Vector Calculus Questions and Answers

Write the equation for ellipse vertices 7 1 17 1 CV 5 7 5 9

A bag contains 4 white 5 red and 6 blue balls Three balls are drawn at random from the bag What is the probability that all of them are red 1 mark

Jason kept a tally of 100 vehicles passing through an intersection near his school Here are the results 6 marks a Car Pickup truck van SUV Other What is the probability expressed as a fraction that the next vehicle to pass through that intersection will be i ii iii iv v vi 4 a car A pickup truck A van An SUV Another type of vehicle A van or an SUV otigal did you calculate in part a

A card is drawn from a pack of 52 cards The probability of getting a queen of clubs or a 1 mark king of hearts is what

In an inter school volleyball league a total of 30 games are left this season 3 marks a Team A has a winning probability of 7 10 Team B has a winning probability of 0 427 Which team has the higher probability of winning b About how many of the remaining games is Team B likely to win c About how many of the remaining games is Team A likely to lose

On her way to work Sylvia drives through 3 sets of traffic light The probability of each set of lights being green is 3 What is the probability that they are all green 1 mark

3 In a recent raffle 12 460 tickets were purchased Prizes were awarded to 750 winners a What was the probability as a fraction as a decimal and as a percent of winning a prize 3 marks if one ticket was purchased Fraction b Decimal Percent Which type of probability experimental or theoretical did you calculate in part a 1 mark

6 The information below shown in table form represents sets of regional sales figures in thousands for a given company Using this information please construct using any suitable means a graph of your own design that accurately displays this data 5 marks Region Western Region Southern Region Eastern Region Regional Sales Figures in thousands for 1997 1st Quarter 2nd Quarter 3rd Quarter 8 10 8 12 10 6 575 5 7 14 4th Quarter 10 2 8

If Ax x where A 0 3 0 3 3 determine the eigenvalues of the matrix A and 2 3 1 eigenvector corresponding to each eigenvalue

Part 7 10 Part 8 of 10 g The range in interval notation is 0 0 0 0 0 0 0 0 0 QUO

Homework C255 Question 2 of 10 1 point 1

2 S 2x For h x a Identify the horizo b If the graph of the Write numbers as inte If there is more than

Question 2 of 10 1 point 2 3 Refer to the graph of the functic T in T 1 1

1 Question 7 of 10 1 point Questi For r x 2 4x 8x 1 x 4 3 a Identify the horizontal asymptotes if b If the graph of t

1 Question 1 of 10 1 point Question Atte f x 2 X Write the domain of the function in interval not 9 3 x 3 4

Question 3 Which of the given funci V

Find the critical points of the following function Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum or saddle point If the Second Derivative Test is inconclusive determine the behavior of the function at the critical points f x y x y 4x 32y 1 What are the critical points GEXER Type an ordered pair Use a comma to separate answers as needed

Convert the angle 600 to radians Give the exact value and use pi for

9 Solve by using real or fake Gauss Jordan pivots matrix by hand OR by using Cramer s Rule determinant by hand 4 points 3x y 7 2x 3y 1

Evaluate the following limit by direct evaluation Change the form of the function if necessary lim x 0 3x X Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim 3x Simplify your answer X 0 X B The limit does not exist

an is playing a game of chance in which he rolls a number cube with des numbered from 1 to 6 The number cube is fair so a side is rolled random his game is this Ivan rolls the number cube once He wins 1 if a 1 is lled 2 if a 2 is rolled 3 if a 3 is rolled and 4 if a 4 is rolled He loses 75 if a 5 or 6 is rolled f necessary consult a list of formulas a Find the expected value of playing the game dollars b What can Ivan expect in the long run after playing the game many times O Ivan can expect to gain money He can expect to win dollars per roll Ivan can expect to lose money

Let Pn be the following proposition n 2n 1 7n 1 6 n 1 n 2 2n We would like to use mathematical induction to prove that this proposition is true for all positive integers 24

The function f x ax bx kc passes through the points k 4 k 2 and 2 2k Find the values of k that result in no solution no existing function f x

work Section 8 3 Ho square meter equals 10 000 c 2 cm

Question 9 10 points A partial set of values for the function of g x is given X g x 2 1 4 75 4 5 0 12 1 2 O O O 11 0 4 Determine the average rate of change from x 1 to x 2 10 10 points nintr 1 3 2 1

rk Questi Par mine a the area and b the perimeter of the qua

The legs of a picnic table form an isoscele

Use the polygon to the right to complete parts a Name the polygon If the polygon is a quad b State whether or not the polygon is a regu a What is the name of the polygon O Dodecagon

Given that z 50 and arg z Find z 5T 4 Give your answer in the form a bi

21 Write log a C 3 d log5 b log 2 8 log 4 2 log 4 5 3 3 3 1 log8 log4 2 82 4 2 54 1 log 2 8 log 4 2 1 3 3 as an algebraic sum of logarithms log 4 5 log8 log4 2 log5 3

12 4x 2 83x 1 x a 1 11 b 1 C 1 d 1

10 log77 17 7 X X X a 1 b 1 c 49 d 1 49

1 Determine the sum of Hexagon The sum of the meas

Lines and 12 are parallel lines Determine the me 412

4 Use the figure to find CFNIF

Identify the figure as a line half line ray line segment open I B G Which of the following descriptions and symbols correspond to

Find a correct to 2 decimal places NOTE The triangle is NOT drawn to scale 111 52 X 39 O

Let P 3 2 Q 3 6 R 1 4 Part 1 Find the component form and magnitude of the vector Simplify radicals if possible Round your answers to the thousandth 1 PQ Find the Component form Do not put any spaces between the numbers and the symbols

ve by using substitution or elimination by a 6x 9y 8 18x 27y 25 ect the correct choice below and fill in any A The solution is Type an ordered

Sketch a polynomial that only has real zeros at x 6 multiplicity 2 x 3 x 2 multiplicity 3 and x 7 multiplicity 3 as well as 2 zeros that are complex with imaginary components and a negative coefficient

8 6 7 1 r udo ES W 2011 na obs 5 Let u 3 6 If is perpendicular to u and u determine the component form of If there is more than one possible answer find all possibilities You may choose to use the grid to help you If 1 and 1 then u v 1 v w u v w 10 If 1 and 1 then u 2 7 6 G 3 2 1 10 9 8 7 6 5 4 3 2 1 1 2 3 4 7 In 6 8 write true or false to the left of each statement Justify your answers An answer without justification will receive no credit 0 1 8 9 10 2 6 8 9 10 10 w samomo A to obutingsM

2 3 4 and 3 2 Determine each of the following Give answers correct to three decimal places An answer without justification will receive no credit Component form of Component form of 30 Magnitude of Direction angle of il Angle between i and 3 Given the points A 6 11 and B 4 8 write the component form of AB

6 Use Lagrange multipliers to find the maximum and minimum values and points x y 1 1 which they occur of f x y subject to the constraint x y

If u then u with direction angle tan 2 placed in the appropriate quadrant Dot Product of Two Vectors in the Plane and v v u v U V Angle Between Two Vectors and v cos 1 2 refer to the vectors u 3 4 and 3 2 1 Graph and label on the grid the vectors u v 20 an 10 4 5 9 8 7 6 4 3 2 0 1 10 9 8 7 6 5 4 3 2 1 1 2 5 6 0 1 2 3 V v 4 E 5 6 7 8 9 10

2 An object needs to be moved from point A 10 2 4 to point B 5 5 6 in R You have the choice of doing so by applying 100 N of force in one of three directions namely the directions of the vectors 1 1 1 1 1 2 or s 1 1 3 A Calculate the projections of the vectors 2 and 3 onto the displacement vector pointing from A to B B Which of the three choices of moving the object accomplishes the most work Explain C Bonus Of all the vectors 1 1 A where X can be any real number which one accomplishes the most work when you apply 100 N of force in the direction of to move the object from A to B

f x X 6 3 3x What is the x intercept What is the y intercept Find any vertical asymptotes Find any horizontal asymptotes Graph the function

Suppose the total cost in maunufacturing x units of a certain product is C x dollars a What does C x measure Give units b What can you say about the sign of C c Given that C 1 000 16 estimate the additional cost in producing the 1 001st unit of the product

4 21 20 h x x 6 3 2 graph h Describe the transformations from the graph of f x x to the graph of h 21 h x 2 x 6 22 h t x 3 2

hamed Salad Attempt 1 Question 1 0 5 points Listen Evaluate 6 6y y 84 94 074 dy

14 A bowl contains apples 3 oranges and o bananas Without looking Cart chose one piece of fruit for himself What is the probability that he chose an apple or an orange 15 Bob wants to create a password to protect his computer If he uses passwords with a total of 7 characters 3 letters followed by 4 numbers how many possible passwords can be created TEST 13 35 8 31 808 16 The probability that Stacy will pass a math test is and the probability that Sophie will pass the same What is the probability that Stacy will not pass her test and Sophie will 17 There are 6 colored pencils and 8 markers in Cameron s art bag Without looking Cameron chooses 1 item 82 from the bag What is the probability that she chooses a colored pencil 6 14 math test is Use the followin