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Question Number 144618 Answers: 0 Comments: 1

Question Number 144614 Answers: 2 Comments: 0

^ Given that x = tan 23°, find the value of cos 16° in terms of x._

$$\overset{} {\:}\mathrm{Given}\:\mathrm{that}\:{x}\:=\:\mathrm{tan}\:\mathrm{23}°,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\:\mathrm{of}\:\:\mathrm{cos}\:\mathrm{16}°\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{x}\underset{} {.} \\ $$

Question Number 144609 Answers: 1 Comments: 0

How many digits doest the number 2021^(2022) have.?

$${How}\:{many}\:{digits}\:{doest}\:{the}\:{number} \\ $$$$\mathrm{2021}^{\mathrm{2022}} \:\:{have}.? \\ $$

Question Number 144608 Answers: 1 Comments: 0

find all aplication f in R→R f∈C^2 ∀x∈R. f′′(x)+f(−x)=x

$${find}\:{all}\:{aplication}\:{f}\:{in}\:\mathbb{R}\rightarrow\mathbb{R}\:\:{f}\in{C}^{\mathrm{2}} \\ $$$$\forall{x}\in\mathbb{R}.\:\:{f}''\left({x}\right)+{f}\left(−{x}\right)={x} \\ $$

Question Number 144607 Answers: 1 Comments: 0

Question Number 144603 Answers: 1 Comments: 0

Let a,b,c > 0 and (a+b)(b+c) = 4. Prove that (2a+b)(a+b)+(b+2c)(b+c) ≥ 8+(1/2)(a+2b+c)(c+a) Determine when equality holds.

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{b}\right)\left({b}+{c}\right)\:=\:\mathrm{4}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}{a}+{b}\right)\left({a}+{b}\right)+\left({b}+\mathrm{2}{c}\right)\left({b}+{c}\right)\:\geqslant\:\mathrm{8}+\frac{\mathrm{1}}{\mathrm{2}}\left({a}+\mathrm{2}{b}+{c}\right)\left({c}+{a}\right)\:\:\:\:\:\:\: \\ $$$$\mathrm{Determine}\:\mathrm{when}\:\mathrm{equality}\:\mathrm{holds}.\:\:\: \\ $$

Question Number 144602 Answers: 1 Comments: 0

Question Number 144600 Answers: 1 Comments: 0

if x,y,z>0 ; xy+yz+zx=1 prove that: xyz + (((1+x^3 )(1+y^3 )(1+z^3 )))^(1/3) ≥ 1

$${if}\:{x},{y},{z}>\mathrm{0}\:;\:{xy}+{yz}+{zx}=\mathrm{1}\:{prove}\:{that}: \\ $$$${xyz}\:+\:\sqrt[{\mathrm{3}}]{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{y}^{\mathrm{3}} \right)\left(\mathrm{1}+{z}^{\mathrm{3}} \right)}\:\geqslant\:\mathrm{1} \\ $$

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.

Question Number 144579 Answers: 2 Comments: 1