Show that the connected sum of two compact surfaces is a compact surface.

Expert Solution

Colby Messinger answered 1 year ago

Surface energy is the sum of the energies of all surfaces and the preferred shape of...

Surface energy is the sum of the energies of all surfaces and the preferred shape of a crystal that is bounded by free surfaces is the one that minimizes its total interfacial energy. a) In simple metal solids, the preferred shape is nearly spherical. Please explain why. b) Ionic solids tend to have polygonal shapes with large, flat facets parallel to the low-energy planes. Please explain why. c) Use the NaCl ionic structure to explain what you described in (b).

show that lR is not compact!

1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the...

1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the subspace topology given by τs. 2. Let f: X → Y continue. We say that f is open if it sends open of X in open of Y. Show that the canonical projection ρi: X1 × X2 → Xi (x1, x2) −→ xi It is continuous and open, for i = 1, 2, where (X1, τ1) and (X2, τ2) are two topological spaces and...

Show that the surfaces are tangent to each other at the given point by showing that...

Show that the surfaces are tangent to each other at the given point by showing that the surfaces have the same tangent plane at this point. x2 + y2 + z2 − 20x − 16y + 2z + 115 = 0, x2 + y2 + 6z = 17, (5, 4, −4) Both surfaces have the tangent plane of (answer ) at (5, 4, −4), therefore they are tangent to each other at this point.

Prove that the intersection of two compact sets is compact, using criterion (2).

Question: Prove that the intersection of two compact sets is compact, using criterion (2). Prove that the intersection of two compact sets is compact, using criterion (1). Prove that the intersection of two compact sets is compact, using criterion (3). Probably the most important new idea you'll encounter in real analysis is the concept of compactness. It's the compactness of [a, b] that makes a continuous function reach its maximum and that makes the Riemann in- tegral exist. For...

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a...

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a massless string to a hook where M2 can be increased smoothly. The pulley has a negligible mass & no friction. When M2= 3.266 kg it begins to accelerate downward at a rate of 2.110 m/s2. Calculate us - uk between M1 and the surface.

1. Show that when two equal resistances are connected in parallel the equivalent resistance is just...

1. Show that when two equal resistances are connected in parallel the equivalent resistance is just one half that of either resistor. 2. Suppose that we replaced one of the bulbs in the setup with one rated at 6V, 7.5W. show that a 1A fuse in the circuit would blow out when this bulb is given power. What is the operating resistance of the filament in this bulb? Show Calculation

A block of mass m1 = 0.500 kg sits on a frictionless surface and is connected...

A block of mass m1 = 0.500 kg sits on a frictionless surface and is connected by a weightless string to a weight of mass m2 = 0.200 kg that hangs from a pulley. The system is initially at rest. If the mass m2 is released and drops for 1.00 m, what is the speed of the system? Assume that mass m1 does not reach the edge of the surface. Use energy considerations, not force considerations. What is the speed...

A block with mass mA = 15.0 kg on a smooth horizontal surface is connected by...

A block with mass mA = 15.0 kg on a smooth horizontal surface is connected by a thin cord that passes over a pulley to a second block with mass mB = 6.0 kg which hangs vertically. Determine the magnitude of the acceleration of the system. Express your answer to two significant figures and include the appropriate units. If initially mA is at rest 1.250 m from the edge of the table, how long does it take to reach the...

The total surface area is the sum of the triangular area and rectangular area. Complete the...

The total surface area is the sum of the triangular area and rectangular area. Complete the following code to compute the total surface area of the shape. ??????? ???? = 12 ∗ ???? ∗ ????h? + ???? ∗ ????h This Java program prompts for and reads in the value of height, base, and width in feet.This program uses two methods: Train_area and Rect_area to calculate the area of the triangle and the area of the rectangle, respectively. The following parameters:...

Question