x}^{\mathrm{2}} ={x}+\mathrm{1} \\ $$$$\left.\mathrm{4}\right)\:{prove}\:{that}\:\forall{n}\geqslant\mathrm{2}\:\:{x}_{\mathrm{0}} ^{{n}−\mathrm{2}} \leqslant{u}_{{n}} \leqslant{x}_{\mathrm{0}} ^{{n}−\mathrm{1}} \:. \\ $$

Question Number 43585 Answers: 2 Comments: 2

Question Number 43531 Answers: 1 Comments: 1

the circumference of a circular track is 9 km. A cyclist rides round it a number of times and stops after covering a distance of 302 km. How far is the cyclist from the starting point? [take Π=((22)/7)]

$$\mathrm{the}\:\mathrm{circumference}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circular}\:\mathrm{track}\:\mathrm{is}\:\mathrm{9}\:\mathrm{km}.\:\mathrm{A}\:\mathrm{cyclist} \\ $$$$\mathrm{rides}\:\mathrm{round}\:\mathrm{it}\:\mathrm{a}\:\mathrm{number}\:\mathrm{of}\:\mathrm{times}\:\mathrm{and}\:\mathrm{stops}\:\mathrm{after} \\ $$$$\mathrm{covering}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{302}\:\mathrm{km}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{is}\:\mathrm{the}\:\mathrm{cyclist} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{point}?\:\left[\mathrm{take}\:\Pi=\frac{\mathrm{22}}{\mathrm{7}}\right] \\ $$

Question Number 43517 Answers: 0 Comments: 1

Question Number 43514 Answers: 0 Comments: 0

Question Number 43589 Answers: 1 Comments: 3

Question Number 43587 Answers: 1 Comments: 0

a and b are the digit in a four digit number 12ab.if 12ab is divisble by 5 and 9 .find the sum of all possible value of a.

$${a}\:{and}\:{b}\:\:{are}\:{the}\:{digit}\:{in}\:{a}\:{four}\:{digit} \\ $$$${number}\:\mathrm{12}{ab}.{if}\:\mathrm{12}{ab}\:{is}\:{divisble}\:{by}\: \\ $$$$\mathrm{5}\:{and}\:\mathrm{9}\:.{find}\:{the}\:{sum}\:{of}\:{all}\:{possible} \\ $$$${value}\:{of}\:\:{a}. \\ $$

Question Number 43496 Answers: 1 Comments: 4

(√(a−(√(a+x)))) + (√(a+(√(a−x)))) =2x Solve for “ x ” in terms of “ a ”

$$\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}\:\:+\:\:\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}\:\:=\mathrm{2x}\: \\ $$$$\mathrm{Solve}\:\mathrm{for}\:``\:\mathrm{x}\:''\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\:``\:\:\mathrm{a}\:\:'' \\ $$$$ \\ $$

Question Number 43490 Answers: 1 Comments: 2

evaluate ∫(√(tan𝛉 dθ))

$$\boldsymbol{\mathrm{evaluate}} \\ $$$$\int\sqrt{\boldsymbol{\mathrm{tan}\theta}\:\boldsymbol{\mathrm{d}}\theta} \\ $$

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