ifo = 90°-Θ.what i st he u alueofsin2 Θ + sín.Θ ifo = 90°-Θ.what i st he u alueofsin2 Θ + sín.Θ
3. A general surface of revolution is r(u, θ)-(f( u') cos θ , f(u) sin θ, υ), θΕ[0, 27), where f(u) is a positive function. For the following choices of f(u), find the principal, Gaus- sian, and mean curvatures at arbitrary (u, θ), and classify each point on the surface as elliptic, hyperbolic, parabolic, or planar. (a) f(u)u, u E [0, 00) (b) f(uV1 - u2,u e[-1,1].
Find θ if θ is between 0° and 90°. Round your answer to the nearest tenth of a degree. cos θ = 0.8890 Find θ if θ is between 0° and 90°. Round your answer to the nearest tenth of a degree. sin θ = 0.9831 Find θ if θ is between 0° and 90°. Round your answer to the nearest tenth of a degree. csc θ = 1.6195
V X2 + y2 and θ u(r(z, y), θ(x, y))--sech2 r tanh r sin θ 6. [Sec. I 1.5] Letr tan l (y/z) be the usual polar rectangular coordinates relationships. Furthermore, define and u(r(z, y),θ(z, y)) sech2 r tanh r cos θ Show that tanh r
et (X1,··· ,Xn) be a sample from U[0,θ], where θ ∈ (0,1) is unknown, and θ has a prior distribution U[0,1].
5. Solve u(a,8) = 0. Answer: u(r,θ)-2(d-r) 5. Solve u(a,8) = 0. Answer: u(r,θ)-2(d-r)
3. (10 points) Consider the utility function U(q;θ) = q1−θ−1, where 0 < θ < 1 is a utility parameter. (a) Compute the marginal utility function, MU(q; θ) = U0(q; θ). (b) Show that MU(q; θ) is decreasing. 3. (10 points) Consider the utility function U(g; e )-Te 1, where 0 < θ < 1 is a utility parameter. (a) (5 points) Compute the marginal utility function, MU(q:e) U'(q;e) (b) (5 points) Show that MU(q:0) is decreasing.
Vectors pure and applied Exercise 11.5.9 Let U and V be finite dimensional spaces over F and let θ : U linear map. v be a (i) Show that o is injective if and only if, given any finite dimensional vector space W map : V W such that over F and given any linear map α : U-+ W, there is a linear (ii) Show that θ is surjective if and only if, given any finite dimensional vector space...
C.The diagram on the left shows a curve banked past vertical so that θ > 90° θ > 90, is there a speed great enough so that the car stays on the road?
Use eigenfunction expansion to solve this IBVP. v) u(0,6) bounded , -π < θ < π v) u(0,6) bounded , -π
16, Let x: U R2-, R, where x(8, φ) (sin θ cos φ, sin θ sin φ, cos θ), be a parametrization of the unit sphere S2. Let and show that a new parametrization of the coordinate neighborhood x(U) = V can be given by y(u, (sech u cos e, sech u sin e, tanh u Prove that in the parametrization y the coefficients of the first fundamental form are Thus, y-1: V : S2 → R2 is a conformal...