MAT 127 Final: S07final

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turquoisegnu128

31 Jan 2019

School

University of Maine

Department

Mathematics and Statistics

Course

MAT 127

Professor

All

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Document Summary

Your university id number: no calculators are allowed on this exam, please show all your work. You may use backs of pages if necessary. You may not receive full credit for a correct answer if there is no work shown. Part i: (12 pts) compute z x2 x2 dx. 2x: (15 pts) (a) use a riemann sum with n = 4 rectangles to approximate z 9 (2x + 3)9dx. 1 (you don"t need to simplify). (b) compute the exact value of the integral: (12 pts) compute z x sin(x)dx (15 pts) the feeding trough pictured below is full of slop. Find the work done by the pigs in sucking the slop out the top of the trough. 4 m: (15 pts) compute the following integral: [ 1 x2]3 dx: (16 pts) use calculus to prove that a sphere of radius r has volume v = (recall that the equation of the semicircle is y = r2.

Related Questions

1. Evaluate the expression 2x - 2 for the value of x = -3

2. Factor: xsquare + 4x - 32 (x-4)(x+8) (x-4)(x-8) (x-4)(x-8) (x-16)

3. Factor: xsquare - 25 (x-5) (x+5)2 (x+5)(x-5) (x-5)(x-5)

4. Evaluate -u2v3 when u=4 and v=-2 128 64 32 -128

5. Using an online calculator, determine whether the value of x=7 is a solution of the equation. x Yes No

6. Explain why x=7 IS or IS NOT a solution of the equation. 7 + 1/x+2=8

7. Solve the equation and check your solution: -2 - 4x = 30

8. Solve the equation and check your solution: 67x - 24 = 3x + 8(8x - 3) 67 -3 -67 All real numbers

9. Solve the equation and check your solution. 5x/2 - x/6 = 14 10 6 7 9

10. Solve the quadratic equation by factoring: xsquare - 6x + 5 = 0 -1, 5 -1,-5 1,-5 1,5

11. The imaginary number i represents:

12. Find real numbers a and b such that the equation is true: a+ bi = 14 + 2i a=16, b=4 a=18, b=6 a=14, b=2 a=15, b=14

13. Find all solutions to the following equation. /4x - 8 = /4x + 9 x = -17/4 x=9 No solution x=-17

14. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for Jamesâ miles.

15. Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz. 10h - .25=450 10h + .25(10h)=450 h -.25 (10h)=450 10h - .25(10h)=450

16. Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work. 17. The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width. Hint: Perimeter = width + length + width + length

18. Twice a number is added to the number and the answer is 80. Write an equation to solve this problem. 2n + n=80 2n = 80 2n + 80=n 80 + n=2n

19. If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20. Multiply the following binomials: (x + 5)(x - 5)

Given the following main program

#main
a = [5,2,9,6,3] doubleList(a) print a

Implement the function named doubleList that takes one list argument and modifies the list so that each element in the list is doubled. The statement print(a) in the main program will then have to print [10,4,18,12,6]
Given the following main program

#main
a = [5,2,9,6,3]
b = reversedList(a) print b
print a

Implement the function named reversedList that takes one list argument and returns a list that contains the elements in the list argument in reverse order. The statement print(b) in the main program will then have to print [3,6,9,2,5]. The statement print(a) must print the original list [5,2,9,6,3] unaffected. This means your function should not modify the list argument.
Given the following main program

#main
a = [5,2,9,6,3] reverseList(a) print a

Implement the function named reverseList that takes one list argument and reverses the list so that the modified list contains the same elements in reverse order. The statement print(a) in the main program will then have to print [3,6,9,2,5]
What is the return value of the functions doubleList, reversedList and reverseList in questions 1, 2, and 3 above?

Given the following main program

#main
a = [5,2,9,6,3]
b = evenElements(a) print b

Implement the function named evenElements that takes one list argument and returns a list that contains the elements in the list argument that are even integers. The statement print(b) in the main program will then have to print [2,6]. What is the return value of the function? Your function should not modify the list argument.
Given the following main program

#main
a = [5, 2, 9, 6, 3, 7, 19, 4, 8, 17, 21, 20, 15] removeOddElements(a)
print a

Implement the function named removeOddElements that takes one list argument and modifies the list so that all odd integers in the list are removed. The statement print(a) in the main program will then have to print [2,6,4,8,20]. What is the return value of the function?
Part A
#Main program A=[5,8,2,0,-5,3] n=-5
answer = isFound(A, n) if answer == True:

print "The integer is found in the list" else:

print "The integer is not found in the list."

Consider the main program shown above. Write a Python function named isFound that takes a list of integers and an integer as arguments and returns True if the integer is found in the list; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, you must write a loop to go through the elements of the list.

Part B

Give the following main program

#main
A = [5,2,9,6,3]
B = [2,4,3,9,7,1,6,5]
flag = isList1InList2(A, B) if flag:

print "The list", A, "is contained in the list", B else:

print "The list", A, "is not contained in the list", B

Implement the function named isList1InList2 that takes two list arguments and returns True if and only if each element of the first list argument are found in the second list argument; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, if you wish, you can use the function you wrote in Part A.

For the lists shown in the main program, your function must return True because each element of list A is found in list B.

A given List is known as Palindrome List if the reverse of the List contains the same elements in the same order of the original List. For example the List of integers [2, 5, 0, 3, 3, 0, 5, 2] is a Palindrome because the reverse of the List which is [2, 5, 0, 3, 3, 0, 5, 2] contains the same elements in the same order as the given List. However the List [1, 2, '2', 1] is not Palindrome because its reverse which is [1, '2', 2, 1] does not contain the same elements in the same order as the given List.

Write a Python function named isPalindrome that takes a List as argument and returns True if the argument is a Palindrome List; otherwise it returns False. You don't need to write the main program; just write the function. If you would like to test your function, then it is ok to write the main program too but you will not get any mark for the main program.
Given your function in question #7 above, what is the output of the following code: a=[]

b = [5,2,9,6,3]

print isList1InList2(a,b)
Given your function in question #7 above, what is the output of the following code:

a=[]
b=[]
print isList1InList2(a,b)
Given your function in question #7 above, what is the output of the following code: a = [5,2,9,6,3]

b=[]

print isList1InList2(a,b)

Given the following main program

#main
a=[]
n = readListElements(a)
print "The user entered", n, "elements to the list" print a

Implement the function named readListElements that takes one list argument and modifies the list by repeatedly asking the user to enter integer values and then appending them to the list. The process stops when the user enters -1000. The stopping value -1000 should not be appended to the list. Moreover your function must count the appended elements and return it. Example if the user enters the integers 31, -4, 9, 1,-1000 then your function must modify the list a to a = [31, -4, 9, 1] and return the number elements added which is 4.
Write a function named createRandomList that takes an integer argument n and returns a list with n elements. The elements must be random numbers in the range [0,100]

Given the following main program:

#main

   n = int(input("How many elements do you want in your list? "))
   a = createList(n)
   s1 = sumOfElementsAtEvenIndexes(a)
   print s1

   s2 = sumOfElementsAtOddIndexes(a)
   print s2
   s3 = sumOfAllElements1(a)
   print s3

   s4 = sumOfEvenElements(a)
   print s4
   s5 = sumOfOddElements(a)
   print s5

   s6 = sumOfAllElements2(a)
   print s6
   if (s3 != s6):

         print "Something is wrong in your program."
   else:

         print "Looks like you have done a good job."

Implement the functions as follows:

createList: returns a list object with n elements. The elements are generated randomly so that each element is in the range [15,45]
sumOfElementsAtEvenIndexes: returns the sum of the elements at even indexes. Use a for loop or a while loop.
sumOfElementsAtOddIndexes: returns the sum of the elements at odd indexes. Use a for loop or a while loop.
sumOfAllElements_A: returns the sum of all the elements in the list using the functionssumOfElementsAtEvenIndexes and sumOfElementsAtOddIndexes. Here you are NOT allowed to use any loop; instead make function calls as described.
sumOfEvenElements: returns the sum of the even integer elements in the list. Use a for loop or a while loop.
sumOfOddElements: returns the sum of the odd integer elements in the list. Use a for loop or a while loop.
sumOfAllElementsB: returns the sum of all the elements in the list using the functions sumOfEvenElements and sumOfOddElements. Here you are NOT allowed to use any loop; instead make function calls as described.

17. Most data compression algorithms like winzip, gzip, lzip and etc are based on the frequency distribution of characters in a given string. Write a function named getFreqDistribution that takes a string argument and returns a LIST that has length 26 such that the first element of the list is the number of appearance of 'a' or 'A' in the string, the second element is number of appearance of 'b' or 'B', and so on so forth.

I'm studying python 2 and have a lot of troubles with solving these homework questions.