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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.


Show that (p → q) ∧ (p → r) and p → (q ∧ r) are logically equivalent using

logical equivalence laws.


(y - xy)dx + xdy = 0



 Aqueous solutions of sodium sulfide, Na2S, and copper nitrate, Cu(NO3)2, are mixed.  A precipitate of copper sulfide, CuS, forms at once.  Left behind is a solution of sodium nitrate, NaNO3.   Write the net ionic equation for this reaction.


The distance between two successive crests in a wave is 1.25 m, and the source generates 15 crests in 5.0 s. What is the speed of the wave?


A ship with a mass of 52 000 metric tons is capable of producing a thrust force of 25 800 kN while a total resistive force of 5 000 kN is against it, what is the acceleration of the ship? *


Question 1: Write a program that uses java.io.BufferReader to read the lines from the text file that is stored on disk. Handle the exceptions with following two ways:

1. Using try-catch-finally block

2. By throwing it up the call stack to the caller method.


How much load is needed to elongate a steel wire to 0.5 %of its original length ? The diameter of the wire is 2mm and youngest modulus of the material of the wire is 20×10^10 N/m^2

259L oil of compressibility k=20×10^-6 atm^-1is subjected to a hydraulic press. Find the decrease in the value of the oil when it is subjected to pressure 1.6×10^7

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