Sequences & Series Questions and Answers

Using a calculator or statistical software find the linear regression line for the following table of values Then use the equation to estimate the value of y when x is 8 Round the values of a and b in the regression equation to the nearest hundredth then use the equation to solve for y when x 8 Round the final answer to the nearest hundredth if necessary x X 1 2 3 4 y 3 82 6 06 6 62 6 53

a Find the surface area only exterior faces and the volume of the composite solid given box your answer 16 cm KOO 5cm 6cm

Find the pivot in the simplex table Do not solve x2 s1 s2 6 1 0 x1 4 6 16 4 12 0 O4 in R1 and C1 O4 in R2 and C2 0 6 in R2 and C1 6 in R1 and C2 1 0 Z 0 0 1 24 42 0

Determine the perimeter and area of following shaded figure 2 cm K www bonecamp com square 2 cm 0 2 cm square

2 CHHO 3 1 Let y 4 9 5 The distance is 1 7 Find the distance from y to the plane in R3 spanned by u and u

The graph below represents y 2 Select one O True O False ty 11 4 2 2 2 4 x 1 x 21 X 6

Use the age transition matrix L and age distribution vector x to find the age distribution vectors x2 and X3 X2 x3 L x t O IN 02 0 11 11 X 14 14 Then find a stable age distribution vector

Find the domain and the range of the relation shown on the graph to the right Use the vertical line test to determine whether the graph is the graph of a function OA The domain of the relation is the single value Type an integer or simplified fraction 10 OB The domain of the relation is the interval Type your answer in interval notation k 10 Determine the domain of the relation Select the correct choice below and fill in the answer box to complete your c G

a Find the equation of the cross section of the mirror if the vertex is at the origin 6 points b Find the exact coordinates of the point where the light will be concentrated 4 points c Sketch the graph of the cross section 3 points d Indicate approximately and label the location of the point where the light will be concentrated 2 points Conic Sections

In the answer box below type an exact answer only l e no decimals You do not need to fully simplify reduce fractions and radical expressions If sin sin 26 112 113 with din quadrant Ill then find sin 20

is the equation y x 5 5 linear or not not linear linear Use the graphing tool to graph the equation Click to enlame 10

ay Attempt 2 Determine the intervals of increase and decrease for the given rational function graph Increasing 3 3 0 Decreasing 0 3 3

Which of the following represents the graph of y O 15 12 9 6 3 15 12 9 6 3 3 6 9 12 15 EE H 411 3 6 9 12 15 202 x 1

Given Point M is the midpoint of LQ and NP and ZLNM and ZOPM are right angles Prove ALIMNAOPM The students are asked to construct an argument to prove ALMN AOPM Some of the students responses are given below Which of the arguments prove the congruence of the two triangles Select all that apply A D M a M H LNM and 240PM are right angles Given LM is the hypotenuse of ALNM and OM is the hypotenuse of AOPM Definition of a hypotenuse Point is the midpoint of LO and NP Given LM OM and NMPM Definition of midpoint and definition of congruent segments ALNM AOPM Hypotenuse Leg Congruence Theorem LNM and ZOPM are right angles Given ZLNM 20PM Right angles are congruent Point is the midpoint of B and NP Given LM OM and MM 2 PM Definition of midpoint and definition of congruent ALNM AOPM SAS Theorem Point is the midpoint of LC and NP Given LM OM and NMPM Definition of midpoint and definition of congruent segments ZEMN 20MF Vertical angles are congruent ALNMADPM SAS Theorem Point LM segment IN UP Congruent Parts of Congruent Triangles are Conscient ALUM AOPAS 555 Theorene is the midpoint of IU and NP Given OM and MM 2 FM Definition of midpoint and definition of congruent ZLNM and OPM are is angl Given ZLNM ZOPM Richture are constient

Complete the table for the equation x y 5 and graph the equation X 0 7 2 1 y 0 Use the graphing tool to graph the line using two points Click to enlarge graph 10 8 D 10 8 6 4 2 Ay 2 6 8

toring Just one of the methods we will use in College Algebra to solve quadratic equations Another method we will use is the quadratic formula This formula can give use some messy expressions to evaluate so let s practice using our calculator to evaluate the expressions and then simplify the answers as much as possible to 2 2 4 1 3 2 1 1 You may want to simplify the inside of the radical first To evaluate 2 4 1 3 you d type the following into your calculator Ex Evaluate TI calculator 2 2 4x1x 3 Casio calculator 2 x 12 4x1x3 2 Now let s evaluate the rest We have 2 4 2 2 16 2 Since we know 16 Then we d split it up and calculate the two answers separately 2 4 What did you get and 2 4 2 we can simplify that further Pa

In the circle below SU is a diameter Suppose m ST 70 and mZSTV 20 Find the following a mZTSU b m ZUTV U m2TSU UTV 0

Given the 3 different functions below which of the following statements is NOT true f x g x X y 0 1 16 h x 2x 3 Og 3 f 3 1 1 4 Oh 2 g 2 Ax 2 3 4 5 64 14 16 16 f x has intervals in which the average rate of change is positive and some in which the average rate of change is negative

The data in the chart shows the maximum and corresponding resting heart ra rate for a resting heart rate of 40 55 and 76 resting 50 60 70 80 90 maximum 169 172 174 175 177 Choose the correct regression line OA y 0 19x 160 1 OC y 0 19x 160 1 is The coefficient of correlation rounded to 3 decimal places Is the regression line a good fit OYes O No The predicted maximum heart rate for a resting heart rate of 40 is Round to the nearest integer The predicted maximum heart rate for a resting heart rate of 55 is Round to the nearest integer The predicted maximum heart rate for a resting heart rate of 76 Round to the nearest integer is

Use Green s Theorem to calculate the circulation of G around the curve oriented counterclockwise G 3yi xyl around the circle of radi centered at the origin f G df x

Algebra Prove that f x 1 sin n x n is continuous on all of R

Solve triangle ABC Round your answers to one decimal place a LA LB LC A O O O 12 C 47 46

how that the sequence is divergent Plot the first 8 terms of the sequence to illustrate 72 1 our result

firm will break even no profit and no loss as long as revenue just equals COST alue of x the number of items produced and sold where C x R x is called he break even point Assume that the below table can be expressed as a linear function Find a the Cost function b the evenue function and c the profit function d Find the break even point and decide whether the product should be produced given the restrictions on sales Fixed cost Variable cost Price of item 30 450 15 According to the restriction no more than 20 units can be sold a The cost function is C x Simplify your answer b The revenue function is R x Simplify your answer c The profit function is P x Simplify your answer d Select the correct choice below and fill in the answer box within your choice Type a whole number OA The break even point is the restriction on sales units Thus the product should be produced given units Thus the product should not be produced B The break even point is given the restriction on sales

Decide whether the following relation defines a function 2 4 1 4 4 4 Is the set of ordered pairs a function O No Yes

Let f x 4x1 h x x 4 Find f o h 3 foh 3

time Question 7 1 point When is the rate of change zero What is the significance of this time in the context of the problem N

5 If a gas was in a 5 liter flexible container under 1 8 atmospheres of pressure how would the volume of the gas change and what would it be if the pressure was decreased to 0 3 atmospere keeping all the other variables constant Write your answer in the space provi

12 In business there is a formula used to find simple interest on an account The formula is rate x time x principle interest The rate is the percentage rate usually per year and time is in years with principle being the amount of money put into the account originally The interest will be the money earned on the account Determine whether the following statement is true or false Interest and rate are a direct relationship assuming the remaining variables are kept constant O True O False

Show ALL work to find the sum of the first 12 terms of the given geometric series Round answers to the nearest hundredth if necessary 3 6 12

Show all steps to find the sum of the first 17 terms of the geometric series given 3 6 12

1 Name a pair of similar triangles and use calculations to explain why they are similar a b 20 mm B A 20 1 cm 30 mm 43 mm D9 0 cm G C 40 mm E 40 2 cm 36 0 cm 60 mm 86 mm K F

Rewrite sin x in terms of sin x and cos x

The files that a company has for its employees dealing with utilities occupy 100 120 60 90 110 45 30 70 60 50 40 25 65 25 55 35 45 60 75 30 120 100 60 90 85 sectors If after operating systems are installed a disk can store up to 480 sectors determine the number of disks needed to store the utilities when the specified heuristic is used to pack the disks with files Give your answers as whole numbers a next fit c first fit b next fit decreasing d first fit decreasing

Graph two full periods of the function f x 2x 3r 4x 2 WAA AA M 3 4 1 1 4 4 3 4 x 27 2 3r 4 3 2x O midine 4 12 1 4 1 State the amplitude period and midine amplitude 19 period 2n y 2 14123 Determine the exact maximum and minimum y values and their corresponding x values for one period where x 0 For answer use the first occurrence for which x 0

2 A 14 9 16 10 1 Check if A is defective or not 2 Find eat using diagonalization or Jordan for 3 Find Ak using Cayley Hamilton theorem

Using the data below what is the value of RMSE Week Time Series Value Forecast 1 2 3 4 C 3 5 2 8 Submit 5 00 3 00 2 00 4 00

Given the following proof attempt explain what is wrong with it and how you w go about correcting it fixing it 1 cos 8 sin 0 sin 0 1 cos8 sin 0 1 cos 0 1 cos 8 1 cos 0 1 cos 0 Cos 0 sin 8 sin coto 1 cos 0 sin 1 cos 0 cos 0 1 cos to sin 0 1 cest cest cos 0 sin 0 1 cos 0 sin 8 sin 0 1 cos 0 sin 0 sin 8 1 cos2 e 1 cos 0 sin 0 1 cos sin 0 Os 0

Complete the table of ordered pairs for the linear equation y 7x X 0 1 y 2 Type integers or simplified fractions X 0 1 y 2 GICKH

Graph the polar equation Identify the name of the shape 28 r 2 5 sin 0 a Finish the table 0 T cos 0 0 T 2 7 2 7 2 3 2 2 2 O 3 o B 0 8 b Plot the points below no need to connec them Clear All Draw c Identify the shape inner loop limacon

5 A quadratic function is defined by p x x 1 x 3 Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex The quadratic function P x x 1 x 3 can be rewritten in the following forms Standard form P x x 2x 3 p x x 1 4 Vertex form

Find the sum of the following series 3 5 1 1 b 47 27 37 n 1 n 0

The graph on the right shows the remaining life expectancy E in years for females of age x Find the average rate of change between the ages of 50 and 60 Describe what the average rate of change means in this situation Life Expectancy in years 60 40 20 40 44 7 50 35 8 60 27 6 70 20 9 20 40 60 80 The average rate of change of life expectancy between the ages of 50 and 60 is O Q

Click here to watch the video Solve x 6 26 Select the correct choice below and fill in any answer boxes in your choice A The solution set is Simplify your answer Type your answer in interval notation

find the exact of the trigonometric function given that sin v 3 5 and cos V 8 17 Both Vand I are in avad rent III II je sin u v

5 points Find the values of a and b such that the following function a x 2 b x 3 f x 8 if if x 1 if x 1 if x 1 x 1 4x is continuous at x 1 Justify your answer by the definition of the continuity

Find the length of the space curve given below r t 521 4 cost 4 smrk 0 3 041 O 6 41 03 O 41 3 41

3 Inequalities Solve the inequality graph the solution set and write the answer in interval notation Show all work 3 x 1 5 2

Graph one full period of the function starting at 0 F x 4 cos 2 x 38 2 4 H hebr 2 period 6 amplitude midline 4 4 6 State the amplitude period and midine 4 A 2 minimum x y 37 Determine the exact maximum and minimum y values and their corresponding values for one period where x 0 For each answer use the first occurrence for which x 0 maximum 5 State the phase shift and vertical shift 2n

Let A 2 a Find the eigenvalues and eigenvectors of A b Verify that det A is the product of its eigenvalues c Is matrix A diagonalizable If yes find matrix P and diagonal matrix D such that A PDP 1 otherw explain why not d If matrix A is diagonalizable compute A and write the final result as a 2 x 2 matrix Find