a =?, b = 42.5, c = 60, α =?, β = 32◦ , δ =?, φ =? and γ =?.
use Sin rule and cos rule
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2. (a) State, without proof, the compound angle formulae for sin(a + β) and sin(α-β). 2 marks (b) Let θ be a fixed real number with 0 < θ < π. Show that, for all real x, sin(z+θ)- sin(z-Asin(z + φ) where φ (π + θ)/2 and A-2 sin(θ/2) (Hint: use part (a) above). 10 marks] (c) Determine φ if A = V2 and if A = V3. [9 marks] The physical interpretation of the result in part (b) above...
5. Stability of marriage. There are four men, α, β, γ, δ, and four women, A, B,C,D, The first number of each second number is the ranking of men by the women. For example, a-male ranks women C on third place, while C ranks α on the first place. A marriage profile is a pairing of men to women. A marriage profile is stable if there is no pair of a man and a woman who are not married to...
If three sentences of TFL, α, β and γ, are jointly inconsistent, what is (a Λ β) ^ (3) a. A tautology. b. A contradiction. c. A contingent sentence. d. Not enough information to decide. If three sentences of TFL, α, β and γ, are jointly inconsistent, what is (a Λ β) ^ (3) a. A tautology. b. A contradiction. c. A contingent sentence. d. Not enough information to decide. If three sentences of TFL, α, β and γ, are...
The general solution to the second-order differential equation d2ydt2−4dydt+7y=0d2ydt2−4dydt+7y=0 is in the form y(x)=eαx(c1cosβx+c2sinβx).y(x)=eαx(c1cosβx+c2sinβx). Find the values of αα and β,β, where β>0.β>0.Answer: α=α= and β=β=
Solve the triangle (a is the side opposite α, b is opposite β, and c is opposite γ ). You may estimate to the nearest hundredth but be sure to indicate it is only an estimate, not an exact answer. 1. β=30°, γ=45°, a=5. 2. γ=40°, a=1, b=2 3. a=6, b=2, c=5
1. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides. (Round your answers to one decimal place.) α = 48°; β = 83°; c = 112 a= b= 2. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides....
b. Suppose ~ Γ(α, β), with α > 0, β > 0 and let Y-eu. Find the probability density function of Y Find EY and var(Y)
Suppose X and Y are independent and Prove the following a) U=X+Y~gamma(α + β,γ) b) V=X/(X + Y ) ∼ beta(α,β) c) U, V independent d) ~gamma(1/2, 1/2) when W~N(0,1) X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image
23.13 List the two monosaccharides of sucrose. a) b) c) d) α-D-Glucopyranose, α-D-fructofuranose α-D-Glucopyranose, β-D-fructofuranose β-D-Glucopyranose, α-D-fructofuranose β-D-Glucopyranose, B-D-fructofuranose 23.12 Give the products from the periodic oxidation of D-fructose. a) HCHO CO2+ HCOOH b) HCHO+ HCOOH c) HCHO CO.2 d) CO2+ HCOOH
Y = C + I + G + NX (1) C = α + β(1 − t)Y (α > 0; 0 < β < 1) (2) I = θ − δi (θ > 0; δ > 0) (3) G = g + T (g > 0) (4) NX = (X − M) (5) Using differential calculus: solve for the change in national GDP(Y) with respects to a change in government expenditure(g)