A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 69 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder.

What is her new rotation frequency, in revolutions per second?

find the pH of a 40 mL buffer solution + 1.0 mL of 6.0 M HCl (aq)

I know this question is pretty simple, but do I need to know what the buffer is made of? Is it important? if not how would I set up the ICE table? thank you!

A heavy rainstorm dumps 1.0 cm of rain on a city 7 km wide and 8 km long in a 2-h period.

part a) How many metric tons (1 metricton = 10³ kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10^-3 kg.)

Express your answer using one significant figure.

part b) How many gallons of water fell on the city? (1 gal = 3.785 L.)

Express your answer using one significant figure.

copper fin 1.0 mm thick is placed on a circular tube. The out side daiameter of the tube is 2.5 cm. The fin long is 8 mm and the thermal conductivity is 379 W/m °C. The tube wall is maintained at 473K. The fin is exposed to an environment with h = 30 W/m "C and T∞= 288K. %3D Calculate the heat lost by the fin.

29.       You were trying to prepare 1.0 liter of a 1.0M solution of NaCl. By mistake you went over the desired final volume and the final volume of the solution was 1.2 liter. What is the actual concentration of the solution? The molecular weight of NaCl is 56 g/mol.

3. A cube of Brass (B = 70 GPa) measuring 1.0 m on each side is submerged under water. It is lowerd to a depth where a force "F" is acting perpendicularly into each side, reduces the cube's volume by 1.8 %.

(a) Calculate the size of this force.

2.A researcher examines a piece of fresh human cartilage, with an area of 1.9 cm2. She observes that when subjected to a tensile force of 194 N it stretches by 4.8 %.

(a) Calculate the elastic modulus of cartilage.

1. A student pushes on the end of a helical spring, which in turn presses a 1.25 kg, wooden block onto a vertical wall. The coefficient of static friction between the block and wall is 0.5. She compresses the spring 5.2 cm.

(a) Calculate the minimum spring constant necessaary to prevent the block from sliding down the wall.

You are managing a portfolio of $1.0 million. Your target duration is 15 years, and you can choose from two bonds: a zero-coupon bond with maturity five years, and a perpetuity, each currently yielding 5%.

a. How much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio?

Zero-coupon bond ___ %

Perpetuity bond ____ %

How will these fractions change next year if target duration is now fourteen years?

Zero-coupon bond ___ %

Perpetuity bond ____ %

You are managing a portfolio of $1.0 million. Your target duration is 29 years, and you can choose from two bonds: a zero-coupon bond with maturity five years, and a perpetuity, each currently yielding 2%. a. How much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. How will these fractions change next year if target duration is now twenty eight years? zero-coupon bond? perpetuity bond? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Stock X has a 10.5% expected return, a beta coefficient of 1.0, and a 30% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 30.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations. CVx = CVy = Which stock is riskier for a diversified investor? For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X. Calculate each stock's required rate of return. Round your answers to two decimal places. rx = % ry = % On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor? Calculate the required return of a portfolio that has $3,000 invested in Stock X and $6,500 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places. rp = % If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return? Check My Work