The masses and coordinates of four particles are as follows: 45 g, x = 1.0 cm, y = 2.0 cm; 45 g, x = 0.0 cm, y = 4.0 cm; 25 g, x = -3.0 cm, y = -3.0 cm, 30 g, x = -1.0 cm, y = 4.0cm. What is the rotational inertia of this collection with aspect to the x-axis ( kg m²)?

What is the rotational inertia of this collection with aspect to the y-axis?

What is the rotational inertia of this collection with aspect to the z-axis?

Buffer Solution from Strong Base and Weak Acid

Solution=
30.0 mL of 1.0 M CH3COOH
5.0 mL of 1.0 M NaOH

1. Calculate the total volume. 35 mL

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

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

4. Calculate the expected pH of this buffer solution.

5. Measured pH of this buffer solution. 3.89

A common stock is expected to pay no dividends during the next 7 quarters but at the end of 6th quarter, it is expected to pay DPS of $1.0 and thereafter dividends are expected to be paid quarterly and into indefinite future. The quarterly growth rate of dividends stream is 1.0% and it is expected to stay the same into indefinite future. The required expected rate of return on the common stock is 12% per annum.

Find:

(i)The current price per share of the stock.

(ii)The expected price per share at the beginning of the 8th quarter.

Consider the following reaction and associated equilibrium constant:
aA(g)+bB(g)⇌cC(g), Kc = 5.0

Part A. Find the equilibrium concentrations of A, B, and C for a=1, b=1, and c=2. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction.

Part B. Find the equilibrium concentrations of A, B, and C for a=1, b=1, and c=1. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction.

A 1.0-m lamp cord leads from the 110-V outlet to a lamp having a 75-W lightbulb. The cord consists of two insulated parallel wires 5.0 mm apart and held together by the insulation. One wire carries the current into the bulb, and the other carries it out.

4)Compare the field between 1.0 mm from one of the wires in the same plane in which the two wires lie with Earth’s magnetic field? (Express your answer to two significant figures.)

20. The chemical equation for the reaction between hydrochloric acid and potassium hydroxide is HCl(aq) + NaOH(aq) NaCl(aq) + H2O(l)

When 25 mL of 1.0 M HCl (36.5 g/mol) is mixed with 25 mL of 1.0 M NaOH (40 g/mol), the temperature change of the mixture is 6.9 oC. The density of the mixture is 1.00 g/mL and the specific heat of the solution is 4.18 J/ g oC. What is the enthalpy change for this reaction?

1. Given f(x) = exp x sinx. Find exact first derivative at x = 1.0. In addition, find approximate first derivative using forward, backward, central and higher order scheme for first derivative. Set h = 0.1 for approximation.

2. Given f(x) = xlnx. Find exact and approximate second derivatives at x = 1.0. Set h = 0.1 for approximation.

3. Develop a 4th order accurate symmetric scheme to approximate the second derivative of f(x) at x.

The specific heat capacity of silver is 0.24J/C.g .

Calculate the energy required to raise the temperature of 151.0 g from 278 K to 299 K.

Energy = J

Calculate the energy required to raise the temperature of 1.0 mole of by 1.0°C (called the molar heat capacity of silver).

Molar heat capacity = J/°C ⋅ mol

It takes 1.38 kJ of energy to heat a sample of pure silver from 11.4°C to 15.1°C.

Calculate the mass of the sample of silver. Mass = g

A bank has Federal funds totaling $25 million with an interest rate sensitivity weight of 1.0. This bank also has loans of $105 million and investments of $65 million with interest rate sensitivity weights of 1.40 and 1.15 respectively. This bank also has $135 million in interest-bearing deposits with an interest rate sensitivity weight of .90 and other money market borrowings of $75 million with an interest rate sensitivity weight of 1.0. What is the weighted interest-sensitive gap for this bank?

Write a program that reads three double numbers from the keyboard representing, respectively, the three coefficients a, b, and c of a quadratic equation. Solve the equation using the following formulas:

x1 = ( - b + square root (b2 – 4ac)) / (2a),

x2 = ( - b + square root (b2 – 4ac)) / (2a)

Run your program on the following sample values:

a=1.0, b=3.0,c=2.0

a=0.5, b=0.5,c=0.125

a=1.0, b=3.0,c=10.0