Civil and Environmental Engineering Answers

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.

A bridge 10-m wide is to be placed across a proposed underpass. This underpass is designed to have a grade of -4% and an ascending grade of +8%, where its vertex will be located at 4+420 with an elevation of 140m. It is required that the centerline of the bridge is exactly placed above the vertex of the curve, its bottom elevation is 148.10m and it should have a minimum vertical clearance of 6m under it.

a) Determine the length of the vertical parabolic curve.

b) Determine the location of the lowest point of the

curve.

c) Determine the elevation of the lowest point.

d) Determine the stationing and elevation of PC.

e) Determine the stationing and elevation of PT.

Find the increment and differential of each of the following functions for the given values of the

variables and their increments.

𝑦 tan^-1 𝑥𝑦; 𝑥 = 2, 𝑦 = 0.5, ∆𝑥 = −0.05, ∆𝑦 = 0.01

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.