A capacitor consists of two concentric spherical shells. The outer radius of the inner shell is a = 0.1 m and the inner radius of the outer shell is b = 0.2 m. a. What is the capacitance, C, of this capacitor? b. Suppose the maximum possible electric field at the outer surface of the inner shell before the air starts to ionize E max(r=a) = 3.0*10^6 V/m . What is the maximum possible charge on the inner capacitor? c. What is the maximum amount of energy stored in this capacitor? d. When E (r=a) = 3.0*10^6 V/m, what is the potential difference between the shells?

Pete Corp. issued $30 million of 7%, 15-year convertible bonds at 102 on January 1, 2021. The bonds pay interest semiannually each June 30 and December 31. Each $1,000 bond is convertible into 50 shares of Pete's no par common stock. Pete recently issued similar, but non-convertible, bonds at 98.  

61 % of the bonds were converted when the common stock had a price of $23/share and the remaining premium was $0.2 million ($200,000).

For what amount would Pete credit Common Stock when 61% of the bonds are converted?

Enter in dollars (e.g. enter $10 million as 10,000,000).

Two long, straight wires are perpendicular to the plane of the paper and at a distance 0.2 m from each other, as shown in the figure. The wires carry currents of I1 = 2.6 A and I2 = 5 A in the direction indicated (out of the page). Find the magnitude and direction of the magnetic field (in µT) at a point A midway between the wires. You need to indicate the direction with a positive or a negative value for the magnetic field. Keep in mind that a vector is positive if directed to the right and negative if directed to the left on the x axis and it is positive if directed up and negative if directed down on the y axis. Your answer should be a number with two decimal places, do not include the unit.

The following are the load and gage lengths from a stainless steel. The diameter of the bar is 0.506 inch. Plot engineering stress versus engineering strain for the data shown. Find the 0.2% offset yield strength for this steel.

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and Y1...Xn independent of each other. Assume that the common population SD σ is known but the two means are not. Consider testing the hypothesis null: μx = μy vs alternative: μx ≠ μy.

d. Assume σ=1 and n=20. How large must δ be for the size 0.01 test to have power at least 0.99?

e. Assume σ=1and δ=0.2. How large must n be for the size 0.01 test to have power at least 0.99?

Historically, the one-year returns follow approximately the normal distribution. The one-year return for the S&P 500 was +27% (that is, 0.27) and its standard deviation is 20% (that is, 0.2). What is the probability that a stock in the S&P 500 gained 30% or more last year?

(a) 0.0668 (i.e., 6.68%)
(b) 0.4404 (i.e., 44.04%)
(c) 0.5596 (i.e., 55.96%)
(d) 0.9332 (i.e., 93.32%)

What is the probability that a stock in the S&P 500 lost 10% or more last year?

(a) 0.1814 (i.e., 18.14%)
(b) 0.0082 (i.e., 0.82%)
(c) 0.0322 (i.e., 3.22%)
(d) 0.0743 (i.e., 7.43%)

Given the following information,

a) What are the expected returns for stock A and B, respectively?

b) What is the standard deviation/risk for stock A? List the formula and input the number, no calculation needed.

c) What is the portfolio return given that you have $10,000 and allocate $3,000 in stock A and the rest in stock B? List the formula and input the number, no calculation needed.

d) The principle of diversification states that as the number of stocks under the portfolio increases, the portfolio risk more likely A) increases or B) decreases?

Suppose you plan to take a survey of math students asked about their overall grades. 22 students were surveyed, and it was found that the average GPA of the 22 sampled students was a 3.2, with a standard deviation of 0.9 points. Suppose you want to re-sample the population to reduce the margin of error. If you plan to calculate a 90% confidence interval for the true mean GPA of math students, how many samples would be necessary to reduce the margin of error to 0.2 points? Round your answer to the nearest whole number, and remember it's always better to sample too many rather than not enough.

A 240 V DC shunt motor draws 40 A while driving a constant torque load. The armature resistance is Ra = 0.2 Ω, the field resistance is Rf = 240 Ω and machine constant is Ka = 120. The part of magnetization characteristic (field flux versus field current) related to the question is:

If (A) :      0.70 0.80 0.86 0.90 1.00 1.10 1.20 1.30 1.40

ϕ (mWb) : 5.80 6.30 6.59 6.70 7.20 7.60 7.96 8.20 8.45

The constant rotational loss is 240 W and the armature reaction is neglected. Find

a. the internal torque developed by the motor

b. speed    

c. efficiency    

A laboratory scale experiment has been planned to
study the vortex shedding induced loading on a
structural member. For doing this, the accurate
measurements of flow velocity and vortex shedding
frequency is of prime importance. The member is
placed vertically across the flow having mean flow
velocity of 50 m/s. The diameter of the member is 5
cm. If the Strouhal number is 0.2, determine the
following:

appropriate sensor type for measurements and its
characteristics ?

vortex shedding frequency?

sampling frequency required to resolve the
frequency content?

sampling frequency necessary to reconstruct the
waveform and amplitude?

would you filter the signal before acquisition, if yes
then mention reasons?