http://www.math.ucla.edu/~dinov/10a.3.01s/ |

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**HW_4_1.cpp/exe/txt**) A person invests**$P**dollars in a savings account yielding**r**percent_{1}__monthly__interest. Assuming that all interest is left on deposit in the account, calculate and print the amount of money in the account at the end of**n**months. Write a program that collects the values of*P*, the initial principal,*r*, the monthly interest and_{1}*n*, the number of months and computes*A*,the final amount in the account. Use the following formula for determining the*compound*interest:**A =P (1 +r**, where_{1})^{n}*A*is the final amount,*P*is the initial principal,*r*is the monthly interest and_{1}*n*is the number of months the money is invested. In addition, suppose the same amount of money is invested in a second account at**r2**APR (__annual__percentage rate) interest,**r**. Using the formula for APR interest (A = P + P.r_{2}=r_{1}. 12_{1}.n = P + P.r_{2}.n/12) compute the amount in the second account at the end of the**n**months of investment. Let us assume 0<=n<=12. Entering initial principal of $0, completes the program. Explain the differences between the two final amounts. Are they the same? Why?

**Sample Run:**

%> Enter P, the initial principal in dollars ($) [Enter $0 to exit]:

%> 100.00

%> Enter r, the monthly interest rate (as double):

%> 0.01

%> Enter n, the number of months the money is invested, (0<=n<=12)

%> 12

%> Final amount, using the compound interest: $112.68

%> Final amount, using APR interest: $112.00

%> Enter P, the initial principal in dollars ($) [Enter $0 to exit]:

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**HW_4_2.cpp/exe**)*Pythagorean Triples*. Consider right triangles that have sides that are all integers. The set of three integer values for the sides of a right triangle is called a**Pythagorean triple**. These three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the third one (hypotenuse). Write a program that collects 3 integers form the user and tests/reports whether the numbers form a Pythagorean Triple. The program should run iteratively until the user enters**0 0 0**.[Hint: Always first determine the**largest**of the 3 numbers entered and check if its square equals the sum of the squares of the other 2 sides - this uses the fact that the**hypotenuse**is the largest side of the right triangle.]

**Sample Run:**

%> This is a program that checks if three numbers form a**Pythagorean Triple**

%> Enter the 3 integer sizes of the triangle

%> 3 5 4

%> This is right triangle with hypotenuse of size 5;**Pythagorean Triple**(3, 4, 5)

%> Enter the 3 integer sizes of the triangle

%> 2 5 4

%> This is NOT a right triangle - not a**Pythagorean Triple**

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**HW_4_3.cpp/exe**) The values of P ( =*Pi*~ 3.1415...) may be calculated from the infinite series:

P = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ... + (-1) ^{n}4/(2n+1) + ...

where**(-1)**is the^{n}4/(2n+1)**n**-th term, n = 0, 1, 2, 3, .... . Write a program that asks the user for an integer,**n**, representing the number of terms of the series to be used to*approximate*P, and then reports the approximation value. For example, if n = 0, then the approximation will be: P ~= 4; and if n=2, then P ~= 4 - 4/3 + 4/5. As usual, run the computation in a loop until a*negative*number (n < 0) is entered. You should test run your program with increasing values of**n**and convince yourself the approximations improve and converge as**n**increases.

**Sample Run:**

%> This is a program that**approximates**P (Pi) with arbitrary accuracy

%> Enter the number of terms to be used in the approximation (integer)

%> 0

%> The 0-term approximation of P (Pi) is: 4

%> Enter the number of terms to be used in the approximation (integer)

%> 1

%> The 1-term approximation of P (Pi) is: 2.66666

%> Enter the number of terms to be used in the approximation (integer)

%> 2

%> The 2-term approximation of P (Pi) is: 3.46666

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