(c) The metric describing the miverse as whole is usually written as ds2dt where a(t) 0...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
Matching A. Metric unit of force B. Unit of work in the metric system C. Metric unit of power D. Unit of work in English system E. Unit of pressure in metric system named after the scientist Torricelli F. Mass per unit volume G. The force that is dependent on the masses and distance between them H. A unit of angular measure I. The acceleration of and object traveling with a circular motion J. The displacement of an object as...
Al. Practice with complex numbers: Every complex number z can be written in the form z r + iy where r and y are real; we call r the real part of z, written Re z, and likewise y is the imaginary part of z, y - Im z We further define the compler conjugate of z aszT-iy a) Prove the following relations that hold for any complex numbers z, 21 and 22: 2i Re (2122)(Re z) (Re z2) -...
Q1 2016 a) We want to develop a method for calculating the function f(x) = sin(t)/t dt for small or moderately small values of x. this is a special function called the sine integral, and it is related to another special function called the exponential integral. it rises in diffraction problems. Derive a Taylor-series expression for f(x), and give an upper bound for the error when the series is terminated after the n-th order term. sint = see image b)we...
please answer them in detail. The concentration C(x, t) of a pollutant in a semi-infinite pipe diffuses according to the PDE over 0<<o for > 0, where the diffusivity D is a given positive constant. An experiment is performed in which the initial concentration is zero everywhere, so that C(x, 0)0 for all r 20. Once t > 0 a fixed concentration of C(0, t) Co is imposed at x-0, where Co is a constant, and it is also assumed...
4. (a) What is meant by an "adverse pressure gradient what makes t adverse? [2] (b) Why will a lamınar boundary layer separate more easily than a turbulent one? (c) A simple approach for solving for the development of a boundary using the Momentum Integral Equation dx used is to assume a shape for the velocity profile. The following fom has sometimes been 3 where u, is the velocity at the edge of the boundary layer, y [6] [4] (i)...
Ball has initial velocity v m/s in x direction Cliff Ball strikes sea at point (s,0) Sea (0,0) 3(c) [7 Marks] A golf ball is struck with velocityv (meters per second) from the edge of a cliff which rises h metres above sea level. Referring to figure (3) the golf ball starts at the point (0, h) follows a parabola and strikes the sea some time later at the point (8,0). It can be shown that the (x, y) location...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a potential for F. Let r,y be that potential, then Use the first component of F to find an expression for ф(x, y)-Po(x,y) + g(y), where ф(x,y) in the form: Differentiate ф(x,y) with respect to y and determine g(y) e Using the...
where c> 0 ro The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y)=c In Vx2 + y2 is a constant and ro is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c. wherer= x2 + y2. Rewrite E in terms b. Show that the electric field at a point in the xy-plane...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o are known. Consider testing Ho : 0 = O0 vs. Hi 0 700 Q1(4pt): Using Likelihood Ratio Test (LRT) to obtain a level a test that rejects Ho if Уп(X — во) VП(х — во) <21-a/2 21-a/2 or о Q2(1pt): Is the two-sided test derived in 1) an uniformly most powerful test? If not, briefly state your reasons Q3 (1pt): Note that the test...