Sequences & Series Questions and Answers

Find a singular value decomposition A PDQT where A 3 1 1 1 1 Enter the matrices P D and QT below Any empty entries are assumed to be 0 P D QT

Draw the graph of the solution set of the inequality X 2 Click Reply Then click Attach Canvas Then click Use Topic Canvas Click the pencil icon to choose a color Than use your mouse or stylus to draw the graph When you have the answer you want to submit click Attach and then Post 5 4 3 2 1 0 1 2 3

Match each expression to its simplified value Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE 5 2 3 5 2 3 5 2 3 5 2 3 III 27 90 13 31

5 What is a possible equation of the rational function graphed below Explain your reasoning x 2 x 3 x 1 x 3 x 1 A y B y C y D y x 2 x 2 x 3 x 1 x 2 x 2 x 3 x 1 A o ty

Select each number that is a solution of the inequality x 6 8 Select one or more answers and submit For kayboard navigation SHOW MORE 3 Co b C Multiple answers Multiple answers are accepted for this question d 1 2 3 1 9

Select the inequality whose solution set corresponds to the given graph Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer 3 b x 10 x 10 4 2 0246 8 10 12 C X 10

Solve the equation using logarithm

Write an equation of the line that passes through 4 5 and is parallel to the line defined by 3x y 3 Write the answer in slope intercept form if possible and in standard form 4x By C with smallest Integer coefficients Use the Cannot be written button if applicable

Given that the graph is an exponential function identify the domain range 10 8 6 10 8 6 42 2 246 8 10 2 4 6 8 10

Use a graphing utility to graph each of the five functions shown below f x x4 9x f x 5x4 10x f3 x 2 x 2 x 25 Graph f x x4 9x Choose the correct graph below O A V 2 2 1 by 0 20 2 f4 x x x 2 x 2 f5 x x 4 x 2 x 2 Q OB 5 5 1 by 30 10 4 O C M Q 2 2 1 by 20 0 2 O D N 5 5 1 by 10

State whether the following statement is true or false 2 The function f x x 15 is increasing on the interval Choose the correct answer below O False True

Use a calculator or program to compute the first 10 iterations of Newton s method for the given function and initial approximatio f x 3 sinx x 4 xo 1 3 Complete the table Do not round until the final answer Then round to six decimal places as needed k Xk k Xk 6 7 8 9 10 1 2 3 4 5

19 Suppose that R is a ring and let z E R If there exists a unique y R such that zy z Show that yr

A linear function is shown in the table below Find its slope y intercept and formula in slope intercept form X y 9 6 33 24 Slope y intercept y 35 15 0 6 3 3 6 12 9 21

Find the value of the given Greatest Integer function for the given input for x Function Input F x 2x 4 3 6 A 1 B 2 C 3 D 4

2 4 points The labeled pictures for two different trig equations are shown If we were trying to find solutions in R from these pictures we only need one formula to give the solutions for Case 1 but we need two formulas to give the solutions for Case 2 Explain what about the pictures makes this happen Case 1 5T 4 PA Case 2 79 7T 4 Solutions in R Solutions in R kr where k is an in 2km and 7 2km teger where k is an integer Explanation

hemist has a 100 gram sample of a radioactive material He records the amount of radioactive material every week for reeks and obtains the following data Complete parts a f Week x 0 1 2 3 4 5 6 Weight y in grams 100 0 80 1 62 4 51 7 39 9 31 7 25 2 a Treating week x as the independent variable use a graphing utility to fit an exponential functi y ab 100 3991 0 7946 Round to four decimal places as needed b Express the function found in part a in the form A t A e kt A t Round to four decimal places as needed

Use one of the provided formulas to solve the problem Round your answer to 2 decimal places A P 1 P A 1 Formulas A Pert P Aert l prt A t Aet Find the amount that results after investing 2000 at a rate of 6 over 5 years compounded continuously

The one to one functions g and h are defined as follows g 9 5 1 9 5 7 7 1 8 6 h x 3x 2 Find the following b 7 oh 8 X S

Use the functions f and g in C 1 1 to find f 9 g and df g for the inner product f x g x dx g x e x f x 5x a f g 25 e b c g d d f g x

A rancher is selling off 7 of her ranch each year If she owns 2000 square miles in about how many years will she own only 600 square miles If she starts with 100 of the land and sells 7 she will have 93 of the land left After n years she will have 2000 0 93 of the land left 600 2000 0 93 0 3 0 9372 log 0 3 log 0 93 log0 3 n log0 93 log0 3 log 0 93 n 0 3 0 93 0 49 n A negative value does not make sense The rancher will never have only 600 square miles of land log n

The graph of a rational function f is shown below Assume that all asymptotes and intercepts are shown and that the graph has no holes Use the graph to complete the following a Write the equations for all vertical and horizontal asymptotes Enter the equations using the and button as necessary Select None as necessary Vertical asymptote s Horizontal asymptote s b Find the domain and range of f Write each answer as an interval or union of intervals Domain 0 c Find all x intercepts and y intercepts Check all that apply x intercept s 0 4 4 2 None y intercept s 0 2 2 Range 4 None 2 08 0 0 None 0 0 and 0 0 0 0 0 0 8 X DVD 8

2 Without graphing determine whether the function represents exponential growth or decay Give a reason for your answer Find the y intercept a y 129 1 63 100 2 4 b y

1 point Let f x y e 5x sin 3y a Using difference quotients with Ax 0 1 and Ay 0 1 we estimate fx 2 1 2 5209E 5 fy 2 1 1 2996E 4 b Using difference quotients with Ax 0 01 and Ay 0 01 we find better estimates fx 2 1 3 1247E 5 f 2 1 1 3453E 4

Find the radius of a circle of latitude at a latitude of L 59 5245 N Use the radius of the earth as 3960 mi Round the radius of the circle of latitude to the nearest mile radius 90 Jat 3960 mi

a If 80 000 is invested at 8 compounded annually find the future value in 2 years 93312 Simplify your answer Round to the nearest cent as needed b If 80 000 is invested at 8 interest compounded continuously the future value is 93 880 87 How does this compare to the result from par The amount found with continuous compounding yields more Round to the nearest cent as needed

Which radical of 49 49 343 and 343 simplify to 7 Choose the correct answer below 3 343 O 49 O 3 343 49

For the function find the inverse and the domain and range of the function and its inverse Determine whether the inverse is a function f x x 7 The inverse is f x Simplify your answer

The computational complexities of some common operations with 12 by n matrices are given in the table below Operations Matrix matrix multiplication Matrix vector multiplication LU factorization Cholesky factorization Back forward substitution Tridiagonal solve 0 027 seconds 7 4E 6 seconds 4 3 minutes 8 7 minutes Flops 2n 3 2n 2n 3 0 n n 3 0 n You have a 2 6 GHz workstation with 6 cores where each core can do 2 floating point operations per clock cycle Estimate how long it will take to solve the n by n linear system Ax b where A is upper triangular and n 28 997 72 8n You have a 2 6 GHz workstation with 6 cores where each core can do 2 floating point operations per clock cycle Estimate how long it will take to solve the n by n linear system Ax b where A is upper triangular and n 28 997

Problem26 Let ABC be a triangle with X and Y midpoints of the sides as shown Let area of ACXY M and area trapezoid AXYB N How are M and N related B N 2M A N M E N 4M 4MB C N 2M AAS MC X M N D N 3M Y

What is the average rate of change over the interval 1 2 X a x 03 02 01 1 0 3 2 1 1 2 6 3 13

A board of length 9x 9x 9 meters is to be cut into three pieces of the same length Find the length of each piece Next question

Compute the flux of the vector field F through the surface S 7 27 37 zk and S is a closed cylinder of radius 2 centered on the z axis with 3 szs 3 and oriented outware 50m F dA x

5x 2y 1 se the graphing tool to graph the equation Use the slope and the y intercep Click to enlarge graph 12 10 18 cc di 14

Simplify the radical expression Use absolute value symbols when needed 16x Select one O a 4x O b 14x1 O c 4 x O d 8x O e 81x1 Check

Analyze the following graph of a system of two equation Determine the r and y values of the solution of the syst

Jill makes a blend of brownies for the garage sale The double chocolate brownies are 6 00 per plate and the chocolate mint brownies are 6 00 per plate Jill sells less than 9 plates total Jill also sells more than 24 50 worth of brownies Using this information what is the inequality showing that Jill sells less than 9 plates total 6x 6y 24 5 x y 9 x y 9 6x 6y 24 5

1 Solve the systems of linear equations using the substit y x 4 20x 30y 75 9 O 10 10 31 O 1 10 O A 31 9 31 O 10 10 10 A Ele 5 Given the formula A ab solve for a 0 O A

6 Solve the inequality 6 6x y 31x 54 Oy 9 bx 6 Oy 9 bx Oy 9 5x Ous 9 Oy 9 x Oy 9 5 x 5 5 5 X

quad the constant term f x 6x 13x 18 Quadratic term Linear term Constant term 15 Convert the following to standard form then write the quadratic term the linear term and the constant term in the space provided x 2 x 6 12 Quadratic term Linear term x

6 Find the vertex and the line of symmetry for each equation y x 3 Vertex Line symmetry x 7 Find the vertex and the line of symmetry for each equation y x 2x 5 Vertex Line symmetry x

Determine the domain and range of the function 4 3 2 3 2 1 2 3 4 2 3

The function given by y f x shows the value of 5000 invested at 4 interest compounded continuously x years after the money was originally invested Round your answers to the nearest cent Value of 5000 with Continuous Compounding at 4 24000 Value 16000 12000 1000 y f x 4000 Part 0 3 Part 1 of 3 10 7459 5 6107 25 13 591 20 11 128 Number of Years 21

Use the graph of y f x to answer the following V K 6 5 4 3 2 Part 0 8 O Part 1 of 8 F 5 4 3 2 14 B y f x 2 3 T 5 6 a Determine f 4 2 3 4 5 6

8 Karl Yates needs 21 000 to pay for the remodeling work on his house A contractor agrees to do the work in 4 months What is the present value of 21 000 at 7 1 simple interest in order to accumulate the 21 000 in 4 months The present value is Round to the nearest cent as needed

Your science class wants to double the area of its study garden Strips of the same width will be added to one end and one side to form a rectangle If the bed is now 17m length by 12m width what are the dimensions of the new garden patch I drew a picture to get you started Always begin by drawing a picture of the situation Round your answers to the nearest ter length of new garden meters width of new garden X 12 meters

Use the discriminant to determine the amount o real number roots the equation has 3x 9 3x 0 O one real root O two real roots O three real roots O no real roots Use the discriminant to determine the amount o real number roots the equation has 2x 9 2x 0 The equation has real number root s

Given f x 7e3x 2x2 If p x is the second Taylor polynomial of fat xo 0 then p 1 3

10 Test the series for convergence or divergence 0 1 3 1 X 453 19 3 1 m 1 Lim ads DOL11

Find the domain and range of the inverse of the given function f x x 9 Domain and range all real numbers Domain all real numbers range 9 Domain 9 range 0 Domain 0 range 9