For the following, give constructions using a straightedge and a compass with memory. You must prove that your construction works.

We say that a positive real number a is constructible if whenever we are given a line segment of length c , we can construct a line segment of length ac . Suppose that a and b are constructible real numbers. Show that ab is also constructible.

A construction worker riding an open elevator is moving upward with a speed of 6.0 m/s. When he is 42 m above the ground he accidentally drops a hammer. What are the maximum height reached by the hammer, the time it takes for the hammer to fall to the ground and speed of the hammer when it hits the ground? Please answer all parts, thank you!

A construction company decided to purchase a concrete mixer truck for $85,000 with a trade-in of their old mixer. The old mixer has a trade-in value of $10,000. The new mixer will be kept for 10 years before being sold. Its estimated salvage value at that time is expected to be $5,000. Assume interest to be 12%. Determine the 8th year BVB by Sinking Fund Method.

Topic: Construction - Soils

(Note: Briefly discuss in your own words, 2-3 paragraphs minimum, add reference if using any.)

Create a Technical report about "Soils conditions requiring drainage and drainage types and methods". Your report should include charts/tables and other tabulated information collected from your research of this topic.

According to the census bureau publication: current construction reports, the mean price of new mobile homes is 63,500. The standard deviation of the prices is 5,500.

a). For samples 100 new mobile homes, determine the mean and standard deviation of all possible sample mean prices (hint: find u-_x and o-_x)

b). Repeat part a for samples of size 200

1. In practice, an LFSR sequence would not be used as keystream for a stream cipher, due to the linear complexity. Answer the following questions about linear complexity.

1. What is the linear complexity of a maximal length LFSR output sequence?
2. Describe one method using LFSRs to produce a binary output sequence but with increased linear complexity. Draw a diagram to illustrate your construction.

A construction unit Class C Basic Toolroom has a 110 volt 20A circuit has the following items: three 200 watt lights, a 2500 watt heating machine, a 1000 watt heating machine and a ¼ hp motor (use 1000 watts/hp). All of these items act as a load on the circuit. As measured in amperes, determine the circuit load.

3. Please provide a case study about a construction project having serious problems because of excessive amounts of settlement due to consolidation (14 points). ***Note: Ten (10) bonus points will be given to those who can include a supporting article found for a case study. (A TITLE TO AN ARTICLE THAT COVERS THIS WOULD BE PERFECT! AND MORE THAN ENOUGH)

Topic: Construction - Soil

1.) Create a 1-2 pages minimum technical report about the "Index Properties of Soils". Your report should include types and condition of soil, and provide their structural properties, compressibility, shear strength and compactness (relative density) characteristics.  

2.) Provide technical references from at least one source to support your points.

By thinking about the properties of materials…

What two alternatives to concrete could have been used?

Fill in the table below for three different materials:

What are the issues at each stage that you should know about as a designer…?