Computer Science 1620

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Computer Science 1620

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Title: Computer Science 1620

1
Computer Science 1620

Math Library

Remember this program?
suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) one year, b) two years c) three years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) one year, b) two years c) three years

include ltiostreamgt using namespace std int
main() cout ltlt "Year 1 " ltlt 25000 1.08
ltlt endl cout ltlt "Year 2 " ltlt 25000 1.08
1.08 ltlt endl cout ltlt "Year 3 " ltlt 25000
1.08 1.08 1.08 ltlt endl return 0
4

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) one year, b) two years c) three years

include ltiostreamgt using namespace std int
main() double balance 25000.0 balance
balance 1.08 cout ltlt "Year 1 " ltlt
balance ltlt endl balance balance 1.08
cout ltlt "Year 2 " ltlt balance ltlt endl
balance balance 1.08 cout ltlt "Year 3 "
ltlt balance ltlt endl return 0
5
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6

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) one year, b) two years c) three years

include ltiostreamgt include ltiomanipgt using
namespace std int main() cout ltlt fixed ltlt
showpoint ltlt setprecision(2) cout ltlt "Year 1
" ltlt 25000 1.08 ltlt endl cout ltlt "Year 2 "
ltlt 25000 1.08 1.08 ltlt endl cout ltlt "Year
3 " ltlt 25000 1.08 1.08 1.08 ltlt endl
return 0
7

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) one year, b) two years c) three years

include ltiostreamgt include ltiomanipgt using
namespace std int main() double balance
25000.0 cout ltlt fixed ltlt showpoint ltlt
setprecision(2) balance balance 1.08
cout ltlt "Year 1 " ltlt balance ltlt endl
balance balance 1.08 cout ltlt "Year 2 "
ltlt balance ltlt endl balance balance 1.08
cout ltlt "Year 3 " ltlt balance ltlt endl
return 0
8
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9

Suppose we alter the program?
suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

include ltiostreamgt include ltiomanipgt using
namespace std int main() cout ltlt fixed ltlt
showpoint ltlt setprecision(2) cout ltlt "Year 10
" ltlt 25000 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 ltlt endl cout
ltlt "Year 20 " ltlt 25000 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 ltlt endl cout ltlt "Year 30
" ltlt 25000 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 ltlt endl return
0
14

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

include ltiostreamgt include ltiomanipgt using
namespace std int main() double balance
25000.0 cout ltlt fixed ltlt showpoint ltlt
setprecision(2) balance balance 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
1.08 1.08 cout ltlt "Year 10 " ltlt balance ltlt
endl balance balance 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 1.08
cout ltlt "Year 20 " ltlt balance ltlt endl
balance balance 1.08 1.08 1.08 1.08
1.08 1.08 1.08 1.08 1.08 1.08 cout
ltlt "Year 30 " ltlt balance ltlt endl return 0
15
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16

The previous example worked, but
to calculate 1.0830 required that we manually
type in thirty multiplications
suppose we had wanted to know the balance after
100 years?

pow(b,e)
to compute b raised to the power of e, one can
use the pow function
syntax
the pow statement itself is an expression
value the first expression raised to the power
of the second expression

pow( , )
numeric expression
numeric expression
18

Example

include ltiostreamgt include ltcmathgt using
namespace std int main() cout ltlt
pow(3.0, 3.0) ltlt endl cout ltlt pow(3, 4.0) ltlt
endl cout ltlt pow(4.0, 3) ltlt endl int x
5 double y 6.0 cout ltlt pow(x, y) ltlt
endl cout ltlt pow(x, y) pow(3.0, 3.0) ltlt
endl cout ltlt pow( pow(x, y), pow(3.0, 3.0)
) ltlt endl return 0
19

A note about pow
you cannot send it two integer expressions
cout ltlt pow(3, 4) ltlt endl // compiler error
this has to do with function overloading
we will examine functions later
for now, just know that one expression has to be
a floating point type

The cmath library

Function Description
abs(x) Returns the absolute value of x
pow(x, y) Returns xy
sqrt(x) Returns the square root of x
sin(x) Returns the sine of x
cos(x) Returns the cosine of x
tan(x) Returns the tangent of x
log(x) Returns the natural logarithm of x ln x
log10(x) Returns log10 x
exp(x) Returns ex
floor(x) Returns the closest whole number lt x
ceil(x) Returns the closest whole number gt x
21

A Note about Types
when using a math function (from previous slide),
the type of the expression is the same as the
type of the input expression, with some
exceptions
an integer expression is converted to a double
for the pow function, the type of the expression
is the largest of the base and exponent
expressions
for abs
integers are not converted to doubles
shorts and chars are converted to ints

22
Expression Type
sqrt(2.0) double
sin(2.0f) float
cos(2) double
log(3 4.0f) float
exp(2) exp(2.0) double
abs(75) int
floor(3.5) double
23

A Note about the Trig Functions
the input expression is considered to be radians
hence, sin(30.0) -0.988032, not 0.5
to convert radians to degrees, multiply the value
by (p / 180)

Example

include ltiostreamgt include ltcmathgt using
namespace std int main() const double PI
3.14159 cout ltlt sin(30) ltlt endl cout ltlt
sin(30 PI / 180) ltlt endl return 0
25
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26

Back to our previous example
suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
cout ltlt fixed ltlt showpoint ltlt setprecision(2)
cout ltlt "Year 10 " ltlt 25000 pow(1.08, 10) ltlt
endl cout ltlt "Year 10 " ltlt 25000 pow(1.08,
20) ltlt endl cout ltlt "Year 10 " ltlt 25000
pow(1.08, 30) ltlt endl return 0
29

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
double balance 25000.0 cout ltlt fixed ltlt
showpoint ltlt setprecision(2) balance
balance pow(1.08, 10) cout ltlt "Year 10 "
ltlt balance ltlt endl balance balance
pow(1.08, 10) cout ltlt "Year 20 " ltlt balance
ltlt endl balance balance pow(1.08, 10)
cout ltlt "Year 30 " ltlt balance ltlt endl
return 0
31

Suppose that I invest 25000 into a mutual fund
that returns 8 per year. Write a program to
calculate how much the fund will be worth after
a) ten years, b) twenty years c) thirty years

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
double balance 25000.0 double increase
pow(1.08, 10) cout ltlt fixed ltlt showpoint ltlt
setprecision(2) balance balance
increase cout ltlt "Year 10 " ltlt balance ltlt
endl balance balance increase cout ltlt
"Year 20 " ltlt balance ltlt endl balance
balance increase cout ltlt "Year 30 " ltlt
balance ltlt endl return 0
32

Example 2 Suppose you have a cannon. Given an
initial velocity of a cannonball and the angle of
the cannon ?, output (1) the time that the ball
remains in the air and (2) the maximum height of
its trajectory

33
Arithmetic Data and Operators

Given a value ? and initial velocity v0, we can
calculate the time that the ball stays in the
air
and its maximum height

g is approximately -9.81 m/s at sea level

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
const double PI 3.14159 const double G
-9.81 double v0 cout ltlt "Initial velocity
(m/s) " cin gtgt v0 double theta cout
ltlt "Angle of trajectory (degrees) " cin gtgt
theta theta theta PI / 180.0
double time -2 v0 sin(theta) / G
double height -pow(v0 sin(theta), 2) / (2
G) cout ltlt fixed ltlt showpoint ltlt
setprecision(2) cout ltlt "Hangtime (s) " ltlt
time ltlt endl cout ltlt "Height (m) " ltlt
height ltlt endl return 0
35

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
const double PI 3.14159 const double G
-9.81 double v0 cout ltlt "Initial velocity
(m/s) " cin gtgt v0 double theta cout
ltlt "Angle of trajectory (degrees) " cin gtgt
theta theta theta PI / 180.0
double time -2 v0 sin(theta) / -9.81
double height -pow(v0 sin(theta), 2) / (2
G) cout ltlt fixed ltlt showpoint ltlt
setprecision(2) cout ltlt "Hangtime (s) " ltlt
time ltlt endl cout ltlt "Height (m) " ltlt
height ltlt endl return 0
cmath call
41

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
const double PI 3.14159 const double G
-9.81 double v0 cout ltlt "Initial velocity
(m/s) " cin gtgt v0 double theta cout
ltlt "Angle of trajectory (degrees) " cin gtgt
theta theta theta PI / 180.0
double time -2 v0 sin(theta) / -9.81
double height -pow(v0 sin(theta), 2) / (2
G) cout ltlt fixed ltlt showpoint ltlt
setprecision(2) cout ltlt "Hangtime (s) " ltlt
time ltlt endl cout ltlt "Height (m) " ltlt
height ltlt endl return 0
Magic Number
42

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
const double PI 3.14159 const double G
-9.81 double v0 cout ltlt "Initial velocity
(m/s) " cin gtgt v0 double theta cout
ltlt "Angle of trajectory (degrees) " cin gtgt
theta theta theta 3.14159 / 180.0
double time -2 v0 sin(theta) / G
double height -pow(v0 sin(theta), 2) / (2
G) cout ltlt fixed ltlt showpoint ltlt
setprecision(2) cout ltlt "Hangtime (s) " ltlt
time ltlt endl cout ltlt "Height (m) " ltlt
height ltlt endl return 0
Magic Number
44

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

Write a program that accepts an initial velocity
and the angle of trajectory, and computes the
hangtime and the maximum height of the
cannonball. Output to three decimal places.

include ltiostreamgt include ltcmathgt include
ltiomanipgt using namespace std int main()
const double PI 3.14159 const double G
-9.81 double v0 cout ltlt "Initial velocity
(m/s) " cin gtgt v0 double theta cout
ltlt "Angle of trajectory (degrees) " cin gtgt
theta theta theta PI / 180.0
double time -2 v0 sin(theta) / G
double height -pow(v0 sin(theta), 2) / (2
G) cout ltlt fixed ltlt showpoint ltlt
setprecision(3) cout ltlt "Hangtime (s) " ltlt
time ltlt endl cout ltlt "Height (m) " ltlt
height ltlt endl return 0
50
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