Problem 1. Find the metric system units of a, b, c, and d in the following...
8) Prove that C([O, 1]) is a metric space with the metric .1 d(f, g) = / If(x)-g(x)| dx. 9) Let (X, di) and (Y, d2) be metric spaces. a) Prove that X × Y is a metric space with the metric b) Prove that X x Y is a metric space with the metric
Problem 1. Let (X, d) be a metric space and t the metric topology on X. (a) Fix a E X. Prove that the map f :(X, T) + R defined by f(x) = d(a, x) is continuous. (b) If {x'n} and {yn} are Cauchy sequences, prove that {d(In, Yn)} is a Cauchy sequence in R.
THE METRIC SYSTEM OF MEASUREMENT AND ROAD MAPS QUESTIONS - EXERCISE 1 Convert the following English units to Metric units. Show your work for credit! 100 miles - ft 528,000 ft inches 6,336,000 inches centimeters 16,093,440 centimeters meters 160,934 meters kilometers On your Guide to Greensboro map shown on Page 4 with a scale of 1: 67,000 (1 cm on the map equals 67,000 em on the ground). What is the linear distance between A&T State University and.......? a. Bennett...
Which of the following units is not part of the metric system? O Meters O Grams O Gallons ⓔ Degrees Celsius Liters
S*x221) dx B) 2604 C) 15,624 D) 1302 7) 7) An object at the end of a spring is immersed in liquid. Its velocity (in cm/sec) is then described by the equation v 2e-2.se-9, where t is the time (in sec). Find the displacements as a function of tifs=-1 cm fort=0 sec. A) s-e-2.490 C)s=-2-4-9. D)s=219, Find the area bounded by the given curves. 8) y = x, y = 4x A) 16 Solve the problem. Round your answer, if...
1. (a) Let d be a metric on a non-empty set X. Prove that each of the following are metrics on X: a a + i. d(1)(, y) = kd(x, y), where k >0; [3] ii. dr,y) d(2) (1, y) = [10] 1+ d(,y) The proof of the triangle inequality for d(2) boils down to showing b + > 1fc 1+a 1+b 1+c for all a, b, c > 0 with a +b > c. Proceed as follows to prove...
6 6. Let (X, d) be a metric space and T the topology induced on X by d. Let Y be a subset of X and di the metric on Y obtained by restricting d; that is, di(a, b) d(a, b) for all a and b in Y. If T1 is the topology induced orn Y by di and T2 is the subspace topology on Y (induced by T on X), prove that Ti -T2. [This shows that every subspace...
Suppose A = B^xC^y, where the units in meters and seconds of A, B, C are respectively m.s, m2/s, and m.s2. Then the exponents x and y have the values: A) 2/3 ; 1/3 B) 4/5 ; -1/5 C) 1/5 ; 3/5 D) 2 ; 3
(1 point) The graph shows the displacement from equilibrium of a mass-spring system as a function of time after the vertically hanging system was set in motion at time t0. Assume that the units of time are seconds, and the units of displacement are centimeters. The first t-intercept is (0.75, 0) and the first minimum has coordinates (1.25,-1) (a) What is the period T of the periodic motion? seconds (b) What is the frequency f in Hertz? What is the...
PART A PART B PART C PART D (1 point) A mass m = 4 kg is attached to both a spring with spring constant k = 197 N/m and a dash-pot with damping constant c=4N s/m. The mass is started in motion with initial position to 3 m and initial velocity vo = 6 m/s. Determine the position function r(t) in meters. x(1) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can...