# SciLab

Please see the attached file for the fully formatted problems.

Problem 1

Consider the following two functions

C x =∫0

x

cost2 dt S  x =∫0

x

sin t2 dt

Write a program called <name>1.sce generates plots of these functions over the range 0≤x≤8 on a

single figure. Format the figure so that it is very readable and visually appealing - something you could

show in a PowerPoint presentation, for example. Look up the legend command using Scilab's help

function and use this to include a legend in your figure.

Problem 2

The function p v is defined implicitly by the relation p tan p=v2−p2 and the condition

0≤p≤/2 . Write a program called <name>2.sce that implements the function p v in Scilab and

generates a plot of p v for 0≤v≤3 /2 . Format the figure so that it is very readable and visually

appealing.

Problem 3

Write a program called <name>3.sce that defines a function

[h,d]=hitfacet(v,r,u)

where v is a 3-by-3 matrix in which each column gives the x,y,z coordinates of a point in space. These

three points represent the vertices of a triangular "facet" in space. r and u are 3-by-1 column vectors.

The function should determine if a line from the point r traveling in the direction u "hits" (intersects)

the facet. If not, then h='F' while if so then h='T' and d is the distance from r to the point of

intersection.

Problem 4

Consider a copper wire of length L and diameter D as shown below.

The size of wire is often specified by American Wire Gauge (AWG) values. The diameter of the wire

in inches is given by

D= 5

1000 92

36−nAWG

39 inch

where the integer nAWG is the AWG gauge. The resistance of a piece of wire is proportional to its

length and inversely proportional to its cross-sectional area A=D/22 . That is

R∝ L

A

Assume that 1000 feet of AWG 16 wire (that is n AWG=16 ) has a resistance of 4 .

We might want to know what gauge of wire is needed to carry a certain current I. The power dissipated

in the wire will be Pd=I2 R . The surface area of the wire is S= D L . We might specify that the

dissipated power per unit surface area never exceed a certain value, or else the wire will not be able to

efficiently get rid of the heat generated by the resistive dissipation. Let us take as our standard that

AWG 16 wire can carry a maximum of 10 amps of current.

Write a program called <name>4.sce that contains a Scilab function awg(I) that outputs the nAWG

value required to carry the current I. Remember that nAWG must be an integer and the specified

maximum Pd / S cannot be exceed. You program should generate a plot of nAWG vs. I for

#### Solution Summary

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