Civil and Environmental Engineering Answers

Find the increment and differential of each of the following functions for the given values of the variables and their increments.

𝑥 ln 𝑦 + 𝑦 ln 𝑥; 𝑥 = 𝑦 = 1, ∆𝑥 = 0.01, ∆𝑦 = 0.02

Find by use of differentials the approximate total area of a right circular cone whose base radius

and height are 5.03 inches and 11.89 inches, respectively.

Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches

high, if the metal is 1/32 inches thick.

I. Explain the difference between Taniguchi “top-down approach” to the “bottom-up approach” of Drexler.

II. Explain the importance of coating superparamagnetic colloids In Vivo and In Vitro applications.

III. Discuss the potential applications of nanotechnology in the field of energy and environment.

Direction. Show the solution for each of the problem below:

I. Consider Teflon, the polymer made from tetrafluoroethylene.

Draw a portion of the Teflon molecule.

Calculate the molar mass of a Teflon molecule that contains 5.0 x 104 CF2 units.

What are the mass percents of C and F in Teflon?

II. For alanine, Ka1 = 5.1 x 10 -3, Ka2 = 1.8 x 10 -10

a) Calculate the ratios [Z] / [] and [Z] / [] at pH = 10.50

b) Calculate the pH when [Z] = [] and when [Z] = [] if pH= - log []

Direction. Show the solution for each of the problem below:

I. Consider Teflon, the polymer made from tetrafluoroethylene.

Draw a portion of the Teflon molecule.

Calculate the molar mass of a Teflon molecule that contains 5.0 x 104 CF2 units.

What are the mass percents of C and F in Teflon?

II. For alanine, Ka1 = 5.1 x 10 -3, Ka2 = 1.8 x 10 -10

a) Calculate the ratios [Z] / [] and [Z] / [] at pH = 10.50

b) Calculate the pH when [Z] = [] and when [Z] = [] if pH= - log []

The positions, of a particle moving along a horizontal straight line is given by the equation s=6t² - 4, where s is in meter and t is the time in seconds. The particle is 4m to the right of the origin when t = 0.

A.1. Determine the displacement of the particle during the time interval from t = 2s to t = 4s.

A.2. Determine the velocity and acceleration of the particle when t = 4s.

a = 12t²t³ + t, Determine velocity equation and position equation

The magnitude of the linear acceleration of a point moving along a vertical path is given by the equation a = 6t - 24, where a is in m/s and t is in seconds. The acceleration is upward when t = 5s; The point is 4m below the origin when t = 0 and 23 m above the origin when t = 3 s.Determine:

B.1. The velocity when t = 3 sec

B.2. The displacement during the time interval from t = 0 tot = 4 s

B.3. The total distance travelled during the time interval from t = 0 tot = 4s

x = 12t²t³ + t, Determine velocity equation and acceleration equation.