http://assets.openstudy.com/updates/attachments/505e733ce4b02e139410318a-fellowroot-1348371250917-untitled7.gif
Refer to the Fellowroot’s graphic, untitled7.gif, at the site above.
In[11]:=
Clear@"Global`*"D; $Line = 0;
Make time[x] a function that yields the time it takes to traverse the route for a given x. The statement below makes
time[x] a permanent Mathematica function. User defined functions are prented in the color blue.
2102 + H750 - xL2
x
In[1]:=
time@x_D :=
+
12
5
Test the time(x) function. Some simplication will be done automatically.
In[2]:=
time@xD
1
Out[2]=
44 100 + H750 - xL2 +
5
x
12
Plot time(x) from x=0 through x=960 ft. The verticle axis is scconds.
In[3]:=
Plot@time@xD, 8x, 0, 960<D
150
140
130
Out[3]=
120
110
200
400
600
800
Although difficult to read, the single Matematica statement, shown below, can solve the problem given the function
time(x).
The answer is 101 seconds after rounding to the nearest second.
Mathematica took 5381 millionths of a second to solve the problem on a mid 2010 Apple IMac.
In[4]:=
Out[4]=
Timing@
Round@N @time@xD . Solve@D@time@xD, xD Š 0, xDD, 1D D
80.005381, 8101<<
Took the derivative of time(x) with respect to x
In[5]:=
D@time@xD, xD
1
750 - x
-
Out[5]=
12
5
44 100 + H750 - xL2
equated the result to zero and solved for x. Mathematica provides exact symbolic answers when possible. The answer
below, Out[6], is a Mathematica replacement rule.
2
ComputerSolution.nb
1
In[6]:=
SolveB
750 - x
Š 0, xF
12
5
2
44 100 + H750 - xL
150
Out[6]=
::x ®
119 N>>
J85 17
Replaced every occurance of x in the time(x) function using Out[6],
150
In[7]:=
time@xD . :x ®
J85 -
119 N>
17
25
1
J85 -
Out[7]=
119 N +
34
5
J85 17
Simplified the result above
In[8]:=
%  Simplify
1
J125 + 7
Out[8]=
119 N
2
and calculated the decimal number equivalent.
1
In[9]:=
Out[9]=
J125 + 7
2
100.68
119 N  N
Rounded the answer above to the nearest foot.
In[10]:=
Out[10]=
[email protected], 1D
101
2
150
44 100 + 750 -
119 N