Programming Questions

$2.(6$ points$)$ The U$.$S$.$ Census Bureau projects population based on the

following assumptions:

a$.$ One birth every $7$ seconds

b$.$ One death every $13$ seconds

c$.$ One new immigrant every $45$ seconds

Write a program to display the population for each of the next five years. Assume that the current population is $312,032,486,$ and one year has $365$ days.

Here is a sample run:

year $1$: $314812582$

year $2$: $317592679$

year $3$: $320372776$

year $4$: $323152872$

year $5$: $325932969$

$3.(8$ points$)$ Write a program that prompts the user to enter the seconds $($e$.$g$.,1$ billion$),$ and displays the number of years, days, hours, minutes, and seconds. For simplicity, assume a year has $365$ days.

Here is a sample run:

Enter number of seconds $($e$.$g$.,1$ billion$)1987000000$

In $1987000000$ there are: $63$ years

In $1987000000$ there are: $2$ days

In $1987000000$ there are: $16$ hours

In $1987000000$ there are: $26$ minutes

In $1987000000$ there are: $40$ seconds

$4.(8$ points$)$ Write a program that generates a lottery of a three$-$digit number. The program prompts the user to enter a three$-$digit number and determines whether the user wins according to the following rules:

a$.$ If the user input matches the lottery number in the exact order, the award is $$10,000.$

b$.$ If all digits in the user input match all digits in the lottery number, the award is $$3,000.$

c$.$ If one digit in the user input matches a digit in the lottery number, the award is $$1,000.$

Here are sample runs:

Enter your lottery pick $($three digits$)$: $591$

Lottery is $248$

Sorry, no match

Enter your lottery pick $($three digits$)$: $987$

Lottery is $637$

Match one digit: you win $$1,000$

Enter your lottery pick $($three digits$)$: $683$

Lottery is $836$

Match all digits: you win $$3,000$

Enter your lottery pick $($three digits$)$: $494$

Lottery is $494$

Exact match: you win $$10,000$

$5.(6$ points$)$ Write a program that prompts the user to enter the center coordinates and radii of two circles and determines whether the second circle is inside the first or overlaps with the first, as shown in the below figure.

Hint:

circle$2$ is inside circle$1$ if the distance between the two centers $<=$ r$1-$ r$2$

circle$2$ overlaps circle$1$ if the distance between the two centers $<=$ r$1+$ r$2.$

Test your program to cover all cases.

Here are sample runs:

Enter circle$1$s center x$-,$ y$-$coordinates, and radius: $0\mathrm{.}55\mathrm{.}113$

Enter circle$2$s center x$-,$ y$-$coordinates, and radius: $11\mathrm{.}74\mathrm{.}5$

circle$2$ is inside circle$1$

Enter circle$1$s center x$-,$ y$-$coordinates, and radius: $3\mathrm{.}45\mathrm{.}75\mathrm{.}5$

Enter circle$2$s center x$-,$ y$-$coordinates, and radius: $6\mathrm{.}73\mathrm{.}53$

circle$2$ overlaps circle$1$

Enter circle$1$s center x$-,$ y$-$coordinates, and radius: $3\mathrm{.}45\mathrm{.}51$

Enter circle$2$s center x$-,$ y$-$coordinates, and radius: $5\mathrm{.}57\mathrm{.}21$

circle$2$ does not overlap circle$1$