the six periods of technology development.

Explain the concept of “technology convergence.”

Consider the hemispherical closed surface in the figure below. The hemisphere is in a uniform magnetic field that makes an angle ? with the vertical.

(a) Calculate the magnetic flux (?B) through the flat surface S1. (Use any variable or symbol stated above along with the following as necessary: pie.)

?B = __________.

(b) Calculate the magnetic flux (?B) through the hemispherical surface S2. (Use any variable or symbol stated above along with the following as necessary: pie.)

?B =__________.

Assume that the DJIA closed at 11,875 one day recently, and the divisor was 0.12493117.

a. What is the sum of the prices of the 20 stocks in the index, given this information?

b. Assume that one stock in the index, Pfizer, moved $4.40 that day, while the index itself moved about 105 points (to close at 10,875). What percentage of the total movement in the DJIA that day was accounted for by the movement in Pfizer?

c. Now assume that one of the 20 stocks had an initial price of $47.50 and the same stock had a 4-for-1 stock split that day. What would the new divisor have to be to keep the index unchanged at 11,875?

Suppose that the closed economy of an island H is described by the following equations: GDP (Y) = 10000, government expenditures (G) = 600, Taxes (T) = 2000, Consumption (C) = 400 + 3/4 (Y-T), and investment (I) = 200 – 1400 r

a. Write and explain the equation of the GDP

b. Compute

1. Private saving

2. Public saving

3. National saving

4. Equilibrium interest rate

c. What can you conclude about the economy of Island H?

Suppose f maps a closed and bounded set D to the reals is continuous. Then the Uniform Continuity Theorem says f is uniformly continuous on D. To prove this, we will suppose it is not true, and arrive at a contradiction.

So, suppose f is not uniformly continuous on D. If f is not uniformly continuous on D, then there exists epsilon greater than zero and sequences (a_n) and (b_n) in D for which |a_n -b_n| < 1/n and |f(a_n) - f(b_n)| > epsilon. Give comment as to why this must be true if f is not uniformly continuous on D.

Nothing says the sequences (a_n) and (b_n) converge. But, because f is continuous on D, there exists subsequences of (a_n) and (b_n), say (a_nk) and (b_nk) respectively, that do converge. Give comment as to why this would be true.

Show that both limits of the subsequences must lie in D and that they are in fact equal. Explain why this is leads to a contradiction. Finish the proof.

2. A circuit contains 3 resistors connected in series and no battery. It is a closed circuit and has dimensions of 18 cm by 42 cm. The resistor values are 12, 15 and 18 ohms. A magnetic field directed out of the plane of the circuit changes from 52 T to 0 T in 2.9 sec.

a. Sketch the circuit and indicate the direction of the initial magnetic field.

b. What is the magnetic flux through the circuit when the magnetic field is at its starting value? What is the flux when the field is at its final value?

c. What is the direction of the current in the circuit as the magnetic field is changing? Explain.

d. What is the induced emf and current in the circuit as the magnetic field is changing?

e. What is the direction of the current after the magnetic field reaches its final value?

a dead body was found within a closed room of a house where the temperature was at 21°C. at the time of discovery the core temperature of the body was determined to be 28°C. One hour later the second measurement show that the core temperature of the body was 25°C. assume that the time of death corresponds to t = 0 and that the core temperature at the time was 37°C. determine how many hours elapsed before the body was found. [ Hint: Let t1 > 0 denote the time that the body was discovered.] (Round your answer to one decimal place.)

_____ hr

A 0.75 L bottle is cleaned, dried, and closed in a room where the air is 20°C and 44% relative humidity (that is, the water vapor in the air is 0.44 of the equilibrium vapor pressure at 20°C). The bottle is brought outside and stored at 0.0°C. (See Table 5.2) vapor pressure of 20 degrees is 17.5 torr and 0 degrees is 4.6 torr

What mass of water condenses inside the bottle?