Two charged proteins P1 and P2 are located at positions (1m,1m) and (-1m,1m) respectively on a Cartesian coordinate system. They have charges of 1.0 nC and -1.0 nV respectively. A key enzyme E1 which regulates an important biochemical pathway, is localed at the origin of the coordinate system.

1. compute the electrical potential V at the position of E1
2. Draw a vector diagram for the electrical field vector ETOT, at the position of E1.
3. show, or argue that the y component of the electrical field vector ETOT,Y at the position of E1, is equal to zero
4. Compute the electrical field vector ETOT, at the position of E1. Hint: ETOT is a vector!

The RBE (relative biological effectiveness factor) for several different types of radiation is shown in the chart below. Type of Radiation RBE X-rays and gamma rays 1.0 Beta particles 1.0 – 1.7 Alpha particles 10 – 20 Thermal neutrons 2 – 5 Fast neutrons and protons to the eye 32 Fast neutrons and protons 10 Heavy ions 20 Using the above chart, determine the dose in Gy for the maximum biological effectiveness from each of the following. (a) A 2.13 rad exposure to x-ray Gy (b) A 48.7 mSv exposure to α particles Gy (c) A 21.2 mrem exposure to β− particles

A rocket ship is launched from rest from a space station. Its destinations 1.0 x 10^11 m away. The ship is programmed to accelerate at 7.4 m/s^2 for 12 hours. After 12 hours, the ship will travel at constant velocity until it comes within 1.0 x 10^10 m of its destination. Then, it will fire its retrorockets to land safely.

Event 1: t= , r= , v= ,

Event 2: t= , r= , v= ,

Event 3: t= , r= , v= ,

Event 4: t= , r= , v= ,

a(12)= , a(23)= , a(34)=

Mathematical Analysis?

A 10 cm long thin glass rod uniformly charged to +10 nC and a 10 cm long thin plastic rod uniformly charged to -10nC are placed side by side 4 cm apart.

a. Find the electric field at distances 1.0 cm, 2.0 cm and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods. (Hint: treat the rods as a uniform line of charges.)

b. If the plastic rod is exchanged for a glass rod of the same size uniformly charged to +10 nC, what is the new electric field at 1.0 cm, 2.0 cm and 3.0 cm?

Computing Present Value of Terminal Period FCFF

Use the following data to compute the present value of the terminal period free cash flows to the firm for each of the four firms A, B, C, and D. The forecast horizon included four years.

Round answers to the nearest whole number.

1. The pH of a solution made of 1.0 M acetic acid and 0.1 M potassium acetate is (K_a = 1.8 x 10^-5) to which 0.001 mol of KOH has been added: a) pH = 4.74 b) pH = 4.73 c) pH = 8.92 d) pH = 4.46 e) pH = 11.55 The answer is not 4.74!!

2. The pH of a solution made of 1.0 M acetic acid and 0.1 M potassium acetate is (K_a = 1.8 x 10^-5)​ to which 0.001 mol of HCl has been added: a) pH = 1.64 b) pH = 4.75 c) pH = 3.28 d) pH = 8.90

IV. Comparing Buffering Capacity

A. pH of Pure Water

i. Measure out 30.0 mL DI H2O into a beaker.

1. Calculate the expected pH of pure water.                        pH ________

2. Measured pH of pure water.                                                 pH ___3.88______

3. What is the percent error between the calculated and measured value? What are some of the possible sources of this error?

% error __________

B. pH of Water and Strong Acid

i. Measure out 30.0 mL DI H2O and 2.0 mL of 1.0 M HCl into a beaker.

1. Calculate the expected pH of this solution.                      pH _________

2. Measured pH of this solution.                                               pH ___1.64______

3. What is the percent error between the calculated and measured value? What are some of the possible sources of this error?

% error ____

C. pH of Water and Strong Base

i. Measure out 30.0 mL DI H2O and 2.0 mL of 1.0 M NaOH into a beaker.

1. Calculate the expected pH of this solution.                      pH _________

2. Measured pH of this solution. pH __12.03_______

3. What is the percent error between the calculated and measured value? What are some of the possible sources of this error?

% error ____

D. pH of Buffer solution

i. Measure out 50.0 mL 1.0 M CH3COOH and 50.0 mL of 1.0 M NaCH3COO into a beaker.

1. Calculate the total volume. (include units)      Vol __________

2. What is the concentration of acetic acid in this solution after mixing. (include units)

[CH3COOH] _________

3. What is the concentration of acetate ion in this solution after mixing. (include units)

[CH3COO-] ___________

4. Calculate the expected pH of this buffer solution.                        pH __________

5. Measured pH of this buffer solution.                                                 pH __4.56________

6. What is the percent error between the calculated and measured value? What are some of the possible sources of this error?

% error __________

E. pH of Buffer after the addition of the Strong Acid

Measure out 50.0 mL the buffer in part D and add 2.0 mL of 1.0 M HCl into a clean beaker.

1. Calculate the expected pH of this solution.                      pH _________

2. Measured pH of this solution.                                               pH ____5.30_____

3. What is the percent error between the calculated and measured value? What are some of the possible sources of this error?

% error ____

F. pH of Buffer after the addition of the Strong Base

Measure out 50.0 mL the buffer in part D and 2.0 mL of 1.0 M NaOH into a clean beaker.

1. Calculate the expected pH of this solution.                      pH _________

2. Measured pH of this solution. pH _4.57________

3. What is the percent error between the calculated and measured value? What are some of the possible sources of this error?

% error ____

BBT Production is promoting a concert in Kuala Lumpur. The bands will receive a flat fee of RM7 million in cash. The concert will be shown worldwide on closed-circuit television. BBT will collect 100% of the receipts and will return 30% to the individual local closed-circuit theater managers. BBT expects to sell 1.1 million seats at a net average price of RM13 each.

Required:

1. Suppose Mary has an income of $315 per month and eats out for $15 a dinner and sees movies at a cost of $9 per movie.

a.Explain why you do not need to graph her budget constraint to determine the slope, given the information above. What is the value of the slope of the budget constraint?

b.Suppose Mary finds a new job and now makes $360 per month. However, her local movie theater raises ticket prices to $12. Draw Mary’s new budget constraint, with the quantity of movies on the vertical axis and dinners on the horizontal axis, appropriately labeling the values for the x-intercept and y-intercept.

c.Is it feasible for Mary to go out to dinner 12 times and go to the movies 17 times during the month with her new income? Explain your answer.