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Question Number 144597 Answers: 2 Comments: 0

let ϕ(x)=(1/(3+cosx)) developp f at fourier serie

$$\mathrm{let}\:\varphi\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{3}+\mathrm{cosx}} \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 144589 Answers: 1 Comments: 0

Find the value of Σ_(k=1) ^(90) sin k°+Σ_(k=1) ^(90) cos (90°+k°)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{90}} {\sum}}\mathrm{sin}\:{k}°+\underset{{k}=\mathrm{1}} {\overset{\mathrm{90}} {\sum}}\mathrm{cos}\:\left(\mathrm{90}°+{k}°\right) \\ $$

Question Number 144584 Answers: 0 Comments: 0

b. An experiment consists of flipping an unbiased coin and flipping again if a head occuors and yet again if a second bead occours , list the elements of the sample space . find the probability of exactly two tosses. c. if then prove that probability that X occours but not Y = probability that X occours − probabulity that Y occours CLO−1.

$$\mathrm{b}.\:\mathrm{An}\:\mathrm{experiment}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{flipping}\:\mathrm{an}\:\mathrm{unbiased}\:\mathrm{coin} \\ $$$$\mathrm{and}\:\mathrm{flipping}\:\mathrm{again}\:\mathrm{if}\:\mathrm{a}\:\mathrm{head}\:\mathrm{occuors}\:\mathrm{and}\:\mathrm{yet} \\ $$$$\mathrm{again}\:\mathrm{if}\:\mathrm{a}\:\mathrm{second}\:\mathrm{bead}\:\mathrm{occours}\:,\:\mathrm{list}\:\mathrm{the}\:\mathrm{elements} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{space}\:.\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{of}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{tosses}. \\ $$$$\mathrm{c}.\:\mathrm{if}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{X}\:\:\mathrm{occours}\:\mathrm{but} \\ $$$$\mathrm{not}\:\mathrm{Y}\:=\:\mathrm{probability}\:\mathrm{that}\:\mathrm{X}\:\mathrm{occours}\:−\:\mathrm{probabulity}\:\mathrm{that}\:\mathrm{Y}\:\mathrm{occours} \\ $$$$\mathrm{CLO}−\mathrm{1}.\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 144582 Answers: 0 Comments: 0

Q. 1. throw two dice list, the elements of the sample space of the experement. let A be the event that the sum of the fa4es is odd and B be tbe event that at least one occurs. find the subset of the sample space in which i. event A and B occurs togather. ii. event A occurs or event B occurs. iii. event A occours but not B.

$$\mathrm{Q}.\:\mathrm{1}.\:\mathrm{throw}\:\mathrm{two}\:\mathrm{dice}\:\:\mathrm{list},\:\mathrm{the}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{space} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{experement}.\:\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{fa4es}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{B}\:\mathrm{be}\:\mathrm{tbe}\:\mathrm{event}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\: \\ $$$$\mathrm{one}\:\mathrm{occurs}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{subset}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{space} \\ $$$$\mathrm{in}\:\mathrm{which}\: \\ $$$$\mathrm{i}.\:\mathrm{event}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{occurs}\:\mathrm{togather}. \\ $$$$\mathrm{ii}.\:\mathrm{event}\:\mathrm{A}\:\mathrm{occurs}\:\mathrm{or}\:\mathrm{event}\:\mathrm{B}\:\mathrm{occurs}. \\ $$$$\mathrm{iii}.\:\mathrm{event}\:\mathrm{A}\:\mathrm{occours}\:\mathrm{but}\:\mathrm{not}\:\mathrm{B}. \\ $$

Question Number 144579 Answers: 2 Comments: 1

Question Number 144679 Answers: 0 Comments: 2

Question Number 144564 Answers: 1 Comments: 1

Question Number 144563 Answers: 2 Comments: 0

log_4 (x) = log(y) = log_(25) (x+y) Find (x/y) = ?

$$\boldsymbol{{log}}_{\mathrm{4}} \left(\boldsymbol{{x}}\right)\:=\:\boldsymbol{{log}}\left(\boldsymbol{{y}}\right)\:=\:\boldsymbol{{log}}_{\mathrm{25}} \left(\boldsymbol{{x}}+\boldsymbol{{y}}\right) \\ $$$${Find}\:\:\frac{{x}}{{y}}\:=\:? \\ $$

Question Number 144558 Answers: 3 Comments: 0

lim_(x→−∞) (((2x−(√(3x^2 +3x)))/(x−1)))=?

$$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\left(\frac{\mathrm{2x}−\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3x}}}{\mathrm{x}−\mathrm{1}}\right)=? \\ $$

Question Number 144556 Answers: 2 Comments: 0

lim_(x→0) (((1−cos x(√(cos 2x)))/x^2 )) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{x}^{\mathrm{2}} }\right)\:=? \\ $$

Question Number 144554 Answers: 1 Comments: 0

Question Number 144553 Answers: 1 Comments: 0

Solve for natural numbers: (1^4 /z) + (2^4 /(z+1)) + (3^4 /(z+2)) + ... + ((10^4 )/(z+9)) = 3025

$${Solve}\:{for}\:{natural}\:{numbers}: \\ $$$$\frac{\mathrm{1}^{\mathrm{4}} }{\boldsymbol{{z}}}\:+\:\frac{\mathrm{2}^{\mathrm{4}} }{\boldsymbol{{z}}+\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{4}} }{\boldsymbol{{z}}+\mathrm{2}}\:+\:...\:+\:\frac{\mathrm{10}^{\mathrm{4}} }{\boldsymbol{{z}}+\mathrm{9}}\:=\:\mathrm{3025} \\ $$

Question Number 144550 Answers: 0 Comments: 0

Question Number 144549 Answers: 1 Comments: 0

Question Number 144544 Answers: 2 Comments: 1

lim_(x→(π/2)) (cosx)^(cotx)

$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({cosx}\right)^{{cotx}} \\ $$

Question Number 144539 Answers: 1 Comments: 0

Let 0°<θ<45°, find the value of sin^2 (45°+θ)+sin^2 (45°−θ)

$$\mathrm{Let}\:\mathrm{0}°<\theta<\mathrm{45}°,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}°+\theta\right)+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}°−\theta\right) \\ $$

Question Number 144537 Answers: 2 Comments: 0

Let a,b>0 and a+b = 2. Prove that (1) ((a^3 +b^3 )/2)−2(1−ab) ≥ 1 (2) ((a^2 +b^2 )/2)−2(1−ab) ≤ 1

$$\mathrm{Let}\:{a},{b}>\mathrm{0}\:\mathrm{and}\:{a}+{b}\:=\:\mathrm{2}.\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} }{\mathrm{2}}−\mathrm{2}\left(\mathrm{1}−{ab}\right)\:\geqslant\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}−\mathrm{2}\left(\mathrm{1}−{ab}\right)\:\leqslant\:\mathrm{1} \\ $$

Question Number 144534 Answers: 2 Comments: 0

Find the shortest distance from the origin to the hyperbola x^2 +8xy+7y^2 =225 ,z=0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{from}\: \\ $$$$\mathrm{the}\:\mathrm{origin}\:\mathrm{to}\:\mathrm{the}\:\mathrm{hyperbola}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{8xy}+\mathrm{7y}^{\mathrm{2}} =\mathrm{225}\:,\mathrm{z}=\mathrm{0}\: \\ $$

Question Number 144532 Answers: 1 Comments: 0

A rectangular box,open at the top is to have a volume of 32 cube feet What must be the dimensions so that the total surface is a minimum?

$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{box},\mathrm{open}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{top}\:\mathrm{is}\:\mathrm{to}\:\mathrm{have}\:\mathrm{a}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{32}\:\mathrm{cube}\:\mathrm{feet} \\ $$$$\mathrm{What}\:\mathrm{must}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimensions} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{total}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{a}\:\mathrm{minimum}? \\ $$

Question Number 144530 Answers: 2 Comments: 0

∫_0 ^( π/2) ((cos^2 x)/((2cos x+sin x)^2 )) dx =?

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

Question Number 144528 Answers: 1 Comments: 0

Find the volume of the region bounded by the elliptic paraboloid z = 4−x^2 −(1/4)y^2 and the plane z=0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\: \\ $$$$\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{elliptic}\:\mathrm{paraboloid} \\ $$$$\mathrm{z}\:=\:\mathrm{4}−\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\mathrm{y}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{z}=\mathrm{0} \\ $$$$ \\ $$

Question Number 144527 Answers: 2 Comments: 0

..... Calculus (I )..... P:= ((∫_(0 ) ^( (π/2)) ( xcos(x)+1 )e^( sin(x)) dx )/(∫_0 ^( (π/2)) ( xsin(x) −1 )e^( cos(x )) dx))=?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:.....\:\:\:\mathrm{Calculus}\:\:\left(\mathrm{I}\:\right)..... \\ $$$$\mathrm{P}:=\:\frac{\int_{\mathrm{0}\:} ^{\:\:\frac{\pi}{\mathrm{2}}} \left(\:{xcos}\left({x}\right)+\mathrm{1}\:\right){e}^{\:{sin}\left({x}\right)} {dx}\:}{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\:{xsin}\left({x}\right)\:−\mathrm{1}\:\right){e}^{\:{cos}\left({x}\:\right)} {dx}}=? \\ $$

Question Number 144517 Answers: 1 Comments: 0

Question Number 144515 Answers: 1 Comments: 1

S_(15) −S_(25) =150 S_(30) =?

$${S}_{\mathrm{15}} −{S}_{\mathrm{25}} =\mathrm{150} \\ $$$${S}_{\mathrm{30}} =? \\ $$

Question Number 144513 Answers: 1 Comments: 0

Question Number 144509 Answers: 0 Comments: 0

S_n =((Cos1)/1^2 )+((Cos2)/2^2 )+((Cos3)/3^2 )+...+((Cosn)/n^2 ) Indicates that S_(n ) is a cauchy suite?

$$ \\ $$$${S}_{{n}} =\frac{{Cos}\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{{Cos}\mathrm{2}}{\mathrm{2}^{\mathrm{2}} }+\frac{{Cos}\mathrm{3}}{\mathrm{3}^{\mathrm{2}} }+...+\frac{{Cosn}}{{n}^{\mathrm{2}} } \\ $$$${Indicates}\:{that}\:{S}_{{n}\:} \:{is}\:{a}\:{cauchy}\:{suite}? \\ $$

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