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Question Number 103622 Answers: 2 Comments: 0

Given a = Σ_(n=1) ^(24) (1/((√(n+1))+(√n))) then the value of a + (1/(log _a (bc)+1)) + (1/(log _b (ac)+1)) + (1/(log _c (ab)+1)) = ?

$${Given}\:{a}\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{24}} {\sum}}\frac{\mathrm{1}}{\sqrt{{n}+\mathrm{1}}+\sqrt{{n}}}\:{then}\:{the}\:{value}\:{of} \\ $$$${a}\:+\:\frac{\mathrm{1}}{\mathrm{log}\:_{{a}} \left({bc}\right)+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{log}\:_{{b}} \left({ac}\right)+\mathrm{1}}\:+ \\ $$$$\frac{\mathrm{1}}{\mathrm{log}\:_{{c}} \left({ab}\right)+\mathrm{1}}\:=\:? \\ $$

Question Number 103620 Answers: 1 Comments: 0

If a^2 −bc, b^2 −ac, c^2 −ab is AP where a+c = 12, find the value of a+b+c

$${If}\:{a}^{\mathrm{2}} −{bc},\:{b}^{\mathrm{2}} −{ac},\:{c}^{\mathrm{2}} −{ab}\:{is}\:{AP}\:{where}\:{a}+{c} \\ $$$$=\:\mathrm{12},\:{find}\:{the}\:{value}\:{of}\:{a}+{b}+{c}\: \\ $$

Question Number 103607 Answers: 1 Comments: 0

what is the value of ∫_c (x+2y)dx+(4−2x)dy around the ellipse C: (x^2 /(16))+(y^2 /8)=1 in the counterclockwise direction ?

$${what}\:{is}\:{the}\:{value}\:{of}\:\int_{{c}} \left({x}+\mathrm{2}{y}\right){dx}+\left(\mathrm{4}−\mathrm{2}{x}\right){dy} \\ $$$${around}\:{the}\:{ellipse}\:{C}:\:\frac{{x}^{\mathrm{2}} }{\mathrm{16}}+\frac{{y}^{\mathrm{2}} }{\mathrm{8}}=\mathrm{1} \\ $$$${in}\:{the}\:{counterclockwise} \\ $$$${direction}\:?\: \\ $$

Question Number 103606 Answers: 3 Comments: 1

an integer n between 1 and 98 , inclusive is to be chosen at random. what is the probability that n(n+1) will be divisible by 3

$${an}\:{integer}\:{n}\:{between}\:\mathrm{1}\:{and}\:\mathrm{98}\:, \\ $$$${inclusive}\:{is}\:{to}\:{be}\:{chosen}\:{at} \\ $$$${random}.\:{what}\:{is}\:{the}\:{probability} \\ $$$${that}\:{n}\left({n}+\mathrm{1}\right)\:{will}\:{be}\:{divisible}\:{by}\:\mathrm{3} \\ $$

Question Number 103603 Answers: 0 Comments: 1

Question Number 103597 Answers: 0 Comments: 2

pls help solve this differential equation (3x^2 sin ((1/x)) + y)dx = xcos((1/x)) −xdy

$$\boldsymbol{{pls}}\:\boldsymbol{{help}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{differential}}\:\boldsymbol{{equation}} \\ $$$$\left(\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} \mathrm{sin}\:\left(\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)\:+\:\boldsymbol{{y}}\right)\boldsymbol{{dx}}\:=\:\boldsymbol{{xcos}}\left(\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)\:−\boldsymbol{{xdy}} \\ $$

Question Number 103593 Answers: 1 Comments: 0

calculate ∫_(−∞) ^∞ (dx/((x^2 +x +1)^2 (2x^2 +5)^2 ))

$$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}\:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5}\right)^{\mathrm{2}} } \\ $$

Question Number 103591 Answers: 1 Comments: 4

calculate ∫_3 ^(+∞) (dx/((x^2 −1)^3 (x+2)^2 ))

$$\mathrm{calculate}\:\:\int_{\mathrm{3}} ^{+\infty} \:\:\:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$

Question Number 103586 Answers: 1 Comments: 0

Question Number 103584 Answers: 0 Comments: 0

Question Number 103585 Answers: 1 Comments: 0

Question Number 103582 Answers: 0 Comments: 3

Question Number 103574 Answers: 0 Comments: 0

Question Number 103721 Answers: 2 Comments: 0

∫_0 ^∞ ((cosx)/(x^2 +1))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{cosx}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 103563 Answers: 2 Comments: 0

find laplase transform of the function f(t)=sin^2 t cos^3 t ?

$${find}\:{laplase}\:{transform}\:{of}\:{the}\:{function} \\ $$$${f}\left({t}\right)={sin}^{\mathrm{2}} {t}\:\:{cos}^{\mathrm{3}} {t}\:\:? \\ $$

Question Number 103560 Answers: 3 Comments: 1

S=Σ_(k=1) ^(17) k∙2^k =?

$$\mathrm{S}=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{17}} {\sum}}\mathrm{k}\centerdot\mathrm{2}^{\mathrm{k}} =? \\ $$

Question Number 103553 Answers: 3 Comments: 0

Question Number 103515 Answers: 1 Comments: 0

given f(x) = f(x+(π/6)) ∀x∈R if ∫_0 ^(π/6) f(x)dx = T then ∫_π ^(7π/3) f(x+π) dx ?

$${given}\:{f}\left({x}\right)\:=\:{f}\left({x}+\frac{\pi}{\mathrm{6}}\right)\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{6}} {\int}}{f}\left({x}\right){dx}\:=\:{T}\:{then}\:\underset{\pi} {\overset{\mathrm{7}\pi/\mathrm{3}} {\int}}{f}\left({x}+\pi\right) \\ $$$${dx}\:? \\ $$

Question Number 103513 Answers: 2 Comments: 0

coefficient of x^5 in expansion (1+x^2 )^5 (1+x)^4 equal to (a) 40 (b) 45 (c) 50 (d) 55 (e) 60

$${coefficient}\:{of}\:{x}^{\mathrm{5}} \:{in}\:{expansion} \\ $$$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{5}} \left(\mathrm{1}+{x}\right)^{\mathrm{4}} \:{equal}\:{to}\: \\ $$$$\left({a}\right)\:\mathrm{40}\:\:\:\:\:\:\left({b}\right)\:\mathrm{45}\:\:\:\:\:\left({c}\right)\:\mathrm{50}\:\:\:\:\left({d}\right)\:\mathrm{55} \\ $$$$\left({e}\right)\:\mathrm{60} \\ $$

Question Number 103512 Answers: 2 Comments: 2

∫ ((x dx)/((cot x+tan x)^2 )) = (a) (x/(16))−((x sin 4x)/(32))−((cos 4x)/(128))+c (b) (x/(16))+((x sin 4x)/(32))−((cos 4x)/(128))+c (c) (x/(16))+((xsin 4x)/(64))+((cos 4x)/(128))+c (d)(x/(16))+((xcos 4x)/(32))+((sin 4x)/(128))+c

Question Number 103511 Answers: 1 Comments: 1

∫ (dx/((√x) ((x)^(1/4) +1))) =__ (a) −((9 (x)^(1/4) +1)/(18((x)^(1/4) +1)^9 )) + c (b) ((9 (x)^(1/4) +1)/(18((x)^(1/4) +1)^9 )) +c (c) −((9 (x)^(1/4) −1)/(18((x)^(1/4) +1)^9 )) +c (d) ((9 (x)^(1/4) +1)/(8((x)^(1/4) +1)^9 )) + c

Question Number 103510 Answers: 1 Comments: 5

Question Number 103504 Answers: 0 Comments: 0

Question Number 103503 Answers: 2 Comments: 0

Solve : 3^x = 4x

$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{Solve}\:: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}^{{x}} \:=\:\mathrm{4}{x} \\ $$

Question Number 103497 Answers: 0 Comments: 0

Question Number 103655 Answers: 0 Comments: 3

lim_(x→∞) (−ln((10)/(17)))^(((17)/(10))x) =???

$${li}\underset{{x}\rightarrow\infty} {{m}}\left(−{ln}\frac{\mathrm{10}}{\mathrm{17}}\right)^{\frac{\mathrm{17}}{\mathrm{10}}{x}} =??? \\ $$

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