Permutations and Combinations Questions and Answers

5 Find tan a B given cos a 12 13 sin 4 5 a 90 180 and BE 180 270

A Use method 1 from the middle of page 180 to divide 8 15 by 4 9 B Use method 2 from the middle of page 180 to divide 8 15 by 4 9 C Use a calculator to divide 8 15 by 4 9 D Let B B in the cosine of a sum identity to derive the cosine of a difference identity E Use ID 4 s pair of IDs to simplify each of the following to a single trig expression E1 cos 90 9 E2 cos 90 8 E3 cos nt 0 E4 cos It 0 F Use ID 4 s pair of IDs to simplify each of the following to a real number F1 cos 82 cos 98 sin 82 sin 98 F2 cos 5n 12 cos n 4 sin 5n 12 sin n 4 G Answers to exercises in E F above sin 0 sin 0 cos 0 cos 0 1 sqrt 3 2

A piece of rectangular sheet metal is 32 inches wide It is to be made into a drain gutter by turning up the edges to form parallel sides Let x represent the length of each of the parallel sides Choose the function A that gives the area of a cross section of a gutter A A x x OB A x x 32 2x C A x x x 32 D A x 32 2x The value of x for which A will be a maximum is Simplify your answer Type an integer or a decimal The maximum area of the cross section is square inches Simplify your answer Type an integer or a decimal C 32 in 32 2x X

1 Modify the FTBS method in to study numerically the Burgers nonlinear PDE 10 x 0 Send me your code and the graphs you obtain You will see that unlike the linear advection PDE different parts of the graph move with different speeds Explain why does this happen by comparing Burgers PDE with the advection PDE

Skyler Kaitlyn 729 9 7299729 9 36 9 9 9 36 3 6x 9 3x 1 6x 2 X X 90632 Kaitlyn all solve the same exponential problem but have different approaches Robert X 3 X 6 x 3 1 Explain Sklyer s processes Is Skyler correct If not where did she go wrong 2 Explain Robert s processes Is Robert correct If not where did he go wrong 3 Explain Kaitlyn s processes Is Kaitlyn correct If not where did she go wrong

Write each element of D4 as a permutation in S4 Remember to use the basic square with vertices given by 4 3

10 sin The number of real solutions of the equation i 1 1 2 2 0 2 1 2 COS 2 i 1 i 1 lying in the interval 1 21 is Here the inverse trigonometric functions sin x and cos x assume values in i 1 TC TC Let x and 0 respectively 15

Calculate the following trace Tr Y V y P Y y P V Vv P V

Question 2 20 points Consider the matrix 2 3 5 2 1 0 A X 1 a 12 pts Use elementary row operations to find the inverse of A if exists 1 0 b 8 pts Use part i to find the possible solution s to the linear system Ax b where X1 x2 and b 0

Use the one to one property of logarithms to solve log 1 34 log 1 8 3x

Select one True O False The graph below represents y sin x sin x 7 1 2 ty Of Select one O True O False T 3 X 2T

The graph below represents y 3 sin 2x 2 0 2 T2 Select one O True O False 3 2 2T 51 2

1 Simplify each expression Use absolute value symbols when necessary 36a8 1 2 49b2 27x 7y5 2 3 x5y 4 b 273

From the box and whisker plot shown below which value is represented by the letter D A Select one B a Third Quartile Ob Median OC Greatest Value Od First Quartile C D E

One card is selected from a deck of cards Find the probability of selecting a queen or a diamond O 13 52 SO 17 52 O 16 52 SO 14 52 O 15 52

2 635 1 0 087050 where represents the year with t 0 corresponding to 2000 a Use the model to find the populations of the city in thousands in the years 2000 2003 2010 2015 and 2019 Round your answers to three decimal places 2000 P2424 103 2003 P2383 106 2010 P2304 452 thousand people thousand people thousand people 2015 P 2225 170 thousand people 2019 PP15109 thousand people b Use a graphing utility to graph the function Use the graph to determine the year in which the population reached 2 2 million The population will reach 2 2 million in O Confirm your answer to part b algebraically The population will reach 2 2 million in

The following matrix gives occupational Lion probabies initial generation nonfarming farming 0 2 nonfarming C 0 8 farming a If the father is a farmer what is the probability that the son will be a farmer next generation b If there are 15 000 in the nonfarming category and 2 000 in the farming category at a certain time what will the distribution be one generation after the initial generation 41 What will the distribution be four generations after the initial generation c If a man is a farmer what is the probability that his grandson will not be a farmer

3 i Express y as a function of x given 3 log xy 2 log xy 2 3 log y Clearly state the relevant logarithm rules you use

There is a ch CKDOX Question 1 Multiple Choice Worth 5 points 05 02 LC Which equation does the graph below represent y 10 8 86 6 4 2 do Na 5 4 3 2 10 1 2 3 4 5 2 6 8 10 X

Ken bought some apples oranges and pears for 27 30 The amount of money he spent on apples oranges and pears was in the ratio 5 1 7 1 The number of oranges he bought was the number of apples and the number a b 6 1 of oranges he bought was the number of pears Each apple cost 0 25 3 How many apples did Ken buy How much did Ken pay for each pear

1 2 5 413 If we want to use a block cipher to encode the 2 5 message MULTIVERSE OF MADNESS which letter would the letter D be replaced with Given that o

A point has rectangular coordinates 9 4 Convert to polar coordinates with r 0 and 0 0 2 r 0 Enter your answer as an ordered pair of polar coordinates enclosed within parentheses Give in radians Round the numbers in your answer to 2 places after the decimal point

a Graph f x 17x1 b Find f 1 and f 2 c State the domain of the function ww a Choose the correct graph to the right O A O C 5 Ay 57 OB O D Ay X

1 point If T R R is a linear transformation such that then the standard matrix of T is A D and T 10 9 4 7 5

6 Piecewise functions Evaluate the piecewise function f x f 0 f 2 x 2 X x 1 if x 2 if 2 x 2 if x 2 f 3

Solve the system of equations 9x 3y 4 3x y 17 Select the correct choice below and if necessary fill in the answer box to complete your OA There is one solution The solution of the system is Simplify your answer Type an ordered pair OB The solution set of the system is x y 9x 3y 4 OC The solution set is

Use the substitution method to solve the following system of equations 7x y 5 5x 2y 10 Select the correct choice below and if necessary fill in the answer box to complete your choic OA There is one solution The solution of the system is Simplify your answer Type an ordered pair OB The solution set of the system is x y 7x y 5

Consider the simplex tableau given below P 1 0 0 1 0 0 X 1 4 9 X1 1 0 0 x 4 X2 4 42 34 2 A The pivot element is located in column and row B The entering variable is C The exiting variable is D Enter the values after one pivot operation in the tableau belo S1 1 4 9 2 P 0 0 1 0 0 0 1 0 1 4 30 0 4 14

20 16 12 8 4 4 he 8 12 16 20 20 12 8 y axis 80 x axis 12 16 20 1 Does the graph open upward or downward 2 Is the vertex a minimum or a maximum 3 What are the coordinates of the vertex point 4 What are the coordinates of the zeros or x intercents 5 What are the coordinates of the

et T R2x2 ind p2 be a linear transformation satisfying 1 3 x x 2 2 4 1 72 1 1 7 2x 5x 1 HINT Write 72 1 7 as a linear combination of 1 2 2 3 and 1 1

rind the vertical asymptote s for the following f x 3c 12 52 6 Select one O a x 5 and x 6 O b No solution O c x 6 and x 1 d x 3 and x 2

Use the graph of the following function f x to ind f 3 10 8 Ay 6 4 2 AB 10 X 10 www f 3

A home on a homesharing site rents for 100 per night for the first three nights 90 per night for the next three nights and 80 a night for each remaining night The total cost C is a function of x the number of nights that a guest rents the home Fill in each blank with the simplified expression or number for the piecewise defined function that represents this situation blank1 if 0 x blank2 blank3 if blank4 x blank5 blank6 if x blank7 C x a Blank1 b Blank2 c Blank3 d Blank4 e Blanks f Blank6 g Blank7 Write your response here Type your answer here Write your response here Type your answer here Type your answer here Write your response here Type your answer here 4

Click on the graph of the given function 3x if x 0 f x x 1 if x 0 A B C D

Enter the appropriate number in each blank if x 4 if 4 x 1 if x 1 f x x x 2 x 1 x 1 a f 5 Type your answer here b f 4 Type your answer here c f 1 Type your answer here e f 1 d f 0 Type your answer here Type your answer here f f 5 Type your answer here

cording to the results of the experiment the probability that the sum of the dios is less than 4 or greater than 10 le implify your answer Type an integer or a decimal Experiment Results Roll 123456CTOR F 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 First Die Second Die 6 6 2 5 6 6 6 3 2 4 2 6 2 6 3 5 4 2 3 1 3 6 4 3 6 2 2 1 1 4 5 1 6 3 2 6 3 1 2 3 6 3 1 2 1 5 2 1 2 5 Roll 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 First Die Second Die 4 5 2 6 3 4 5 3 2 4 3 6 6 6 3 1 2 6 1 3 1 4 5 3 3 5 5 2 4 1 3 3 3 3 1 3 2 5 3 1 6 2 5 3 4 4 2 1 2 1

Explain the Error For breakfast Sarah can choose eggs granola or oatmeal as a main course and orange juice or milk for a drink Sarah says that the sample space for choosing one of each contains 3 9 outcomes What is her error Explain

3 Solve Volterra integral equation using the method of successive approximations fint on calculation of limit consider that values of r are fixed p x 2 3 3 2 x 4 1 dt 0

2 Let F R2 R be given by f x y x xy x y 3xy a Why is f differentiable b Find dF z y c Find and interpret dF 2 1 d Find and interpret dF 2 1 3 1

Supply the missing quantities Outcome P An C P An D P B n C PIB 0 6 Figure 0 0 A B 0 4 0 9 Descr C D C D

The function H gives the height above the ground of a point on a spinning wheel The function A gives the height of a point on a different spinning wheel and is defined by A t 1 9H 5t For both functions t is time in seconds since the wheels started moving How does the spinning wheel modeled by function A compare to the wheel for H Explain how you know

1 Two similar triangles ABC and XYZ are such that AB 6 and XY 4 Which of the following statements are true More than one answer may be correct mark all correct answers The ratio of AB to XZ is 2 3 If AC 12 then XZ 8 If BC 15 then 20 of YZ is 4 None of the statements are true

2 Given two points 8 1 and following statements are true T 5 which of the More than one answer may be correct select all correct answers The ordered pair 4 1 is a solution to the line that passes through the two points The slope of the line that passes through the points is 2 The y intercept of the line that passes through the points is 3

If 3000 is invested at an interest rate of 5 25 per year compounded continuously find the value of the investment a 3 years 3511 b 6 years 4110 c 9 years 4809 X X I X

Using math symbols write the following seven less tha ten times a number is equal to one quarter the same number decreased by ten O 7 10n in 10 O 10n 7 n 10 O 10n 7 10 n O 7 10n 10 n

11 Find the sum of the geometric series 7 4 1 2 12 Find the sum of the geometric series a 4374 a5 54 r Sr

9 11 13 15 17 S5 2 Find the sum of the arithmetic series if an 97 n 16 and d 4 16 O S16 2032 16 O S16 16 2025 O S16 O S16 2046 O None of these are correct 2035 3 Find the sum of the arithmetic series if

1 Choose one of these polynomial functions then factor it completely A x x 9x 8x B f x 2x 4x 30x In the answer box share your process to factor the polynomial function Be sure to share some strategies you use to factor

2 Write the linear equation in standard form Your answer should be inputted into boxes in two parts Put t 11y 10x 1

12 Determine if the equation is a linear equation x 9y 20 O yes O no