3.3.5 Show that the curve (t) (at bsin t, a -b cost ), where a and...
5, (25 points 4 pages max) Suppose that γ(t) = (x(t), y(t)) is a smooth (infinitely differentiable) plane curve. For curves such that lh'(t) 0, the (signed) curvature is defined to be the quantity K(t) (a) Suppose the curve γ(t) is the graph of a function, ie x(t)-t and y(t) f(t) for some function f. Write the formula for the curve in this case. Suppose you were at a critical point of the graph of f. What does the curvature...
(sin(π/z) -1dd 2. Compute the integral: sin(π/s)-.--d γ is the cl γ is the curve shown in the 2. where 721-1 following figure: arked points on the coordinate axes correspond to T,-T, 2, 2. (sin(π/z) -1dd 2. Compute the integral: sin(π/s)-.--d γ is the cl γ is the curve shown in the 2. where 721-1 following figure: arked points on the coordinate axes correspond to T,-T, 2, 2.
a) show that for a solid steam, it behaves like an ideal gas, the sublimation curve has the form P = -B / T + A where A and B are constants. b) For Mg at 700k, B 7527. Calculate the heat of sublimation of Mg at this temperature in cal / mol. c) Is the equation deduced in a) useful to determine the sublimation curve?
(3 points) Consider the ordinary differential equation where w- 1.8 and the values of bn are constants (a) Find the particular solution to the non-homogeneous equation using the method of undetermined coefficients sin(nt) Your answer should be expressed in terms of n and bn (type bn as bn) b) Consider the function f(t) defined by 1, 0
Question 16. A maximal plane graph is a plane graph G = (V, E) with n ≥ 3 vertices such that if we join any two non-adjacent vertices in G, we obtain a non-plane graph. (a) Draw a maximal plane graphs on six vertices. (b) Show that a maximal plane graph on n points has 3n − 6 edges and 2n − 4 faces. (c) A triangulation of an n-gon is a plane graph whose infinite face boundary is a...
3. Let W (x, t) = (coswt)(a cos nx+b sin nx) and (x, t) = (exp -kn-t)(a cos nx+ bsin nx). Here n is a positive integer, 2,t are real variables, and a, b,w, k are real constants with k positive. a. Evaluate W(x,0), H (2,0) and əW/ət(x,0) for all c. b. Show OH/ət = k(32H/8x2) for all x,t. c. Find some positive constant c so that w2w/at2 = c(32W/8x?) for all x, t.
coG+{Y-T) Elbi M PYL) (i) = L-ci G=G T-T MEM Where T.G.L.M.c.7.b.cc. are all non-negative variables, whose values are determined exogenously, outside of the model (1) Suppose b=0. draw the IS curve in this case. Explain brietly your result. (4 points) Now suppose there is a decrease in G by AG <0. (2) Consider the IS relation only. How much is the impact on y G by AGCO under two scenarios b = 0 and b>0. Show ion only. How...
A maximal plane graph is a plane graph G = (V, E) with n ≥ 3 vertices such that if we join any two non-adjacent vertices in G, we obtain a non-plane graph. A maximal plane graph is a plane graph G = (V, E) with n-3 vertices such that if we join any two non-adjacent vertices in G, we obtain a non-plane graph. (a) Draw a maximal plane graphs on six vertices b) Show that a maximal plane graph...
show steps 7 pts) Consider an FSK system where bits 1 and 0 are transmitted using signals si(t) and s2(t) 2Eb 2Eb where θ1 and 02 are the phases of the two signals. (a) (3 pt) Find the correlation between the signal s1(t) ard salt), i.e., find oin(t)s2(t)dt. b) (2 pt) Assuming non-coherent carriers, i.e., θ|メ02, state the condition for which the correlation derived in part (a) goes to zero. (c) (2 pt) Repeat part (b) for the case where...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...