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Question Number 87647 Answers: 1 Comments: 0

If a_1 = 1 , a_(n+1 ) = 2a_n + 5 , n = 1,2,3,.... then a_(100) = ?

$$\mathrm{If}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{1}\:,\:\mathrm{a}_{\mathrm{n}+\mathrm{1}\:} =\:\mathrm{2a}_{\mathrm{n}} \:+\:\mathrm{5}\:,\:\mathrm{n}\:=\: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},....\:\mathrm{then}\:\mathrm{a}_{\mathrm{100}} \:=\:? \\ $$

Question Number 87656 Answers: 1 Comments: 3

((1+sin((1/8))π+i cos((1/8))π)/(1+sin((1/8))π−i cos((1/8))π))=?

$$\frac{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi+{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi−{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}=? \\ $$

Question Number 87643 Answers: 0 Comments: 0

Given a random variable X of image set X(Ω)=[1;−1;2] with probabilities P(X=1)=e^a , P(X=−1)=e^b , and P(X=2)=e^c where a, b, and c are in an Arithmetic Progression. Assuming the mathematical expection E(X) of X is equal to 1. 1∙ Suppose the common difference of the Arithmetic Progression is r a∙ Determine the exact values of the real numbers a, b, and c. b. Show that the variance V(X) of X is equal to ((22)/7).

$${Given}\:{a}\:{random}\:{variable}\:\boldsymbol{{X}}\:{of}\:{image}\:{set} \\ $$$${X}\left(\Omega\right)=\left[\mathrm{1};−\mathrm{1};\mathrm{2}\right]\:{with}\:{probabilities}\:{P}\left({X}=\mathrm{1}\right)={e}^{{a}} , \\ $$$${P}\left({X}=−\mathrm{1}\right)={e}^{{b}} ,\:{and}\:{P}\left({X}=\mathrm{2}\right)={e}^{{c}} \:{where}\:{a},\:{b},\:{and}\:{c}\: \\ $$$${are}\:{in}\:\:{an}\:{Arithmetic}\:{Progression}. \\ $$$${Assuming}\:{the}\:{mathematical}\:{expection}\:{E}\left({X}\right)\:{of}\:{X}\: \\ $$$${is}\:{equal}\:{to}\:\mathrm{1}. \\ $$$$\mathrm{1}\centerdot\:{Suppose}\:{the}\:{common}\:{difference}\:{of}\:{the}\:{Arithmetic}\:{Progression}\:{is}\:\boldsymbol{{r}} \\ $$$$\boldsymbol{{a}}\centerdot\:{Determine}\:{the}\:{exact}\:{values}\:{of}\:{the}\:{real}\:{numbers}\:{a},\:{b},\:{and}\:{c}. \\ $$$$\boldsymbol{{b}}.\:{Show}\:{that}\:{the}\:{variance}\:{V}\left({X}\right)\:{of}\:{X}\:{is}\:{equal}\:{to}\:\frac{\mathrm{22}}{\mathrm{7}}. \\ $$$$ \\ $$$$ \\ $$

Question Number 87637 Answers: 1 Comments: 0

((∣x−3∣^(x+1) ))^(1/(4 )) = ((∣x−3∣^(x−2) ))^(1/(3 ))

$$\sqrt[{\mathrm{4}\:\:}]{\mid\mathrm{x}−\mathrm{3}\mid^{\mathrm{x}+\mathrm{1}} }\:=\:\sqrt[{\mathrm{3}\:\:}]{\mid\mathrm{x}−\mathrm{3}\mid^{\mathrm{x}−\mathrm{2}} } \\ $$

Question Number 87625 Answers: 2 Comments: 0

if f(x)=sin^(−1) (cos[x]) find Df and Rf the function notice/ [...] is floor

$${if}\:{f}\left({x}\right)={sin}^{−\mathrm{1}} \left({cos}\left[{x}\right]\right) \\ $$$${find}\:{Df}\:{and}\:\:{Rf}\:{the}\:{function} \\ $$$$ \\ $$$${notice}/\:\left[...\right]\:{is}\:{floor} \\ $$

Question Number 87624 Answers: 0 Comments: 1

find minimum value of cos^2 w + sec^2 w

$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{w}\:+ \\ $$$$\mathrm{sec}\:^{\mathrm{2}} \mathrm{w}\: \\ $$

Question Number 87614 Answers: 1 Comments: 0

{ (((x+y).2^(y−2x) =6.25)),(((x+y)^(1/(2x−y)) =5)) :}

$$\begin{cases}{\left({x}+{y}\right).\mathrm{2}^{{y}−\mathrm{2}{x}} =\mathrm{6}.\mathrm{25}}\\{\left({x}+{y}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}−{y}}} =\mathrm{5}}\end{cases} \\ $$

Question Number 87613 Answers: 1 Comments: 1

Question Number 87630 Answers: 0 Comments: 1

Question Number 87598 Answers: 0 Comments: 1

Question Number 87586 Answers: 1 Comments: 0

l.c.m of two numbers is p^2 q^4 r^4 p q r are primes.find the possible no. of pairs

$${l}.{c}.{m}\:{of}\:{two}\:{numbers}\:{is}\:{p}^{\mathrm{2}} {q}^{\mathrm{4}} {r}^{\mathrm{4}} \:{p}\:{q}\:{r}\:{are} \\ $$$${primes}.{find}\:{the}\:{possible}\:{no}.\:{of}\:{pairs} \\ $$

Question Number 87585 Answers: 1 Comments: 0

Question Number 87581 Answers: 2 Comments: 1

Question Number 110350 Answers: 2 Comments: 0

((bob)/(hans)) (1)lim_(x→3) ((sin (x−(9/x)))/(tan (x−3)cos ((9/x)−x)))= (2)(x tan^(−1) (y))dx +( (x^2 /(2(1+y^2 )))). dy =0

$$\:\:\:\frac{{bob}}{{hans}} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\mathrm{9}}{{x}}\right)}{\mathrm{tan}\:\left({x}−\mathrm{3}\right)\mathrm{cos}\:\left(\frac{\mathrm{9}}{{x}}−{x}\right)}= \\ $$$$\left(\mathrm{2}\right)\left({x}\:\mathrm{tan}^{−\mathrm{1}} \left({y}\right)\right){dx}\:+\left(\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{1}+{y}^{\mathrm{2}} \right)}\right).\:{dy}\:=\mathrm{0}\: \\ $$

Question Number 87563 Answers: 1 Comments: 5

Which of the two numbers ((1+2+2^2 +2^3 +...+2^(n−1) )/(1+2+2^2 +2^3 +...+2^n )) and ((1+3+3^2 +3^3 +...+3^(n−1) )/(1+3+3^2 +3^3 +...+3^n )) is greater?

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{numbers} \\ $$$$\frac{\mathrm{1}+\mathrm{2}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{3}} +...+\mathrm{2}^{\mathrm{n}−\mathrm{1}} }{\mathrm{1}+\mathrm{2}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{3}} +...+\mathrm{2}^{\mathrm{n}} }\:\mathrm{and}\: \\ $$$$\frac{\mathrm{1}+\mathrm{3}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +...+\mathrm{3}^{\mathrm{n}−\mathrm{1}} }{\mathrm{1}+\mathrm{3}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +...+\mathrm{3}^{\mathrm{n}} }\:\mathrm{is}\:\mathrm{greater}? \\ $$

Question Number 87561 Answers: 0 Comments: 3

for x,y ∈R , x ,y > 0 satisfy the equation { ((x^3 y−xy^3 = 24)),((x^2 +y^2 = 10 )) :} find the possible value of x+y? (a) 6 (b) 5 (c) 4 (d) 3(√2) (e) 2

$$\mathrm{for}\:\mathrm{x},\mathrm{y}\:\in\mathbb{R}\:,\: \\ $$$$\mathrm{x}\:,\mathrm{y}\:>\:\mathrm{0}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{3}} \mathrm{y}−\mathrm{xy}^{\mathrm{3}} \:=\:\mathrm{24}}\\{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{10}\:}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{6}\:\:\:\left(\mathrm{b}\right)\:\mathrm{5}\:\:\:\left(\mathrm{c}\right)\:\mathrm{4}\:\:\:\left(\mathrm{d}\right)\:\mathrm{3}\sqrt{\mathrm{2}}\:\:\left(\mathrm{e}\right)\:\mathrm{2} \\ $$

Question Number 87556 Answers: 1 Comments: 1